Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

David Engelmann; Martin Sinkwitz; Francesca di Mare; Björn Koppe; Ronald Mailach; Jordi Ventosa-Molina; Jochen Fröhlich; Tobias Schubert; Reinhard Niehuis

doi:10.3390/ijtpp6020009

Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

Engelmann, David;Sinkwitz, Martin;di Mare, Francesca;Koppe, Björn;Mailach, Ronald;Ventosa-Molina, Jordi;Fröhlich, Jochen;Schubert, Tobias;Niehuis, Reinhard 2021-05-08 00:00:00 International Journal of Turbomachinery Propulsion and Power Article Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project 1 , 1 1 2 2 David Engelmann * , Martin Sinkwitz , Francesca di Mare , Björn Koppe , Ronald Mailach , 3 3 4 4 Jordi Ventosa-Molina , Jochen Fröhlich , Tobias Schubert and Reinhard Niehuis Chair of Thermal Turbomachines and Aeroengines, Department of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, 44801 Bochum, Germany; martin.sinkwitz@rub.de (M.S.); francesca.dimare@rub.de (F.d.M.) Chair of Turbomachinery and Flight Propulsion, Institute of Fluid Mechanics, Technische Universität Dresden, 01062 Dresden, Germany; bjoern.koppe@tu-dresden.de (B.K.); ronald.mailach@tu-dresden.de (R.M.) Chair of Fluid Mechanics, Institute of Fluid Mechanics, Technische Universität Dresden, 01062 Dresden, Germany; jordi.ventosa_molina@tu-dresden.de (J.V.-M.); jochen.froehlich@tu-dresden.de (J.F.) Institute of Jet Propulsion, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany; tobias.schubert@unibw.de (T.S.); reinhard.niehuis@unibw.de (R.N.) * Correspondence: david.engelmann@rub.de Abstract: This article provides a summarizing account of the results obtained in the current collabora- tive work of four research institutes concerning near-wall ﬂow in turbomachinery. Speciﬁc questions regarding the inﬂuences of boundary layer development on blades and endwalls as well as loss mech- anisms due to secondary ﬂow are investigated. These address skewness, periodical distortion, wake interaction and heat transfer, among others. Several test rigs with modiﬁable conﬁgurations are used Citation: Engelmann, D.; Sinkwitz, for the experimental investigations including an axial low speed compressor, an axial high-speed M.; di Mare, F.; Koppe, B.; Mailach, R.; wind tunnel, and an axial low-speed turbine. Approved stationary and time resolving measurements Ventosa-Molina, J.; Fröhlich, J.; techniques are applied in combination with custom hot-ﬁlm sensor-arrays. The experiments are Schubert, T.; Niehuis, R. Near-Wall complemented by URANS simulations, and one group focusses on turbulence-resolving simulations Flow in Turbomachinery to elucidate the speciﬁc impact of rotation. Juxtaposing and interlacing their results the four groups Cascades—Results of a German provide a broad picture of the underlying phenomena, ranging from compressors to turbines, from Collaborative Project. Int. J. isothermal to non-adiabatic, and from incompressible to compressible ﬂows. Turbomach. Propuls. Power 2021, 6, 9. https://doi.org/10.3390/ijtpp6020009 Keywords: near-wall ﬂow; boundary layer; wake interaction; compressor; turbine; cascade; experi- mental investigation; CFD; large eddy simulation; direct numerical simulation Academic Editor: Piotr Doerffer Received: 6 January 2021 Accepted: 22 April 2021 1. Introduction Published: 8 May 2021 Present goals in the development of turbomachines for ﬂight propulsion are oriented Publisher’s Note: MDPI stays neutral towards a further increase of pressure ratio and efﬁciency with a simultaneous reduction with regard to jurisdictional claims in of the number of blades and stages of compressor and turbine [1]. For stationary gas published maps and institutional afﬁl- turbines used to generate electric power, challenging demands on ﬂexibility and operation iations. under partial load result from the volatile availability of renewable energies [2]. These requirements on both types of systems lead to high aerodynamic loads on the blade rows and to an increase in losses due to secondary ﬂows [3]. The latter occur mainly in regions close to sidewalls and have been the focus of scientiﬁc investigations for many years [4–10]. Copyright: © 2021 by the authors. Still, however, understanding is incomplete but is required for increasing efﬁciency in order Licensee MDPI, Basel, Switzerland. to meet economic and ecologic concerns. This article is an open access article While in current design processes the ﬂow is mostly considered in its temporal av- distributed under the terms and erage [11], the real ﬂow in axial compressors and turbines is strongly unsteady, with conditions of the Creative Commons turbulence and periodic contributions resulting from the aerodynamic interaction of the Attribution (CC BY-NC-ND) license blade rows moving relative to each other [12–15]. It exhibits high complexity due to the (https://creativecommons.org/ inner and outer sidewalls and the effects generated by rotation. In fact, the near-wall ﬂow is licenses/by-nc-nd/4.0/). Int. J. Turbomach. Propuls. Power 2021, 6, 9. https://doi.org/10.3390/ijtpp6020009 https://www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2021, 6, 9 2 of 40 characterized by the wall boundary layer, blade boundary layers and the interaction of sev- eral secondary ﬂow phenomena, such as radial gap vortex, horseshoe vortex and channel vortices, all of them being periodically unsteady in a ﬂow ﬁeld which is partly transitional and turbulent on top [16]. The cited effects occur in both, axial compressors as well as axial turbines, but differ considerably according to design features and aerodynamic blade or stage load, so that the different secondary ﬂow phenomena have different characteristics. The intensity of the aerodynamic interaction between the blade rows qualitatively and quantitatively depends on a number of geometric and aerodynamic parameters, such as axial gap width, wake width, velocity deﬁcit of the wake, Strouhal number, ﬂow coefﬁcient, etc. In numerous studies these effects have been investigated with linear cascades [17,18], and disregard of heat transfer in the case of turbines. On the opposite side, there are many studies on machines of realistic or close-to realistic complexity, with measurements usually complicated by practical aspects [19,20]. On this background four groups at three German universities have joined forces in a government-funded collaborative project aiming at the detailed investigation of the ﬂow in the near-wall area of turbomachinery. In particular, the joined effort is dedicated to ﬁll the gap between the two antipodes, linear isothermal cascade and complex machine with heat transfer. On the one hand, it addresses aspects of heat transfer at the sidewall during transient inﬂow, which have not been investigated in linear cascades so far. On the other hand, the connection between stationary linear and rotating ring cascades is investigated. The relevant aspects are the fanned blades in the ring cascade, the radial pressure gradient, the Coriolis forces and the jumps in the circumferential speed between rotor and stator generating strongly twisted sidewall boundary layers at the entry into the blade rows. The overarching goal is to investigate to which extent studies in linear cascades can provide information about the near-wall ﬂows in the machine and how, if necessary, the data from linear cascades must be interpreted to obtain such information. This gradual increase in complexity allows to decompose the respective inﬂuences, which in the machine can only be considered as a whole, interacting with each other. To the knowledge of the authors, detailed investigations of this kind have not been available, so far. The present paper was conceived to provide the community with a timely, condensed synopsis over the recent results achieved in this collaboration, highlighting the larger picture and, if necessary, referring to separate publications for details and side studies. To this end, the paper is structured in line with the project structure featuring four sub-projects A to D. Sub-project A deals with skewness and periodic distortion of the sidewall boundary layer in an axial compressor cascade. Experimental investigations inside a low speed axial research compressor are performed with several conﬁgurations including rotating and ﬁxed hub walls. Numerical studies using a URANS-code complement the experimental ﬁndings. Sub-project B employs highly accurate turbulence-resolving simulations, DNS and LES, to perform well-controlled numerical experiments based on a compressor rotor proﬁle under the same or similar conditions as investigated experimentally in sub-project A. These investigations focus on the stepwise increase in complexity between the linear grid and the full rotating grid, addressing the impact of fanned geometry compared to linear geometry, relative motion of the sidewall, Coriolis forces, etc. An issue not discussed in the present paper is the work performed on improving the simulation methodology. While the ﬁrst two sub-projects are concerned with compressor proﬁles sub-project C and D are oriented towards turbines. Sub-project C is conducting experimental investigations of a T106 low pressure turbine proﬁle in a high-speed cascade wind tunnel and complements these with URANS simulations. A major focus is put on unsteady inﬂow conditions which impact both the inlet endwall boundary layer and the blade loading. These issues are important to clarify because of their particular inﬂuence on the heat transfer at the sidewalls. Sub- project D employs a speciﬁcally modiﬁed T106 proﬁle suitable for the low speed turbine conﬁguration on site. Experimental and numerical studies with wake generators are conducted to study the unsteady behavior of the boundary layers developing on the Int. J. Turbomach. Propuls. Power 2021, 6, 9 3 of 40 low pressure turbine stator blades as well as their effect on the secondary ﬂow patterns under the inﬂuence of unperturbed and periodically perturbed inﬂow. For this purpose, high-resolution time resolving measurement techniques including hot-ﬁlm probes are used. The long-term goal of this research is to enhance the physical understanding of the transient near-wall ﬂow effects for compressor and turbine, thus providing action points to reduce the secondary losses resulting from the aerodynamic interactions in the near-wall ﬂow below the current state of the art, so as to improve upon present efﬁciencies and environmental impact. 2. Sub-Project A—Periodically Transient Near-Wall Flow within Rotating Compressor Cascades 2.1. Scope of Sub-Project A Within sub-project A experimental investigations on different setups of a low speed research compressor are performed to achieve steps of abstraction between a linear cascade and an axial compressor. This allows for a separate analysis of different forces and effects corresponding to the rotating system, where the main considered features are the Coriolis- and centrifugal forces, the ﬂow channel curvature, the incoming boundary layer (BL) and its skewness as well as the relative motion (RM) between the blade tip and its corresponding endwall. Furthermore, the inﬂuence of an incoming periodic distortion on the development of the tip leakage vortex (TLV) in a compressor rotor, as well as on the global parameters of ﬂow turning, losses and total pressure rise is investigated with varying tip clearances. The presented results give an overview of the ﬁndings from recent and current work. Thereby focusing on the effect of varying wall motion in the vicinity of a stator row and the periodic distorted inﬂow to a rotor row on the secondary ﬂow in either passage. The former allows to examine the inﬂuence of a skewed inﬂow boundary layer, a relative motion between the stator vane tips, and the underlying hub endwall or the combination of these two on the tip leakage vortex originating from the stator vanes with hub gap. 2.2. Experimental Setup 2.2.1. Test Facility The investigations are conducted using the Low Speed Research Compressor (LSRC) operated by the Chair of Turbomachinery and Flight Propulsion at the Technische Uni- versität Dresden. The 4.5 stages, including an inlet guide vane (IGV) and four repeating stages, of this axial compressor are built vertically with a downward facing air ﬂow, see Figure 1. The studied blading is derived from a middle stage of a high pressure jet engine compressor and the main characteristics are given in Table 1. For further information on the LSRC please refer to Boos et al. [21] and Künzelmann et al. [22]. To evaluate the effects of varying motion of the wall and incoming periodic distortions two major setups are observed, shown in Figure 1. For the ﬁrst conﬁguration (a) the object of investigations is the stator of stage 1 (hereinafter referred to as stator 1). An adjusted IGV with 83 vanes produces the proper inﬂow conditions and allows direct periodicity for the later numerical computations. The blades of stage 1 are dismounted from the rotor disk, which can be set to the design rotational speed inducing a skew of the sidewall boundary layer. Replacing the rotor disk with a stationary band consisting of 12 circumferentially divided segments allows investigations with stationary sidewalls and thus suppressed inlet BL skew to stator 1 (S1). In addition to the change of the hub endwall upstream of S1, the shroud ring of the stator can be replaced by a rotating hub ring allowing a relative motion between hub and stator vanes. For the latter case, the stationary ring over the rotor hub cannot be used due to constructive restrictions, thus three different cases can be investigated experimentally, see Table 2. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 4 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 4 of 40 over the rotor hub cannot be used due to constructive restrictions, thus three different cases can be investigated experimentally, see Table 2. Figure 1. Low Speed Research Compressor (LSRC)—cross section of investigated setups with sta- Figure 1. Low Speed Research Compressor (LSRC)—cross section of investigated setups with stator tor S1 (a) and rotor R1 (b). S1 (a) and rotor R1 (b). Comparing these configurations allows to evaluate the influence of a skewed inflow Comparing these conﬁgurations allows to evaluate the inﬂuence of a skewed inﬂow BL, which is associated with the movement of the hub wall at the rotor of stage 1 (herein- BL, which is associated with the movement of the hub wall at the rotor of stage 1 (hereinafter after referred to as rotor 1), and the relative motion between the vane tip and the adjacent referred to as rotor 1), and the relative motion between the vane tip and the adjacent wall, wall, which is induced by not using shrouded stator vanes. These investigations are car- which is induced by not using shrouded stator vanes. These investigations are carried ried out with different stator hub clearances. For stationary hub endwall the no clearance out with different stator hub clearances. For stationary hub endwall the no clearance (s/C = 0.0%) and three gap sizes with clearance heights (s) normalized by chord length (C) (s/C = 0.0%) and three gap sizes with clearance heights (s) normalized by chord length of s/C = 2.0%, s/C = 5.4% and s/C = 6.7% are realized, while a few non-clearance vanes (C) of s/C = 2.0%, s/C = 5.4% and s/C = 6.7% are realized, while a few non-clearance supported the shroud ring. With rotating hub endwall only non-zero clearances are tested. vanes supported the shroud ring. With rotating hub endwall only non-zero clearances are Leakage flow through axial gaps in the hub is considered negligible due to a minor pres- tested. Leakage ﬂow through axial gaps in the hub is considered negligible due to a minor sure difference between the rotor drum and the flow channel, as well as small gaps of pressure difference between the rotor drum and the ﬂow channel, as well as small gaps under 1 mm. Downstream of S1 all blades and vanes are dismounted except of stage 4, of under 1 mm. Downstream of S1 all blades and vanes are dismounted except of stage 4, which is used to drive the flow. which is used to drive the ﬂow. Table 1. Reference setup specifications of the LSRC Table 1. Reference setup speciﬁcations of the LSRC. Test Rig Operating Point Test Rig Operating Point Shroud diameter 1500 mm Rotational speed at DP 1000 rpm Shroud diameter 1500 mm Rotational speed at DP 1000 rpm Hub to tip ratio 0.84 Mass flow m at DP 25.35 kg/s Hub to tip ratio 0.84 Mass ﬂow m at DP 25.35 kg/s Rotor R1 Stator S1 Rotor R1 Stator S1 No. of blades 63 No. of vanes 83 No. of blades 63 No. of vanes 83 Chord length 110 mm Chord length 89 mm Chord length 110 mm Chord length 89 mm Solidity, MS 1.597 Solidity, MS 1.709 Solidity, MS 1.597 Solidity, MS 1.709 Reynolds Reynolds number number Reynolds Reynonumber lds number 5 5 6.5 10 3.7 10 6.5 ⋅ 10 3.7 ⋅ 10 at entry, MS at entry, MS at entry, MS at entry, MS Mach number Mach number 0.25 0.18 Mach number Mach number at entry, MS at entry, MS 0.25 0.18 Flow coefﬁcient , MS 0.651 Diffusion factor, MS 0.37 at entry, MS at entry, MS Dh t 1 1 0.489 Loading coefﬁcient , MS Flow coefficient 2φ, MS 0.651 Diffusion factor, MS 0.37 : atLoad 10% higher ing coe mass fficient ﬂow than DP , MS due to the discarded IGV in test setup (b). 0.489 : at 10% higher mass flow than DP due to the discarded IGV in test setup (b). For test setup (b) only rotor 1 (R1) is bladed. Two tip gap sizes of s/C = 1.36% and s/C = 4.55% are observed which allows to evaluate the inﬂuence of incoming periodic For test setup (b) only rotor 1 (R1) is bladed. Two tip gap sizes of s/C = 1.36% and s/C distortions in dependence upon the tip clearance size. Either installing or discarding a = 4.55% are observed which allows to evaluate the influence of incoming periodic distor- wake generator (WG) produces the distorted, from here on unsteady, or the not distorted, tions in dependence upon the tip clearance size. Either installing or discarding a wake from here on steady, inﬂow. The WG consists of 83 circumferentially arranged circular bars generator (WG) produces the distorted, from here on unsteady, or the not distorted, from with a diameter of D = 2 mm. They are mounted 65.6% C upstream of the R1 leading edge (LE). This approach allows the analysis of the effect of an isolated wake disregarding the complex secondary ﬂow ﬁeld of a stator row. Furthermore, it enables a more direct comparison to linear cascade investigations where an analog setup was examined, cf. Krug et al. [23]. Due to the discarded IGV, the mass-ﬂow rate is adjusted to ensure the same rotor entry incidences as for the design point (DP) resulting in an adjusted design point at Int. J. Turbomach. Propuls. Power 2021, 6, 9 5 of 40 10% higher mass-ﬂow. All rotor data shown here correspond to this operating point. As this paper gives a short overview of the work done, only the nominal tip clearance cases, s/C = 2.0% for the stator and s/C = 1.36% for the rotor, will be presented here. Table 2. Conﬁgurations of varying wall speed for test setup (a). Conﬁguration Rotor R1 Hub Wall Stator S1 Hub Wall Un-skewed, w/o RM Stationary Stationary Skewed, w/o RM Rotating Stationary Skewed, with RM Rotating Rotating 2.2.2. Measurement Techniques The ﬂow ﬁeld can be captured in several measuring planes (MP) perpendicular to the machine axis, see Figure 1, using various probes. For the presented results only two MP are of interest. The ﬁrst one is MP4 which is located 26.8% C downstream of ax,R1 the trailing edge (TE) of R1, and at once located 16.3% C upstream of the LE of S1. ax,S1 The second one, MP5, is positioned 21% C downstream of the TE of S1. At both ax,S1 positions the measuring probes can be traversed radially and rotated around their axis. All stator rows are rotated simultaneously around the machine axis to alter the relative position between probe and stator vanes in pitchwise direction. Five-Hole-Probes (FHP) with spherical heads of a diameter of 2 mm are used to capture the steady ﬂow ﬁeld. Balancing the pressures in the two lateral holes via probe rotation allowed to measure the magnitude and direction of the velocity in absolute frame of reference with an accuracy of Dv = 0.3 m/s and D = 0.26 , respectively. The unsteady ﬂow ﬁeld is acquired using a fast measuring pressure probe (FMP), designed and manufactured at the chair of Turbomachinery and Flight Propulsion in Dresden. This one-hole-probe is equipped with a piezoresistive pressure sensor, see also Lange et al. [24]. Measurements with the FMP are performed at three different angles (D = 30 ) virtually creating a three-hole-probe. In the presented results the unsteady ﬂow ﬁeld data is analyzed by either looking at the time or ensemble average. 2.3. Numerical Setup TM The commercial ﬂow solver FINE /Turbo by NUMECA is applied to calculate the three-dimensional RANS equations for the investigated stator cases. Analog to the experiments the combination of IGV and S1 is simulated in a single passage with periodic boundary conditions. The upstream generated wake is passed-through the domain using a perfect connection interface (Full Non Matching Frozen Rotor). The Explicit Algebraic Reynolds Stress Model (EARSM) is exploited to close the system of equations, which was found to deliver the best agreement with experimental results compared with other RANS turbulence models available in the ﬂow solver for the LSRC, see also Lange et al. [24]. The domain is discretized applying a block-structured mesh with O4H-topology around the vanes, OH-topology in the tip gap and H-topology in the remaining parts. A preceding sensitivity study ensured a minimized spatial discretization error. Herein, especially the number of cells in streamwise direction within the empty duct between IGV and S1 was found to have a noticeable effect on the sustaining of the wake, see also Busse et al. [25]. As the BL is of particular interest, it is resolved, leading to dimensionless wall distances y of around 1. In spanwise direction the average density of grid nodes in the tip gap is held constant at a ratio of 22 cells per 1% of gap size normalized by channel height (s/H). The number of cells in the remaining ﬂow channel is adjusted analogously resulting 7 7 in ﬁnal meshes with 1.0 10 up to 1.5 10 grid points. 2.4. Current Investigations and Results 2.4.1. Inﬂuence of the Inlet Boundary Layer Skew The inﬂuence of a skewed inlet BL is investigated by comparing the shrouded stator cases with the rotating R1 disk, inducing a skewed BL, and the cases with the stationary Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 6 of 41 tip gap is held constant at a ratio of 22 cells per 1% of gap size normalized by channel height (s/H). The number of cells in the remaining flow channel is adjusted analogously resulting in final meshes with 1.0 ⋅ 10 up to 1.5 ⋅ 10 grid points. 2.4. Current Investigations and Results Int. J. Turbomach. Propuls. Power 2021, 6, 9 6 of 40 2.4.1. Influence of the Inlet Boundary Layer Skew The influence of a skewed inlet BL is investigated by comparing the shrouded stator cases with the rotating R1 disk, inducing a skewed BL, and the cases with the stationary band, suppressing the skewness and thereby producing an un-skewed BL. The difference in in- band, suppressing the skewness and thereby producing an un-skewed BL. The difference flow can be seen in Figure 2, where the pitchwise averaged radial distributions of total in inﬂow can be seen in Figure 2, where the pitchwise averaged radial distributions of total pr pressu essurere p p (in t (in b black) lack and ) and ﬂow flow angle ang inle absolute in absol frame ute frof am refer e ofence refere (in nce orange) α (in orange) are are shown for shown fo MP4. Her r M eP lines, 4. Her solid e line fors, un-skewed solid for uand n-skew dashed ed an for d d skewed ashed for BL, skewe represent d BrL esults , represent from computational ﬂuid dynamics (CFD) calculations and the symbols, square for un-skewed results from computational fluid dynamics (CFD) calculations and the symbols, square and delta for skewed BL, denote to the experimental data (EXP). for un-skewed and delta for skewed BL, denote to the experimental data (EXP). The skew of the incoming BL is clearly detectable by the strong drift of ﬂow angle The skew of the incoming BL is clearly detectable by the strong drift of flow angle α towards lower values at relative channel heights (r/H) below 5% for the test conﬁguration towards lower values at relative channel heights (r/H) below 5% for the test configuration with rotating R1 disc, cf. Figure 2. The resulting turning of the ﬂow corresponds to higher with rotating R1 disc, cf. Figure 2. The resulting turning of the flow corresponds to higher total pressure in this area as it induces energy into the ﬂow. In contrary a decrease in total pressure in this area as it induces energy into the flow. In contrary a decrease in total total pressure values towards the hub can be seen for the test case with a stationary band pressure values towards the hub can be seen for the test case with a stationary band up- upstream of S1 forming a typical BL. This is accompanied by a constant decline in ﬂow stream of S1 forming a typical BL. This is accompanied by a constant decline in flow angle angle down to the hub endwall in the depicted channel region remaining at higher values down to the hub endwall in the depicted channel region remaining at higher values com- compared to the skewed BL conﬁguration. pared to the skewed BL configuration. α[°] 20 30 40 50 0.1 0.08 EXP un-skewed BL 0.06 CFD un-skewed BL EXP skewed BL 0.04 CFD skewed BL 0.02 99,000 100,000 101,000 p [Pa] Figure 2. Pitchwise averaged total pressure pt (black) and flow angle α (orange) upstream of S1 Figure 2. Pitchwise averaged total pressure p (black) and ﬂow angle (orange) upstream of S1 (MP4) in the hub endwall region, s/C = 2.0%, EXP vs. CFD. (MP4) in the hub endwall region, s/C = 2.0%, EXP vs. CFD. To analyze the secondary ﬂow in the downstream measuring plane (MP5) the non- To analyze the secondary flow in the downstream measuring plane (MP5) the non- dimensional total pressure loss coefﬁcient is deﬁned by dimensional total pressure loss coefficient ζ is defined by p −p! (x ⃗) ( ) p p x ζ x ⃗ = . (1) ! t,ref t x = , . (1) dyn,ref Here the pitchwise averaged total and dynamic pressure in the upstream plane (MP4) at midspan (MS), p and p , are used as reference. For the nominal Here the pitchwise averaged total and dynamic pressure in the upstream plane (MP4) ,, ,, at clearance c midspan a (MS), se of s/C = 2.0% the p and pζ contours in , arMP e used 5 are shown for skewed an as reference. For the nominal d un-skew clear ed - t,MP4,MS dyn,MP4,MS ance inflow BL case of wit s/C hout = 2.0% relathe tive mot contours ion (Rin M) MP5 of th ar e hub e shown endwal for skewed l in Figu and re 3un-skewed a,b. A deviat inﬂow ion in BL without relative motion (RM) of the hub endwall in Figure 3a,b. A deviation in position position of the TLV, represented by the circular areas of high ζ, is apparent with an ap- of the TLV, represented by the circular areas of high , is apparent with an approximated proximated shift of the core of 0.15 θ/PStator in pitchwise direction, where θ/PStator corre- shift sponds to the circumferent of the core of 0.15 /P ial distance n in pitchwise ormal dir ized by ection, wher S1 pitch. In e /P a compressor c corresponds asc to ade thea Stator Stator circumferential distance normalized by S1 pitch. In a compressor cascade a skewed inlet skewed inlet BL reduces the cross passage flow in the vicinity of the hub as its direction BL reduces the cross passage ﬂow in the vicinity of the hub as its direction of inﬂuence of influence directly opposes the pressure gradient from pressure side (PS) to suction side directly opposes the pressure gradient from pressure side (PS) to suction side (SS) of two (SS) of two adjacent vanes. This weakens the passage vortex and was observed for a linear adjacent vanes. This weakens the passage vortex and was observed for a linear compressor cascade by Moore and Richardson [26]. In the current work these ﬁndings were conﬁrmed for the axial machine in a non-clearance case for S1, cf. Koppe et al. [27]. r/H[-] Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 7 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 7 of 40 compressor cascade by Moore and Richardson [26]. In the current work these findings were confirmed for the axial machine in a non-clearance case for S1, cf. Koppe et al. [27]. Figure Figure 3. 3. Effe Effect ct of vary of varying ing hu hub b wall wall momotion tion on n on on- non-dimensional dimensional total pressure loss coe total pressure loss fficient coefﬁcient (⟨ ⟩) downstream of S1 (MP5) (a–c) EXP, (d–g) CFD, and on the TLV trajectory (λ v ⃗ = −10 ) (h–k) downstream of S1 (MP5) (a–c) EXP, (d–g) CFD, and on the TLV trajectory ( (h vi) = 10 ) (h–k) CFD, s/C = 2.0%. CFD, s/C = 2.0%. The reduced strength of the passage vortex implicitly decreases its influence on the The reduced strength of the passage vortex implicitly decreases its inﬂuence on the TLV, as these two vortices have opposing directions of rotation. Furthermore, the drift to TLV, as these two vortices have opposing directions of rotation. Furthermore, the drift to smaller values of flow angle in absolute frame of reference (α) in the vicinity of the hub smaller values of ﬂow angle in absolute frame of reference () in the vicinity of the hub endwall leads to higher loaded profiles at vane tip, favoring a detachment of the flow from endwall leads to higher loaded proﬁles at vane tip, favoring a detachment of the ﬂow from the SS. The result can be seen in Figure 3b for the skewed BL case, where the TLV detaches the SS. The result can be seen in Figure 3b for the skewed BL case, where the TLV detaches from the stator vane somewhere along the chord and moves pitchwise into the passage. from the stator vane somewhere along the chord and moves pitchwise into the passage. The trajectory of the TLV follows the SS of the vane for an un-skewed incoming BL and The trajectory of the TLV follows the SS of the vane for an un-skewed incoming BL and thereby a connected area of high non-dimensional total pressure loss coefficient of the thereby a connected area of high non-dimensional total pressure loss coefﬁcient of the TLV TLV and the vane wake can be seen, cf. Figure 3a. A decrease in effect of the boundary and the vane wake can be seen, cf. Figure 3a. A decrease in effect of the boundary layer layer skewness on the TLV is observed with increasing tip clearance height, not shown skewness on the TLV is observed with increasing tip clearance height, not shown here, cf. [27]. This is expected as the area of inﬂuence of this phenomenon is restricted close to the endwall. Radial proﬁles of ﬂow angle in the absolute frame of reference are plotted for S1 test conﬁgurations with varying hub endwall motion in Figure 4. At relative channel heights between 5 and 25% higher ﬂow angle values representing higher turning over the stator Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 8 of 41 here, cf. [27]. This is expected as the area of influence of this phenomenon is restricted Int. J. Turbomach. Propuls. Power 2021, 6, 9 8 of 40 close to the endwall. Radial profiles of flow angle in the absolute frame of reference are plotted for S1 test configurations with varying hub endwall motion in Figure 4. At relative channel heights between 5 and 25% higher flow angle values representing higher turning over the stator row are detectable for the skewed BL case without relative motion between vane tip and row are detectable for the skewed BL case without relative motion between vane tip and underlying hub endwall. Below 5% r/H the relation reverses and lower values of ﬂow underlying hub endwall. Below 5% r/H the relation reverses and lower values of flow angle can be seen for the skewed BL setup. This coincides with the reduction in cross angle can be seen for the skewed BL setup. This coincides with the reduction in cross pas- passage ﬂow in the vicinity of the hub for an incoming skewed BL. sage flow in the vicinity of the hub for an incoming skewed BL. 0.35 0.3 0.25 un-skewed BL, w/o RM 0.2 skewed BL, w/o RM 0.15 un-skewed BL, with RM 0.1 skewed BL, with RM 0.05 50 60 70 80 α[°] Figure 4. Effect of varying hub wall motion on pitchwise averaged flow angle in absolute frame of Figure 4. Effect of varying hub wall motion on pitchwise averaged ﬂow angle in absolute frame of reference downstream of S1 (MP5), s/C = 2.0%, CFD. reference downstream of S1 (MP5), s/C = 2.0%, CFD. 2.4.2. Inﬂuence of Relative Motion between Vane Tip and Corresponding Endwall 2.4.2. Influence of Relative Motion between Vane Tip and Corresponding Endwall Due to constructive restrictions it is not possible to experimentally evaluate the isolated Due to constructive restrictions it is not possible to experimentally evaluate the iso- effect of the relative motion between the vane tips and the underlying hub endwall on the lated effect of the relative motion between the vane tips and the underlying hub endwall TLV, see also Section 2.2.1. For this purpose, the numerical method is conducted. This is on the TLV, see also Section 2.2.1. For this purpose, the numerical method is conducted. suitable as the results from the CFD show good agreement with the experiments for the This is suitable as the results from the CFD show good agreement with the experiments other three cases, see Figure 3. An overprediction of the losses associated with the TLV is for the other three cases, see Figure 3. An overprediction of the losses associated with the apparent for the numerical results, which is assumed to be due to the computational model TLV is apparent for the numerical results, which is assumed to be due to the computa- not being able to correctly capture the turbulent structures of the TLV. Nevertheless, size tional model not being able to correctly capture the turbulent structures of the TLV. Nev- and position of the TLV agree for the different endwall motion cases between numerical ertheless, size and position of the TLV agree for the different endwall motion cases be- and experimental data to a sufﬁcient extent rendering the following discussion valid, see tween numerical and experimental data to a sufficient extent rendering the following dis- also Koppe et al. [27]. cussion valid, see also Koppe et al. [27]. To evaluate the inﬂuence of a relative motion between the vane tip and its correspond- To evaluate the influence of a relative motion between the vane tip and its corre- ing endwall on the TLV the two cases, one with stationary and one with rotating hub sponding endwall on the TLV the two cases, one with stationary and one with rotating at S1, without an incoming BL skew are observed, see Figure 3d,f. For the combination hub at S1, without an incoming BL skew are observed, see Figure 3d,f. For the combination of un-skewed BL without relative motion the TLV stays attached to the SS of the vane, of un-skewed BL without relative motion the TLV stays attached to the SS of the vane, indicated by the big area of high non-dimensional total pressure loss coefﬁcient located indicated by the big area of high non-dimensional total pressure loss coefficient located adjoining to the vane wake region of high , see Figure 3d. Introducing a relative motion of adjoining to the vane wake region of high ζ, see Figure 3d. Introducing a relative motion the hub endwall a reduction in spanwise size of the affected passage area as well as a drift of the hub endwall a reduction in spanwise size of the affected passage area as well as a of the vortex core towards the adjacent vane PS is apparent, see Figure 3f. drift of the vortex core towards the adjacent vane PS is apparent, see Figure 3f. The ﬂow in the vicinity of the hub endwall features two opposing secondary ﬂows The flow in the vicinity of the hub endwall features two opposing secondary flows when the stationary shroud ring is installed. The ﬁrst resulting from the pressure gradient when the stationary shroud ring is installed. The first resulting from the pressure gradient between the pressure and suction side of two adjacent vanes, the cross passage ﬂow, and between the pressure and suction side of two adjacent vanes, the cross passage flow, and the second arising from the ﬂow over a vane tip, the tip leakage ﬂow, which rolls up into the second arising from the flow over a vane tip, the tip leakage flow, which rolls up into the TLV and continues further downstream. The cross passage ﬂow aids to the tendency the TLV and continues further downstream. The cross passage flow aids to the tendency of the TLV to follow the SS contour of the vane where it emerged. The vortical structures of the TLV to follow the SS contour of the vane where it emerged. The vortical structures within the lower half of the stator passage are visualized via isosurfaces of the (h vi) (⟨ ⟩) within the lower half of the stator passage are visualized via isosurfaces of the λ v ⃗ vortex identiﬁcation criterion, cf. [28], in Figure 3h. Here an additional smaller secondary vortex identification criterion, cf. [28], in Figure 3h. Here an additional smaller secondary vortex is identiﬁable next to the TLV which is induced by the interaction of the cross vortex is identifiable next to the TLV which is induced by the interaction of the cross pas- passage ﬂow and the TLV. Its rotational direction is opposing to the TLV’s and thereby sage flow and the TLV. Its rotational direction is opposing to the TLV’s and thereby add- adding to the prior described trend of following the SS contour. For the case with RM the ing to the prior described trend of following the SS contour. For the case with RM the cross cross passage ﬂow is suppressed by the no-slip condition on the hub endwall, which also has a dragging effect on the TLV. Hence, a shift of the TLV’s trajectory in the direction of the wall movement, which is towards the adjacent vanes PS, is apparent. This dragging effect as well as a higher interaction of the TLV with the free passage ﬂow reduces its extension in spanwise direction. The apparent decreased values of non-dimensional total r/H[-] Int. J. Turbomach. Propuls. Power 2021, 6, 9 9 of 40 pressure loss coefﬁcient in MP5, see Figure 3f, must be put into perspective considering the insertion of energy into the boundary layer ﬂow of the hub endwall due to its rotation. The aforementioned secondary induced vortex is not distinctly identiﬁable here, see Figure 3j. Looking at the pitchwise averaged distributions of ﬂow angle , Figure 4, an increase in values between 5 and 25% of relative channel heights is visible for the un-skewed BL case with RM compared to the case without, as was seen for the skewed BL conﬁguration, cf. Section 2.4.1. Here, the distributions follow a similar trend down to around 11% r/H where a sudden further increase in ﬂow angle is detected for the setup with relative motion. Comparing to the 2D plot of non-dimensional total pressure loss, this relative channel height corresponds to the upper bound of regions with higher losses associated with the TLV, see Figure 3f. With the relative endwall motion reducing the spanwise and increasing the pitchwise expansion of the TLV, the overall inﬂuence of the vortex on the pitchwise averaged ﬂow angle at these radial positions will increase. As the orientation of rotation of the TLV favors higher ﬂow angles in the upper part of the vortex, the sudden increase in values is reasonable. Below the vortex core this trend will reverse adding to the extensive inﬂuence of the moving endwall resulting in the clear drift towards smaller ﬂow angle values for the case with RM in the vicinity of the hub (r/H = 0), see Figure 4. 2.4.3. Combined Inﬂuence of Boundary Layer Skew and Relative Motion between Vane Tip and Corresponding Endwall Setting the hub endwall for stage 1 to the design rotational speed the combined effect of a skewed inﬂow boundary layer and a relative motion between the vane tip and the underlying wall can be analyzed. Comparing Figure 3a,c for the experimental and Figure 3d,g for the numerical results, it becomes clear that the inﬂuence upon the trajectory of the TLV increases. Both phenomena weaken or rather eliminate the cross passage ﬂow between the PS and SS of two adjacent stator vanes in the vicinity of the hub, which in return decreases the passage vortex in this area considerably. Consequently, the progression of the TLV is less inﬂuenced by this contra rotating secondary ﬂow. The dragging effect arising from the no-slip condition on the hub endwall further accommodates the drift of the TLV away from its originating vane towards the adjacent PS. The numerical comparison of analog conﬁgurations within a linear compressor cascade shows similar inﬂuence on the secondary ﬂow, see Section 3.4.4. The decrease of for the case with rotating hub endwall, cf. Figure 3c,g, again, must be put in perspective as the rotation of the hub under S1 induces a ﬂow turning and by this adding energy to the ﬂuid. It is clear, however, that the inﬂuence of the high loss region associated with the TLV on the free passage ﬂow is far smaller for the case with a skewed BL and RM. 2.4.4. Inﬂuence of Incoming Periodic Wakes To evaluate the inﬂuence of incoming periodic distortions on the passage ﬂow of rotor 1 essentially isolated wakes are produced upstream using the WG. Looking at time- and pitchwise averaged radial proﬁles of axial velocity normalized by the midspan value at MP4 a minor redistribution in mass ﬂow over the blade height is apparent for the unsteady case with incoming wakes, cf. Figure 5a. Here steady state measurements of the FHP (solid lines) and time resolved data from the FMP (dashed-dotted lines) are shown. Although these differ marginally in absolute value, the trends correspond well, especially when comparing the differences between the steady and unsteady R1 cases. At spanwise positions between r/H = 0.5 and 0.72 higher axial velocity can be seen for the undisturbed rotor (black lines) for both probes. In regions below midspan down to r/H = 0.19 the steady case shows lower relative axial velocity compared to the periodically disturbed rotor (red lines). The corresponding 2D ﬂow ﬁeld at MP4, captured by the FMP, is shown in Figure 5b. Here the aforementioned redistribution is evident in a weaker SS ﬂow separation in the lower half of the passage, which is represented by the broadened area of low non-dimensional axial velocity in the blade wake. Furthermore, minor changes in the tip region can be observed for the unsteady case where the extend of low relative axial velocity decreases in size compared to the steady inﬂow condition. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 10 of 41 case shows lower relative axial velocity compared to the periodically disturbed rotor (red lines). The corresponding 2D flow field at MP4, captured by the FMP, is shown in Figure 5b. Here the aforementioned redistribution is evident in a weaker SS flow separation in the lower half of the passage, which is represented by the broadened area of low non- Int. J. Turbomach. Propuls. Power 2021, 6, 9 10 of 40 dimensional axial velocity in the blade wake. Furthermore, minor changes in the tip re- gion can be observed for the unsteady case where the extend of low relative axial velocity decreases in size compared to the steady inflow condition. (a) (b) steady unsteady 1 1 0.8 0.8 0.8 PS SS PS SS 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.8 0.9 1 250 300 350 400 v /v [-] θ/P [-] θ/P [-] x [mm] ax ax,MS Rotor Rotor FHP steady FMP steady FHP unsteady v /v [-]: 0.45 0.55 0.65 0.75 0.85 0.95 1.05 FMP unsteady ax ax,MS (c) Δθ/P =0.00=1.00 Δθ/P =0.25 Δθ/P =0.50 Δθ/P =0.75 WG WG WG WG 1 1 1 1 0.8 0.8 0.8 0.8 PS SS 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 θ/P [-] θ/P [-] θ/P [-] θ/P [-] Rotor Rotor Rotor Rotor Figure Figure 5. 5. Effe Effect ct of ofincom incoming ing periodi periodic c transie transi nt wak ent wakes es on (aon ) time- and pitchwise average (a) time- and pitchwise averaged d data up- data (MP3) and downstream (MP4) of R1, (b) ensemble- and pitchwise averaged FMP data and (c) en- up- (MP3) and downstream (MP4) of R1, (b) ensemble- and pitchwise averaged FMP data and semble averaged FMP data at discrete relative positions between WG and R1 downstream of R1 (c) ensemble averaged FMP data at discrete relative positions between WG and R1 downstream of R1 (MP4), s/C= 1.36%, EXP. (MP4), s/C= 1.36%, EXP. A closer look at the unsteady case is given in Figure 5c where four distinct relative A closer look at the unsteady case is given in Figure 5c where four distinct relative positions between WG and R1 are shown. Here, a fluctuation of the TLV can be observed positions between WG and R1 are shown. Here, a ﬂuctuation of the TLV can be observed by the change in the region of low non-dimensional axial velocity throughout the four by the change in the region of low non-dimensional axial velocity throughout the four time steps. At each time step the remains of incoming bar wakes are marked with yellow time steps. At each time step the remains of incoming bar wakes are marked with yellow dashed lines and can be identified by areas of reduced relative axial velocity. They pro- dashed lines and can be identiﬁed by areas of reduced relative axial velocity. They progress gress from left to right with each time step. From relative position one (Δθ/PWG = 0.00) to from left to right with each time step. From relative position one (D/P = 0.00) to two WG two (Δθ/PWG = 0.25) a reduction in low non-dimensional axial velocity is observed in the (D/P = 0.25) a reduction in low non-dimensional axial velocity is observed in the tip WG tip region where the deterioration progresses as the bar wake approaches the rotor. After region where the deterioration progresses as the bar wake approaches the rotor. After passing the rotor wake, the area of low relative axial velocity in the vicinity of the blade passing the rotor wake, the area of low relative axial velocity in the vicinity of the blade tip tip strengthens again and increases with growing distance of the WG wake, as can be seen strengthens again and increases with growing distance of the WG wake, as can be seen in in time steps three (Δθ/PWG = 0.50) and four (Δθ/PWG = 0.75). time steps three (D/P = 0.50) and four (D/P = 0.75). WG WG In the lower half of the passage an effect of the WG wake on the suction side separa- In the lower half of the passage an effect of the WG wake on the suction side separation tion is observed. Here, a decrease is particularly apparent when the incoming wake is in is observed. Here, a decrease is particularly apparent when the incoming wake is in the vicinity of the rotor wake, see time steps D/P = 0.25 and D/P = 0.50 of Figure 5c. WG WG This leads to the assumption that the incoming wake inﬂuences the transition on the blade proﬁle, which was observed for the linear compressor cascade as well as for the axial turbine conﬁguration, see Sections 3.4.5 and 5.4.2 respectively. Another explanation could be radially varying pressure proﬁles on the rotor surface due to the change of the TLV in the tip region. Further investigations are necessary to verify these hypotheses. WGwake r/H[-] r/H[-] r/H[-] s s s r/H[-] r/H[-] R[mm] r/H[-] s r/H[-] s Int. J. Turbomach. Propuls. Power 2021, 6, 9 11 of 40 2.5. Work in Progress Further analysis of the effect of incoming wakes on the TLV of the low-speed com- pressor rotor with increased tip clearance is under investigation and will be compared with corresponding data from previous linear cascade tests. Additional data will be ob- tained through particle image velocimetry (PIV) within the blade passage and hot-ﬁlm CTA measurements of the proﬁle boundary layer development. This data will be used to validate own URANS and LES results of sub-project B. Joint analysis will deepen the physical understanding. 