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Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow within a High-Pressure Gas Turbine Stage

Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow within a High-Pressure Gas... International Journal of Turbomachinery Propulsion and Power Article Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow within a High-Pressure Gas Turbine Stage Paolo Gaetani and Giacomo Persico * Laboratory of Fluid-Machines, Energy Department, Politecnico di Milano Via Lambruschini 4, 20156 Milano, Italy; paolo.gaetani@polimi.it * Correspondence: giacomo.persico@polimi.it; Tel.: +39-02-2399-8605 † This manuscript is an extended version of our meeting paper published in the Proceedings of the 14th European Turbomachinery Conference, Gdansk, Poland, 12–16 April, 2021. Abstract: In stator–rotor interaction studies on axial turbines, the attention is commonly focused on the unsteady rotor aerodynamics resulting from the periodic perturbations induced by the stator flow structures. Conversely, less interest has been historically attracted regarding the influence of the rotor on the flow released by the stator, correlated to propagation of the blade potential field upstream of the rotor leading edge. In this paper, experiments in the research high-pressure turbine of the Laboratory of Fluid-Machines of the Politecnico di Milano, performed by applying a fast- response aerodynamic pressure probe, alongside fully-3D time-accurate CFD simulations of the flow, are combined with the aim of discussing the rotor-to-stator interaction. While rotating, the rotor induces periodic perturbations on the pressure and velocity field in the stator–rotor gap, altering the evolution of the total quantities and the flow rate discharged by each stator channel and eventually triggering energy-separation effects which result in total pressure and total temperature oscillations in the stator-exit flow. Such oscillations were found to rise up to almost 10% of the stage total temperature drop. Citation: Gaetani, P.; Persico, G. Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow Keywords: high-pressure turbines; blade-row interaction; cascade potential field; energy separation; within a High-Pressure Gas Turbine unsteady measurements; time-accurate CFD Stage. Int. J. Turbomach. Propuls. Power 2021, 6, 28. https://doi.org/ 10.3390/ijtpp6030028 1. Introduction Academic Editor: Claus Sieverding The need for continuous improvements in gas turbine performance, in terms of effi- ciency and rangeability, alongside the need of a deeper understanding of the flow physics, Received: 26 June 2021 still asks for important theoretical and experimental efforts and research. A key field of Accepted: 6 July 2021 interest—among the many involved in gas turbine studies—is thermo-fluid-dynamics, Published: 13 July 2021 pillar for getting a holistic comprehension of turbomachinery and for their optimal design. In this context, one of the major interests in present-day research is the interaction between Publisher’s Note: MDPI stays neutral system components, as well as stationary and rotating rows of turbomachinery. Multi- with regard to jurisdictional claims in ple classes of problems can be acknowledged, such as the combustor–1st turbine stage published maps and institutional affil- interaction, the stator–rotor interaction in both high-pressure and low-pressure turbines, iations. the last turbine stage–diffuser interaction, the impeller–diffuser interaction and the surge in compressors. With specific reference to turbines stages, the stator–rotor interaction consists of potential field interference, wake/shock/vortex-blade interaction, wake-wake interaction Copyright: © 2021 by the authors. and wake/vortex-secondary flow interaction [1–13]. In general, most of the papers focus Licensee MDPI, Basel, Switzerland. on the effect of the stator flow structures on the rotor aerodynamics and performance, as the This article is an open access article spatial non uniformities at the stator exit result in time-varying inlet boundary conditions distributed under the terms and for the rotor. Only a few studies report about the effects of the rotor potential field on conditions of the Creative Commons the stator, for example, [14] for subsonic turbines and [15] for transonic high-pressure Attribution (CC BY-NC-ND) license turbines; these studies typically include measured data on the stator blade surface. Thanks (https://creativecommons.org/ licenses/by-nc-nd/4.0/). to the recent improvements in measuring techniques—such as fast response aerodynamic Int. J. Turbomach. Propuls. Power 2021, 6, 28. https://doi.org/10.3390/ijtpp6030028 https://www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2021, 6, 28 2 of 17 pressure probes—and CFD codes, it is now possible to more proficiently track these features, also considering the detailed flow configuration in-between the blade rows, i.e., in the stator–rotor axial gap. When discussing the flow unsteadiness in turbomachines, one basic observation is the inherent link between unsteady flow and work exchange [16], related to the coupling, valid for inviscid flows, between the material derivative of the total enthalpy and the local time-derivative of the static pressure: Dh ¶p r = (1) Dt ¶t The same concept, when applied to a wake incoming on a turbine cascade and impinging on the blades, was observed to produce a local increase in the total enthalpy and pressure, due to onset of energy separation effects [17]. Similar features may apply also to the potential field, with the important difference that the pressure field also propagates upstream of a cascade (at least up to the sonic throat of the upstream cascade, if this latter is choked) which might lead, in case of a rotor, to the onset of unexpected flow features within the stator–rotor axial gap. Such features, not visible if applying time-mean measurement techniques or steady computational models, can instead be highlighted by resorting to unsteady measurements and time-accurate CFD simulations. This is indeed the focus of the present paper, which aims at discussing the effect of the rotor potential field on the flow released by the stator, thanks to a combined experimental and numerical approach. The paper is structured as follows: at first the experimental and numerical approaches are described, then the experimental results are discussed with the support of CFD results for physical interpretations and, finally, some conclusions are derived. 2. Test Facility and Measuring Techniques The test rig and instrumentation applied in the present research work are already described in other papers: see, for example, [18]. In this section, they are briefly recalled. 2.1. Test Rig and Axial Turbine Stage The test rig run for the present investigation is the high-speed test rig for turbine and compressor located at the Laboratory of Fluid Machine (LFM) of the Energy dept. of the Politecnico di Milano. It consists of a radial section where a centrifugal compressor is run and, in the present investigation, it feeds the turbine with the proper pressure ratio and flow rate; its maximum rotational speed is 45,000 rpm with a power available upstream of the gearbox of 800 kW. The radial section is then followed by a cooler to set the temperature level of the rig, a venturi pipe to measure the flow rate and a throttling section to control the expansion ratio made available to the turbine. The turbine is located in an axial section, whose maximum rotational speed is 20,000 rpm. The axial turbine stage is a single stage, not cooled, representative of a high pressure one. The main features are reported in Table 1; in addition, the stator blade is leaned by 12 on the pressure side and at midspan it has a geometrical discharge angle of 75.4 . The rotor is bowed with a constant outlet angle of 67.7 , it has a clearance at tip of 0.6 mm and a blade height of 50 mm (clearance included). The axial distance between the stator and the rotor is equal to one stator axial chord (30.6 mm), easing the probe insertion. Int. J. Turbomach. Propuls. Power 2021, 6, 28 3 of 17 Table 1. Stage geometry and operating conditions. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 3 of 18 n [rpm] G [kg/s] Tt [K] in Operating Condition 1.35 7000 3.5 323 h [mm] t /h D (mm) gap/c C M x,V Geometry Table 1. Stage geometry and operating conditions. 50 0.015 350 1.00 Blade Rows Nb  AR " β n [rpm] G [kg/s] Ttin [K] Vane 22 1.20 0.83 75.2 Operating Condition 1.35 7000 3.5 323 Rotor 25 1.25 0.91 115.3 h [mm] tC/h DM (mm) gap/cx,V Geometry 50 0.015 350 1.00 Measurements were taken at 71% of the stator axial chord downstream of the stator Blade Rows Nb σ AR ε trailing edge, all over the channel height: the measurement grid counts 320 points (16 points Vane 22 1.20 0.83 75.2 on the stator pitch, 20 points along the blade span) on each stator channel. Figure 1 reports Rotor 25 1.25 0.91 115.3 a picture of the stage and a sketch of the meridional section. (a) (b) Figure 1. Picture of the turbine stage (a) and sketch of the meridional section (b). Figure 1. Picture of the turbine stage (a) and sketch of the meridional section (b). 2.2. Measurement Techniques 2.2. Measurement Techniques In the present study, besides the instrumentation for the rig management, only a Fast In the present study, besides the instrumentation for the rig management, only a Fast Response Aerodynamic Pressure Probe (FRAPP) was applied. The reader is referred to Response Aerodynamic Pressure Probe (FRAPP) was applied. The reader is referred to [19] [19] for a picture of the present-day FRAPP, design, operation and technology available for a picture of the present-day FRAPP, design, operation and technology available at at Politecnico di Milano and to [11,13,18] for the FRAPP application in the rig. Politecnico di Milano and to [11,13,18] for the FRAPP application in the rig. The FRAPP here applied has a cylindrical head (diameter of 2 mm) where a single The FRAPP here applied has a cylindrical head (diameter of 2 mm) where a single sensor sensor is is inserted inserted (K (Kulite, ulite, model model XCQ XCQ062) 062) and and conn connected ected to to the the e external xternal env envir ironment onment b by y a hole whose diameter is 0.35 mm. The probe promptness, evaluated on a shock tube, is a hole whose diameter is 0.35 mm. The probe promptness, evaluated on a shock tube, is 100 kHz after digital compensation thanks to the very small size of the line-cavity system 100 kHz after digital compensation thanks to the very small size of the line-cavity system facing facing the se the sensor nsor. . The The prpr obe obis e is appl appliedied in in theth absolute e absolu frame te frame of refer of r ence eference as a virtual as a virt 3 holes ual 3 pr holes obe p by rob rotating e by ro itta ar tin ound g it a itsround own stem its oand wn s then tem and re-phasing then r the e-pmeasur hasing the ements memaking asuremen use ts of the key-phasor. Each pressure data set is acquired at 500 kHz and has 500,000 samples. making use of the key-phasor. Each pressure data set is acquired at 500 kHz and has In addition to the standard use described in the aforementioned papers, by applying 500,000 samples. the methodology proposed in [20], it is possible to have a qualitative evaluation of the In addition to the standard use described in the aforementioned papers, by applying turbulence level. Thanks to this quantity, it is possible to track and evaluate the viscous the methodology proposed in [20], it is possible to have a qualitative evaluation of the structure released by the stator. turbulence level. Thanks to this quantity, it is possible to track and evaluate the viscous For the specific investigation, each rotor pitch has been discretized by means of structure released by the stator. 40 points. For the specific investigation, each rotor pitch has been discretized by means of 40 As for the rig instrumentation, the inlet and outlet temperatures are monitored by T points. thermocouple, whose uncertainty after calibration is 0.3 C. As for the rig instrumentation, the inlet and outlet temperatures are monitored by T The stage inlet and outlet pressure level are measured by means of Kulite transducers thermocouple, whose uncertainty after calibration is 0.3 °C. (model XT190) whose uncertainty, after calibration, is 60 Pascal. The stage inlet and outlet pressure level are measured by means of Kulite transducers (model XT190) whose uncertainty, after calibration, is 60 Pascal. FRAPP data reduction is based on the phase-averaging techniques. First, the pressure measurements are phase averaged by referring to the key-phasor signal: the averaged value in each interval (40 per rotor pitch) is thus the result of about 12,000 samples. Sec- ond, by applying the calibration matrices, they are used to derive the flow quantities in Int. J. Turbomach. Propuls. Power 2021, 6, 28 4 of 17 FRAPP data reduction is based on the phase-averaging techniques. First, the pressure measurements are phase averaged by referring to the key-phasor signal: the averaged value in each interval (40 per rotor pitch) is thus the result of about 12,000 samples. Second, by applying the calibration matrices, they are used to derive the flow quantities in terms of total and static pressure, flow angle. Finally, assuming a total temperature constant across the stator, the velocity field is determined and—by the peripheral speed—the flow conditions in the rotating frame of reference are calculated. As it will be discussed in the last section, the total temperature fluctuates by about 1 K; the corresponding velocity fluctuation is expected to be of the order of 0.1% and, hence, negligible, also considering that the Mach number is correct coming from a phase-resolved data reduction. Overall, pressure values have an averaged uncertainty of 0.5% of the kinetic head measured by the FRAPP. The phase averaged signals for the different stator positions (in all the blade span positions) are re-organized in order to map the stator—rotor interaction for the different stator to rotor positions. The time mean quantities in the absolute frame of reference are calculated by averaging in time the phase averaged flow quantities. The time mean quantities in the rotating frame of reference are calculated by averaging the stator to rotor interaction positions, acknowledging the rotor pitch periodicity. 3. CFD Model and Experimental Validation In this study, CFD simulations mainly act as support to the interpretation of the experimental result. The calculations were performed using ANSYS-CFX, applying the flow model developed at Politecnico di Milano for turbomachinery flow simulations, discussed in detail in [21] and briefly summarized in the following. Fully 3D and time-resolved calculations were performed, modeling the fluid as perfect gas and introducing turbulence effects by resorting to the fully-turbulent k-! SST model. The near-wall resolution was specified so to guarantee y < 1 on endwalls and on blade surfaces, thus avoiding the use of wall functions. Unsteady terms are discretized with an implicit second order scheme, the advection terms with a high-resolution total-variation-diminishing scheme, the diffusive terms with a second order central scheme. Simulations were performed by assigning, at the inlet, the measured radial profile of total pressure, uniform total temperature, axial flow direction and a uniform turbulence intensity of 2.5%, resulting from dedicated hot-wire measurements (the eddy viscosity ratio was set equal to 25, following the recommended expression proposed by the solver). A radial-equilibrium distribution of static pressure was assigned at the outlet. Coupled stator–rotor simulations were performed, first resolving the flow in steady- state fashion using a mixing-plane stator–rotor interface for initialization and then moving to time-resolved analysis. Given the different blade numbers between the stator and the rotor, to simulate the full stator–rotor coupling (i.e., also the rotor-to-stator interaction and not only the stator-to-rotor interaction as was conducted in [21] where only the unsteady flow in the rotor was solved) while saving computational cost, the time-inclined solution strategy proposed in [22] was adopted. By virtue of this method, spatial-temporal solutions are obtained so to guarantee automatically the phase-lag between periodic boundaries and neither multiple channels nor alteration of the cascade solidity (or blade scaling) are required. The solver integrates the equations over structured meshes composed by hexahedral elements. A grid-dependence study was performed to select the proper spatial resolution. The study was conducted by keeping constant the near-wall resolution so that the boundary layer is properly resolved on both blade walls and hub and shroud walls for each of the tested meshes. The mesh dimension ranged from 2.2 million to 18.4 million cells for the entire stage; overall cascade/stage performance data as well as detailed spanwise profiles were considered to judge the influence of spatial resolution. Grid-independent results were achieved for stator and rotor meshes composed by 4.6 million cells, for a total of 9.2 million cells (the difference in stage efficiency with respect to the result obtained with the finest Int. J. Turbomach. Propuls. Power 2021, 6, 28 5 of 17 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 5 of 18 mesh resulted below 0.1%). The final meshes of each blade row, reported in Figure 2, are composed by 140 cells in spanwise direction and 33,000 cells in each blade-to-blade layer. (a) (b) Figure 2. Computational meshes of the stator (a) and rotor (b) blade rows after grid-dependence study. Figure 2. Computational meshes of the stator (a) and rotor (b) blade rows after grid-dependence study. The The tim timeestep stepwas was se set t to to 1/56 1/56of of th thee ro rotor tor b blade lade p passing assing p period eriod ( (corr corresp esponding ondingto to about about 0. 