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Turbine Cascades of Last Stage Blades for Wide Range of Operating Conditions

Turbine Cascades of Last Stage Blades for Wide Range of Operating Conditions International Journal of Turbomachinery Propulsion and Power Article Turbine Cascades of Last Stage Blades for Wide Range of Operating Conditions 1 1 2 3 4 , Ondrej Novak , Marek Bobcik , Martin Luxa , Jaroslav Fort , Bartolomej Rudas *, 4 2 3 3 3 2 Jaroslav Synac , David Simurda , Jiri Furst , Jan Halama , Vladimir Hric , Jaromir Prihoda and Zdenek Simka Research and Development, Doosan Skoda Power, Ltd., 30128 Pilsen, Czech Republic; novak-ondrej@email.cz (O.N.); marekbobcik@seznam.cz (M.B.); zdenek.simka@doosan.com (Z.S.) Institute of Thermomechanics of the Czech Academy of Sciences, 182 00 Prague, Czech Republic; luxa@it.cas.cz (M.L.); simurda@it.cas.cz (D.S.); prihoda@it.cas.cz (J.P.) Faculty of Mechanical Engineering, Czech Technical University, 160 00 Prague, Czech Republic; jaroslav.fort@fs.cvut.cz (J.F.); jiri.furst@fs.cvut.cz (J.F.); jan.halama@fs.cvut.cz (J.H.); vladimir.hric@fs.cvut.cz (V.H.) Faculty of Mechanical Engineering, West Bohemian University, 301 00 Pilsen, Czech Republic; synac@kke.zcu.cz * Correspondence: bartolomej.rudas@doosan.com y This Paper is an Extended Version of Our Paper Published in Proceedings of the European Turbomachinery Conference ETC13, Lausanne, Switzerland, 8–12 April 2019, Paper No. 350. Received: 22 July 2019; Accepted: 6 September 2019; Published: 24 September 2019 Abstract: Recent trends in the electric energy market such as biomass, waste incineration or combined cycle power plants require innovative solutions in steam turbine design. Variable operating conditions cause significant changes in flow field surrounding the steam turbine last stage blades. Therefore, the enlargement of operating range for last stage blades presents new challenges in design of turbine cascades. Several turbine cascades were designed and analyzed by commercial and in-house software of CTU Prague. Selected profiles were experimentally validated in the high-speed wind tunnel for 2D cascade measurements of the Institute of Thermomechanics of the Czech Academy of Sciences which is equipped by an adjustable supersonic inlet nozzle, perforated inserts at side walls and adjustable perforated tailboard. Comparisons are presented of numerical results with optical and pneumatic measurements for a wide range of inlet and outlet Mach numbers for optimized hub and tip profile cascades. Keywords: turbine; cascade; last stage blade; CFD; experimental validation 1. Introduction The last stage rotating blade is a key component of each steam turbine, directly contributing to overall eciency of the thermal cycle. There are many challenges in the development and validation process of last stage blades both in terms of thermodynamic and mechanical design. High tip/hub ratio results in dense hub cascades and rare tip cascades. The proper stator blade design with advanced 3D shaping is highly important because it has significant impact on the relative velocity in the vicinity of the rotating blade. However, the relative Mach numbers exceeding 1 are commonly present in flow field surrounding the rotating blade due to high tangential velocities and even supersonic flow with inlet shock wave can occur, especially in the case of ultra-long full speed (3000 or 3600 RPM) last stage blades [1]. Final mechanical design must fulfill criteria of static strength which determines strict distribution of area for each section along the blade span. The combination of these requirements limits the design space and leads to the demanding process of optimal solution searching. Int. J. Turbomach. Propuls. Power 2019, 4, 33; doi:10.3390/ijtpp4040033 www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 2 of 10 of these requirements limits the design space and leads to the demanding process of optimal Int. J. Turbomach. Propuls. Power 2019, 4, 33 2 of 10 solution searching. Analytical methods investigating flow field are an essential part of aerodynamic design process Analytical methods investigating flow field are an essential part of aerodynamic design process of of turbine cascades of last stage blades. Obtaining reliable calculated data can be challenging task turbine cascades of last stage blades. Obtaining reliable calculated data can be challenging task both both due to very dense hub cascades with low convergence of channel and due to very rare tip due to very dense hub cascades with low convergence of channel and due to very rare tip cascades cascades with supersonic flow velocities in the channel [2]. with supersonic flow velocities in the channel [2]. The experimental measurements of turbine blade cascades are an indispensable part of The experimental measurements of turbine blade cascades are an indispensable part of validation validation process of the analytical methods and the final aerodynamic solution. The careful design process of the analytical methods and the final aerodynamic solution. The careful design of the of the experiment together with a combination of suitable measurement methods is needed to experiment together with a combination of suitable measurement methods is needed to analyze analyze supersonic flow field [3,4]. Optical methods such as interferometry are particularly useful supersonic flow field [3,4]. Optical methods such as interferometry are particularly useful tool for tool for spatial resolved analysis of high-speed aerodynamics investigations of various blade spatial resolved analysis of high-speed aerodynamics investigations of various blade cascades [5]. cascades [5]. 2. Investigated Blade Cascades 2. Investigated Blade Cascades Blade cascades described in the paper represent the tip section and the hub section. Original and Blade cascades described in the paper represent the tip section and the hub section. Original innovative designs of the tip section are shown in Figure 1b. Whereas in the case of the original design and innovative designs of the tip section are shown in Figure 1b. Whereas in the case of the original the profiles are cambered in order to form the divergent interblade channel, profiles of the innovative design the profiles are cambered in order to form the divergent interblade channel, profiles of the design are practically flat with only the leading edge on the suction side and the trailing edge on the innovative design are practically flat with only the leading edge on the suction side and the trailing pressure side contoured. edge on the pressure side contoured. Hub section blade cascades are shown in Figure 1a. Both were designed for the straight fir tree Hub section blade cascades are shown in Figure 1a. Both were designed for the straight fir tree root dovetail. The main di erence lies in the higher outlet metal angle and incidence angle of the root dovetail. The main difference lies in the higher outlet metal angle and incidence angle of the original design. This was due to the requirement of low exit loss and straight fir tree root. In the case original design. This was due to the requirement of low exit loss and straight fir tree root. In the case of the innovative design, the exit flow angle is lower and the incidence angle is zero. These favourable of the innovative design, the exit flow angle is lower and the incidence angle is zero. These di erences were made possible thanks to the redesign of guide vanes. favourable differences were made possible thanks to the redesign of guide vanes. (a) (b) Figure 1. Schematics of blade cascades—original designs (a) and innovative designs (b). Figure 1. Schematics of blade cascades—original designs (a) and innovative designs (b). 3. Experimental Setup 3. Experimental Setup The optical measurements of transonic and supersonic flow fields were performed in a high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of Thermomechanics of the Czech Academy The optical measurements of transonic and supersonic flow fields were performed in a of Sciences in Novy Knin. The atmospheric air treated by silica gel drier and filters is accelerated by high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of Thermomechanics of the Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 3 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, 33 3 of 10 Czech Academy of Sciences in Novy Knin. The atmospheric air treated by silica gel drier and filters is accelerated by inlet nozzle and enters the test section displayed in Figure 2. The perforated inlet nozzle and enters the test section displayed in Figure 2. The perforated tailboard and sucked tailboard and sucked perforated wall prevent shock waves reflecting back to the measured flow perforated wall prevent shock waves reflecting back to the measured flow field. field. A Mach–Zehnder interferometer in an infinite fringe setting was used for capturing of A Mach–Zehnder interferometer in an infinite fringe setting was used for capturing of interferograms presented in this paper. This experimental setup is described in detail in [5] and [3]. interferograms presented in this paper. This experimental setup is described in detail in [5] and [3]. Static pressure was measured on both sides of the interblade channel during the optical measurement Static pressure was measured on both sides of the interblade channel during the optical which allows evaluation of the distribution of isentropic Mach number M along the suction and is measurement which allows evaluation of the distribution of isentropic Mach number Mis along the pressure side of the measured profile. suction and pressure side of the measured profile. Figure 2. Test section for an investigation of the flow in a prismatic profile cascade with a small flow Figure 2. Test section for an investigation of the flow in a prismatic profile cascade with a small flow turning angle and supersonic inlet velocity. turning angle and supersonic inlet velocity. 4. Numerical Methods 4. Numerical Methods An in-house code developed at the Faculty of Mechanical Engineering, Czech Technical University, An in-house code developed at the Faculty of Mechanical Engineering, Czech Technical Prague, was used for calculation of transonic and supersonic flow fields. The code is based on the University, Prague, was used for calculation of transonic and supersonic flow fields. The code is solution of the Favre averaged Navier–Stokes equations and k–! SST turbulence model by implicit based on the solution of the Favre averaged Navier–Stokes equations and k–ω SST turbulence model finite volume method with AUSMPW+ scheme in high-resolution formulation. The detailed description by implicit finite volume method with AUSMPW+ scheme in high-resolution formulation. The of the numerical method can be found in [2]. Simulations were done also with the correlation based detailed description of the numerical method can be found in [2]. Simulations were done also with -Re transition and turbulence model by [6]; for details see [7]. the correlation based -Re transition and turbulence model by [6]; for details see [7]. Ansys Fluent software package (v18, Ansys Inc., Canonsburg, PA, USA) was used as representative Ansys Fluent software package (v18, Ansys Inc., Canonsburg, PA, USA) was used as commercial code for calculation of the same geometries at similar thermodynamic boundary conditions. representative commercial code for calculation of the same geometries at similar thermodynamic The set of density averaged Navier–Stokes equations closed with the k–! SST turbulence model. boundary conditions. The set of density averaged Navier–Stokes equations closed with the k–ω SST Although both codes are based on similar models and similar numerical methods, they turbulence model. di er in some details including the implementation of boundary conditions and the solution Although both codes are based on similar models and similar numerical methods, they differ in procedure. Our experience show that the ANSYS Fluent has, despite very good overall performance, some details including the implementation of boundary conditions and the solution procedure. Our some diculties with regimes with M1 ~ 1. Therefore, the in-house code was used for these experience show that the ANSYS Fluent has, despite very good overall performance, some problematic regimes. difficulties with regimes with M1 ~ 1. Therefore, the in-house code was used for these problematic For all calculations 2D single profile geometry with the periodicity boundary condition on the regimes. channel boundaries was used. The position of the inlet and outlet plane is far from the cascade For all calculations 2D single profile geometry with the periodicity boundary condition on the compared to the axial chord. In case of the tip section simulations with in-house code, inlet and outlet channel boundaries was used. The position of the inlet and outlet plane is far from the cascade were positioned in the distance of two chords upstream of the cascade and one chord downstream of compared to the axial chord. In case of the tip section simulations with in-house code, inlet and the cascade, respectively. In the simulations with Ansys Fluent for both tip sections and root sections, outlet were positioned in the distance of two chords upstream of the cascade and one chord inlet and outlet were positioned in the distance of one chord from the blade cascade. A non-reflecting downstream of the cascade, respectively. In the simulations with Ansys Fluent for both tip sections boundary condition was applied at outlet plane. and root sections, inlet and outlet were positioned in the distance of one chord from the blade cascade. A non-reflecting boundary condition was applied at outlet plane. 