3. Sub-Project B—High Fidelity Numerical Investigations of the Secondary Flow in a Linear Compressor Cascade 3.1. Scope of Sub-Project B The general approach of sub-project B in the collaborative project is to use numerical simulations with two complementary objectives. First, the physics of secondary ﬂows in the near-wall area of a compressor cascade is investigated with the goal of identifying the role of different issues, in particular those distinguishing the situation in a linear cascade from an annular cascade, with the long-term goal to elucidate the transferability of results from linear cascade studies to annular cascades. In this perspective, speciﬁc parameters, such as the relative wall motion, are investigated concerning their effect on the dominating vortical structures inside the cascade, such as the tip leakage vortex (TLV). The second goal of sub-project B is to improve the simulation methodology in the context of LES for turbomachinery ﬂows. This unfolds in two aspects, assessing the modelling in the endwall region and identifying speciﬁc requirements in linear and annular cascades. Based on these objectives, results of Large Eddy Simulation (LES) of a linear com- pressor cascade are presented. As a validation step, the modelling introduced through LES is ﬁrst assessed against highly resolved data obtained by means of Direct Numerical Simulation (DNS). 3.2. Geometry The studied geometry was deﬁned according to the linear cascade setup of the Chair of Turbomachinery and Flight Propulsion at TU Dresden conducting sub-project A [23]. The blade proﬁle represents a scaled tip section of the reference built rotor of the LSRC [21,22] described in Section 2.2.1. In the current investigations the linear cascade has a chord length of C = 159.6 mm, an aspect ratio of H/C = 1.133, and is mounted with a stagger angle of 46.9 . The leading and trailing edge proﬁle angles are = 60.75 and = 40 , LE TE respectively. The cascade has a solidity of = C/P = 1.55. Furthermore, the present case features a tip gap of width s/C = 3% (s/H = 2.65%) between the endwall and the blade tip. The endwall is located at the bottom of the computational domain, where z = 0. A sketch of the blade proﬁle is depicted in Figure 6. 3.3. Numerical Setup and Grid The in-house code LESOCC2 [29] was used to solve the Navier-Stokes equations in their incompressible non-dimensional form. It features 2nd order ﬁnite volume discretiza- tion in space, and time integration is performed through a 3-step 2nd order Runge-Kutta scheme. The solver has been used previously in DNS studies of linear turbine cascades, including secondary ﬂows, providing good results [30–32]. In the following mainly results of Wall-Resolving Large Eddy Simulations (WRLES) at Re = 3 10 are presented. This set-up matches the conﬁguration of Krug et al. [23]. Inlet velocity jj v jj and blade chord C were used to deﬁne the Reynolds number. For the LES, ref the WALE model [33] was used to model the subgrid scales. Additionally, results obtained through DNS and WRLES at Re = 1.46 10 are ﬁrst discussed for validation of the method. The lower Reynolds number was chosen to obtain sound reference data by simulating the conﬁguration described using DNS with reasonable computational resources. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 12 of 41 3.3. Numerical Setup and Grid The in-house code LESOCC2 [29] was used to solve the Navier-Stokes equations in their incompressible non-dimensional form. It features 2nd order finite volume discreti- zation in space, and time integration is performed through a 3-step 2nd order Runge- Kutta scheme. The solver has been used previously in DNS studies of linear turbine cas- cades, including secondary flows, providing good results [30–32]. In the following mainly results of Wall-Resolving Large Eddy Simulations (WRLES) at Re =3 ⋅ 10 are presented. This set-up matches the configuration of Krug et al. [23]. Inlet velocity |v ⃗ | and blade chord C were used to define the Reynolds number. For the LES, the WALE model [33] was used to model the subgrid scales. Additionally, results obtained through DNS and WRLES at Re =1.46 ⋅ 10 are first discussed for validation Int. J. Turbomach. Propuls. Power 2021, 6, 9 12 of 40 of the method. The lower Reynolds number was chosen to obtain sound reference data by simulating the configuration described using DNS with reasonable computational re- sources. In In all cases the computational dom all cases the computational domain aincovers covers one one period period of the c of the cascade ascade (F (Figur igur ee 6) 6) which which reaches from reaches from x/ x/C C = = − 0.437 0.437 to to x/ x/C C = = 1.367 1.367 and and was discretized using block- was discretized using block- structured grids. For the WRLES, grid sizes with y 1 at the walls were ensured, resulting structured grids. For the WRLES, grid sizes with y ≈1 at the walls were ensured, re- in a grid of 90 MCV (million control volumes). For the DNS case at Re = 1.46 10 , sulting in a grid of 90 MCV (million control volumes). For the DNS case at Re =1.46 ⋅ besides the wall grid sizes, it was ensured that the cell size, deﬁned as the cubic root of 10 , besides the wall grid sizes, it was ensured that the cell size, defined as the cubic root the cell volume, is smaller than the Kolmogorov scale, which was estimated using the of the cell volume, is smaller than the Kolmogorov scale, which was estimated using the turbulent dissipation. This resulted in a grid of 350 MCV, with 304 cells in the spanwise turbulent dissipation. This resulted in a grid of 350 MCV, with 304 cells in the spanwise direction, 84 of them within the gap region. For the analogous WRLES only the restriction direction, 84 of them within the gap region. For the analogous WRLES only the restriction on wall resolution y was kept, together with the corresponding tangential resolution on wall resolution y was kept, together with the corresponding tangential resolution requirements [34], allowing to decrease the overall number of grid points down to 60 MCV requirements [34], allowing to decrease the overall number of grid points down to 60 MCV for Re = 1.46 10 . for Re = 1.46 ⋅ 10 . Figure 6. Top down view of the simulated linear cascade proﬁle with zoom of the computational Figure 6. Top down view of the simulated linear cascade profile with zoom of the computational domain (shaded region), repeated in y-direction (grey). Coordinates are scaled using the blade chord. domain (shaded region), repeated in y-direction (grey). Coordinates are scaled using the blade Red dashed line at x/C = 0.89 depicts the stage outlet plane. chord. Red dashed line at x/C = 0.89 depicts the stage outlet plane. Regarding boundary conditions, an unsteady turbulent ﬂow was imposed at the Regarding boundary conditions, an unsteady turbulent flow was imposed at the do- domain inlet and a convective condition was set at the outlet. The turbulent inﬂow main inlet and a convective condition was set at the outlet. The turbulent inflow condi- conditions were generated through a precursor simulation, enforcing mean and ﬂuc- tions were generated through a precursor simulation, enforcing mean and fluctuation pro- tuation proﬁles from experiments [23], with a boundary layer thickness at the inlet of files from experiments [23], with a boundary layer thickness at the inlet of δ /C = /C = 0.222 ( /H = 0.198) and a turbulence intensity TI < 1% at midspan [35]. At the 1 1 0.222 (δ /H = 0.198) and a turbulence intensity TI < 1% at midspan [35]. At the end- endwall, no-slip conditions were imposed, while at the midplane symmetry conditions wall, no-slip conditions were imposed, while at the midplane symmetry conditions were were applied. The domain size in spanwise direction is large enough so that the midplane applied. The domain size in spanwise direction is large enough so that the midplane boundary conditions do not inﬂuence the secondary ﬂow. boundary conditions do not influence the secondary flow. The simulations were run for 5 ﬂow through times (FTT) before averaging was carried The simulations were run for 5 flow through times (FTT) before averaging was car- out for another 15 FTT. Here, a FTT is deﬁned based on the axial chord length C and the ried out for another 15 FTT. Here, a FTT is defined based on the axial chord length C and velocity at the inlet midplane jj v jj. Simulations with still longer time integration were ref the velocity at the inlet midplane |v ⃗ | . Simulations with still longer time integration performed to ensure that the time integration applied here is long enough. were performed to ensure that the time integration applied here is long enough. 3.4. Current Investigations and Results 3.4.1. Validation of WRLES with Respect to DNS Data The ﬁrst step taken towards the analysis of the secondary ﬂows in the compressor cascade is to assess the effects of the modelling approach. To this end WRLES of the com- pressor cascade is compared against DNS for Re = 1.46 10 . As discussed in Section 3.3 the WRLES approach required only a 6th of the grid points. The overall ﬂow structure, visualised through (h vi) isosurfaces exhibits no remarkable differences (Figure 7a shows only WRLES) between both approaches. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 13 of 41 3.4. Current Investigations and Results 3.4.1. Validation of WRLES with Respect to DNS Data The first step taken towards the analysis of the secondary flows in the compressor cascade is to assess the effects of the modelling approach. To this end WRLES of the com- pressor cascade is compared against DNS for Re =1.46 ⋅ 10 . As discussed in Section 3.3 Int. J. Turbomach. Propuls. Power 2021, 6, 9 13 of 40 th the WRLES approach required only a 6 of the grid points. The overall flow structure, visualised through λ (⟨v ⃗⟩) isosurfaces exhibits no remarkable differences (Figure 7a shows only WRLES) between both approaches. (a) (b) Figure Figure 7. 7. Linea Linear r com compr pressor essor c cascade ascade at at Re Re =1 = 1.46 .46 ⋅1 10 0 . ( . (a a)) Vortical stru Vortical structur cture evisu visualized alized throu through gh λ ( (⟨h v v ⃗⟩)i)=− = 22 . ( . b (b ) Pitchwi ) Pitchwise se averaged total averaged total pressure pressurelosses downstream o losses downstream of f the bla the blade de at at x/C x/C==0.89 0.89 . . Slight differences are related to small vortices not resolved by the LES since they are Slight differences are related to small vortices not resolved by the LES since they are smaller than the grid size. At the outlet plane similar trends between DNS and WRLES are smaller than the grid size. At the outlet plane similar trends between DNS and WRLES observed. For instance, pressure losses at the exit plane for the WRLES case, see Figure 7b, are observed. For instance, pressure losses at the exit plane for the WRLES case, see Figure are in very good agreement with the DNS result, with slightly higher losses for the WRLES. 7b, are in very good agreement with the DNS result, with slightly higher losses for the Similarly, the pitchwise averaged exit ﬂow angle shows a very good match. The deviations WRLES. Similarly, the pitchwise averaged exit flow angle shows a very good match. The occur mainly away from the endwall. The reason for this behaviour is that near walls the deviations occur mainly away from the endwall. The reason for this behaviour is that near WRLES grid is close to DNS resolution. Therefore, boundary layer ﬂows around walls in walls the WRLES grid is close to DNS resolution. Therefore, boundary layer flows around the WRLES case are resolved with high ﬁdelity. Away from the endwall differences result walls in the WRLES case are resolved with high fidelity. Away from the endwall differ- from a difference in the ﬂow separation at the blade TE. This is observed, for instance, ences result from a difference in the flow separation at the blade TE. This is observed, for through the friction coefﬁcient instance, through the friction coefficient c = / jj v | jj| /2 (2) (2) c =τ /(ρ v ⃗ /2) f ref at different spanwise locations, shown in Figure 8a, revealing overall very good agree- at different spanwise locations, shown in Figure 8a, revealing overall very good agreement, ment, except for (x/C 0.9) , where the WRLES predicts lower c values and a later but except for (x/C > 0.9), where the WRLES predicts lower c values and a later but somewhat somewhat stronger increase. Similar findings were observed in simulations of a turbine stronger increase. Similar ﬁndings were observed in simulations of a turbine stage by stage by Michelassi et al. [36]. These differences lead to differences in the wake, which Michelassi et al. [36]. These differences lead to differences in the wake, which beside beside the modelling uncertainty, result in the deviations presented. Nonetheless, apart the modelling uncertainty, result in the deviations presented. Nonetheless, apart from from the trailing edge region the DNS data are well reproduced, with a 6-fold reduction the trailing edge region the DNS data are well reproduced, with a 6-fold reduction in in computational resources. computational resources. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 14 of 41 The aerodynamic blade loading is shown in Figure 8b by means of the pressure co- The aerodynamic blade loading is shown in Figure 8b by means of the pressure efficient coefﬁcient ! ! c = (p( x ) p )/(jj v jj /2) (3) ref ref c = (p(x ⃗) −p )/(ρ |v ⃗ | /2) (3) at different spanwise positions on the blade. Here, the reference is reproduced extremely at different spanwise positions on the blade. Here, the reference is reproduced extremely well. well. (a) (b) Figure 8. Comparison of WRLES and DNS results along the blade at different spanwise positions. Figure 8. Comparison of WRLES and DNS results along the blade at different spanwise (a) Friction c along the SS and (b) pressure c along PS and SS. positions. (a) Friction c along the SS and (b) pressure c along PS and SS. 3.4.2. Validation of WRLES with Respect to Experimental Data Further validation is now performed with experimental data for Re =3 ⋅ 10 , matching the configuration of Krug et al. [23]. Figure 9 presents a comparison of the pres- sure coefficient at the endwall. Overall good agreement is found, with pressure isolines showing similar distributions. A pressure minimum at the tip gap somewhat larger in size is obtained in the present numerical simulations, but measuring at such a position is not free of error. Beyond the position of this pressure minimum, the TLV departs from the blade (x/C ≈ 0.3), still remaining relatively close to the blade. Between the blades, pres- sure isolines exhibit a mirrored S-shape. The reason for this is the TLV, as stated in [23,37,38]. This was confirmed by looking at the pressure in planes perpendicular to the blades’ camberline. It exhibits a minimum at these positions matching the location of the TLV. (a) (b) Figure 9. Time averaged pressure coefficient at the endwall (z=0). Results from (a) WRLES and (b) experiments [23]. Lastly, total pressure losses and flow angle deviation are compared in Figure 10. Overall, very good agreement is obtained, with a slightly higher deviation in the simula- tion. This slightly overprediction of WRLES with respect to the reference has also been Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 14 of 41 at different spanwise positions on the blade. Here, the reference is reproduced extremely well. (a) (b) Figure 8. Comparison of WRLES and DNS results along the blade at different spanwise Int. J. Turbomach. Propuls. Power 2021, 6, 9 14 of 40 positions. (a) Friction c along the SS and (b) pressure c along PS and SS. 3.4.2. Validation of WRLES with Respect to Experimental Data 3.4.2. Validation of WRLES with Respect to Experimental Data Further validation is now performed with experimental data for Re =3 ⋅ 10 , matching the Further validation configuration is now of Kr performed ug et al. [23]. Figure with experimental 9 presents a co data for mparison o Re = 3 10f the pres- , match- ing the conﬁguration of Krug et al. [23]. Figure 9 presents a comparison of the pressure sure coefficient at the endwall. Overall good agreement is found, with pressure isolines coef showing ﬁcientsimilar at the endwall. distributio Overall ns. A pre good ssuagr re mini eement mum is a found, t the tip ga with p somewha pressure isolines t larger in siz show-e ing similar distributions. A pressure minimum at the tip gap somewhat larger in size is is obtained in the present numerical simulations, but measuring at such a position is not obtained in the present numerical simulations, but measuring at such a position is not free free of error. Beyond the position of this pressure minimum, the TLV departs from the of error. Beyond the position of this pressure minimum, the TLV departs from the blade blade (x/C ≈ 0.3), still remaining relatively close to the blade. Between the blades, pres- (x/C 0.3), still remaining relatively close to the blade. Between the blades, pressure iso- sure isolines exhibit a mirrored S-shape. The reason for this is the TLV, as stated in lines exhibit a mirrored S-shape. The reason for this is the TLV, as stated in [23,37,38]. This [23,37,38]. This was confirmed by looking at the pressure in planes perpendicular to the was conﬁrmed by looking at the pressure in planes perpendicular to the blades’ camberline. blades’ camberline. It exhibits a minimum at these positions matching the location of the It exhibits a minimum at these positions matching the location of the TLV. TLV. (a) (b) Figure 9. Time averaged pressure coefficient at the endwall (z=0). Results from (a) WRLES and Figure 9. Time averaged pressure coefﬁcient at the endwall (z = 0). Results from (a) WRLES and (b (b ) ) experiments [23] experiments [23]. . Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 15 of 41 Lastly, total pressure losses and ﬂow angle deviation are compared in Figure 10. Over- Lastly, total pressure losses and flow angle deviation are compared in Figure 10. all, very good agreement is obtained, with a slightly higher deviation in the simulation. Overall, very good agreement is obtained, with a slightly higher deviation in the simula- This slightly overprediction of WRLES with respect to the reference has also been high- tion. This slightly overprediction of WRLES with respect to the reference has also been lighted in the previous section and may be related to modelling uncertainties affecting the highlighted in the previous section and may be related to modelling uncertainties affect- boundary layer state towards the TE. ing the boundary layer state towards the TE. Finally, it is noted that the results obtained with the two Reynolds numbers, besides Finally, it is noted that the results obtained with the two Reynolds numbers, besides the expected differences in magnitude, in both cases feature practically the same size of the the expected differences in magnitude, in both cases feature practically the same size of region inﬂuenced by the secondary ﬂow, approximately z/H 0 . . . 0.25. Hence, it appears the region influenced by the secondary flow, approximately z/H ≈ 0 … 0.25. Hence, it ap- that the size of the secondary ﬂow region is not dependent on the Reynolds number. pears that the size of the secondary flow region is not dependent on the Reynolds number. (a) (b) Figure 10. Pitchwise averaged (a) total pressure losses and (b) ﬂow angle deviation D , down- Figure 10. Pitchwise averaged (a) total pressure losses ζ and (b) flow angle deviation Δβ , down- str stream of the eam of the blade blade (p (plane lane at at x/ x/C C = = 0.89). 0.89). Ex Experimental perimental data data from from Kr Kru ugget et al al. . [23] [23]. . 3.4.3. Secondary Flow Effects in Compressor Cascade The overall vortical structure of the flow in this configuration is visualized through ⟨ ⟩ isocontours of λ ( v ⃗ )=−2 in Figure 11. The dip in the pressure isolines within the pas- sage shown in Figure 9 matches with the trajectory of the TLV identified through λ (⟨v ⃗⟩). The induced vortex, that is visible by the λ (⟨v ⃗⟩)-isosurface, is not detectable through the pressure at the endwall due to its smaller magnitude. Figure 11. Vortical structure (λ (⟨v ⃗⟩) =−2) for the linear compressor cascade at Re =3 ⋅ 10 . Focusing on the blade, the aerodynamic load is mostly towards the front, Figure 12a, with an almost vanishing pressure gradient at the PS and a mild negative pressure at the SS, exhibiting a minimum towards the front. The effect of the secondary flow is to reduce the blade loading, as evidenced by the differences between the pressure coefficient on PS and SS near the blade tip (z/H = 0.06) compared to the midspan region (z/H = 0.3), as seen in Figure 12a. Furthermore, the local minimum at the SS for z/H = 0.06 is shifted downstream. Its position is slightly downstream of the position where the TLV departs from the blade. Furthermore, the minimum in the pressure at the SS at each spanwise height coincides in position with the start of the decrease of the friction levels shown in Figure 12b. For instance, at the midspan the pressure minimum is at x/C ≈ 0.1 and the local friction maximum at x/C ≈ 0.05. Figure 13 shows the state of the boundary layer along the SS by means of the shape factor H and by wall-normal profiles of the TKE. At the tip (z/H = 0.06) the shape factor Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 15 of 41 highlighted in the previous section and may be related to modelling uncertainties affect- ing the boundary layer state towards the TE. Finally, it is noted that the results obtained with the two Reynolds numbers, besides the expected differences in magnitude, in both cases feature practically the same size of the region influenced by the secondary flow, approximately z/H ≈ 0 … 0.25. Hence, it ap- pears that the size of the secondary flow region is not dependent on the Reynolds number. (a) (b) Int. J. Turbomach. Propuls. Power 2021, 6, 9 15 of 40 Figure 10. Pitchwise averaged (a) total pressure losses ζ and (b) flow angle deviation Δβ , down- stream of the blade (plane at x/C = 0.89). Experimental data from Krug et al. [23]. 3.4.3. Secondary Flow Effects in Compressor Cascade 3.4.3. Secondary Flow Effects in Compressor Cascade The overall vortical structure of the ﬂow in this conﬁguration is visualized through The overall vortical structure of the flow in this configuration is visualized through isocontours of (h vi) = 2 in Figure 11. The dip in the pressure isolines within the isocontours of λ (⟨v ⃗⟩)=−2 in Figure 11. The dip in the pressure isolines within the pas- passage shown in Figure 9 matches with the trajectory of the TLV identiﬁed through sag! e shown in Figure 9 matches with the trajectory of th! e TLV identified through λ (⟨v ⃗⟩). (h vi). The induced vortex, that is visible by the (h vi)-isosurface, is not detectable 2 2 The induced vortex, that is visible by the λ (⟨v ⃗⟩)-isosurface, is not detectable through the through the pressure at the endwall due to its smaller magnitude. pressure at the endwall due to its smaller magnitude. Figure 11. Vortical structure (λ (⟨v ⃗⟩) =−2) for the linear compressor cascade at Re =3 ⋅ 10 . Figure 11. Vortical structure ( ( v ) = 2) for the linear compressor cascade at Re = 3 10 . Focusing on the blade, the aerodynamic load is mostly towards the front, Figure 12a, Focusing on the blade, the aerodynamic load is mostly towards the front, Figure 12a, with an almost vanishing pressure gradient at the PS and a mild negative pressure at the with an almost vanishing pressure gradient at the PS and a mild negative pressure at the SS, exhibiting a minimum towards the front. The effect of the secondary ﬂow is to reduce SS, exhibiting a minimum towards the front. The effect of the secondary flow is to reduce the blade loading, as evidenced by the differences between the pressure coefﬁcient on PS the blade loading, as evidenced by the differences between the pressure coefficient on PS and SS near the blade tip (z/H = 0.06) compared to the midspan region (z/H = 0.3), as and SS near the blade tip (z/H = 0.06) compared to the midspan region (z/H = 0.3), as seen in Figure 12a. Furthermore, the local minimum at the SS for z/H = 0.06 is shifted seen in Figure 12a. Furthermore, the local minimum at the SS for z/H = 0.06 is shifted downstream. Its position is slightly downstream of the position where the TLV departs downstream. Its position is slightly downstream of the position where the TLV departs from the blade. Furthermore, the minimum in the pressure at the SS at each spanwise from the blade. Furthermore, the minimum in the pressure at the SS at each spanwise height coincides in position with the start of the decrease of the friction levels shown in height coincides in position with the start of the decrease of the friction levels shown in Figure 12b. For instance, at the midspan the pressure minimum is at x/C 0.1 and the Figure 12b. For instance, at the midspan the pressure minimum is at x/C ≈ 0.1 and the local friction maximum at x/C 0.05. local friction maximum at x/C ≈ 0.05. Figure 13 shows the state of the boundary layer along the SS by means of the shape Figure 13 shows the state of the boundary layer along the SS by means of the shape factor H and by wall-normal proﬁles of the TKE. At the tip (z/H = 0.06) the shape factor factor H and by wall-normal profiles of the TKE. At the tip (z/H = 0.06) the shape factor is small all along the wall. Hence, the boundary layer at this height is turbulent throughout the whole blade chord. Furthermore, no marked change in shape factor related to the departure of the TLV at x/C 0.3 is observed. The friction coefﬁcient near the tip, shown in Figure 12b, on the other hand, exhibits a marked change. Once the TLV moves away from the blade the friction coefﬁcient decreases by a factor of more than two. Away from the blade wall an increase in TKE is observed for 0.3 x/C 0.4, which is directly related to the location of the TLV. Downstream of the blade, at x/C = 0.89, these higher ﬂuctuations are also observed around the TLV core, as seen in Figure 14. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 16 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 16 of 41 is small all along the wall. Hence, the boundary layer at this height is turbulent throughout is small all along the wall. Hence, the boundary layer at this height is turbulent throughout the whole blade chord. Furthermore, no marked change in shape factor related to the de- the whole blade chord. Furthermore, no marked change in shape factor related to the de- parture of the TLV at x/C ≈ 0.3 is observed. The friction coefficient near the tip, shown parture of the TLV at x/C ≈ 0.3 is observed. The friction coefficient near the tip, shown in Figure 12b, on the other hand, exhibits a marked change. Once the TLV moves away in Figure 12b, on the other hand, exhibits a marked change. Once the TLV moves away from the blade the friction coefficient decreases by a factor of more than two. Away from from the blade the friction coefficient decreases by a factor of more than two. Away from the blade wall an increase in TKE is observed for 0.3 ≤ x/C ≤0.4, which is directly re- the blade wall an increase in TKE is observed for 0.3 ≤ x/C ≤0.4, which is directly re- Int. J. Turbomach. Propuls. Power 2021, 6, 9 16 of 40 lated to the location of the TLV. Downstream of the blade, at x/C =0.89, these higher lated to the location of the TLV. Downstream of the blade, at x/C =0.89, these higher fluctuations are also observed around the TLV core, as seen in Figure 14. fluctuations are also observed around the TLV core, as seen in Figure 14. (b) (a) (b) (a) Figure 12. Pressure (a) and friction (b) coefficients on the blade at two different spanwise posi- Figure Figure 12. 12. Pres Pressur sure ( e (a a)) and friction ( and friction (b b)) coef coeffi ﬁcients cients on the b on the blade lade at at two two dif diff fer erent spanwise ent spanwise posi- positions, tions, near the blade tip (z/H = 0.06) and at midspan (z/H = 0.3). tions, near the blade tip (z/H = 0.06) and at midspan (z/H = 0.3). near the blade tip (z/H = 0.06) and at midspan (z/H = 0.3). Now turning to the blade midspan (z/H = 0.3), the shape factor is much larger near Now turning to the blade midspan (z/H = 0.3), the shape factor is much larger near Now turning to the blade midspan (z/H = 0.3), the shape factor is much larger near the leading edge peaking around x/C ≈ 0.35 then dropping to values around 1.5. the leading edge peaking around x/C 0.35 then dropping to values around 1.5. Hence, the leading edge peaking around x/C ≈ 0.35 then dropping to values around 1.5. the Hence, the b boundaryo layer undary la initially yer i isnlaminar itially isand lami under nar agoes nd undergoes tra transition to ansi turbulent tion to aboundary turbulent Hence, the boundary layer initially is laminar and undergoes transition to a turbulent layer boundar around y layat er aro thisu position, nd at this p which ositiis on, also which reﬂected is also by reflected by a minimum of a minimum of the friction the fric- factor boundary layer around at this position, which is also reflected by a minimum of the fric- at tion f thisaaxial ctor at position this axia (Figur l posie tion ( 12b). FiThe guredif 12fer b).ence The di inff ﬂuctuation erence in fllevels uctuatat ion the level LEs between at the LE tion factor at this axial position (Figure 12b). The difference in fluctuation levels at the LE midspan between midspa and tip n regi anon d tip is dir region ectlyis di related rectl to y rela the higher ted to the hi ﬂuctuations gher fluctua within tio the ns wi incoming thin the between midspan and tip region is directly related to the higher fluctuations within the boundary layer. At the TE very similar proﬁles are observed for both spanwise positions, incoming boundary layer. At the TE very similar profiles are observed for both spanwise incoming boundary layer. At the TE very similar profiles are observed for both spanwise indicating a small inﬂuence of the TLV on the TE part of the blade. This is also observed positions, indicating a small influence of the TLV on the TE part of the blade. This is also positions, indicating a small influence of the TLV on the TE part of the blade. This is also in the pressure distribution (Figure 12a), c values at the TE for both spanwise positions observed in the pressure distribution (Figure p 12a), c values at the TE for both spanwise observed in the pressure distribution (Figure 12a), c values at the TE for both spanwise are similar. positions are similar. positions are similar. Figure 13. Blade suction side boundary layer state, characterized through the turbulent kinetic Figure 13. Blade suction side boundary layer state, characterized through the turbulent kinetic energy Figure 13. Blade suction side boundary layer state, characterized through the turbulent kinetic energy (TKE) in normal direction to the blade (η/C) and the shape factor (H ). (TKE) energy (TKE) i in normal n normal direction to direction to the blade the bla (/Cd ) e ( and η/the C) and the shape factor shape factor ( (H ). H ). The The departur departuree of the TLV r of the TLV results esults in the seco in the secondary ndary fl ﬂow owinﬂuencing influencingalmost almostthe the e entir ntire e The departure of the TLV results in the secondary flow influencing almost the entire pitch pitch at the outlet plane (F at the outlet plane (Figur igur ee 14), wit 14), with hits its core core locat located approxim ed approximately ately at at the middle of the middle of pitch at the outlet plane (Figure 14), with its core located approximately at the middle of the the pa passage ssage pitch. The wi pitch. The wiggly ggly isosurfaces isosurfaces in Fig in Figur ure e 11 11hint hint towar towar ds dsthe the incr incre eased ased level levelssof of the passage pitch. The wiggly isosurfaces in Figure 11 hint towards the increased levels of turbulent ﬂuctuations around the TLV and away from the blade. turbulent fluctuations around the TLV and away from the blade. turbulent fluctuations around the TLV and away from the blade. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 17 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 17 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 17 of 40 (a) (b) (a) (b) Figure 14. Cutplanes downstream of the blade (plane at x/C = 0.89) of (a) total pressure losses and (b) TKE. Pitchwise coordinate normalized by cascade pitch P with origin such Figure 14. Cutplanes downstream of the blade (plane at x/C = 0.89) of (a) total pressure losses Figure 14. Cutplanes downstream of the blade (plane at x/C = 0.89) of (a) total pressure and tha (t b the wa ) TKE. Pitchwise ke is locacoor ted dinate at the centre, normalized PS on the l by cascade eft. pitch P with origin such that the wake is losses and (b) TKE. Pitchwise coordinate normalized by cascade pitch P with origin such located at the centre, PS on the left. that the wake is located at the centre, PS on the left. 3.4.4. Effect of Relative Endwall Motion 3.4.4. Effect of Relative Endwall Motion In a previous study, the described configuration was used to study the effect of the 3.4.4. Ef In afect previous of Relastudy tive En , the dwal de l Mot scribed ion conﬁguration was used to study the effect of relative endwall motion on the flow structure through DNS at Re =1.46 ⋅ 10 [35]. Due the relative endwall motion on the ﬂow structure through DNS at Re = 1.46 10 [35]. In a previous study, the described configuration was used to study the effect of the to the low Reynolds number, viscous effects are higher in this case as would be in typical Due to the low Reynolds number, viscous effects are higher in this case as would be in relative endwall motion on the flow structure through DNS at Re =1.46 ⋅ 10 [35]. Due applications. Once the methodology was validated, simulations were carried out at Re = typical applications. Once the methodology was validated, simulations were carried out to the low Reynolds number, viscous effects are higher in this case as would be in typical 3⋅10 and accounting for relative endwall motion, with value |v ⃗ |sin β in pure at Re = 3 10 and accounting for relative endwall motion, with value jj v jj sin in applications. Once the methodology was validated, simulations were carried out ref at Re LE = pitchwise (𝑦 ) direction. pure pitchwise (y) direction. 3⋅10 and accounting for relative endwall motion, with value |v ⃗ |sin β in pure The flow field, represented through the main vortical structures, is shown in Figure The ﬂow ﬁeld, represented through the main vortical structures, is shown in Figure 15. pitchwise (𝑦 ) direction. 15. Here, similar trends are observed here as in the previous study at Re =1.46 ⋅ 10 Here, similar trends are observed here as in the previous study at Re = 1.46 10 [35]. The flow field, represented through the main vortical structures, is shown in Figure [35]. Relative endwall motion induces a departure of the TLV away from the blade in con- Relative endwall motion induces a departure of the TLV away from the blade in contrast to 15. Here, similar trends are observed here as in the previous study at Re =1.46 ⋅ 10 trast to the case without endwall motion (Figure 11). Still, at the lower Reynolds the TLV the case without endwall motion (Figure 11). Still, at the lower Reynolds the TLV followed [35]. Relative endwall motion induces a departure of the TLV away from the blade in con- followed a straight path, at the current Reynolds number the TLV core follows a straight a straight path, at the current Reynolds number the TLV core follows a straight path initially, trast to the case without endwall motion (Figure 11). Still, at the lower Reynolds the TLV path initially, then, further downstream assumes a curved path, enforced by the main then, further downstream assumes a curved path, enforced by the main passage ﬂow. A followed a straight path, at the current Reynolds number the TLV core follows a straight passage flow. A further effect of the relative motion is the weakening of the induced vor- further effect of the relative motion is the weakening of the induced vortices. path initially, then, further downstream assumes a curved path, enforced by the main tices. passage flow. A further effect of the relative motion is the weakening of the induced vor- tices. Figure 15. Vortical structure ( ((h vi (⟨ ) = ⟩)2) for ) the linear compressor cascade at Re = 3 10 Figure 15. Vortical structure 2 λ v ⃗ =−2 for the linear compressor cascade c at Re = with relative motion between blade and endwall. Black lines with arrows at the bottom denote the 3⋅10 with relative motion between blade and endwall. Black lines with arrows at the ( (⟨ ⟩) ) endwall Figure 15. motion. Vortical structure λ v ⃗ =−2 for the linear compressor cascade at Re = bottom denote the endwall motion. 3⋅10 with relative motion between blade and endwall. Black lines with arrows at the At the cascade outlet, shown in Figure 16, the most noticeable effect of the relative At the cascade outlet, shown in Figure 16, the most noticeable effect of the relative bottom denote the endwall motion. endwall endwall mot motion ion is is a a st stratiﬁcation ratification of t of the he ﬂow flow ﬁeld. field. Th The e endwa endwall ll mo motion tion ent entrains rains ﬂuid fluid inin At the cascade outlet, shown in Figure 16, the most noticeable effect of the relative pitchwise pitchwise d direction irection t thushcr us c eating reatiang fairly a fa uniform irly unif ﬂow orm f near low near t the endwall, he endwa in terms ll, in t of str erms of eam- endwall motion is a stratification of the flow field. The endwall motion entrains fluid in wise stream velocity wise v , pr elocit essur ye, , p and ressﬂow ure, an angle, d flow similar angle, to similar to the st the study in [35]. udy The in TKE [35]. The also becomes TKE also pitchwise direction thus creating a fairly uniform flow near the endwall, in terms of stratiﬁed, becomes strat with ified, w lower levels ith lower leve towardsls to the wards the en endwall due dwall d to the imposed ue to the imposed shear generated shear gen- by streamwise velocity, pressure, and flow angle, similar to the study in [35]. The TKE also the relative motion. As a result, these quantities mostly vary in spanwise direction (i.e., becomes stratified, with lower levels towards the endwall due to the imposed shear gen- z-direction). Furthermore, the stratiﬁcation of the velocity leads to a redistribution of the pressure losses, which are more evenly distributed and exhibit a smaller peak, compared to Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 18 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 18 of 40 erated by the relative motion. As a result, these quantities mostly vary in spanwise direc- tion (i.e. z-direction). Furthermore, the stratification of the velocity leads to a redistribu- tion of the pressure losses, which are more evenly distributed and exhibit a smaller peak, the case without relative endwall motion. The trends described here for the linear cascade compared to the case without relative endwall motion. The trends described here for the match those observed in the rotating ring cascade in Figure 3. Despite the lower peak linear cascade match those observed in the rotating ring cascade in Figure 3. Despite the values, the pitchwise averaged total pressure losses reveal that the relative motion lead lower peak values, the pitchwise averaged total pressure losses reveal that the relative to overall higher losses near the wall and slightly lower losses between the peak and motion lead to overall higher losses near the wall and slightly lower losses between the the midplane (0.1 z/H 0.25). Lastly, both cases, with and without relative motion, peak and the midplane (0.1 ≤ z/H ≤ 0.25). Lastly, both cases, with and without relative show the secondary losses to be of relevance up to z/H 0.25, thus indicating that with motion, show the secondary losses to be of relevance up to z/H ≈ 0.25, thus indicating and without relative endwall motion secondary ﬂow effects are of relevance up to similar that with and without relative endwall motion secondary flow effects are of relevance up spanwise positions. In the previous study at Re = 1.46 10 [35], a similar spanwise to similar spanwise positions. In the previous study at Re =1.46 ⋅ 10 [35], a similar behavior was found. Hence, the size of the region inﬂuenced by secondary losses is not spanwise behavior was found. Hence, the size of the region influenced by secondary dependent on the Reynolds number nor on the relative motion. losses is not dependent on the Reynolds number nor on the relative motion. (a) (b) (c) Figure 16. Effect of relative motion downstream of the blade (plane at x/C = 0.89). Cutplane of (a) Figure 16. Effect of relative motion downstream of the blade (plane at x/C = 0.89). Cutplane of total pressure and (b) TKE. In these two figures, the pitch is normalized by cascade pitch P and its (a) total pressure and (b) TKE. In these two ﬁgures, the pitch is normalized by cascade pitch P and origin such that the wake appears in the centre. (c) Pitchwise averaged total pressure losses. Ex- its origin such that the wake appears in the centre. (c) Pitchwise averaged total pressure losses. perimental data from Krug et al. [23]. Experimental data from Krug et al. [23]. 3.4.5. Incoming, Periodically Perturbed Flow Field 3.4.5. Incoming, Periodically Perturbed Flow Field A further point of interest is the effect an inflow perturbed inflow perturbed by wakes A further point of interest is the effect an inﬂow perturbed inﬂow perturbed by wakes may have on the blade performance characteristics. Here, in particular, similarities and may have on the blade performance characteristics. Here, in particular, similarities and differences between the blade tip region (near the endwall) and the midspan region will differences between the blade tip region (near the endwall) and the midspan region will be be addressed. To this end a WRLES featuring a perturbed inflow was conducted. The pe- addressed. To this end a WRLES featuring a perturbed inﬂow was conducted. The periodic riodic perturbation corresponded to wakes of 2 mm circular bars, as used in the corre- perturbation corresponded to wakes of 2 mm circular bars, as used in the corresponding sponding experiment [23]. The instantaneous fluctuations were provided to the present experiment [23]. The instantaneous ﬂuctuations were provided to the present authors by authors by Wissink and Rodi from their simulation of a circular cylinder [39]. The wake Wissink and Rodi from their simulation of a circular cylinder [39]. The wake was then was then superimposed to the instantaneous flow field of the turbulent boundary layer superimposed to the instantaneous ﬂow ﬁeld of the turbulent boundary layer ﬂow and flow and introduced at the domain inlet. The flow perturbation had a frequency with a introduced at the domain inlet. The ﬂow perturbation had a frequency with a Strouhal Strouhal number Sr = 1.56. For this particular frequency a wake moves half of the blade number Sr = 1.56. For this particular frequency a wake moves half of the blade chord in chord in streamwise direction while it traverses the whole pitch in pitchwise direction. streamwise direction while it traverses the whole pitch in pitchwise direction. Hence, for Hence, for a particular phase of the period, two wakes affect the flow within a single blade a particular phase of the period, two wakes affect the ﬂow within a single blade passage. passage. The effect of the inflow perturbations on the blade performance is characterized The effect of the inﬂow perturbations on the blade performance is characterized here by here by the phase averaged pressure and friction coefficients, depicted in Figure 17. the phase averaged pressure and friction coefﬁcients, depicted in Figure 17. Phase averages were computed as ensemble averages over the bar passing period. Phase averages were computed as ensemble averages over the bar passing period. Overall the pressure coefficient in Figure 17a shows increasing unsteadiness towards the Overall the pressure coefﬁcient in Figure 17a shows increasing unsteadiness towards the TE, depicted through the shaded regions in the figure. This indicates a higher sensitivity TE, depicted through the shaded regions in the ﬁgure. This indicates a higher sensitiv- of the flow at the TE with respect to the incoming wakes. Additionally, fluctuation levels ity of the ﬂow at the TE with respect to the incoming wakes. Additionally, ﬂuctuation are slightly higher towards the blade tip (z/H = 0.06) than at the midspan region (z/H = levels are slightly higher towards the blade tip (z/H = 0.06) than at the midspan region 0.30). Hence, periodic disturbances affect the blade loading over the entire blade span. (z/H = 0.30). Hence, periodic disturbances affect the blade loading over the entire blade This phenomenon observed for the compressor stage is also observed in the turbine cas- span. This phenomenon observed for the compressor stage is also observed in the turbine cade, as discussed in Section 5.4.2 below. cascade, as discussed in Section 5.4.2 below. Considering the friction coefficient, the opposite trend is found. Near the blade tip incoming Considering wakes ha the ve a re friction duced coef influe ﬁcient, nce. In contr the opposite ast, in the trend mid is found. span region Near the end o the blade f tip incoming the boundar wakes y layer t have rans air tieduced on pointinﬂuence. is directly In infcontrast, luenced by t in h the e inc midspan oming w ra egion kes, moving the end of the boundary layer transition point is directly inﬂuenced by the incoming wakes, moving backwards as the wake sweeps the blade suction side, indicating an inﬂuence of the periodic perturbances on the transition to turbulence. Furthermore, at the second half of the blade chord ﬂuctuations are more prominent at the midspan region. In contrast, a direct Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 19 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 19 of 40 backwards as the wake sweeps the blade suction side, indicating an influence of the peri- odic perturbances on the transition to turbulence. Furthermore, at the second half of the blade chord fluctuations are more prominent at the midspan region. In contrast, a direct influence of periodical inflow perturbations on the friction levels at the hub of a turbine inﬂuence of periodical inﬂow perturbations on the friction levels at the hub of a turbine stator is given and explained in detail in Section 5.4.2. This demonstrates that, in the region stator is given and explained in detail in Section 5.4.2. This demonstrates that, in the region near the blade tip the TLV imposes the flow dynamics and “shields” the blade from the near the blade tip the TLV imposes the ﬂow dynamics and “shields” the blade from the periodic perturbations. periodic perturbations. (a) (b) (c) Figure 17. Effect of incoming wakes on blade performance characteristics at the suction side near Figure 17. Effect of incoming wakes on blade performance characteristics at the suction side near the blade tip (z/H = 0.06) and in the midspan region (z/H = 0.30). (a) Time averaged pressure the blade tip (z/H = 0.06) and in the midspan region (z/H = 0.30). (a) Time averaged pressure coefficient (Equation 3) with shaded areas denoting the span of transient fluctuations. (b,c) Friction coefﬁcient (Equation 3) with shaded areas denoting the span of transient ﬂuctuations. (b,c) Friction coefficient (c ) near the blade tip and in the midspan region, respectively. coefﬁcient (c ) near the blade tip and in the midspan region, respectively. 