0.25 25°) ); ; t the he unsteady unsteadysolution solutionr esulted resulted smooth smooth (d (due ue to the to the s ubsonic subsonic flow reg flow regime) ime) and and further further re reductions ductions of of the the time time step wer step weree not not found found to to alter alter the the per performance formance pred prediction iction and and the the flow flow morphology morphology. . The The specif specific ic time time step step value valu was e wsel as se ected lected to optimize to optimithe ze the sampling sampliof ng the 3D solution for post-processing (since the stage periodicity 22 25 is close to 7 8 and of the 3D solution for post-processing (since the stage periodicity 22 × 25 is close to 7 × 8 56 is the least common value of these two numbers). The periodic solution was achieved and 56 is the least common value of these two numbers). The periodic solution was after 20 periods (the first 12 ones run with a larger time step, 1/25 of the rotor blade passing achieved after 20 periods (the first 12 ones run with a larger time step, 1/25 of the rotor period). The computational cost of the time-resolved simulation was about one week on a blade passing period). The computational cost of the time-resolved simulation was about 40-processor cluster. one week on a 40-processor cluster. Before simulations are used to aid the interpretation of the experiments, experiments Before simulations are used to aid the interpretation of the experiments, experiments are used to assess the simulation results. Figure 3 shows a set of spanwise profiles, com- are used to assess the simulation results. Figure 3 shows a set of spanwise profiles, com- paring the computations and measurements both at the stator and rotor exit. The top-left paring the computations and measurements both at the stator and rotor exit. The top-left frame of Figure 3 reports the distribution of total pressure loss coefficient (Yloss) at the frame of Figure 3 reports the distribution of total pressure loss coefficient (Yloss) at the stator exit and shows a remarkable agreement between experiment and calculations. It is to stator exit and shows a remarkable agreement between experiment and calculations. It is be noted that the experimental trend interrupts at 10% span, due to limitations in the probe to be noted that the experimental trend interrupts at 10% span, due to limitations in the traversing, so the severe increase of loss in the hub region predicted by the numerical trend probe traversing, so the severe increase of loss in the hub region predicted by the numer- cannot be entirely visible in the measurements (but it is outlined in the bottom part of the ical trend cannot be entirely visible in the measurements (but it is outlined in the bottom experimental profile). This generation of loss in the hub region is driven by a hub clearance part of the experimental profile). This generation of loss in the hub region is driven by a in the region of the blade tail, whose effect combines with the inherent cascade corner hub clearance in the region of the blade tail, whose effect combines with the inherent cas- vortex to generate a wide vortex counter-rotating with the hub passage vortex. More details cade corner vortex to generate a wide vortex counter-rotating with the hub passage vor- on the stator aerodynamic will be discussed later, when analyzing the flow configuration. tex. More details on the stator aerodynamic will be discussed later, when analyzing the The remaining three frames of Figure 3 report the spanwise profiles of Mach number, flow configuration. deviation angle (defined as the difference between the relative flow angle and the blade metallic angle) and absolute flow angle downstream of the rotor. Again, a good agreement was found between simulations and experiments, especially below 80% span. The spanwise flow configuration appears highly non uniform, marking the presence of large over-turning (i.e., low/negative deviation angle) region at 20% and 80% span caused by the secondary flows and an underturning region at midspan, where the two large rotor passage vortices come to interact. The simulations capture well the radial extension and the spanwise migration of the vortices, as well as their impact on the flow angle. Larger discrepancies appear only in the top 20% span, where a wide tip leakage vortex develops and proves to be challenging for the turbulence modeling used in this study. Int. J. Turbomach. Propuls. Power 2021, 6, 28 6 of 17 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 6 of 18 (a) (b) (c) (d) Figure 3. Measured and computed spanwise profiles. (a) Yloss at stator- exit; (b) Mach number at rotor exit. (c) rotor-exit Figure 3. Measured and computed spanwise profiles. (a) Yloss at stator- exit; (b) Mach number at rotor exit. (c) rotor-exit deviation angle; (d) and absolute flow angle. deviation angle; (d) and absolute flow angle. The remaining three frames of Figure 3 report the spanwise profiles of Mach number, Accordingly, a very good quantitative agreement is also obtained in terms of cascade deviation angle (defined as the difference between the relative flow angle and the blade and stage efficiency. The overall stator loss coefficient, estimated from the experiments metallic angle) and absolute flow angle downstream of the rotor. Again, a good agreement equal to 5.9%, resulted 5.4% from the simulation (averaging over the span covered by the was found between simulations and experiments, especially below 80% span. The measurement traverse). The total-total stage efficiency, calculated as the ratio between the spanwise Euler work flow (computed configuration a as theppears highly non difference between uniform, ma the UV terms rkin weight g the presenc ed on the e of lar flowge rate over-t upstr urn eam ing (i. and e.,downstr low/negeam ativeof dev the iat rio otor) n anand gle) the regitotal on atto 20% static and 80% isentr sp opic anenthalpy caused by drthe secon op, is estimated dary flow as s 86.4% and an under from experiments, turning reg with ion at anmidspan uncertainty , where the quantified two in large 0.5% rotor and parss esulted age voequal rtices com to 85.5% e to iin nter the act CFD . The simulation. simulations capture well the radial extension and The quantitative and qualitative reliability resulting from this assessment study indi- the spanwise migration of the vortices, as well as their impact on the flow angle. Larger cate that the present simulation can be used as an effective tool for the physical interpreta- discrepancies appear only in the top 20% span, where a wide tip leakage vortex develops tion of experimental data. and proves to be challenging for the turbulence modeling used in this study. Accordingly, a very good quantitative agreement is also obtained in terms of cascade 4. Results and stage efficiency. The overall stator loss coefficient, estimated from the experiments This section presents the results of the flow downstream of the stator, first neglecting equal to 5.9%, resulted 5.4% from the simulation (averaging over the span covered by the the stator–rotor interaction and then highlighting its effect. The flow field is discussed first measurement traverse). The total-total stage efficiency, calculated as the ratio between the from the perspective of a stationary observer, to show what discharged by the stator and Euler work (computed as the difference between the 𝑈𝑉 terms weighted on the flow rate then in the rotating frame of reference, to present what enters into the rotor according to its upstream and downstream of the rotor) and the total to static isentropic enthalpy drop, is own perspective. estimated as 86.4% from experiments, with an uncertainty quantified in ±0.5% and re- Results will be presented first in a time-mean form to evidence the gross features of sulted equal to 85.5% in the CFD simulation. the flow and secondly by the description of the different interaction phases between the The quantitative and qualitative reliability resulting from this assessment study in- stator and the rotor. dicate that the present simulation can be used as an effective tool for the physical inter- pretation of experimental data. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 7 of 18 4. Results This section presents the results of the flow downstream of the stator, first neglecting the stator–rotor interaction and then highlighting its effect. The flow field is discussed first from the perspective of a stationary observer, to show what discharged by the stator and then in the rotating frame of reference, to present what enters into the rotor according to its own perspective. Results will be presented first in a time-mean form to evidence the gross features of the flow and secondly by the description of the different interaction phases between the Int. J. Turbomach. Propuls. Power 2021, 6, 28 7 of 17 stator and the rotor. 4.1. Time Averaged Quantities 4.1.1. Absolute Frame of Reference 4.1. Time Averaged Quantities One of the most important physical quantity to describe is the total pressure and its 4.1.1. Absolute Frame of Reference related total pressure loss coefficient. In stators, losses are generated by the blade bound- One of the most important physical quantity to describe is the total pressure and its ary layers, the wake shed downstream of the blade trailing edge and the secondary vorti- related total pressure loss coefficient. In stators, losses are generated by the blade boundary ces and their mutual interaction (shock losses being absent due to subsonic character of layers, the wake shed downstream of the blade trailing edge and the secondary vortices and the flow). Given such occurrence, a typical distribution of total pressure loss coefficient their mutual interaction (shock losses being absent due to subsonic character of the flow). downstream of the stator located in the present test rig is reported in the frame (a) of Given such occurrence, a typical distribution of total pressure loss coefficient downstream Figure 4, as measured by FRAPP (top) and predicted by CFD (bottom) within the stator– of the stator located in the present test rig is reported in the frame (a) of Figure 4, as rotor gap. measured by FRAPP (top) and predicted by CFD (bottom) within the stator–rotor gap. (a) (b) Figure 4. Time-averaged contours at the stator exit. Left-to-right: (a) Total pressure loss (Yloss); (b) Static pressure coeffi- Figure 4. Time-averaged contours at the stator exit. Left-to-right: (a) Total pressure loss (Yloss); (b) Static pressure coefficient cient (Cps). Top: experiment. Bottom: CFD predictions. (Cps). Top: experiment. Bottom: CFD predictions. As extensively discussed in [11,18] the narrow loss trace along the span is the wake, As extensively discussed in [11,18] the narrow loss trace along the span is the wake, whereas the two cores, one at the hub and the second one at 75% span, are related to the whereas the two cores, one at the hub and the second one at 75% span, are related to the secondary flows and to their interaction with the wake. The wake, evidenced both in the secondary flows and to their interaction with the wake. The wake, evidenced both in the total pressure and loss field, is distorted by the action of the secondary flows, by the blade total pressure and loss field, is distorted by the action of the secondary flows, by the blade twist and lean resulting in a spanwise variation of flow angle from 85° at the tip to 64° at twist and lean resulting in a spanwise variation of flow angle from 85 at the tip to 64 at the hub. These features are properly captured by the code, demonstrating the fidelity of the hub. These features are properly captured by the code, demonstrating the fidelity of the simulation tool also on a distributed level. In the hub region, a wide loss core appears, induced by the hub clearance. Even though measurements are not available in this region (the bottom and top limits of the measurement surface are marked in the computed field by white lines), the very bottom part of the measurement plane indicates an increase of loss coefficient in the central part of the channel (far away from the wake) consistent with what predicted by the code. While this feature is weakly visible here (though present and marked by black arrows), it clearly appeared in the five-hole probe measurement data presented in [18] for that the probe design allowed to extend the measurement grid closer to the hub end wall. The static pressure field, shown in Figure 4b evidences the usual radial pressure gradient due to the radial equilibrium, combined to a circumferential perturbation resulting from the suction/pressure gradient across the blade passage still not completely Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 8 of 18 the simulation tool also on a distributed level. In the hub region, a wide loss core appears, induced by the hub clearance. Even though measurements are not available in this region (the bottom and top limits of the measurement surface are marked in the computed field by white lines), the very bottom part of the measurement plane indicates an increase of loss coefficient in the central part of the channel (far away from the wake) consistent with what predicted by the code. While this feature is weakly visible here (though present and marked by black arrows), it clearly appeared in the five-hole probe measurement data presented in [18] for that the probe design allowed to extend the measurement grid closer Int. J. Turbomach. Propuls. Power 2021, 6, 28 8 of 17 to the hub end wall. The static pressure field, shown in Figure 4b evidences the usual radial pressure gradient due to the radial equilibrium, combined to a circumferential per- turbation resulting from the suction/pressure gradient across the blade passage still not completely decayed at this axial position. The pressure field marks the perturbation pro- decayed at this axial position. The pressure field marks the perturbation produced by the duced by the hub vortex, also evident in the experiment. hub vortex, also evident in the experiment. All All fframes rames a appearing ppearing at at tthe he top top of of Fi Figur gure e 4 w 4 wer ere o e obtained btained b by y time-averaging time-averaging the the FRA FRAPP PP da dat ta a and and for for thi this s r re eason ason the the p periodic eriodic uns unsteadiness teadiness g given iven b by y the the ro rotor tor is is fi filter ltered. ed. Exp Exploiting loiting th the e FR FRAP APP P p pr ro omptness mptness and ap and applying plying the so-c the so-called alled trip triple le decom decomposition position to the to the pressu pressur re e signal, signal, it it is is possible possible to to extract extracthe t thr e re esolved solved (periodic) (periodic and ) and unr unr esolved esolve unsteadiness d unsteadi- of the flow. Filtering only the periodic component, the resulting signal can be interpreted ness of the flow. Filtering only the periodic component, the resulting signal can be inter- as the random total pressure oscillation due to turbulence and its standard deviation RMSP preted as the random total pressure oscillation due to turbulence and its standard devia- can be used as marker of regions of high turbulence [22]. All the low total pressure regions tion RMSP can be used as marker of regions of high turbulence [22]. All the low total identified above find perfect correspondence with high RMSP regions, as visible from the pressure regions identified above find perfect correspondence with high RMSP regions, RMSP map reported in Figure 5, assessing the interpretation of such regions as viscous as visible from the RMSP map reported in Figure 5, assessing the interpretation of such flow structures released by the stator. This observation, which appears trivial on a time- regions as viscous flow structures released by the stator. This observation, which appears averaged basis, will become less trivial when we will focus on the stator–rotor interaction trivial on a time-averaged basis, will become less trivial when we will focus on the stator– in Section 4.2 of the paper. rotor interaction in Section 4.2 of the paper. Figure 5. Standard deviation of the absolute total pressure (RMSP) at the stator exit Figure 5. Standard deviation of the absolute total pressure (RMSP) at the stator exit. 4.1.2. Rotating Frame of Reference 4.1.2. Rotating Frame of Reference When the perspective is changed from the stationary to the rotating frame of refer- When the perspective is changed from the stationary to the rotating frame of refer- ence, different flow features can be highlighted. In the rotating frame, usual meaningful ence, different flow features can be highlighted. In the rotating frame, usual meaningful quantities are the relative total pressure (and its related coefficient Cptr) and the relative quantities are the relative total pressure (and its related coefficient Cptr) and the relative Mach number (Mr) entering the rotor, whose measured distributions are reported in the Mach number (Mr) entering the rotor, whose measured distributions are reported in the two top frames of Figure 6. two top frames of Figure 6. As for the Cptr distribution in circumferential direction, it shows a peak and a sink As for the Cptr distribution in circumferential direction, it shows a peak and a sink per pitch, thus evidencing a periodic trend; the same feature is found for the Mach number, per pitch, thus evidencing a periodic trend; the same feature is found for the Mach num- which presents a trend opposite to that of the static pressure. The shape of the low Cptr ber, which presents a trend opposite to that of the static pressure. The shape of the low region (highlighted by black dashed lines in Figure 6), which has a nearly constant extension Cptr region (highlighted by black dashed lines in Figure 6), which has a nearly constant in circumferential direction along the whole channel span, suggests that it is not related to the stator wake (which, instead, is strongly bended); thus, another effect is acting here, clearly related to the rotor. If, somehow artificially, the time-mean distribution of absolute total pressure perceived by a rotating observer is analyzed, one may expect to see a uniform trend in circumferential direction; the same conclusion applies to the RMSP, whose distribution was found to corre- spond to the one of the absolute total pressure for stationary observers. This expectation is disregarded by measurements, also being visible in the two bottom frames of Figure 6. As a matter of fact, only the RMSP evidences an azimuthally uniform distribution, whereas the Pt distribution shows an evident perturbation whose spatial periodicity coincides with that of the rotor. The low total pressure region cannot be acknowledged as the stator wake Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 9 of 18 extension in circumferential direction along the whole channel span, suggests that it is not related to the stator wake (which, instead, is strongly bended); thus, another effect is act- ing here, clearly related to the rotor. If, somehow artificially, the time-mean distribution of absolute total pressure per- ceived by a rotating observer is analyzed, one may expect to see a uniform trend in cir- cumferential direction; the same conclusion applies to the RMSP, whose distribution was found to correspond to the one of the absolute total pressure for stationary observers. This expectation is disregarded by measurements, also being visible in the two bottom frames Int. J. Turbomach. Propuls. Power 2021, 6, 28 9 of 17 of Figure 6. As a matter of fact, only the RMSP evidences an azimuthally uniform distri- bution, whereas the Pt distribution shows an evident perturbation whose spatial perio- dicity coincides with that of the rotor. The low total pressure region cannot be acknowl- edged as the st or as the secondary ator wak loss e or regi as the on since secon no dary lo characteristic ss region since no c features of har those acteris phenomena tic featurescan of those be found. phenomena can be found. (a) (b) (c) (d) Figure 6. Experimental time-averaged flow in the rotating frame of reference; (a) relative total pressure coefficient