5. Results and Discussion 5. Results and Discussion Two very high values of aerodynamic loading representing two operation points of the innovative tip cascade of ultra-long last stage blade can be seen in Figures 3 and 4. In both supersonic regimes Two very high values of aerodynamic loading representing two operation points of the the tip cascade exhibits impressive aerodynamic performance with only very small area where the innovative tip cascade of ultra-long last stage blade can be seen in Figures 3 and 4. In both aerodynamic force acts in the opposite direction, decreasing the overall torque of the last stage blade. supersonic regimes the tip cascade exhibits impressive aerodynamic performance with only very small area where the aerodynamic force acts in the opposite direction, decreasing the overall torque of the last stage blade. Int. J. Turbomach. Propuls. Power 2019, 4, 33 4 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 4 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 4 of 10 Figure 3. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 3. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 3. Interferogram and isentropic Mach number distribution along the innovative tip profile for the flow conditions: M1 = 1.19, Mis = 1.70. the flow conditions: M = 1.19, M = 1.70. 1 is the flow conditions: M1 = 1.19, Mis = 1.70. In Figure 3 the perpendicular inlet shock wave can be seen as a result of supersonic inlet Mach In Figure 3 the perpendicular inlet shock wave can be seen as a result of supersonic inlet Mach In Figure 3 the perpendicular inlet shock wave can be seen as a result of supersonic inlet Mach number. The inlet shock wave interacts with the pressure side of the neighboring profile which leads number. The inlet shock wave interacts with the pressure side of the neighboring profile which leads to number. The inlet shock wave interacts with the pressure side of the neighboring profile which leads to a decrease of Mis near the 70% of axial chord as can be seen from Mach number distribution in a decrease of M near the 70% of axial chord as can be seen from Mach number distribution in Figure 3. is to a decrease of Mis near the 70% of axial chord as can be seen from Mach number distribution in Figure 3. The complicated flow structure can be seen at cascade exit including the inner and outer The complicated flow structure can be seen at cascade exit including the inner and outer branch of the Figure 3. The complicated flow structure can be seen at cascade exit including the inner and outer branch of the exit shock wave together with wake. Furthermore, the parasitic shock wave reflected exit shock wave together with wake. Furthermore, the parasitic shock wave reflected into measured branch of the exit shock wave together with wake. Furthermore, the parasitic shock wave reflected into measured area from the exit flow boundary is present resulting in artificial decrease of Mis in the area from the exit flow boundary is present resulting in artificial decrease of M in the vicinity of the is into measured area from the exit flow boundary is present resulting in artificial decrease of Mis in the vicinity of the suction side of profile at 60% of axial chord. suction side of profile at 60% of axial chord. vicinity of the suction side of profile at 60% of axial chord. Figure 4. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 4. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 4. Interferogram and isentropic Mach number distribution along the innovative tip profile for the flow conditions: M1 = 1.21, Mis = 1.91. the flow conditions: M1 = 1.21, Mis = 1.91. the flow conditions: M = 1.21, M = 1.91. 1 is In Figure 4 the similar behavior of the perpendicular inlet shock wave together with interaction In Figure 4 the similar behavior of the perpendicular inlet shock wave together with interaction In Figure 4 the similar behavior of the perpendicular inlet shock wave together with interaction at at pressure side of the corresponding profile can be seen. However, the differences appear behind at pressure side of the corresponding profile can be seen. However, the differences appear behind pressure side of the corresponding profile can be seen. However, the di erences appear behind the the trailing edge of the profile with variation in angles of the inner and outer branch of the exit shock the trailing edge of the profile with variation in angles of the inner and outer branch of the exit shock trailing edge of the profile with variation in angles of the inner and outer branch of the exit shock wave wave and wake indicating higher outlet velocity. Moreover, the parasitic shock wave is not present wave and wake indicating higher outlet velocity. Moreover, the parasitic shock wave is not present and wake indicating higher outlet velocity. Moreover, the parasitic shock wave is not present which which results in a less complicated flow field better reflecting the real cascade performance. which results in a less complicated flow field better reflecting the real cascade performance. results in a less complicated flow field better reflecting the real cascade performance. In numerical methods there are serious complications for supersonic inlet due to the unique In numerical methods there are serious complications for supersonic inlet due to the unique In numerical methods there are serious complications for supersonic inlet due to the unique incidence rule (see [4]) which states that the value of the incidence angle corresponding to a incidence rule (see [4]) which states that the value of the incidence angle corresponding to a incidence rule (see [4]) which states that the value of the incidence angle corresponding to a particular particular inlet Mach number is dependent on the cascade geometry only. The inlet conditions and particular inlet Mach number is dependent on the cascade geometry only. The inlet conditions and inlet Mach number is dependent on the cascade geometry only. The inlet conditions and the overall the overall flow field vary extensively with each 0.1° change of inlet incidence angle. the overall flow field vary extensively with each 0.1° change of inlet incidence angle. flow field vary extensively with each 0.1 change of inlet incidence angle. The regime closest to the measured ones was computed using in-house code with -Re The regime closest to the measured ones was computed using in-house code with -Re The regime closest to the measured ones was computed using in-house code with -Re transition transition and turbulence model and the result is shown in Figure 5. Inlet Mach number is relatively transition and turbulence model and the result is shown in Figure 5. Inlet Mach number is relatively and turbulence model and the result is shown in Figure 5. Inlet Mach number is relatively close to close to 1.2 and the isentropic exit Mach number is just between that of interferograms in Figures 3 close to 1.2 and the isentropic exit Mach number is just between that of interferograms in Figures 3 1.2 and the isentropic exit Mach number is just between that of interferograms in Figures 3 and 4. and 4. The flow structure is well predicted with the normal shock standing in front of the leading and 4. The flow structure is well predicted with the normal shock standing in front of the leading edge. Interaction of the inner branch of exit shock wave with the suction side boundary layer edge. Interaction of the inner branch of exit shock wave with the suction side boundary layer resulting in the local flow separation is in agreement with the experiments. The distribution of Mis resulting in the local flow separation is in agreement with the experiments. The distribution of Mis Int. J. Turbomach. Propuls. Power 2019, 4, 33 5 of 10 The flow structure is well predicted with the normal shock standing in front of the leading edge. Interaction of the inner branch of exit shock wave with the suction side boundary layer resulting in Int. J. Turbo Int. J. Turbo m m ach. ach. Propuls. Power Propuls. Power 2019 2019 , , 44 , x FOR PE , x FOR PE ER RE ER RE VI VI EE W W 5 5 of of 10 10 the local flow separation is in agreement with the experiments. The distribution of M along profiles is also corresponds well to the experimental results. The di erence in the level of M on the suction is along along pro pro ff iles also iles also corre corre spo spo n n ds we ds we ll to th ll to th e exper e exper imental re imental re sults. Th sults. Th e difference e difference in the in the level of level of M M isis on on side behind x/b ~ 0.55 can be partially attributed to diculties with evaluation of interferograms and th thee s suuccttio ion si n siddee be behi hinndd x/b ~ x/b ~ 0. 0.55 55 ca can be pa n be partial rtially ly a attri ttribbuted to dif uted to diffficicul ultities wi es with ev th evaaluati luation of on of presence of aperiodic flow phenomena. interfero interfero g g rams and rams and prese prese n n ce of ce of aper aper io io dic dic flow phen flow phen omena. omena. 2.52.5 2.02.0 1.51.5 1.01.0 0.50.5 0.00.0 0.00.000.1.10.20.200.3.30.40.400.5.50.60.600.7.70.80.800.9.91.01.0 x/b x/b (-) (-) Figure Figure 5. Figure 5. 5. Mach Ma Ma ch number isoli ch number isoli number isolines nnes and i es and i and isentr ssentropic Ma entropic Ma opic Mach ch nu ch nu number mber distribution along the innovative tip mber distribution along the innovative tip distribution along the innovative tip pr profile profile ofile calculated calcu calcu lat lat ed by ed by by in-house in-hou in-hou se se code code code (g-Re (g (g -Re -Re Q Q m model) m oo del) del) for th for for th thee f e f flow low con low con conditions: d d it iion tion ss : M : M M 1 = 1 1= = 1 1.135, .135, M .135, M Misis = = =1.796 1.796 1.796. . . Q 1 is Operation point with the slightly supersonic inlet Mach number M = 1.03 was calculated by Operat Operation po ion point int wit withh t thhe s e slight lightly ly s suuper perssonic onic inlet inlet M Maach n ch nuumber mber M M 111 = 1.03 = 1.03 was cal was calccula ulatted ed by by in-house code as can be seen in Figure 6. There is no normal inlet shock wave in front of the leading in-ho in-ho u u se co se co d d ee a a ss c c aa n be n be se se en in en in Fi Fi gure gure 6 6 . There . There is is no no normal normal in in let let s s h h ock wave ock wave in in front front o o ff t t h h e e le le ad ad ing ing edge of profile. Instead, the supersonic area ending by shock wave at 20% of axial chord is present edge of pro edge of pro ffile. Instead ile. Instead , the superson , the superson ic ic are are aa endin endin gg by shock w by shock w aave ve at 20% o at 20% o ff axial chord axial chord is pr is pr esent esent near the leading edge at the pressure side of the profile. M distribution is in the vicinity of suction is near the near the le le ad ad ing edg ing edg ee at the pressure at the pressure side of the profile side of the profile . M . M isis d d is is tt rr ib ib u u tt io io nn i i ss i n in t t hh ee v v ic ic in in it it yy o o ff s s u u cc tt io io nn side with a drop between 40% and 50% which is in good agreement with experimental results. This side w side w it it h h a d a d rr op op b b ee tt w w een 40% een 40% and and 55 00 % % which i which i ss in in gg ood agr ood agr eem eem ee n n tt wit wit h h exp exp ee rim rim ee nt nt al al res res u u lt lt s. This s. This regime corresponds to M between the two measured aerodynamic loadings. is regime regime corresponds to M corresponds to M isis between the two measured between the two measured aero aero dyn dyn aa mic mic lo lo adin adin gs. gs. Figure 6. Mach number isolines and isentropic Mach number distribution along the innovative tip Figure 6. Figure 6. Ma Ma ch number isoli ch number isolinnes and i es and issentropic Ma entropic Ma ch nu ch nu mber distribution along the innovative tip mber distribution along the innovative tip profile calculated by in-house code for the flow conditions: M = 1.03, M = 1.79. 1 is profile profile calcu calcu lat lat ed by ed by in-hou in-hou se se code code for the f for the f lo lo w w condit condit ions ions : : M M 1 = 1 1 = 1 .03, M .03, M isis = = 1.79 1.79 . . The results of commercial code calculation are shown in Figure 7 together with results of the The resu The resultlts o s off commerci commerciaal code c l code caalc lcul ulaattion are ion are sho show wn in F n in Fig iguure re 7 t 7 tooget gethher w er witithh res resuultlts o s off tthhe e in-house code. In this case inlet Mach number is even smaller, M = 0.88, since for higher inlet in-ho in-ho u u se co se co d d ee . In t . In t h h is is ca ca se se inlet inlet Mach Mach n n u u mber i mber i ss eve eve n n sma sma lle lle r, r, M M 1 = 1 = 0. 0. 