3.5. Work in Progress 3.5. Work in Progress The work presented here is focused on increasing the physical and modelling complex- The work presented here is focused on increasing the physical and modelling com- ity in the study of axial gas turbine compressors, with particular emphasis on the secondary plexity in the study of axial gas turbine compressors, with particular emphasis on the sec- ﬂow. Further work involves moving towards geometries with cylindrical symmetry, i.e., ondary flow. Further work involves moving towards geometries with cylindrical sym- annular blade rows, and increasing the modelling effort by employing wall models in metry, i.e. annular blade rows, and increasing the modelling effort by employing wall the LES. models in the LES. 4. Sub-Project C – Periodically Transient Near-Wall Flow in the T106 Turbine Row 4. Sub-Project C – Periodically Transient Near-Wall Flow in the T106 Turbine Row 4.1. Scope of Sub-Project C Sub-project C deals with far-reaching aspects of endwall ﬂow in a low-pressure turbine 4.1. Scope of Sub-Project C cascade at realistic ﬂow conditions (M = 0.59, Re = 2 10 ). The basis of the exit,th exit,th Sub-project C deals with far-reaching aspects of endwall flow in a low-pressure tur- investigation comprises measurements in the High-Speed Cascade Wind Tunnel (HGK) bine cascade at realistic flow conditions (Mexit,th = 0.59, Reexit,th = 2 × 10 ). The basis of the of the Institute of Jet Propulsion at the Bundeswehr University Munich [40]. URANS investigation comprises measurements in the High-Speed Cascade Wind Tunnel (HGK) simulations provide additional information in areas of limited accessibility and in return, of the Institute of Jet Propulsion at the Bundeswehr University Munich [40]. URANS sim- the measurements are utilized to evaluate the computational approach. A major focus ulations provide additional information in areas of limited accessibility and in return, the is put on the different effects on endwall ﬂow, caused by unsteady inﬂow conditions, measurements are utilized to evaluate the computational approach. A major focus is put changing inlet endwall boundary layer conditions, and blade loading. In this context, on the different effects on endwall flow, caused by unsteady inflow conditions, changing particular attention is given to the components of endwall loss development inside the inlet endwall boundary layer conditions, and blade loading. In this context, particular at- blade passage and the downstream secondary ﬂow ﬁeld. Furthermore, an additional goal tention is given to the components of endwall loss development inside the blade passage of sub-project C is investigating the aspect of endwall heat transfer. and the downstream secondary flow field. Furthermore, an additional goal of sub-project C is investigating the aspect of endwall heat transfer. 4.2. Experimental Setup The present investigations are conducted using a linear cascade design of the T106A 4.2. Experimental Setup low-pressure turbine proﬁle, which was speciﬁcally developed for experimental endwall The present investigations are conducted using a linear cascade design of the T106A ﬂow investigations at high-speed conditions and unsteady inﬂow. The periodically incom- low-pressure turbine profile, which was specifically developed for experimental endwall ing wakes are generated by moving bars with a diameter of 2 mm, i.e., 111% of the T106 flow investigations at high-speed conditions and unsteady inflow. The periodically in- trailing edge diameter. The moving bar plane, which runs parallel to the blade passage coming wakes are generated by moving bars with a diameter of 2 mm, i.e. 111% of the inlet plane, is located 86% C upstream of the blade leading edge. The ratio of bars to T106 trailing edge diameter. The moving bar plane, which runs parallel to the blade pas- blade count is two-to-one, i.e., P /P = 0.5 and the bar speed is v = 20 m/s. The resulting b b sage inlet plane, is located 86% C upstream of the blade leading edge. The ratio of bars to ﬂow conditions are listed in Table 3, including Strouhal number Sr and ﬂow coefﬁcient , blade count is two-to-one, i.e. Pb/P = 0.5 and the bar speed is vb = 20 m/s. The resulting which describe the number and orientation of wakes present in the blade passage at any given instant. Int. J. Turbomach. Propuls. Power 2021, 6, 9 20 of 40 Table 3. T106A linear turbine cascade. Geometric Parameters: Chord length C 100 mm Pitch-to-chord ratio P/C 0.799 Aspect ratio H/C 1.31 Flow Conditions: Mach number at exit M 0.59 exit,th Reynolds number at exit Re 2 10 exit,th Design inﬂow pitch angle 127.7 Design outﬂow pitch angle 26.8 Turbulence intensity TI 6.8% Unsteady Inﬂow Conditions: Strouhal number Sr 0.66 Flow coefﬁcient 3.8 Previous experimental and numerical studies of the T106A turbine cascade have shown that increased bar velocity (higher Sr and lower ) results in intensiﬁed effects on the secondary ﬂow [41]. However, within a reasonable range of unsteady inﬂow parameters, the observed trends remain unchanged. Furthermore, when keeping a constant value of Strouhal number by varying the bar speed proportionally to the bar pitch, the inﬂuence of the ﬂow coefﬁcient is relatively minor. Therefore, the present investigation on loss generation is highly relevant for a wide range of unsteady inﬂows, including more realistic high-Sr-low--cases. The design of the particular turbine cascade was mainly motivated by an unfavorable aerodynamic circumstance in previous experimental setups [42–44]. The issue arises from a gap, needed for the moving bar wake generator, between the wind tunnel and the cascade endwalls, upstream of the blade passages. Due to a negative pressure gradient a leakage ﬂow is formed in the bar gap. While the freestream ﬂow remains unaffected, it is acting as a suction on the endwall boundary layer, ultimately leading to weak secondary ﬂow in measurements, RANS simulations and DNS, which were compared in cooperation with sub-project B [31,32]. Compared to a conventional turbine cascade, the present design, which is discussed in detail in [45], delivers several improvements regarding aerodynamics and integration of measurement techniques. The main feature is an integrated ﬂat plate at part-span which serves as a turbine cascade endwall and provides well deﬁned, and adjustable, inlet endwall boundary layer conditions. The ﬂat plate is split into two parts, one upstream and one downstream of the moving bars, which generate the unsteady inﬂow conditions. Integrating the ﬂat plate at part-span divides the overall ﬂow channel into two spanwise sections as shown in Figure 18. The larger main channel is used for all ﬂow investigations, where the lower channel half near the ﬂat plate is of particular interest. The smaller bypass channel on the other hand is not considered in the investigations. As opposed to the ﬁxed position of the downstream plate, the upstream plate can be displaced in spanwise direction, varying the boundary layer augmentation on the aft plate. The value of Dz denotes the misalignment of the two ﬂat plates, with Dz < 0 resulting in decreased inlet endwall boundary layer height, as shown by the velocity proﬁles in Figure 18b, along with a lower turbulence intensity peak [45]. Int. J. Turbomach. Propuls. Power 2021, 6, 9 21 of 40 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 21 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 21 of 41 Figure 18. Effect of the flat plate misalignment on the inlet endwall boundary layer of the T106A Figure 18. Effect of the flat plate misalignment on the inlet endwall boundary layer of the T106A Figure 18. Effect of the ﬂat plate misalignment on the inlet endwall boundary layer of the T106A cas- cascade. cascade. cade. Measurement Techniques Measurement Techniques Measurement Techniques The HGK test facility is a continuously operating, open loop wind tunnel with a lin- The HGK test facility is a continuously operating, open loop wind tunnel with a lin- The HGK test facility is a continuously operating, open loop wind tunnel with a linear ear cascade test section. The wind tunnel itself is located inside a cylindrical pressure ear cascade test section. The wind tunnel itself is located inside a cylindrical pressure cascade test section. The wind tunnel itself is located inside a cylindrical pressure chamber, chamber, which enables an independent Mach and Reynolds number variation. Measure- chamber, which enables an independent Mach and Reynolds number variation. Measure- which enables an independent Mach and Reynolds number variation. Measurements of ment ment s of t s of t he t he t uu rbine exit rbine exit f f lo lo w fie w fie ld wer ld wer ee perf perf ormed ormed usin using a g a five five--hole-probe t hole-probe tr raverse averse in in the turbine exit ﬂow ﬁeld were perf ormed using a ﬁve-hole-probe traverse in MP2 (cf. MP2 (cf. sub-project A), located at 34% C, i.e., 40% C downstream of the blade passage. MP2 (cf. sub-project A), located at 34% C, i.e., 40% C downstream of the blade passage. sub-project A), located at 34% C, i.e., 40% C downstream of the blade passage. A single A single blad A single blad e pitch center e pitch center ed around ed around the traili the trailing e ng ed dg gee extension extension is covered ove is covered over r the full the full blade pitch centered around the trailing edge extension is covered over the full blade span blb ade lade sp sp an an inin t t hh e fie e fie ld t ld t raverse. The raverse. The clos clos est est wal walll d diist staan nce is ce is z z = = 3. 3.5 5 m mm m or eq or equa uall lly z/ y z/H H = = in the ﬁeld traverse. The closest wall distance is z = 3.5 mm or equally z/H = 2.7%. The 2.7%. The maximum FHP measurement errors based on linear error propagation are M2,err 2.7%. The maximum FHP measurement errors based on linear error propagation are M2,err maximum FHP measurement errors based on linear error propagation are M = 0.0043, 2,err = 0.0043, ζ2,err = 0.321%, β2,err = 0.093°, and α2,err = 0.14°. All integral values of the experi- = 0.0043, ζ2,err = 0.321%, β2,err = 0.093°, and α2,er r = 0.14°. All integral values of the experi- = 0.321%, = 0.093 , and = 0.14 . All integral values of the experimental and 2,err 2,err 2,err ment ment alal and and C C FD d FD d at aa t re a re fer fer t o to a a ma ma ss ss -f -f lo lo w-weight w-weighteed d--a aver vera age. ge. Inl Inle ett bound bounda ary ry la layer me yer meas as-- CFD data refer to a mass-ﬂow-weighted-average. Inlet boundary layer measurements were urements were conducted using a CTA-probe with a tungsten wire of 1.25 mm length and urements were conducted using a CTA-probe with a tungsten wire of 1.25 mm length and conducted using a CTA-probe with a tungsten wire of 1.25 mm length and 5 m diameter. 5 μm diameter. The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration 5 μm diameter. The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration was performed in was performed in a range of 0.0 ≤ M ≤ 0.5 at constant angles of pitch, yaw, and pressure was performed in a range of 0.0 ≤ M ≤ 0.5 at constant angles of pitch, yaw, and pressure a range of 0.0 M 0.5 at constant angles of pitch, yaw, and pressure levels with respect levels with respect to the ensuing measurements. The overall uncertainty estimate of a levels with respect to the ensuing measurements. The overall uncertainty estimate of a to the ensuing measurements. The overall uncertainty estimate of a velocity sample is velocity sample is Δv ≤ 2.5 m/s. Further details on the experimental setup, measurement velocity sample is Δv ≤ 2.5 m/s. Further details on the experimental setup, measurement Dv 2.5 m/s. Further details on the experimental setup, measurement techniques, the techniques, the particular turbine cascade design, which was implemented, and a discus- techniques, the particular turbine cascade design, which was implemented, and a discus- particular turbine cascade design, which was implemented, and a discussion of the full sion of the full experimental results can be found in [45]. sion of the full experimental results can be found in [45]. experimental results can be found in [45]. 4.3. Numerical Setup 4.3. Numerical Setup 4.3. Numerical Setup The numerical simulations were performed using the URANS flow solver TRACE by The numerical simulations were performed using the URANS ﬂow solver TRACE The numerical simulations were performed using the URANS flow solver TRACE by DLR with the k− ω turbulence model by Wilcox [46] and γRe transition model by by DLR with the k ! turbulence model by Wilcox [46] and Re transition model DLR with the k− ω turbulence model by Wilcox [46] and γRe tra t nsition model by Langtry and Menter [47]. The computational domain shown in Figure 19 covers a single by Langtry and Menter [47]. The computational domain shown in Figure 19 covers a Langtry and Menter [47]. The computational domain shown in Figure 19 covers a single blade pitch with periodic boundary conditions. It is divided into an upstream block group single blade pitch with periodic boundary conditions. It is divided into an upstream block blade pitch with periodic boundary conditions. It is divided into an upstream block group encompassing the front plate, the moving domain containing two bar pitches, and a group encompassing the front plate, the moving domain containing two bar pitches, and a encompassing the front plate, the moving domain containing two bar pitches, and a downstream block group which encompasses the blade passage and aft plate. downstream block group which encompasses the blade passage and aft plate. downstream block group which encompasses the blade passage and aft plate. Figure 19. Block topology in the computational domain of the T106A cascade with an integrated Figure 19. Block topology in the computational domain of the T106A cascade with an integrated Figure 19. Block topology in the computational domain of the T106A cascade with an integrated two-part flat plate and a moving bar wake generator. two-part flat plate and a moving bar wake generator. two-part ﬂat plate and a moving bar wake generator. Int. Int. J. Turbo J. Turbomach. mach. Pr Propuls. Power opuls. Power 2021 2021 , 6 , ,69 , x FOR PEER REVIEW 22 22 of of 40 41 Due to the asymmetric geometry caused by the integrated flat plate, the full blade Due to the asymmetric geometry caused by the integrated ﬂat plate, the full blade span including the lower bypass channel is resolved in the computation. The blade pas- span including the lower bypass channel is resolved in the computation. The blade sage is discretized using an OCGH-topology and low-Reynolds wall treatment (y ≤ 1), passage is discretized using an OCGH-topology and low-Reynolds wall treatment (y 1), resulting in high boundary layer resolution. Sufficient spatial and temporal discretization resulting in high boundary layer resolution. Sufﬁcient spatial and temporal discretization is is ensured by a sensitivity study, which leads to an overall number of nodes of approxi- ensured by a sensitivity study, which leads to an overall number of nodes of approximately mately 8⋅10 and a number of time steps per moving domain period of 800. Leakage 8 10 and a number of time steps per moving domain period of 800. Leakage panels panels are incorporated at the bar gap boundaries to simulate the leakage flow. The im- are incorporated at the bar gap boundaries to simulate the leakage ﬂow. The imposed posed static pressure condition is determined based on experimental data. The flow con- static pressure condition is determined based on experimental data. The ﬂow conditions pr di escribed tions prescri at the bed a in- and t the i outlet n- anplane d outlet pl match anthe e match th wind tunnel e wind tunnel condition conditions in the experiment s in the ex- (M periment ( , ReM =,Rfe(Tt1, p =t1, f(T𝑡1, p3)p𝑡1, and p3) TI ). and A detailed TI ). Adescription detailed descr of the iptio computational n of the com- exit,th exit,th , , 1 putational approach can be found in [48]. approach can be found in [48]. 4.4. Current Investigations and Results 4.4. Current Investigations and Results The isentropic blade Mach number distribution at midspan, shown in Figure 20, The isentropic blade Mach number distribution at midspan, shown in Figure 20, is is the most important gauge for evaluating the numerical prediction of the 2D turbine the most important gauge for evaluating the numerical prediction of the 2D turbine cas- cascade ﬂow. cade flow. Figure 20. Comparison of the predicted and measured isentropic Mach number distributions at Figure 20. Comparison of the predicted and measured isentropic Mach number distributions at midspan of the T106A turbine cascade at M = 0.59, Re =2 · 1 50 . , , midspan of the T106A turbine cascade at M = 0.59, Re = 210 . exit,th exit,th The T106A is a predominantly aft-loaded profile which features a very small separa- The T106A is a predominantly aft-loaded proﬁle which features a very small separation bubble tion bubble at at the investigated the investigsteady ated steady inﬂow inflow conditions conditions (see T(see able T 3a ),ble caused 3), caby used the by adverse the ad- pr verse pressur essure gradient e gradient in the aft in section the aft sect of the ion of blade the blade suction suction surface.sur The face. The nume numerical predictions rical pre- match dictions m well with atch well with t the measured he measured distributiondistrib except ufor tion e a mor xcept for a m e pronounced ore pronounc separationed sepa- bubble in rathe tion bubble in the CFD, loca CFD, located at approx. ted a x/Ct a = pprox. x/C 0.95. This x = discr 0.95 epancy . This di is screpa attributed ncy is a tottribu a quicker ted to turbulence decay in the computational domain resulting in a locally lower turbulence a quicker turbulence decay in the computational domain resulting in a locally lower tur- intensity, even though TI matches the experimental level. The turbulent dissipation bulence intensity, even though TI matches the experimental level. The turbulent dis- 1, CFD rate could be adjusted by tweaking the inlet level of the turbulent length scale, however, a sipation rate could be adjusted by tweaking the inlet level of the turbulent length scale, low level of this quantity is imperative for an accurate prediction of the loss generation. however, a low level of this quantity is imperative for an accurate prediction of the loss In the case of unsteady inﬂow conditions, a pitchwise incidence of i = 1.5 is induced, generation. In the case of unsteady inflow conditions, a pitchwise incidence of i= −1.5° resulting in decreased blade loading in the front part of the blade suction surface. At the is induced, resulting in decreased blade loading in the front part of the blade suction sur- aft section of the suction surface the separation bubble is suppressed due to wake induced face. At the aft section of the suction surface the separation bubble is suppressed due to transition. Both these effects are predicted well in the numerical simulations [48]. wake induced transition. Both these effects are predicted well in the numerical simula- The level of secondary ﬂow and the effects of the incoming wakes as well as the inlet tions [48]. boundary layer variation by ﬂat plate misalignment are gauged by ﬁeld measurements of The level of secondary flow and the effects of the incoming wakes as well as the inlet the turbine exit ﬂow in MP2. The results are illustrated over the entire channel height in boundary layer variation by flat plate misalignment are gauged by field measurements of Figure 21 and as spanwise distributions of pitchwise-average values in Figure 22. the turbine exit flow in MP2. The results are illustrated over the entire channel height in Figure 21 and as spanwise distributions of pitchwise-average values in Figure 22. Int. J. Turbomach. Propuls. Power 2021, 6, 9 23 of 40 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 23 of 41 Figure 21. Measured total pressure losses at different endwall boundary layer conditions, (a–c) Figure 21. Measured total pressure losses at different endwall boundary layer conditions, (a–c) with with and (d–f) without periodically incoming wakes in MP2. and (d–f) without periodically incoming wakes in MP2. The secondary outflow angle ∆β and the secondary total pressure losses ζ The secondary outﬂow angle D , and the secondary total pressure losses , 2, sec 2, sec are defined by are deﬁned by D = (4) 2,sec 2 2,MS Δβ =β − β , , (4) = with (5) 2,sec 2 2,MS ζ =ζ − ζ with (5) , p p , t1 t2 = (6) p p t1 3 p −p ζ = It is apparent that the different inlet endwall boundary layer conditions result in vary- (6) p −p ing degrees of secondary ﬂow in the lower channel half near the integrated ﬂat plate. The It is apparent that the different inlet endwall boundary layer conditions result in var- case of Dz = 0, representing the thickest boundary layer, exhibits the strongest secondary ﬂow ying de . Lowering grees the of second inlet boundary ary flow layer in the lo thickness wer ch inannel the cases half near the integrated of Dz =1% C and Dzflat plate. = 2% C,The case results in of a rΔ eduction z = 0, representi of peak ng the thi values of over ckest bounda -/underturning ry layer, exhi as wellbi as ts the strongest sec- secondary losses. Additionally, the regions of secondary losses and over-/underturning are shifted towards ondary flow. Lowering the inlet boundary layer thickness in the cases of Δz = −1% C and the endwall. This is caused by a less pronounced liftoff of the passage vortex. Δz = −2% C, results in a reduction of peak values of over-/underturning as well as second- aryComparing losses. Addit theion turbine ally, thexit e reg ﬂow ions o infcases second with ary l steady osses and and ov unsteady er-/undert inﬂow urn,ing it is are apparent that the periodically incoming wakes also cause an attenuation of the time- shifted towards the endwall. This is caused by a less pronounced liftoff of the passage averaged secondary ﬂow. In Figure 22, it is particularly noticeable that the reduction in vortex. time-averaged peak values of and D as well as the spanwise shift by means of Comparing the turbine ex 2,sec it flow in c 2,sec ases with steady and unsteady inflow, it is ap- unsteady inﬂow conditions is very similar to the effect of decreasing the inlet endwall parent that the periodically incoming wakes also cause an attenuation of the time-aver- boundary layer height, especially in the underturning region. aged secondary flow. In Figure 22, it is particularly noticeable that the reduction in time- Although not shown here, the numerical simulations offer a good prediction of the averaged peak values of ζ and Δβ as well as the spanwise shift by means of un- , , spanwise distributions as well as the effects of unsteady inﬂow and endwall boundary steady inflow conditions is very similar to the effect of decreasing the inlet endwall layer variation [48]. A slightly narrower region of elevated secondary losses in combination boundary layer height, especially in the underturning region. with an overshoot of the loss peak is commonly observed in numerical simulations solving Although not shown here, the numerical simulations offer a good prediction of the the URANS equations with an eddy-viscosity model. The important quantity of overall spanwise distributions as well as the effects of unsteady inflow and endwall boundary losses, deﬁned here as integral half-span losses, are predicted with very good accuracy by layer variation [48]. A slightly narrower region of elevated secondary losses in combina- tion with an overshoot of the loss peak is commonly observed in numerical simulations Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 24 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 24 of 40 solving the URANS equations with an eddy-viscosity model. The important quantity of overall losses, defined here as integral half-span losses, are predicted with very good ac- curacy by the simulations, e.g. in the Δz = −1% C case ζ =4.7% ≈ ζ = the simulations, e.g. in the Dz = 1% C case ( ) = 4.7% ( ) = 4.6%. For , , 2, HS 2, HS EXP CFD this speciﬁc comparison, the CFD value was integrated only within the experimentally 4.6%. For this specific comparison, the CFD value was integrated only within the experi- accessible area of 0.027 z/H 0.5. mentally accessible area of 0.027 ≤ z/H ≤ 0.5. Figure Figure 22. 22. Measur Measu ed red spanwis spanwise distributions e distributions of the of the pitchwise-averaged pitchwise-averaged se secondary condary pitch angle pitch angle D 2, sec and secondary total pressure losses under different endwall boundary layer conditions, with ∆β and secondary total pressure losses ζ under different endwall boundary layer condi- , 2, sec , and tions, without with and periodically without perio incoming dically wakes incoin miMP2. ng wakes in MP2. For a further description of the effect of periodically incoming wakes, the numerical For a further description of the effect of periodically incoming wakes, the numerical predictions of the time resolved ﬂow ﬁeld in MP2 is shown at two distinct times in Figure 23. predictions of the time resolved flow field in MP2 is shown at two distinct times in Figure In order to evaluate the effects of incoming wakes on the blade passage loss generation, the 23. In order to evaluate the effects of incoming wakes on the blade passage loss generation, integral losses in Figure 23a are corrected by subtracting the time-averaged values upstream the integral losses in Figure 23a are corrected by subtracting the time-averaged values the blade passage D = . The ﬁrst time resolved ﬂow ﬁeld at t/T = 0.125 2 2 x BP upstream the blade passage ∆ζ r=ζ ef − ζ . The first time resolved flow field at t/T = corresponds to the maximum overall losses (integral over half span) in the moving bar 0.125 corresponds to the maximum overall losses (integral over half span) in the moving period T . Around this instant, the remains of an incoming bar wake, which has been BP bar period T . Around this instant, the remains of an incoming bar wake, which has been subjected to stretching and bowing in the blade passage, ﬁrst interact with the passage subjected to stretching and bowing in the blade passage, first interact with the passage vortex in MP2. Moments later, the bar wake travels in pitchwise direction, where it affects vortex in MP2. Moments later, the bar wake travels in pitchwise direction, where it affects the blade suction surface and ultimately overlaps with the blade wake at y/P=0.5 which the blade suction surface and ultimately overlaps with the blade wake at y/P=0.5 which corresponds to the extension of the blade trailing edge. This leads to a very wide blade corresponds to the extension of the blade trailing edge. This leads to a very wide blade wake and maximum pitchwise-averaged midspan losses. Considering the deﬁnition of the wake and maximum pitchwise-averaged midspan losses. Considering the definition of secondary losses, the peaks of midspan and overall losses occur around the same time as the secondary losses, the peaks of midspan and overall losses occur around the same time the secondary loss minimum. as the secondary loss minimum. This is conﬁrmed by the streamwise vorticity plot in Figure 23d, where a temporary This is confirmed by the streamwise vorticity plot in Figure 23d, where a temporary attenuation of the passage vortex can be seen. The reduced liftoff of the secondary vortex attenuation of the passage vortex can be seen. The reduced liftoff of the secondary vortex system correlates with a less distinct horseshoe vortex pressure side leg, which has already system correlates with a less distinct horseshoe vortex pressure side leg, which has already begun to merge with the passage vortex in MP2. The same observation is made in the begun to merge with the passage vortex in MP2. The same observation is made in the low- low-speed annular cascade adaptation of the T106A in sub-project D (see Section 5.1). The speed annular cascade adaptation of the T106A in sub-project D (see Section 5.1). The sec- second instant at t/T = 0.7 exhibits further pitchwise distance between the bar wake BP ond instant at t/T =0.7 exhibits further pitchwise distance between the bar wake and and the blade wake in MP2, so there is no overlapping. Additionally, bar wake induced the blade wake in MP2, so there is no overlapping. Additionally, bar wake induced tran- transition forces a temporary suppression of the separation bubble on the blade suction sition forces a temporary suppression of the separation bubble on the blade suction sur- surface. These combined circumstances result in a very narrow blade wake and relatively face. These combined circumstances result in a very narrow blade wake and relatively low low levels of corrected midspan, overall, and secondary losses around this instant, even levels of corrected midspan, overall, and secondary losses around this instant, even falling falling below the steady state. When evaluating a time resolved downstream ﬂow ﬁeld, it below the steady state. When evaluating a time resolved downstream flow field, it is im- is important to understand that the local ﬂow properties are not only inﬂuenced by the portant to understand that the local flow properties are not only influenced by the bar bar wake in that speciﬁc location, but especially by upstream interactions with the blade wake in that specific location, but especially by upstream interactions with the blade pas- passage ﬂow. The level of disturbance of the turbine exit ﬂow during a moving bar period, sage flow. The level of disturbance of the turbine exit flow during a moving bar period, originating upstream, is reliant on the unsteady inﬂow conditions, deﬁned by Strouhal originating upstream, is reliant on the unsteady inflow conditions, defined by Strouhal number Sr and ﬂow coefﬁcient . Since multi-row axial turbines usually operate at much higher Strouhal numbers it is safe to assume that the passage ﬂow is constantly in a state of varying disturbance. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 25 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 25 of 41 number Sr and flow coefficient φ. Since multi-row axial turbines usually operate at much Int. J. Turbomach. Propuls. Power 2021, 6number Sr , 9 and flow coefficient φ. Since multi-row axial turbines usually operate at 25 much of 40 higher Strouhal numbers it is safe to assume that the passage flow is constantly in a state higher Strouhal numbers it is safe to assume that the passage flow is constantly in a state of varying disturbance. of varying disturbance. Figure 23. Numerical prediction of the change in (a) integral- and (b,c) local total pressure losses Figure Figure 23. 23. Numerical Numerical pred prediction iction of the of the c chan hange ge in in ( (a) a) integral- integral- and and ( (bb ,c,)c) local locatotal l total pr pres essur su ere lo losses sses as as well as (d,e) streamwise vorticity over time in MP2 with unsteady inflow conditions. as well as (d,e) streamwise vorticity over time in MP2 with unsteady inflow conditions. well as (d,e) streamwise vorticity over time in MP2 with unsteady inﬂow conditions. After investigating the secondary ﬂow in MP2, where unsteady inﬂow conditions and After investigating the secondary flow in MP2, where unsteady inflow conditions After investigating the secondary flow in MP2, where unsteady inflow conditions changing inlet boundary layers showed similar time-averaged effects, questions arise as to and changing inlet boundary layers showed similar time-averaged effects, questions arise and changing inlet boundary layers showed similar time-averaged effects, questions arise the upstream endwall ﬂow development and corresponding loss generation throughout as to the upstream endwall flow development and corresponding loss generation as to the upstream endwall flow development and corresponding loss generation the blade passage. Comparing the time-averaged axial change in non-dimensionalized tt h h roughout roughout t t h h e b e b lade lade p p aa ss ss aa ge. ge. C C oo m m p p ar ar in in g t g t h h e t e t im im ee -- aa v v ee rage rage d d axi axi aa l chan l chan ge ge in no in no n-dim n-dim ee n n -- entropy in Figure 24 in case of unsteady inﬂow conditions to the steady state shows an sionalized entropy in Figure 24 in case of unsteady inflow conditions to the steady state sionalized entropy in Figure 24 in case of unsteady inflow conditions to the steady state accelerated overall loss increase in the front part of the blade passage. This is caused shows an accelerated overall loss increase in the front part of the blade passage. This is shows an accelerated overall loss increase in the front part of the blade passage. This is by increased blade proﬁle losses due to the perturbation of the blade surface boundary caused by increased blade profile losses due to the perturbation of the blade surface caused by increased blade profile losses due to the perturbation of the blade surface layers by the incoming bar wakes with high levels of turbulence. Unlike the proﬁle losses, boundary layers by the incoming bar wakes with high levels of turbulence. Unlike the boundary layers by the incoming bar wakes with high levels of turbulence. Unlike the the secondary loss generation is not increased by the incoming wakes inside the blade profile losses, the secondary loss generation is not increased by the incoming wakes inside profile losses, the secondary loss generation is not increased by the incoming wakes inside passage (0 x/C 1). In fact, the interaction of the wakes with the endwall boundary the blad the blade passag e passage ( e (0≤ 0≤ xx//CC ≤1 ≤1)). In fa . In fact, the i ct, the inntera teracti ctioon of the wakes wi n of the wakes with the th the endwal endwall l layer in the front part of the passage delays the roll-up of the passage vortex and its boundary layer in the front part of the passage delays the roll-up of the passage vortex boundary layer in the front part of the passage delays the roll-up of the passage vortex pressure-driven translation towards the suction surface, which leads to an attenuation of and its pressure-driven translation towards the suction surface, which leads to an attenu- and its pressure-driven translation towards the suction surface, which leads to an attenu- the secondary loss further downstream. Outside the near-endwall region, the incoming ation of the secondary loss further downstream. Outside the near-endwall region, the in- ation of the secondary loss further downstream. Outside the near-endwall region, the in- wakes periodically force an earlier turbulent transition on the blade suction surface, which coming wakes periodically force an earlier turbulent transition on the blade suction sur- coming wakes periodically force an earlier turbulent transition on the blade suction sur- leads to the suppression of the separation bubble. ff aa ce, whi ce, whi cc h lea h lea d d s to the suppressi s to the suppressi on on of t of t h h e sep e sep aa rat rat ion ion bubble. bubble. Figure 24. Axial entropy development throughout the T106A blade passage with steady and un- Figure 24. Axial entropy development throughout the T106A blade passage with steady and un- Figure 24. Axial entropy development throughout the T106A blade passage with steady and unsteady steady inflow conditions. steady inflow conditions. inﬂow conditions. Therefore, the rapid increase of the proﬁle losses near the trailing edge (x/C = 1) in the steady case is attenuated by the unsteady inﬂow conditions. In sum, the steady case level of overall losses is catching up to the unsteady inﬂow case and the entropy lines converge with further distance downstream of the blade passage. Thus, despite the ﬂow Int. J. Turbomach. Propuls. Power 2021, 6, 9 26 of 40 ﬁeld changes, seen in MP2 (Figures 22 and 23), the effect of the periodically incoming wakes on the time-averaged integral losses in the turbine exit ﬂow is very small. This ﬁnding is consistent with the total pressure ﬁeld measurements [45] as well as DNS of a previous T106A cascade [31,32]. Overall, the effect of unsteady inﬂow conditions can be summarized as a spatial redistribution of the loss generation with a premature loss increase due to wake interaction with the blade surface boundary layer followed by attenuation of the proﬁle- and secondary loss generation in the aft-section of the blade passage. A more comprehensive analysis of the secondary ﬂow development and the local sources of loss inside the blade passage can be found in [48]. Contrary to the axially varying effect of unsteady inﬂow conditions, decreasing the inlet endwall boundary layer height results in a nearly constant reduction of the endwall loss generation, beginning around the midpoint of the blade passage where the secondary ﬂow is formed. Lastly, the effect of increased frontal blade loading leads to a rise in proﬁle losses in the front part of the passage followed by increased secondary losses due to stronger transverse pressure gradients [49]. 4.5. Work in Progress Upcoming work in sub-project C includes expanding the experimental data set with time-resolved measurements and optical measurements. A particular area of interest is the secondary ﬂow interaction with the blade suction surface ﬂow. Additionally, great effort is being invested in an investigation of the aspect of endwall heat transfer. This goal is planned to be achieved by deploying the progressive measurement technique of ultra-high-speed temperature sensitive paint on the cascade endwall surface. The capability of this measurement technique has recently been veriﬁed successfully on a ﬂat plate with a frame rate of up to 40 kHz. 5. Sub-Project D—Inﬂuence of Periodic Wakes on the Transient Near-Wall Flow in an Annular Axial Turbine Cascade 5.1. Scope of Sub-Project D Especially in a LPT environment, periodic ﬂow perturbations induced by rotor-stator interaction exert pronounced consequences on the blade proﬁle boundary layers, which are inherently unstable and prone to separation due to the high LPT stage loading and the prevailing low Reynolds numbers [50]. Despite decades of highly accurate, profound research addressing the different aspects of rotor-stator interaction, a deeper physical understanding regarding the highly unsteady interplay of the transported wake structures, the involved boundary layers and the blade row’s secondary ﬂow system is still sought. Therefore, in sub-project D, experimental investigations in a large-scale annular test rig for the time-resolved analysis of wake-stator BL ﬂow interaction within a turbine environment are conducted. This way, the inﬂuences of curvilinear endwalls, non-uniform, radially increasing pitch and radial ﬂow migration are incorporated, increasing the degree RUB of complexity over linear setups. The modiﬁed stator blade proﬁle, labeled as T106 , was developed within this collaborative project for matching the transition and separation characteristics of the original T106 proﬁle (also applied in sub-project C) at low ﬂow speeds, thus facilitating measurements to be taken in an annular, large-scale test rig (see [51]). The stator ﬂow is periodically perturbed by incoming wakes from a rotating wake generator. The aim of the current activities is to establish a connection between the incoming, periodically wake-perturbed ﬂow ﬁeld, the highly-unsteady situation in the stator blade row (stator proﬁle and passage ﬂow) as well as the exit ﬂow containing the secondary ﬂow structures in an annular LPT environment. For this, multiple measurement techniques upstream, within the stator blade row and downstream are connected to provide an exten- sive set of experimental data. This allows to study the unsteady behavior of the boundary layers developing on the LPT stator proﬁles and their effect on secondary ﬂow patterns under the inﬂuence of periodic inﬂow perturbations. The transition phenomena occurring in the proﬁle boundary layers are investigated under both unperturbed and periodically Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 27 of 41 flow structures in an annular LPT environment. For this, multiple measurement tech- niques upstream, within the stator blade row and downstream are connected to provide Int. J. Turbomach. Propuls. Power 2021, 6 an extensiv , 9 e set of experimental data. This allows to study the unsteady behavior of th 27 of e 40 boundary layers developing on the LPT stator profiles and their effect on secondary flow patterns under the influence of periodic inflow perturbations. The transition phenomena occurring in the profile boundary layers are investigated under both unperturbed and perturbed inﬂow by means of spectral analysis, the semi-quantitative characterization of periodically perturbed inflow by means of spectral analysis, the semi-quantitative charac- the wall-stress system and an evaluation of the statistic quantities. Using experimental terization of the wall-stress system and an evaluation of the statistic quantities. Using ex- hot-ﬁlm data from different positions of blade span, the BL ﬂow behavior can be linked to perimental hot-film data from different positions of blade span, the BL flow behavior can the temporal evolution of the secondary ﬂow structures, which is assessed with the help be linked to the temporal evolution of the secondary flow structures, which is assessed of temporal and spatially highly resolved ﬂow ﬁeld traverses downstream of the blade with the help of temporal and spatially highly resolved flow field traverses downstream row in focus. To the best knowledge of the authors, until today only a few studies were of the blade row in focus. To the best knowledge of the authors, until today only a few presented, comparing appropriate time-resolved data from the midspan section with data studies were presented, comparing appropriate time-resolved data from the midspan sec- from the near-wall region, where secondary ﬂow effects have to be considered. Ultimately, tion with data from the near-wall region, where secondary flow effects have to be consid- the acquired measurement data provide highly resolved validation data for accompanying ered. Ultimately, the acquired measurement data provide highly resolved validation data URANS and LES computations. for accompanying URANS and LES computations. The presented investigations give a brief outline of key ﬁndings from recent publica- The presented investigations give a brief outline of key findings from recent publica- tions by the authors, where the unsteady impact of periodic bar wakes on the ﬂow ﬁeld tions by the authors, where the unsteady impact of periodic bar wakes on the flow field downstream of the stator row as well as on the stator proﬁle pressures and boundary layers downstream of the stator row as well as on the stator profile pressures and boundary were discussed. For details, please see [51–58]. layers were discussed. For details, please see [51–58]. 5.2. Experimental Setup 5.2. Experimental Setup The experimental activities described in this contribution were carried out in the large- The experimental activities described in this contribution were carried out in the scale, axial ﬂow turbine test facility Axial Turbine II at the Chair of Thermal Turbomachines large-scale, axial flow turbine test facility Axial Turbine II at the Chair of Thermal Tur- and Aeroengines of Ruhr University Bochum. The facility was designed to allow highly bomachines and Aeroengines of Ruhr University Bochum. The facility was designed to resolved measurements of the unsteady interaction between the stator proﬁle ﬂow and allow highly resolved measurements of the unsteady interaction between the stator pro- periodically impinging wake structures within an annular setup. For this purpose, the test file flow and periodically impinging wake structures within an annular setup. For this rig was used in a 1.5 stage conﬁguration with an IGV row, a rotating wake generator and purpose, the test rig was used in a 1.5 stage configuration with an IGV row, a rotating RUB the T106 stator row under investigation, presented in Figure 25. The large dimensions RUB wake generator and the T106 stator row under investigation, presented in Figure 25. of the ﬂow channel allow detailed ﬂow measurements with negligible perturbation by The large dimensions of the flow channel allow detailed flow measurements with negli- installed probes. Rotatable casing elements with multiple probe accesses facilitate the gible perturbation by installed probes. Rotatable casing elements with multiple probe ac- recording of two-dimensional ﬂow ﬁeld traverses in various planes. Following, the most cesses facilitate the recording of two-dimensional flow field traverses in various planes. important information regarding the setup are given, a more detailed description was Following, the most important information regarding the setup are given, a more detailed provided in [51–53]. description was provided in [51–53]. Figure 25. Test facility Axial Turbine II: sectional view (a), 3D illustration (b). Figure 25. Test facility Axial Turbine II: sectional view (a), 3D illustration (b). Following a combination of flow straightener cells, a turbulence grid and a contrac- Following a combination of ﬂow straightener cells, a turbulence grid and a contraction for tion for gene generating rat uniform ing unifor inﬂow m inflow w withinitthe hin t settling he settlchamber ing chamber, , the ﬂow the flow pa passesss an es an IGV IGV row RUB RUB row (NACA 8408 profiles) to ensure proper inflow angles to the T106 stator whilst leav- (NACA 8408 proﬁles) to ensure proper inﬂow angles to the T106 stator whilst leaving the ing t ﬂow he fl as ow far asas far possible as possib unaf le una fected ffect by ed wakes by wakes and and secondary secondar ﬂow y fl .ow. W With both ith bot 60 hIGV 60 IGV and RUB RUB RUB RUB T106 and T106 proﬁles, profiles, it it is ensur is en ed sured that that ev every T106 ery T106passage passage face faces identical s identical inﬂow inflo conditions. w condi- The tions. The IGV is IG placed V is p 261% laced C 26upstr 1% Ceam upstof rea the m of t wake he w generator ake gener . ator. T To simu o simulate late t the he unst unsteady eady r rotor otor-st -stator ator int interaction eraction o of f an an axi axia al l tturbomachine, urbomachine, th the e ro rotor tor RUB RUB disk between the IGV and the T106 stator was equipped with radially stacked, circular disk between the IGV and the T106 stator was equipped with radially stacked, circular steel bars (bar diameter D = 2 mm, bar length L = 168 mm). The use of periodically b b passing circular bars facilitates to isolate both velocity defect and turbulence increase of typical rotor blade wakes without the secondary ﬂow structures emerging in a real rotor passage. Wakes are generated at an axial distance of 33% C upstream in a plane parallel to the stator leading edges, representing a typical axial gap width in a LPT. The investigations were carried out for a bar pitch of P = 78 mm, matching the pitch of both the IGV and RUB the T106 . Int. J. Turbomach. Propuls. Power 2021, 6, 9 28 of 40 The aft-loaded blade proﬁle (cylindrical geometry) under investigation, labeled as RUB T106 , is an in-house modiﬁcation of the well-known T106 LPT blade, with modiﬁed distributions of proﬁle thickness and curvature. It was developed to match Reynolds number, blade loading distribution c at midspan and thus an equivalent boundary layer development of the original T106 proﬁle at the rig’s low Mach number ﬂow. The principles of the transformation procedure were described by Sinkwitz et al. [51]. The test facility is operated with ambient air, continuously in an open circuit. Flow is induced by a 150 kW variable speed engine coupled to a radial blower providing a mass ﬂow capacity of m 13 kg/s. To avoid inﬂow perturbations, the blower is placed downstream of the test section, thus the rig is operated in suction mode. Table 4 summarizes the most important details. Table 4. Main test rig properties and turbine stage parameters. Test Rig Turbine Stage Outer diameter (Casing) 1660 mm Chord length IGV 137 mm Inner diameter (Hub) 1320 mm Stagger angle IGV 25.5 RUB Chord length T106 100 mm RUB Stagger angle T106 30.7 RUB Blade count IGV, T106 60 Operating Point, Design Point Design Flow Angles, Midspan Mass ﬂow m 12.8 kg/s IGV inlet 90.0 Reynolds number IGV outlet = 5 RUB at exit Re 2 10 T106 inlet 52.3 exit,th 2 Mach number RUB at exit M 0.091 T106 outlet 153.2 exit,th 5.3. Measurement Techniques Monitoring of the operating point was realized with Prandtl-probes at different char- acteristic planes and a combined temperature/humidity sensor at the rig inlet. A detailed description of the applied transducers and devices is provided in [51–54]. To quantify the bar wake impact on the stator ﬂow and the resulting secondary ﬂow structures, ﬂow ﬁeld traverses were carried out in relevant planes, including the axial gap RUB between the wake generator and the T106 stator and the exit ﬂow ﬁeld downstream RUB of the T106 stator. Two-dimensional ﬂow ﬁeld traverses in the exit ﬂow (38 radial RUB and 25 circumferential positions, distributed over two T106 stator passages) have been RUB carried out at 15% C and 35% C downstream of T106 TE. For this, hot-wire anemometry measurements (CTA mode) were conducted using a Dantec Dynamics StreamLine 90N10 CTA anemometer (incorporating three 90C10 CTA modules) and both straight and slanted 1-wire probes in the inﬂow and Split-Fiber probes (SFP, types 55R56 and 55R57) in the wake-ﬂow, shown in Figure 26a. In the wake regions, characterized by intense ﬂow angle variations, SFP have proven superior usability. Due to this and their increased durability, they have been chosen for most of the measurements. All probes were subjected to a multi- dimensional calibration prior to the measurements, during which the corresponding ﬂow angle and velocity were varied within the anticipated range. Using the two voltage values resulting from the SFP measurement, the respective ﬂow angle as well as the magnitude of the velocity (giving a 2D ﬂow vector) were reconstructed. By combining two consecutive measurements with SFP 55R56 and 55R57, the phase-averaged 3D ﬂow vector was ﬁnally reconstructed by analyzing the data sets of both probe measurements simultaneously. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 29 of 41 resulting from the SFP measurement, the respective flow angle as well as the magnitude of the velocity (giving a 2D flow vector) were reconstructed. By combining two consecu- tive measurements with SFP 55R56 and 55R57, the phase-averaged 3D flow vector was Int. J. Turbomach. Propuls. Power 2021, 6, 9 29 of 40 finally reconstructed by analyzing the data sets of both probe measurements simultane- ously. Figure Figure 26. 26. Sel Selected ected dev devices ices fo for r the acqu the acquisition isition of ti of time-r me-resol esolved ved measurement data: Dante measurement data: Dantec c Dynam- Dynamics RU RUB B ics type 55R56 and 55R57 SFP (a), assembly of modular T106 blade with suction side hot-film type 55R56 and 55R57 SFP (a), assembly of modular T106 blade with suction side hot-ﬁlm instrumentation (b), arrangement of Kulite LQ-125 sensors along the profile (c). instrumentation (b), arrangement of Kulite LQ-125 sensors along the proﬁle (c). RUB RUB RUB RUB For For exper experimental imental d data ata ac acquisition quisition w within ithin t the he T1 T106 06 stator pass stator passage, age, seve several ral T T106 106 pr profiles were oﬁles were equipped equipped with with sur surface-mounted face-mounted hot-ﬁlm hot-film sen sensor sor arrays, arrays Kulite-sensors , Kulite-sensors (10(sen- 10 sors sensors of typ of type LQ-125, e LQ-125, se sealed aled g gage age v variant) ariant) an and static d static prpressu essurere t taps. aps Hot-ﬁlms . Hot-films (thickness (thickness 0.05 ≈ 0.05 mm, mm custom-fabricated , custom-fabricated b by Ty ao Tao of of Systems System Integration s Integration Inc.,) Inc., featur ) feat e u 24 re sensor 24 sensor e elements le- on ments on the SS la the SS layout, 20yout, elements 20 el on ements on the PS la the PS layout and a yout a constant nd a consta spacingnt sp of 6 mm acinbetween g of 6 mm the individual between the individ sensor elements. ual sensor elements. For For hot-ﬁlm sensor hot-fi operation lm sensor oper and data ation an acquisition d data acq also uisthe i- tion also the StreamLine 90N10 CTA anemometer along with three 90C10 CTA modules StreamLine 90N10 CTA anemometer along with three 90C10 CTA modules was applied. For wasdata applacquisition ied. For data of ac hot-wir quisition o e and f hot hot-ﬁlm -wire and measur hot-ements, film measu a National rements, Instr a Nat uments ional In- NI 9215 struments NI module was 9215 module employed. was emplo More details yed. More regarding detthe ails re hot-ﬁlm gardin setup g the hot are pr -fiovided lm setuin p ar [54 e ]. provided in [54]. Signals have been recorded at a rate of up to 100 kHz (550 times higher than the maximum Signals h barapassing ve been recorde frequency d at for a r the ate of shown up tinvestigations), o 100 kHz (550 t trigger imes highe ed by r t ahone an th per e rmaximum evolution ba signal r pasfr sing om fr an eqinductive uency for t encoder he shown oninve thest rigat otorions shaft. ), trigger Due ed by to the a boundary one per layer revolution analysis sign to al from be evaluated an inductive in the enc course oder on of the the rotor shaf hot-ﬁlm measur t. Due to the bounda ements and the ry la higher yer statistical analysis to be moments evaluated used in for the course this purpose, of th ae hot-film corresponding measurement database s an is necessary d the hig.hT er statis herefor -e, for ticathe l moments used for this purp phase averaging of each hot-ﬁlm ose, a correspondin sensor-depending g database on is ne the operating cessary. Ther point/speed efore, for the phase averaging of each hot-film sensor-depending on the operating point/speed of of the wake generator-up to 3000 samples were recorded. In this case, a sample is deﬁned as the wake genera the continuous tor-up to period30 of 00 sa 3 bar mpl wakes. es were reco For the rdetime-intensive d. In this case, ameasur sampleement is defin of edtwo- as dimensional the continuous peri ﬂow ﬁelds od ofwith 3 bar wa in part kes. For the ti over 1000me- measuring intensive measurement of positions (SFP measur two-di ements), men- the sion number al flow of fields w samples ith in inevitably part over 1 had 0 to 00 be mea reduced. suring Nevertheless, positions (SFP a meas minimum ureme number nts), the of 1000 number o samples f samples was still inev maintained itably hadher to be e. reduced. Nevertheless, a minimum number of RUB 1000 s To ample facilitate s was T106 still main pr taoﬁle ined here. hot-ﬁlm, Kulite and static pressure measurements in RUB RUB various To f radial acilitat (dir e Tection 106 of pro blade file hot height) -film, Ku positions, lite and a st modular atic press T106 ure meablade surement wass in realized. var- RUB The iousmodular radial (dblade irection is of made blade up hei of multiple, ght) positstackable ions, a modul element ar T1 s 0 and 6 can blade be was equipped realized. with various The modular instrumented blade is made modules up ofat mdif ultip fer le, ent sta blade ckable ele height men positions ts and can be equ within the ippe modular d with blade. various in In Figur strumented mo e 26b the assembled dules at diffe modular rent bl blade ade hei containing ght positi aons wi module thiwith n the SS modula hot-ﬁlm r instr blade umentation . In Figure 2 at6midspan b the assembled position mo is dul shown. ar blade Figur co ent 26 ainin c gives g a the module Kulite wsensor ith SS hot locations. -film instrumentation at midspan position is shown. Figure 26c gives the Kulite sensor loca- 5.4. Current Investigations and Results tions. As stated in the introduction, in multistage turbomachinery conﬁgurations, the proﬁle 5.4. Current Investigations and Results ﬂow is periodically affected by wakes of upstream proﬁles, perceivable by cyclical patterns regarding the ﬂow quantities. Dependent on Strouhal number Sr and ﬂow coefﬁcient As stated in the introduction, in multistage turbomachinery configurations, the pro- , individual components of the vortex system show a wake-induced, recurrent cycle file flow is periodically affected by wakes of upstream profiles, perceivable by cyclical of formation, weakening and displacement. For all investigations the same theoretical patterns regarding the flow quantities. Dependent on Strouhal number Sr and flow coef- RUB RUB (isentropic) T106 exit Reynolds number Re (based on T106 chord length C and ficient φ, individual components of the vortex exit,th system show a wake-induced, recurrent the theoretical exit velocity v analogous to sub-project C) was applied for the deﬁnition exit,th and adjustment of the operating point, deﬁned by Re = 210 and representing a exit,th typical value for LPT operation. To study the effect of periodic ﬂow perturbation, the RUB conditions of unperturbed T106 inﬂow were compared to two other cases, one with a moderate frequency of perturbation (Sr = 0.43, = 2.97) and another one with a high frequency of perturbation (Sr = 1.33, = 0.97), whereas Sr was deﬁned with ﬂow quantities RUB at midspan. From the hot-wire traverses, the turbulence intensity at the T106 inlet was Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 30 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 30 of 41 cycle of formation, weakening and displacement. For all investigations the same theoret- cycle of formation, weakening and displacement. For all investigations the same theoret- RUB RUB ical (isentropic) T106 RUB exit Reynolds number Re (based on T10 RUB 6 chord length C ical (isentropic) T106 exit Reynolds number Re , (based on T106 chord length C and the theoretical exit velocity v analogous to sub-project C) was applied for the and the theoretical exit velocity v , analogous to sub-project C) was applied for the definition and adjustment of the operating point, defined by Re =2 ∙ 10 and repre- definition and adjustment of the operating point, defined by Re =2 ∙ 10 and repre- senting a typical value for LPT operation. To study the effect of periodic flow perturba- senting a typical value for LPT operation. To study the effect of periodic flow perturba- RUB RUB tion, the cond tion, the cond itions o itions o f funpe unpe rturbed T rturbed T 106 106 in in flow w flow w ere compared t ere compared t o two other c o two other c ases, one ases, one Int. J. Turbomach. Propuls. Power 2021, 6, 9 30 of 40 with a moderate frequency of perturbation (Sr = 0.43, φ = 2.97) and another one with a high with a moderate frequency of perturbation (Sr = 0.43, φ = 2.97) and another one with a high frequenc frequenc y y o o f perturbation f perturbation ( S (S r = 1. r = 1. 33, 33, φ = 0.97), wher φ = 0.97), wher eas eas Sr w Sr w as de as de fine fine d with d with flow flow quantities quantities RUB RUB a att mi mi dspa dspa n. From the hot-wi n. From the hot-wi re tra re tra vv erse erse s, the turbulence i s, the turbulence i ntensi ntensi ty ta y ta the T106 t the T106 inl inl et wa et wa s s estimated estimated to b estimated to b to beebetween e between TI = 0.5% between TI = 0.5% TI = 0.5% in in the free in the free the free str stst re eam re am am an and an d TI = 2 d TI = 2 TI = 2.5% .5% .5% in in in tthe ht e IG he IG IGV V wake V wake wake wit without wit hout hout bar wake perturbation, whereas the bar wakes induce a periodic TI increase, reaching val- bar bar w wake akeperturbation, perturbation, wh wher erea eas s t the he ba bar r wake wakes s ind induce uce a per a periodic iodic TITI incre incr aease, se, reac reaching hing val- values ues of of it up to it up TI = to TI20%. = 20%. ues of it up to TI = 20%. 5.4.1. Incoming, Periodically Perturbed Flow Field 5.4.1. Incoming, Periodically Perturbed Flow Field 5.4.1. Incoming, Periodically Perturbed Flow Field For the characterization of the immediate bar wake impact, Figures 27 and 28 show For the characterization of the immediate bar wake impact, Figures 27 and 28 show For the characterization of the immediate bar wake impact, Figures 27 and 28 show RUB RUB hot-wire data, acquired in the axial gap between the wake generator and the T106 hot-wire data, acquired in the axial gap between the wake generator and the T106 RUB lead- hot-wire data, acquired in the axial gap between the wake generator and the T106 lead- leading edges with radial traverses. ing edges with radial traverses. ing edges with radial traverses. Figure 27. Time-resolved ﬂow ﬁeld quantities downstream of the rotating wake generator: velocity v Figure 27. Time-resolved flow field quantities downstream of the rotating wake generator: veloc- Figure 27. Time-resolved flow field quantities downstream of the rotating wake generator: veloc- (a ity v ( ), ﬂow a),angle flow a in ngle in c circumfer ircu ential mferential d direction irect i(o bn ) and α (b) and turbulence intensity TI ( turbulence intensity TI (c) over c) over channel channel height ity v (a), flow angle in circumferential direction α (b) and turbulence intensity TI (c) over channel height R/H for Sr = 1.33, φ = 0.97. R/H for Sr = 1.33, = 0.97. height R/H for Sr = 1.33, φ = 0.97. Figure 28. Time-averaged distributions of velocity v (a), flow angle in circumferential direction α Figure 28. Time-averaged distributions of velocity v (a), flow angle in circumferential direction α Figure (b) and turbulence intensity TI ( 28. Time-averaged distributions c) over channel height R/H downst of velocity v (a), ﬂow angle ream of the rotating wake gen- in circumferential direction (b) and turbulence intensity TI (c) over channel height R/H downstream of the rotating wake gen- erator for Sr = 1.33, φ = 0.97 and clean inflow, see [58]. (b) and turbulence intensity TI (c) over channel height R/H downstream of the rotating wake erator for Sr = 1.33, φ = 0.97 and clean inflow, see [58]. generator for Sr = 1.33, = 0.97 and clean inﬂow, see [58]. Thus, in Figure 27 the temporal evolution (phase-averaged quantities) of the velocity Thus, in Figure 27 the temporal evolution (phase-averaged quantities) of the velocity Thus, in Figure 27 the temporal evolution (phase-averaged quantities) of the velocity v (a), the flow angle in circumferential direction α (b) and the turbulence intensity TI (c) v (a), the flow angle in circumferential direction α (b) and the turbulence intensity TI (c) vover the channel height R/H are given for Sr = (a), the ﬂow angle in circumferential direction 1.33, φ (b) = 0.97 and . From al the turbulence l three flintensity ow quanti TI ties, (c) over the channel height R/H are given for Sr = 1.33, φ = 0.97. From all three flow quantities, over the channel height R/H are given for Sr = 1.33, = 0.97. From all three ﬂow quanti- minor but still detectable remains of the IGV secondary flow structures are evident. How- minor but still detectable remains of the IGV secondary flow structures are evident. How- ties, ever, much minor but more promin still detectable ent are the remains bar wak of thee IGV induc secondary ed effects, ﬂow causin structur g a comb es arinat e evident. ion of RUB ever, much more prominent are the bar wake induced effects, causing a combination of However, much more prominent are the bar wake induced effects, causing a combination periodic T106 inflow incidence (Δα ≈ 10°), a velocity defect (Δv > 5 m/s) and a turbu- RUB RUB periodic T106 inflow incidence (Δα ≈ 10°), a velocity defect (Δv > 5 m/s) and a turbu- of lence incr periodicease from the unperturbed level of TI T106 inﬂow incidence (D 10 )≈ , a 1.5 velocity % up todefect levels o (Dfv T> I 5 > m/s) 15% iand n the a turbulence lence incrincr ease from the unperturbed level of TI ease from the unperturbed level of TI≈ 11.5% .5% u up p tto o llevels evels o off T TII> >15% 15% i inn the the midspan section. Additionally, Figure 28 gives an overview regarding the time-averaged distributions of the discussed ﬂow ﬁeld quantities for the unperturbed and the two per- turbed cases. Despite the additional periodic, bar wake induced perturbations, a certain degree of homogenization for the velocity and the ﬂow angle can be assessed concerning the IGV non-uniformities near the endwalls. In terms of turbulence intensity, the increased rotational speed of the wake generator and thus the higher relative velocities for higher Sr also increases the general level of turbulence from TI < 2% (undisturbed) to TI 8% for Sr = 1.33 at midspan. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 31 of 41 midspan section. Additionally, Figure 28 gives an overview regarding the time-averaged distributions of the discussed flow field quantities for the unperturbed and the two per- turbed cases. Despite the additional periodic, bar wake induced perturbations, a certain degree of homogenization for the velocity and the flow angle can be assessed concerning the IGV non-uniformities near the endwalls. In terms of turbulence intensity, the in- creased rotational speed of the wake generator and thus the higher relative velocities for Int. J. Turbomach. Propuls. Power 2021, 6, 9 31 of 40 higher Sr also increases the general level of turbulence from TI < 2% (undisturbed) to TI ≈ 8% for Sr = 1.33 at midspan. RUB RUB 5.4.2. 5.4.2. Situation Situation wit within hin t the he T106 T106 Blade Blade Row Row RUB RUB W Wi ithin thinthe the T T106 106 blade blade ro row w, the incom , the incoming ing bar w bar wakes akes evoke evoke both large-scale both large-scale (blade (blade row kinematics) and micro-scale (proﬁle boundary layer properties) effects, wherefore the row kinematics) and micro-scale (profile boundary layer properties) effects, wherefore the following analysis is divided into two parts. following analysis is divided into two parts. First, Figure 29 describes the impact of the periodic perturbation on the blade loading First, Figure 29 describes the impact of the periodic perturbation on the blade loading c (referring to the exit state downstream of the stator row) in time-averaged view (a) c p (referring to the exit state downstream of the stator row) in time-averaged view (a) and and for time-resolved measurement data (b), where S/S represents the proportion of the for time-resolved measurement data (b), where S/S represents the proportion of the suc- ∗ ∗ suction or pressure side length. Thus, S/S = 0 describes the LE and S/S = 1 the TE. tion or pressure side length. Thus, S/S =0 describes the LE and S/S =1 the TE. The The time-averaged results (a) do not exhibit prominent changes between the undisturbed time-averaged results (a) do not exhibit prominent changes between the undisturbed and and the two disturbed cases. However, employing time-resolved data from ﬂush-mounted the two disturbed cases. However, employing time-resolved data from flush-mounted Kulite sensors (b), an evaluation of the extrema in proﬁle pressures at every sensor location Kulite sensors (b), an evaluation of the extrema in profile pressures at every sensor loca- indicates generally increasing unsteadiness and thus progressively unsteady blade loading tion indicates generally increasing unsteadiness and thus progressively unsteady blade with increasing Sr. This increasing unsteadiness is also observed in the simulations of the loading with increasing Sr. This increasing unsteadiness is also observed in the simula- periodically perturbed compressor cascade, investigates in sub-project B (see Section 3.4.5). tions of the periodically perturbed compressor cascade, investigates in sub-project B (see Interestingly, despite a general reduction in ﬂuctuation amplitudes for the lower Sr case Section 3.4.5). Interestingly, despite a general reduction in fluctuation amplitudes for the (Sr = 0.43), close to the proﬁle TE, the amplitudes are not reduced but feature a maximum lower Sr case (Sr = 0.43), close to the profile TE, the amplitudes are not reduced but feature excitation, which will be analyzed in the following. a maximum excitation, which will be analyzed in the following. RUB Figure 29. cp distributions for clean and perturbed inflow at T106 midspan, time-averaged re- RUB Figure 29. c distributions for clean and perturbed inﬂow at T106 midspan, time-averaged results sults (a), superposition of maximal fluctuation values (b), see [58]. (a), superposition of maximal ﬂuctuation values (b), see [58]. For a time-resolved analysis of the involved phenomena, Figure 30 shows the tem- For a time-resolved analysis of the involved phenomena, Figure 30 shows the temporal RUB poral evolution of the pressure fluctuations along the T10 RUB 6 profile at midspan for the evolution of the pressure ﬂuctuations along the T106 proﬁle at midspan for the already already introduced cases (Sr = 0.43, Sr = 1.33) and an intermediate perturbation frequency introduced cases (Sr = 0.43, Sr = 1.33) and an intermediate perturbation frequency (Sr = 0.90). (Sr = 0.90). In this depiction , 0<S/S <1 describes the suction side flow, whereas −1 < In this depiction, 0 < S/S < 1 describes the suction side ﬂow, whereas 1 < S/S < 0 ∗ ∗ S/S <0 represents the pressure side flow with S/S =0 marking the LE. For all three represents the pressure side ﬂow with S/S = 0 marking the LE. For all three cases, the cases, the periodic pressure fluctuations (as response on the bar wake convection) can be periodic pressure ﬂuctuations (as response on the bar wake convection) can be determined determined clearly across the profile surface, both on the pressure and the suction side. clearly across the proﬁle surface, both on the pressure and the suction side. Near the Near the suction side, the passage flow is compressed and accelerated by the approaching suction side, the passage ﬂow is compressed and accelerated by the approaching wake wake structure, so that the wake pushes a regime of accelerated flow in front of it, fol- structure, so that the wake pushes a regime of accelerated ﬂow in front of it, followed by a lowed by a region of low velocity fluid, which is vice versa on the pressure side, shaping region of low velocity ﬂuid, which is vice versa on the pressure side, shaping the typical, the typical, negative jet like structure of a wake within a blade passage [59,60]. negative jet like structure of a wake within a blade passage [59,60]. A direct comparison between the three shown scenarios indicates a shift of the re- A direct comparison between the three shown scenarios indicates a shift of the regions on gions on the the suctionsuction side side, which ar , which are mo e most excitedst exci by the ted by the periodic periodic perturbation. perturbation. From an From an exclusive exclusive major excitation centered around S/S* = 0.5 for Sr = 1.33, for decreasing Sr a major excitation centered around S/S* = 0.5 for Sr = 1.33, for decreasing Sr a weakening of this zone and a co-occurring augmentation of the periodic excitation towards the trailing edge is evident, while wake strength decreases and the time between wake events increases. The underlying phenomena, which are responsible for this behavior and take place in the proﬁle boundary layers, are discussed on the basis of hot-ﬁlm data. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 32 of 41 weakening of this zone and a co-occurring augmentation of the periodic excitation to- wards the trailing edge is evident, while wake strength decreases and the time between wake events increases. The underlying phenomena, which are responsible for this behav- Int. J. Turbomach. Propuls. Power 2021, 6, 9 32 of 40 ior and take place in the profile boundary layers, are discussed on the basis of hot-film data. RUBRUB Figure 30. Temporal evolution of pressure fluctuations along the T106 profile at midspan for Sr Figure 30. Temporal evolution of pressure ﬂuctuations along the T106 proﬁle at midspan for = 0.43 (a), Sr = 0.90 (b) and Sr = 1.33 (c), see [58]. Sr = 0.43 (a), Sr = 0.90 (b) and Sr = 1.33 (c), see [58]. For this, Figure 31 shows the time-resolved evolution of quasi wall shear stress (QWSS) For this, Figure 31 shows the time-resolved evolution of quasi wall shear stress RUB RUB along the T106 suction side at midspan for the low and high Sr cases. For means of (QWSS) along the T106 suction side at midspan for the low and high Sr cases. For comparison, on top of the diagrams the QWSS distribution for undisturbed ﬂow is added. means of comparison, on top of the diagrams the QWSS distribution for undisturbed flow The practicable quantity of QWSS is used as a qualitative means for the description of is added. The practicable quantity of QWSS is used as a qualitative means for the descrip- the boundary layer. Following the approach of Hodson [61], the measured voltage values tion of the boundary layer. Following the approach of Hodson [61], the measured voltage (E) are combined with the sensors’ behavior under zero-ﬂow conditions (E ) for a semi- values (E) are combined with the sensors’ behavior under zero-flow conditions 0 (E0) for a quantitative analysis of the wall shear stress : semi-quantitative analysis of the wall shear stress τw: 2 2 E E (7) τ ~ = QWSS. = QWSS. (7) Besides the already mentioned distortion of the local pressure and velocity field (neg- ative jet effect), the connected energy transfer introduces small-scale oscillations from the Besides the already mentioned distortion of the local pressure and velocity ﬁeld (nega- highly turbulent wake flow into the boundary layer flow, increasing the wall shear stress tive jet effect), the connected energy transfer introduces small-scale oscillations from the intermittently. For Sr = 1.33 the suction side boundary layer downstream of S/S* = 0.78 highly turbulent wake ﬂow into the boundary layer ﬂow, increasing the wall shear stress alternates between a state of low (but compared to the undisturbed reference case, still intermittently. For Sr = 1.33 the suction side boundary layer downstream of S/S* = 0.78 slightly increased) and distinctly elevated QWSS. Obviously, the period of time between alternates between a state of low (but compared to the undisturbed reference case, still indiv slightly idual w incra eased) ke events is and distinctly not suffic elevated ient enough QWSS. for t Obviously he bound,athe ry la period yer in t of he re time arbetween part of the suction individualside to fully rec wake events is o not ver, as the sufﬁcient unpert enough urbed st for the ate (shown ab boundary layer ove) is not re in the rear ached partin of between individual w the suction side to fully ake rs. This might b ecover, as the unperturbed e reasoned by st a combin ate (shown atio above) n of th is e f not ollo reached wing asin - pects: between individual wakes. This might be reasoned by a combination of the following as- pects: • Wake-induced boundary layer instabilities, like locally confined turbulent patches or Wake-induced boundary layer instabilities, like locally conﬁned turbulent patches or Klebanoff-Streaks, which are induced in the front part of the profile boundary layer Klebanoff-Streaks, which are induced in the front part of the proﬁle boundary layer far upstream, propagate slower (0.5 < v/vFS < 0.88 ) than the free stream (FS) and the far upstream, propagate slower (0.5 < v/v < 0.88) than the free stream (FS) and the FS wakes [62]. wakes [62]. • Calmed regions exert a damping effect on the boundary layer instabilities, thus coun- Calmed regions exert a damping effect on the boundary layer instabilities, thus teract transition and separation and spread while propagating downstream [63], counteract transition and separation and spread while propagating downstream [63], while their velocity of convection is also considerably reduced (0.3 < v/vFS < 0.5) while their velocity of convection is also considerably reduced (0.3 < v/v < 0.5). FS Summarized, these effects cause the characteristic QWSS evolution of Figure 31b, in- Summarized, these effects cause the characteristic QWSS evolution of Figure 31b, indi- dicating wake-induced transition. The turbulent regions of high wall shear stress, follow- cating wake-induced transition. The turbulent regions of high wall shear stress, following ing the wakes, are characterized by the stated propagation/velocity paths and are followed the wakes, are characterized by the stated propagation/velocity paths and are followed by by the calmed regions with still elevated QWSS, in turn. the calmed regions with still elevated QWSS, in turn. Int. J. Turbomach. Propuls. Power 2021, 6, 9 33 of 40 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 33 of 41 RUB Figure 31. Temporal evolution of QWSS along the T106 profile suction side at midspan for Sr = RUB Figure 31. Temporal evolution of QWSS along the T106 proﬁle suction side at midspan for 0.43 (a) and Sr = 1.33 (b), undisturbed condition shown above, see [58]. Sr = 0.43 (a) and Sr = 1.33 (b), undisturbed condition shown above, see [58]. Different than the continuous paths, which are evident for Sr = 1.33, for Sr = 0.43, a Different than the continuous paths, which are evident for Sr = 1.33, for Sr = 0.43, a wake-path discontinuity becomes obvious between S/S* = 0.6 and S/S* = 0.82. This altered wake-path discontinuity becomes obvious between S/S* = 0.6 and S/S* = 0.82. This altered pattern is essentially based on the differences in wake structure concerning flow angle pattern is essentially based on the differences in wake structure concerning ﬂow angle and and turbulence carried by the wakes. The less steep wake flow angle for lower Sr shifts turbulence carried by the wakes. The less steep wake ﬂow angle for lower Sr shifts the the position of wake impingent downstream. The path, labeled with (I) in Figure 31, rep- position of wake impingent downstream. The path, labeled with (I) in Figure 31, represents resents the accelerated fluid upstream of the actual wake, which slightly increase the the accelerated ﬂuid upstream of the actual wake, which slightly increase the QWSS, but does QWSS, but does not ca not carry substantial rry incr substa eased ntial turbulence increased turbulence for for a more pronounced a more pronounc effect. Path ed effect. (II) repr Path ( esents II) represents the actual subsequent the actual subsequent wake ﬂow. The wakcontained e flow. The turbulence contained turb now induces ulence now a mor in e - pronounced effect of the QWSS level. Nevertheless, the wake strength is reduced compared duces a more pronounced effect of the QWSS level. Nevertheless, the wake strength is to reduced Sr = 1.33, com resulting pared to in Sr = 1. an intermittent 33, resultin rg e-emer in an int ging erof mit atlocally ent re-em conﬁned erging separation. of a locally For con- Sr = 1.33 this separation is prevented. fined separation. For Sr = 1.33 this separation is prevented. 5.4.3. Impact on the Secondary Flow Structures 5.4.3. Impact on the Secondary Flow Structures In this last section, the combined impact of the bar wakes and the described modiﬁed In this last section, the combined impact of the bar wakes and the described modified boundary layer system on the secondary ﬂow system is portrayed on the basis of three boundary layer system on the secondary flow system is portrayed on the basis of three equidistant ﬂow ﬁeld snapshots of one bar wake period in Figure 32 for Sr = 1.33, = 0.97. equidistant flow field snapshots of one bar wake period in Figure 32 for Sr = 1.33, φ = 0.97. The shown quantity in the top of the ﬁgure (a) is the axial vorticity (AVO), which was The shown quantity in the top of the figure (a) is the axial vorticity (AVO), which was derived from the spatial gradients of the time-resolved velocity vector components. The derived from the spatial gradients of the time-resolved velocity vector components. The proﬁle TEs are highlighted with dashed lines. Comparing the three AVO-distributions, profile TEs are highlighted with dashed lines. Comparing the three AVO-distributions, both a vortex displacement as well as a weakening become evident, resulting from the both a vortex displacement as well as a weakening become evident, resulting from the RUB wake-boundary layer interaction in the T106 blade passage. Thus, especially in the hub RUB wake-boundary layer interaction in the T106 blade passage. Thus, especially in the hub region, a distinction between passage vortex (PV) and the pressure side leg of the horse region, a distinction between passage vortex (PV) and the pressure side leg of the horse shoe vortex (HSV-PL) is enabled for t/T = 1/3, as the HSV-PL slides beneath the PV and BP shoe vortex (HSV-PL) is enabled for t/TBP = 1/3, as the HSV-PL slides beneath the PV and pushes it along the suction side trailing edge radially inward, before it blends again with pushes it along the suction side trailing edge radially inward, before it blends again with the PV. As could be shown in detail in [52,53,55,56], this periodic and short-duration event the PV. As could be shown in detail in [52,53,55,56], this periodic and short-duration event is based on the upstream wake impact on the developing HSV-PL, which is massively is based on the upstream wake impact on the developing HSV-PL, which is massively diverted in the front part of the blade passage by the impinging wake structure. Also, the diverted in the front part of the blade passage by the impinging wake structure. Also, the unsteadiness of the suction side corner separation, shaping the concentrated shed vortex unsteadiness of the suction side corner separation, shaping the concentrated shed vortex (CSV) can be realized. Additionally, in the lower half of the ﬁgure the temporal evolution (CSV) can be realized. Additionally, in the lower half of the figure the temporal evolution of the turbulence intensity (TI) is shown. Different from the vorticity representation, the of the turbulence intensity (TI) is shown. Different from the vorticity representation, the turbulence intensity not only highlights the secondary ﬂow regions, but also emphasizes turbulence intensity not only highlights the secondary flow regions, but also emphasizes the inﬂuence of the bar wake with its increased turbulence. This becomes especially evident the influence of the bar wake with its increased turbulence. This becomes especially evi- for t/T = 2/3, when the wake becomes evident in the center of the passage between BP dent for t/TBP = 2/3, when the wake becomes evident in the center of the passage between the two Tes. Even after passing through the passage, the wake still transports signiﬁcant the two Tes. Even after passing through the passage, the wake still transports significant turbulence. Thus, in multistage environments, the subsequent blade row and the transition turbulence. Thus, in multistage environments, the subsequent blade row and the transi- processes occurring therein are still inevitably affected. tion processes occurring therein are still inevitably affected. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 34 of 41 Int. Int.J. J.T Turb urbomach. omach.Pr Prop opuls. uls. P Power ower 2021 2021 , , 66 , , x FOR PEER REVI 9 EW 34 34 of of 40 41 RUB Figure 32. Temporal flow field evolution in the T106 RUB exit flow field (Δx = 0.16 C) at 3 equidistant RUB Figure Figure 32. 32. T Temporal flow emporal ﬂow ﬁeld field evo evolution lution in in the the T106 T106 exit flow exit ﬂow ﬁeld field (D (Δ xx = = 0.16 0.16 C) at 3 C) at 3 equidistant equidistant time steps, Sr = 1.33, φ = 0.97. Axial vorticity (AVO) (a) and turbulence intensity (TI) (b). time steps, Sr = 1.33, φ = 0.97. Axial vorticity (AVO) (a) and turbulence intensity (TI) (b). time steps, Sr = 1.33, = 0.97. Axial vorticity (AVO) (a) and turbulence intensity (TI) (b). Finally Finally, , Figur Figuere 33 33 is me is meant ant toto clar clarifyify this this vortex vortex behavior even furth behavior even further by er by usin using suitable g suit- Finally, Figure 33 is meant to clarify this vortex behavior even further by using suit- A able VO iso-contours AVO iso-cont for ours the for individual the indivvortices idual vor and tices their and the temporal ir tempora evolution. l evolution. able AVO iso-contours for the individual vortices and their temporal evolution. RUB Figure 33. Temporal AVO ﬂow ﬁeld evolution (iso-contours) in the T106 exit ﬂow ﬁeld (Dx = 0.16 RUB Figure 33. Temporal AVO flow field evolution (iso-contours) in the T106RUB exit flow field (Δx = Figure 33. Temporal AVO flow field evolution (iso-contours) in the T106 exit flow field (Δx = C) with the time as the third dimension, Sr = 1.33, = 0.97. View of radial-circumferential plane (a), 0.16 C) with the time as the third dimension, Sr = 1.33, φ = 0.97. View of radial-circumferential 0.16 C) with the time as the third dimension, Sr = 1.33, φ = 0.97. View of radial-circumferential of radial-axial plane (b) and of the lower half of the secondary ﬂow system in a three-dimensional plane (a), of radial-axial plane (b) and of the lower half of the secondary flow system in a three- plane (a), of radial-axial plane (b) and of the lower half of the secondary flow system in a three- depiction (c), see [58]. dimensional depiction (c), see [58]. dimensional depiction (c), see [58]. In Figure 33a the familiar view against the axial ﬂow direction is given, showing In Figure 33a the familiar view against the axial flow direction is given, showing the In Figure 33a the familiar view against the axial flow direction is given, showing the the colored vortices of PV and CSV, whereas Figure 33b shows this situation with the colored vortices of PV and CSV, whereas Figure 33b shows this situation with the view colored vortices of PV and CSV, whereas Figure 33b shows this situation with the view view onto the time-axis (t/T ), indicating the wave-like behavior of the vortex-dynamics. BP onto the time-axis (t/TBP), indicating the wave-like behavior of the vortex-dynamics. Fur- onto the time-axis (t/TBP), indicating the wave-like behavior of the vortex-dynamics. Fur- Furthermore, this method of data representation clearly illustrates the combination of thermore, this method of data representation clearly illustrates the combination of peri- thermore, this method of data representation clearly illustrates the combination of peri- periodic weakening and the connected displacement, deﬁning the unsteadiness of the odic weakening and the connected displacement, defining the unsteadiness of the second- odic weakening and the connected displacement, defining the unsteadiness of the second- secondary ﬂow system. On the one hand, the interaction mechanisms between HSV-PL ary flow system. On the one hand, the interaction mechanisms between HSV-PL and PV ary flow system. On the one hand, the interaction mechanisms between HSV-PL and PV and PV (periodic displacement and weakening) can be detected. On the other hand, (periodic displacement and weakening) can be detected. On the other hand, the consider- (periodic displacement and weakening) can be detected. On the other hand, the consider- the considerable magnitude of radial CSV-displacement resulting from HSV-PL and PV able magnitude of radial CSV-displacement resulting from HSV-PL and PV manipulation able magnitude of radial CSV-displacement resulting from HSV-PL and PV manipulation manipulation is realized. Following the short-duration weakening of PV and HSV-PL, is realized. Following the short-duration weakening of PV and HSV-PL, the CSV is shifted is realized. Following the short-duration weakening of PV and HSV-PL, the CSV is shifted the CSV is shifted towards the endwalls shortly after, as well. Supplementing, Figure 33c towards the endwalls shortly after, as well. Supplementing, Figure 33c shows a three-di- towards the endwalls shortly after, as well. Supplementing, Figure 33c shows a three-di- shows a three-dimensional depiction of the lower ﬂow channel half between R/H = 0 and mensional depiction of the lower flow channel half between R/H = 0 and R/H = 0.5, thus mensional depiction of the lower flow channel half between R/H = 0 and R/H = 0.5, thus R/H = 0.5, thus only the near-hub part of the secondary ﬂow system. This helps to clarify only the near-hub part of the secondary flow system. This helps to clarify the dynamics of only the near-hub part of the secondary flow system. This helps to clarify the dynamics of the dynamics of interaction between PV and HSV-PL, illustrating the approaching HSV-PL, its impact on the PV and the following radial PV-displacement. Int. J. Turbomach. Propuls. Power 2021, 6, 9 35 of 40 5.5. Work in Progress Upcoming activities in sub-project D include the application of particle image ve- RUB locimetry (PIV) for an extended insight into the T106 passage ﬂow, the consideration of tip leakage ﬂow, the resulting tip leakage vortices and their impact on the secondary ﬂow RUB system. For this, a radial gap is realized between the T106 -proﬁles and the hub endwall contour. This increase in complexity means another step from the scientiﬁc point of view towards multistage turbomachine ﬂow. 6. Summary and Conclusions The current paper presents investigations of four German research institutes from a joint research project on near-wall ﬂow in axial compressors and axial turbines. Both numerical and experimental methods were exploited on linear and annular setups to evaluate the inﬂuence of incoming periodic disturbances, which can be seen in rotor- stator-interactions, on the ﬂow in a passage of turbomachinery. Furthermore, analyzing factors arising from the problem of transformation between a linear cascade and the rotating machine, such as the relative motion between blades/vanes and the corresponding sidewall, broadened the understanding of the secondary ﬂow phenomena and allowed the assessment of the transferability of the obtained ﬁndings. In sub-project A the comparison of a periodically disturbed and un-disturbed single rotor row is used to evaluate the inﬂuence of incoming wakes on the secondary ﬂow, especially the tip leakage vortex, in the blade passage. The presented results show a redistribution of mass ﬂow over the channel height and a periodic effect of the incoming wakes on the TLV as well as on the suction side separation. Changing the hub wall motion in a stator conﬁguration allowed the examination of the inﬂuence of incoming boundary layer skew, the relative motion between vane tip and corresponding endwall, and a combined effect on the tip leakage vortex. Sub-project B considered a linear compressor cascade where the investigated vane was derived from the tip proﬁle of the rotor considered in sub-project A. Investigations were conducted using high resolving DNS and Wall-Resolving LES. In doing so, the effects of relative wall motion and thickness of the boundary layer on the vortical structures within the cascade were studied. It is clearly shown that the relative wall motion causes a departure of the tip leakage vortex from the blade proﬁle and furthermore, a stratiﬁcation of the ﬂow ﬁeld at the cascade exit. Complementary, a linear low-pressure turbine cascade was used for high-speed wind tunnel measurements and URANS simulations in sub-project C. As the authors illustrate, a decrease of the inlet endwall boundary layer height and periodically incoming wakes both lead to secondary ﬂow attenuation in the turbine exit ﬂow. Inside the blade passage, the variation of inlet boundary layer thickness inﬂuences the endwall loss development starting around the midpoint of the blade passage. Furthermore, it could be shown that the unsteady inﬂow conditions lead to a spatial redistribution of the loss generation inside the blade passage. A premature loss increase due to wake interaction with the blade surface boundary layer is followed by attenuation of the proﬁle- and secondary losses in the aft-section of the blade passage. However, the level of integral loss in the turbine exit ﬂow ﬁeld remains almost unchanged. Finally, in sub-project D a large-scale annular turbine test rig was considered using modiﬁed blades of those that were studied in sub-project C. Customized surface-mounted hot-ﬁlm sensor arrays were used to investigate the near-wall ﬂow for several perturbation frequencies of upstream installed rotating bars. Thus, it was possible to discover in detail, how periodically incoming wakes lead to a recurrent cycle of formation, weakening and displacement of speciﬁc components of the underlying vortex structures as well as a periodic manipulation of the proﬁle boundary layer system. To sum it up, the collaborative activity of the four research institutes, presented in this publication, helps to deepen the understanding of near-wall ﬂow, vortex systems and corresponding ﬂow phenomena in turbomachines. The investigation of periodically Int. J. Turbomach. Propuls. Power 2021, 6, 9 36 of 40 distortions by incoming wakes and their interaction with the near-wall ﬂow ﬁeld in all investigated conﬁgurations (compressor and turbine, linear and annular cascades) revealed a strong inﬂuence of the wakes on the blade proﬁle boundary layer development, especially through wake induced transition processes, while the secondary ﬂow vortex system fea- tures a periodic displacement and changing strength. Regarding the systematic increase of complexity through the different geometric modiﬁcations and test rigs and thus activation of speciﬁc ﬂow effects it can be concluded that the inlet boundary layer is of high relevance for the turbine endwall secondary ﬂows, where no radial clearances are present. In a linear compressor cascade with radial clearance only the skew of the inlet boundary layer but not its thickness showed a relevant effect on the ﬂow ﬁeld. Experimental and numerical analysis in sub-project A and B clearly illustrated the effect of the relative side wall velocity on the development of the tip leakage vortex and its loss of coherence towards the exit of the blade passage. Ongoing work will apply additional measurement techniques (optical measurements, temperature sensitive paint, etc.) to provide further high-quality data for the validation of advanced numerical methods and improved physical understanding. Author Contributions: Conceptualization, D.E., J.F., R.M., R.N.; Data curation, B.K., J.V.-M., M.S., T.S.; Formal analysis, B.K., J.V.-M., M.S., T.S.; Funding acquisition, D.E., J.F., R.M., R.N.; Investigation, B.K., J.V.-M., M.S., T.S.; Methodology, B.K., J.V.-M., M.S., T.S.; Project administration, R.M.; Resources, D.E., J.F., F.d.M., R.M., R.N.; Supervision, D.E., J.F., F.d.M., R.M., R.N.; Validation, B.K., J.V.-M., M.S., T.S.; Visualization, B.K., J.V.-M., M.S., T.S.; Writing—original draft preparation, D.E., B.K., J.V.-M., M.S., T.S.; Writing—review and editing, D.E., B.K., J.F, J.V.-M., R.M., R.N.; M.S., T.S. All authors have read and agreed to the published version of the manuscript. Funding: The investigations reported in this article were conducted within the framework of the joint research project “Near-Wall Flow in Turbomachinery Cascades” which was funded and supported by the Deutsche Forschungsgemeinschaft (DFG) under grant number PAK 948. The responsibility for the contents of this publication lies entirely by the authors. Data Availability Statement: Not applicable. Acknowledgments: J.V.-M. and J.F. acknowledge the computational resources provided by the Centre for Information Services and High Performance Computing (ZIH) at the TU Dresden. Additionally, the help of M. Plath and G. Bobbe is thanked. Conﬂicts of Interest: The authors declare no conﬂict of interest. Abbreviations The following symbols and abbreviations are used in this manuscript: Roman Symbols ax Axial Direction (for the annular cascade) C Chord c Friction Coefﬁcient c Pressure Coefﬁcient D Diameter H Passage Height, Channel Height H Shape Factor Dh Change in Total Enthalpy M Mach Number m Mass Flow P Pitch Distance p, p , p Static, Dynamic and Total Pressure dyn r Spanwise Direction (for the annular cascade) Re Reynolds Number Int. J. Turbomach. Propuls. Power 2021, 6, 9 37 of 40 s Gap Size S Distance along Blade Proﬁle Ds Change in Entropy Sr Strouhal Number t Time T Bar Passing Period BP TI Turbulence Intensity [%] u Circumferential speed v Velocity x Axial Direction y Pitchwise Direction (for the linear cascade) y+ Non-Dimensional Wall Distance z Spanwise Direction (for the linear cascade) Greek Symbols Yaw Angle, Flow Angle (1 for inﬂow, 2 for outﬂow) with respect to pitchwise direction Flow Angle in Pitchwise Direction with respect to axial direction Boundary Layer Thickness Normal Distance to a Wall Total Pressure Loss Coefﬁcient (Equation (1) for compressor, Equation (6) for turbine) Pitch Distance (For the annular cascade) 2nd Eigenvalue of Velocity Tensor Density Wall Shear Stress Flow Coefﬁcient Abbreviations AVO Axial Vorticity b Bar (used as a subscript) BL Boundary Layer CFD Computational Fluid Dynamics CSV Concentrated Shed Vortex CTA Constant Temperature Anemometry CV Corner Vortex DNS Direct Numerical Simulation DP Design Point EARSM Explicit Algebraic Reynolds Stress Model EXP Experiment FHP Five Hole Probe FMP Fast Measuring Pressure Probe FS Free Stream FTT Flow Through Time HGK High-Speed Cascade Wind Tunnel (Hochgeschwindigkeits-Gitterwindkanal) HS Half-Span HSV Horse Shoe Vortex IGV Inlet Guide Vane LSRC Low-Speed Research Compressor LE Leading Edge LES Large Eddy Simulation LPT Low Pressure Turbine MCV Million Control Volumes MP Measuring Plane MS Midspan NI National Instruments PIV Particle Image Velocimetry PL Pressure Side Leg Int. 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Abstract