Cptr; Figure 6. Experimental time-averaged flow in the rotating frame of reference; (a) relative total pressure coefficient Cptr; (b) (b) relative Mach number Mr; (c) unresolved total pressure unsteadiness RMSP; (d) total pressure coefficient Cpt. relative Mach number Mr; (c) unresolved total pressure unsteadiness RMSP; (d) total pressure coefficient Cpt. CFD simulation results, reported in Figure 7, confirm the regular and typical trend CFD simulation results, reported in Figure 7, confirm the regular and typical trend of relative Mach number and, especially, the unexpected distribution of absolute total of relative Mach number and, especially, the unexpected distribution of absolute total pressure. The pressure. The reason reasonfor forth these ese results m results must ust be se be sear arch ched ed for forin the in thestator stator–ro –rotor tor in interaction teraction Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 10 of 18 phenomena, deeply presented and discussed in the following section. phenomena, deeply presented and discussed in the following section. (a) (b) Figure 7. Computed time-averaged relative Mach number (a) and absolute total pressure (b) in the rotating frame of ref- Figure 7. Computed time-averaged relative Mach number (a) and absolute total pressure (b) in the rotating frame of erence at the stator exit. reference at the stator exit. 4.2. Rotor–Stator Interaction Effects By exploiting the FRAPP promptness and the phase averaging techniques, it is pos- sible to map the different instants of the stator–rotor interaction and, specifically for this analysis, the effect of the rotor on the flow field released by the stator. The first quantity described is the RMSP, plotted over half of the stator blade row in Figure 8. As a preliminary note, in this kind of plots adjacent channels reproduce different stator–rotor interaction phases, due to the phase-lag resulting from the different number of stator and rotor blade rows. As clearly visible, the distribution is nearly periodic with the stator pitch, being mainly related to the stator viscous structures (labelled as W) that are only marginally affected by the rotor–stator interaction. It is also clearly visible a pe- riodicity over the whole crown of about 120° degrees as a consequence of the rotor and stator blade number (25/22 ≈ 8/7, that means 3 nearly periodic configurations over the whole annulus). The outlines of eight rotor adjacent channels are also marked by black lines and the resulting total arc is also reported. Figure 8. Snapshot of RMSP distribution over multiple channels in different stator–rotor positions. When studying the instantaneous distribution of Pt, reported in Figure 9, the stator wakes, acknowledged as regions of low Pt/high RMSP in the stationary time-averaged maps, become no longer clearly visible, as shown in Figure 8. In the Figure 9 and in the following two figures, the black lines labelled with “W” mark the wake traces identified from RMSP in Figure 8, and are also renamed from A to G to consider the different chan- nel. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 10 of 18 (a) (b) Int. J. Turbomach. Propuls. Power 2021, 6, 28 10 of 17 Figure 7. Computed time-averaged relative Mach number (a) and absolute total pressure (b) in the rotating frame of ref- erence at the stator exit. 4.2. 4.2. Rotor–Stator Rotor–Stator Inte Interaction ractionEffects Effects By By exploiting exploiting the the F FRAPP RAPpr P p omptness romptness and an the d the phase phase averaging averaging techniques, techniques, it is p it is possible os- to sib map le to m the dif apfer thent e diinstants fferent iof nstthe ants stator of the –r s otor tator interaction –rotor inter and, action specifically and, speci for ficthis ally for analysis, this analysis, the effect of the rotor on the flow field released by the stator. the effect of the rotor on the flow field released by the stator. The Thfirst e firsquantity t quantity d described escribed is is the the RMSP RMSP , , p plotted lotted ov over er hal half f o of f th the e s stator tator b blade lade ro row w in in Figure 8. As a preliminary note, in this kind of plots adjacent channels reproduce different Figure 8. As a preliminary note, in this kind of plots adjacent channels reproduce different stator–rotor interaction phases, due to the phase-lag resulting from the different number stator–rotor interaction phases, due to the phase-lag resulting from the different number of stator and rotor blade rows. As clearly visible, the distribution is nearly periodic with of stator and rotor blade rows. As clearly visible, the distribution is nearly periodic with the stator pitch, being mainly related to the stator viscous structures (labelled as W) that the stator pitch, being mainly related to the stator viscous structures (labelled as W) that are only marginally affected by the rotor–stator interaction. It is also clearly visible a pe- are only marginally affected by the rotor–stator interaction. It is also clearly visible a riodicity over the whole crown of about 120° degrees as a consequence of the rotor and periodicity over the whole crown of about 120 degrees as a consequence of the rotor and stator blade number (25/22 ≈ 8/7, that means 3 nearly periodic configurations over the stator blade number (25/22  8/7, that means 3 nearly periodic configurations over the whole annulus). The outlines of eight rotor adjacent channels are also marked by black whole annulus). The outlines of eight rotor adjacent channels are also marked by black lines and the resulting total arc is also reported. lines and the resulting total arc is also reported. Figure 8. Snapshot of RMSP distribution over multiple channels in different stator–rotor positions. Figure 8. Snapshot of RMSP distribution over multiple channels in different stator–rotor positions. When studying the instantaneous distribution of Pt, reported in Figure 9, the stator When studying the instantaneous distribution of Pt, reported in Figure 9, the stator wakes, acknowledged as regions of low Pt/high RMSP in the stationary time-averaged wakes, acknowledged as regions of low Pt/high RMSP in the stationary time-averaged maps, become no longer clearly visible, as shown in Figure 8. In the Figure 9 and in the maps, become no longer clearly visible, as shown in Figure 8. In the Figure 9 and in the following two figures, the black lines labelled with “W” mark the wake traces identified following two figures, the black lines labelled with “W” mark the wake traces identified Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 11 of 18 from RMSP in Figure 8, and are also renamed from A to G to consider the different chan- from RMSP in Figure 8, and are also renamed from A to G to consider the different channel. nel. Figure 9. Snapshot of Cpt distribution over multiple channels in different stator–rotor positions. Figure 9. Snapshot of Cpt distribution over multiple channels in different stator–rotor positions. With reference to Figure 9 and starting from left, a low Pt region coincides with black continuous line A, i.e., the stator wake, but another low Pt zone appears on the right (high- lighted with a dashed line), not merged with the former; this second low Pt region is nearly uniform in spanwise direction. As the adjacent channel is considered (wake B), the low Pt zone corresponding to the black line still remains (with marginal difference with respect to the wake A), while the low Pt region ‘moves’ towards the wake and partially overlaps with the latter. For wake C, the two low Pt zones perfectly overlap, leading to the deepest total pressure deficit. Furthermore, shifting from one channel to the adjacent one (wake C to wake D, to E, etc.) the second low Pt region progressively ‘moves’ leftward with respect to the stator wake. The same consideration can be done on the high total pressure region, typically referred to as the isentropic region, where the level is modulated passing from one channel to the adjacent one. The time average of this process in the ab- solute frame, which is the average among the different stator channels appearing in this plot, has been already reported in Figure 4. Moreover, if the pressure level is considered, the time-averaged value Pt in the free stream is 1.345 bar (which corresponds to the up- stream one), while the phase resolved one is up to 1.36 bar. Since across the stator the total pressure cannot increase, the azimuthal perturbation of Pt discussed above is clearly an effect of the rotor on the flow released by the stator. As a further proof of that, this Pt perturbation rotates consistently with the sweeping of the rotor blades. In fact, as the rotor sweeps downstream of the stator outlet section, the rotor potential field propagates upstream with a wave of high and low static pressure, which also induces corresponding changes in the local flow direction. This also induces a local redistribution of mechanical energy, conceptually corresponding to an ‘internal’ work exchange between different portions of the flow, which ultimately alters the total pressure. In Section 5 a quantification of the periodic change in total temperature on the fluid upstream of the rotor, resulting from the process discussed above, will be proposed. Considering the absolute flow angle, reported in Figure 10, the rotor-induced pertur- bation is observed to alter the flow direction. In particular, the interaction positions la- belled as wake C and D show the maximum over-turning (high angles) in the midspan region and the maximum under-turning (low angles) condition at hub. The maximum cross flow at the tip is for the interaction position E, F, where also the lowest total pressure is found. The Mach number field, reported in Figure 11, shows a modulation among the adjacent channels. This feature evidences that changes in the flow rate released by the stator channel depend on the rotor position, as the blade leading edge creates a blockage at the outlet of the stator channel. The lowest Mach number, as an average on the passage, is found in the channel between wakes D and E. Int. J. Turbomach. Propuls. Power 2021, 6, 28 11 of 17 With reference to Figure 9 and starting from left, a low Pt region coincides with black continuous line A, i.e., the stator wake, but another low Pt zone appears on the right (highlighted with a dashed line), not merged with the former; this second low Pt region is nearly uniform in spanwise direction. As the adjacent channel is considered (wake B), the low Pt zone corresponding to the black line still remains (with marginal difference with respect to the wake A), while the low Pt region ‘moves’ towards the wake and partially overlaps with the latter. For wake C, the two low Pt zones perfectly overlap, leading to the deepest total pressure deficit. Furthermore, shifting from one channel to the adjacent one (wake C to wake D, to E, etc.) the second low Pt region progressively ‘moves’ leftward with respect to the stator wake. The same consideration can be done on the high total pressure region, typically referred to as the isentropic region, where the level is modulated passing from one channel to the adjacent one. The time average of this process in the absolute frame, which is the average among the different stator channels appearing in this plot, has been already reported in Figure 4. Moreover, if the pressure level is considered, the time-averaged value Pt in the free stream is 1.345 bar (which corresponds to the upstream one), while the phase resolved one is up to 1.36 bar. Since across the stator the total pressure cannot increase, the azimuthal perturbation of Pt discussed above is clearly an effect of the rotor on the flow released by the stator. As a further proof of that, this Pt perturbation rotates consistently with the sweeping of the rotor blades. In fact, as the rotor sweeps downstream of the stator outlet section, the rotor potential field propagates upstream with a wave of high and low static pressure, which also induces corresponding changes in the local flow direction. This also induces a local redistribution of mechanical energy, conceptually corresponding to an ‘internal’ work exchange between different portions of the flow, which ultimately alters the total pressure. In Section 5 a quantification of the periodic change in total temperature on the fluid upstream of the rotor, resulting from the process discussed above, will be proposed. Considering the absolute flow angle, reported in Figure 10, the rotor-induced per- turbation is observed to alter the flow direction. In particular, the interaction positions labelled as wake C and D show the maximum over-turning (high angles) in the midspan region and the maximum under-turning (low angles) condition at hub. The maximum cross flow at the tip is for the interaction position E, F, where also the lowest total pressure is found. The Mach number field, reported in Figure 11, shows a modulation among the adjacent channels. This feature evidences that changes in the flow rate released by the stator channel depend on the rotor position, as the blade leading edge creates a blockage at the outlet of the stator channel. The lowest Mach number, as an average on the passage, is Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 12 of 18 found in the channel between wakes D and E. Figure 10. Snapshot of absolute flow angle distribution over multiple channels in different stator– Figure 10. Snapshot of absolute flow angle distribution over multiple channels in different stator– rotor positions. rotor positions. Figure 11. Snapshot of M distribution over multiple channels in different stator–rotor positions. The scenario resulting from the analysis of the time-resolved experiments in-between the stator–rotor gap demonstrates a significant interference between the stator and rotor aerodynamics. While several effects are well known and properly discussed in Literature, for other quantities (like the absolute total pressure) an explanation is required. To this end, the CFD simulations were considered and Figure 12 summarizes relevant features— unavailable in the experiments—such as the flow configuration and the distribution of absolute total quantities, entropy and pressure on a blade-to-blade surface at midspan. The left frame of Figure 12 shows the streamlines constructed with the absolute velocity vector upstream and within the rotor channel. Streamlines clearly mark the local flow turning occurring around the rotor leading edge and in particular the absolute flow un- dergoes a local acceleration and deflection close to the front suction side of the rotor blade. This is the motivation for the azimuthal variability of flow angle observed in the experi- ments, recognized when commenting Figure 10. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 12 of 18 Int. J. Turbomach. Propuls. Power 2021, 6, 28 12 of 17 Figure 10. Snapshot of absolute flow angle distribution over multiple channels in different stator– rotor positions. Figure 11. Snapshot of M distribution over multiple channels in different stator–rotor positions. Figure 11. Snapshot of M distribution over multiple channels in different stator–rotor positions. The The scenario scenario resulting resulting from from the the an analysis alysisof ofthe the time time-r -re esolved solved experi experiments ments in in-between -between the stator–rotor gap demonstrates a significant interference between the stator and rotor the stator–rotor gap demonstrates a significant interference between the stator and rotor aerodynamics. While several effects are well known and properly discussed in Literature, aerodynamics. While several effects are well known and properly discussed in Literature, for other quantities (like the absolute total pressure) an explanation is required. To this for other quantities (like the absolute total pressure) an explanation is required. To this end, the CFD simulations were considered and Figure 12 summarizes relevant features— end, the CFD simulations were considered and Figure 12 summarizes relevant features— unavailable in the experiments—such as the flow configuration and the distribution of unavailable in the experiments—such as the flow configuration and the distribution of absolute total quantities, entropy and pressure on a blade-to-blade surface at midspan. absolute total quantities, entropy and pressure on a blade-to-blade surface at midspan. The The left frame of Figure 12 shows the streamlines constructed with the absolute velocity left frame of Figure 12 shows the streamlines constructed with the absolute velocity vector vector upstream and within the rotor channel. Streamlines clearly mark the local flow upstream and within the rotor channel. Streamlines clearly mark the local flow turning turning occurring around the rotor leading edge and in particular the absolute flow un- occurring around the rotor leading edge and in particular the absolute flow undergoes dergoes a local acceleration and deflection close to the front suction side of the rotor blade. a local acceleration and deflection close to the front suction side of the rotor blade. This This is the motivation for the azimuthal variability of flow angle observed in the experi- is the motivation for the azimuthal variability of flow angle observed in the experiments, ments, recognized when commenting Figure 10. recognized when commenting Figure 10. The change in flow angle is associated to a change in the angular momentum of the fluid, which increases locally, because the rotor blade has locally imparted torque to the flow: this process has ultimately increased the mechanical energy of the flow upstream of the blade. This variation of mechanical energy has opposite sign with respect to the one expected in a turbine, thus leading to the local absolute total pressure increase and explaining the unexpected rise of Pt upstream of the rotor. This phenomenon is clearly visible in the corresponding Pt distribution reported in Figure 12, which shows how the high Pt region propagates upstream, producing a significant effect also on the stator wake, as appearing in this interaction phase. It is interesting to note that this process does not alter the entropy level in the flow upstream of the rotor: the entropy field shows how the stator wake is bowed by the interaction with the rotor blade, but it also highlights that no further entropy production occurs, thus confirming the quasi-isentropic character of the effect here discussed. The field of Tt at midspan exhibits an azimuthal perturbation propagating upstream, along the black dashed lines reported in Figure 12, thus testifying that the flow deflection upstream of the rotor is the main player of the process. Thanks to the near-uniformity of the total temperature background field, one can properly appreciate the sinusoidal character of the perturbation, as well as its crucial dependence on the design of the front part of the blade, especially on the suction side. From this perspective, the comparison with the static pressure field indicates that the Pt-Tt perturbations are not linked to