88 88 , , since since f f oo r highe r highe rr in in le le tt Mach Mach Mach numbers, commercial code predicted non-physical phenomena at inlet of the blade cascade. numbers, co numbers, commercia mmercial co l code predict de predicteedd non-phys non-physica ical phenomena at inlet of l phenomena at inlet of the blade c the blade caascade scade. . Agreement between the two codes in this regime is good. Both predicted a very small supersonic Agreement Agreement between the t between the tw wo code o codes s in t in thhis reg is regime ime is is good. Both p good. Both prredicted edicted a ve a very ry small supe small supersonic rsonic region terminated by a normal shock wave on the pressure side at the leading edge. The calculated region t region t ee rm rm in in at at ed b ed b yy a nor a nor m m al al shock w shock w aa vv ee on t on t hh e e pre pre ssur ssur ee side side at t at t hh e le e le adin adin g ed g ed ge. The c ge. The c aa lculated lculated exit exit f flow low fie field corre ld correspond spondss we wellll t too t thhe e resu result lts o s off exp expeeriment riments s and and ca calcu lculat lations ions wit withh in in-hou -houssee codes codes presented ab presented ab ove. ove. M (-) Mis (-) is Int. J. Turbomach. Propuls. Power 2019, 4, 33 6 of 10 exit flow field corresponds well to the results of experiments and calculations with in-house codes Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 6 of 10 presented above. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 6 of 10 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 Ansys 0.5 Ansys Fluent 0.0 Fluent 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 x/b 0 (-).6 0.8 1.0 x/b (-) Figure 7. Mach number isolines and isentropic Mach number distribution along the innovative tip Figure 7. Mach number isolines and isentropic Mach number distribution along the innovative tip Figure 7. Mach number isolines and isentropic Mach number distribution along the innovative tip profile calculated by commercial and in-house code for the flow conditions: M1 = 0.87, Mis = 1.76. profile calculated by commercial and in-house code for the flow conditions: M1 = 0.87, Mis = 1.76. profile calculated by commercial and in-house code for the flow conditions: M = 0.87, M = 1.76. 1 is A useful criterion for comparison of aerodynamic behavior of two different profiles of a A useful criterion for comparison of aerodynamic behavior of two different profiles of a A useful criterion for comparison of aerodynamic behavior of two di erent profiles of a rotating rotating blade at the same thermodynamic boundary conditions (such as space and time blade rotating blade at the same thermo at the same thermodynamic boundary dynamiconditions c boundary cond (such asitspace ions (s and uchtime as space distributions and time of distributions of pressure, enthalpy and velocity vector of working fluid) is the ratio of tangential and distributions of pressure, enthalpy and velocity vector of working fluid) is the ratio of tangential and pressure, enthalpy and velocity vector of working fluid) is the ratio of tangential and axial component axial component of force affecting each profile. As the principle of the turbine is conversion of fluid of axial force component a ecting each of fopr rce affecting each ofile. As the principle profile. As of the thturbine e princip isle o conversion f the turbin of e is fluid cothermodynamic nversion of fluid thermodynamic fre thermodynamic fre e ener e ener gy to torque gy to torque of the rotor, of the rotor, th th e tangential e tangential component of the force c component of the force caa n n be seen be seen free energy to torque of the rotor, the tangential component of the force can be seen as beneficial as bene (contributing as bene ficial fici (cont al to (cont rtor ibut rque), ibut ingin t contrary g o t to o t rque orque to ), c ), the o cnt oaxial nt rary t rary t component o t o t hh e ax e ax ia ial comp rl comp elatedonent onent with rel rel ener a at gy teed d wit leavi withh ng ener ener the gy gy cascade leav leav ing ing the cascade without doing work. This means that profile with higher force ratio at the same without doing work. This means that profile with higher force ratio at the same thermodynamic the cascade without doing work. This means that profile with higher force ratio at the same conditions thermodynamic condit is more ecient ions in is more the ener effic gy ient in the to torque conversion. energy to torque conversion. thermodynamic conditions is more efficient in the energy to torque conversion. The comparison of force ratio for original and innovative tip profile depending on flow inlet The comparison of force ratio for original and innovative tip profile depending on flow inlet The comparison of force ratio for original and innovative tip profile depending on flow inlet angle angle at at two two different aero di erent aerodynamic dynamic loadings loadings is is shown shown in in F Figur igue re 8.8.The The orig original inal pr profile ofile w was as described described angle at two different aerodynamic loadings is shown in Figure 8. The original profile was described in detail by [4]. The innovative tip profile exhibits a similar evolution of the force ratio for both in detail by [4]. The innovative tip profile exhibits a similar evolution of the force ratio for both in detail by [4]. The innovative tip profile exhibits a similar evolution of the force ratio for both aer aerod odynamic ynamicloadings loadings wh while ile t the heoriginal original t tip ippr prof ofile ileshows showssignificantly significantlyworse worsefor for ce ce ratio ratiofor for l low ow aerodynamic loadings while the original tip profile shows significantly worse force ratio for low aerodynamic loading. aerodynamic loading. aerodynamic loading. Figure 8. Comparison of force ratio of tangential and axial component of force f or original tip (blue lines) and innovative tip (red lines) at low (solid lines) and high (dashed lines) aerodynamic loading. Figure 8. Comparison of force ratio of tangential and axial component of force for original tip (blue Figure 8. Comparison of force ratio of tangential and axial component of force for original tip (blue lines) and innovative tip (red lines) at low (solid lines) and high (dashed lines) aerodynamic loading. lines) and innovative tip (red lines) at low (solid lines) and high (dashed lines) aerodynamic loading. The full potential of innovative tip profile has been demonstrated by measurement in a high-speed tunnel. Comparison of measured profile loss for original and innovative tip profile for The full potential of innovative tip profile has been demonstrated by measurement in a high-speed The full potential of innovative tip profile has been demonstrated by measurement in a two values 1.0 and 1.2 of inlet Mach number is shown in Figure 9. There can be seen a similar low tunnel. Comparison of measured profile loss for original and innovative tip profile for two values 1.0 high-speed tunnel. Comparison of measured profile loss for original and innovative tip profile for value of profile losses in a wide range of outlet Mach number for both values 1.0 and 1.2 of inlet and 1.2 of inlet Mach number is shown in Figure 9. There can be seen a similar low value of profile two values 1.0 and 1.2 of inlet Mach number is shown in Figure 9. There can be seen a similar low Mach number for innovative design. Conversely, the profile losses of original tip profile rise value of profile losses in a wide range of outlet Mach number for both values 1.0 and 1.2 of inlet significantly both for higher inlet Mach number and lower outlet Mach number. From these results Mach number for innovative design. Conversely, the profile losses of original tip profile rise is apparent that the innovative tip cascade provides strong benefits in a large operating range. significantly both for higher inlet Mach number and lower outlet Mach number. From these results is apparent that the innovative tip cascade provides strong benefits in a large operating range. M (-) M (-) is is Int. J. Turbomach. Propuls. Power 2019, 4, 33 7 of 10 losses in a wide range of outlet Mach number for both values 1.0 and 1.2 of inlet Mach number for innovative design. Conversely, the profile losses of original tip profile rise significantly both for higher inlet Mach number and lower outlet Mach number. From these results is apparent that the innovative Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 7 of 10 tip cascade provides strong benefits in a large operating range. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 7 of 10 Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red lines) Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red for M = 1.0 (solid lines) and M = 1.2 (dashed lines). 1 1 lines) for M1 = 1.0 (solid lines) and M1 = 1.2 (dashed lines). The flow field in the vicinity of the hub profile di ers significantly from the tip cascade flow The flow fields discussed field in t above. he vic The indense ity of t channel he huwith b profil low e conver differs significan gence results intly from the t slow steady acceleration ip cascad of e flow the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with fields discussed above. The dense channel with low convergence results in slow steady acceleration wake and outer branch of the shock wave are visible both in the interferogram and in the computed of the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring profile wake and outer branch of the shock wave are visible both in the interferogram and in the computed Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red near 90% of axial chord and results in a decrease of the Mach number in the vicinity of suction side lines) for M1 = 1.0 (solid lines) and M1 = 1.2 (dashed lines). Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring trailing edge. profile near 90% of axial chord and results in a decrease of the Mach number in the vicinity of In Figures 12 and 13 the di erent operating point with significantly higher aerodynamic loading The flow field in the vicinity of the hub profile differs significantly from the tip cascade flow suction side trailing edge. and thus with higher M is present. The flow acceleration is slow and steady in the main portion 2is fields discussed above. The dense channel with low convergence results in slow steady acceleration of the channel in agreement with the previous case. The main di erence is near the last 15% of axial of the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with chord where the rapid acceleration takes place with peak value up to M = 1.8. The sharper angle of is wake and outer branch of the shock wave are visible both in the interferogram and in the computed inner and outer branch of the shock wave also confirms the higher outlet Mach number. The inner Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring branch of the exit shock misses the suction side of neighbor profile indicating the operation beyond the profile near 90% of axial chord and results in a decrease of the Mach number in the vicinity of limit load condition. suction side trailing edge. Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile for the flow conditions: nominal inlet angle, Mis = 1.18. Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile for for the flow conditions: nominal inlet angle, Mis = 1.18. the flow conditions: nominal inlet angle, M = 1.18. is Figure 11. Mach number isolines and isentropic Mach number distribution along the hub innovative Figure 11. Mach number isolines and isentropic Mach number distribution along the hub innovative profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.08. profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.08. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 7 of 10 Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red lines) for M1 = 1.0 (solid lines) and M1 = 1.2 (dashed lines). The flow field in the vicinity of the hub profile differs significantly from the tip cascade flow fields discussed above. The dense channel with low convergence results in slow steady acceleration of the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with wake and outer branch of the shock wave are visible both in the interferogram and in the computed Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring profile near 90% of axial chord and results in a decrease of the Mach number in the vicinity of suction side trailing edge. Int. J. Turbomach. Propuls. Power 2019, 4, 33 8 of 10 Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile for the flow conditions: nominal inlet angle, Mis = 1.18. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 8 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 8 of 10 In Figures 12 and 13 the different operating point with significantly higher aerodynamic In Figures 12 and 13 the different operating point with significantly higher aerodynamic loading and thus with higher M2is is present. The flow acceleration is slow and steady in the main loading and thus with higher M2is is present. The flow acceleration is slow and steady in the main portion of the channel in agreement with the previous case. The main difference is near the last 15% portion of the channel in agreement with the previous case. The main difference is near the last 15% of axial chord where the rapid acceleration takes place with peak value up to Mis = 1.8. The sharp er of axial chord where the rapid acceleration takes place with peak value up to Mis = 1.8. The sharper angle of inner and outer branch of the shock wave also confirms the higher outlet Mach number. The Figure Figure 11. 