International Journal of Turbomachinery Propulsion and Power Article Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project 1 , 1 1 2 2 David Engelmann * , Martin Sinkwitz , Francesca di Mare , Björn Koppe , Ronald Mailach , 3 3 4 4 Jordi Ventosa-Molina , Jochen Fröhlich , Tobias Schubert and Reinhard Niehuis Chair of Thermal Turbomachines and Aeroengines, Department of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, 44801 Bochum, Germany; martin.sinkwitz@rub.de (M.S.); francesca.dimare@rub.de (F.d.M.) Chair of Turbomachinery and Flight Propulsion, Institute of Fluid Mechanics, Technische Universität Dresden, 01062 Dresden, Germany; bjoern.koppe@tu-dresden.de (B.K.); ronald.mailach@tu-dresden.de (R.M.) Chair of Fluid Mechanics, Institute of Fluid Mechanics, Technische Universität Dresden, 01062 Dresden, Germany; jordi.ventosa_molina@tu-dresden.de (J.V.-M.); jochen.froehlich@tu-dresden.de (J.F.) Institute of Jet Propulsion, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany; tobias.schubert@unibw.de (T.S.); reinhard.niehuis@unibw.de (R.N.) * Correspondence: david.engelmann@rub.de Abstract: This article provides a summarizing account of the results obtained in the current collabora- tive work of four research institutes concerning near-wall ﬂow in turbomachinery. Speciﬁc questions regarding the inﬂuences of boundary layer development on blades and endwalls as well as loss mech- anisms due to secondary ﬂow are investigated. These address skewness, periodical distortion, wake interaction and heat transfer, among others. Several test rigs with modiﬁable conﬁgurations are used Citation: Engelmann, D.; Sinkwitz, for the experimental investigations including an axial low speed compressor, an axial high-speed M.; di Mare, F.; Koppe, B.; Mailach, R.; wind tunnel, and an axial low-speed turbine. Approved stationary and time resolving measurements Ventosa-Molina, J.; Fröhlich, J.; techniques are applied in combination with custom hot-ﬁlm sensor-arrays. The experiments are Schubert, T.; Niehuis, R. Near-Wall complemented by URANS simulations, and one group focusses on turbulence-resolving simulations Flow in Turbomachinery to elucidate the speciﬁc impact of rotation. Juxtaposing and interlacing their results the four groups Cascades—Results of a German provide a broad picture of the underlying phenomena, ranging from compressors to turbines, from Collaborative Project. Int. J. isothermal to non-adiabatic, and from incompressible to compressible ﬂows. Turbomach. Propuls. Power 2021, 6, 9. https://doi.org/10.3390/ijtpp6020009 Keywords: near-wall ﬂow; boundary layer; wake interaction; compressor; turbine; cascade; experi- mental investigation; CFD; large eddy simulation; direct numerical simulation Academic Editor: Piotr Doerffer Received: 6 January 2021 Accepted: 22 April 2021 1. Introduction Published: 8 May 2021 Present goals in the development of turbomachines for ﬂight propulsion are oriented Publisher’s Note: MDPI stays neutral towards a further increase of pressure ratio and efﬁciency with a simultaneous reduction with regard to jurisdictional claims in of the number of blades and stages of compressor and turbine [1]. For stationary gas published maps and institutional afﬁl- turbines used to generate electric power, challenging demands on ﬂexibility and operation iations. under partial load result from the volatile availability of renewable energies [2]. These requirements on both types of systems lead to high aerodynamic loads on the blade rows and to an increase in losses due to secondary ﬂows [3]. The latter occur mainly in regions close to sidewalls and have been the focus of scientiﬁc investigations for many years [4–10]. Copyright: © 2021 by the authors. Still, however, understanding is incomplete but is required for increasing efﬁciency in order Licensee MDPI, Basel, Switzerland. to meet economic and ecologic concerns. This article is an open access article While in current design processes the ﬂow is mostly considered in its temporal av- distributed under the terms and erage [11], the real ﬂow in axial compressors and turbines is strongly unsteady, with conditions of the Creative Commons turbulence and periodic contributions resulting from the aerodynamic interaction of the Attribution (CC BY-NC-ND) license blade rows moving relative to each other [12–15]. It exhibits high complexity due to the (https://creativecommons.org/ inner and outer sidewalls and the effects generated by rotation. In fact, the near-wall ﬂow is licenses/by-nc-nd/4.0/). Int. J. Turbomach. Propuls. Power 2021, 6, 9. https://doi.org/10.3390/ijtpp6020009 https://www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2021, 6, 9 2 of 40 characterized by the wall boundary layer, blade boundary layers and the interaction of sev- eral secondary ﬂow phenomena, such as radial gap vortex, horseshoe vortex and channel vortices, all of them being periodically unsteady in a ﬂow ﬁeld which is partly transitional and turbulent on top [16]. The cited effects occur in both, axial compressors as well as axial turbines, but differ considerably according to design features and aerodynamic blade or stage load, so that the different secondary ﬂow phenomena have different characteristics. The intensity of the aerodynamic interaction between the blade rows qualitatively and quantitatively depends on a number of geometric and aerodynamic parameters, such as axial gap width, wake width, velocity deﬁcit of the wake, Strouhal number, ﬂow coefﬁcient, etc. In numerous studies these effects have been investigated with linear cascades [17,18], and disregard of heat transfer in the case of turbines. On the opposite side, there are many studies on machines of realistic or close-to realistic complexity, with measurements usually complicated by practical aspects [19,20]. On this background four groups at three German universities have joined forces in a government-funded collaborative project aiming at the detailed investigation of the ﬂow in the near-wall area of turbomachinery. In particular, the joined effort is dedicated to ﬁll the gap between the two antipodes, linear isothermal cascade and complex machine with heat transfer. On the one hand, it addresses aspects of heat transfer at the sidewall during transient inﬂow, which have not been investigated in linear cascades so far. On the other hand, the connection between stationary linear and rotating ring cascades is investigated. The relevant aspects are the fanned blades in the ring cascade, the radial pressure gradient, the Coriolis forces and the jumps in the circumferential speed between rotor and stator generating strongly twisted sidewall boundary layers at the entry into the blade rows. The overarching goal is to investigate to which extent studies in linear cascades can provide information about the near-wall ﬂows in the machine and how, if necessary, the data from linear cascades must be interpreted to obtain such information. This gradual increase in complexity allows to decompose the respective inﬂuences, which in the machine can only be considered as a whole, interacting with each other. To the knowledge of the authors, detailed investigations of this kind have not been available, so far. The present paper was conceived to provide the community with a timely, condensed synopsis over the recent results achieved in this collaboration, highlighting the larger picture and, if necessary, referring to separate publications for details and side studies. To this end, the paper is structured in line with the project structure featuring four sub-projects A to D. Sub-project A deals with skewness and periodic distortion of the sidewall boundary layer in an axial compressor cascade. Experimental investigations inside a low speed axial research compressor are performed with several conﬁgurations including rotating and ﬁxed hub walls. Numerical studies using a URANS-code complement the experimental ﬁndings. Sub-project B employs highly accurate turbulence-resolving simulations, DNS and LES, to perform well-controlled numerical experiments based on a compressor rotor proﬁle under the same or similar conditions as investigated experimentally in sub-project A. These investigations focus on the stepwise increase in complexity between the linear grid and the full rotating grid, addressing the impact of fanned geometry compared to linear geometry, relative motion of the sidewall, Coriolis forces, etc. An issue not discussed in the present paper is the work performed on improving the simulation methodology. While the ﬁrst two sub-projects are concerned with compressor proﬁles sub-project C and D are oriented towards turbines. Sub-project C is conducting experimental investigations of a T106 low pressure turbine proﬁle in a high-speed cascade wind tunnel and complements these with URANS simulations. A major focus is put on unsteady inﬂow conditions which impact both the inlet endwall boundary layer and the blade loading. These issues are important to clarify because of their particular inﬂuence on the heat transfer at the sidewalls. Sub- project D employs a speciﬁcally modiﬁed T106 proﬁle suitable for the low speed turbine conﬁguration on site. Experimental and numerical studies with wake generators are conducted to study the unsteady behavior of the boundary layers developing on the Int. J. Turbomach. Propuls. Power 2021, 6, 9 3 of 40 low pressure turbine stator blades as well as their effect on the secondary ﬂow patterns under the inﬂuence of unperturbed and periodically perturbed inﬂow. For this purpose, high-resolution time resolving measurement techniques including hot-ﬁlm probes are used. The long-term goal of this research is to enhance the physical understanding of the transient near-wall ﬂow effects for compressor and turbine, thus providing action points to reduce the secondary losses resulting from the aerodynamic interactions in the near-wall ﬂow below the current state of the art, so as to improve upon present efﬁciencies and environmental impact. 2. Sub-Project A—Periodically Transient Near-Wall Flow within Rotating Compressor Cascades 2.1. Scope of Sub-Project A Within sub-project A experimental investigations on different setups of a low speed research compressor are performed to achieve steps of abstraction between a linear cascade and an axial compressor. This allows for a separate analysis of different forces and effects corresponding to the rotating system, where the main considered features are the Coriolis- and centrifugal forces, the ﬂow channel curvature, the incoming boundary layer (BL) and its skewness as well as the relative motion (RM) between the blade tip and its corresponding endwall. Furthermore, the inﬂuence of an incoming periodic distortion on the development of the tip leakage vortex (TLV) in a compressor rotor, as well as on the global parameters of ﬂow turning, losses and total pressure rise is investigated with varying tip clearances. The presented results give an overview of the ﬁndings from recent and current work. Thereby focusing on the effect of varying wall motion in the vicinity of a stator row and the periodic distorted inﬂow to a rotor row on the secondary ﬂow in either passage. The former allows to examine the inﬂuence of a skewed inﬂow boundary layer, a relative motion between the stator vane tips, and the underlying hub endwall or the combination of these two on the tip leakage vortex originating from the stator vanes with hub gap. 2.2. Experimental Setup 2.2.1. Test Facility The investigations are conducted using the Low Speed Research Compressor (LSRC) operated by the Chair of Turbomachinery and Flight Propulsion at the Technische Uni- versität Dresden. The 4.5 stages, including an inlet guide vane (IGV) and four repeating stages, of this axial compressor are built vertically with a downward facing air ﬂow, see Figure 1. The studied blading is derived from a middle stage of a high pressure jet engine compressor and the main characteristics are given in Table 1. For further information on the LSRC please refer to Boos et al. [21] and Künzelmann et al. [22]. To evaluate the effects of varying motion of the wall and incoming periodic distortions two major setups are observed, shown in Figure 1. For the ﬁrst conﬁguration (a) the object of investigations is the stator of stage 1 (hereinafter referred to as stator 1). An adjusted IGV with 83 vanes produces the proper inﬂow conditions and allows direct periodicity for the later numerical computations. The blades of stage 1 are dismounted from the rotor disk, which can be set to the design rotational speed inducing a skew of the sidewall boundary layer. Replacing the rotor disk with a stationary band consisting of 12 circumferentially divided segments allows investigations with stationary sidewalls and thus suppressed inlet BL skew to stator 1 (S1). In addition to the change of the hub endwall upstream of S1, the shroud ring of the stator can be replaced by a rotating hub ring allowing a relative motion between hub and stator vanes. For the latter case, the stationary ring over the rotor hub cannot be used due to constructive restrictions, thus three different cases can be investigated experimentally, see Table 2. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 4 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 4 of 40 over the rotor hub cannot be used due to constructive restrictions, thus three different cases can be investigated experimentally, see Table 2. Figure 1. Low Speed Research Compressor (LSRC)—cross section of investigated setups with sta- Figure 1. Low Speed Research Compressor (LSRC)—cross section of investigated setups with stator tor S1 (a) and rotor R1 (b). S1 (a) and rotor R1 (b). Comparing these configurations allows to evaluate the influence of a skewed inflow Comparing these conﬁgurations allows to evaluate the inﬂuence of a skewed inﬂow BL, which is associated with the movement of the hub wall at the rotor of stage 1 (herein- BL, which is associated with the movement of the hub wall at the rotor of stage 1 (hereinafter after referred to as rotor 1), and the relative motion between the vane tip and the adjacent referred to as rotor 1), and the relative motion between the vane tip and the adjacent wall, wall, which is induced by not using shrouded stator vanes. These investigations are car- which is induced by not using shrouded stator vanes. These investigations are carried ried out with different stator hub clearances. For stationary hub endwall the no clearance out with different stator hub clearances. For stationary hub endwall the no clearance (s/C = 0.0%) and three gap sizes with clearance heights (s) normalized by chord length (C) (s/C = 0.0%) and three gap sizes with clearance heights (s) normalized by chord length of s/C = 2.0%, s/C = 5.4% and s/C = 6.7% are realized, while a few non-clearance vanes (C) of s/C = 2.0%, s/C = 5.4% and s/C = 6.7% are realized, while a few non-clearance supported the shroud ring. With rotating hub endwall only non-zero clearances are tested. vanes supported the shroud ring. With rotating hub endwall only non-zero clearances are Leakage flow through axial gaps in the hub is considered negligible due to a minor pres- tested. Leakage ﬂow through axial gaps in the hub is considered negligible due to a minor sure difference between the rotor drum and the flow channel, as well as small gaps of pressure difference between the rotor drum and the ﬂow channel, as well as small gaps under 1 mm. Downstream of S1 all blades and vanes are dismounted except of stage 4, of under 1 mm. Downstream of S1 all blades and vanes are dismounted except of stage 4, which is used to drive the flow. which is used to drive the ﬂow. Table 1. Reference setup specifications of the LSRC Table 1. Reference setup speciﬁcations of the LSRC. Test Rig Operating Point Test Rig Operating Point Shroud diameter 1500 mm Rotational speed at DP 1000 rpm Shroud diameter 1500 mm Rotational speed at DP 1000 rpm Hub to tip ratio 0.84 Mass flow m at DP 25.35 kg/s Hub to tip ratio 0.84 Mass ﬂow m at DP 25.35 kg/s Rotor R1 Stator S1 Rotor R1 Stator S1 No. of blades 63 No. of vanes 83 No. of blades 63 No. of vanes 83 Chord length 110 mm Chord length 89 mm Chord length 110 mm Chord length 89 mm Solidity, MS 1.597 Solidity, MS 1.709 Solidity, MS 1.597 Solidity, MS 1.709 Reynolds Reynolds number number Reynolds Reynonumber lds number 5 5 6.5 10 3.7 10 6.5 ⋅ 10 3.7 ⋅ 10 at entry, MS at entry, MS at entry, MS at entry, MS Mach number Mach number 0.25 0.18 Mach number Mach number at entry, MS at entry, MS 0.25 0.18 Flow coefﬁcient , MS 0.651 Diffusion factor, MS 0.37 at entry, MS at entry, MS Dh t 1 1 0.489 Loading coefﬁcient , MS Flow coefficient 2φ, MS 0.651 Diffusion factor, MS 0.37 : atLoad 10% higher ing coe mass fficient ﬂow than DP , MS due to the discarded IGV in test setup (b). 0.489 : at 10% higher mass flow than DP due to the discarded IGV in test setup (b). For test setup (b) only rotor 1 (R1) is bladed. Two tip gap sizes of s/C = 1.36% and s/C = 4.55% are observed which allows to evaluate the inﬂuence of incoming periodic For test setup (b) only rotor 1 (R1) is bladed. Two tip gap sizes of s/C = 1.36% and s/C distortions in dependence upon the tip clearance size. Either installing or discarding a = 4.55% are observed which allows to evaluate the influence of incoming periodic distor- wake generator (WG) produces the distorted, from here on unsteady, or the not distorted, tions in dependence upon the tip clearance size. Either installing or discarding a wake from here on steady, inﬂow. The WG consists of 83 circumferentially arranged circular bars generator (WG) produces the distorted, from here on unsteady, or the not distorted, from with a diameter of D = 2 mm. They are mounted 65.6% C upstream of the R1 leading edge (LE). This approach allows the analysis of the effect of an isolated wake disregarding the complex secondary ﬂow ﬁeld of a stator row. Furthermore, it enables a more direct comparison to linear cascade investigations where an analog setup was examined, cf. Krug et al. [23]. Due to the discarded IGV, the mass-ﬂow rate is adjusted to ensure the same rotor entry incidences as for the design point (DP) resulting in an adjusted design point at Int. J. Turbomach. Propuls. Power 2021, 6, 9 5 of 40 10% higher mass-ﬂow. All rotor data shown here correspond to this operating point. As this paper gives a short overview of the work done, only the nominal tip clearance cases, s/C = 2.0% for the stator and s/C = 1.36% for the rotor, will be presented here. Table 2. Conﬁgurations of varying wall speed for test setup (a). Conﬁguration Rotor R1 Hub Wall Stator S1 Hub Wall Un-skewed, w/o RM Stationary Stationary Skewed, w/o RM Rotating Stationary Skewed, with RM Rotating Rotating 2.2.2. Measurement Techniques The ﬂow ﬁeld can be captured in several measuring planes (MP) perpendicular to the machine axis, see Figure 1, using various probes. For the presented results only two MP are of interest. The ﬁrst one is MP4 which is located 26.8% C downstream of ax,R1 the trailing edge (TE) of R1, and at once located 16.3% C upstream of the LE of S1. ax,S1 The second one, MP5, is positioned 21% C downstream of the TE of S1. At both ax,S1 positions the measuring probes can be traversed radially and rotated around their axis. All stator rows are rotated simultaneously around the machine axis to alter the relative position between probe and stator vanes in pitchwise direction. Five-Hole-Probes (FHP) with spherical heads of a diameter of 2 mm are used to capture the steady ﬂow ﬁeld. Balancing the pressures in the two lateral holes via probe rotation allowed to measure the magnitude and direction of the velocity in absolute frame of reference with an accuracy of Dv = 0.3 m/s and D = 0.26 , respectively. The unsteady ﬂow ﬁeld is acquired using a fast measuring pressure probe (FMP), designed and manufactured at the chair of Turbomachinery and Flight Propulsion in Dresden. This one-hole-probe is equipped with a piezoresistive pressure sensor, see also Lange et al. [24]. Measurements with the FMP are performed at three different angles (D = 30 ) virtually creating a three-hole-probe. In the presented results the unsteady ﬂow ﬁeld data is analyzed by either looking at the time or ensemble average. 2.3. Numerical Setup TM The commercial ﬂow solver FINE /Turbo by NUMECA is applied to calculate the three-dimensional RANS equations for the investigated stator cases. Analog to the experiments the combination of IGV and S1 is simulated in a single passage with periodic boundary conditions. The upstream generated wake is passed-through the domain using a perfect connection interface (Full Non Matching Frozen Rotor). The Explicit Algebraic Reynolds Stress Model (EARSM) is exploited to close the system of equations, which was found to deliver the best agreement with experimental results compared with other RANS turbulence models available in the ﬂow solver for the LSRC, see also Lange et al. [24]. The domain is discretized applying a block-structured mesh with O4H-topology around the vanes, OH-topology in the tip gap and H-topology in the remaining parts. A preceding sensitivity study ensured a minimized spatial discretization error. Herein, especially the number of cells in streamwise direction within the empty duct between IGV and S1 was found to have a noticeable effect on the sustaining of the wake, see also Busse et al. [25]. As the BL is of particular interest, it is resolved, leading to dimensionless wall distances y of around 1. In spanwise direction the average density of grid nodes in the tip gap is held constant at a ratio of 22 cells per 1% of gap size normalized by channel height (s/H). The number of cells in the remaining ﬂow channel is adjusted analogously resulting 7 7 in ﬁnal meshes with 1.0 10 up to 1.5 10 grid points. 2.4. Current Investigations and Results 2.4.1. Inﬂuence of the Inlet Boundary Layer Skew The inﬂuence of a skewed inlet BL is investigated by comparing the shrouded stator cases with the rotating R1 disk, inducing a skewed BL, and the cases with the stationary Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 6 of 41 tip gap is held constant at a ratio of 22 cells per 1% of gap size normalized by channel height (s/H). The number of cells in the remaining flow channel is adjusted analogously resulting in final meshes with 1.0 ⋅ 10 up to 1.5 ⋅ 10 grid points. 2.4. Current Investigations and Results Int. J. Turbomach. Propuls. Power 2021, 6, 9 6 of 40 2.4.1. Influence of the Inlet Boundary Layer Skew The influence of a skewed inlet BL is investigated by comparing the shrouded stator cases with the rotating R1 disk, inducing a skewed BL, and the cases with the stationary band, suppressing the skewness and thereby producing an un-skewed BL. The difference in in- band, suppressing the skewness and thereby producing an un-skewed BL. The difference flow can be seen in Figure 2, where the pitchwise averaged radial distributions of total in inﬂow can be seen in Figure 2, where the pitchwise averaged radial distributions of total pr pressu essurere p p (in t (in b black) lack and ) and ﬂow flow angle ang inle absolute in absol frame ute frof am refer e ofence refere (in nce orange) α (in orange) are are shown for shown fo MP4. Her r M eP lines, 4. Her solid e line fors, un-skewed solid for uand n-skew dashed ed an for d d skewed ashed for BL, skewe represent d BrL esults , represent from computational ﬂuid dynamics (CFD) calculations and the symbols, square for un-skewed results from computational fluid dynamics (CFD) calculations and the symbols, square and delta for skewed BL, denote to the experimental data (EXP). for un-skewed and delta for skewed BL, denote to the experimental data (EXP). The skew of the incoming BL is clearly detectable by the strong drift of ﬂow angle The skew of the incoming BL is clearly detectable by the strong drift of flow angle α towards lower values at relative channel heights (r/H) below 5% for the test conﬁguration towards lower values at relative channel heights (r/H) below 5% for the test configuration with rotating R1 disc, cf. Figure 2. The resulting turning of the ﬂow corresponds to higher with rotating R1 disc, cf. Figure 2. The resulting turning of the flow corresponds to higher total pressure in this area as it induces energy into the ﬂow. In contrary a decrease in total pressure in this area as it induces energy into the flow. In contrary a decrease in total total pressure values towards the hub can be seen for the test case with a stationary band pressure values towards the hub can be seen for the test case with a stationary band up- upstream of S1 forming a typical BL. This is accompanied by a constant decline in ﬂow stream of S1 forming a typical BL. This is accompanied by a constant decline in flow angle angle down to the hub endwall in the depicted channel region remaining at higher values down to the hub endwall in the depicted channel region remaining at higher values com- compared to the skewed BL conﬁguration. pared to the skewed BL configuration. α[°] 20 30 40 50 0.1 0.08 EXP un-skewed BL 0.06 CFD un-skewed BL EXP skewed BL 0.04 CFD skewed BL 0.02 99,000 100,000 101,000 p [Pa] Figure 2. Pitchwise averaged total pressure pt (black) and flow angle α (orange) upstream of S1 Figure 2. Pitchwise averaged total pressure p (black) and ﬂow angle (orange) upstream of S1 (MP4) in the hub endwall region, s/C = 2.0%, EXP vs. CFD. (MP4) in the hub endwall region, s/C = 2.0%, EXP vs. CFD. To analyze the secondary ﬂow in the downstream measuring plane (MP5) the non- To analyze the secondary flow in the downstream measuring plane (MP5) the non- dimensional total pressure loss coefﬁcient is deﬁned by dimensional total pressure loss coefficient ζ is defined by p −p! (x ⃗) ( ) p p x ζ x ⃗ = . (1) ! t,ref t x = , . (1) dyn,ref Here the pitchwise averaged total and dynamic pressure in the upstream plane (MP4) at midspan (MS), p and p , are used as reference. For the nominal Here the pitchwise averaged total and dynamic pressure in the upstream plane (MP4) ,, ,, at clearance c midspan a (MS), se of s/C = 2.0% the p and pζ contours in , arMP e used 5 are shown for skewed an as reference. For the nominal d un-skew clear ed - t,MP4,MS dyn,MP4,MS ance inflow BL case of wit s/C hout = 2.0% relathe tive mot contours ion (Rin M) MP5 of th ar e hub e shown endwal for skewed l in Figu and re 3un-skewed a,b. A deviat inﬂow ion in BL without relative motion (RM) of the hub endwall in Figure 3a,b. A deviation in position position of the TLV, represented by the circular areas of high ζ, is apparent with an ap- of the TLV, represented by the circular areas of high , is apparent with an approximated proximated shift of the core of 0.15 θ/PStator in pitchwise direction, where θ/PStator corre- shift sponds to the circumferent of the core of 0.15 /P ial distance n in pitchwise ormal dir ized by ection, wher S1 pitch. In e /P a compressor c corresponds asc to ade thea Stator Stator circumferential distance normalized by S1 pitch. In a compressor cascade a skewed inlet skewed inlet BL reduces the cross passage flow in the vicinity of the hub as its direction BL reduces the cross passage ﬂow in the vicinity of the hub as its direction of inﬂuence of influence directly opposes the pressure gradient from pressure side (PS) to suction side directly opposes the pressure gradient from pressure side (PS) to suction side (SS) of two (SS) of two adjacent vanes. This weakens the passage vortex and was observed for a linear adjacent vanes. This weakens the passage vortex and was observed for a linear compressor cascade by Moore and Richardson [26]. In the current work these ﬁndings were conﬁrmed for the axial machine in a non-clearance case for S1, cf. Koppe et al. [27]. r/H[-] Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 7 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 7 of 40 compressor cascade by Moore and Richardson [26]. In the current work these findings were confirmed for the axial machine in a non-clearance case for S1, cf. Koppe et al. [27]. Figure Figure 3. 3. Effe Effect ct of vary of varying ing hu hub b wall wall momotion tion on n on on- non-dimensional dimensional total pressure loss coe total pressure loss fficient coefﬁcient (⟨ ⟩) downstream of S1 (MP5) (a–c) EXP, (d–g) CFD, and on the TLV trajectory (λ v ⃗ = −10 ) (h–k) downstream of S1 (MP5) (a–c) EXP, (d–g) CFD, and on the TLV trajectory ( (h vi) = 10 ) (h–k) CFD, s/C = 2.0%. CFD, s/C = 2.0%. The reduced strength of the passage vortex implicitly decreases its influence on the The reduced strength of the passage vortex implicitly decreases its inﬂuence on the TLV, as these two vortices have opposing directions of rotation. Furthermore, the drift to TLV, as these two vortices have opposing directions of rotation. Furthermore, the drift to smaller values of flow angle in absolute frame of reference (α) in the vicinity of the hub smaller values of ﬂow angle in absolute frame of reference () in the vicinity of the hub endwall leads to higher loaded profiles at vane tip, favoring a detachment of the flow from endwall leads to higher loaded proﬁles at vane tip, favoring a detachment of the ﬂow from the SS. The result can be seen in Figure 3b for the skewed BL case, where the TLV detaches the SS. The result can be seen in Figure 3b for the skewed BL case, where the TLV detaches from the stator vane somewhere along the chord and moves pitchwise into the passage. from the stator vane somewhere along the chord and moves pitchwise into the passage. The trajectory of the TLV follows the SS of the vane for an un-skewed incoming BL and The trajectory of the TLV follows the SS of the vane for an un-skewed incoming BL and thereby a connected area of high non-dimensional total pressure loss coefficient of the thereby a connected area of high non-dimensional total pressure loss coefﬁcient of the TLV TLV and the vane wake can be seen, cf. Figure 3a. A decrease in effect of the boundary and the vane wake can be seen, cf. Figure 3a. A decrease in effect of the boundary layer layer skewness on the TLV is observed with increasing tip clearance height, not shown skewness on the TLV is observed with increasing tip clearance height, not shown here, cf. [27]. This is expected as the area of inﬂuence of this phenomenon is restricted close to the endwall. Radial proﬁles of ﬂow angle in the absolute frame of reference are plotted for S1 test conﬁgurations with varying hub endwall motion in Figure 4. At relative channel heights between 5 and 25% higher ﬂow angle values representing higher turning over the stator Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 8 of 41 here, cf. [27]. This is expected as the area of influence of this phenomenon is restricted Int. J. Turbomach. Propuls. Power 2021, 6, 9 8 of 40 close to the endwall. Radial profiles of flow angle in the absolute frame of reference are plotted for S1 test configurations with varying hub endwall motion in Figure 4. At relative channel heights between 5 and 25% higher flow angle values representing higher turning over the stator row are detectable for the skewed BL case without relative motion between vane tip and row are detectable for the skewed BL case without relative motion between vane tip and underlying hub endwall. Below 5% r/H the relation reverses and lower values of ﬂow underlying hub endwall. Below 5% r/H the relation reverses and lower values of flow angle can be seen for the skewed BL setup. This coincides with the reduction in cross angle can be seen for the skewed BL setup. This coincides with the reduction in cross pas- passage ﬂow in the vicinity of the hub for an incoming skewed BL. sage flow in the vicinity of the hub for an incoming skewed BL. 0.35 0.3 0.25 un-skewed BL, w/o RM 0.2 skewed BL, w/o RM 0.15 un-skewed BL, with RM 0.1 skewed BL, with RM 0.05 50 60 70 80 α[°] Figure 4. Effect of varying hub wall motion on pitchwise averaged flow angle in absolute frame of Figure 4. Effect of varying hub wall motion on pitchwise averaged ﬂow angle in absolute frame of reference downstream of S1 (MP5), s/C = 2.0%, CFD. reference downstream of S1 (MP5), s/C = 2.0%, CFD. 2.4.2. Inﬂuence of Relative Motion between Vane Tip and Corresponding Endwall 2.4.2. Influence of Relative Motion between Vane Tip and Corresponding Endwall Due to constructive restrictions it is not possible to experimentally evaluate the isolated Due to constructive restrictions it is not possible to experimentally evaluate the iso- effect of the relative motion between the vane tips and the underlying hub endwall on the lated effect of the relative motion between the vane tips and the underlying hub endwall TLV, see also Section 2.2.1. For this purpose, the numerical method is conducted. This is on the TLV, see also Section 2.2.1. For this purpose, the numerical method is conducted. suitable as the results from the CFD show good agreement with the experiments for the This is suitable as the results from the CFD show good agreement with the experiments other three cases, see Figure 3. An overprediction of the losses associated with the TLV is for the other three cases, see Figure 3. An overprediction of the losses associated with the apparent for the numerical results, which is assumed to be due to the computational model TLV is apparent for the numerical results, which is assumed to be due to the computa- not being able to correctly capture the turbulent structures of the TLV. Nevertheless, size tional model not being able to correctly capture the turbulent structures of the TLV. Nev- and position of the TLV agree for the different endwall motion cases between numerical ertheless, size and position of the TLV agree for the different endwall motion cases be- and experimental data to a sufﬁcient extent rendering the following discussion valid, see tween numerical and experimental data to a sufficient extent rendering the following dis- also Koppe et al. [27]. cussion valid, see also Koppe et al. [27]. To evaluate the inﬂuence of a relative motion between the vane tip and its correspond- To evaluate the influence of a relative motion between the vane tip and its corre- ing endwall on the TLV the two cases, one with stationary and one with rotating hub sponding endwall on the TLV the two cases, one with stationary and one with rotating at S1, without an incoming BL skew are observed, see Figure 3d,f. For the combination hub at S1, without an incoming BL skew are observed, see Figure 3d,f. For the combination of un-skewed BL without relative motion the TLV stays attached to the SS of the vane, of un-skewed BL without relative motion the TLV stays attached to the SS of the vane, indicated by the big area of high non-dimensional total pressure loss coefﬁcient located indicated by the big area of high non-dimensional total pressure loss coefficient located adjoining to the vane wake region of high , see Figure 3d. Introducing a relative motion of adjoining to the vane wake region of high ζ, see Figure 3d. Introducing a relative motion the hub endwall a reduction in spanwise size of the affected passage area as well as a drift of the hub endwall a reduction in spanwise size of the affected passage area as well as a of the vortex core towards the adjacent vane PS is apparent, see Figure 3f. drift of the vortex core towards the adjacent vane PS is apparent, see Figure 3f. The ﬂow in the vicinity of the hub endwall features two opposing secondary ﬂows The flow in the vicinity of the hub endwall features two opposing secondary flows when the stationary shroud ring is installed. The ﬁrst resulting from the pressure gradient when the stationary shroud ring is installed. The first resulting from the pressure gradient between the pressure and suction side of two adjacent vanes, the cross passage ﬂow, and between the pressure and suction side of two adjacent vanes, the cross passage flow, and the second arising from the ﬂow over a vane tip, the tip leakage ﬂow, which rolls up into the second arising from the flow over a vane tip, the tip leakage flow, which rolls up into the TLV and continues further downstream. The cross passage ﬂow aids to the tendency the TLV and continues further downstream. The cross passage flow aids to the tendency of the TLV to follow the SS contour of the vane where it emerged. The vortical structures of the TLV to follow the SS contour of the vane where it emerged. The vortical structures within the lower half of the stator passage are visualized via isosurfaces of the (h vi) (⟨ ⟩) within the lower half of the stator passage are visualized via isosurfaces of the λ v ⃗ vortex identiﬁcation criterion, cf. [28], in Figure 3h. Here an additional smaller secondary vortex identification criterion, cf. [28], in Figure 3h. Here an additional smaller secondary vortex is identiﬁable next to the TLV which is induced by the interaction of the cross vortex is identifiable next to the TLV which is induced by the interaction of the cross pas- passage ﬂow and the TLV. Its rotational direction is opposing to the TLV’s and thereby sage flow and the TLV. Its rotational direction is opposing to the TLV’s and thereby add- adding to the prior described trend of following the SS contour. For the case with RM the ing to the prior described trend of following the SS contour. For the case with RM the cross cross passage ﬂow is suppressed by the no-slip condition on the hub endwall, which also has a dragging effect on the TLV. Hence, a shift of the TLV’s trajectory in the direction of the wall movement, which is towards the adjacent vanes PS, is apparent. This dragging effect as well as a higher interaction of the TLV with the free passage ﬂow reduces its extension in spanwise direction. The apparent decreased values of non-dimensional total r/H[-] Int. J. Turbomach. Propuls. Power 2021, 6, 9 9 of 40 pressure loss coefﬁcient in MP5, see Figure 3f, must be put into perspective considering the insertion of energy into the boundary layer ﬂow of the hub endwall due to its rotation. The aforementioned secondary induced vortex is not distinctly identiﬁable here, see Figure 3j. Looking at the pitchwise averaged distributions of ﬂow angle , Figure 4, an increase in values between 5 and 25% of relative channel heights is visible for the un-skewed BL case with RM compared to the case without, as was seen for the skewed BL conﬁguration, cf. Section 2.4.1. Here, the distributions follow a similar trend down to around 11% r/H where a sudden further increase in ﬂow angle is detected for the setup with relative motion. Comparing to the 2D plot of non-dimensional total pressure loss, this relative channel height corresponds to the upper bound of regions with higher losses associated with the TLV, see Figure 3f. With the relative endwall motion reducing the spanwise and increasing the pitchwise expansion of the TLV, the overall inﬂuence of the vortex on the pitchwise averaged ﬂow angle at these radial positions will increase. As the orientation of rotation of the TLV favors higher ﬂow angles in the upper part of the vortex, the sudden increase in values is reasonable. Below the vortex core this trend will reverse adding to the extensive inﬂuence of the moving endwall resulting in the clear drift towards smaller ﬂow angle values for the case with RM in the vicinity of the hub (r/H = 0), see Figure 4. 2.4.3. Combined Inﬂuence of Boundary Layer Skew and Relative Motion between Vane Tip and Corresponding Endwall Setting the hub endwall for stage 1 to the design rotational speed the combined effect of a skewed inﬂow boundary layer and a relative motion between the vane tip and the underlying wall can be analyzed. Comparing Figure 3a,c for the experimental and Figure 3d,g for the numerical results, it becomes clear that the inﬂuence upon the trajectory of the TLV increases. Both phenomena weaken or rather eliminate the cross passage ﬂow between the PS and SS of two adjacent stator vanes in the vicinity of the hub, which in return decreases the passage vortex in this area considerably. Consequently, the progression of the TLV is less inﬂuenced by this contra rotating secondary ﬂow. The dragging effect arising from the no-slip condition on the hub endwall further accommodates the drift of the TLV away from its originating vane towards the adjacent PS. The numerical comparison of analog conﬁgurations within a linear compressor cascade shows similar inﬂuence on the secondary ﬂow, see Section 3.4.4. The decrease of for the case with rotating hub endwall, cf. Figure 3c,g, again, must be put in perspective as the rotation of the hub under S1 induces a ﬂow turning and by this adding energy to the ﬂuid. It is clear, however, that the inﬂuence of the high loss region associated with the TLV on the free passage ﬂow is far smaller for the case with a skewed BL and RM. 2.4.4. Inﬂuence of Incoming Periodic Wakes To evaluate the inﬂuence of incoming periodic distortions on the passage ﬂow of rotor 1 essentially isolated wakes are produced upstream using the WG. Looking at time- and pitchwise averaged radial proﬁles of axial velocity normalized by the midspan value at MP4 a minor redistribution in mass ﬂow over the blade height is apparent for the unsteady case with incoming wakes, cf. Figure 5a. Here steady state measurements of the FHP (solid lines) and time resolved data from the FMP (dashed-dotted lines) are shown. Although these differ marginally in absolute value, the trends correspond well, especially when comparing the differences between the steady and unsteady R1 cases. At spanwise positions between r/H = 0.5 and 0.72 higher axial velocity can be seen for the undisturbed rotor (black lines) for both probes. In regions below midspan down to r/H = 0.19 the steady case shows lower relative axial velocity compared to the periodically disturbed rotor (red lines). The corresponding 2D ﬂow ﬁeld at MP4, captured by the FMP, is shown in Figure 5b. Here the aforementioned redistribution is evident in a weaker SS ﬂow separation in the lower half of the passage, which is represented by the broadened area of low non-dimensional axial velocity in the blade wake. Furthermore, minor changes in the tip region can be observed for the unsteady case where the extend of low relative axial velocity decreases in size compared to the steady inﬂow condition. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 10 of 41 case shows lower relative axial velocity compared to the periodically disturbed rotor (red lines). The corresponding 2D flow field at MP4, captured by the FMP, is shown in Figure 5b. Here the aforementioned redistribution is evident in a weaker SS flow separation in the lower half of the passage, which is represented by the broadened area of low non- Int. J. Turbomach. Propuls. Power 2021, 6, 9 10 of 40 dimensional axial velocity in the blade wake. Furthermore, minor changes in the tip re- gion can be observed for the unsteady case where the extend of low relative axial velocity decreases in size compared to the steady inflow condition. (a) (b) steady unsteady 1 1 0.8 0.8 0.8 PS SS PS SS 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.8 0.9 1 250 300 350 400 v /v [-] θ/P [-] θ/P [-] x [mm] ax ax,MS Rotor Rotor FHP steady FMP steady FHP unsteady v /v [-]: 0.45 0.55 0.65 0.75 0.85 0.95 1.05 FMP unsteady ax ax,MS (c) Δθ/P =0.00=1.00 Δθ/P =0.25 Δθ/P =0.50 Δθ/P =0.75 WG WG WG WG 1 1 1 1 0.8 0.8 0.8 0.8 PS SS 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 θ/P [-] θ/P [-] θ/P [-] θ/P [-] Rotor Rotor Rotor Rotor Figure Figure 5. 5. Effe Effect ct of ofincom incoming ing periodi periodic c transie transi nt wak ent wakes es on (aon ) time- and pitchwise average (a) time- and pitchwise averaged d data up- data (MP3) and downstream (MP4) of R1, (b) ensemble- and pitchwise averaged FMP data and (c) en- up- (MP3) and downstream (MP4) of R1, (b) ensemble- and pitchwise averaged FMP data and semble averaged FMP data at discrete relative positions between WG and R1 downstream of R1 (c) ensemble averaged FMP data at discrete relative positions between WG and R1 downstream of R1 (MP4), s/C= 1.36%, EXP. (MP4), s/C= 1.36%, EXP. A closer look at the unsteady case is given in Figure 5c where four distinct relative A closer look at the unsteady case is given in Figure 5c where four distinct relative positions between WG and R1 are shown. Here, a fluctuation of the TLV can be observed positions between WG and R1 are shown. Here, a ﬂuctuation of the TLV can be observed by the change in the region of low non-dimensional axial velocity throughout the four by the change in the region of low non-dimensional axial velocity throughout the four time steps. At each time step the remains of incoming bar wakes are marked with yellow time steps. At each time step the remains of incoming bar wakes are marked with yellow dashed lines and can be identified by areas of reduced relative axial velocity. They pro- dashed lines and can be identiﬁed by areas of reduced relative axial velocity. They progress gress from left to right with each time step. From relative position one (Δθ/PWG = 0.00) to from left to right with each time step. From relative position one (D/P = 0.00) to two WG two (Δθ/PWG = 0.25) a reduction in low non-dimensional axial velocity is observed in the (D/P = 0.25) a reduction in low non-dimensional axial velocity is observed in the tip WG tip region where the deterioration progresses as the bar wake approaches the rotor. After region where the deterioration progresses as the bar wake approaches the rotor. After passing the rotor wake, the area of low relative axial velocity in the vicinity of the blade passing the rotor wake, the area of low relative axial velocity in the vicinity of the blade tip tip strengthens again and increases with growing distance of the WG wake, as can be seen strengthens again and increases with growing distance of the WG wake, as can be seen in in time steps three (Δθ/PWG = 0.50) and four (Δθ/PWG = 0.75). time steps three (D/P = 0.50) and four (D/P = 0.75). WG WG In the lower half of the passage an effect of the WG wake on the suction side separa- In the lower half of the passage an effect of the WG wake on the suction side separation tion is observed. Here, a decrease is particularly apparent when the incoming wake is in is observed. Here, a decrease is particularly apparent when the incoming wake is in the vicinity of the rotor wake, see time steps D/P = 0.25 and D/P = 0.50 of Figure 5c. WG WG This leads to the assumption that the incoming wake inﬂuences the transition on the blade proﬁle, which was observed for the linear compressor cascade as well as for the axial turbine conﬁguration, see Sections 3.4.5 and 5.4.2 respectively. Another explanation could be radially varying pressure proﬁles on the rotor surface due to the change of the TLV in the tip region. Further investigations are necessary to verify these hypotheses. WGwake r/H[-] r/H[-] r/H[-] s s s r/H[-] r/H[-] R[mm] r/H[-] s r/H[-] s Int. J. Turbomach. Propuls. Power 2021, 6, 9 11 of 40 2.5. Work in Progress Further analysis of the effect of incoming wakes on the TLV of the low-speed com- pressor rotor with increased tip clearance is under investigation and will be compared with corresponding data from previous linear cascade tests. Additional data will be ob- tained through particle image velocimetry (PIV) within the blade passage and hot-ﬁlm CTA measurements of the proﬁle boundary layer development. This data will be used to validate own URANS and LES results of sub-project B. Joint analysis will deepen the physical understanding. 3. Sub-Project B—High Fidelity Numerical Investigations of the Secondary Flow in a Linear Compressor Cascade 3.1. Scope of Sub-Project B The general approach of sub-project B in the collaborative project is to use numerical simulations with two complementary objectives. First, the physics of secondary ﬂows in the near-wall area of a compressor cascade is investigated with the goal of identifying the role of different issues, in particular those distinguishing the situation in a linear cascade from an annular cascade, with the long-term goal to elucidate the transferability of results from linear cascade studies to annular cascades. In this perspective, speciﬁc parameters, such as the relative wall motion, are investigated concerning their effect on the dominating vortical structures inside the cascade, such as the tip leakage vortex (TLV). The second goal of sub-project B is to improve the simulation methodology in the context of LES for turbomachinery ﬂows. This unfolds in two aspects, assessing the modelling in the endwall region and identifying speciﬁc requirements in linear and annular cascades. Based on these objectives, results of Large Eddy Simulation (LES) of a linear com- pressor cascade are presented. As a validation step, the modelling introduced through LES is ﬁrst assessed against highly resolved data obtained by means of Direct Numerical Simulation (DNS). 