the recompression induced by the rotor leading edge (which propagates upstream along the red dashed line), but it conversely occurs in a region of the flow featuring a relatively low static pressure; Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 13 of 18 in particular, the total temperature/total pressure rise begins exactly where maximum (in absolute value) negative azimuthal pressure gradients is found. Figure 12. Computed instantaneous absolute flow field across the rotor at midspan. Left: streamlines of absolute velocity Figure 12. Computed instantaneous absolute flow field across the rotor at midspan. Left: streamlines of absolute velocity vector (coloured by the velocity magnitude). Center: Pt (top) and entropy (bottom) fields. Right: Tt (top), P (bottom) fields. vector (coloured by the velocity magnitude). Center: Pt (top) and entropy (bottom) fields. Right: Tt (top), P (bottom) fields. The change in flow angle is associated to a change in the angular momentum of the fluid, which increases locally, because the rotor blade has locally imparted torque to the flow: this process has ultimately increased the mechanical energy of the flow upstream of the blade. This variation of mechanical energy has opposite sign with respect to the one expected in a turbine, thus leading to the local absolute total pressure increase and ex- plaining the unexpected rise of Pt upstream of the rotor. This phenomenon is clearly visi- ble in the corresponding Pt distribution reported in Figure 12, which shows how the high Pt region propagates upstream, producing a significant effect also on the stator wake, as appearing in this interaction phase. It is interesting to note that this process does not alter the entropy level in the flow upstream of the rotor: the entropy field shows how the stator wake is bowed by the interaction with the rotor blade, but it also highlights that no further entropy production occurs, thus confirming the quasi-isentropic character of the effect here discussed. The field of Tt at midspan exhibits an azimuthal perturbation propagating upstream, along the black dashed lines reported in Figure 12, thus testifying that the flow deflection upstream of the rotor is the main player of the process. Thanks to the near-uniformity of the total temperature background field, one can properly appreciate the sinusoidal char- acter of the perturbation, as well as its crucial dependence on the design of the front part of the blade, especially on the suction side. From this perspective, the comparison with the static pressure field indicates that the Pt-Tt perturbations are not linked to the recom- pression induced by the rotor leading edge (which propagates upstream along the red dashed line), but it conversely occurs in a region of the flow featuring a relatively low static pressure; in particular, the total temperature/total pressure rise begins exactly where maximum (in absolute value) negative azimuthal pressure gradients is found. Int. J. Turbomach. Propuls. Power 2021, 6, 28 13 of 17 5. Discussion: Energy Separation Effect One of the consequences of the rotor-induced periodic flow fluctuation is that the rotor pressurises and depressurizes the flow field in the stator–rotor gap: if, as in this case, the flow is subsonic, no shock waves establish and the time-average of this perturbation is null, namely the time-mean flow corresponds to the steady-state flow condition. As shown by CFD results, the rotation of the rotor potential field induces quasi-isentropic unsteady perturbations of total temperature (or total enthalpy) propagating upstream. The observed effect can be analytically justified by resorting to equation 1, which establishes a link, rigorously valid only for inviscid flows, between the material derivative of the total enthalpy and the local (partial) derivative of the static pressure. The capability of static pressure unsteadiness to ‘redistribute’ total quantities is often called, in Literature, energy separation effect. Energy separation was widely documented to occur in the Von Karman vortex streets featuring the wake of cylinders in cross-flow [23,24] and was also observed to occur in the blade-wake interaction phenomena [18]. In the present case, the source of the static pressure unsteadiness has to be found in the rotor pressure field travelling with the blade itself. As a result of the blade motion, the azimuthal gradients of pressure on the relative frame covert into static pressure unsteadiness according to the formula [25]: ¶p ¶p = U j (2) rel ¶t ¶y By plugging expression (2) into Equation (1), one gets a differential relation between the rotor pressure field and the total enthalpy rise: Dh ¶p r = U j (3) rel Dt ¶y Equation (3) demonstrates analytically the experimental and computational finding of this study, i.e., that the rotor pressure field is able to trigger energy separation effects in the stator–rotor axial gap of a high pressure gas turbine. If the rotor aerodynamic loading is high (as usual in present-day gas turbine stages) and the stator–rotor axial gap is small (as usual in turbines) this effect might influence in a non-negligible way the stator blade aerodynamics and heat transfer. The statements above and, in a broader sense, the technical relevance of the energy separation effect here discussed demand for a proper quantification. In fact, a direct quantitative evaluation of the total enthalpy/total temperature oscillation upstream of the rotor is not feasible, since no unsteady measurements of total temperature are available (neither a fast-response temperature probe nor a rotating probe are available for such high speed rotors). Nevertheless, the isentropic character of the energy separation effect allows estimating the total temperature increase from experiments, by applying the isentropic thermodynamic relations to the measured total pressure perturbations. Considering as ref- erence values the pitchwise-averages of the measured total pressure and total temperature distributions, the local phase-resolved total temperature is calculated by the phase-resolved total pressure as follows: g1 Pt Tt = Tt (4) Pt It is interesting to note that the pitchwise averages Pt and Tt are effective reference conditions, as the average filters the effect of the rotor potential field. The total temperature fluctuation due to energy separation can be finally evaluated as DTt = Tt Tt. The results of this quantification are reported in Figure 13a over two rotor pitches and show—for the present operating condition—a temperature fluctuation DTt of 0.9 K; this value corresponds to about 8% of the total temperature drop across the stage (21.5 K). The slight tangential shift between the high temperature level at the hub and at the tip depends on the rotor blade twisting, on the spanwise trend of the azimuthal leading edge position Int. J. Turbomach. Propuls. Power 2021, 6, 28 14 of 17 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 15 of 18 of the rotor blade and on the leading edge loading. Interestingly, Figure 13b reports the of the rotor blade and on the leading edge loading. Interestingly, Figure 13b reports the distribution of over two rotor pitches as directly extracted from CFD simulation (i.e., distribution of DTt over two rotor pitches as directly extracted from CFD simulation (i.e., using the actual unsteady total temperature values predicted by the solver). The excellent using the actual unsteady total temperature values predicted by the solver). The excellent comparison between the experimental estimate and the simulation demonstrates not only comparison between the experimental estimate and the simulation demonstrates not only the ‘qualitativethe ’ va‘qu lidialitative’ ty of the in validity terpreta oftion the, b interpr ut also the etation, qu but antialso tativthe e requantitative levance of the relevance of the energy separation a energy pproa separation ch. approach. (a) (b) Figure 13. Amplitude of the periodic fluctuations of total temperature upstream of the rotor due to Figure 13. Amplitude of the periodic fluctuations of total temperature upstream of the rotor due to rotor-driven perturbation; rotor-driven perturbation; (a) estimated from total pressure measurements; (b) predicted by CFD. (a) estimated from total pressure measurements; (b) predicted by CFD. Ultimately, the operating condition here presented is one out of the four ones actually Ultimately, the operating condition here presented is one out of the four ones actually available, taken at higher and lower expansion ratio (though still all subsonic) and here available, taken at higher and lower expansion ratio (though still all subsonic) and here not not shown for sake of brevity: it is important to highlight that, for all such different oper- shown for sake of brevity: it is important to highlight that, for all such different operating ating conditions, the total temperature fluctuation always results of about 10% of the stage conditions, the total temperature fluctuation always results of about 10% of the stage total total temperature drop. temperature drop. 6. Conclusions 6. Conclusions The paper has presented, by combining experiments and CFD simulations, the flow The paper has presented, by combining experiments and CFD simulations, the flow within the stator–rotor gap of a subsonic high-pressure turbine and on how this is influ- within the stator–rotor gap of a subsonic high-pressure turbine and on how this is influ- enced by the rotor potential field propagating upstream. enced by the rotor potential field propagating upstream. First, a validation of the CFD model against the experimental data has been pro- First, a validation of the CFD model against the experimental data has been provided, vided, showing a very good agreement in terms of overall cascade and stage performance, showing a very good agreement in terms of overall cascade and stage performance, spanwise profiles of pitch-wise averaged data and distributed flow field. spanwise profiles of pitch-wise averaged data and distributed flow field. Then, the flow released by the stator has been investigated considering two alternative Then, the flow released by the stator has been investigated considering two alterna- perspectives, i.e., for stationary and rotating observers, both in terms of time mean and tive perspectives, i.e., for stationary and rotating observers, both in terms of time mean phase-resolved quantities. The analysis in the stationary frame shows the well-known wake and phase-resolved quantities. The analysis in the stationary frame shows the well-known and secondary flows pattern, the radial equilibrium issues and loss mechanisms typical of wake and secondary flows pattern, the radial equilibrium issues and loss mechanisms a subsonic modern stator. In the rotating frame of reference, the relative quantities show a typical of a subsonic modern stator. In the rotating frame of reference, the relative quan- periodic pattern with a shape and periodicity related to the rotor pitch. On the contrary, tities show a periodic pattern with a shape and periodicity related to the rotor pitch. On the absolute total pressure perceived by a rotating observer evidences a periodic pattern the contrary, the absolute total pressure perceived by a rotating observer evidences a pe- featuring the rotor angular periodicity, thus revealing an influence of the rotor potential riodic pattern featuring the rotor angular periodicity, thus revealing an influence of the field on the total pressure field in the stator–rotor gap. rotor potential field on the total pressure field in the stator–rotor gap. When the phase-resolved flow field is analyzed, the impact of the rotor aerodynamics When the phase-resolved flow field is analyzed, the impact of the rotor aerodynamics on the flow in the stator–rotor gap is found on most quantities, such as the total pressure, on the flow in the stator–rotor gap is found on most quantities, such as the total pressure, the Mach number, the flow angle, while the viscous dissipative structures released by the the Mach number, the flow angle, while the viscous dissipative structures released by the stator appear only weakly affected by the rotor. These effects can only be connected to stator appear only weakly affected by the rotor. These effects can only be connected to the the rotor potential field, which is the unique rotor feature which can propagate upstream. rotor potential field, which is the unique rotor feature which can propagate upstream. The The Mach number distribution exhibits a periodic blockage of the stator channel flow Mach number distribution exhibits a periodic blockage of the stator channel flow rate. The rate. The flow angle also shows a periodic increase in the tangential component of the flow angle also shows a periodic increase in the tangential component of the absolute ve- absolute velocity. The total pressure experiences a periodic increase with respect to the locity. The total pressure experiences a periodic increase with respect to the stator up- stator upstream, thus apparently violating the energy and momentum balances. CFD stream, thus apparently violating the energy and momentum balances. CFD simulations simulations reveal the inherent link between these observations, suggesting that the total 𝛥𝑇𝑡 Int. J. Turbomach. Propuls. Power 2021, 6, 28 15 of 17 pressure rise is caused by the deflection imposed to the absolute flow when turning around the front part of the rotor blade. Predictions also show local and periodic total temperature rise in correspondence to the total pressure one, also marking a nearly-isentropic process. An analytical approach allows explaining the observed feature and to classify it as a new energy separation effect, not described up to now in the scientific literature according to authors’ knowledge, in which the static pressure unsteadiness is triggered by the rotation of the rotor potential field. On the quantitative ground, this energy separation effect impacts the total temperature field, which is periodically altered by about 8% with respect to the mean temperature drop across the stage. Such an effect might play a role on the aerodynamics and, especially, on the heat trans- fer in the rear section of the stator blade, especially for new-generation gas turbines stages featuring high rotor loading and small axial gap in-between the blade rows. Moreover, in case of transonic turbines (except for the very rare, saturated condition) the onset of supersonic flows and shock wave patterns within the stator–rotor gap would likely alter the isentropic character of the process, with potential impact on the performance. Future works will extend the present study considering transonic stages and more realistic axial gaps, with special focus on the aero-thermal stator behavior. Beside the physical aspects, the present findings also show the importance of the design of the front part of the rotor blade, that is, one of the main geometrical features that determines the propagation upstream of the rotor potential field. Further studies on this feature and its implication may lead to novel design remarks for both the rotor and the stator optimization. Author Contributions: Conceptualization, P.G. and G.P.; methodology, P.G. and G.P.; software, P.G. and G.P.; experiments, P.G.; CFD and its validation, G.P.; formal analysis, P.G. and G.P.; writing— original draft preparation, P.G. and G.P.; writing—review and editing, G.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Nomenclature Int. J. Turbomach. Propuls. Power 2021, 6, 28 16 of 17 Latin c stator axial chord x:V D stage mean diameter G mass flow rate h blade height h Total Enthalpy Mr relative Mach number n rotational speed N blade number Ps static pressure Pt absolute total pressure Ptr relative total pressure Pt pitchwise-averaged total pressure t time t tip clearance Tt absolute total temperature Tt pitchwise-averaged total temperature Tt inlet total temperature in U peripheral speed Vt tangential velocity Yloss total pressure loss coefficient Greek total to static expansion ratio D difference " flow deflection at midspan ratio of specific heat capacities density blade solidity at midspan (chord/pitch) Q circumferential coordinate D angular rotor pitch Subscripts reference condition re f Abbreviations AR blade aspect ratio (height/chord) CFD Computational Fluid Dynamics Cps = (P-P )/(Pt -P ) pressure coefficient ref ref ref Cpt = (Pt-P )/(Pt -P ) total pressure coefficient ref ref ref Cptr = (Ptr-P )/(Pt -P ) relative total pressure coefficient ref ref ref FRAPP fast response aerodynamic pressure probe TPV Tip Passage Vortex Int. J. Turbomach. Propuls. Power 2021, 6, 28 17 of 17 References 1. Sharma, O.P.; Pickett, G.F.; Ni, R.H. Assessment of unsteady flows in turbines. J. Turbomach. 1992, 114, 79–90. [CrossRef] 2. Zaccaria, M.A.; Lakshminarayana, B. Unsteady flow field due to nozzle wake interaction with the rotor in an axial flow turbine: Part I-Rotor passage flow field. J. Turbomach. 1997, 119, 210–222. [CrossRef] 3. Chaluvadi, V.S.P.; Kalfas, A.I.; Benieghbal, M.R.; Hodson, H.P.; Denton, J.D. Blade-row interaction in a high-pressure turbine. J. Propul. Power 2001, 17, 892–901. [CrossRef] 4. Schlienger, J.; Kalfas, A.I.; Abhari, R.S. Vortex-wake-blade interaction in a shrouded axial turbine. J. Turbomach. 2005, 127, 699–707. [CrossRef] 5. Dénos, R.; Arts, T.; Paniagua, G.; Michelassi, V.; Martelli, F. Investigation of the unsteady rotor aerodynamics in a transonic turbine stage. J. Turbomach. 2001, 123, 81–89. [CrossRef] 6. Chaluvadi, V.S.P.; Kalfas, A.I.; Hodson, H.P.; Ohyama, H.; Watanabe, E. Blade row interaction in a high-pressure steam turbine. J. Turbomach. 2003, 125, 14–24. [CrossRef] 7. Miller, R.J.; Moss, R.W.; Ainsworth, R.W.; Horwood, C.K. Time-resolved vane-rotor interaction in a high-pressure turbine stage. J. Turbomach. 2003, 125, 1–13. [CrossRef] 8. Hodson, H.P.; Howell, R.J. Bladerow interactions, transition, and high-lift aerofoils in low-pressure turbines. Annu. Rev. Fluid Mech. 2005, 37, 71–98. [CrossRef] 9. Dénos, R.; Paniagua, G. Effect of vane-rotor interaction on the unsteady flowfield downstream of a transonic high pressure turbine. Proc. Inst. Mech. Eng. Part A J. Power Energy 2005, 219, 431–442. [CrossRef] 10. Göttlich, E.; Woisetschläger, J.; Pieringer, P.; Hampel, B.; Heitmeir, F. Investigation of vortex shedding and wake-wake interaction in a transonic turbine stage using laser-doppler-velocimetry and particle-image-velocimetry. J. Turbomach. 2006, 128, 178–187. [CrossRef] 11. Gaetani, P.; Persico, G.; Dossena, V.; Osnaghi, C. Investigation of the flow field in a HP turbine stage for two stator-rotor axial gaps: Part II–Unsteady flow field. J. Turbomach. 2007, 129, 580–590. [CrossRef] 12. Paniagua, G.; Yasa, T.; De La Loma, A.; Castillon, L.; Coton, T. Unsteady strong shock interactions in a transonic turbine: Experimental and numerical analysis. J. Propul. Power 2008, 24, 722–731. [CrossRef] 13. Gaetani, P.; Persico, G.V.; Osnaghi, C. Effects of axial gap on the vane-rotor interaction in a low aspect ratio turbine stage. J. Propul. Power 2010, 26, 325–334. [CrossRef] 14. Dring, R.P.; Joslyn, H.D.; Hardin, L.W.; Wagner, J.H. Turbine rotor-stator interaction. J. Eng. Power 1982, 104, 729–742. [CrossRef] 15. Miller, R.J.; Moss, R.W.; Ainsworth, R.W.; Harvey, N.W. Wake, shock and potential field interaction in a 1.5 stage turbine–Part I: Vane-rotor and rotor-vane interaction. J. Turbomach. 2003, 125, 33–39. [CrossRef] 16. Dean, R.C. On the necessity of unsteady flow in fluid machines. J. Basic Eng. 1959, 81, 24–28. [CrossRef] 17. Hodson, H.P.; Dawes, W.N. On the Interpretation of measured profile losses in unsteady wake turbine blade interaction studies. J. Turbomach. 1998, 120, 276–284. [CrossRef] 18. Gaetani, P.; Persico, G.; Spinelli, A. Coupled effect of expansion ratio and blade loading on the aerodynamics of a high-pressure gas turbine. Appl. Sci. 2017, 7, 259. [CrossRef] 19. Gaetani, P.; Persico, G. Technology development of Fast-Response Aerodynamic Pressure Probes. Int. J. Turbomach. Propuls. Power 2020, 5, 6. [CrossRef] 20. Persico, G.; Mora, A.; Gaetani, P.; Savini, M. Unsteady aerodynamics of a low aspect ratio turbine stage: Modeling issues and flow physics. J. Turbomach. 2012, 134. [CrossRef] 21. Giles, M.B. Stator/rotor interaction in a transonic turbine. J. Propul. Power 1990, 6, 621–627. [CrossRef] 22. Persico, G.; Gaetani, P.; Paradiso, B. Estimation of turbulence by single-sensor pressure probes. In Proceedings of the XIX Symposium on Measuring Techniques in Transonic and Supersonic Flow in Cascades and Turbomachines, Rhode-St-Genese, Belgium, 7–8 April 2008. 23. Eckert, E.R.G. Cross transport of energy in fluid streams. Wärme-und Stoffübertragung 1987, 21, 73–81. [CrossRef] 24. Aleksyuk, A.I. The Eckert–Weise effect and energy separation under the flow interference behind side-by-side cylinders. J. Fluid Mech. 2021, 915. [CrossRef] 25. Hodson, H.P.; Hynes, T.P.; Greitzer, E.M.; Tan, C.S. A physical Interpretation of Stagnation Pressure and Enthalpy Changes in Unsteady Flow. J. Turbomach. 2012, 134, 060902. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Turbomachinery, Propulsion and Power Multidisciplinary Digital Publishing Institute

Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow within a High-Pressure Gas Turbine Stage

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International Journal of Turbomachinery Propulsion and Power Article Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow within a High-Pressure Gas Turbine Stage Paolo Gaetani and Giacomo Persico * Laboratory of Fluid-Machines, Energy Department, Politecnico di Milano Via Lambruschini 4, 20156 Milano, Italy; paolo.gaetani@polimi.it * Correspondence: giacomo.persico@polimi.it; Tel.: +39-02-2399-8605 † This manuscript is an extended version of our meeting paper published in the Proceedings of the 14th European Turbomachinery Conference, Gdansk, Poland, 12–16 April, 2021. Abstract: In stator–rotor interaction studies on axial turbines, the attention is commonly focused on the unsteady rotor aerodynamics resulting from the periodic perturbations induced by the stator flow structures. Conversely, less interest has been historically attracted regarding the influence of the rotor on the flow released by the stator, correlated to propagation of the blade potential field upstream of the rotor leading edge. In this paper, experiments in the research high-pressure turbine of the Laboratory of Fluid-Machines of the Politecnico di Milano, performed by applying a fast- response aerodynamic pressure probe, alongside fully-3D time-accurate CFD simulations of the flow, are combined with the aim of discussing the rotor-to-stator interaction. While rotating, the rotor induces periodic perturbations on the pressure and velocity field in the stator–rotor gap, altering the evolution of the total quantities and the flow rate discharged by each stator channel and eventually triggering energy-separation effects which result in total pressure and total temperature oscillations in the stator-exit flow. Such oscillations were found to rise up to almost 10% of the stage total temperature drop. Citation: Gaetani, P.; Persico, G. Influence of the Rotor-Driven Perturbation on the Stator-Exit Flow Keywords: high-pressure turbines; blade-row interaction; cascade potential field; energy separation; within a High-Pressure Gas Turbine unsteady measurements; time-accurate CFD Stage. Int. J. Turbomach. Propuls. Power 2021, 6, 28. https://doi.org/ 10.3390/ijtpp6030028 1. Introduction Academic Editor: Claus Sieverding The need for continuous improvements in gas turbine performance, in terms of effi- ciency and rangeability, alongside the need of a deeper understanding of the flow physics, Received: 26 June 2021 still asks for important theoretical and experimental efforts and research. A key field of Accepted: 6 July 2021 interest—among the many involved in gas turbine studies—is thermo-fluid-dynamics, Published: 13 July 2021 pillar for getting a holistic comprehension of turbomachinery and for their optimal design. In this context, one of the major interests in present-day research is the interaction between Publisher’s Note: MDPI stays neutral system components, as well as stationary and rotating rows of turbomachinery. Multi- with regard to jurisdictional claims in ple classes of problems can be acknowledged, such as the combustor–1st turbine stage published maps and institutional affil- interaction, the stator–rotor interaction in both high-pressure and low-pressure turbines, iations. the last turbine stage–diffuser interaction, the impeller–diffuser interaction and the surge in compressors. With specific reference to turbines stages, the stator–rotor interaction consists of potential field interference, wake/shock/vortex-blade interaction, wake-wake interaction Copyright: © 2021 by the authors. and wake/vortex-secondary flow interaction [1–13]. In general, most of the papers focus Licensee MDPI, Basel, Switzerland. on the effect of the stator flow structures on the rotor aerodynamics and performance, as the This article is an open access article spatial non uniformities at the stator exit result in time-varying inlet boundary conditions distributed under the terms and for the rotor. Only a few studies report about the effects of the rotor potential field on conditions of the Creative Commons the stator, for example, [14] for subsonic turbines and [15] for transonic high-pressure Attribution (CC BY-NC-ND) license turbines; these studies typically include measured data on the stator blade surface. Thanks (https://creativecommons.org/ licenses/by-nc-nd/4.0/). to the recent improvements in measuring techniques—such as fast response aerodynamic Int. J. Turbomach. Propuls. Power 2021, 6, 28. https://doi.org/10.3390/ijtpp6030028 https://www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2021, 6, 28 2 of 17 pressure probes—and CFD codes, it is now possible to more proficiently track these features, also considering the detailed flow configuration in-between the blade rows, i.e., in the stator–rotor axial gap. When discussing the flow unsteadiness in turbomachines, one basic observation is the inherent link between unsteady flow and work exchange [16], related to the coupling, valid for inviscid flows, between the material derivative of the total enthalpy and the local time-derivative of the static pressure: Dh ¶p r = (1) Dt ¶t The same concept, when applied to a wake incoming on a turbine cascade and impinging on the blades, was observed to produce a local increase in the total enthalpy and pressure, due to onset of energy separation effects [17]. Similar features may apply also to the potential field, with the important difference that the pressure field also propagates upstream of a cascade (at least up to the sonic throat of the upstream cascade, if this latter is choked) which might lead, in case of a rotor, to the onset of unexpected flow features within the stator–rotor axial gap. Such features, not visible if applying time-mean measurement techniques or steady computational models, can instead be highlighted by resorting to unsteady measurements and time-accurate CFD simulations. This is indeed the focus of the present paper, which aims at discussing the effect of the rotor potential field on the flow released by the stator, thanks to a combined experimental and numerical approach. The paper is structured as follows: at first the experimental and numerical approaches are described, then the experimental results are discussed with the support of CFD results for physical interpretations and, finally, some conclusions are derived. 2. Test Facility and Measuring Techniques The test rig and instrumentation applied in the present research work are already described in other papers: see, for example, [18]. In this section, they are briefly recalled. 2.1. Test Rig and Axial Turbine Stage The test rig run for the present investigation is the high-speed test rig for turbine and compressor located at the Laboratory of Fluid Machine (LFM) of the Energy dept. of the Politecnico di Milano. It consists of a radial section where a centrifugal compressor is run and, in the present investigation, it feeds the turbine with the proper pressure ratio and flow rate; its maximum rotational speed is 45,000 rpm with a power available upstream of the gearbox of 800 kW. The radial section is then followed by a cooler to set the temperature level of the rig, a venturi pipe to measure the flow rate and a throttling section to control the expansion ratio made available to the turbine. The turbine is located in an axial section, whose maximum rotational speed is 20,000 rpm. The axial turbine stage is a single stage, not cooled, representative of a high pressure one. The main features are reported in Table 1; in addition, the stator blade is leaned by 12 on the pressure side and at midspan it has a geometrical discharge angle of 75.4 . The rotor is bowed with a constant outlet angle of 67.7 , it has a clearance at tip of 0.6 mm and a blade height of 50 mm (clearance included). The axial distance between the stator and the rotor is equal to one stator axial chord (30.6 mm), easing the probe insertion. Int. J. Turbomach. Propuls. Power 2021, 6, 28 3 of 17 Table 1. Stage geometry and operating conditions. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 3 of 18 n [rpm] G [kg/s] Tt [K] in Operating Condition 1.35 7000 3.5 323 h [mm] t /h D (mm) gap/c C M x,V Geometry Table 1. Stage geometry and operating conditions. 50 0.015 350 1.00 Blade Rows Nb  AR " β n [rpm] G [kg/s] Ttin [K] Vane 22 1.20 0.83 75.2 Operating Condition 1.35 7000 3.5 323 Rotor 25 1.25 0.91 115.3 h [mm] tC/h DM (mm) gap/cx,V Geometry 50 0.015 350 1.00 Measurements were taken at 71% of the stator axial chord downstream of the stator Blade Rows Nb σ AR ε trailing edge, all over the channel height: the measurement grid counts 320 points (16 points Vane 22 1.20 0.83 75.2 on the stator pitch, 20 points along the blade span) on each stator channel. Figure 1 reports Rotor 25 1.25 0.91 115.3 a picture of the stage and a sketch of the meridional section. (a) (b) Figure 1. Picture of the turbine stage (a) and sketch of the meridional section (b). Figure 1. Picture of the turbine stage (a) and sketch of the meridional section (b). 2.2. Measurement Techniques 2.2. Measurement Techniques In the present study, besides the instrumentation for the rig management, only a Fast In the present study, besides the instrumentation for the rig management, only a Fast Response Aerodynamic Pressure Probe (FRAPP) was applied. The reader is referred to Response Aerodynamic Pressure Probe (FRAPP) was applied. The reader is referred to [19] [19] for a picture of the present-day FRAPP, design, operation and technology available for a picture of the present-day FRAPP, design, operation and technology available at at Politecnico di Milano and to [11,13,18] for the FRAPP application in the rig. Politecnico di Milano and to [11,13,18] for the FRAPP application in the rig. The FRAPP here applied has a cylindrical head (diameter of 2 mm) where a single The FRAPP here applied has a cylindrical head (diameter of 2 mm) where a single sensor sensor is is inserted inserted (K (Kulite, ulite, model model XCQ XCQ062) 062) and and conn connected ected to to the the e external xternal env envir ironment onment b by y a hole whose diameter is 0.35 mm. The probe promptness, evaluated on a shock tube, is a hole whose diameter is 0.35 mm. The probe promptness, evaluated on a shock tube, is 100 kHz after digital compensation thanks to the very small size of the line-cavity system 100 kHz after digital compensation thanks to the very small size of the line-cavity system facing facing the se the sensor nsor. . The The prpr obe obis e is appl appliedied in in theth absolute e absolu frame te frame of refer of r ence eference as a virtual as a virt 3 holes ual 3 pr holes obe p by rob rotating e by ro itta ar tin ound g it a itsround own stem its oand wn s then tem and re-phasing then r the e-pmeasur hasing the ements memaking asuremen use ts of the key-phasor. Each pressure data set is acquired at 500 kHz and has 500,000 samples. making use of the key-phasor. Each pressure data set is acquired at 500 kHz and has In addition to the standard use described in the aforementioned papers, by applying 500,000 samples. the methodology proposed in [20], it is possible to have a qualitative evaluation of the In addition to the standard use described in the aforementioned papers, by applying turbulence level. Thanks to this quantity, it is possible to track and evaluate the viscous the methodology proposed in [20], it is possible to have a qualitative evaluation of the structure released by the stator. turbulence level. Thanks to this quantity, it is possible to track and evaluate the viscous For the specific investigation, each rotor pitch has been discretized by means of structure released by the stator. 40 points. For the specific investigation, each rotor pitch has been discretized by means of 40 As for the rig instrumentation, the inlet and outlet temperatures are monitored by T points. thermocouple, whose uncertainty after calibration is 0.3 C. As for the rig instrumentation, the inlet and outlet temperatures are monitored by T The stage inlet and outlet pressure level are measured by means of Kulite transducers thermocouple, whose uncertainty after calibration is 0.3 °C. (model XT190) whose uncertainty, after calibration, is 60 Pascal. The stage inlet and outlet pressure level are measured by means of Kulite transducers (model XT190) whose uncertainty, after calibration, is 60 Pascal. FRAPP data reduction is based on the phase-averaging techniques. First, the pressure measurements are phase averaged by referring to the key-phasor signal: the averaged value in each interval (40 per rotor pitch) is thus the result of about 12,000 samples. Sec- ond, by applying the calibration matrices, they are used to derive the flow quantities in Int. J. Turbomach. Propuls. Power 2021, 6, 28 4 of 17 FRAPP data reduction is based on the phase-averaging techniques. First, the pressure measurements are phase averaged by referring to the key-phasor signal: the averaged value in each interval (40 per rotor pitch) is thus the result of about 12,000 samples. Second, by applying the calibration matrices, they are used to derive the flow quantities in terms of total and static pressure, flow angle. Finally, assuming a total temperature constant across the stator, the velocity field is determined and—by the peripheral speed—the flow conditions in the rotating frame of reference are calculated. As it will be discussed in the last section, the total temperature fluctuates by about 1 K; the corresponding velocity fluctuation is expected to be of the order of 0.1% and, hence, negligible, also considering that the Mach number is correct coming from a phase-resolved data reduction. Overall, pressure values have an averaged uncertainty of 0.5% of the kinetic head measured by the FRAPP. The phase averaged signals for the different stator positions (in all the blade span positions) are re-organized in order to map the stator—rotor interaction for the different stator to rotor positions. The time mean quantities in the absolute frame of reference are calculated by averaging in time the phase averaged flow quantities. The time mean quantities in the rotating frame of reference are calculated by averaging the stator to rotor interaction positions, acknowledging the rotor pitch periodicity. 3. CFD Model and Experimental Validation In this study, CFD simulations mainly act as support to the interpretation of the experimental result. The calculations were performed using ANSYS-CFX, applying the flow model developed at Politecnico di Milano for turbomachinery flow simulations, discussed in detail in [21] and briefly summarized in the following. Fully 3D and time-resolved calculations were performed, modeling the fluid as perfect gas and introducing turbulence effects by resorting to the fully-turbulent k-! SST model. The near-wall resolution was specified so to guarantee y < 1 on endwalls and on blade surfaces, thus avoiding the use of wall functions. Unsteady terms are discretized with an implicit second order scheme, the advection terms with a high-resolution total-variation-diminishing scheme, the diffusive terms with a second order central scheme. Simulations were performed by assigning, at the inlet, the measured radial profile of total pressure, uniform total temperature, axial flow direction and a uniform turbulence intensity of 2.5%, resulting from dedicated hot-wire measurements (the eddy viscosity ratio was set equal to 25, following the recommended expression proposed by the solver). A radial-equilibrium distribution of static pressure was assigned at the outlet. Coupled stator–rotor simulations were performed, first resolving the flow in steady- state fashion using a mixing-plane stator–rotor interface for initialization and then moving to time-resolved analysis. Given the different blade numbers between the stator and the rotor, to simulate the full stator–rotor coupling (i.e., also the rotor-to-stator interaction and not only the stator-to-rotor interaction as was conducted in [21] where only the unsteady flow in the rotor was solved) while saving computational cost, the time-inclined solution strategy proposed in [22] was adopted. By virtue of this method, spatial-temporal solutions are obtained so to guarantee automatically the phase-lag between periodic boundaries and neither multiple channels nor alteration of the cascade solidity (or blade scaling) are required. The solver integrates the equations over structured meshes composed by hexahedral elements. A grid-dependence study was performed to select the proper spatial resolution. The study was conducted by keeping constant the near-wall resolution so that the boundary layer is properly resolved on both blade walls and hub and shroud walls for each of the tested meshes. The mesh dimension ranged from 2.2 million to 18.4 million cells for the entire stage; overall cascade/stage performance data as well as detailed spanwise profiles were considered to judge the influence of spatial resolution. Grid-independent results were achieved for stator and rotor meshes composed by 4.6 million cells, for a total of 9.2 million cells (the difference in stage efficiency with respect to the result obtained with the finest Int. J. Turbomach. Propuls. Power 2021, 6, 28 5 of 17 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 5 of 18 mesh resulted below 0.1%). The final meshes of each blade row, reported in Figure 2, are composed by 140 cells in spanwise direction and 33,000 cells in each blade-to-blade layer. (a) (b) Figure 2. Computational meshes of the stator (a) and rotor (b) blade rows after grid-dependence study. Figure 2. Computational meshes of the stator (a) and rotor (b) blade rows after grid-dependence study. The The tim timeestep stepwas was se set t to to 1/56 1/56of of th thee ro rotor tor b blade lade p passing assing p period eriod ( (corr corresp esponding ondingto to about about 0. 