11. Mach Mach nu number mber isolines and isentro isolines and isentropic pic Mach nu Mach number mber distributio distribution n along the hub innovative along the hub innovative angle of inner and outer branch of the shock wave also confirms the higher outlet Mach number. The inner branch of the exit shock misses the suction side of neighbor profile indicating the operation pr profile calcu ofile calculated lated by bycommer commercial code cial code for for the theflow flow con conditions: ditions: nominal nominal inlet inletangle, angle, M M is = 1 = 1.08. .08. is inner branch of the exit shock misses the suction side of neighbor profile indicating the operation beyond the limit load condition. beyond the limit load condition. Figure 12. Interferogram and isentropic Mach number distribution along the hub innovative profile Figure 12. Interferogram and isentropic Mach number distribution along the hub innovative profile for Figure 12. Interferogram and isentropic Mach number distribution along the hub innovative profile for the flow conditions: nominal inlet angle, Mis = 1.597. the flow conditions: nominal inlet angle, M = 1.597. is for the flow conditions: nominal inlet angle, Mis = 1.597. Figure 13. Mach number isolines and isentropic Mach number distribution along the hub innovative Figure 13. Mach number isolines and isentropic Mach number distribution along the hub innovative Figure 13. Mach number isolines and isentropic Mach number distribution along the hub innovative profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.64. profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.64. profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.64. There can be seen high conformity in experimental and calculated results for both operating There can be seen high conformity in experimental and calculated results for both operating regimes of hub cascade in terms of flow field pattern and isentropic Mach number distribution. On regimes of hub cascade in terms of flow field pattern and isentropic Mach number distribution. On the other hand, significant discrepancy can be seen for integral profile loss evaluation. the other hand, significant discrepancy can be seen for integral profile loss evaluation. The profile loss function on aerodynamic loading represented by Mis can be seen in Figure 14. The profile loss function on aerodynamic loading represented by Mis can be seen in Figure 14. For the original hub profile (presented in [3]) the calculated values are almost the same for both For the original hub profile (presented in [3]) the calculated values are almost the same for both in-house and commercial code. Furthermore, the trend of increasing of profile loss with higher in-house and commercial code. Furthermore, the trend of increasing of profile loss with higher aerodynamic loading of the hub cascade can be seen in experimental results as well, although the aerodynamic loading of the hub cascade can be seen in experimental results as well, although the absolute value of the profile losses is approximately 1% higher. absolute value of the profile losses is approximately 1% higher. Int. J. Turbomach. Propuls. Power 2019, 4, 33 9 of 10 There can be seen high conformity in experimental and calculated results for both operating regimes of hub cascade in terms of flow field pattern and isentropic Mach number distribution. On the other hand, significant discrepancy can be seen for integral profile loss evaluation. The profile loss function on aerodynamic loading represented by M can be seen in Figure 14. is For the original hub profile (presented in [3]) the calculated values are almost the same for both in-house and commercial code. Furthermore, the trend of increasing of profile loss with higher aerodynamic loading of the hub cascade can be seen in experimental results as well, although the absolute value of Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 9 of 10 the profile losses is approximately 1% higher. Figure 14. Comparison of measured profile loss for original hub (blue lines) and innovative hub Figure 14. Comparison of measured profile loss for original hub (blue lines) and innovative hub (red (red lines) for experiment (solid lines), in-house code (dashed lines) and commercial code (dotted lines). lines) for experiment (solid lines), in-house code (dashed lines) and commercial code (dotted lines). On the other hand, for the presented innovative hub profile the profile loss evolution is more On the other hand, for the presented innovative hub profile the profile loss evolution is more complicated. The calculated results for in-house and commercial code agree with each other up to complicated. The calculated results for in-house and commercial code agree with each other up to M = 1.4. For higher aerodynamic loading the in-house code predicts the decrease in the profile losses. is Mis = 1.4. For higher aerodynamic loading the in-house code predicts the decrease in the profile The non-linear dependency is confirmed with experimental data as well. The di erence in profile losses. The non-linear dependency is confirmed with experimental data as well. The difference in losses is again around 1% but with lower profile losses for the experimental data. profile losses is again around 1% but with lower profile losses for the experimental data. The significantly higher experimental profile losses by 3% can be associated with more complicated The significantly higher experimental profile losses by 3% can be associated with more structure of flow field for original hub cascade leading to higher energy dissipation as is described in complicat more detail ed struct by [3 ure of ]. This flo imp w fie ortant ld fo information r original hconfirms ub cascade thelea necessity ding toof higher en experimental ergy di verifi ssipat cation ion as of is describe calculated d in more det results especially ail by [3for ]. Thi complicated s important transonic informand ation con supersonic firms t flow he neces fieldssin ity o the f exper vicinity iment last al stage blade cascades. verification of calculated results especially for complicated transonic and supersonic flow fields in the vicinity last stage blade cascades. 6. Conclusions 5. Conclus Advanced ions hub and tip profiles of ultra-long last stage blade were analyzed by both experimental and numerical methods. The optical measurements of transonic and supersonic flow fields Advanced hub and tip profiles of ultra-long last stage blade were analyzed by both were performed in high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of experimental and numerical methods. The optical measurements of transonic and supersonic flow Thermomechanics of the Czech Academy of Sciences. Commercial and in-house software of CTU fields were performed in high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of Prague were used for calculating the corresponding flow fields. Thermomechanics of the Czech Academy of Sciences. Commercial and in-house software of CTU For the tip cascade, the perpendicular inlet shock wave was observed as a result of supersonic Prague were used for calculating the corresponding flow fields. inlet Mach number. This phenomenon could not be reproduced by tested numerical codes. The flow For the tip cascade, the perpendicular inlet shock wave was observed as a result of supersonic structure at cascade exit includes the inner and outer branch of the exit shock wave together with wake. inlet Mach number. This phenomenon could not be reproduced by tested numerical codes. The flow These structures were well reproduced by numerical calculations including position of interaction of stru the ctuinner re at ca branch scade e of the xit i exit nclu shock des the i withnsuction ner and side oute ofr branch neighboring of th pr e exit ofile. shock wave together with wake. These structures The dense hub channel were well with re lowproduced by convergence numeric results inaslow l calc steady ulations acceleration including pos of theition of flow. The high conformity in experimental and calculated results in terms of flow field pattern and isentropic interaction of the inner branch of the exit shock with suction side of neighboring profile. Mach number distribution was in contrast with significant discrepancy of integral profile loss evaluation. The dense hub channel with low convergence results in slow steady acceleration of the flow. The high conformity in experimental and calculated results in terms of flow field pattern and isentropic Mach number distribution was in contrast with significant discrepancy of integral profile loss evaluation. Both hub and tip cascades were compared with the similar profiles presented in the past. The overall aerodynamic performance was significantly improved in both cases. The comparison of experimental and numerical results shows limits of both methods. In particular, in the experiment, the parasitic shock wave reflected into measured area from the test section wall resulting in artificial decrease of isentropic Mach number near the suction side of the profile. On the other hand, the numerical methods had issues with supersonic inlet and integral profile loss evaluation. The in-house code exhibits lower overall discrepancy of loss evaluation for the innovative hub cascade. Author Contributions: Ondrej Novak: publication, data management, vane and blade design; Marek Bobcik: new vane and rotor blade design, loss coefficient calculation, stage design; Martin Luxa: conducting of optical Int. J. Turbomach. Propuls. Power 2019, 4, 33 10 of 10 Both hub and tip cascades were compared with the similar profiles presented in the past. The overall aerodynamic performance was significantly improved in both cases. The comparison of experimental and numerical results shows limits of both methods. In particular, in the experiment, the parasitic shock wave reflected into measured area from the test section wall resulting in artificial decrease of isentropic Mach number near the suction side of the profile. On the other hand, the numerical methods had issues with supersonic inlet and integral profile loss evaluation. The in-house code exhibits lower overall discrepancy of loss evaluation for the innovative hub cascade. Author Contributions: O.N.: publication, data management, vane and blade design; M.B.: new vane and rotor blade design, loss coecient calculation, stage design; M.L.: conducting of optical measurements and its evaluation; analysis of results; J.F. (Jaroslav Fort): CFD team management, analysis of CFD results; B.R.: CFD calculations with commercional code ANSYS FLUENT, results evaluation; J.S.: original vane and blade design, new vane design, stage design; D.S.: conducting of pneumatic traverses and loss evaluation; analysis of results; J.F. (Jiri Furst): development of the in-house code, implementation of turbulence models; J.H.: analysis of CFD results; V.H.: CFD simulations including pre- and post-processing; J.P.: proposal of turbulence models for in-house codes; Z.S.: 1D throughflow calculations and design. Funding: The authors would like to express their thanks to the Technology Agency of the Czech Republic, which supported this research under grant No. TA02020057. The APC was funded by Euroturbo. Conflicts of Interest: The authors declare no conflict of interest. References 1. Senoo, S.; Ono, H. Development of Design Method for Supersonic Turbine Aerofoils near the Tip of Long Blades in Steam Turbines, Part 2: Configuration Details and Validation. In Proceedings of the ASME Turbo Expo 2013, GT2013-94039, San Antonio, TX, USA, 3–7 June 2013. 2. Bobcik, M.; Fort, J.; Furst, J.; Halama, J.; Hric, V.; Louda, P.; Luxa, M.; Rudas, B.; Synac, J.; Simurda, D. Investigation of Transonic and Supersonic Flow in Rotor Tip Section of Last LP Steam Turbine Cascade under Di erent Turbulence Level. In Proceedings of the 12th European Conference on Turbomachinery, Stockholm, Sweden, 3–7 April 2017. 3. Hala, J.; Luxa, M.; Simurda, D.; Bobcik, M.; Novak, O.; Synac, J.; Rudas, B. Optimization of Root Section for Ultra Long Steam Turbine Rotor Blade. In Proceedings of the 13th International Symposium on Experimental Computational Aerothermodynamics of Internal Flows, Okinawa, Japan, 7–11 May 2017. 4. Luxa, M.; Simurda, D.; Fort, J.; Furst, P.; Safarik, P.; Synac, J.; Rudas, B. Aerodynamic Investigation of the Tip Section for Titanium Blade 54”. In Proceedings of the 11th European Conference on Turbomachinery, Madrid, Spain, 23–27 March 2015. 5. Safarik, P.; Luxa, M. Using Optical Methods in High-Speed Aerodynamic Research. In Proceedings of the Measurement Techniques in Turbomachinery XX, Firenze, Italy, 21–22 September 2000; pp. 1–7. 6. Langtry, R.B.; Menter, F.R. Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes. AIAA J. 2000, 47, 2894–2906. [CrossRef] 7. Musil, J.; Pr ˇíhoda, J.; Fürst, J. Simulation of Supersonic Flow through the Tip-Section Turbine Blade Cascade with a Flat Profile. In Problems of Fluid Mechanics; Šimurda, D., Bodnár, T., Eds.; Topical: Prague, Czech Republic, 2019; pp. 169–174. © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (http://creativecommons.org/licenses/by-nc-nd/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Turbomachinery, Propulsion and Power Multidisciplinary Digital Publishing Institute

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Abstract