3.2. Geometry The studied geometry was deﬁned according to the linear cascade setup of the Chair of Turbomachinery and Flight Propulsion at TU Dresden conducting sub-project A [23]. The blade proﬁle represents a scaled tip section of the reference built rotor of the LSRC [21,22] described in Section 2.2.1. In the current investigations the linear cascade has a chord length of C = 159.6 mm, an aspect ratio of H/C = 1.133, and is mounted with a stagger angle of 46.9 . The leading and trailing edge proﬁle angles are = 60.75 and = 40 , LE TE respectively. The cascade has a solidity of = C/P = 1.55. Furthermore, the present case features a tip gap of width s/C = 3% (s/H = 2.65%) between the endwall and the blade tip. The endwall is located at the bottom of the computational domain, where z = 0. A sketch of the blade proﬁle is depicted in Figure 6. 3.3. Numerical Setup and Grid The in-house code LESOCC2 [29] was used to solve the Navier-Stokes equations in their incompressible non-dimensional form. It features 2nd order ﬁnite volume discretiza- tion in space, and time integration is performed through a 3-step 2nd order Runge-Kutta scheme. The solver has been used previously in DNS studies of linear turbine cascades, including secondary ﬂows, providing good results [30–32]. In the following mainly results of Wall-Resolving Large Eddy Simulations (WRLES) at Re = 3 10 are presented. This set-up matches the conﬁguration of Krug et al. [23]. Inlet velocity jj v jj and blade chord C were used to deﬁne the Reynolds number. For the LES, ref the WALE model [33] was used to model the subgrid scales. Additionally, results obtained through DNS and WRLES at Re = 1.46 10 are ﬁrst discussed for validation of the method. The lower Reynolds number was chosen to obtain sound reference data by simulating the conﬁguration described using DNS with reasonable computational resources. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 12 of 41 3.3. Numerical Setup and Grid The in-house code LESOCC2 [29] was used to solve the Navier-Stokes equations in their incompressible non-dimensional form. It features 2nd order finite volume discreti- zation in space, and time integration is performed through a 3-step 2nd order Runge- Kutta scheme. The solver has been used previously in DNS studies of linear turbine cas- cades, including secondary flows, providing good results [30–32]. In the following mainly results of Wall-Resolving Large Eddy Simulations (WRLES) at Re =3 ⋅ 10 are presented. This set-up matches the configuration of Krug et al. [23]. Inlet velocity |v ⃗ | and blade chord C were used to define the Reynolds number. For the LES, the WALE model [33] was used to model the subgrid scales. Additionally, results obtained through DNS and WRLES at Re =1.46 ⋅ 10 are first discussed for validation Int. J. Turbomach. Propuls. Power 2021, 6, 9 12 of 40 of the method. The lower Reynolds number was chosen to obtain sound reference data by simulating the configuration described using DNS with reasonable computational re- sources. In In all cases the computational dom all cases the computational domain aincovers covers one one period period of the c of the cascade ascade (F (Figur igur ee 6) 6) which which reaches from reaches from x/ x/C C = = − 0.437 0.437 to to x/ x/C C = = 1.367 1.367 and and was discretized using block- was discretized using block- structured grids. For the WRLES, grid sizes with y 1 at the walls were ensured, resulting structured grids. For the WRLES, grid sizes with y ≈1 at the walls were ensured, re- in a grid of 90 MCV (million control volumes). For the DNS case at Re = 1.46 10 , sulting in a grid of 90 MCV (million control volumes). For the DNS case at Re =1.46 ⋅ besides the wall grid sizes, it was ensured that the cell size, deﬁned as the cubic root of 10 , besides the wall grid sizes, it was ensured that the cell size, defined as the cubic root the cell volume, is smaller than the Kolmogorov scale, which was estimated using the of the cell volume, is smaller than the Kolmogorov scale, which was estimated using the turbulent dissipation. This resulted in a grid of 350 MCV, with 304 cells in the spanwise turbulent dissipation. This resulted in a grid of 350 MCV, with 304 cells in the spanwise direction, 84 of them within the gap region. For the analogous WRLES only the restriction direction, 84 of them within the gap region. For the analogous WRLES only the restriction on wall resolution y was kept, together with the corresponding tangential resolution on wall resolution y was kept, together with the corresponding tangential resolution requirements [34], allowing to decrease the overall number of grid points down to 60 MCV requirements [34], allowing to decrease the overall number of grid points down to 60 MCV for Re = 1.46 10 . for Re = 1.46 ⋅ 10 . Figure 6. Top down view of the simulated linear cascade proﬁle with zoom of the computational Figure 6. Top down view of the simulated linear cascade profile with zoom of the computational domain (shaded region), repeated in y-direction (grey). Coordinates are scaled using the blade chord. domain (shaded region), repeated in y-direction (grey). Coordinates are scaled using the blade Red dashed line at x/C = 0.89 depicts the stage outlet plane. chord. Red dashed line at x/C = 0.89 depicts the stage outlet plane. Regarding boundary conditions, an unsteady turbulent ﬂow was imposed at the Regarding boundary conditions, an unsteady turbulent flow was imposed at the do- domain inlet and a convective condition was set at the outlet. The turbulent inﬂow main inlet and a convective condition was set at the outlet. The turbulent inflow condi- conditions were generated through a precursor simulation, enforcing mean and ﬂuc- tions were generated through a precursor simulation, enforcing mean and fluctuation pro- tuation proﬁles from experiments [23], with a boundary layer thickness at the inlet of files from experiments [23], with a boundary layer thickness at the inlet of δ /C = /C = 0.222 ( /H = 0.198) and a turbulence intensity TI < 1% at midspan [35]. At the 1 1 0.222 (δ /H = 0.198) and a turbulence intensity TI < 1% at midspan [35]. At the end- endwall, no-slip conditions were imposed, while at the midplane symmetry conditions wall, no-slip conditions were imposed, while at the midplane symmetry conditions were were applied. The domain size in spanwise direction is large enough so that the midplane applied. The domain size in spanwise direction is large enough so that the midplane boundary conditions do not inﬂuence the secondary ﬂow. boundary conditions do not influence the secondary flow. The simulations were run for 5 ﬂow through times (FTT) before averaging was carried The simulations were run for 5 flow through times (FTT) before averaging was car- out for another 15 FTT. Here, a FTT is deﬁned based on the axial chord length C and the ried out for another 15 FTT. Here, a FTT is defined based on the axial chord length C and velocity at the inlet midplane jj v jj. Simulations with still longer time integration were ref the velocity at the inlet midplane |v ⃗ | . Simulations with still longer time integration performed to ensure that the time integration applied here is long enough. were performed to ensure that the time integration applied here is long enough. 3.4. Current Investigations and Results 3.4.1. Validation of WRLES with Respect to DNS Data The ﬁrst step taken towards the analysis of the secondary ﬂows in the compressor cascade is to assess the effects of the modelling approach. To this end WRLES of the com- pressor cascade is compared against DNS for Re = 1.46 10 . As discussed in Section 3.3 the WRLES approach required only a 6th of the grid points. The overall ﬂow structure, visualised through (h vi) isosurfaces exhibits no remarkable differences (Figure 7a shows only WRLES) between both approaches. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 13 of 41 3.4. Current Investigations and Results 3.4.1. Validation of WRLES with Respect to DNS Data The first step taken towards the analysis of the secondary flows in the compressor cascade is to assess the effects of the modelling approach. To this end WRLES of the com- pressor cascade is compared against DNS for Re =1.46 ⋅ 10 . As discussed in Section 3.3 Int. J. Turbomach. Propuls. Power 2021, 6, 9 13 of 40 th the WRLES approach required only a 6 of the grid points. The overall flow structure, visualised through λ (⟨v ⃗⟩) isosurfaces exhibits no remarkable differences (Figure 7a shows only WRLES) between both approaches. (a) (b) Figure Figure 7. 7. Linea Linear r com compr pressor essor c cascade ascade at at Re Re =1 = 1.46 .46 ⋅1 10 0 . ( . (a a)) Vortical stru Vortical structur cture evisu visualized alized throu through gh λ ( (⟨h v v ⃗⟩)i)=− = 22 . ( . b (b ) Pitchwi ) Pitchwise se averaged total averaged total pressure pressurelosses downstream o losses downstream of f the bla the blade de at at x/C x/C==0.89 0.89 . . Slight differences are related to small vortices not resolved by the LES since they are Slight differences are related to small vortices not resolved by the LES since they are smaller than the grid size. At the outlet plane similar trends between DNS and WRLES are smaller than the grid size. At the outlet plane similar trends between DNS and WRLES observed. For instance, pressure losses at the exit plane for the WRLES case, see Figure 7b, are observed. For instance, pressure losses at the exit plane for the WRLES case, see Figure are in very good agreement with the DNS result, with slightly higher losses for the WRLES. 7b, are in very good agreement with the DNS result, with slightly higher losses for the Similarly, the pitchwise averaged exit ﬂow angle shows a very good match. The deviations WRLES. Similarly, the pitchwise averaged exit flow angle shows a very good match. The occur mainly away from the endwall. The reason for this behaviour is that near walls the deviations occur mainly away from the endwall. The reason for this behaviour is that near WRLES grid is close to DNS resolution. Therefore, boundary layer ﬂows around walls in walls the WRLES grid is close to DNS resolution. Therefore, boundary layer flows around the WRLES case are resolved with high ﬁdelity. Away from the endwall differences result walls in the WRLES case are resolved with high fidelity. Away from the endwall differ- from a difference in the ﬂow separation at the blade TE. This is observed, for instance, ences result from a difference in the flow separation at the blade TE. This is observed, for through the friction coefﬁcient instance, through the friction coefficient c = / jj v | jj| /2 (2) (2) c =τ /(ρ v ⃗ /2) f ref at different spanwise locations, shown in Figure 8a, revealing overall very good agree- at different spanwise locations, shown in Figure 8a, revealing overall very good agreement, ment, except for (x/C 0.9) , where the WRLES predicts lower c values and a later but except for (x/C > 0.9), where the WRLES predicts lower c values and a later but somewhat somewhat stronger increase. Similar findings were observed in simulations of a turbine stronger increase. Similar ﬁndings were observed in simulations of a turbine stage by stage by Michelassi et al. [36]. These differences lead to differences in the wake, which Michelassi et al. [36]. These differences lead to differences in the wake, which beside beside the modelling uncertainty, result in the deviations presented. Nonetheless, apart the modelling uncertainty, result in the deviations presented. Nonetheless, apart from from the trailing edge region the DNS data are well reproduced, with a 6-fold reduction the trailing edge region the DNS data are well reproduced, with a 6-fold reduction in in computational resources. computational resources. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 14 of 41 The aerodynamic blade loading is shown in Figure 8b by means of the pressure co- The aerodynamic blade loading is shown in Figure 8b by means of the pressure efficient coefﬁcient ! ! c = (p( x ) p )/(jj v jj /2) (3) ref ref c = (p(x ⃗) −p )/(ρ |v ⃗ | /2) (3) at different spanwise positions on the blade. Here, the reference is reproduced extremely at different spanwise positions on the blade. Here, the reference is reproduced extremely well. well. (a) (b) Figure 8. Comparison of WRLES and DNS results along the blade at different spanwise positions. Figure 8. Comparison of WRLES and DNS results along the blade at different spanwise (a) Friction c along the SS and (b) pressure c along PS and SS. positions. (a) Friction c along the SS and (b) pressure c along PS and SS. 3.4.2. Validation of WRLES with Respect to Experimental Data Further validation is now performed with experimental data for Re =3 ⋅ 10 , matching the configuration of Krug et al. [23]. Figure 9 presents a comparison of the pres- sure coefficient at the endwall. Overall good agreement is found, with pressure isolines showing similar distributions. A pressure minimum at the tip gap somewhat larger in size is obtained in the present numerical simulations, but measuring at such a position is not free of error. Beyond the position of this pressure minimum, the TLV departs from the blade (x/C ≈ 0.3), still remaining relatively close to the blade. Between the blades, pres- sure isolines exhibit a mirrored S-shape. The reason for this is the TLV, as stated in [23,37,38]. This was confirmed by looking at the pressure in planes perpendicular to the blades’ camberline. It exhibits a minimum at these positions matching the location of the TLV. (a) (b) Figure 9. Time averaged pressure coefficient at the endwall (z=0). Results from (a) WRLES and (b) experiments [23]. Lastly, total pressure losses and flow angle deviation are compared in Figure 10. Overall, very good agreement is obtained, with a slightly higher deviation in the simula- tion. This slightly overprediction of WRLES with respect to the reference has also been Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 14 of 41 at different spanwise positions on the blade. Here, the reference is reproduced extremely well. (a) (b) Figure 8. Comparison of WRLES and DNS results along the blade at different spanwise Int. J. Turbomach. Propuls. Power 2021, 6, 9 14 of 40 positions. (a) Friction c along the SS and (b) pressure c along PS and SS. 3.4.2. Validation of WRLES with Respect to Experimental Data 3.4.2. Validation of WRLES with Respect to Experimental Data Further validation is now performed with experimental data for Re =3 ⋅ 10 , matching the Further validation configuration is now of Kr performed ug et al. [23]. Figure with experimental 9 presents a co data for mparison o Re = 3 10f the pres- , match- ing the conﬁguration of Krug et al. [23]. Figure 9 presents a comparison of the pressure sure coefficient at the endwall. Overall good agreement is found, with pressure isolines coef showing ﬁcientsimilar at the endwall. distributio Overall ns. A pre good ssuagr re mini eement mum is a found, t the tip ga with p somewha pressure isolines t larger in siz show-e ing similar distributions. A pressure minimum at the tip gap somewhat larger in size is is obtained in the present numerical simulations, but measuring at such a position is not obtained in the present numerical simulations, but measuring at such a position is not free free of error. Beyond the position of this pressure minimum, the TLV departs from the of error. Beyond the position of this pressure minimum, the TLV departs from the blade blade (x/C ≈ 0.3), still remaining relatively close to the blade. Between the blades, pres- (x/C 0.3), still remaining relatively close to the blade. Between the blades, pressure iso- sure isolines exhibit a mirrored S-shape. The reason for this is the TLV, as stated in lines exhibit a mirrored S-shape. The reason for this is the TLV, as stated in [23,37,38]. This [23,37,38]. This was confirmed by looking at the pressure in planes perpendicular to the was conﬁrmed by looking at the pressure in planes perpendicular to the blades’ camberline. blades’ camberline. It exhibits a minimum at these positions matching the location of the It exhibits a minimum at these positions matching the location of the TLV. TLV. (a) (b) Figure 9. Time averaged pressure coefficient at the endwall (z=0). Results from (a) WRLES and Figure 9. Time averaged pressure coefﬁcient at the endwall (z = 0). Results from (a) WRLES and (b (b ) ) experiments [23] experiments [23]. . Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 15 of 41 Lastly, total pressure losses and ﬂow angle deviation are compared in Figure 10. Over- Lastly, total pressure losses and flow angle deviation are compared in Figure 10. all, very good agreement is obtained, with a slightly higher deviation in the simulation. Overall, very good agreement is obtained, with a slightly higher deviation in the simula- This slightly overprediction of WRLES with respect to the reference has also been high- tion. This slightly overprediction of WRLES with respect to the reference has also been lighted in the previous section and may be related to modelling uncertainties affecting the highlighted in the previous section and may be related to modelling uncertainties affect- boundary layer state towards the TE. ing the boundary layer state towards the TE. Finally, it is noted that the results obtained with the two Reynolds numbers, besides Finally, it is noted that the results obtained with the two Reynolds numbers, besides the expected differences in magnitude, in both cases feature practically the same size of the the expected differences in magnitude, in both cases feature practically the same size of region inﬂuenced by the secondary ﬂow, approximately z/H 0 . . . 0.25. Hence, it appears the region influenced by the secondary flow, approximately z/H ≈ 0 … 0.25. Hence, it ap- that the size of the secondary ﬂow region is not dependent on the Reynolds number. pears that the size of the secondary flow region is not dependent on the Reynolds number. (a) (b) Figure 10. Pitchwise averaged (a) total pressure losses and (b) ﬂow angle deviation D , down- Figure 10. Pitchwise averaged (a) total pressure losses ζ and (b) flow angle deviation Δβ , down- str stream of the eam of the blade blade (p (plane lane at at x/ x/C C = = 0.89). 0.89). Ex Experimental perimental data data from from Kr Kru ugget et al al. . [23] [23]. . 3.4.3. Secondary Flow Effects in Compressor Cascade The overall vortical structure of the flow in this configuration is visualized through ⟨ ⟩ isocontours of λ ( v ⃗ )=−2 in Figure 11. The dip in the pressure isolines within the pas- sage shown in Figure 9 matches with the trajectory of the TLV identified through λ (⟨v ⃗⟩). The induced vortex, that is visible by the λ (⟨v ⃗⟩)-isosurface, is not detectable through the pressure at the endwall due to its smaller magnitude. Figure 11. Vortical structure (λ (⟨v ⃗⟩) =−2) for the linear compressor cascade at Re =3 ⋅ 10 . Focusing on the blade, the aerodynamic load is mostly towards the front, Figure 12a, with an almost vanishing pressure gradient at the PS and a mild negative pressure at the SS, exhibiting a minimum towards the front. The effect of the secondary flow is to reduce the blade loading, as evidenced by the differences between the pressure coefficient on PS and SS near the blade tip (z/H = 0.06) compared to the midspan region (z/H = 0.3), as seen in Figure 12a. Furthermore, the local minimum at the SS for z/H = 0.06 is shifted downstream. Its position is slightly downstream of the position where the TLV departs from the blade. Furthermore, the minimum in the pressure at the SS at each spanwise height coincides in position with the start of the decrease of the friction levels shown in Figure 12b. For instance, at the midspan the pressure minimum is at x/C ≈ 0.1 and the local friction maximum at x/C ≈ 0.05. Figure 13 shows the state of the boundary layer along the SS by means of the shape factor H and by wall-normal profiles of the TKE. At the tip (z/H = 0.06) the shape factor Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 15 of 41 highlighted in the previous section and may be related to modelling uncertainties affect- ing the boundary layer state towards the TE. Finally, it is noted that the results obtained with the two Reynolds numbers, besides the expected differences in magnitude, in both cases feature practically the same size of the region influenced by the secondary flow, approximately z/H ≈ 0 … 0.25. Hence, it ap- pears that the size of the secondary flow region is not dependent on the Reynolds number. (a) (b) Int. J. Turbomach. Propuls. Power 2021, 6, 9 15 of 40 Figure 10. Pitchwise averaged (a) total pressure losses ζ and (b) flow angle deviation Δβ , down- stream of the blade (plane at x/C = 0.89). Experimental data from Krug et al. [23]. 3.4.3. Secondary Flow Effects in Compressor Cascade 3.4.3. Secondary Flow Effects in Compressor Cascade The overall vortical structure of the ﬂow in this conﬁguration is visualized through The overall vortical structure of the flow in this configuration is visualized through isocontours of (h vi) = 2 in Figure 11. The dip in the pressure isolines within the isocontours of λ (⟨v ⃗⟩)=−2 in Figure 11. The dip in the pressure isolines within the pas- passage shown in Figure 9 matches with the trajectory of the TLV identiﬁed through sag! e shown in Figure 9 matches with the trajectory of th! e TLV identified through λ (⟨v ⃗⟩). (h vi). The induced vortex, that is visible by the (h vi)-isosurface, is not detectable 2 2 The induced vortex, that is visible by the λ (⟨v ⃗⟩)-isosurface, is not detectable through the through the pressure at the endwall due to its smaller magnitude. pressure at the endwall due to its smaller magnitude. Figure 11. Vortical structure (λ (⟨v ⃗⟩) =−2) for the linear compressor cascade at Re =3 ⋅ 10 . Figure 11. Vortical structure ( ( v ) = 2) for the linear compressor cascade at Re = 3 10 . Focusing on the blade, the aerodynamic load is mostly towards the front, Figure 12a, Focusing on the blade, the aerodynamic load is mostly towards the front, Figure 12a, with an almost vanishing pressure gradient at the PS and a mild negative pressure at the with an almost vanishing pressure gradient at the PS and a mild negative pressure at the SS, exhibiting a minimum towards the front. The effect of the secondary ﬂow is to reduce SS, exhibiting a minimum towards the front. The effect of the secondary flow is to reduce the blade loading, as evidenced by the differences between the pressure coefﬁcient on PS the blade loading, as evidenced by the differences between the pressure coefficient on PS and SS near the blade tip (z/H = 0.06) compared to the midspan region (z/H = 0.3), as and SS near the blade tip (z/H = 0.06) compared to the midspan region (z/H = 0.3), as seen in Figure 12a. Furthermore, the local minimum at the SS for z/H = 0.06 is shifted seen in Figure 12a. Furthermore, the local minimum at the SS for z/H = 0.06 is shifted downstream. Its position is slightly downstream of the position where the TLV departs downstream. Its position is slightly downstream of the position where the TLV departs from the blade. Furthermore, the minimum in the pressure at the SS at each spanwise from the blade. Furthermore, the minimum in the pressure at the SS at each spanwise height coincides in position with the start of the decrease of the friction levels shown in height coincides in position with the start of the decrease of the friction levels shown in Figure 12b. For instance, at the midspan the pressure minimum is at x/C 0.1 and the Figure 12b. For instance, at the midspan the pressure minimum is at x/C ≈ 0.1 and the local friction maximum at x/C 0.05. local friction maximum at x/C ≈ 0.05. Figure 13 shows the state of the boundary layer along the SS by means of the shape Figure 13 shows the state of the boundary layer along the SS by means of the shape factor H and by wall-normal proﬁles of the TKE. At the tip (z/H = 0.06) the shape factor factor H and by wall-normal profiles of the TKE. At the tip (z/H = 0.06) the shape factor is small all along the wall. Hence, the boundary layer at this height is turbulent throughout the whole blade chord. Furthermore, no marked change in shape factor related to the departure of the TLV at x/C 0.3 is observed. The friction coefﬁcient near the tip, shown in Figure 12b, on the other hand, exhibits a marked change. Once the TLV moves away from the blade the friction coefﬁcient decreases by a factor of more than two. Away from the blade wall an increase in TKE is observed for 0.3 x/C 0.4, which is directly related to the location of the TLV. Downstream of the blade, at x/C = 0.89, these higher ﬂuctuations are also observed around the TLV core, as seen in Figure 14. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 16 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 16 of 41 is small all along the wall. Hence, the boundary layer at this height is turbulent throughout is small all along the wall. Hence, the boundary layer at this height is turbulent throughout the whole blade chord. Furthermore, no marked change in shape factor related to the de- the whole blade chord. Furthermore, no marked change in shape factor related to the de- parture of the TLV at x/C ≈ 0.3 is observed. The friction coefficient near the tip, shown parture of the TLV at x/C ≈ 0.3 is observed. The friction coefficient near the tip, shown in Figure 12b, on the other hand, exhibits a marked change. Once the TLV moves away in Figure 12b, on the other hand, exhibits a marked change. Once the TLV moves away from the blade the friction coefficient decreases by a factor of more than two. Away from from the blade the friction coefficient decreases by a factor of more than two. Away from the blade wall an increase in TKE is observed for 0.3 ≤ x/C ≤0.4, which is directly re- the blade wall an increase in TKE is observed for 0.3 ≤ x/C ≤0.4, which is directly re- Int. J. Turbomach. Propuls. Power 2021, 6, 9 16 of 40 lated to the location of the TLV. Downstream of the blade, at x/C =0.89, these higher lated to the location of the TLV. Downstream of the blade, at x/C =0.89, these higher fluctuations are also observed around the TLV core, as seen in Figure 14. fluctuations are also observed around the TLV core, as seen in Figure 14. (b) (a) (b) (a) Figure 12. Pressure (a) and friction (b) coefficients on the blade at two different spanwise posi- Figure Figure 12. 12. Pres Pressur sure ( e (a a)) and friction ( and friction (b b)) coef coeffi ﬁcients cients on the b on the blade lade at at two two dif diff fer erent spanwise ent spanwise posi- positions, tions, near the blade tip (z/H = 0.06) and at midspan (z/H = 0.3). tions, near the blade tip (z/H = 0.06) and at midspan (z/H = 0.3). near the blade tip (z/H = 0.06) and at midspan (z/H = 0.3). Now turning to the blade midspan (z/H = 0.3), the shape factor is much larger near Now turning to the blade midspan (z/H = 0.3), the shape factor is much larger near Now turning to the blade midspan (z/H = 0.3), the shape factor is much larger near the leading edge peaking around x/C ≈ 0.35 then dropping to values around 1.5. the leading edge peaking around x/C 0.35 then dropping to values around 1.5. Hence, the leading edge peaking around x/C ≈ 0.35 then dropping to values around 1.5. the Hence, the b boundaryo layer undary la initially yer i isnlaminar itially isand lami under nar agoes nd undergoes tra transition to ansi turbulent tion to aboundary turbulent Hence, the boundary layer initially is laminar and undergoes transition to a turbulent layer boundar around y layat er aro thisu position, nd at this p which ositiis on, also which reﬂected is also by reflected by a minimum of a minimum of the friction the fric- factor boundary layer around at this position, which is also reflected by a minimum of the fric- at tion f thisaaxial ctor at position this axia (Figur l posie tion ( 12b). FiThe guredif 12fer b).ence The di inff ﬂuctuation erence in fllevels uctuatat ion the level LEs between at the LE tion factor at this axial position (Figure 12b). The difference in fluctuation levels at the LE midspan between midspa and tip n regi anon d tip is dir region ectlyis di related rectl to y rela the higher ted to the hi ﬂuctuations gher fluctua within tio the ns wi incoming thin the between midspan and tip region is directly related to the higher fluctuations within the boundary layer. At the TE very similar proﬁles are observed for both spanwise positions, incoming boundary layer. At the TE very similar profiles are observed for both spanwise incoming boundary layer. At the TE very similar profiles are observed for both spanwise indicating a small inﬂuence of the TLV on the TE part of the blade. This is also observed positions, indicating a small influence of the TLV on the TE part of the blade. This is also positions, indicating a small influence of the TLV on the TE part of the blade. This is also in the pressure distribution (Figure 12a), c values at the TE for both spanwise positions observed in the pressure distribution (Figure p 12a), c values at the TE for both spanwise observed in the pressure distribution (Figure 12a), c values at the TE for both spanwise are similar. positions are similar. positions are similar. Figure 13. Blade suction side boundary layer state, characterized through the turbulent kinetic Figure 13. Blade suction side boundary layer state, characterized through the turbulent kinetic energy Figure 13. Blade suction side boundary layer state, characterized through the turbulent kinetic energy (TKE) in normal direction to the blade (η/C) and the shape factor (H ). (TKE) energy (TKE) i in normal n normal direction to direction to the blade the bla (/Cd ) e ( and η/the C) and the shape factor shape factor ( (H ). H ). The The departur departuree of the TLV r of the TLV results esults in the seco in the secondary ndary fl ﬂow owinﬂuencing influencingalmost almostthe the e entir ntire e The departure of the TLV results in the secondary flow influencing almost the entire pitch pitch at the outlet plane (F at the outlet plane (Figur igur ee 14), wit 14), with hits its core core locat located approxim ed approximately ately at at the middle of the middle of pitch at the outlet plane (Figure 14), with its core located approximately at the middle of the the pa passage ssage pitch. The wi pitch. The wiggly ggly isosurfaces isosurfaces in Fig in Figur ure e 11 11hint hint towar towar ds dsthe the incr incre eased ased level levelssof of the passage pitch. The wiggly isosurfaces in Figure 11 hint towards the increased levels of turbulent ﬂuctuations around the TLV and away from the blade. turbulent fluctuations around the TLV and away from the blade. turbulent fluctuations around the TLV and away from the blade. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 17 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 17 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 17 of 40 (a) (b) (a) (b) Figure 14. Cutplanes downstream of the blade (plane at x/C = 0.89) of (a) total pressure losses and (b) TKE. Pitchwise coordinate normalized by cascade pitch P with origin such Figure 14. Cutplanes downstream of the blade (plane at x/C = 0.89) of (a) total pressure losses Figure 14. Cutplanes downstream of the blade (plane at x/C = 0.89) of (a) total pressure and tha (t b the wa ) TKE. Pitchwise ke is locacoor ted dinate at the centre, normalized PS on the l by cascade eft. pitch P with origin such that the wake is losses and (b) TKE. Pitchwise coordinate normalized by cascade pitch P with origin such located at the centre, PS on the left. that the wake is located at the centre, PS on the left. 3.4.4. Effect of Relative Endwall Motion 3.4.4. Effect of Relative Endwall Motion In a previous study, the described configuration was used to study the effect of the 3.4.4. Ef In afect previous of Relastudy tive En , the dwal de l Mot scribed ion conﬁguration was used to study the effect of relative endwall motion on the flow structure through DNS at Re =1.46 ⋅ 10 [35]. Due the relative endwall motion on the ﬂow structure through DNS at Re = 1.46 10 [35]. In a previous study, the described configuration was used to study the effect of the to the low Reynolds number, viscous effects are higher in this case as would be in typical Due to the low Reynolds number, viscous effects are higher in this case as would be in relative endwall motion on the flow structure through DNS at Re =1.46 ⋅ 10 [35]. Due applications. Once the methodology was validated, simulations were carried out at Re = typical applications. Once the methodology was validated, simulations were carried out to the low Reynolds number, viscous effects are higher in this case as would be in typical 3⋅10 and accounting for relative endwall motion, with value |v ⃗ |sin β in pure at Re = 3 10 and accounting for relative endwall motion, with value jj v jj sin in applications. Once the methodology was validated, simulations were carried out ref at Re LE = pitchwise (𝑦 ) direction. pure pitchwise (y) direction. 3⋅10 and accounting for relative endwall motion, with value |v ⃗ |sin β in pure The flow field, represented through the main vortical structures, is shown in Figure The ﬂow ﬁeld, represented through the main vortical structures, is shown in Figure 15. pitchwise (𝑦 ) direction. 15. Here, similar trends are observed here as in the previous study at Re =1.46 ⋅ 10 Here, similar trends are observed here as in the previous study at Re = 1.46 10 [35]. The flow field, represented through the main vortical structures, is shown in Figure [35]. Relative endwall motion induces a departure of the TLV away from the blade in con- Relative endwall motion induces a departure of the TLV away from the blade in contrast to 15. Here, similar trends are observed here as in the previous study at Re =1.46 ⋅ 10 trast to the case without endwall motion (Figure 11). Still, at the lower Reynolds the TLV the case without endwall motion (Figure 11). Still, at the lower Reynolds the TLV followed [35]. Relative endwall motion induces a departure of the TLV away from the blade in con- followed a straight path, at the current Reynolds number the TLV core follows a straight a straight path, at the current Reynolds number the TLV core follows a straight path initially, trast to the case without endwall motion (Figure 11). Still, at the lower Reynolds the TLV path initially, then, further downstream assumes a curved path, enforced by the main then, further downstream assumes a curved path, enforced by the main passage ﬂow. A followed a straight path, at the current Reynolds number the TLV core follows a straight passage flow. A further effect of the relative motion is the weakening of the induced vor- further effect of the relative motion is the weakening of the induced vortices. path initially, then, further downstream assumes a curved path, enforced by the main tices. passage flow. A further effect of the relative motion is the weakening of the induced vor- tices. Figure 15. Vortical structure ( ((h vi (⟨ ) = ⟩)2) for ) the linear compressor cascade at Re = 3 10 Figure 15. Vortical structure 2 λ v ⃗ =−2 for the linear compressor cascade c at Re = with relative motion between blade and endwall. Black lines with arrows at the bottom denote the 3⋅10 with relative motion between blade and endwall. Black lines with arrows at the ( (⟨ ⟩) ) endwall Figure 15. motion. Vortical structure λ v ⃗ =−2 for the linear compressor cascade at Re = bottom denote the endwall motion. 3⋅10 with relative motion between blade and endwall. Black lines with arrows at the At the cascade outlet, shown in Figure 16, the most noticeable effect of the relative At the cascade outlet, shown in Figure 16, the most noticeable effect of the relative bottom denote the endwall motion. endwall endwall mot motion ion is is a a st stratiﬁcation ratification of t of the he ﬂow flow ﬁeld. field. Th The e endwa endwall ll mo motion tion ent entrains rains ﬂuid fluid inin At the cascade outlet, shown in Figure 16, the most noticeable effect of the relative pitchwise pitchwise d direction irection t thushcr us c eating reatiang fairly a fa uniform irly unif ﬂow orm f near low near t the endwall, he endwa in terms ll, in t of str erms of eam- endwall motion is a stratification of the flow field. The endwall motion entrains fluid in wise stream velocity wise v , pr elocit essur ye, , p and ressﬂow ure, an angle, d flow similar angle, to similar to the st the study in [35]. udy The in TKE [35]. The also becomes TKE also pitchwise direction thus creating a fairly uniform flow near the endwall, in terms of stratiﬁed, becomes strat with ified, w lower levels ith lower leve towardsls to the wards the en endwall due dwall d to the imposed ue to the imposed shear generated shear gen- by streamwise velocity, pressure, and flow angle, similar to the study in [35]. The TKE also the relative motion. As a result, these quantities mostly vary in spanwise direction (i.e., becomes stratified, with lower levels towards the endwall due to the imposed shear gen- z-direction). Furthermore, the stratiﬁcation of the velocity leads to a redistribution of the pressure losses, which are more evenly distributed and exhibit a smaller peak, compared to Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 18 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 18 of 40 erated by the relative motion. As a result, these quantities mostly vary in spanwise direc- tion (i.e. z-direction). Furthermore, the stratification of the velocity leads to a redistribu- tion of the pressure losses, which are more evenly distributed and exhibit a smaller peak, the case without relative endwall motion. The trends described here for the linear cascade compared to the case without relative endwall motion. The trends described here for the match those observed in the rotating ring cascade in Figure 3. Despite the lower peak linear cascade match those observed in the rotating ring cascade in Figure 3. Despite the values, the pitchwise averaged total pressure losses reveal that the relative motion lead lower peak values, the pitchwise averaged total pressure losses reveal that the relative to overall higher losses near the wall and slightly lower losses between the peak and motion lead to overall higher losses near the wall and slightly lower losses between the the midplane (0.1 z/H 0.25). Lastly, both cases, with and without relative motion, peak and the midplane (0.1 ≤ z/H ≤ 0.25). Lastly, both cases, with and without relative show the secondary losses to be of relevance up to z/H 0.25, thus indicating that with motion, show the secondary losses to be of relevance up to z/H ≈ 0.25, thus indicating and without relative endwall motion secondary ﬂow effects are of relevance up to similar that with and without relative endwall motion secondary flow effects are of relevance up spanwise positions. In the previous study at Re = 1.46 10 [35], a similar spanwise to similar spanwise positions. In the previous study at Re =1.46 ⋅ 10 [35], a similar behavior was found. Hence, the size of the region inﬂuenced by secondary losses is not spanwise behavior was found. Hence, the size of the region influenced by secondary dependent on the Reynolds number nor on the relative motion. losses is not dependent on the Reynolds number nor on the relative motion. (a) (b) (c) Figure 16. Effect of relative motion downstream of the blade (plane at x/C = 0.89). Cutplane of (a) Figure 16. Effect of relative motion downstream of the blade (plane at x/C = 0.89). Cutplane of total pressure and (b) TKE. In these two figures, the pitch is normalized by cascade pitch P and its (a) total pressure and (b) TKE. In these two ﬁgures, the pitch is normalized by cascade pitch P and origin such that the wake appears in the centre. (c) Pitchwise averaged total pressure losses. Ex- its origin such that the wake appears in the centre. (c) Pitchwise averaged total pressure losses. perimental data from Krug et al. [23]. Experimental data from Krug et al. [23]. 3.4.5. Incoming, Periodically Perturbed Flow Field 3.4.5. Incoming, Periodically Perturbed Flow Field A further point of interest is the effect an inflow perturbed inflow perturbed by wakes A further point of interest is the effect an inﬂow perturbed inﬂow perturbed by wakes may have on the blade performance characteristics. Here, in particular, similarities and may have on the blade performance characteristics. Here, in particular, similarities and differences between the blade tip region (near the endwall) and the midspan region will differences between the blade tip region (near the endwall) and the midspan region will be be addressed. To this end a WRLES featuring a perturbed inflow was conducted. The pe- addressed. To this end a WRLES featuring a perturbed inﬂow was conducted. The periodic riodic perturbation corresponded to wakes of 2 mm circular bars, as used in the corre- perturbation corresponded to wakes of 2 mm circular bars, as used in the corresponding sponding experiment [23]. The instantaneous fluctuations were provided to the present experiment [23]. The instantaneous ﬂuctuations were provided to the present authors by authors by Wissink and Rodi from their simulation of a circular cylinder [39]. The wake Wissink and Rodi from their simulation of a circular cylinder [39]. The wake was then was then superimposed to the instantaneous flow field of the turbulent boundary layer superimposed to the instantaneous ﬂow ﬁeld of the turbulent boundary layer ﬂow and flow and introduced at the domain inlet. The flow perturbation had a frequency with a introduced at the domain inlet. The ﬂow perturbation had a frequency with a Strouhal Strouhal number Sr = 1.56. For this particular frequency a wake moves half of the blade number Sr = 1.56. For this particular frequency a wake moves half of the blade chord in chord in streamwise direction while it traverses the whole pitch in pitchwise direction. streamwise direction while it traverses the whole pitch in pitchwise direction. Hence, for Hence, for a particular phase of the period, two wakes affect the flow within a single blade a particular phase of the period, two wakes affect the ﬂow within a single blade passage. passage. The effect of the inflow perturbations on the blade performance is characterized The effect of the inﬂow perturbations on the blade performance is characterized here by here by the phase averaged pressure and friction coefficients, depicted in Figure 17. the phase averaged pressure and friction coefﬁcients, depicted in Figure 17. Phase averages were computed as ensemble averages over the bar passing period. Phase averages were computed as ensemble averages over the bar passing period. Overall the pressure coefficient in Figure 17a shows increasing unsteadiness towards the Overall the pressure coefﬁcient in Figure 17a shows increasing unsteadiness towards the TE, depicted through the shaded regions in the figure. This indicates a higher sensitivity TE, depicted through the shaded regions in the ﬁgure. This indicates a higher sensitiv- of the flow at the TE with respect to the incoming wakes. Additionally, fluctuation levels ity of the ﬂow at the TE with respect to the incoming wakes. Additionally, ﬂuctuation are slightly higher towards the blade tip (z/H = 0.06) than at the midspan region (z/H = levels are slightly higher towards the blade tip (z/H = 0.06) than at the midspan region 0.30). Hence, periodic disturbances affect the blade loading over the entire blade span. (z/H = 0.30). Hence, periodic disturbances affect the blade loading over the entire blade This phenomenon observed for the compressor stage is also observed in the turbine cas- span. This phenomenon observed for the compressor stage is also observed in the turbine cade, as discussed in Section 5.4.2 below. cascade, as discussed in Section 5.4.2 below. Considering the friction coefficient, the opposite trend is found. Near the blade tip incoming Considering wakes ha the ve a re friction duced coef influe ﬁcient, nce. In contr the opposite ast, in the trend mid is found. span region Near the end o the blade f tip incoming the boundar wakes y layer t have rans air tieduced on pointinﬂuence. is directly In infcontrast, luenced by t in h the e inc midspan oming w ra egion kes, moving the end of the boundary layer transition point is directly inﬂuenced by the incoming wakes, moving backwards as the wake sweeps the blade suction side, indicating an inﬂuence of the periodic perturbances on the transition to turbulence. Furthermore, at the second half of the blade chord ﬂuctuations are more prominent at the midspan region. In contrast, a direct Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 19 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 19 of 40 backwards as the wake sweeps the blade suction side, indicating an influence of the peri- odic perturbances on the transition to turbulence. Furthermore, at the second half of the blade chord fluctuations are more prominent at the midspan region. In contrast, a direct influence of periodical inflow perturbations on the friction levels at the hub of a turbine inﬂuence of periodical inﬂow perturbations on the friction levels at the hub of a turbine stator is given and explained in detail in Section 5.4.2. This demonstrates that, in the region stator is given and explained in detail in Section 5.4.2. This demonstrates that, in the region near the blade tip the TLV imposes the flow dynamics and “shields” the blade from the near the blade tip the TLV imposes the ﬂow dynamics and “shields” the blade from the periodic perturbations. periodic perturbations. (a) (b) (c) Figure 17. Effect of incoming wakes on blade performance characteristics at the suction side near Figure 17. Effect of incoming wakes on blade performance characteristics at the suction side near the blade tip (z/H = 0.06) and in the midspan region (z/H = 0.30). (a) Time averaged pressure the blade tip (z/H = 0.06) and in the midspan region (z/H = 0.30). (a) Time averaged pressure coefficient (Equation 3) with shaded areas denoting the span of transient fluctuations. (b,c) Friction coefﬁcient (Equation 3) with shaded areas denoting the span of transient ﬂuctuations. (b,c) Friction coefficient (c ) near the blade tip and in the midspan region, respectively. coefﬁcient (c ) near the blade tip and in the midspan region, respectively. 3.5. Work in Progress 3.5. Work in Progress The work presented here is focused on increasing the physical and modelling complex- The work presented here is focused on increasing the physical and modelling com- ity in the study of axial gas turbine compressors, with particular emphasis on the secondary plexity in the study of axial gas turbine compressors, with particular emphasis on the sec- ﬂow. Further work involves moving towards geometries with cylindrical symmetry, i.e., ondary flow. Further work involves moving towards geometries with cylindrical sym- annular blade rows, and increasing the modelling effort by employing wall models in metry, i.e. annular blade rows, and increasing the modelling effort by employing wall the LES. models in the LES. 4. Sub-Project C – Periodically Transient Near-Wall Flow in the T106 Turbine Row 4. Sub-Project C – Periodically Transient Near-Wall Flow in the T106 Turbine Row 4.1. Scope of Sub-Project C Sub-project C deals with far-reaching aspects of endwall ﬂow in a low-pressure turbine 4.1. Scope of Sub-Project C cascade at realistic ﬂow conditions (M = 0.59, Re = 2 10 ). The basis of the exit,th exit,th Sub-project C deals with far-reaching aspects of endwall flow in a low-pressure tur- investigation comprises measurements in the High-Speed Cascade Wind Tunnel (HGK) bine cascade at realistic flow conditions (Mexit,th = 0.59, Reexit,th = 2 × 10 ). The basis of the of the Institute of Jet Propulsion at the Bundeswehr University Munich [40]. URANS investigation comprises measurements in the High-Speed Cascade Wind Tunnel (HGK) simulations provide additional information in areas of limited accessibility and in return, of the Institute of Jet Propulsion at the Bundeswehr University Munich [40]. URANS sim- the measurements are utilized to evaluate the computational approach. A major focus ulations provide additional information in areas of limited accessibility and in return, the is put on the different effects on endwall ﬂow, caused by unsteady inﬂow conditions, measurements are utilized to evaluate the computational approach. A major focus is put changing inlet endwall boundary layer conditions, and blade loading. In this context, on the different effects on endwall flow, caused by unsteady inflow conditions, changing particular attention is given to the components of endwall loss development inside the inlet endwall boundary layer conditions, and blade loading. In this context, particular at- blade passage and the downstream secondary ﬂow ﬁeld. Furthermore, an additional goal tention is given to the components of endwall loss development inside the blade passage of sub-project C is investigating the aspect of endwall heat transfer. and the downstream secondary flow field. Furthermore, an additional goal of sub-project C is investigating the aspect of endwall heat transfer. 