0.25 25°) ); ; t the he unsteady unsteadysolution solutionr esulted resulted smooth smooth (d (due ue to the to the s ubsonic subsonic flow reg flow regime) ime) and and further further re reductions ductions of of the the time time step wer step weree not not found found to to alter alter the the per performance formance pred prediction iction and and the the flow flow morphology morphology. . The The specif specific ic time time step step value valu was e wsel as se ected lected to optimize to optimithe ze the sampling sampliof ng the 3D solution for post-processing (since the stage periodicity 22 25 is close to 7 8 and of the 3D solution for post-processing (since the stage periodicity 22 × 25 is close to 7 × 8 56 is the least common value of these two numbers). The periodic solution was achieved and 56 is the least common value of these two numbers). The periodic solution was after 20 periods (the first 12 ones run with a larger time step, 1/25 of the rotor blade passing achieved after 20 periods (the first 12 ones run with a larger time step, 1/25 of the rotor period). The computational cost of the time-resolved simulation was about one week on a blade passing period). The computational cost of the time-resolved simulation was about 40-processor cluster. one week on a 40-processor cluster. Before simulations are used to aid the interpretation of the experiments, experiments Before simulations are used to aid the interpretation of the experiments, experiments are used to assess the simulation results. Figure 3 shows a set of spanwise profiles, com- are used to assess the simulation results. Figure 3 shows a set of spanwise profiles, com- paring the computations and measurements both at the stator and rotor exit. The top-left paring the computations and measurements both at the stator and rotor exit. The top-left frame of Figure 3 reports the distribution of total pressure loss coefficient (Yloss) at the frame of Figure 3 reports the distribution of total pressure loss coefficient (Yloss) at the stator exit and shows a remarkable agreement between experiment and calculations. It is to stator exit and shows a remarkable agreement between experiment and calculations. It is be noted that the experimental trend interrupts at 10% span, due to limitations in the probe to be noted that the experimental trend interrupts at 10% span, due to limitations in the traversing, so the severe increase of loss in the hub region predicted by the numerical trend probe traversing, so the severe increase of loss in the hub region predicted by the numer- cannot be entirely visible in the measurements (but it is outlined in the bottom part of the ical trend cannot be entirely visible in the measurements (but it is outlined in the bottom experimental profile). This generation of loss in the hub region is driven by a hub clearance part of the experimental profile). This generation of loss in the hub region is driven by a in the region of the blade tail, whose effect combines with the inherent cascade corner hub clearance in the region of the blade tail, whose effect combines with the inherent cas- vortex to generate a wide vortex counter-rotating with the hub passage vortex. More details cade corner vortex to generate a wide vortex counter-rotating with the hub passage vor- on the stator aerodynamic will be discussed later, when analyzing the flow configuration. tex. More details on the stator aerodynamic will be discussed later, when analyzing the The remaining three frames of Figure 3 report the spanwise profiles of Mach number, flow configuration. deviation angle (defined as the difference between the relative flow angle and the blade metallic angle) and absolute flow angle downstream of the rotor. Again, a good agreement was found between simulations and experiments, especially below 80% span. The spanwise flow configuration appears highly non uniform, marking the presence of large over-turning (i.e., low/negative deviation angle) region at 20% and 80% span caused by the secondary flows and an underturning region at midspan, where the two large rotor passage vortices come to interact. The simulations capture well the radial extension and the spanwise migration of the vortices, as well as their impact on the flow angle. Larger discrepancies appear only in the top 20% span, where a wide tip leakage vortex develops and proves to be challenging for the turbulence modeling used in this study. Int. J. Turbomach. Propuls. Power 2021, 6, 28 6 of 17 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 6 of 18 (a) (b) (c) (d) Figure 3. Measured and computed spanwise profiles. (a) Yloss at stator- exit; (b) Mach number at rotor exit. (c) rotor-exit Figure 3. Measured and computed spanwise profiles. (a) Yloss at stator- exit; (b) Mach number at rotor exit. (c) rotor-exit deviation angle; (d) and absolute flow angle. deviation angle; (d) and absolute flow angle. The remaining three frames of Figure 3 report the spanwise profiles of Mach number, Accordingly, a very good quantitative agreement is also obtained in terms of cascade deviation angle (defined as the difference between the relative flow angle and the blade and stage efficiency. The overall stator loss coefficient, estimated from the experiments metallic angle) and absolute flow angle downstream of the rotor. Again, a good agreement equal to 5.9%, resulted 5.4% from the simulation (averaging over the span covered by the was found between simulations and experiments, especially below 80% span. The measurement traverse). The total-total stage efficiency, calculated as the ratio between the spanwise Euler work flow (computed configuration a as theppears highly non difference between uniform, ma the UV terms rkin weight g the presenc ed on the e of lar flowge rate over-t upstr urn eam ing (i. and e.,downstr low/negeam ativeof dev the iat rio otor) n anand gle) the regitotal on atto 20% static and 80% isentr sp opic anenthalpy caused by drthe secon op, is estimated dary flow as s 86.4% and an under from experiments, turning reg with ion at anmidspan uncertainty , where the quantified two in large 0.5% rotor and parss esulted age voequal rtices com to 85.5% e to iin nter the act CFD . The simulation. simulations capture well the radial extension and The quantitative and qualitative reliability resulting from this assessment study indi- the spanwise migration of the vortices, as well as their impact on the flow angle. Larger cate that the present simulation can be used as an effective tool for the physical interpreta- discrepancies appear only in the top 20% span, where a wide tip leakage vortex develops tion of experimental data. and proves to be challenging for the turbulence modeling used in this study. Accordingly, a very good quantitative agreement is also obtained in terms of cascade 4. Results and stage efficiency. The overall stator loss coefficient, estimated from the experiments This section presents the results of the flow downstream of the stator, first neglecting equal to 5.9%, resulted 5.4% from the simulation (averaging over the span covered by the the stator–rotor interaction and then highlighting its effect. The flow field is discussed first measurement traverse). The total-total stage efficiency, calculated as the ratio between the from the perspective of a stationary observer, to show what discharged by the stator and Euler work (computed as the difference between the 𝑈𝑉 terms weighted on the flow rate then in the rotating frame of reference, to present what enters into the rotor according to its upstream and downstream of the rotor) and the total to static isentropic enthalpy drop, is own perspective. estimated as 86.4% from experiments, with an uncertainty quantified in ±0.5% and re- Results will be presented first in a time-mean form to evidence the gross features of sulted equal to 85.5% in the CFD simulation. the flow and secondly by the description of the different interaction phases between the The quantitative and qualitative reliability resulting from this assessment study in- stator and the rotor. dicate that the present simulation can be used as an effective tool for the physical inter- pretation of experimental data. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 7 of 18 4. Results This section presents the results of the flow downstream of the stator, first neglecting the stator–rotor interaction and then highlighting its effect. The flow field is discussed first from the perspective of a stationary observer, to show what discharged by the stator and then in the rotating frame of reference, to present what enters into the rotor according to its own perspective. Results will be presented first in a time-mean form to evidence the gross features of the flow and secondly by the description of the different interaction phases between the Int. J. Turbomach. Propuls. Power 2021, 6, 28 7 of 17 stator and the rotor. 4.1. Time Averaged Quantities 4.1.1. Absolute Frame of Reference 4.1. Time Averaged Quantities One of the most important physical quantity to describe is the total pressure and its 4.1.1. Absolute Frame of Reference related total pressure loss coefficient. In stators, losses are generated by the blade bound- One of the most important physical quantity to describe is the total pressure and its ary layers, the wake shed downstream of the blade trailing edge and the secondary vorti- related total pressure loss coefficient. In stators, losses are generated by the blade boundary ces and their mutual interaction (shock losses being absent due to subsonic character of layers, the wake shed downstream of the blade trailing edge and the secondary vortices and the flow). Given such occurrence, a typical distribution of total pressure loss coefficient their mutual interaction (shock losses being absent due to subsonic character of the flow). downstream of the stator located in the present test rig is reported in the frame (a) of Given such occurrence, a typical distribution of total pressure loss coefficient downstream Figure 4, as measured by FRAPP (top) and predicted by CFD (bottom) within the stator– of the stator located in the present test rig is reported in the frame (a) of Figure 4, as rotor gap. measured by FRAPP (top) and predicted by CFD (bottom) within the stator–rotor gap. (a) (b) Figure 4. Time-averaged contours at the stator exit. Left-to-right: (a) Total pressure loss (Yloss); (b) Static pressure coeffi- Figure 4. Time-averaged contours at the stator exit. Left-to-right: (a) Total pressure loss (Yloss); (b) Static pressure coefficient cient (Cps). Top: experiment. Bottom: CFD predictions. (Cps). Top: experiment. Bottom: CFD predictions. As extensively discussed in [11,18] the narrow loss trace along the span is the wake, As extensively discussed in [11,18] the narrow loss trace along the span is the wake, whereas the two cores, one at the hub and the second one at 75% span, are related to the whereas the two cores, one at the hub and the second one at 75% span, are related to the secondary flows and to their interaction with the wake. The wake, evidenced both in the secondary flows and to their interaction with the wake. The wake, evidenced both in the total pressure and loss field, is distorted by the action of the secondary flows, by the blade total pressure and loss field, is distorted by the action of the secondary flows, by the blade twist and lean resulting in a spanwise variation of flow angle from 85° at the tip to 64° at twist and lean resulting in a spanwise variation of flow angle from 85 at the tip to 64 at the hub. These features are properly captured by the code, demonstrating the fidelity of the hub. These features are properly captured by the code, demonstrating the fidelity of the simulation tool also on a distributed level. In the hub region, a wide loss core appears, induced by the hub clearance. Even though measurements are not available in this region (the bottom and top limits of the measurement surface are marked in the computed field by white lines), the very bottom part of the measurement plane indicates an increase of loss coefficient in the central part of the channel (far away from the wake) consistent with what predicted by the code. While this feature is weakly visible here (though present and marked by black arrows), it clearly appeared in the five-hole probe measurement data presented in [18] for that the probe design allowed to extend the measurement grid closer to the hub end wall. The static pressure field, shown in Figure 4b evidences the usual radial pressure gradient due to the radial equilibrium, combined to a circumferential perturbation resulting from the suction/pressure gradient across the blade passage still not completely Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 8 of 18 the simulation tool also on a distributed level. In the hub region, a wide loss core appears, induced by the hub clearance. Even though measurements are not available in this region (the bottom and top limits of the measurement surface are marked in the computed field by white lines), the very bottom part of the measurement plane indicates an increase of loss coefficient in the central part of the channel (far away from the wake) consistent with what predicted by the code. While this feature is weakly visible here (though present and marked by black arrows), it clearly appeared in the five-hole probe measurement data presented in [18] for that the probe design allowed to extend the measurement grid closer Int. J. Turbomach. Propuls. Power 2021, 6, 28 8 of 17 to the hub end wall. The static pressure field, shown in Figure 4b evidences the usual radial pressure gradient due to the radial equilibrium, combined to a circumferential per- turbation resulting from the suction/pressure gradient across the blade passage still not completely decayed at this axial position. The pressure field marks the perturbation pro- decayed at this axial position. The pressure field marks the perturbation produced by the duced by the hub vortex, also evident in the experiment. hub vortex, also evident in the experiment. All All fframes rames a appearing ppearing at at tthe he top top of of Fi Figur gure e 4 w 4 wer ere o e obtained btained b by y time-averaging time-averaging the the FRA FRAPP PP da dat ta a and and for for thi this s r re eason ason the the p periodic eriodic uns unsteadiness teadiness g given iven b by y the the ro rotor tor is is fi filter ltered. ed. Exp Exploiting loiting th the e FR FRAP APP P p pr ro omptness mptness and ap and applying plying the so-c the so-called alled trip triple le decom decomposition position to the to the pressu pressur re e signal, signal, it it is is possible possible to to extract extracthe t thr e re esolved solved (periodic) (periodic and ) and unr unr esolved esolve unsteadiness d unsteadi- of the flow. Filtering only the periodic component, the resulting signal can be interpreted ness of the flow. Filtering only the periodic component, the resulting signal can be inter- as the random total pressure oscillation due to turbulence and its standard deviation RMSP preted as the random total pressure oscillation due to turbulence and its standard devia- can be used as marker of regions of high turbulence [22]. All the low total pressure regions tion RMSP can be used as marker of regions of high turbulence [22]. All the low total identified above find perfect correspondence with high RMSP regions, as visible from the pressure regions identified above find perfect correspondence with high RMSP regions, RMSP map reported in Figure 5, assessing the interpretation of such regions as viscous as visible from the RMSP map reported in Figure 5, assessing the interpretation of such flow structures released by the stator. This observation, which appears trivial on a time- regions as viscous flow structures released by the stator. This observation, which appears averaged basis, will become less trivial when we will focus on the stator–rotor interaction trivial on a time-averaged basis, will become less trivial when we will focus on the stator– in Section 4.2 of the paper. rotor interaction in Section 4.2 of the paper. Figure 5. Standard deviation of the absolute total pressure (RMSP) at the stator exit Figure 5. Standard deviation of the absolute total pressure (RMSP) at the stator exit. 4.1.2. Rotating Frame of Reference 4.1.2. Rotating Frame of Reference When the perspective is changed from the stationary to the rotating frame of refer- When the perspective is changed from the stationary to the rotating frame of refer- ence, different flow features can be highlighted. In the rotating frame, usual meaningful ence, different flow features can be highlighted. In the rotating frame, usual meaningful quantities are the relative total pressure (and its related coefficient Cptr) and the relative quantities are the relative total pressure (and its related coefficient Cptr) and the relative Mach number (Mr) entering the rotor, whose measured distributions are reported in the Mach number (Mr) entering the rotor, whose measured distributions are reported in the two top frames of Figure 6. two top frames of Figure 6. As for the Cptr distribution in circumferential direction, it shows a peak and a sink As for the Cptr distribution in circumferential direction, it shows a peak and a sink per pitch, thus evidencing a periodic trend; the same feature is found for the Mach number, per pitch, thus evidencing a periodic trend; the same feature is found for the Mach num- which presents a trend opposite to that of the static pressure. The shape of the low Cptr ber, which presents a trend opposite to that of the static pressure. The shape of the low region (highlighted by black dashed lines in Figure 6), which has a nearly constant extension Cptr region (highlighted by black dashed lines in Figure 6), which has a nearly constant in circumferential direction along the whole channel span, suggests that it is not related to the stator wake (which, instead, is strongly bended); thus, another effect is acting here, clearly related to the rotor. If, somehow artificially, the time-mean