International Journal of Turbomachinery Propulsion and Power Article Turbine Cascades of Last Stage Blades for Wide Range of Operating Conditions 1 1 2 3 4 , Ondrej Novak , Marek Bobcik , Martin Luxa , Jaroslav Fort , Bartolomej Rudas *, 4 2 3 3 3 2 Jaroslav Synac , David Simurda , Jiri Furst , Jan Halama , Vladimir Hric , Jaromir Prihoda and Zdenek Simka Research and Development, Doosan Skoda Power, Ltd., 30128 Pilsen, Czech Republic; novak-ondrej@email.cz (O.N.); marekbobcik@seznam.cz (M.B.); zdenek.simka@doosan.com (Z.S.) Institute of Thermomechanics of the Czech Academy of Sciences, 182 00 Prague, Czech Republic; luxa@it.cas.cz (M.L.); simurda@it.cas.cz (D.S.); prihoda@it.cas.cz (J.P.) Faculty of Mechanical Engineering, Czech Technical University, 160 00 Prague, Czech Republic; jaroslav.fort@fs.cvut.cz (J.F.); jiri.furst@fs.cvut.cz (J.F.); jan.halama@fs.cvut.cz (J.H.); vladimir.hric@fs.cvut.cz (V.H.) Faculty of Mechanical Engineering, West Bohemian University, 301 00 Pilsen, Czech Republic; synac@kke.zcu.cz * Correspondence: bartolomej.rudas@doosan.com y This Paper is an Extended Version of Our Paper Published in Proceedings of the European Turbomachinery Conference ETC13, Lausanne, Switzerland, 8–12 April 2019, Paper No. 350. Received: 22 July 2019; Accepted: 6 September 2019; Published: 24 September 2019 Abstract: Recent trends in the electric energy market such as biomass, waste incineration or combined cycle power plants require innovative solutions in steam turbine design. Variable operating conditions cause significant changes in flow field surrounding the steam turbine last stage blades. Therefore, the enlargement of operating range for last stage blades presents new challenges in design of turbine cascades. Several turbine cascades were designed and analyzed by commercial and in-house software of CTU Prague. Selected profiles were experimentally validated in the high-speed wind tunnel for 2D cascade measurements of the Institute of Thermomechanics of the Czech Academy of Sciences which is equipped by an adjustable supersonic inlet nozzle, perforated inserts at side walls and adjustable perforated tailboard. Comparisons are presented of numerical results with optical and pneumatic measurements for a wide range of inlet and outlet Mach numbers for optimized hub and tip profile cascades. Keywords: turbine; cascade; last stage blade; CFD; experimental validation 1. Introduction The last stage rotating blade is a key component of each steam turbine, directly contributing to overall eciency of the thermal cycle. There are many challenges in the development and validation process of last stage blades both in terms of thermodynamic and mechanical design. High tip/hub ratio results in dense hub cascades and rare tip cascades. The proper stator blade design with advanced 3D shaping is highly important because it has significant impact on the relative velocity in the vicinity of the rotating blade. However, the relative Mach numbers exceeding 1 are commonly present in flow field surrounding the rotating blade due to high tangential velocities and even supersonic flow with inlet shock wave can occur, especially in the case of ultra-long full speed (3000 or 3600 RPM) last stage blades [1]. Final mechanical design must fulfill criteria of static strength which determines strict distribution of area for each section along the blade span. The combination of these requirements limits the design space and leads to the demanding process of optimal solution searching. Int. J. Turbomach. Propuls. Power 2019, 4, 33; doi:10.3390/ijtpp4040033 www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 2 of 10 of these requirements limits the design space and leads to the demanding process of optimal Int. J. Turbomach. Propuls. Power 2019, 4, 33 2 of 10 solution searching. Analytical methods investigating flow field are an essential part of aerodynamic design process Analytical methods investigating flow field are an essential part of aerodynamic design process of of turbine cascades of last stage blades. Obtaining reliable calculated data can be challenging task turbine cascades of last stage blades. Obtaining reliable calculated data can be challenging task both both due to very dense hub cascades with low convergence of channel and due to very rare tip due to very dense hub cascades with low convergence of channel and due to very rare tip cascades cascades with supersonic flow velocities in the channel [2]. with supersonic flow velocities in the channel [2]. The experimental measurements of turbine blade cascades are an indispensable part of The experimental measurements of turbine blade cascades are an indispensable part of validation validation process of the analytical methods and the final aerodynamic solution. The careful design process of the analytical methods and the final aerodynamic solution. The careful design of the of the experiment together with a combination of suitable measurement methods is needed to experiment together with a combination of suitable measurement methods is needed to analyze analyze supersonic flow field [3,4]. Optical methods such as interferometry are particularly useful supersonic flow field [3,4]. Optical methods such as interferometry are particularly useful tool for tool for spatial resolved analysis of high-speed aerodynamics investigations of various blade spatial resolved analysis of high-speed aerodynamics investigations of various blade cascades [5]. cascades [5]. 2. Investigated Blade Cascades 2. Investigated Blade Cascades Blade cascades described in the paper represent the tip section and the hub section. Original and Blade cascades described in the paper represent the tip section and the hub section. Original innovative designs of the tip section are shown in Figure 1b. Whereas in the case of the original design and innovative designs of the tip section are shown in Figure 1b. Whereas in the case of the original the profiles are cambered in order to form the divergent interblade channel, profiles of the innovative design the profiles are cambered in order to form the divergent interblade channel, profiles of the design are practically flat with only the leading edge on the suction side and the trailing edge on the innovative design are practically flat with only the leading edge on the suction side and the trailing pressure side contoured. edge on the pressure side contoured. Hub section blade cascades are shown in Figure 1a. Both were designed for the straight fir tree Hub section blade cascades are shown in Figure 1a. Both were designed for the straight fir tree root dovetail. The main di erence lies in the higher outlet metal angle and incidence angle of the root dovetail. The main difference lies in the higher outlet metal angle and incidence angle of the original design. This was due to the requirement of low exit loss and straight fir tree root. In the case original design. This was due to the requirement of low exit loss and straight fir tree root. In the case of the innovative design, the exit flow angle is lower and the incidence angle is zero. These favourable of the innovative design, the exit flow angle is lower and the incidence angle is zero. These di erences were made possible thanks to the redesign of guide vanes. favourable differences were made possible thanks to the redesign of guide vanes. (a) (b) Figure 1. Schematics of blade cascades—original designs (a) and innovative designs (b). Figure 1. Schematics of blade cascades—original designs (a) and innovative designs (b). 3. Experimental Setup 3. Experimental Setup The optical measurements of transonic and supersonic flow fields were performed in a high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of Thermomechanics of the Czech Academy The optical measurements of transonic and supersonic flow fields were performed in a of Sciences in Novy Knin. The atmospheric air treated by silica gel drier and filters is accelerated by high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of Thermomechanics of the Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 3 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, 33 3 of 10 Czech Academy of Sciences in Novy Knin. The atmospheric air treated by silica gel drier and filters is accelerated by inlet nozzle and enters the test section displayed in Figure 2. The perforated inlet nozzle and enters the test section displayed in Figure 2. The perforated tailboard and sucked tailboard and sucked perforated wall prevent shock waves reflecting back to the measured flow perforated wall prevent shock waves reflecting back to the measured flow field. field. A Mach–Zehnder interferometer in an infinite fringe setting was used for capturing of A Mach–Zehnder interferometer in an infinite fringe setting was used for capturing of interferograms presented in this paper. This experimental setup is described in detail in [5] and [3]. interferograms presented in this paper. This experimental setup is described in detail in [5] and [3]. Static pressure was measured on both sides of the interblade channel during the optical measurement Static pressure was measured on both sides of the interblade channel during the optical which allows evaluation of the distribution of isentropic Mach number M along the suction and is measurement which allows evaluation of the distribution of isentropic Mach number Mis along the pressure side of the measured profile. suction and pressure side of the measured profile. Figure 2. Test section for an investigation of the flow in a prismatic profile cascade with a small flow Figure 2. Test section for an investigation of the flow in a prismatic profile cascade with a small flow turning angle and supersonic inlet velocity. turning angle and supersonic inlet velocity. 4. Numerical Methods 4. Numerical Methods An in-house code developed at the Faculty of Mechanical Engineering, Czech Technical University, An in-house code developed at the Faculty of Mechanical Engineering, Czech Technical Prague, was used for calculation of transonic and supersonic flow fields. The code is based on the University, Prague, was used for calculation of transonic and supersonic flow fields. The code is solution of the Favre averaged Navier–Stokes equations and k–! SST turbulence model by implicit based on the solution of the Favre averaged Navier–Stokes equations and k–ω SST turbulence model finite volume method with AUSMPW+ scheme in high-resolution formulation. The detailed description by implicit finite volume method with AUSMPW+ scheme in high-resolution formulation. The of the numerical method can be found in [2]. Simulations were done also with the correlation based detailed description of the numerical method can be found in [2]. Simulations were done also with -Re transition and turbulence model by [6]; for details see [7]. the correlation based -Re transition and turbulence model by [6]; for details see [7]. Ansys Fluent software package (v18, Ansys Inc., Canonsburg, PA, USA) was used as representative Ansys Fluent software package (v18, Ansys Inc., Canonsburg, PA, USA) was used as commercial code for calculation of the same geometries at similar thermodynamic boundary conditions. representative commercial code for calculation of the same geometries at similar thermodynamic The set of density averaged Navier–Stokes equations closed with the k–! SST turbulence model. boundary conditions. The set of density averaged Navier–Stokes equations closed with the k–ω SST Although both codes are based on similar models and similar numerical methods, they turbulence model. di er in some details including the implementation of boundary conditions and the solution Although both codes are based on similar models and similar numerical methods, they differ in procedure. Our experience show that the ANSYS Fluent has, despite very good overall performance, some details including the implementation of boundary conditions and the solution procedure. Our some diculties with regimes with M1 ~ 1. Therefore, the in-house code was used for these experience show that the ANSYS Fluent has, despite very good overall performance, some problematic regimes. difficulties with regimes with M1 ~ 1. Therefore, the in-house code was used for these problematic For all calculations 2D single profile geometry with the periodicity boundary condition on the regimes. channel boundaries was used. The position of the inlet and outlet plane is far from the cascade For all calculations 2D single profile geometry with the periodicity boundary condition on the compared to the axial chord. In case of the tip section simulations with in-house code, inlet and outlet channel boundaries was used. The position of the inlet and outlet plane is far from the cascade were positioned in the distance of two chords upstream of the cascade and one chord downstream of compared to the axial chord. In case of the tip section simulations with in-house code, inlet and the cascade, respectively. In the simulations with Ansys Fluent for both tip sections and root sections, outlet were positioned in the distance of two chords upstream of the cascade and one chord inlet and outlet were positioned in the distance of one chord from the blade cascade. A non-reflecting downstream of the cascade, respectively. In the simulations with Ansys Fluent for both tip sections boundary condition was applied at outlet plane. and root sections, inlet and outlet were positioned in the distance of one chord from the blade cascade. A non-reflecting boundary condition was applied at outlet plane. 