4.2. Experimental Setup The present investigations are conducted using a linear cascade design of the T106A 4.2. Experimental Setup low-pressure turbine proﬁle, which was speciﬁcally developed for experimental endwall The present investigations are conducted using a linear cascade design of the T106A ﬂow investigations at high-speed conditions and unsteady inﬂow. The periodically incom- low-pressure turbine profile, which was specifically developed for experimental endwall ing wakes are generated by moving bars with a diameter of 2 mm, i.e., 111% of the T106 flow investigations at high-speed conditions and unsteady inflow. The periodically in- trailing edge diameter. The moving bar plane, which runs parallel to the blade passage coming wakes are generated by moving bars with a diameter of 2 mm, i.e. 111% of the inlet plane, is located 86% C upstream of the blade leading edge. The ratio of bars to T106 trailing edge diameter. The moving bar plane, which runs parallel to the blade pas- blade count is two-to-one, i.e., P /P = 0.5 and the bar speed is v = 20 m/s. The resulting b b sage inlet plane, is located 86% C upstream of the blade leading edge. The ratio of bars to ﬂow conditions are listed in Table 3, including Strouhal number Sr and ﬂow coefﬁcient , blade count is two-to-one, i.e. Pb/P = 0.5 and the bar speed is vb = 20 m/s. The resulting which describe the number and orientation of wakes present in the blade passage at any given instant. Int. J. Turbomach. Propuls. Power 2021, 6, 9 20 of 40 Table 3. T106A linear turbine cascade. Geometric Parameters: Chord length C 100 mm Pitch-to-chord ratio P/C 0.799 Aspect ratio H/C 1.31 Flow Conditions: Mach number at exit M 0.59 exit,th Reynolds number at exit Re 2 10 exit,th Design inﬂow pitch angle 127.7 Design outﬂow pitch angle 26.8 Turbulence intensity TI 6.8% Unsteady Inﬂow Conditions: Strouhal number Sr 0.66 Flow coefﬁcient 3.8 Previous experimental and numerical studies of the T106A turbine cascade have shown that increased bar velocity (higher Sr and lower ) results in intensiﬁed effects on the secondary ﬂow [41]. However, within a reasonable range of unsteady inﬂow parameters, the observed trends remain unchanged. Furthermore, when keeping a constant value of Strouhal number by varying the bar speed proportionally to the bar pitch, the inﬂuence of the ﬂow coefﬁcient is relatively minor. Therefore, the present investigation on loss generation is highly relevant for a wide range of unsteady inﬂows, including more realistic high-Sr-low--cases. The design of the particular turbine cascade was mainly motivated by an unfavorable aerodynamic circumstance in previous experimental setups [42–44]. The issue arises from a gap, needed for the moving bar wake generator, between the wind tunnel and the cascade endwalls, upstream of the blade passages. Due to a negative pressure gradient a leakage ﬂow is formed in the bar gap. While the freestream ﬂow remains unaffected, it is acting as a suction on the endwall boundary layer, ultimately leading to weak secondary ﬂow in measurements, RANS simulations and DNS, which were compared in cooperation with sub-project B [31,32]. Compared to a conventional turbine cascade, the present design, which is discussed in detail in [45], delivers several improvements regarding aerodynamics and integration of measurement techniques. The main feature is an integrated ﬂat plate at part-span which serves as a turbine cascade endwall and provides well deﬁned, and adjustable, inlet endwall boundary layer conditions. The ﬂat plate is split into two parts, one upstream and one downstream of the moving bars, which generate the unsteady inﬂow conditions. Integrating the ﬂat plate at part-span divides the overall ﬂow channel into two spanwise sections as shown in Figure 18. The larger main channel is used for all ﬂow investigations, where the lower channel half near the ﬂat plate is of particular interest. The smaller bypass channel on the other hand is not considered in the investigations. As opposed to the ﬁxed position of the downstream plate, the upstream plate can be displaced in spanwise direction, varying the boundary layer augmentation on the aft plate. The value of Dz denotes the misalignment of the two ﬂat plates, with Dz < 0 resulting in decreased inlet endwall boundary layer height, as shown by the velocity proﬁles in Figure 18b, along with a lower turbulence intensity peak [45]. Int. J. Turbomach. Propuls. Power 2021, 6, 9 21 of 40 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 21 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 21 of 41 Figure 18. Effect of the flat plate misalignment on the inlet endwall boundary layer of the T106A Figure 18. Effect of the flat plate misalignment on the inlet endwall boundary layer of the T106A Figure 18. Effect of the ﬂat plate misalignment on the inlet endwall boundary layer of the T106A cas- cascade. cascade. cade. Measurement Techniques Measurement Techniques Measurement Techniques The HGK test facility is a continuously operating, open loop wind tunnel with a lin- The HGK test facility is a continuously operating, open loop wind tunnel with a lin- The HGK test facility is a continuously operating, open loop wind tunnel with a linear ear cascade test section. The wind tunnel itself is located inside a cylindrical pressure ear cascade test section. The wind tunnel itself is located inside a cylindrical pressure cascade test section. The wind tunnel itself is located inside a cylindrical pressure chamber, chamber, which enables an independent Mach and Reynolds number variation. Measure- chamber, which enables an independent Mach and Reynolds number variation. Measure- which enables an independent Mach and Reynolds number variation. Measurements of ment ment s of t s of t he t he t uu rbine exit rbine exit f f lo lo w fie w fie ld wer ld wer ee perf perf ormed ormed usin using a g a five five--hole-probe t hole-probe tr raverse averse in in the turbine exit ﬂow ﬁeld were perf ormed using a ﬁve-hole-probe traverse in MP2 (cf. MP2 (cf. sub-project A), located at 34% C, i.e., 40% C downstream of the blade passage. MP2 (cf. sub-project A), located at 34% C, i.e., 40% C downstream of the blade passage. sub-project A), located at 34% C, i.e., 40% C downstream of the blade passage. A single A single blad A single blad e pitch center e pitch center ed around ed around the traili the trailing e ng ed dg gee extension extension is covered ove is covered over r the full the full blade pitch centered around the trailing edge extension is covered over the full blade span blb ade lade sp sp an an inin t t hh e fie e fie ld t ld t raverse. The raverse. The clos clos est est wal walll d diist staan nce is ce is z z = = 3. 3.5 5 m mm m or eq or equa uall lly z/ y z/H H = = in the ﬁeld traverse. The closest wall distance is z = 3.5 mm or equally z/H = 2.7%. The 2.7%. The maximum FHP measurement errors based on linear error propagation are M2,err 2.7%. The maximum FHP measurement errors based on linear error propagation are M2,err maximum FHP measurement errors based on linear error propagation are M = 0.0043, 2,err = 0.0043, ζ2,err = 0.321%, β2,err = 0.093°, and α2,err = 0.14°. All integral values of the experi- = 0.0043, ζ2,err = 0.321%, β2,err = 0.093°, and α2,er r = 0.14°. All integral values of the experi- = 0.321%, = 0.093 , and = 0.14 . All integral values of the experimental and 2,err 2,err 2,err ment ment alal and and C C FD d FD d at aa t re a re fer fer t o to a a ma ma ss ss -f -f lo lo w-weight w-weighteed d--a aver vera age. ge. Inl Inle ett bound bounda ary ry la layer me yer meas as-- CFD data refer to a mass-ﬂow-weighted-average. Inlet boundary layer measurements were urements were conducted using a CTA-probe with a tungsten wire of 1.25 mm length and urements were conducted using a CTA-probe with a tungsten wire of 1.25 mm length and conducted using a CTA-probe with a tungsten wire of 1.25 mm length and 5 m diameter. 5 μm diameter. The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration 5 μm diameter. The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration was performed in was performed in a range of 0.0 ≤ M ≤ 0.5 at constant angles of pitch, yaw, and pressure was performed in a range of 0.0 ≤ M ≤ 0.5 at constant angles of pitch, yaw, and pressure a range of 0.0 M 0.5 at constant angles of pitch, yaw, and pressure levels with respect levels with respect to the ensuing measurements. The overall uncertainty estimate of a levels with respect to the ensuing measurements. The overall uncertainty estimate of a to the ensuing measurements. The overall uncertainty estimate of a velocity sample is velocity sample is Δv ≤ 2.5 m/s. Further details on the experimental setup, measurement velocity sample is Δv ≤ 2.5 m/s. Further details on the experimental setup, measurement Dv 2.5 m/s. Further details on the experimental setup, measurement techniques, the techniques, the particular turbine cascade design, which was implemented, and a discus- techniques, the particular turbine cascade design, which was implemented, and a discus- particular turbine cascade design, which was implemented, and a discussion of the full sion of the full experimental results can be found in [45]. sion of the full experimental results can be found in [45]. experimental results can be found in [45]. 4.3. Numerical Setup 4.3. Numerical Setup 4.3. Numerical Setup The numerical simulations were performed using the URANS flow solver TRACE by The numerical simulations were performed using the URANS ﬂow solver TRACE The numerical simulations were performed using the URANS flow solver TRACE by DLR with the k− ω turbulence model by Wilcox [46] and γRe transition model by by DLR with the k ! turbulence model by Wilcox [46] and Re transition model DLR with the k− ω turbulence model by Wilcox [46] and γRe tra t nsition model by Langtry and Menter [47]. The computational domain shown in Figure 19 covers a single by Langtry and Menter [47]. The computational domain shown in Figure 19 covers a Langtry and Menter [47]. The computational domain shown in Figure 19 covers a single blade pitch with periodic boundary conditions. It is divided into an upstream block group single blade pitch with periodic boundary conditions. It is divided into an upstream block blade pitch with periodic boundary conditions. It is divided into an upstream block group encompassing the front plate, the moving domain containing two bar pitches, and a group encompassing the front plate, the moving domain containing two bar pitches, and a encompassing the front plate, the moving domain containing two bar pitches, and a downstream block group which encompasses the blade passage and aft plate. downstream block group which encompasses the blade passage and aft plate. downstream block group which encompasses the blade passage and aft plate. Figure 19. Block topology in the computational domain of the T106A cascade with an integrated Figure 19. Block topology in the computational domain of the T106A cascade with an integrated Figure 19. Block topology in the computational domain of the T106A cascade with an integrated two-part flat plate and a moving bar wake generator. two-part flat plate and a moving bar wake generator. two-part ﬂat plate and a moving bar wake generator. Int. Int. J. Turbo J. Turbomach. mach. Pr Propuls. Power opuls. Power 2021 2021 , 6 , ,69 , x FOR PEER REVIEW 22 22 of of 40 41 Due to the asymmetric geometry caused by the integrated flat plate, the full blade Due to the asymmetric geometry caused by the integrated ﬂat plate, the full blade span including the lower bypass channel is resolved in the computation. The blade pas- span including the lower bypass channel is resolved in the computation. The blade sage is discretized using an OCGH-topology and low-Reynolds wall treatment (y ≤ 1), passage is discretized using an OCGH-topology and low-Reynolds wall treatment (y 1), resulting in high boundary layer resolution. Sufficient spatial and temporal discretization resulting in high boundary layer resolution. Sufﬁcient spatial and temporal discretization is is ensured by a sensitivity study, which leads to an overall number of nodes of approxi- ensured by a sensitivity study, which leads to an overall number of nodes of approximately mately 8⋅10 and a number of time steps per moving domain period of 800. Leakage 8 10 and a number of time steps per moving domain period of 800. Leakage panels panels are incorporated at the bar gap boundaries to simulate the leakage flow. The im- are incorporated at the bar gap boundaries to simulate the leakage ﬂow. The imposed posed static pressure condition is determined based on experimental data. The flow con- static pressure condition is determined based on experimental data. The ﬂow conditions pr di escribed tions prescri at the bed a in- and t the i outlet n- anplane d outlet pl match anthe e match th wind tunnel e wind tunnel condition conditions in the experiment s in the ex- (M periment ( , ReM =,Rfe(Tt1, p =t1, f(T𝑡1, p3)p𝑡1, and p3) TI ). and A detailed TI ). Adescription detailed descr of the iptio computational n of the com- exit,th exit,th , , 1 putational approach can be found in [48]. approach can be found in [48]. 4.4. Current Investigations and Results 4.4. Current Investigations and Results The isentropic blade Mach number distribution at midspan, shown in Figure 20, The isentropic blade Mach number distribution at midspan, shown in Figure 20, is is the most important gauge for evaluating the numerical prediction of the 2D turbine the most important gauge for evaluating the numerical prediction of the 2D turbine cas- cascade ﬂow. cade flow. Figure 20. Comparison of the predicted and measured isentropic Mach number distributions at Figure 20. Comparison of the predicted and measured isentropic Mach number distributions at midspan of the T106A turbine cascade at M = 0.59, Re =2 · 1 50 . , , midspan of the T106A turbine cascade at M = 0.59, Re = 210 . exit,th exit,th The T106A is a predominantly aft-loaded profile which features a very small separa- The T106A is a predominantly aft-loaded proﬁle which features a very small separation bubble tion bubble at at the investigated the investigsteady ated steady inﬂow inflow conditions conditions (see T(see able T 3a ),ble caused 3), caby used the by adverse the ad- pr verse pressur essure gradient e gradient in the aft in section the aft sect of the ion of blade the blade suction suction surface.sur The face. The nume numerical predictions rical pre- match dictions m well with atch well with t the measured he measured distributiondistrib except ufor tion e a mor xcept for a m e pronounced ore pronounc separationed sepa- bubble in rathe tion bubble in the CFD, loca CFD, located at approx. ted a x/Ct a = pprox. x/C 0.95. This x = discr 0.95 epancy . This di is screpa attributed ncy is a tottribu a quicker ted to turbulence decay in the computational domain resulting in a locally lower turbulence a quicker turbulence decay in the computational domain resulting in a locally lower tur- intensity, even though TI matches the experimental level. The turbulent dissipation bulence intensity, even though TI matches the experimental level. The turbulent dis- 1, CFD rate could be adjusted by tweaking the inlet level of the turbulent length scale, however, a sipation rate could be adjusted by tweaking the inlet level of the turbulent length scale, low level of this quantity is imperative for an accurate prediction of the loss generation. however, a low level of this quantity is imperative for an accurate prediction of the loss In the case of unsteady inﬂow conditions, a pitchwise incidence of i = 1.5 is induced, generation. In the case of unsteady inflow conditions, a pitchwise incidence of i= −1.5° resulting in decreased blade loading in the front part of the blade suction surface. At the is induced, resulting in decreased blade loading in the front part of the blade suction sur- aft section of the suction surface the separation bubble is suppressed due to wake induced face. At the aft section of the suction surface the separation bubble is suppressed due to transition. Both these effects are predicted well in the numerical simulations [48]. wake induced transition. Both these effects are predicted well in the numerical simula- The level of secondary ﬂow and the effects of the incoming wakes as well as the inlet tions [48]. boundary layer variation by ﬂat plate misalignment are gauged by ﬁeld measurements of The level of secondary flow and the effects of the incoming wakes as well as the inlet the turbine exit ﬂow in MP2. The results are illustrated over the entire channel height in boundary layer variation by flat plate misalignment are gauged by field measurements of Figure 21 and as spanwise distributions of pitchwise-average values in Figure 22. the turbine exit flow in MP2. The results are illustrated over the entire channel height in Figure 21 and as spanwise distributions of pitchwise-average values in Figure 22. Int. J. Turbomach. Propuls. Power 2021, 6, 9 23 of 40 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 23 of 41 Figure 21. Measured total pressure losses at different endwall boundary layer conditions, (a–c) Figure 21. Measured total pressure losses at different endwall boundary layer conditions, (a–c) with with and (d–f) without periodically incoming wakes in MP2. and (d–f) without periodically incoming wakes in MP2. The secondary outflow angle ∆β and the secondary total pressure losses ζ The secondary outﬂow angle D , and the secondary total pressure losses , 2, sec 2, sec are defined by are deﬁned by D = (4) 2,sec 2 2,MS Δβ =β − β , , (4) = with (5) 2,sec 2 2,MS ζ =ζ − ζ with (5) , p p , t1 t2 = (6) p p t1 3 p −p ζ = It is apparent that the different inlet endwall boundary layer conditions result in vary- (6) p −p ing degrees of secondary ﬂow in the lower channel half near the integrated ﬂat plate. The It is apparent that the different inlet endwall boundary layer conditions result in var- case of Dz = 0, representing the thickest boundary layer, exhibits the strongest secondary ﬂow ying de . Lowering grees the of second inlet boundary ary flow layer in the lo thickness wer ch inannel the cases half near the integrated of Dz =1% C and Dzflat plate. = 2% C,The case results in of a rΔ eduction z = 0, representi of peak ng the thi values of over ckest bounda -/underturning ry layer, exhi as wellbi as ts the strongest sec- secondary losses. Additionally, the regions of secondary losses and over-/underturning are shifted towards ondary flow. Lowering the inlet boundary layer thickness in the cases of Δz = −1% C and the endwall. This is caused by a less pronounced liftoff of the passage vortex. Δz = −2% C, results in a reduction of peak values of over-/underturning as well as second- aryComparing losses. Addit theion turbine ally, thexit e reg ﬂow ions o infcases second with ary l steady osses and and ov unsteady er-/undert inﬂow urn,ing it is are apparent that the periodically incoming wakes also cause an attenuation of the time- shifted towards the endwall. This is caused by a less pronounced liftoff of the passage averaged secondary ﬂow. In Figure 22, it is particularly noticeable that the reduction in vortex. time-averaged peak values of and D as well as the spanwise shift by means of Comparing the turbine ex 2,sec it flow in c 2,sec ases with steady and unsteady inflow, it is ap- unsteady inﬂow conditions is very similar to the effect of decreasing the inlet endwall parent that the periodically incoming wakes also cause an attenuation of the time-aver- boundary layer height, especially in the underturning region. aged secondary flow. In Figure 22, it is particularly noticeable that the reduction in time- Although not shown here, the numerical simulations offer a good prediction of the averaged peak values of ζ and Δβ as well as the spanwise shift by means of un- , , spanwise distributions as well as the effects of unsteady inﬂow and endwall boundary steady inflow conditions is very similar to the effect of decreasing the inlet endwall layer variation [48]. A slightly narrower region of elevated secondary losses in combination boundary layer height, especially in the underturning region. with an overshoot of the loss peak is commonly observed in numerical simulations solving Although not shown here, the numerical simulations offer a good prediction of the the URANS equations with an eddy-viscosity model. The important quantity of overall spanwise distributions as well as the effects of unsteady inflow and endwall boundary losses, deﬁned here as integral half-span losses, are predicted with very good accuracy by layer variation [48]. A slightly narrower region of elevated secondary losses in combina- tion with an overshoot of the loss peak is commonly observed in numerical simulations Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 24 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, 9 24 of 40 solving the URANS equations with an eddy-viscosity model. The important quantity of overall losses, defined here as integral half-span losses, are predicted with very good ac- curacy by the simulations, e.g. in the Δz = −1% C case ζ =4.7% ≈ ζ = the simulations, e.g. in the Dz = 1% C case ( ) = 4.7% ( ) = 4.6%. For , , 2, HS 2, HS EXP CFD this speciﬁc comparison, the CFD value was integrated only within the experimentally 4.6%. For this specific comparison, the CFD value was integrated only within the experi- accessible area of 0.027 z/H 0.5. mentally accessible area of 0.027 ≤ z/H ≤ 0.5. Figure Figure 22. 22. Measur Measu ed red spanwis spanwise distributions e distributions of the of the pitchwise-averaged pitchwise-averaged se secondary condary pitch angle pitch angle D 2, sec and secondary total pressure losses under different endwall boundary layer conditions, with ∆β and secondary total pressure losses ζ under different endwall boundary layer condi- , 2, sec , and tions, without with and periodically without perio incoming dically wakes incoin miMP2. ng wakes in MP2. For a further description of the effect of periodically incoming wakes, the numerical For a further description of the effect of periodically incoming wakes, the numerical predictions of the time resolved ﬂow ﬁeld in MP2 is shown at two distinct times in Figure 23. predictions of the time resolved flow field in MP2 is shown at two distinct times in Figure In order to evaluate the effects of incoming wakes on the blade passage loss generation, the 23. In order to evaluate the effects of incoming wakes on the blade passage loss generation, integral losses in Figure 23a are corrected by subtracting the time-averaged values upstream the integral losses in Figure 23a are corrected by subtracting the time-averaged values the blade passage D = . The ﬁrst time resolved ﬂow ﬁeld at t/T = 0.125 2 2 x BP upstream the blade passage ∆ζ r=ζ ef − ζ . The first time resolved flow field at t/T = corresponds to the maximum overall losses (integral over half span) in the moving bar 0.125 corresponds to the maximum overall losses (integral over half span) in the moving period T . Around this instant, the remains of an incoming bar wake, which has been BP bar period T . Around this instant, the remains of an incoming bar wake, which has been subjected to stretching and bowing in the blade passage, ﬁrst interact with the passage subjected to stretching and bowing in the blade passage, first interact with the passage vortex in MP2. Moments later, the bar wake travels in pitchwise direction, where it affects vortex in MP2. Moments later, the bar wake travels in pitchwise direction, where it affects the blade suction surface and ultimately overlaps with the blade wake at y/P=0.5 which the blade suction surface and ultimately overlaps with the blade wake at y/P=0.5 which corresponds to the extension of the blade trailing edge. This leads to a very wide blade corresponds to the extension of the blade trailing edge. This leads to a very wide blade wake and maximum pitchwise-averaged midspan losses. Considering the deﬁnition of the wake and maximum pitchwise-averaged midspan losses. Considering the definition of secondary losses, the peaks of midspan and overall losses occur around the same time as the secondary losses, the peaks of midspan and overall losses occur around the same time the secondary loss minimum. as the secondary loss minimum. This is conﬁrmed by the streamwise vorticity plot in Figure 23d, where a temporary This is confirmed by the streamwise vorticity plot in Figure 23d, where a temporary attenuation of the passage vortex can be seen. The reduced liftoff of the secondary vortex attenuation of the passage vortex can be seen. The reduced liftoff of the secondary vortex system correlates with a less distinct horseshoe vortex pressure side leg, which has already system correlates with a less distinct horseshoe vortex pressure side leg, which has already begun to merge with the passage vortex in MP2. The same observation is made in the begun to merge with the passage vortex in MP2. The same observation is made in the low- low-speed annular cascade adaptation of the T106A in sub-project D (see Section 5.1). The speed annular cascade adaptation of the T106A in sub-project D (see Section 5.1). The sec- second instant at t/T = 0.7 exhibits further pitchwise distance between the bar wake BP ond instant at t/T =0.7 exhibits further pitchwise distance between the bar wake and and the blade wake in MP2, so there is no overlapping. Additionally, bar wake induced the blade wake in MP2, so there is no overlapping. Additionally, bar wake induced tran- transition forces a temporary suppression of the separation bubble on the blade suction sition forces a temporary suppression of the separation bubble on the blade suction sur- surface. These combined circumstances result in a very narrow blade wake and relatively face. These combined circumstances result in a very narrow blade wake and relatively low low levels of corrected midspan, overall, and secondary losses around this instant, even levels of corrected midspan, overall, and secondary losses around this instant, even falling falling below the steady state. When evaluating a time resolved downstream ﬂow ﬁeld, it below the steady state. When evaluating a time resolved downstream flow field, it is im- is important to understand that the local ﬂow properties are not only inﬂuenced by the portant to understand that the local flow properties are not only influenced by the bar bar wake in that speciﬁc location, but especially by upstream interactions with the blade wake in that specific location, but especially by upstream interactions with the blade pas- passage ﬂow. The level of disturbance of the turbine exit ﬂow during a moving bar period, sage flow. The level of disturbance of the turbine exit flow during a moving bar period, originating upstream, is reliant on the unsteady inﬂow conditions, deﬁned by Strouhal originating upstream, is reliant on the unsteady inflow conditions, defined by Strouhal number Sr and ﬂow coefﬁcient . Since multi-row axial turbines usually operate at much higher Strouhal numbers it is safe to assume that the passage ﬂow is constantly in a state of varying disturbance. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 25 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 25 of 41 number Sr and flow coefficient φ. Since multi-row axial turbines usually operate at much Int. J. Turbomach. Propuls. Power 2021, 6number Sr , 9 and flow coefficient φ. Since multi-row axial turbines usually operate at 25 much of 40 higher Strouhal numbers it is safe to assume that the passage flow is constantly in a state higher Strouhal numbers it is safe to assume that the passage flow is constantly in a state of varying disturbance. of varying disturbance. Figure 23. Numerical prediction of the change in (a) integral- and (b,c) local total pressure losses Figure Figure 23. 23. Numerical Numerical pred prediction iction of the of the c chan hange ge in in ( (a) a) integral- integral- and and ( (bb ,c,)c) local locatotal l total pr pres essur su ere lo losses sses as as well as (d,e) streamwise vorticity over time in MP2 with unsteady inflow conditions. as well as (d,e) streamwise vorticity over time in MP2 with unsteady inflow conditions. well as (d,e) streamwise vorticity over time in MP2 with unsteady inﬂow conditions. After investigating the secondary ﬂow in MP2, where unsteady inﬂow conditions and After investigating the secondary flow in MP2, where unsteady inflow conditions After investigating the secondary flow in MP2, where unsteady inflow conditions changing inlet boundary layers showed similar time-averaged effects, questions arise as to and changing inlet boundary layers showed similar time-averaged effects, questions arise and changing inlet boundary layers showed similar time-averaged effects, questions arise the upstream endwall ﬂow development and corresponding loss generation throughout as to the upstream endwall flow development and corresponding loss generation as to the upstream endwall flow development and corresponding loss generation the blade passage. Comparing the time-averaged axial change in non-dimensionalized tt h h roughout roughout t t h h e b e b lade lade p p aa ss ss aa ge. ge. C C oo m m p p ar ar in in g t g t h h e t e t im im ee -- aa v v ee rage rage d d axi axi aa l chan l chan ge ge in no in no n-dim n-dim ee n n -- entropy in Figure 24 in case of unsteady inﬂow conditions to the steady state shows an sionalized entropy in Figure 24 in case of unsteady inflow conditions to the steady state sionalized entropy in Figure 24 in case of unsteady inflow conditions to the steady state accelerated overall loss increase in the front part of the blade passage. This is caused shows an accelerated overall loss increase in the front part of the blade passage. This is shows an accelerated overall loss increase in the front part of the blade passage. This is by increased blade proﬁle losses due to the perturbation of the blade surface boundary caused by increased blade profile losses due to the perturbation of the blade surface caused by increased blade profile losses due to the perturbation of the blade surface layers by the incoming bar wakes with high levels of turbulence. Unlike the proﬁle losses, boundary layers by the incoming bar wakes with high levels of turbulence. Unlike the boundary layers by the incoming bar wakes with high levels of turbulence. Unlike the the secondary loss generation is not increased by the incoming wakes inside the blade profile losses, the secondary loss generation is not increased by the incoming wakes inside profile losses, the secondary loss generation is not increased by the incoming wakes inside passage (0 x/C 1). In fact, the interaction of the wakes with the endwall boundary the blad the blade passag e passage ( e (0≤ 0≤ xx//CC ≤1 ≤1)). In fa . In fact, the i ct, the inntera teracti ctioon of the wakes wi n of the wakes with the th the endwal endwall l layer in the front part of the passage delays the roll-up of the passage vortex and its boundary layer in the front part of the passage delays the roll-up of the passage vortex boundary layer in the front part of the passage delays the roll-up of the passage vortex pressure-driven translation towards the suction surface, which leads to an attenuation of and its pressure-driven translation towards the suction surface, which leads to an attenu- and its pressure-driven translation towards the suction surface, which leads to an attenu- the secondary loss further downstream. Outside the near-endwall region, the incoming ation of the secondary loss further downstream. Outside the near-endwall region, the in- ation of the secondary loss further downstream. Outside the near-endwall region, the in- wakes periodically force an earlier turbulent transition on the blade suction surface, which coming wakes periodically force an earlier turbulent transition on the blade suction sur- coming wakes periodically force an earlier turbulent transition on the blade suction sur- leads to the suppression of the separation bubble. ff aa ce, whi ce, whi cc h lea h lea d d s to the suppressi s to the suppressi on on of t of t h h e sep e sep aa rat rat ion ion bubble. bubble. Figure 24. Axial entropy development throughout the T106A blade passage with steady and un- Figure 24. Axial entropy development throughout the T106A blade passage with steady and un- Figure 24. Axial entropy development throughout the T106A blade passage with steady and unsteady steady inflow conditions. steady inflow conditions. inﬂow conditions. Therefore, the rapid increase of the proﬁle losses near the trailing edge (x/C = 1) in the steady case is attenuated by the unsteady inﬂow conditions. In sum, the steady case level of overall losses is catching up to the unsteady inﬂow case and the entropy lines converge with further distance downstream of the blade passage. Thus, despite the ﬂow Int. J. Turbomach. Propuls. Power 2021, 6, 9 26 of 40 ﬁeld changes, seen in MP2 (Figures 22 and 23), the effect of the periodically incoming wakes on the time-averaged integral losses in the turbine exit ﬂow is very small. This ﬁnding is consistent with the total pressure ﬁeld measurements [45] as well as DNS of a previous T106A cascade [31,32]. Overall, the effect of unsteady inﬂow conditions can be summarized as a spatial redistribution of the loss generation with a premature loss increase due to wake interaction with the blade surface boundary layer followed by attenuation of the proﬁle- and secondary loss generation in the aft-section of the blade passage. A more comprehensive analysis of the secondary ﬂow development and the local sources of loss inside the blade passage can be found in [48]. Contrary to the axially varying effect of unsteady inﬂow conditions, decreasing the inlet endwall boundary layer height results in a nearly constant reduction of the endwall loss generation, beginning around the midpoint of the blade passage where the secondary ﬂow is formed. Lastly, the effect of increased frontal blade loading leads to a rise in proﬁle losses in the front part of the passage followed by increased secondary losses due to stronger transverse pressure gradients [49]. 4.5. Work in Progress Upcoming work in sub-project C includes expanding the experimental data set with time-resolved measurements and optical measurements. A particular area of interest is the secondary ﬂow interaction with the blade suction surface ﬂow. Additionally, great effort is being invested in an investigation of the aspect of endwall heat transfer. This goal is planned to be achieved by deploying the progressive measurement technique of ultra-high-speed temperature sensitive paint on the cascade endwall surface. The capability of this measurement technique has recently been veriﬁed successfully on a ﬂat plate with a frame rate of up to 40 kHz. 5. Sub-Project D—Inﬂuence of Periodic Wakes on the Transient Near-Wall Flow in an Annular Axial Turbine Cascade 5.1. Scope of Sub-Project D Especially in a LPT environment, periodic ﬂow perturbations induced by rotor-stator interaction exert pronounced consequences on the blade proﬁle boundary layers, which are inherently unstable and prone to separation due to the high LPT stage loading and the prevailing low Reynolds numbers [50]. Despite decades of highly accurate, profound research addressing the different aspects of rotor-stator interaction, a deeper physical understanding regarding the highly unsteady interplay of the transported wake structures, the involved boundary layers and the blade row’s secondary ﬂow system is still sought. Therefore, in sub-project D, experimental investigations in a large-scale annular test rig for the time-resolved analysis of wake-stator BL ﬂow interaction within a turbine environment are conducted. This way, the inﬂuences of curvilinear endwalls, non-uniform, radially increasing pitch and radial ﬂow migration are incorporated, increasing the degree RUB of complexity over linear setups. The modiﬁed stator blade proﬁle, labeled as T106 , was developed within this collaborative project for matching the transition and separation characteristics of the original T106 proﬁle (also applied in sub-project C) at low ﬂow speeds, thus facilitating measurements to be taken in an annular, large-scale test rig (see [51]). The stator ﬂow is periodically perturbed by incoming wakes from a rotating wake generator. The aim of the current activities is to establish a connection between the incoming, periodically wake-perturbed ﬂow ﬁeld, the highly-unsteady situation in the stator blade row (stator proﬁle and passage ﬂow) as well as the exit ﬂow containing the secondary ﬂow structures in an annular LPT environment. For this, multiple measurement techniques upstream, within the stator blade row and downstream are connected to provide an exten- sive set of experimental data. This allows to study the unsteady behavior of the boundary layers developing on the LPT stator proﬁles and their effect on secondary ﬂow patterns under the inﬂuence of periodic inﬂow perturbations. The transition phenomena occurring in the proﬁle boundary layers are investigated under both unperturbed and periodically Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 27 of 41 flow structures in an annular LPT environment. For this, multiple measurement tech- niques upstream, within the stator blade row and downstream are connected to provide Int. J. Turbomach. Propuls. Power 2021, 6 an extensiv , 9 e set of experimental data. This allows to study the unsteady behavior of th 27 of e 40 boundary layers developing on the LPT stator profiles and their effect on secondary flow patterns under the influence of periodic inflow perturbations. The transition phenomena occurring in the profile boundary layers are investigated under both unperturbed and perturbed inﬂow by means of spectral analysis, the semi-quantitative characterization of periodically perturbed inflow by means of spectral analysis, the semi-quantitative charac- the wall-stress system and an evaluation of the statistic quantities. Using experimental terization of the wall-stress system and an evaluation of the statistic quantities. Using ex- hot-ﬁlm data from different positions of blade span, the BL ﬂow behavior can be linked to perimental hot-film data from different positions of blade span, the BL flow behavior can the temporal evolution of the secondary ﬂow structures, which is assessed with the help be linked to the temporal evolution of the secondary flow structures, which is assessed of temporal and spatially highly resolved ﬂow ﬁeld traverses downstream of the blade with the help of temporal and spatially highly resolved flow field traverses downstream row in focus. To the best knowledge of the authors, until today only a few studies were of the blade row in focus. To the best knowledge of the authors, until today only a few presented, comparing appropriate time-resolved data from the midspan section with data studies were presented, comparing appropriate time-resolved data from the midspan sec- from the near-wall region, where secondary ﬂow effects have to be considered. Ultimately, tion with data from the near-wall region, where secondary flow effects have to be consid- the acquired measurement data provide highly resolved validation data for accompanying ered. Ultimately, the acquired measurement data provide highly resolved validation data URANS and LES computations. for accompanying URANS and LES computations. The presented investigations give a brief outline of key ﬁndings from recent publica- The presented investigations give a brief outline of key findings from recent publica- tions by the authors, where the unsteady impact of periodic bar wakes on the ﬂow ﬁeld tions by the authors, where the unsteady impact of periodic bar wakes on the flow field downstream of the stator row as well as on the stator proﬁle pressures and boundary layers downstream of the stator row as well as on the stator profile pressures and boundary were discussed. For details, please see [51–58]. layers were discussed. For details, please see [51–58]. 5.2. Experimental Setup 5.2. Experimental Setup The experimental activities described in this contribution were carried out in the large- The experimental activities described in this contribution were carried out in the scale, axial ﬂow turbine test facility Axial Turbine II at the Chair of Thermal Turbomachines large-scale, axial flow turbine test facility Axial Turbine II at the Chair of Thermal Tur- and Aeroengines of Ruhr University Bochum. The facility was designed to allow highly bomachines and Aeroengines of Ruhr University Bochum. The facility was designed to resolved measurements of the unsteady interaction between the stator proﬁle ﬂow and allow highly resolved measurements of the unsteady interaction between the stator pro- periodically impinging wake structures within an annular setup. For this purpose, the test file flow and periodically impinging wake structures within an annular setup. For this rig was used in a 1.5 stage conﬁguration with an IGV row, a rotating wake generator and purpose, the test rig was used in a 1.5 stage configuration with an IGV row, a rotating RUB the T106 stator row under investigation, presented in Figure 25. The large dimensions RUB wake generator and the T106 stator row under investigation, presented in Figure 25. of the ﬂow channel allow detailed ﬂow measurements with negligible perturbation by The large dimensions of the flow channel allow detailed flow measurements with negli- installed probes. Rotatable casing elements with multiple probe accesses facilitate the gible perturbation by installed probes. Rotatable casing elements with multiple probe ac- recording of two-dimensional ﬂow ﬁeld traverses in various planes. Following, the most cesses facilitate the recording of two-dimensional flow field traverses in various planes. important information regarding the setup are given, a more detailed description was Following, the most important information regarding the setup are given, a more detailed provided in [51–53]. description was provided in [51–53]. Figure 25. Test facility Axial Turbine II: sectional view (a), 3D illustration (b). Figure 25. Test facility Axial Turbine II: sectional view (a), 3D illustration (b). Following a combination of flow straightener cells, a turbulence grid and a contrac- Following a combination of ﬂow straightener cells, a turbulence grid and a contraction for tion for gene generating rat uniform ing unifor inﬂow m inflow w withinitthe hin t settling he settlchamber ing chamber, , the ﬂow the flow pa passesss an es an IGV IGV row RUB RUB row (NACA 8408 profiles) to ensure proper inflow angles to the T106 stator whilst leav- (NACA 8408 proﬁles) to ensure proper inﬂow angles to the T106 stator whilst leaving the ing t ﬂow he fl as ow far asas far possible as possib unaf le una fected ffect by ed wakes by wakes and and secondary secondar ﬂow y fl .ow. W With both ith bot 60 hIGV 60 IGV and RUB RUB RUB RUB T106 and T106 proﬁles, profiles, it it is ensur is en ed sured that that ev every T106 ery T106passage passage face faces identical s identical inﬂow inflo conditions. w condi- The tions. The IGV is IG placed V is p 261% laced C 26upstr 1% Ceam upstof rea the m of t wake he w generator ake gener . ator. T To simu o simulate late t the he unst unsteady eady r rotor otor-st -stator ator int interaction eraction o of f an an axi axia al l tturbomachine, urbomachine, th the e ro rotor tor RUB RUB disk between the IGV and the T106 stator was equipped with radially stacked, circular disk between the IGV and the T106 stator was equipped with radially stacked, circular steel bars (bar diameter D = 2 mm, bar length L = 168 mm). The use of periodically b b passing circular bars facilitates to isolate both velocity defect and turbulence increase of typical rotor blade wakes without the secondary ﬂow structures emerging in a real rotor passage. Wakes are generated at an axial distance of 33% C upstream in a plane parallel to the stator leading edges, representing a typical axial gap width in a LPT. The investigations were carried out for a bar pitch of P = 78 mm, matching the pitch of both the IGV and RUB the T106 . Int. J. Turbomach. Propuls. Power 2021, 6, 9 28 of 40 The aft-loaded blade proﬁle (cylindrical geometry) under investigation, labeled as RUB T106 , is an in-house modiﬁcation of the well-known T106 LPT blade, with modiﬁed distributions of proﬁle thickness and curvature. It was developed to match Reynolds number, blade loading distribution c at midspan and thus an equivalent boundary layer development of the original T106 proﬁle at the rig’s low Mach number ﬂow. The principles of the transformation procedure were described by Sinkwitz et al. [51]. The test facility is operated with ambient air, continuously in an open circuit. Flow is induced by a 150 kW variable speed engine coupled to a radial blower providing a mass ﬂow capacity of m 13 kg/s. To avoid inﬂow perturbations, the blower is placed downstream of the test section, thus the rig is operated in suction mode. Table 4 summarizes the most important details. Table 4. Main test rig properties and turbine stage parameters. Test Rig Turbine Stage Outer diameter (Casing) 1660 mm Chord length IGV 137 mm Inner diameter (Hub) 1320 mm Stagger angle IGV 25.5 RUB Chord length T106 100 mm RUB Stagger angle T106 30.7 RUB Blade count IGV, T106 60 Operating Point, Design Point Design Flow Angles, Midspan Mass ﬂow m 12.8 kg/s IGV inlet 90.0 Reynolds number IGV outlet = 5 RUB at exit Re 2 10 T106 inlet 52.3 exit,th 2 Mach number RUB at exit M 0.091 T106 outlet 153.2 exit,th 5.3. Measurement Techniques Monitoring of the operating point was realized with Prandtl-probes at different char- acteristic planes and a combined temperature/humidity sensor at the rig inlet. A detailed description of the applied transducers and devices is provided in [51–54]. To quantify the bar wake impact on the stator ﬂow and the resulting secondary ﬂow structures, ﬂow ﬁeld traverses were carried out in relevant planes, including the axial gap RUB between the wake generator and the T106 stator and the exit ﬂow ﬁeld downstream RUB of the T106 stator. Two-dimensional ﬂow ﬁeld traverses in the exit ﬂow (38 radial RUB and 25 circumferential positions, distributed over two T106 stator passages) have been RUB carried out at 15% C and 35% C downstream of T106 TE. For this, hot-wire anemometry measurements (CTA mode) were conducted using a Dantec Dynamics StreamLine 90N10 CTA anemometer (incorporating three 90C10 CTA modules) and both straight and slanted 1-wire probes in the inﬂow and Split-Fiber probes (SFP, types 55R56 and 55R57) in the wake-ﬂow, shown in Figure 26a. In the wake regions, characterized by intense ﬂow angle variations, SFP have proven superior usability. Due to this and their increased durability, they have been chosen for most of the measurements. All probes were subjected to a multi- dimensional calibration prior to the measurements, during which the corresponding ﬂow angle and velocity were varied within the anticipated range. Using the two voltage values resulting from the SFP measurement, the respective ﬂow angle as well as the magnitude of the velocity (giving a 2D ﬂow vector) were reconstructed. By combining two consecutive measurements with SFP 55R56 and 55R57, the phase-averaged 3D ﬂow vector was ﬁnally reconstructed by analyzing the data sets of both probe measurements simultaneously. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 29 of 41 resulting from the SFP measurement, the respective flow angle as well as the magnitude of the velocity (giving a 2D flow vector) were reconstructed. By combining two consecu- tive measurements with SFP 55R56 and 55R57, the phase-averaged 3D flow vector was Int. J. Turbomach. Propuls. Power 2021, 6, 9 29 of 40 finally reconstructed by analyzing the data sets of both probe measurements simultane- ously. Figure Figure 26. 26. Sel Selected ected dev devices ices fo for r the acqu the acquisition isition of ti of time-r me-resol esolved ved measurement data: Dante measurement data: Dantec c Dynam- Dynamics RU RUB B ics type 55R56 and 55R57 SFP (a), assembly of modular T106 blade with suction side hot-film type 55R56 and 55R57 SFP (a), assembly of modular T106 blade with suction side hot-ﬁlm instrumentation (b), arrangement of Kulite LQ-125 sensors along the profile (c). instrumentation (b), arrangement of Kulite LQ-125 sensors along the proﬁle (c). RUB RUB RUB RUB For For exper experimental imental d data ata ac acquisition quisition w within ithin t the he T1 T106 06 stator pass stator passage, age, seve several ral T T106 106 pr profiles were oﬁles were equipped equipped with with sur surface-mounted face-mounted hot-ﬁlm hot-film sen sensor sor arrays, arrays Kulite-sensors , Kulite-sensors (10(sen- 10 sors sensors of typ of type LQ-125, e LQ-125, se sealed aled g gage age v variant) ariant) an and static d static prpressu essurere t taps. aps Hot-ﬁlms . Hot-films (thickness (thickness 0.05 ≈ 0.05 mm, mm custom-fabricated , custom-fabricated b by Ty ao Tao of of Systems System Integration s Integration Inc.,) Inc., featur ) feat e u 24 re sensor 24 sensor e elements le- on ments on the SS la the SS layout, 20yout, elements 20 el on ements on the PS la the PS layout and a yout a constant nd a consta spacingnt sp of 6 mm acinbetween g of 6 mm the individual between the individ sensor elements. ual sensor elements. For For hot-ﬁlm sensor hot-fi operation lm sensor oper and data ation an acquisition d data acq also uisthe i- tion also the StreamLine 90N10 CTA anemometer along with three 90C10 CTA modules StreamLine 90N10 CTA anemometer along with three 90C10 CTA modules was applied. For wasdata applacquisition ied. For data of ac hot-wir quisition o e and f hot hot-ﬁlm -wire and measur hot-ements, film measu a National rements, Instr a Nat uments ional In- NI 9215 struments NI module was 9215 module employed. was emplo More details yed. More regarding detthe ails re hot-ﬁlm gardin setup g the hot are pr -fiovided lm setuin p ar [54 e ]. provided in [54]. Signals have been recorded at a rate of up to 100 kHz (550 times higher than the maximum Signals h barapassing ve been recorde frequency d at for a r the ate of shown up tinvestigations), o 100 kHz (550 t trigger imes highe ed by r t ahone an th per e rmaximum evolution ba signal r pasfr sing om fr an eqinductive uency for t encoder he shown oninve thest rigat otorions shaft. ), trigger Due ed by to the a boundary one per layer revolution analysis sign to al from be evaluated an inductive in the enc course oder on of the the rotor shaf hot-ﬁlm measur t. Due to the bounda ements and the ry la higher yer statistical analysis to be moments evaluated used in for the course this purpose, of th ae hot-film corresponding measurement database s an is necessary d the hig.hT er statis herefor -e, for ticathe l moments used for this purp phase averaging of each hot-ﬁlm ose, a correspondin sensor-depending g database on is ne the operating cessary. Ther point/speed efore, for the phase averaging of each hot-film sensor-depending on the operating point/speed of of the wake generator-up to 3000 samples were recorded. In this case, a sample is deﬁned as the wake genera the continuous tor-up to period30 of 00 sa 3 bar mpl wakes. es were reco For the rdetime-intensive d. In this case, ameasur sampleement is defin of edtwo- as dimensional the continuous peri ﬂow ﬁelds od ofwith 3 bar wa in part kes. For the ti over 1000me- measuring intensive measurement of positions (SFP measur two-di ements), men- the sion number al flow of fields w samples ith in inevitably part over 1 had 0 to 00 be mea reduced. suring Nevertheless, positions (SFP a meas minimum ureme number nts), the of 1000 number o samples f samples was still inev maintained itably hadher to be e. reduced. Nevertheless, a minimum number of RUB 1000 s To ample facilitate s was T106 still main pr taoﬁle ined here. hot-ﬁlm, Kulite and static pressure measurements in RUB RUB various To f radial acilitat (dir e Tection 106 of pro blade file hot height) -film, Ku positions, lite and a st modular atic press T106 ure meablade surement wass in realized. var- RUB The iousmodular radial (dblade irection is of made blade up hei of multiple, ght) positstackable ions, a modul element ar T1 s 0 and 6 can blade be was equipped realized. with various The modular instrumented blade is made modules up ofat mdif ultip fer le, ent sta blade ckable ele height men positions ts and can be equ within the ippe modular d with blade. various in In Figur strumented mo e 26b the assembled dules at diffe modular rent bl blade ade hei containing ght positi aons wi module thiwith n the SS modula hot-ﬁlm r instr blade umentation . In Figure 2 at6midspan b the assembled position mo is dul shown. ar blade Figur co ent 26 ainin c gives g a the module Kulite wsensor ith SS hot locations. -film instrumentation at midspan position is shown. Figure 26c gives the Kulite sensor loca- 5.4. Current Investigations and Results tions. As stated in the introduction, in multistage turbomachinery conﬁgurations, the proﬁle 5.4. Current Investigations and Results ﬂow is periodically affected by wakes of upstream proﬁles, perceivable by cyclical patterns regarding the ﬂow quantities. Dependent on Strouhal number Sr and ﬂow coefﬁcient As stated in the introduction, in multistage turbomachinery configurations, the pro- , individual components of the vortex system show a wake-induced, recurrent cycle file flow is periodically affected by wakes of upstream profiles, perceivable by cyclical of formation, weakening and displacement. For all investigations the same theoretical patterns regarding the flow quantities. Dependent on Strouhal number Sr and flow coef- RUB RUB (isentropic) T106 exit Reynolds number Re (based on T106 chord length C and ficient φ, individual components of the vortex exit,th system show a wake-induced, recurrent the theoretical exit velocity v analogous to sub-project C) was applied for the deﬁnition exit,th and adjustment of the operating point, deﬁned by Re = 210 and representing a exit,th typical value for LPT operation. To study the effect of periodic ﬂow perturbation, the RUB conditions of unperturbed T106 inﬂow were compared to two other cases, one with a moderate frequency of perturbation (Sr = 0.43, = 2.97) and another one with a high frequency of perturbation (Sr = 1.33, = 0.97), whereas Sr was deﬁned with ﬂow quantities RUB at midspan. From the hot-wire traverses, the turbulence intensity at the T106 inlet was Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 30 of 41 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 30 of 41 cycle of formation, weakening and displacement. For all investigations the same theoret- cycle of formation, weakening and displacement. For all investigations the same theoret- RUB RUB ical (isentropic) T106 RUB exit Reynolds number Re (based on T10 RUB 6 chord length C ical (isentropic) T106 exit Reynolds number Re , (based on T106 chord length C and the theoretical exit velocity v analogous to sub-project C) was applied for the and the theoretical exit velocity v , analogous to sub-project C) was applied for the definition and adjustment of the operating point, defined by Re =2 ∙ 10 and repre- definition and adjustment of the operating point, defined by Re =2 ∙ 10 and repre- senting a typical value for LPT operation. To study the effect of periodic flow perturba- senting a typical value for LPT operation. To study the effect of periodic flow perturba- RUB RUB tion, the cond tion, the cond itions o itions o f funpe unpe rturbed T rturbed T 106 106 in in flow w flow w ere compared t ere compared t o two other c o two other c ases, one ases, one Int. J. Turbomach. Propuls. Power 2021, 6, 9 30 of 40 with a moderate frequency of perturbation (Sr = 0.43, φ = 2.97) and another one with a high with a moderate frequency of perturbation (Sr = 0.43, φ = 2.97) and another one with a high frequenc frequenc y y o o f perturbation f perturbation ( S (S r = 1. r = 1. 33, 33, φ = 0.97), wher φ = 0.97), wher eas eas Sr w Sr w as de as de fine fine d with d with flow flow quantities quantities RUB RUB a att mi mi dspa dspa n. From the hot-wi n. From the hot-wi re tra re tra vv erse erse s, the turbulence i s, the turbulence i ntensi ntensi ty ta y ta the T106 t the T106 inl inl et wa et wa s s estimated estimated to b estimated to b to beebetween e between TI = 0.5% between TI = 0.5% TI = 0.5% in in the free in the free the free str stst re eam re am am an and an d TI = 2 d TI = 2 TI = 2.5% .5% .5% in in in tthe ht e IG he IG IGV V wake V wake wake wit without wit hout hout bar wake perturbation, whereas the bar wakes induce a periodic TI increase, reaching val- bar bar w wake akeperturbation, perturbation, wh wher erea eas s t the he ba bar r wake wakes s ind induce uce a per a periodic iodic TITI incre incr aease, se, reac reaching hing val- values ues of of it up to it up TI = to TI20%. = 20%. ues of it up to TI = 20%. 5.4.1. Incoming, Periodically Perturbed Flow Field 5.4.1. Incoming, Periodically Perturbed Flow Field 5.4.1. Incoming, Periodically Perturbed Flow Field For the characterization of the immediate bar wake impact, Figures 27 and 28 show For the characterization of the immediate bar wake impact, Figures 27 and 28 show For the characterization of the immediate bar wake impact, Figures 27 and 28 show RUB RUB hot-wire data, acquired in the axial gap between the wake generator and the T106 hot-wire data, acquired in the axial gap between the wake generator and the T106 RUB lead- hot-wire data, acquired in the axial gap between the wake generator and the T106 lead- leading edges with radial traverses. ing edges with radial traverses. ing edges with radial traverses. Figure 27. Time-resolved ﬂow ﬁeld quantities downstream of the rotating wake generator: velocity v Figure 27. Time-resolved flow field quantities downstream of the rotating wake generator: veloc- Figure 27. Time-resolved flow field quantities downstream of the rotating wake generator: veloc- (a ity v ( ), ﬂow a),angle flow a in ngle in c circumfer ircu ential mferential d direction irect i(o bn ) and α (b) and turbulence intensity TI ( turbulence intensity TI (c) over c) over channel channel height ity v (a), flow angle in circumferential direction α (b) and turbulence intensity TI (c) over channel height R/H for Sr = 1.33, φ = 0.97. R/H for Sr = 1.33, = 0.97. height R/H for Sr = 1.33, φ = 0.97. Figure 28. Time-averaged distributions of velocity v (a), flow angle in circumferential direction α Figure 28. Time-averaged distributions of velocity v (a), flow angle in circumferential direction α Figure (b) and turbulence intensity TI ( 28. Time-averaged distributions c) over channel height R/H downst of velocity v (a), ﬂow angle ream of the rotating wake gen- in circumferential direction (b) and turbulence intensity TI (c) over channel height R/H downstream of the rotating wake gen- erator for Sr = 1.33, φ = 0.97 and clean inflow, see [58]. (b) and turbulence intensity TI (c) over channel height R/H downstream of the rotating wake erator for Sr = 1.33, φ = 0.97 and clean inflow, see [58]. generator for Sr = 1.33, = 0.97 and clean inﬂow, see [58]. Thus, in Figure 27 the temporal evolution (phase-averaged quantities) of the velocity Thus, in Figure 27 the temporal evolution (phase-averaged quantities) of the velocity Thus, in Figure 27 the temporal evolution (phase-averaged quantities) of the velocity v (a), the flow angle in circumferential direction α (b) and the turbulence intensity TI (c) v (a), the flow angle in circumferential direction α (b) and the turbulence intensity TI (c) vover the channel height R/H are given for Sr = (a), the ﬂow angle in circumferential direction 1.33, φ (b) = 0.97 and . From al the turbulence l three flintensity ow quanti TI ties, (c) over the channel height R/H are given for Sr = 1.33, φ = 0.97. From all three flow quantities, over the channel height R/H are given for Sr = 1.33, = 0.97. From all three ﬂow quanti- minor but still detectable remains of the IGV secondary flow structures are evident. How- minor but still detectable remains of the IGV secondary flow structures are evident. How- ties, ever, much minor but more promin still detectable ent are the remains bar wak of thee IGV induc secondary ed effects, ﬂow causin structur g a comb es arinat e evident. ion of RUB ever, much more prominent are the bar wake induced effects, causing a combination of However, much more prominent are the bar wake induced effects, causing a combination periodic T106 inflow incidence (Δα ≈ 10°), a velocity defect (Δv > 5 m/s) and a turbu- RUB RUB periodic T106 inflow incidence (Δα ≈ 10°), a velocity defect (Δv > 5 m/s) and a turbu- of lence incr periodicease from the unperturbed level of TI T106 inﬂow incidence (D 10 )≈ , a 1.5 velocity % up todefect levels o (Dfv T> I 5 > m/s) 15% iand n the a turbulence lence incrincr ease from the unperturbed level of TI ease from the unperturbed level of TI≈ 11.5% .5% u up p tto o llevels evels o off T TII> >15% 15% i inn the the midspan section. Additionally, Figure 28 gives an overview regarding the time-averaged distributions of the discussed ﬂow ﬁeld quantities for the unperturbed and the two per- turbed cases. Despite the additional periodic, bar wake induced perturbations, a certain degree of homogenization for the velocity and the ﬂow angle can be assessed concerning the IGV non-uniformities near the endwalls. In terms of turbulence intensity, the increased rotational speed of the wake generator and thus the higher relative velocities for higher Sr also increases the general level of turbulence from TI < 2% (undisturbed) to TI 8% for Sr = 1.33 at midspan. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 31 of 41 midspan section. Additionally, Figure 28 gives an overview regarding the time-averaged distributions of the discussed flow field quantities for the unperturbed and the two per- turbed cases. Despite the additional periodic, bar wake induced perturbations, a certain degree of homogenization for the velocity and the flow angle can be assessed concerning the IGV non-uniformities near the endwalls. In terms of turbulence intensity, the in- creased rotational speed of the wake generator and thus the higher relative velocities for Int. J. Turbomach. Propuls. Power 2021, 6, 9 31 of 40 higher Sr also increases the general level of turbulence from TI < 2% (undisturbed) to TI ≈ 8% for Sr = 1.33 at midspan. RUB RUB 5.4.2. 5.4.2. Situation Situation wit within hin t the he T106 T106 Blade Blade Row Row RUB RUB W Wi ithin thinthe the T T106 106 blade blade ro row w, the incom , the incoming ing bar w bar wakes akes evoke evoke both large-scale both large-scale (blade (blade row kinematics) and micro-scale (proﬁle boundary layer properties) effects, wherefore the row kinematics) and micro-scale (profile boundary layer properties) effects, wherefore the following analysis is divided into two parts. following analysis is divided into two parts. First, Figure 29 describes the impact of the periodic perturbation on the blade loading First, Figure 29 describes the impact of the periodic perturbation on the blade loading c (referring to the exit state downstream of the stator row) in time-averaged view (a) c p (referring to the exit state downstream of the stator row) in time-averaged view (a) and and for time-resolved measurement data (b), where S/S represents the proportion of the for time-resolved measurement data (b), where S/S represents the proportion of the suc- ∗ ∗ suction or pressure side length. Thus, S/S = 0 describes the LE and S/S = 1 the TE. tion or pressure side length. Thus, S/S =0 describes the LE and S/S =1 the TE. The The time-averaged results (a) do not exhibit prominent changes between the undisturbed time-averaged results (a) do not exhibit prominent changes between the undisturbed and and the two disturbed cases. However, employing time-resolved data from ﬂush-mounted the two disturbed cases. However, employing time-resolved data from flush-mounted Kulite sensors (b), an evaluation of the extrema in proﬁle pressures at every sensor location Kulite sensors (b), an evaluation of the extrema in profile pressures at every sensor loca- indicates generally increasing unsteadiness and thus progressively unsteady blade loading tion indicates generally increasing unsteadiness and thus progressively unsteady blade with increasing Sr. This increasing unsteadiness is also observed in the simulations of the loading with increasing Sr. This increasing unsteadiness is also observed in the simula- periodically perturbed compressor cascade, investigates in sub-project B (see Section 3.4.5). tions of the periodically perturbed compressor cascade, investigates in sub-project B (see Interestingly, despite a general reduction in ﬂuctuation amplitudes for the lower Sr case Section 3.4.5). Interestingly, despite a general reduction in fluctuation amplitudes for the (Sr = 0.43), close to the proﬁle TE, the amplitudes are not reduced but feature a maximum lower Sr case (Sr = 0.43), close to the profile TE, the amplitudes are not reduced but feature excitation, which will be analyzed in the following. a maximum excitation, which will be analyzed in the following. RUB Figure 29. cp distributions for clean and perturbed inflow at T106 midspan, time-averaged re- RUB Figure 29. c distributions for clean and perturbed inﬂow at T106 midspan, time-averaged results sults (a), superposition of maximal fluctuation values (b), see [58]. (a), superposition of maximal ﬂuctuation values (b), see [58]. For a time-resolved analysis of the involved phenomena, Figure 30 shows the tem- For a time-resolved analysis of the involved phenomena, Figure 30 shows the temporal RUB poral evolution of the pressure fluctuations along the T10 RUB 6 profile at midspan for the evolution of the pressure ﬂuctuations along the T106 proﬁle at midspan for the already already introduced cases (Sr = 0.43, Sr = 1.33) and an intermediate perturbation frequency introduced cases (Sr = 0.43, Sr = 1.33) and an intermediate perturbation frequency (Sr = 0.90). (Sr = 0.90). In this depiction , 0<S/S <1 describes the suction side flow, whereas −1 < In this depiction, 0 < S/S < 1 describes the suction side ﬂow, whereas 1 < S/S < 0 ∗ ∗ S/S <0 represents the pressure side flow with S/S =0 marking the LE. For all three represents the pressure side ﬂow with S/S = 0 marking the LE. For all three cases, the cases, the periodic pressure fluctuations (as response on the bar wake convection) can be periodic pressure ﬂuctuations (as response on the bar wake convection) can be determined determined clearly across the profile surface, both on the pressure and the suction side. clearly across the proﬁle surface, both on the pressure and the suction side. Near the Near the suction side, the passage flow is compressed and accelerated by the approaching suction side, the passage ﬂow is compressed and accelerated by the approaching wake wake structure, so that the wake pushes a regime of accelerated flow in front of it, fol- structure, so that the wake pushes a regime of accelerated ﬂow in front of it, followed by a lowed by a region of low velocity fluid, which is vice versa on the pressure side, shaping region of low velocity ﬂuid, which is vice versa on the pressure side, shaping the typical, the typical, negative jet like structure of a wake within a blade passage [59,60]. negative jet like structure of a wake within a blade passage [59,60]. A direct comparison between the three shown scenarios indicates a shift of the re- A direct comparison between the three shown scenarios indicates a shift of the regions on gions on the the suctionsuction side side, which ar , which are mo e most excitedst exci by the ted by the periodic periodic perturbation. perturbation. From an From an exclusive exclusive major excitation centered around S/S* = 0.5 for Sr = 1.33, for decreasing Sr a major excitation centered around S/S* = 0.5 for Sr = 1.33, for decreasing Sr a weakening of this zone and a co-occurring augmentation of the periodic excitation towards the trailing edge is evident, while wake strength decreases and the time between wake events increases. The underlying phenomena, which are responsible for this behavior and take place in the proﬁle boundary layers, are discussed on the basis of hot-ﬁlm data. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 32 of 41 weakening of this zone and a co-occurring augmentation of the periodic excitation to- wards the trailing edge is evident, while wake strength decreases and the time between wake events increases. The underlying phenomena, which are responsible for this behav- Int. J. Turbomach. Propuls. Power 2021, 6, 9 32 of 40 ior and take place in the profile boundary layers, are discussed on the basis of hot-film data. RUBRUB Figure 30. Temporal evolution of pressure fluctuations along the T106 profile at midspan for Sr Figure 30. Temporal evolution of pressure ﬂuctuations along the T106 proﬁle at midspan for = 0.43 (a), Sr = 0.90 (b) and Sr = 1.33 (c), see [58]. Sr = 0.43 (a), Sr = 0.90 (b) and Sr = 1.33 (c), see [58]. For this, Figure 31 shows the time-resolved evolution of quasi wall shear stress (QWSS) For this, Figure 31 shows the time-resolved evolution of quasi wall shear stress RUB RUB along the T106 suction side at midspan for the low and high Sr cases. For means of (QWSS) along the T106 suction side at midspan for the low and high Sr cases. For comparison, on top of the diagrams the QWSS distribution for undisturbed ﬂow is added. means of comparison, on top of the diagrams the QWSS distribution for undisturbed flow The practicable quantity of QWSS is used as a qualitative means for the description of is added. The practicable quantity of QWSS is used as a qualitative means for the descrip- the boundary layer. Following the approach of Hodson [61], the measured voltage values tion of the boundary layer. Following the approach of Hodson [61], the measured voltage (E) are combined with the sensors’ behavior under zero-ﬂow conditions (E ) for a semi- values (E) are combined with the sensors’ behavior under zero-flow conditions 0 (E0) for a quantitative analysis of the wall shear stress : semi-quantitative analysis of the wall shear stress τw: 2 2 E E (7) τ ~ = QWSS. = QWSS. (7) Besides the already mentioned distortion of the local pressure and velocity field (neg- ative jet effect), the connected energy transfer introduces small-scale oscillations from the Besides the already mentioned distortion of the local pressure and velocity ﬁeld (nega- highly turbulent wake flow into the boundary layer flow, increasing the wall shear stress tive jet effect), the connected energy transfer introduces small-scale oscillations from the intermittently. For Sr = 1.33 the suction side boundary layer downstream of S/S* = 0.78 highly turbulent wake ﬂow into the boundary layer ﬂow, increasing the wall shear stress alternates between a state of low (but compared to the undisturbed reference case, still intermittently. For Sr = 1.33 the suction side boundary layer downstream of S/S* = 0.78 slightly increased) and distinctly elevated QWSS. Obviously, the period of time between alternates between a state of low (but compared to the undisturbed reference case, still indiv slightly idual w incra eased) ke events is and distinctly not suffic elevated ient enough QWSS. for t Obviously he bound,athe ry la period yer in t of he re time arbetween part of the suction individualside to fully rec wake events is o not ver, as the sufﬁcient unpert enough urbed st for the ate (shown ab boundary layer ove) is not re in the rear ached partin of between individual w the suction side to fully ake rs. This might b ecover, as the unperturbed e reasoned by st a combin ate (shown atio above) n of th is e f not ollo reached wing asin - pects: between individual wakes. This might be reasoned by a combination of the following as- pects: • Wake-induced boundary layer instabilities, like locally confined turbulent patches or Wake-induced boundary layer instabilities, like locally conﬁned turbulent patches or Klebanoff-Streaks, which are induced in the front part of the profile boundary layer Klebanoff-Streaks, which are induced in the front part of the proﬁle boundary layer far upstream, propagate slower (0.5 < v/vFS < 0.88 ) than the free stream (FS) and the far upstream, propagate slower (0.5 < v/v < 0.88) than the free stream (FS) and the FS wakes [62]. wakes [62]. • Calmed regions exert a damping effect on the boundary layer instabilities, thus coun- Calmed regions exert a damping effect on the boundary layer instabilities, thus teract transition and separation and spread while propagating downstream [63], counteract transition and separation and spread while propagating downstream [63], while their velocity of convection is also considerably reduced (0.3 < v/vFS < 0.5) while their velocity of convection is also considerably reduced (0.3 < v/v < 0.5). FS Summarized, these effects cause the characteristic QWSS evolution of Figure 31b, in- Summarized, these effects cause the characteristic QWSS evolution of Figure 31b, indi- dicating wake-induced transition. The turbulent regions of high wall shear stress, follow- cating wake-induced transition. The turbulent regions of high wall shear stress, following ing the wakes, are characterized by the stated propagation/velocity paths and are followed the wakes, are characterized by the stated propagation/velocity paths and are followed by by the calmed regions with still elevated QWSS, in turn. the calmed regions with still elevated QWSS, in turn. Int. J. Turbomach. Propuls. Power 2021, 6, 9 33 of 40 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 33 of 41 RUB Figure 31. Temporal evolution of QWSS along the T106 profile suction side at midspan for Sr = RUB Figure 31. Temporal evolution of QWSS along the T106 proﬁle suction side at midspan for 0.43 (a) and Sr = 1.33 (b), undisturbed condition shown above, see [58]. Sr = 0.43 (a) and Sr = 1.33 (b), undisturbed condition shown above, see [58]. Different than the continuous paths, which are evident for Sr = 1.33, for Sr = 0.43, a Different than the continuous paths, which are evident for Sr = 1.33, for Sr = 0.43, a wake-path discontinuity becomes obvious between S/S* = 0.6 and S/S* = 0.82. This altered wake-path discontinuity becomes obvious between S/S* = 0.6 and S/S* = 0.82. This altered pattern is essentially based on the differences in wake structure concerning flow angle pattern is essentially based on the differences in wake structure concerning ﬂow angle and and turbulence carried by the wakes. The less steep wake flow angle for lower Sr shifts turbulence carried by the wakes. The less steep wake ﬂow angle for lower Sr shifts the the position of wake impingent downstream. The path, labeled with (I) in Figure 31, rep- position of wake impingent downstream. The path, labeled with (I) in Figure 31, represents resents the accelerated fluid upstream of the actual wake, which slightly increase the the accelerated ﬂuid upstream of the actual wake, which slightly increase the QWSS, but does QWSS, but does not ca not carry substantial rry incr substa eased ntial turbulence increased turbulence for for a more pronounced a more pronounc effect. Path ed effect. (II) repr Path ( esents II) represents the actual subsequent the actual subsequent wake ﬂow. The wakcontained e flow. The turbulence contained turb now induces ulence now a mor in e - pronounced effect of the QWSS level. Nevertheless, the wake strength is reduced compared duces a more pronounced effect of the QWSS level. Nevertheless, the wake strength is to reduced Sr = 1.33, com resulting pared to in Sr = 1. an intermittent 33, resultin rg e-emer in an int ging erof mit atlocally ent re-em conﬁned erging separation. of a locally For con- Sr = 1.33 this separation is prevented. fined separation. For Sr = 1.33 this separation is prevented. 5.4.3. Impact on the Secondary Flow Structures 5.4.3. Impact on the Secondary Flow Structures In this last section, the combined impact of the bar wakes and the described modiﬁed In this last section, the combined impact of the bar wakes and the described modified boundary layer system on the secondary ﬂow system is portrayed on the basis of three boundary layer system on the secondary flow system is portrayed on the basis of three equidistant ﬂow ﬁeld snapshots of one bar wake period in Figure 32 for Sr = 1.33, = 0.97. equidistant flow field snapshots of one bar wake period in Figure 32 for Sr = 1.33, φ = 0.97. The shown quantity in the top of the ﬁgure (a) is the axial vorticity (AVO), which was The shown quantity in the top of the figure (a) is the axial vorticity (AVO), which was derived from the spatial gradients of the time-resolved velocity vector components. The derived from the spatial gradients of the time-resolved velocity vector components. The proﬁle TEs are highlighted with dashed lines. Comparing the three AVO-distributions, profile TEs are highlighted with dashed lines. Comparing the three AVO-distributions, both a vortex displacement as well as a weakening become evident, resulting from the both a vortex displacement as well as a weakening become evident, resulting from the RUB wake-boundary layer interaction in the T106 blade passage. Thus, especially in the hub RUB wake-boundary layer interaction in the T106 blade passage. Thus, especially in the hub region, a distinction between passage vortex (PV) and the pressure side leg of the horse region, a distinction between passage vortex (PV) and the pressure side leg of the horse shoe vortex (HSV-PL) is enabled for t/T = 1/3, as the HSV-PL slides beneath the PV and BP shoe vortex (HSV-PL) is enabled for t/TBP = 1/3, as the HSV-PL slides beneath the PV and pushes it along the suction side trailing edge radially inward, before it blends again with pushes it along the suction side trailing edge radially inward, before it blends again with the PV. As could be shown in detail in [52,53,55,56], this periodic and short-duration event the PV. As could be shown in detail in [52,53,55,56], this periodic and short-duration event is based on the upstream wake impact on the developing HSV-PL, which is massively is based on the upstream wake impact on the developing HSV-PL, which is massively diverted in the front part of the blade passage by the impinging wake structure. Also, the diverted in the front part of the blade passage by the impinging wake structure. Also, the unsteadiness of the suction side corner separation, shaping the concentrated shed vortex unsteadiness of the suction side corner separation, shaping the concentrated shed vortex (CSV) can be realized. Additionally, in the lower half of the ﬁgure the temporal evolution (CSV) can be realized. Additionally, in the lower half of the figure the temporal evolution of the turbulence intensity (TI) is shown. Different from the vorticity representation, the of the turbulence intensity (TI) is shown. Different from the vorticity representation, the turbulence intensity not only highlights the secondary ﬂow regions, but also emphasizes turbulence intensity not only highlights the secondary flow regions, but also emphasizes the inﬂuence of the bar wake with its increased turbulence. This becomes especially evident the influence of the bar wake with its increased turbulence. This becomes especially evi- for t/T = 2/3, when the wake becomes evident in the center of the passage between BP dent for t/TBP = 2/3, when the wake becomes evident in the center of the passage between the two Tes. Even after passing through the passage, the wake still transports signiﬁcant the two Tes. Even after passing through the passage, the wake still transports significant turbulence. Thus, in multistage environments, the subsequent blade row and the transition turbulence. Thus, in multistage environments, the subsequent blade row and the transi- processes occurring therein are still inevitably affected. tion processes occurring therein are still inevitably affected. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 34 of 41 Int. Int.J. J.T Turb urbomach. omach.Pr Prop opuls. uls. P Power ower 2021 2021 , , 66 , , x FOR PEER REVI 9 EW 34 34 of of 40 41 RUB Figure 32. Temporal flow field evolution in the T106 RUB exit flow field (Δx = 0.16 C) at 3 equidistant RUB Figure Figure 32. 32. T Temporal flow emporal ﬂow ﬁeld field evo evolution lution in in the the T106 T106 exit flow exit ﬂow ﬁeld field (D (Δ xx = = 0.16 0.16 C) at 3 C) at 3 equidistant equidistant time steps, Sr = 1.33, φ = 0.97. Axial vorticity (AVO) (a) and turbulence intensity (TI) (b). time steps, Sr = 1.33, φ = 0.97. Axial vorticity (AVO) (a) and turbulence intensity (TI) (b). time steps, Sr = 1.33, = 0.97. Axial vorticity (AVO) (a) and turbulence intensity (TI) (b). Finally Finally, , Figur Figuere 33 33 is me is meant ant toto clar clarifyify this this vortex vortex behavior even furth behavior even further by er by usin using suitable g suit- Finally, Figure 33 is meant to clarify this vortex behavior even further by using suit- A able VO iso-contours AVO iso-cont for ours the for individual the indivvortices idual vor and tices their and the temporal ir tempora evolution. l evolution. able AVO iso-contours for the individual vortices and their temporal evolution. RUB Figure 33. Temporal AVO ﬂow ﬁeld evolution (iso-contours) in the T106 exit ﬂow ﬁeld (Dx = 0.16 RUB Figure 33. Temporal AVO flow field evolution (iso-contours) in the T106RUB exit flow field (Δx = Figure 33. Temporal AVO flow field evolution (iso-contours) in the T106 exit flow field (Δx = C) with the time as the third dimension, Sr = 1.33, = 0.97. View of radial-circumferential plane (a), 0.16 C) with the time as the third dimension, Sr = 1.33, φ = 0.97. View of radial-circumferential 0.16 C) with the time as the third dimension, Sr = 1.33, φ = 0.97. View of radial-circumferential of radial-axial plane (b) and of the lower half of the secondary ﬂow system in a three-dimensional plane (a), of radial-axial plane (b) and of the lower half of the secondary flow system in a three- plane (a), of radial-axial plane (b) and of the lower half of the secondary flow system in a three- depiction (c), see [58]. dimensional depiction (c), see [58]. dimensional depiction (c), see [58]. In Figure 33a the familiar view against the axial ﬂow direction is given, showing In Figure 33a the familiar view against the axial flow direction is given, showing the In Figure 33a the familiar view against the axial flow direction is given, showing the the colored vortices of PV and CSV, whereas Figure 33b shows this situation with the colored vortices of PV and CSV, whereas Figure 33b shows this situation with the view colored vortices of PV and CSV, whereas Figure 33b shows this situation with the view view onto the time-axis (t/T ), indicating the wave-like behavior of the vortex-dynamics. BP onto the time-axis (t/TBP), indicating the wave-like behavior of the vortex-dynamics. Fur- onto the time-axis (t/TBP), indicating the wave-like behavior of the vortex-dynamics. Fur- Furthermore, this method of data representation clearly illustrates the combination of thermore, this method of data representation clearly illustrates the combination of peri- thermore, this method of data representation clearly illustrates the combination of peri- periodic weakening and the connected displacement, deﬁning the unsteadiness of the odic weakening and the connected displacement, defining the unsteadiness of the second- odic weakening and the connected displacement, defining the unsteadiness of the second- secondary ﬂow system. On the one hand, the interaction mechanisms between HSV-PL ary flow system. On the one hand, the interaction mechanisms between HSV-PL and PV ary flow system. On the one hand, the interaction mechanisms between HSV-PL and PV and PV (periodic displacement and weakening) can be detected. On the other hand, (periodic displacement and weakening) can be detected. On the other hand, the consider- (periodic displacement and weakening) can be detected. On the other hand, the consider- the considerable magnitude of radial CSV-displacement resulting from HSV-PL and PV able magnitude of radial CSV-displacement resulting from HSV-PL and PV manipulation able magnitude of radial CSV-displacement resulting from HSV-PL and PV manipulation manipulation is realized. Following the short-duration weakening of PV and HSV-PL, is realized. Following the short-duration weakening of PV and HSV-PL, the CSV is shifted is realized. Following the short-duration weakening of PV and HSV-PL, the CSV is shifted the CSV is shifted towards the endwalls shortly after, as well. Supplementing, Figure 33c towards the endwalls shortly after, as well. Supplementing, Figure 33c shows a three-di- towards the endwalls shortly after, as well. Supplementing, Figure 33c shows a three-di- shows a three-dimensional depiction of the lower ﬂow channel half between R/H = 0 and mensional depiction of the lower flow channel half between R/H = 0 and R/H = 0.5, thus mensional depiction of the lower flow channel half between R/H = 0 and R/H = 0.5, thus R/H = 0.5, thus only the near-hub part of the secondary ﬂow system. This helps to clarify only the near-hub part of the secondary flow system. This helps to clarify the dynamics of only the near-hub part of the secondary flow system. This helps to clarify the dynamics of the dynamics of interaction between PV and HSV-PL, illustrating the approaching HSV-PL, its impact on the PV and the following radial PV-displacement. Int. J. Turbomach. Propuls. Power 2021, 6, 9 35 of 40 5.5. Work in Progress Upcoming activities in sub-project D include the application of particle image ve- RUB locimetry (PIV) for an extended insight into the T106 passage ﬂow, the consideration of tip leakage ﬂow, the resulting tip leakage vortices and their impact on the secondary ﬂow RUB system. For this, a radial gap is realized between the T106 -proﬁles and the hub endwall contour. This increase in complexity means another step from the scientiﬁc point of view towards multistage turbomachine ﬂow. 6. Summary and Conclusions The current paper presents investigations of four German research institutes from a joint research project on near-wall ﬂow in axial compressors and axial turbines. Both numerical and experimental methods were exploited on linear and annular setups to evaluate the inﬂuence of incoming periodic disturbances, which can be seen in rotor- stator-interactions, on the ﬂow in a passage of turbomachinery. Furthermore, analyzing factors arising from the problem of transformation between a linear cascade and the rotating machine, such as the relative motion between blades/vanes and the corresponding sidewall, broadened the understanding of the secondary ﬂow phenomena and allowed the assessment of the transferability of the obtained ﬁndings. In sub-project A the comparison of a periodically disturbed and un-disturbed single rotor row is used to evaluate the inﬂuence of incoming wakes on the secondary ﬂow, especially the tip leakage vortex, in the blade passage. The presented results show a redistribution of mass ﬂow over the channel height and a periodic effect of the incoming wakes on the TLV as well as on the suction side separation. Changing the hub wall motion in a stator conﬁguration allowed the examination of the inﬂuence of incoming boundary layer skew, the relative motion between vane tip and corresponding endwall, and a combined effect on the tip leakage vortex. Sub-project B considered a linear compressor cascade where the investigated vane was derived from the tip proﬁle of the rotor considered in sub-project A. Investigations were conducted using high resolving DNS and Wall-Resolving LES. In doing so, the effects of relative wall motion and thickness of the boundary layer on the vortical structures within the cascade were studied. It is clearly shown that the relative wall motion causes a departure of the tip leakage vortex from the blade proﬁle and furthermore, a stratiﬁcation of the ﬂow ﬁeld at the cascade exit. Complementary, a linear low-pressure turbine cascade was used for high-speed wind tunnel measurements and URANS simulations in sub-project C. As the authors illustrate, a decrease of the inlet endwall boundary layer height and periodically incoming wakes both lead to secondary ﬂow attenuation in the turbine exit ﬂow. Inside the blade passage, the variation of inlet boundary layer thickness inﬂuences the endwall loss development starting around the midpoint of the blade passage. Furthermore, it could be shown that the unsteady inﬂow conditions lead to a spatial redistribution of the loss generation inside the blade passage. A premature loss increase due to wake interaction with the blade surface boundary layer is followed by attenuation of the proﬁle- and secondary losses in the aft-section of the blade passage. However, the level of integral loss in the turbine exit ﬂow ﬁeld remains almost unchanged. Finally, in sub-project D a large-scale annular turbine test rig was considered using modiﬁed blades of those that were studied in sub-project C. Customized surface-mounted hot-ﬁlm sensor arrays were used to investigate the near-wall ﬂow for several perturbation frequencies of upstream installed rotating bars. Thus, it was possible to discover in detail, how periodically incoming wakes lead to a recurrent cycle of formation, weakening and displacement of speciﬁc components of the underlying vortex structures as well as a periodic manipulation of the proﬁle boundary layer system. To sum it up, the collaborative activity of the four research institutes, presented in this publication, helps to deepen the understanding of near-wall ﬂow, vortex systems and corresponding ﬂow phenomena in turbomachines. The investigation of periodically Int. J. Turbomach. Propuls. Power 2021, 6, 9 36 of 40 distortions by incoming wakes and their interaction with the near-wall ﬂow ﬁeld in all investigated conﬁgurations (compressor and turbine, linear and annular cascades) revealed a strong inﬂuence of the wakes on the blade proﬁle boundary layer development, especially through wake induced transition processes, while the secondary ﬂow vortex system fea- tures a periodic displacement and changing strength. Regarding the systematic increase of complexity through the different geometric modiﬁcations and test rigs and thus activation of speciﬁc ﬂow effects it can be concluded that the inlet boundary layer is of high relevance for the turbine endwall secondary ﬂows, where no radial clearances are present. In a linear compressor cascade with radial clearance only the skew of the inlet boundary layer but not its thickness showed a relevant effect on the ﬂow ﬁeld. Experimental and numerical analysis in sub-project A and B clearly illustrated the effect of the relative side wall velocity on the development of the tip leakage vortex and its loss of coherence towards the exit of the blade passage. Ongoing work will apply additional measurement techniques (optical measurements, temperature sensitive paint, etc.) to provide further high-quality data for the validation of advanced numerical methods and improved physical understanding. Author Contributions: Conceptualization, D.E., J.F., R.M., R.N.; Data curation, B.K., J.V.-M., M.S., T.S.; Formal analysis, B.K., J.V.-M., M.S., T.S.; Funding acquisition, D.E., J.F., R.M., R.N.; Investigation, B.K., J.V.-M., M.S., T.S.; Methodology, B.K., J.V.-M., M.S., T.S.; Project administration, R.M.; Resources, D.E., J.F., F.d.M., R.M., R.N.; Supervision, D.E., J.F., F.d.M., R.M., R.N.; Validation, B.K., J.V.-M., M.S., T.S.; Visualization, B.K., J.V.-M., M.S., T.S.; Writing—original draft preparation, D.E., B.K., J.V.-M., M.S., T.S.; Writing—review and editing, D.E., B.K., J.F, J.V.-M., R.M., R.N.; M.S., T.S. All authors have read and agreed to the published version of the manuscript. Funding: The investigations reported in this article were conducted within the framework of the joint research project “Near-Wall Flow in Turbomachinery Cascades” which was funded and supported by the Deutsche Forschungsgemeinschaft (DFG) under grant number PAK 948. The responsibility for the contents of this publication lies entirely by the authors. Data Availability Statement: Not applicable. Acknowledgments: J.V.-M. and J.F. acknowledge the computational resources provided by the Centre for Information Services and High Performance Computing (ZIH) at the TU Dresden. Additionally, the help of M. Plath and G. Bobbe is thanked. Conﬂicts of Interest: The authors declare no conﬂict of interest. Abbreviations The following symbols and abbreviations are used in this manuscript: Roman Symbols ax Axial Direction (for the annular cascade) C Chord c Friction Coefﬁcient c Pressure Coefﬁcient D Diameter H Passage Height, Channel Height H Shape Factor Dh Change in Total Enthalpy M Mach Number m Mass Flow P Pitch Distance p, p , p Static, Dynamic and Total Pressure dyn r Spanwise Direction (for the annular cascade) Re Reynolds Number Int. J. Turbomach. Propuls. Power 2021, 6, 9 37 of 40 s Gap Size S Distance along Blade Proﬁle Ds Change in Entropy Sr Strouhal Number t Time T Bar Passing Period BP TI Turbulence Intensity [%] u Circumferential speed v Velocity x Axial Direction y Pitchwise Direction (for the linear cascade) y+ Non-Dimensional Wall Distance z Spanwise Direction (for the linear cascade) Greek Symbols Yaw Angle, Flow Angle (1 for inﬂow, 2 for outﬂow) with respect to pitchwise direction Flow Angle in Pitchwise Direction with respect to axial direction Boundary Layer Thickness Normal Distance to a Wall Total Pressure Loss Coefﬁcient (Equation (1) for compressor, Equation (6) for turbine) Pitch Distance (For the annular cascade) 2nd Eigenvalue of Velocity Tensor Density Wall Shear Stress Flow Coefﬁcient Abbreviations AVO Axial Vorticity b Bar (used as a subscript) BL Boundary Layer CFD Computational Fluid Dynamics CSV Concentrated Shed Vortex CTA Constant Temperature Anemometry CV Corner Vortex DNS Direct Numerical Simulation DP Design Point EARSM Explicit Algebraic Reynolds Stress Model EXP Experiment FHP Five Hole Probe FMP Fast Measuring Pressure Probe FS Free Stream FTT Flow Through Time HGK High-Speed Cascade Wind Tunnel (Hochgeschwindigkeits-Gitterwindkanal) HS Half-Span HSV Horse Shoe Vortex IGV Inlet Guide Vane LSRC Low-Speed Research Compressor LE Leading Edge LES Large Eddy Simulation LPT Low Pressure Turbine MCV Million Control Volumes MP Measuring Plane MS Midspan NI National Instruments PIV Particle Image Velocimetry PL Pressure Side Leg Int. 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International Journal of Turbomachinery, Propulsion and Power – Multidisciplinary Digital Publishing Institute

Published: May 8, 2021

Keywords: near-wall flow; boundary layer; wake interaction; compressor; turbine; cascade; experimental investigation; CFD; large eddy simulation; direct numerical simulation

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Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

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Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

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