Numerical Investigation and Non-Axisymmetric Endwall Profiling of a Turbine Stage
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摘要
This paper presents an optimization of a high pressure turbine by constructing non-axisymmetric endwalls to the stator row and the rotor hub. The optimization was quantified by using optimization algorithms based on the multi-objective function. The objective was to increase total-to-total efficiency with the constraint on the mass flow rate equal to the design point value. In order to ensure that global optimum could be achieved, the function of parameters was first approximated through the artificial neural network, and then optimum was achieved by implementing the genetic algorithm. It was adopted through the design and optimization environment of Fine~(TM)/Design3 D. Three individual treatments of the endwalls were presented. Firstly, the hub and the shroud of the stator were optimized together. Secondly, the hub of the rotor was optimized. Thirdly, the rotor hub was optimized in the presence of the optimized stator. The result of the investigation showed that the optimized shape of the endwalls can significantly help to increase the efficiency up to 0.18% with the help of a reduction of the transverse pressure gradient. The coefficient of secondary kinetic energy, entropy coefficient, spanwise mass averaged entropy were reduced. In order to investigate the periodic effects, the design of the optimized turbine under steady simulations was confirmed through unsteady simulations. The last part of the investigation made sure that the performance improvement remained consistent over the full operating line at off-design conditions by the implementation of non-axisymmetric endwalls.
This paper presents an optimization of a high pressure turbine by constructing non-axisymmetric endwalls to the stator row and the rotor hub. The optimization was quantified by using optimization algorithms based on the multi-objective function. The objective was to increase total-to-total efficiency with the constraint on the mass flow rate equal to the design point value. In order to ensure that global optimum could be achieved, the function of parameters was first approximated through the artificial neural network, and then optimum was achieved by implementing the genetic algorithm. It was adopted through the design and optimization environment of Fine~(TM)/Design3 D. Three individual treatments of the endwalls were presented. Firstly, the hub and the shroud of the stator were optimized together. Secondly, the hub of the rotor was optimized. Thirdly, the rotor hub was optimized in the presence of the optimized stator. The result of the investigation showed that the optimized shape of the endwalls can significantly help to increase the efficiency up to 0.18% with the help of a reduction of the transverse pressure gradient. The coefficient of secondary kinetic energy, entropy coefficient, spanwise mass averaged entropy were reduced. In order to investigate the periodic effects, the design of the optimized turbine under steady simulations was confirmed through unsteady simulations. The last part of the investigation made sure that the performance improvement remained consistent over the full operating line at off-design conditions by the implementation of non-axisymmetric endwalls.
This paper presents an optimization of a high pressure turbine by constructing non-axisymmetric endwalls to the stator row and the rotor hub. The optimization was quantified by using optimization algorithms based on the multi-objective function. The objective was to increase total-to-total efficiency with the constraint on the mass flow rate equal to the design point value. In order to ensure that global optimum could be achieved, the function of parameters was first approximated through the artificial neural network, and then optimum was achieved by implementing the genetic algorithm. It was adopted through the design and optimization environment of Fine~(TM)/Design3 D. Three individual treatments of the endwalls were presented. Firstly, the hub and the shroud of the stator were optimized together. Secondly, the hub of the rotor was optimized. Thirdly, the rotor hub was optimized in the presence of the optimized stator. The result of the investigation showed that the optimized shape of the endwalls can significantly help to increase the efficiency up to 0.18% with the help of a reduction of the transverse pressure gradient. The coefficient of secondary kinetic energy, entropy coefficient, spanwise mass averaged entropy were reduced. In order to investigate the periodic effects, the design of the optimized turbine under steady simulations was confirmed through unsteady simulations. The last part of the investigation made sure that the performance improvement remained consistent over the full operating line at off-design conditions by the implementation of non-axisymmetric endwalls.
引文
[1]Denton J.D.,The 1993 IGTI Scholar Lecture:Loss mechanisms in turbomachines.Journal of Turbomachinery,1993,115(4):621-656.
[2]Coull J.D.,Endwall loss in turbine cascades.Journal of Turbomachinery,2017,139(8):081004.
[3]Harrison S.,The influence of blade lean on turbine losses.Journal of Turbomachinery,1992,114(1):184-190.
[4]Sonoda T.,Hasenj?ger M.,Arima T.,Sendhoff B.,Effect of end wall contouring on performance of ultra-low aspect ratio transonic turbine inlet guide vanes.Journal of Turbomachinery,2009,131(1):011020.