5. Results and Discussion 5. Results and Discussion Two very high values of aerodynamic loading representing two operation points of the innovative tip cascade of ultra-long last stage blade can be seen in Figures 3 and 4. In both supersonic regimes Two very high values of aerodynamic loading representing two operation points of the the tip cascade exhibits impressive aerodynamic performance with only very small area where the innovative tip cascade of ultra-long last stage blade can be seen in Figures 3 and 4. In both aerodynamic force acts in the opposite direction, decreasing the overall torque of the last stage blade. supersonic regimes the tip cascade exhibits impressive aerodynamic performance with only very small area where the aerodynamic force acts in the opposite direction, decreasing the overall torque of the last stage blade. Int. J. Turbomach. Propuls. Power 2019, 4, 33 4 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 4 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 4 of 10 Figure 3. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 3. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 3. Interferogram and isentropic Mach number distribution along the innovative tip profile for the flow conditions: M1 = 1.19, Mis = 1.70. the flow conditions: M = 1.19, M = 1.70. 1 is the flow conditions: M1 = 1.19, Mis = 1.70. In Figure 3 the perpendicular inlet shock wave can be seen as a result of supersonic inlet Mach In Figure 3 the perpendicular inlet shock wave can be seen as a result of supersonic inlet Mach In Figure 3 the perpendicular inlet shock wave can be seen as a result of supersonic inlet Mach number. The inlet shock wave interacts with the pressure side of the neighboring profile which leads number. The inlet shock wave interacts with the pressure side of the neighboring profile which leads to number. The inlet shock wave interacts with the pressure side of the neighboring profile which leads to a decrease of Mis near the 70% of axial chord as can be seen from Mach number distribution in a decrease of M near the 70% of axial chord as can be seen from Mach number distribution in Figure 3. is to a decrease of Mis near the 70% of axial chord as can be seen from Mach number distribution in Figure 3. The complicated flow structure can be seen at cascade exit including the inner and outer The complicated flow structure can be seen at cascade exit including the inner and outer branch of the Figure 3. The complicated flow structure can be seen at cascade exit including the inner and outer branch of the exit shock wave together with wake. Furthermore, the parasitic shock wave reflected exit shock wave together with wake. Furthermore, the parasitic shock wave reflected into measured branch of the exit shock wave together with wake. Furthermore, the parasitic shock wave reflected into measured area from the exit flow boundary is present resulting in artificial decrease of Mis in the area from the exit flow boundary is present resulting in artificial decrease of M in the vicinity of the is into measured area from the exit flow boundary is present resulting in artificial decrease of Mis in the vicinity of the suction side of profile at 60% of axial chord. suction side of profile at 60% of axial chord. vicinity of the suction side of profile at 60% of axial chord. Figure 4. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 4. Interferogram and isentropic Mach number distribution along the innovative tip profile for Figure 4. Interferogram and isentropic Mach number distribution along the innovative tip profile for the flow conditions: M1 = 1.21, Mis = 1.91. the flow conditions: M1 = 1.21, Mis = 1.91. the flow conditions: M = 1.21, M = 1.91. 1 is In Figure 4 the similar behavior of the perpendicular inlet shock wave together with interaction In Figure 4 the similar behavior of the perpendicular inlet shock wave together with interaction In Figure 4 the similar behavior of the perpendicular inlet shock wave together with interaction at at pressure side of the corresponding profile can be seen. However, the differences appear behind at pressure side of the corresponding profile can be seen. However, the differences appear behind pressure side of the corresponding profile can be seen. However, the di erences appear behind the the trailing edge of the profile with variation in angles of the inner and outer branch of the exit shock the trailing edge of the profile with variation in angles of the inner and outer branch of the exit shock trailing edge of the profile with variation in angles of the inner and outer branch of the exit shock wave wave and wake indicating higher outlet velocity. Moreover, the parasitic shock wave is not present wave and wake indicating higher outlet velocity. Moreover, the parasitic shock wave is not present and wake indicating higher outlet velocity. Moreover, the parasitic shock wave is not present which which results in a less complicated flow field better reflecting the real cascade performance. which results in a less complicated flow field better reflecting the real cascade performance. results in a less complicated flow field better reflecting the real cascade performance. In numerical methods there are serious complications for supersonic inlet due to the unique In numerical methods there are serious complications for supersonic inlet due to the unique In numerical methods there are serious complications for supersonic inlet due to the unique incidence rule (see [4]) which states that the value of the incidence angle corresponding to a incidence rule (see [4]) which states that the value of the incidence angle corresponding to a incidence rule (see [4]) which states that the value of the incidence angle corresponding to a particular particular inlet Mach number is dependent on the cascade geometry only. The inlet conditions and particular inlet Mach number is dependent on the cascade geometry only. The inlet conditions and inlet Mach number is dependent on the cascade geometry only. The inlet conditions and the overall the overall flow field vary extensively with each 0.1° change of inlet incidence angle. the overall flow field vary extensively with each 0.1° change of inlet incidence angle. flow field vary extensively with each 0.1 change of inlet incidence angle. The regime closest to the measured ones was computed using in-house code with -Re The regime closest to the measured ones was computed using in-house code with -Re The regime closest to the measured ones was computed using in-house code with -Re transition transition and turbulence model and the result is shown in Figure 5. Inlet Mach number is relatively transition and turbulence model and the result is shown in Figure 5. Inlet Mach number is relatively and turbulence model and the result is shown in Figure 5. Inlet Mach number is relatively close to close to 1.2 and the isentropic exit Mach number is just between that of interferograms in Figures 3 close to 1.2 and the isentropic exit Mach number is just between that of interferograms in Figures 3 1.2 and the isentropic exit Mach number is just between that of interferograms in Figures 3 and 4. and 4. The flow structure is well predicted with the normal shock standing in front of the leading and 4. The flow structure is well predicted with the normal shock standing in front of the leading edge. Interaction of the inner branch of exit shock wave with the suction side boundary layer edge. Interaction of the inner branch of exit shock wave with the suction side boundary layer resulting in the local flow separation is in agreement with the experiments. The distribution of Mis resulting in the local flow separation is in agreement with the experiments. The distribution of Mis Int. J. Turbomach. Propuls. Power 2019, 4, 33 5 of 10 The flow structure is well predicted with the normal shock standing in front of the leading edge. Interaction of the inner branch of exit shock wave with the suction side boundary layer resulting in Int. J. Turbo Int. J. Turbo m m ach. ach. Propuls. Power Propuls. Power 2019 2019 , , 44 , x FOR PE , x FOR PE ER RE ER RE VI VI EE W W 5 5 of of 10 10 the local flow separation is in agreement with the experiments. The distribution of M along profiles is also corresponds well to the experimental results. The di erence in the level of M on the suction is along along pro pro ff iles also iles also corre corre spo spo n n ds we ds we ll to th ll to th e exper e exper imental re imental re sults. Th sults. Th e difference e difference in the in the level of level of M M isis on on side behind x/b ~ 0.55 can be partially attributed to diculties with evaluation of interferograms and th thee s suuccttio ion si n siddee be behi hinndd x/b ~ x/b ~ 0. 0.55 55 ca can be pa n be partial rtially ly a attri ttribbuted to dif uted to diffficicul ultities wi es with ev th evaaluati luation of on of presence of aperiodic flow phenomena. interfero interfero g g rams and rams and prese prese n n ce of ce of aper aper io io dic dic flow phen flow phen omena. omena. 2.52.5 2.02.0 1.51.5 1.01.0 0.50.5 0.00.0 0.00.000.1.10.20.200.3.30.40.400.5.50.60.600.7.70.80.800.9.91.01.0 x/b x/b (-) (-) Figure Figure 5. Figure 5. 5. Mach Ma Ma ch number isoli ch number isoli number isolines nnes and i es and i and isentr ssentropic Ma entropic Ma opic Mach ch nu ch nu number mber distribution along the innovative tip mber distribution along the innovative tip distribution along the innovative tip pr profile profile ofile calculated calcu calcu lat lat ed by ed by by in-house in-hou in-hou se se code code code (g-Re (g (g -Re -Re Q Q m model) m oo del) del) for th for for th thee f e f flow low con low con conditions: d d it iion tion ss : M : M M 1 = 1 1= = 1 1.135, .135, M .135, M Misis = = =1.796 1.796 1.796. . . Q 1 is Operation point with the slightly supersonic inlet Mach number M = 1.03 was calculated by Operat Operation po ion point int wit withh t thhe s e slight lightly ly s suuper perssonic onic inlet inlet M Maach n ch nuumber mber M M 111 = 1.03 = 1.03 was cal was calccula ulatted ed by by in-house code as can be seen in Figure 6. There is no normal inlet shock wave in front of the leading in-ho in-ho u u se co se co d d ee a a ss c c aa n be n be se se en in en in Fi Fi gure gure 6 6 . There . There is is no no normal normal in in let let s s h h ock wave ock wave in in front front o o ff t t h h e e le le ad ad ing ing edge of profile. Instead, the supersonic area ending by shock wave at 20% of axial chord is present edge of pro edge of pro ffile. Instead ile. Instead , the superson , the superson ic ic are are aa endin endin gg by shock w by shock w aave ve at 20% o at 20% o ff axial chord axial chord is pr is pr esent esent near the leading edge at the pressure side of the profile. M distribution is in the vicinity of suction is near the near the le le ad ad ing edg ing edg ee at the pressure at the pressure side of the profile side of the profile . M . M isis d d is is tt rr ib ib u u tt io io nn i i ss i n in t t hh ee v v ic ic in in it it yy o o ff s s u u cc tt io io nn side with a drop between 40% and 50% which is in good agreement with experimental results. This side w side w it it h h a d a d rr op op b b ee tt w w een 40% een 40% and and 55 00 % % which i which i ss in in gg ood agr ood agr eem eem ee n n tt wit wit h h exp exp ee rim rim ee nt nt al al res res u u lt lt s. This s. This regime corresponds to M between the two measured aerodynamic loadings. is regime regime corresponds to M corresponds to M isis between the two measured between the two measured aero aero dyn dyn aa mic mic lo lo adin adin gs. gs. Figure 6. Mach number isolines and isentropic Mach number distribution along the innovative tip Figure 6. Figure 6. Ma Ma ch number isoli ch number isolinnes and i es and issentropic Ma entropic Ma ch nu ch nu mber distribution along the innovative tip mber distribution along the innovative tip profile calculated by in-house code for the flow conditions: M = 1.03, M = 1.79. 1 is profile profile calcu calcu lat lat ed by ed by in-hou in-hou se se code code for the f for the f lo lo w w condit condit ions ions : : M M 1 = 1 1 = 1 .03, M .03, M isis = = 1.79 1.79 . . The results of commercial code calculation are shown in Figure 7 together with results of the The resu The resultlts o s off commerci commerciaal code c l code caalc lcul ulaattion are ion are sho show wn in F n in Fig iguure re 7 t 7 tooget gethher w er witithh res resuultlts o s off tthhe e in-house code. In this case inlet Mach number is even smaller, M = 0.88, since for higher inlet in-ho in-ho u u se co se co d d ee . In t . In t h h is is ca ca se se inlet inlet Mach Mach n n u u mber i mber i ss eve eve n n sma sma lle lle r, r, M M 1 = 1 = 0. 0. 