distribution of absolute total pressure perceived by a rotating observer is analyzed, one may expect to see a uniform trend in circumferential direction; the same conclusion applies to the RMSP, whose distribution was found to corre- spond to the one of the absolute total pressure for stationary observers. This expectation is disregarded by measurements, also being visible in the two bottom frames of Figure 6. As a matter of fact, only the RMSP evidences an azimuthally uniform distribution, whereas the Pt distribution shows an evident perturbation whose spatial periodicity coincides with that of the rotor. The low total pressure region cannot be acknowledged as the stator wake Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 9 of 18 extension in circumferential direction along the whole channel span, suggests that it is not related to the stator wake (which, instead, is strongly bended); thus, another effect is act- ing here, clearly related to the rotor. If, somehow artificially, the time-mean distribution of absolute total pressure per- ceived by a rotating observer is analyzed, one may expect to see a uniform trend in cir- cumferential direction; the same conclusion applies to the RMSP, whose distribution was found to correspond to the one of the absolute total pressure for stationary observers. This expectation is disregarded by measurements, also being visible in the two bottom frames Int. J. Turbomach. Propuls. Power 2021, 6, 28 9 of 17 of Figure 6. As a matter of fact, only the RMSP evidences an azimuthally uniform distri- bution, whereas the Pt distribution shows an evident perturbation whose spatial perio- dicity coincides with that of the rotor. The low total pressure region cannot be acknowl- edged as the st or as the secondary ator wak loss e or regi as the on since secon no dary lo characteristic ss region since no c features of har those acteris phenomena tic featurescan of those be found. phenomena can be found. (a) (b) (c) (d) Figure 6. Experimental time-averaged flow in the rotating frame of reference; (a) relative total pressure coefficient Cptr; Figure 6. Experimental time-averaged flow in the rotating frame of reference; (a) relative total pressure coefficient Cptr; (b) (b) relative Mach number Mr; (c) unresolved total pressure unsteadiness RMSP; (d) total pressure coefficient Cpt. relative Mach number Mr; (c) unresolved total pressure unsteadiness RMSP; (d) total pressure coefficient Cpt. CFD simulation results, reported in Figure 7, confirm the regular and typical trend CFD simulation results, reported in Figure 7, confirm the regular and typical trend of relative Mach number and, especially, the unexpected distribution of absolute total of relative Mach number and, especially, the unexpected distribution of absolute total pressure. The pressure. The reason reasonfor forth these ese results m results must ust be se be sear arch ched ed for forin the in thestator stator–ro –rotor tor in interaction teraction Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 10 of 18 phenomena, deeply presented and discussed in the following section. phenomena, deeply presented and discussed in the following section. (a) (b) Figure 7. Computed time-averaged relative Mach number (a) and absolute total pressure (b) in the rotating frame of ref- Figure 7. Computed time-averaged relative Mach number (a) and absolute total pressure (b) in the rotating frame of erence at the stator exit. reference at the stator exit. 4.2. Rotor–Stator Interaction Effects By exploiting the FRAPP promptness and the phase averaging techniques, it is pos- sible to map the different instants of the stator–rotor interaction and, specifically for this analysis, the effect of the rotor on the flow field released by the stator. The first quantity described is the RMSP, plotted over half of the stator blade row in Figure 8. As a preliminary note, in this kind of plots adjacent channels reproduce different stator–rotor interaction phases, due to the phase-lag resulting from the different number of stator and rotor blade rows. As clearly visible, the distribution is nearly periodic with the stator pitch, being mainly related to the stator viscous structures (labelled as W) that are only marginally affected by the rotor–stator interaction. It is also clearly visible a pe- riodicity over the whole crown of about 120° degrees as a consequence of the rotor and stator blade number (25/22 ≈ 8/7, that means 3 nearly periodic configurations over the whole annulus). The outlines of eight rotor adjacent channels are also marked by black lines and the resulting total arc is also reported. Figure 8. Snapshot of RMSP distribution over multiple channels in different stator–rotor positions. When studying the instantaneous distribution of Pt, reported in Figure 9, the stator wakes, acknowledged as regions of low Pt/high RMSP in the stationary time-averaged maps, become no longer clearly visible, as shown in Figure 8. In the Figure 9 and in the following two figures, the black lines labelled with “W” mark the wake traces identified from RMSP in Figure 8, and are also renamed from A to G to consider the different chan- nel. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 10 of 18 (a) (b) Int. J. Turbomach. Propuls. Power 2021, 6, 28 10 of 17 Figure 7. Computed time-averaged relative Mach number (a) and absolute total pressure (b) in the rotating frame of ref- erence at the stator exit. 4.2. 4.2. Rotor–Stator Rotor–Stator Inte Interaction ractionEffects Effects By By exploiting exploiting the the F FRAPP RAPpr P p omptness romptness and an the d the phase phase averaging averaging techniques, techniques, it is p it is possible os- to sib map le to m the dif apfer thent e diinstants fferent iof nstthe ants stator of the –r s otor tator interaction –rotor inter and, action specifically and, speci for ficthis ally for analysis, this analysis, the effect of the rotor on the flow field released by the stator. the effect of the rotor on the flow field released by the stator. The Thfirst e firsquantity t quantity d described escribed is is the the RMSP RMSP , , p plotted lotted ov over er hal half f o of f th the e s stator tator b blade lade ro row w in in Figure 8. As a preliminary note, in this kind of plots adjacent channels reproduce different Figure 8. As a preliminary note, in this kind of plots adjacent channels reproduce different stator–rotor interaction phases, due to the phase-lag resulting from the different number stator–rotor interaction phases, due to the phase-lag resulting from the different number of stator and rotor blade rows. As clearly visible, the distribution is nearly periodic with of stator and rotor blade rows. As clearly visible, the distribution is nearly periodic with the stator pitch, being mainly related to the stator viscous structures (labelled as W) that the stator pitch, being mainly related to the stator viscous structures (labelled as W) that are only marginally affected by the rotor–stator interaction. It is also clearly visible a pe- are only marginally affected by the rotor–stator interaction. It is also clearly visible a riodicity over the whole crown of about 120° degrees as a consequence of the rotor and periodicity over the whole crown of about 120 degrees as a consequence of the rotor and stator blade number (25/22 ≈ 8/7, that means 3 nearly periodic configurations over the stator blade number (25/22  8/7, that means 3 nearly periodic configurations over the whole annulus). The outlines of eight rotor adjacent channels are also marked by black whole annulus). The outlines of eight rotor adjacent channels are also marked by black lines and the resulting total arc is also reported. lines and the resulting total arc is also reported. Figure 8. Snapshot of RMSP distribution over multiple channels in different stator–rotor positions. Figure 8. Snapshot of RMSP distribution over multiple channels in different stator–rotor positions. When studying the instantaneous distribution of Pt, reported in Figure 9, the stator When studying the instantaneous distribution of Pt, reported in Figure 9, the stator wakes, acknowledged as regions of low Pt/high RMSP in the stationary time-averaged wakes, acknowledged as regions of low Pt/high RMSP in the stationary time-averaged maps, become no longer clearly visible, as shown in Figure 8. In the Figure 9 and in the maps, become no longer clearly visible, as shown in Figure 8. In the Figure 9 and in the following two figures, the black lines labelled with “W” mark the wake traces identified following two figures, the black lines labelled with “W” mark the wake traces identified Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 11 of 18 from RMSP in Figure 8, and are also renamed from A to G to consider the different chan- from RMSP in Figure 8, and are also renamed from A to G to consider the different channel. nel. Figure 9. Snapshot of Cpt distribution over multiple channels in different stator–rotor positions. Figure 9. Snapshot of Cpt distribution over multiple channels in different stator–rotor positions. With reference to Figure 9 and starting from left, a low Pt region coincides with black continuous line A, i.e., the stator wake, but another low Pt zone appears on the right (high- lighted with a dashed line), not merged with the former; this second low Pt region is nearly uniform in spanwise direction. As the adjacent channel is considered (wake B), the low Pt zone corresponding to the black line still remains (with marginal difference with respect to the wake A), while the low Pt region ‘moves’ towards the wake and partially overlaps with the latter. For wake C, the two low Pt zones perfectly overlap, leading to the deepest total pressure deficit. Furthermore, shifting from one channel to the adjacent one (wake C to wake D, to E, etc.) the second low Pt region progressively ‘moves’ leftward with respect to the stator wake. The same consideration can be done on the high total pressure region, typically referred to as the isentropic region, where the level is modulated passing from one channel to the adjacent one. The time average of this process in the ab- solute frame, which is the average among the different stator channels appearing in this plot, has been already reported in Figure 4. Moreover, if the pressure level is considered, the time-averaged value Pt in the free stream is 1.345 bar (which corresponds to the up- stream one), while the phase resolved one is up to 1.36 bar. Since across the stator the total pressure cannot increase, the azimuthal perturbation of Pt discussed above is clearly an effect of the rotor on the flow released by the stator. As a further proof of that, this Pt perturbation rotates consistently with the sweeping of the rotor blades. In fact, as the rotor sweeps downstream of the stator outlet section, the rotor potential field propagates upstream with a wave of high and low static pressure, which also induces corresponding changes in the local flow direction. This also induces a local redistribution of mechanical energy, conceptually corresponding to an ‘internal’ work exchange between different portions of the flow, which ultimately alters the total pressure. In Section 5 a quantification of the periodic change in total temperature on the fluid upstream of the rotor, resulting from the process discussed above, will be proposed. Considering the absolute flow angle, reported in Figure 10, the rotor-induced pertur- bation is observed to alter the flow direction. In particular, the interaction positions la- belled as wake C and D show the maximum over-turning (high angles) in the midspan region and the maximum under-turning (low angles) condition at hub. The maximum cross flow at the tip is for the interaction position E, F, where also the lowest total pressure is found. The Mach number field, reported in Figure 11, shows a modulation among the adjacent channels. This feature evidences that changes in the flow rate released by the stator channel depend on the rotor position, as the blade leading edge creates a blockage at the outlet of the stator channel. The lowest Mach number, as an average on the passage, is found in the channel between wakes D and E. Int. J. Turbomach. Propuls. Power 2021, 6, 28 11 of 17 With reference to Figure 9 and starting from left, a low Pt region coincides with black continuous line A, i.e., the stator wake, but another low Pt zone appears on the right (highlighted with a dashed line), not merged with the former; this second low Pt region is nearly uniform in spanwise direction. As the adjacent channel is considered (wake B), the low Pt zone corresponding to the black line still remains (with marginal difference with respect to the wake A), while the low Pt region ‘moves’ towards the wake and partially overlaps with the latter. For wake C, the two low Pt zones perfectly overlap, leading to the deepest total pressure deficit. Furthermore, shifting from one channel to the adjacent one (wake C to wake D, to E, etc.) the second low Pt region progressively ‘moves’ leftward with respect to the stator wake. The same consideration can be done on the high total pressure region, typically referred to as the isentropic region, where the level is modulated passing from one channel to the adjacent one. The time average of this process in the absolute frame, which is the average among the different stator channels appearing in this plot, has been already reported in Figure 4. Moreover, if the pressure level is considered, the time-averaged value Pt in the free stream is 1.345 bar (which corresponds to the upstream one), while the phase resolved one is up to 1.36 bar. Since across the stator the total pressure cannot increase, the azimuthal perturbation of Pt discussed above is clearly an effect of the rotor on the flow released by the stator. As a further proof of that, this Pt perturbation rotates consistently with the sweeping of the rotor blades. In fact, as the rotor sweeps downstream of the stator outlet section, the rotor potential field propagates upstream with a wave of high and low static pressure, which also induces corresponding changes in the local flow direction. This also induces a local redistribution of mechanical energy, conceptually corresponding to an ‘internal’ work exchange between different portions of the flow, which ultimately alters the total pressure. In Section 5 a quantification of the periodic change in total temperature on the fluid upstream of the rotor, resulting from the process discussed above, will be proposed. Considering the absolute flow angle, reported in Figure 10, the rotor-induced per- turbation is observed to alter the flow direction. In particular, the interaction positions labelled as wake C and D show the maximum over-turning (high angles) in the midspan region and the maximum under-turning (low angles) condition at hub. The maximum cross flow at the tip is for the interaction position E, F, where also the lowest total pressure is found. The Mach number field, reported in Figure 11, shows a modulation among the adjacent channels. This feature evidences that changes in the flow rate released by the stator channel depend on the rotor position, as the blade leading edge creates a blockage at the outlet of the stator channel. The lowest Mach number, as an average on the passage, is Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 12 of 18 found in the channel between wakes D and E. Figure 10. Snapshot of absolute flow angle distribution over multiple channels in different stator– Figure 10. Snapshot of absolute flow angle distribution over multiple channels in different stator– rotor positions. rotor positions. Figure 11. Snapshot of M distribution over multiple channels in different stator–rotor positions. The scenario resulting from the analysis of the time-resolved experiments in-between the stator–rotor gap demonstrates a significant interference between the stator and rotor aerodynamics. While several effects are well known and properly discussed in Literature, for other quantities (like the absolute total pressure) an explanation is required. To this end, the CFD simulations were considered and Figure 12 summarizes relevant features— unavailable in the experiments—such as the flow configuration and the distribution of absolute total quantities, entropy and pressure on a blade-to-blade surface at midspan. The left frame of Figure 12 shows the streamlines constructed with the absolute velocity vector upstream and within the rotor channel. Streamlines clearly mark the local flow turning occurring around the rotor leading edge and in particular the absolute flow un- dergoes a local acceleration and deflection close to the front suction side of the rotor blade. This is the motivation for the azimuthal variability of flow angle observed in the experi- ments, recognized when commenting Figure 10. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 12 of 18 Int. J. Turbomach. Propuls. Power 2021, 6, 28 12 of 17 Figure 10. Snapshot of absolute flow angle distribution over multiple channels in different stator– rotor positions. Figure 11. Snapshot of M distribution over multiple channels in different stator–rotor positions. Figure 11. Snapshot of M distribution over multiple channels in different stator–rotor positions. The The scenario scenario resulting resulting from from the the an analysis alysisof ofthe the time time-r -re esolved solved experi experiments ments in in-between -between the stator–rotor gap demonstrates a significant interference between the stator and rotor the stator–rotor gap demonstrates a significant interference between the stator and rotor aerodynamics. While several effects are well known and properly discussed in Literature, aerodynamics. While several effects are well known and properly discussed in Literature, for other quantities (like the absolute total pressure) an explanation is required. To this for other quantities (like the absolute total pressure) an explanation is required. To this end, the CFD simulations were considered and Figure 12 summarizes relevant features— end, the CFD simulations were considered and Figure 12 summarizes relevant features— unavailable in the experiments—such as the flow configuration and the distribution of unavailable in the experiments—such as the flow configuration and the distribution of absolute total quantities, entropy and pressure on a blade-to-blade surface at midspan. absolute total quantities, entropy and pressure on a blade-to-blade surface at midspan. The The left frame of Figure 12 shows the streamlines constructed with the absolute velocity left frame of Figure 12 shows the streamlines constructed with the absolute velocity vector vector upstream and within the rotor channel. Streamlines clearly mark the local flow upstream and within the rotor channel. Streamlines clearly mark the local flow turning turning occurring around the rotor leading edge and in particular the absolute flow un- occurring around the rotor leading edge and in particular the absolute flow undergoes dergoes a local acceleration and deflection close to the front suction side of the rotor blade. a local acceleration and deflection close to the front suction side of the rotor blade. This This is the motivation for the azimuthal variability of flow angle observed in the experi- is the motivation for the azimuthal variability of flow angle observed in the experiments, ments, recognized when commenting Figure 10. recognized when commenting Figure 10. The change in flow angle is associated to a change in the angular momentum of the fluid, which increases locally, because the rotor blade has locally imparted torque to the flow: this process has ultimately increased the mechanical energy of the flow upstream of the blade. This variation of mechanical energy has opposite sign with respect to the one expected in a turbine, thus leading to the local absolute total pressure increase and explaining the unexpected rise of Pt upstream of the rotor. This phenomenon is clearly visible in the corresponding Pt distribution reported in Figure 12, which shows how the high Pt region propagates upstream, producing a significant effect also on the stator wake, as appearing in this interaction phase. It is interesting to note that this process does not alter the entropy level in the flow upstream of the rotor: the entropy field shows how the stator wake is bowed by the interaction with the rotor blade, but it also highlights that no further entropy production occurs, thus confirming the quasi-isentropic character of the effect here discussed. The field of Tt at midspan exhibits an azimuthal perturbation propagating upstream, along the black dashed lines reported in Figure 12, thus testifying that the flow deflection upstream of the rotor is the main player of the process. Thanks to the near-uniformity of the total temperature background field, one can properly appreciate the sinusoidal character of the perturbation, as well as its crucial dependence on the design of the front part of the blade, especially on the suction side. From this perspective, the comparison with the static pressure field indicates that the Pt-Tt perturbations are not linked to the recompression induced by the rotor leading edge (which propagates upstream along the red dashed line), but it conversely occurs in a region of the flow featuring a relatively low static pressure; Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 13 of 18 in particular, the total temperature/total pressure rise begins exactly where maximum (in absolute value) negative azimuthal pressure gradients is found. Figure 12. Computed instantaneous absolute flow field across the rotor at midspan. Left: streamlines of absolute velocity Figure 12. Computed instantaneous absolute flow field across the rotor at midspan. Left: streamlines of absolute velocity vector (coloured by the velocity magnitude). Center: Pt (top) and entropy (bottom) fields. Right: Tt (top), P (bottom) fields. vector (coloured by the velocity magnitude). Center: Pt (top) and entropy (bottom) fields. Right: Tt (top), P (bottom) fields. The change in flow angle is associated to a change in the angular momentum of the fluid, which increases locally, because the rotor blade has locally imparted torque to the flow: this process has ultimately increased the mechanical energy of the flow upstream of the blade. This variation of mechanical energy has opposite sign with respect to the one expected in a turbine, thus leading to the local absolute total pressure increase and ex- plaining the unexpected rise of Pt upstream of the rotor. This phenomenon is clearly visi- ble in the corresponding Pt distribution reported in Figure 12, which shows how the high Pt region propagates upstream, producing a significant effect also on the stator wake, as appearing in this interaction phase. It is interesting to note that this process does not alter the entropy level in the flow upstream of the rotor: the entropy field shows how the stator wake is bowed by the interaction with the rotor blade, but it also highlights that no further entropy production occurs, thus confirming the quasi-isentropic character of the effect here discussed. The field of Tt at midspan exhibits an azimuthal perturbation propagating upstream, along the black dashed lines reported in Figure 12, thus testifying that the flow deflection upstream of the rotor is the main player of the process. Thanks to the near-uniformity of the total temperature background field, one can properly appreciate the sinusoidal char- acter of the perturbation, as well as its crucial dependence on the design of the front part of the blade, especially on the suction side. From this perspective, the comparison with the static pressure field indicates that the Pt-Tt perturbations are not linked to the recom- pression induced by the rotor leading edge (which propagates upstream along the red dashed line), but it conversely occurs in a region of the flow featuring a relatively low static pressure; in particular, the total temperature/total pressure rise begins exactly where maximum (in absolute value) negative azimuthal pressure gradients is found. Int. J. Turbomach. Propuls. Power 2021, 6, 28 13 of 17 5. Discussion: Energy Separation Effect One of the consequences of the rotor-induced periodic flow fluctuation is that the rotor pressurises and depressurizes the flow field in the stator–rotor gap: if, as in this case, the flow is subsonic, no shock waves establish and the time-average of this perturbation is null, namely the time-mean flow corresponds to the steady-state flow condition. As shown by CFD results, the rotation of the rotor potential field induces quasi-isentropic unsteady perturbations of total temperature (or total enthalpy) propagating upstream. The observed effect can be analytically justified by resorting to equation 1, which establishes a link, rigorously valid only for inviscid flows, between the material derivative of the total enthalpy and the local (partial) derivative of the static pressure. The capability of static pressure unsteadiness to ‘redistribute’ total quantities is often called, in Literature, energy separation effect. Energy separation was widely documented to occur in the Von Karman vortex streets featuring the wake of cylinders in cross-flow [23,24] and was also observed to occur in the blade-wake interaction phenomena [18]. In the present case, the source of the static pressure unsteadiness has to be found in the rotor pressure field travelling with the blade itself. As a result of the blade motion, the azimuthal gradients of pressure on the relative frame covert into static pressure unsteadiness according to the formula [25]: ¶p ¶p = U j (2) rel ¶t ¶y By plugging expression (2) into Equation (1), one gets a differential relation between the rotor pressure field and the total enthalpy rise: Dh ¶p r = U j (3) rel Dt ¶y Equation (3) demonstrates analytically the experimental and computational finding of this study, i.e., that the rotor pressure field is able to trigger energy separation effects in the stator–rotor axial gap of a high pressure gas turbine. If the rotor aerodynamic loading is high (as usual in present-day gas turbine stages) and the stator–rotor axial gap is small (as usual in turbines) this effect might influence in a non-negligible way the stator blade aerodynamics and heat transfer. The statements above and, in a broader sense, the technical relevance of the energy separation effect here discussed demand for a proper quantification. In fact, a direct quantitative evaluation of the total enthalpy/total temperature oscillation upstream of the rotor is not feasible, since no unsteady measurements of total temperature are available (neither a fast-response temperature probe nor a rotating probe are available for such high speed rotors). Nevertheless, the isentropic character of the energy separation effect allows estimating the total temperature increase from experiments, by applying the isentropic thermodynamic relations to the measured total pressure perturbations. Considering as ref- erence values the pitchwise-averages of the measured total pressure and total temperature distributions, the local phase-resolved total temperature is calculated by the phase-resolved total pressure as follows: g1 Pt Tt = Tt (4) Pt It is interesting to note that the pitchwise averages Pt and Tt are effective reference conditions, as the average filters the effect of the rotor potential field. The total temperature fluctuation due to energy separation can be finally evaluated as DTt = Tt Tt. The results of this quantification are reported in Figure 13a over two rotor pitches and show—for the present operating condition—a temperature fluctuation DTt of 0.9 K; this value corresponds to about 8% of the total temperature drop across the stage (21.5 K). The slight tangential shift between the high temperature level at the hub and at the tip depends on the rotor blade twisting, on the spanwise trend of the azimuthal leading edge position Int. J. Turbomach. Propuls. Power 2021, 6, 28 14 of 17 Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 15 of 18 of the rotor blade and on the leading edge loading. Interestingly, Figure 13b reports the of the rotor blade and on the leading edge loading. Interestingly, Figure 13b reports the distribution of over two rotor pitches as directly extracted from CFD simulation (i.e., distribution of DTt over two rotor pitches as directly extracted from CFD simulation (i.e., using the actual unsteady total temperature values predicted by the solver). The excellent using the actual unsteady total temperature values predicted by the solver). The excellent comparison between the experimental estimate and the simulation demonstrates not only comparison between the experimental estimate and the simulation demonstrates not only the ‘qualitativethe ’ va‘qu lidialitative’ ty of the in validity terpreta oftion the, b interpr ut also the etation, qu but antialso tativthe e requantitative levance of the relevance of the energy separation a energy pproa separation ch. approach. (a) (b) Figure 13. Amplitude of the periodic fluctuations of total temperature upstream of the rotor due to Figure 13. Amplitude of the periodic fluctuations of total temperature upstream of the rotor due to rotor-driven perturbation; rotor-driven perturbation; (a) estimated from total pressure measurements; (b) predicted by CFD. (a) estimated from total pressure measurements; (b) predicted by CFD. Ultimately, the operating condition here presented is one out of the four ones actually Ultimately, the operating condition here presented is one out of the four ones actually available, taken at higher and lower expansion ratio (though still all subsonic) and here available, taken at higher and lower expansion ratio (though still all subsonic) and here not not shown for sake of brevity: it is important to highlight that, for all such different oper- shown for sake of brevity: it is important to highlight that, for all such different operating ating conditions, the total temperature fluctuation always results of about 10% of the stage conditions, the total temperature fluctuation always results of about 10% of the stage total total temperature drop. temperature drop. 6. Conclusions 6. Conclusions The paper has presented, by combining experiments and CFD simulations, the flow The paper has presented, by combining experiments and CFD simulations, the flow within the stator–rotor gap of a subsonic high-pressure turbine and on how this is influ- within the stator–rotor gap of a subsonic high-pressure turbine and on how this is influ- enced by the rotor potential field propagating upstream. enced by the rotor potential field propagating upstream. First, a validation of the CFD model against the experimental data has been pro- First, a validation of the CFD model against the experimental data has been provided, vided, showing a very good agreement in terms of overall cascade and stage performance, showing a very good agreement in terms of overall cascade and stage performance, spanwise profiles of pitch-wise averaged data and distributed flow field. spanwise profiles of pitch-wise averaged data and distributed flow field. Then, the flow released by the stator has been investigated considering two alternative Then, the flow released by the stator has been investigated considering two alterna- perspectives, i.e., for stationary and rotating observers, both in terms of time mean and tive perspectives, i.e., for stationary and rotating observers, both in terms of time mean phase-resolved quantities. The analysis in the stationary frame shows the well-known wake and phase-resolved quantities. The analysis in the stationary frame shows the well-known and secondary flows pattern, the radial equilibrium issues and loss mechanisms typical of wake and secondary flows pattern, the radial equilibrium issues and loss mechanisms a subsonic modern stator. In the rotating frame of reference, the relative quantities show a typical of a subsonic modern stator. In the rotating frame of reference, the relative quan- periodic pattern with a shape and periodicity related to the rotor pitch. On the contrary, tities show a periodic pattern with a shape and periodicity related to the rotor pitch. On the absolute total pressure perceived by a rotating observer evidences a periodic pattern the contrary, the absolute total pressure perceived by a rotating observer evidences a pe- featuring the rotor angular periodicity, thus revealing an influence of the rotor potential riodic pattern featuring the rotor angular periodicity, thus revealing an influence of the field on the total pressure field in the stator–rotor gap. rotor potential field on the total pressure field in the stator–rotor gap. When the phase-resolved flow field is analyzed, the impact of the rotor aerodynamics When the phase-resolved flow field is analyzed, the impact of the rotor aerodynamics on the flow in the stator–rotor gap is found on most quantities, such as the total pressure, on the flow in the stator–rotor gap is found on most quantities, such as the total pressure, the Mach number, the flow angle, while the viscous dissipative structures released by the the Mach number, the flow angle, while the viscous dissipative structures released by the stator appear only weakly affected by the rotor. These effects can only be connected to stator appear only weakly affected by the rotor. These effects can only be connected to the the rotor potential field, which is the unique rotor feature which can propagate upstream. rotor potential field, which is the unique rotor feature which can propagate upstream. The The Mach number distribution exhibits a periodic blockage of the stator channel flow Mach number distribution exhibits a periodic blockage of the stator channel flow rate. The rate. The flow angle also shows a periodic increase in the tangential component of the flow angle also shows a periodic increase in the tangential component of the absolute ve- absolute velocity. The total pressure experiences a periodic increase with respect to the locity. The total pressure experiences a periodic increase with respect to the stator up- stator upstream, thus apparently violating the energy and momentum balances. CFD stream, thus apparently violating the energy and momentum balances. CFD simulations simulations reveal the inherent link between these observations, suggesting that the total 𝛥𝑇𝑡 Int. J. Turbomach. Propuls. Power 2021, 6, 28 15 of 17 pressure rise is caused by the deflection imposed to the absolute flow when turning around the front part of the rotor blade. Predictions also show local and periodic total temperature rise in correspondence to the total pressure one, also marking a nearly-isentropic process. An analytical approach allows explaining the observed feature and to classify it as a new energy separation effect, not described up to now in the scientific literature according to authors’ knowledge, in which the static pressure unsteadiness is triggered by the rotation of the rotor potential field. On the quantitative ground, this energy separation effect impacts the total temperature field, which is periodically altered by about 8% with respect to the mean temperature drop across the stage. Such an effect might play a role on the aerodynamics and, especially, on the heat trans- fer in the rear section of the stator blade, especially for new-generation gas turbines stages featuring high rotor loading and small axial gap in-between the blade rows. Moreover, in case of transonic turbines (except for the very rare, saturated condition) the onset of supersonic flows and shock wave patterns within the stator–rotor gap would likely alter the isentropic character of the process, with potential impact on the performance. Future works will extend the present study considering transonic stages and more realistic axial gaps, with special focus on the aero-thermal stator behavior. Beside the physical aspects, the present findings also show the importance of the design of the front part of the rotor blade, that is, one of the main geometrical features that determines the propagation upstream of the rotor potential field. Further studies on this feature and its implication may lead to novel design remarks for both the rotor and the stator optimization. Author Contributions: Conceptualization, P.G. and G.P.; methodology, P.G. and G.P.; software, P.G. and G.P.; experiments, P.G.; CFD and its validation, G.P.; formal analysis, P.G. and G.P.; writing— original draft preparation, P.G. and G.P.; writing—review and editing, G.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Nomenclature Int. J. Turbomach. Propuls. Power 2021, 6, 28 16 of 17 Latin c stator axial chord x:V D stage mean diameter G mass flow rate h blade height h Total Enthalpy Mr relative Mach number n rotational speed N blade number Ps static pressure Pt absolute total pressure Ptr relative total pressure Pt pitchwise-averaged total pressure t time t tip clearance Tt absolute total temperature Tt pitchwise-averaged total temperature Tt inlet total temperature in U peripheral speed Vt tangential velocity Yloss total pressure loss coefficient Greek total to static expansion ratio D difference " flow deflection at midspan ratio of specific heat capacities density blade solidity at midspan (chord/pitch) Q circumferential coordinate D angular rotor pitch Subscripts reference condition re f Abbreviations AR blade aspect ratio (height/chord) CFD Computational Fluid Dynamics Cps = (P-P )/(Pt -P ) pressure coefficient ref ref ref Cpt = (Pt-P )/(Pt -P ) total pressure coefficient ref ref ref Cptr = (Ptr-P )/(Pt -P ) relative total pressure coefficient ref ref ref FRAPP fast response aerodynamic pressure probe TPV Tip Passage Vortex Int. 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Journal

International Journal of Turbomachinery, Propulsion and PowerMultidisciplinary Digital Publishing Institute

Published: Jul 13, 2021

Keywords: high-pressure turbines; blade-row interaction; cascade potential field; energy separation; unsteady measurements; time-accurate CFD

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