[5]Rose M.G.,Non-axisymmetric endwall profiling in the HP NGV’s of an axial flow gas turbine.ASME 1994International Gas Turbine and Aeroengine Congress and Exposition,Hague,Netherlands,1994:V001T01A090.
[6]Hartland J.,Gregory-Smith D.,Rose M.,Nonaxisymmetric endwall profiling in a turbine rotor blade.ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition,Stockholm,1998:V001T01A130.
[7]Harvey N.W.,Rose M.G.,Taylor M.D.,Shahpar S.,Hartland J.,Gregory-Smith D.G.,Nonaxisymmetric turbine end wall design:part I-three-dimensional linear design system.Journal of Turbomachinery,2000,122(2):278-285.
[8]Brennan G.,Harvey N.W.,Rose M.G.,Fomison N.,Taylor M.D.,Improving the efficiency of the Trent500-HP turbine using nonaxisymmetric end walls-Part I:Turbine design.Journal of Turbomachinery,2003,125(3):497-504.
[9]Rose M.G.,Harvey N.W.,Seaman P.,Newman D.A.,McManus D.,Improving the efficiency of the Trent 500HP turbine using non-axisymmetric end walls:Part II-Experimental Validation.ASME Turbo Expo,Louisiana,2001,2001-GT-0505.
[10]Harvey N.,Brennan G.,Newman D.,Rose M.,Improving turbine efficiency using non-axisymmetric end walls:Validation in the multi-row environment and with low aspect ratio blading.ASME Turbo Expo,Amsterdam,2002,GT2002-30337:119-126.
[11]Ingram G.,Gregory-Smith D.,Harvey N.,Investigation of a novel secondary flow feature in a turbine cascade with end wall profiling.Journal of Turbomachinery,2005,127(1):209-214.
[12]Poehler T.,Gier J.,Jeschke P.,Numerical and experimental analysis of the effects of non-axisymmetric contoured stator endwalls in an axial turbine.ASMETurbo Expo,Glasgow,2010,GT2010-23350:1549-1559.
[13]Poehler T.,Niewoehner J.,Jeschke P.,Guendogdu Y.,Investigation of nonaxisymmetric endwall contouring and three-dimensional airfoil design in a 1.5-stage axial turbine-Part I:Design and novel numerical analysis method.Journal of Turbomachinery,2015,137(8):081009.
[14]Tang H.,Liu S.,Luo H.,Design optimization of profiled endwall in a high work turbine.ASME Turbo Expo,Dusseldorf,2014,GT2014-26190:V02CT38A029.
[15]Li C.,Guo Z.,Song L.,Li J.,Feng Z.,Design optimization of a 3D parameterized vane cascade with non-axisymmetric endwall based on a modified EGOalgorithm and data mining techniques.ASME Turbo Expo,Charlotte,2017,GT2017-63738:V02CT47A009.
[16]Kim I.,Kim J.,Cho J.,Kang Y.-S.,Non-axisymmetric endwall profile optimization of a high-pressure transonic turbine using approximation model.ASME Turbo Expo,Seoul,2016,GT2016-57970:V02BT38A056.
[17]Menter F.R.,Two-equation eddy-viscosity turbulence models for engineering applications.AIAA Journal,1994,32(8):1598-1605.
[18]Roache P.J.,Perspective:a method for uniform reporting of grid refinement studies.Journal of Fluids Engineering,1994,116(3):405-413.
[19]Goldberg D.E.,Genetic and evolutionary algorithms come of age.Communications of the ACM,1994,37(3):113-120.
[20]Pierret S.,Van den Braembussche R.A.,Turbomachinery blade eesign using a Navier-Stokes solver and artificial neural network.Journal of Turbomachinery,1999,121(2):326-332.
[21]Ingram G.L.,Endwall profiling for the reduction of secondary flow in turbines.University of Durham,UK,2003.
[22]Liu X.,Jin D.,Gui X.,Investigation of non-axisymmetric endwall contouring in a compressor cascade.Journal of Thermal Science,2017,26(6):490-504.
[23]FINETM/Turbo,NUMECA International User Manual.
[24]Rai M.M.,Three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction:Part I-Methodology.Journal of Propulsion and Power,1989,5(3):305-311.
[2]Coull J.D.,Endwall loss in turbine cascades.Journal of Turbomachinery,2017,139(8):081004.
[3]Harrison S.,The influence of blade lean on turbine losses.Journal of Turbomachinery,1992,114(1):184-190.