88 88 , , since since f f oo r highe r highe rr in in le le tt Mach Mach Mach numbers, commercial code predicted non-physical phenomena at inlet of the blade cascade. numbers, co numbers, commercia mmercial co l code predict de predicteedd non-phys non-physica ical phenomena at inlet of l phenomena at inlet of the blade c the blade caascade scade. . Agreement between the two codes in this regime is good. Both predicted a very small supersonic Agreement Agreement between the t between the tw wo code o codes s in t in thhis reg is regime ime is is good. Both p good. Both prredicted edicted a ve a very ry small supe small supersonic rsonic region terminated by a normal shock wave on the pressure side at the leading edge. The calculated region t region t ee rm rm in in at at ed b ed b yy a nor a nor m m al al shock w shock w aa vv ee on t on t hh e e pre pre ssur ssur ee side side at t at t hh e le e le adin adin g ed g ed ge. The c ge. The c aa lculated lculated exit exit f flow low fie field corre ld correspond spondss we wellll t too t thhe e resu result lts o s off exp expeeriment riments s and and ca calcu lculat lations ions wit withh in in-hou -houssee codes codes presented ab presented ab ove. ove. M (-) Mis (-) is Int. J. Turbomach. Propuls. Power 2019, 4, 33 6 of 10 exit flow field corresponds well to the results of experiments and calculations with in-house codes Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 6 of 10 presented above. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 6 of 10 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 Ansys 0.5 Ansys Fluent 0.0 Fluent 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 x/b 0 (-).6 0.8 1.0 x/b (-) Figure 7. Mach number isolines and isentropic Mach number distribution along the innovative tip Figure 7. Mach number isolines and isentropic Mach number distribution along the innovative tip Figure 7. Mach number isolines and isentropic Mach number distribution along the innovative tip profile calculated by commercial and in-house code for the flow conditions: M1 = 0.87, Mis = 1.76. profile calculated by commercial and in-house code for the flow conditions: M1 = 0.87, Mis = 1.76. profile calculated by commercial and in-house code for the flow conditions: M = 0.87, M = 1.76. 1 is A useful criterion for comparison of aerodynamic behavior of two different profiles of a A useful criterion for comparison of aerodynamic behavior of two different profiles of a A useful criterion for comparison of aerodynamic behavior of two di erent profiles of a rotating rotating blade at the same thermodynamic boundary conditions (such as space and time blade rotating blade at the same thermo at the same thermodynamic boundary dynamiconditions c boundary cond (such asitspace ions (s and uchtime as space distributions and time of distributions of pressure, enthalpy and velocity vector of working fluid) is the ratio of tangential and distributions of pressure, enthalpy and velocity vector of working fluid) is the ratio of tangential and pressure, enthalpy and velocity vector of working fluid) is the ratio of tangential and axial component axial component of force affecting each profile. As the principle of the turbine is conversion of fluid of axial force component a ecting each of fopr rce affecting each ofile. As the principle profile. As of the thturbine e princip isle o conversion f the turbin of e is fluid cothermodynamic nversion of fluid thermodynamic fre thermodynamic fre e ener e ener gy to torque gy to torque of the rotor, of the rotor, th th e tangential e tangential component of the force c component of the force caa n n be seen be seen free energy to torque of the rotor, the tangential component of the force can be seen as beneficial as bene (contributing as bene ficial fici (cont al to (cont rtor ibut rque), ibut ingin t contrary g o t to o t rque orque to ), c ), the o cnt oaxial nt rary t rary t component o t o t hh e ax e ax ia ial comp rl comp elatedonent onent with rel rel ener a at gy teed d wit leavi withh ng ener ener the gy gy cascade leav leav ing ing the cascade without doing work. This means that profile with higher force ratio at the same without doing work. This means that profile with higher force ratio at the same thermodynamic the cascade without doing work. This means that profile with higher force ratio at the same conditions thermodynamic condit is more ecient ions in is more the ener effic gy ient in the to torque conversion. energy to torque conversion. thermodynamic conditions is more efficient in the energy to torque conversion. The comparison of force ratio for original and innovative tip profile depending on flow inlet The comparison of force ratio for original and innovative tip profile depending on flow inlet The comparison of force ratio for original and innovative tip profile depending on flow inlet angle angle at at two two different aero di erent aerodynamic dynamic loadings loadings is is shown shown in in F Figur igue re 8.8.The The orig original inal pr profile ofile w was as described described angle at two different aerodynamic loadings is shown in Figure 8. The original profile was described in detail by [4]. The innovative tip profile exhibits a similar evolution of the force ratio for both in detail by [4]. The innovative tip profile exhibits a similar evolution of the force ratio for both in detail by [4]. The innovative tip profile exhibits a similar evolution of the force ratio for both aer aerod odynamic ynamicloadings loadings wh while ile t the heoriginal original t tip ippr prof ofile ileshows showssignificantly significantlyworse worsefor for ce ce ratio ratiofor for l low ow aerodynamic loadings while the original tip profile shows significantly worse force ratio for low aerodynamic loading. aerodynamic loading. aerodynamic loading. Figure 8. Comparison of force ratio of tangential and axial component of force f or original tip (blue lines) and innovative tip (red lines) at low (solid lines) and high (dashed lines) aerodynamic loading. Figure 8. Comparison of force ratio of tangential and axial component of force for original tip (blue Figure 8. Comparison of force ratio of tangential and axial component of force for original tip (blue lines) and innovative tip (red lines) at low (solid lines) and high (dashed lines) aerodynamic loading. lines) and innovative tip (red lines) at low (solid lines) and high (dashed lines) aerodynamic loading. The full potential of innovative tip profile has been demonstrated by measurement in a high-speed tunnel. Comparison of measured profile loss for original and innovative tip profile for The full potential of innovative tip profile has been demonstrated by measurement in a high-speed The full potential of innovative tip profile has been demonstrated by measurement in a two values 1.0 and 1.2 of inlet Mach number is shown in Figure 9. There can be seen a similar low tunnel. Comparison of measured profile loss for original and innovative tip profile for two values 1.0 high-speed tunnel. Comparison of measured profile loss for original and innovative tip profile for value of profile losses in a wide range of outlet Mach number for both values 1.0 and 1.2 of inlet and 1.2 of inlet Mach number is shown in Figure 9. There can be seen a similar low value of profile two values 1.0 and 1.2 of inlet Mach number is shown in Figure 9. There can be seen a similar low Mach number for innovative design. Conversely, the profile losses of original tip profile rise value of profile losses in a wide range of outlet Mach number for both values 1.0 and 1.2 of inlet significantly both for higher inlet Mach number and lower outlet Mach number. From these results Mach number for innovative design. Conversely, the profile losses of original tip profile rise is apparent that the innovative tip cascade provides strong benefits in a large operating range. significantly both for higher inlet Mach number and lower outlet Mach number. From these results is apparent that the innovative tip cascade provides strong benefits in a large operating range. M (-) M (-) is is Int. J. Turbomach. Propuls. Power 2019, 4, 33 7 of 10 losses in a wide range of outlet Mach number for both values 1.0 and 1.2 of inlet Mach number for innovative design. Conversely, the profile losses of original tip profile rise significantly both for higher inlet Mach number and lower outlet Mach number. From these results is apparent that the innovative Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 7 of 10 tip cascade provides strong benefits in a large operating range. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 7 of 10 Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red lines) Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red for M = 1.0 (solid lines) and M = 1.2 (dashed lines). 1 1 lines) for M1 = 1.0 (solid lines) and M1 = 1.2 (dashed lines). The flow field in the vicinity of the hub profile di ers significantly from the tip cascade flow The flow fields discussed field in t above. he vic The indense ity of t channel he huwith b profil low e conver differs significan gence results intly from the t slow steady acceleration ip cascad of e flow the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with fields discussed above. The dense channel with low convergence results in slow steady acceleration wake and outer branch of the shock wave are visible both in the interferogram and in the computed of the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring profile wake and outer branch of the shock wave are visible both in the interferogram and in the computed Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red near 90% of axial chord and results in a decrease of the Mach number in the vicinity of suction side lines) for M1 = 1.0 (solid lines) and M1 = 1.2 (dashed lines). Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring trailing edge. profile near 90% of axial chord and results in a decrease of the Mach number in the vicinity of In Figures 12 and 13 the di erent operating point with significantly higher aerodynamic loading The flow field in the vicinity of the hub profile differs significantly from the tip cascade flow suction side trailing edge. and thus with higher M is present. The flow acceleration is slow and steady in the main portion 2is fields discussed above. The dense channel with low convergence results in slow steady acceleration of the channel in agreement with the previous case. The main di erence is near the last 15% of axial of the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with chord where the rapid acceleration takes place with peak value up to M = 1.8. The sharper angle of is wake and outer branch of the shock wave are visible both in the interferogram and in the computed inner and outer branch of the shock wave also confirms the higher outlet Mach number. The inner Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring branch of the exit shock misses the suction side of neighbor profile indicating the operation beyond the profile near 90% of axial chord and results in a decrease of the Mach number in the vicinity of limit load condition. suction side trailing edge. Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile for the flow conditions: nominal inlet angle, Mis = 1.18. Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile for for the flow conditions: nominal inlet angle, Mis = 1.18. the flow conditions: nominal inlet angle, M = 1.18. is Figure 11. Mach number isolines and isentropic Mach number distribution along the hub innovative Figure 11. Mach number isolines and isentropic Mach number distribution along the hub innovative profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.08. profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.08. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 7 of 10 Figure 9. Comparison of measured profile loss for original tip (blue lines) and innovative tip (red lines) for M1 = 1.0 (solid lines) and M1 = 1.2 (dashed lines). The flow field in the vicinity of the hub profile differs significantly from the tip cascade flow fields discussed above. The dense channel with low convergence results in slow steady acceleration of the flow as can be seen in Figures 10 and 11. The inner branch of the exit shock wave together with wake and outer branch of the shock wave are visible both in the interferogram and in the computed Mach number isolines. The inner branch of the shock wave hits the suction side of neighboring profile near 90% of axial chord and results in a decrease of the Mach number in the vicinity of suction side trailing edge. Int. J. Turbomach. Propuls. Power 2019, 4, 33 8 of 10 Figure 10. Interferogram and isentropic Mach number distribution along the hub innovative profile for the flow conditions: nominal inlet angle, Mis = 1.18. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 8 of 10 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 8 of 10 In Figures 12 and 13 the different operating point with significantly higher aerodynamic In Figures 12 and 13 the different operating point with significantly higher aerodynamic loading and thus with higher M2is is present. The flow acceleration is slow and steady in the main loading and thus with higher M2is is present. The flow acceleration is slow and steady in the main portion of the channel in agreement with the previous case. The main difference is near the last 15% portion of the channel in agreement with the previous case. The main difference is near the last 15% of axial chord where the rapid acceleration takes place with peak value up to Mis = 1.8. The sharp er of axial chord where the rapid acceleration takes place with peak value up to Mis = 1.8. The sharper angle of inner and outer branch of the shock wave also confirms the higher outlet Mach number. The Figure Figure 11. 11. Mach Mach nu number mber isolines and isentro isolines and isentropic pic Mach nu Mach number mber distributio distribution n along the hub innovative along the hub innovative angle of inner and outer branch of the shock wave also confirms the higher outlet Mach number. The inner branch of the exit shock misses the suction side of neighbor profile indicating the operation pr profile calcu ofile calculated lated by bycommer commercial code cial code for for the theflow flow con conditions: ditions: nominal nominal inlet inletangle, angle, M M is = 1 = 1.08. .08. is inner branch of the exit shock misses the suction side of neighbor profile indicating the operation beyond the limit load condition. beyond the limit load condition. Figure 12. Interferogram and isentropic Mach number distribution along the hub innovative profile Figure 12. Interferogram and isentropic Mach number distribution along the hub innovative profile for Figure 12. Interferogram and isentropic Mach number distribution along the hub innovative profile for the flow conditions: nominal inlet angle, Mis = 1.597. the flow conditions: nominal inlet angle, M = 1.597. is for the flow conditions: nominal inlet angle, Mis = 1.597. Figure 13. Mach number isolines and isentropic Mach number distribution along the hub innovative Figure 13. Mach number isolines and isentropic Mach number distribution along the hub innovative Figure 13. Mach number isolines and isentropic Mach number distribution along the hub innovative profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.64. profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.64. profile calculated by commercial code for the flow conditions: nominal inlet angle, Mis = 1.64. There can be seen high conformity in experimental and calculated results for both operating There can be seen high conformity in experimental and calculated results for both operating regimes of hub cascade in terms of flow field pattern and isentropic Mach number distribution. On regimes of hub cascade in terms of flow field pattern and isentropic Mach number distribution. On the other hand, significant discrepancy can be seen for integral profile loss evaluation. the other hand, significant discrepancy can be seen for integral profile loss evaluation. The profile loss function on aerodynamic loading represented by Mis can be seen in Figure 14. The profile loss function on aerodynamic loading represented by Mis can be seen in Figure 14. For the original hub profile (presented in [3]) the calculated values are almost the same for both For the original hub profile (presented in [3]) the calculated values are almost the same for both in-house and commercial code. Furthermore, the trend of increasing of profile loss with higher in-house and commercial code. Furthermore, the trend of increasing of profile loss with higher aerodynamic loading of the hub cascade can be seen in experimental results as well, although the aerodynamic loading of the hub cascade can be seen in experimental results as well, although the absolute value of the profile losses is approximately 1% higher. absolute value of the profile losses is approximately 1% higher. Int. J. Turbomach. Propuls. Power 2019, 4, 33 9 of 10 There can be seen high conformity in experimental and calculated results for both operating regimes of hub cascade in terms of flow field pattern and isentropic Mach number distribution. On the other hand, significant discrepancy can be seen for integral profile loss evaluation. The profile loss function on aerodynamic loading represented by M can be seen in Figure 14. is For the original hub profile (presented in [3]) the calculated values are almost the same for both in-house and commercial code. Furthermore, the trend of increasing of profile loss with higher aerodynamic loading of the hub cascade can be seen in experimental results as well, although the absolute value of Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 9 of 10 the profile losses is approximately 1% higher. Figure 14. Comparison of measured profile loss for original hub (blue lines) and innovative hub Figure 14. Comparison of measured profile loss for original hub (blue lines) and innovative hub (red (red lines) for experiment (solid lines), in-house code (dashed lines) and commercial code (dotted lines). lines) for experiment (solid lines), in-house code (dashed lines) and commercial code (dotted lines). On the other hand, for the presented innovative hub profile the profile loss evolution is more On the other hand, for the presented innovative hub profile the profile loss evolution is more complicated. The calculated results for in-house and commercial code agree with each other up to complicated. The calculated results for in-house and commercial code agree with each other up to M = 1.4. For higher aerodynamic loading the in-house code predicts the decrease in the profile losses. is Mis = 1.4. For higher aerodynamic loading the in-house code predicts the decrease in the profile The non-linear dependency is confirmed with experimental data as well. The di erence in profile losses. The non-linear dependency is confirmed with experimental data as well. The difference in losses is again around 1% but with lower profile losses for the experimental data. profile losses is again around 1% but with lower profile losses for the experimental data. The significantly higher experimental profile losses by 3% can be associated with more complicated The significantly higher experimental profile losses by 3% can be associated with more structure of flow field for original hub cascade leading to higher energy dissipation as is described in complicat more detail ed struct by [3 ure of ]. This flo imp w fie ortant ld fo information r original hconfirms ub cascade thelea necessity ding toof higher en experimental ergy di verifi ssipat cation ion as of is describe calculated d in more det results especially ail by [3for ]. Thi complicated s important transonic informand ation con supersonic firms t flow he neces fieldssin ity o the f exper vicinity iment last al stage blade cascades. verification of calculated results especially for complicated transonic and supersonic flow fields in the vicinity last stage blade cascades. 6. Conclusions 5. Conclus Advanced ions hub and tip profiles of ultra-long last stage blade were analyzed by both experimental and numerical methods. The optical measurements of transonic and supersonic flow fields Advanced hub and tip profiles of ultra-long last stage blade were analyzed by both were performed in high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of experimental and numerical methods. The optical measurements of transonic and supersonic flow Thermomechanics of the Czech Academy of Sciences. Commercial and in-house software of CTU fields were performed in high-speed wind tunnel in the Aerodynamic Laboratory of the Institute of Prague were used for calculating the corresponding flow fields. Thermomechanics of the Czech Academy of Sciences. Commercial and in-house software of CTU For the tip cascade, the perpendicular inlet shock wave was observed as a result of supersonic Prague were used for calculating the corresponding flow fields. inlet Mach number. This phenomenon could not be reproduced by tested numerical codes. The flow For the tip cascade, the perpendicular inlet shock wave was observed as a result of supersonic structure at cascade exit includes the inner and outer branch of the exit shock wave together with wake. inlet Mach number. This phenomenon could not be reproduced by tested numerical codes. The flow These structures were well reproduced by numerical calculations including position of interaction of stru the ctuinner re at ca branch scade e of the xit i exit nclu shock des the i withnsuction ner and side oute ofr branch neighboring of th pr e exit ofile. shock wave together with wake. These structures The dense hub channel were well with re lowproduced by convergence numeric results inaslow l calc steady ulations acceleration including pos of theition of flow. The high conformity in experimental and calculated results in terms of flow field pattern and isentropic interaction of the inner branch of the exit shock with suction side of neighboring profile. Mach number distribution was in contrast with significant discrepancy of integral profile loss evaluation. The dense hub channel with low convergence results in slow steady acceleration of the flow. The high conformity in experimental and calculated results in terms of flow field pattern and isentropic Mach number distribution was in contrast with significant discrepancy of integral profile loss evaluation. Both hub and tip cascades were compared with the similar profiles presented in the past. The overall aerodynamic performance was significantly improved in both cases. The comparison of experimental and numerical results shows limits of both methods. In particular, in the experiment, the parasitic shock wave reflected into measured area from the test section wall resulting in artificial decrease of isentropic Mach number near the suction side of the profile. On the other hand, the numerical methods had issues with supersonic inlet and integral profile loss evaluation. The in-house code exhibits lower overall discrepancy of loss evaluation for the innovative hub cascade. Author Contributions: Ondrej Novak: publication, data management, vane and blade design; Marek Bobcik: new vane and rotor blade design, loss coefficient calculation, stage design; Martin Luxa: conducting of optical Int. J. Turbomach. Propuls. Power 2019, 4, 33 10 of 10 Both hub and tip cascades were compared with the similar profiles presented in the past. The overall aerodynamic performance was significantly improved in both cases. The comparison of experimental and numerical results shows limits of both methods. In particular, in the experiment, the parasitic shock wave reflected into measured area from the test section wall resulting in artificial decrease of isentropic Mach number near the suction side of the profile. On the other hand, the numerical methods had issues with supersonic inlet and integral profile loss evaluation. The in-house code exhibits lower overall discrepancy of loss evaluation for the innovative hub cascade. Author Contributions: O.N.: publication, data management, vane and blade design; M.B.: new vane and rotor blade design, loss coecient calculation, stage design; M.L.: conducting of optical measurements and its evaluation; analysis of results; J.F. (Jaroslav Fort): CFD team management, analysis of CFD results; B.R.: CFD calculations with commercional code ANSYS FLUENT, results evaluation; J.S.: original vane and blade design, new vane design, stage design; D.S.: conducting of pneumatic traverses and loss evaluation; analysis of results; J.F. (Jiri Furst): development of the in-house code, implementation of turbulence models; J.H.: analysis of CFD results; V.H.: CFD simulations including pre- and post-processing; J.P.: proposal of turbulence models for in-house codes; Z.S.: 1D throughflow calculations and design. Funding: The authors would like to express their thanks to the Technology Agency of the Czech Republic, which supported this research under grant No. TA02020057. The APC was funded by Euroturbo. Conflicts of Interest: The authors declare no conflict of interest. References 1. Senoo, S.; Ono, H. Development of Design Method for Supersonic Turbine Aerofoils near the Tip of Long Blades in Steam Turbines, Part 2: Configuration Details and Validation. In Proceedings of the ASME Turbo Expo 2013, GT2013-94039, San Antonio, TX, USA, 3–7 June 2013. 2. Bobcik, M.; Fort, J.; Furst, J.; Halama, J.; Hric, V.; Louda, P.; Luxa, M.; Rudas, B.; Synac, J.; Simurda, D. Investigation of Transonic and Supersonic Flow in Rotor Tip Section of Last LP Steam Turbine Cascade under Di erent Turbulence Level. In Proceedings of the 12th European Conference on Turbomachinery, Stockholm, Sweden, 3–7 April 2017. 3. Hala, J.; Luxa, M.; Simurda, D.; Bobcik, M.; Novak, O.; Synac, J.; Rudas, B. Optimization of Root Section for Ultra Long Steam Turbine Rotor Blade. In Proceedings of the 13th International Symposium on Experimental Computational Aerothermodynamics of Internal Flows, Okinawa, Japan, 7–11 May 2017. 4. Luxa, M.; Simurda, D.; Fort, J.; Furst, P.; Safarik, P.; Synac, J.; Rudas, B. Aerodynamic Investigation of the Tip Section for Titanium Blade 54”. In Proceedings of the 11th European Conference on Turbomachinery, Madrid, Spain, 23–27 March 2015. 5. Safarik, P.; Luxa, M. Using Optical Methods in High-Speed Aerodynamic Research. In Proceedings of the Measurement Techniques in Turbomachinery XX, Firenze, Italy, 21–22 September 2000; pp. 1–7. 6. Langtry, R.B.; Menter, F.R. Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes. AIAA J. 2000, 47, 2894–2906. [CrossRef] 7. Musil, J.; Pr ˇíhoda, J.; Fürst, J. Simulation of Supersonic Flow through the Tip-Section Turbine Blade Cascade with a Flat Profile. In Problems of Fluid Mechanics; Šimurda, D., Bodnár, T., Eds.; Topical: Prague, Czech Republic, 2019; pp. 169–174. © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Journal

International Journal of Turbomachinery, Propulsion and PowerMultidisciplinary Digital Publishing Institute

Published: Sep 24, 2019

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