[4]Sonoda T.,Hasenj?ger M.,Arima T.,Sendhoff B.,Effect of end wall contouring on performance of ultra-low aspect ratio transonic turbine inlet guide vanes.Journal of Turbomachinery,2009,131(1):011020.
[5]Rose M.G.,Non-axisymmetric endwall profiling in the HP NGV’s of an axial flow gas turbine.ASME 1994International Gas Turbine and Aeroengine Congress and Exposition,Hague,Netherlands,1994:V001T01A090.
[6]Hartland J.,Gregory-Smith D.,Rose M.,Nonaxisymmetric endwall profiling in a turbine rotor blade.ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition,Stockholm,1998:V001T01A130.
[7]Harvey N.W.,Rose M.G.,Taylor M.D.,Shahpar S.,Hartland J.,Gregory-Smith D.G.,Nonaxisymmetric turbine end wall design:part I-three-dimensional linear design system.Journal of Turbomachinery,2000,122(2):278-285.
[8]Brennan G.,Harvey N.W.,Rose M.G.,Fomison N.,Taylor M.D.,Improving the efficiency of the Trent500-HP turbine using nonaxisymmetric end walls-Part I:Turbine design.Journal of Turbomachinery,2003,125(3):497-504.
[9]Rose M.G.,Harvey N.W.,Seaman P.,Newman D.A.,McManus D.,Improving the efficiency of the Trent 500HP turbine using non-axisymmetric end walls:Part II-Experimental Validation.ASME Turbo Expo,Louisiana,2001,2001-GT-0505.
[10]Harvey N.,Brennan G.,Newman D.,Rose M.,Improving turbine efficiency using non-axisymmetric end walls:Validation in the multi-row environment and with low aspect ratio blading.ASME Turbo Expo,Amsterdam,2002,GT2002-30337:119-126.
[11]Ingram G.,Gregory-Smith D.,Harvey N.,Investigation of a novel secondary flow feature in a turbine cascade with end wall profiling.Journal of Turbomachinery,2005,127(1):209-214.
[12]Poehler T.,Gier J.,Jeschke P.,Numerical and experimental analysis of the effects of non-axisymmetric contoured stator endwalls in an axial turbine.ASMETurbo Expo,Glasgow,2010,GT2010-23350:1549-1559.
[13]Poehler T.,Niewoehner J.,Jeschke P.,Guendogdu Y.,Investigation of nonaxisymmetric endwall contouring and three-dimensional airfoil design in a 1.5-stage axial turbine-Part I:Design and novel numerical analysis method.Journal of Turbomachinery,2015,137(8):081009.
[14]Tang H.,Liu S.,Luo H.,Design optimization of profiled endwall in a high work turbine.ASME Turbo Expo,Dusseldorf,2014,GT2014-26190:V02CT38A029.
[15]Li C.,Guo Z.,Song L.,Li J.,Feng Z.,Design optimization of a 3D parameterized vane cascade with non-axisymmetric endwall based on a modified EGOalgorithm and data mining techniques.ASME Turbo Expo,Charlotte,2017,GT2017-63738:V02CT47A009.
[16]Kim I.,Kim J.,Cho J.,Kang Y.-S.,Non-axisymmetric endwall profile optimization of a high-pressure transonic turbine using approximation model.ASME Turbo Expo,Seoul,2016,GT2016-57970:V02BT38A056.
[17]Menter F.R.,Two-equation eddy-viscosity turbulence models for engineering applications.AIAA Journal,1994,32(8):1598-1605.
[18]Roache P.J.,Perspective:a method for uniform reporting of grid refinement studies.Journal of Fluids Engineering,1994,116(3):405-413.
[19]Goldberg D.E.,Genetic and evolutionary algorithms come of age.Communications of the ACM,1994,37(3):113-120.
[20]Pierret S.,Van den Braembussche R.A.,Turbomachinery blade eesign using a Navier-Stokes solver and artificial neural network.Journal of Turbomachinery,1999,121(2):326-332.
[21]Ingram G.L.,Endwall profiling for the reduction of secondary flow in turbines.University of Durham,UK,2003.
[22]Liu X.,Jin D.,Gui X.,Investigation of non-axisymmetric endwall contouring in a compressor cascade.Journal of Thermal Science,2017,26(6):490-504.
[23]FINETM/Turbo,NUMECA International User Manual.
[24]Rai M.M.,Three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction:Part I-Methodology.Journal of Propulsion and Power,1989,5(3):305-311.