Numerical study of corner separation in a linear compressor cascade using various turbulence models
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摘要
Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance.Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately.In the present study,numerical study of corner separation in a linear highly loaded prescribed velocity distribution(PVD) compressor cascade has been investigated using seven frequently used turbulence models.The seven turbulence models include Spalart–Allmaras model,standard k–e model,realizable k–e model,standard k–x model,shear stress transport k–x model,v~2–f model and Reynolds stress model.The results of these turbulence models have been compared and analyzed in detail with available experimental data.It is found the standard k–e model,realizable k–e model,v~2–f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade.The Spalart–Allmaras model,standard k–x model and shear stress transport k–x model overestimate corner separation region at incidence of 0°.The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.
Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance.Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately.In the present study,numerical study of corner separation in a linear highly loaded prescribed velocity distribution(PVD) compressor cascade has been investigated using seven frequently used turbulence models.The seven turbulence models include Spalart–Allmaras model,standard k–e model,realizable k–e model,standard k–x model,shear stress transport k–x model,v~2–f model and Reynolds stress model.The results of these turbulence models have been compared and analyzed in detail with available experimental data.It is found the standard k–e model,realizable k–e model,v~2–f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade.The Spalart–Allmaras model,standard k–x model and shear stress transport k–x model overestimate corner separation region at incidence of 0°.The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.
Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance.Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately.In the present study,numerical study of corner separation in a linear highly loaded prescribed velocity distribution(PVD) compressor cascade has been investigated using seven frequently used turbulence models.The seven turbulence models include Spalart–Allmaras model,standard k–e model,realizable k–e model,standard k–x model,shear stress transport k–x model,v~2–f model and Reynolds stress model.The results of these turbulence models have been compared and analyzed in detail with available experimental data.It is found the standard k–e model,realizable k–e model,v~2–f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade.The Spalart–Allmaras model,standard k–x model and shear stress transport k–x model overestimate corner separation region at incidence of 0°.The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.
引文
1.Lei VM,Spakovszky ZS,Greitzer EM.A criterion for axial compressor hub-corner stall.J Turbomach 2008;130(3):031006-10.
2.Denton JD.Loss mechanisms in turbomachines.J Turbomach1993;115:621-56.
3.Schulz HD,Gallus HE.Experimental investigation of the threedimensional flow in an annular compressor cascade.J Turbomach1988;110(4):467-78.
4.Guo S,Lu HW,Chen F,Wu CJ.Vortex control and aerodynamic performance improvement of a highly loaded compressor cascade via inlet boundary layer suction.Exp Fluids 2013;54:1570.
5.Zhang HD,Wu Y,Li YH,Lu HW.Experimental investigation on a high subsonic compressor cascade flow.Chin J Aeronaut 2015;28(4):1034-43.
6.Scillitoe AD,Tucker PG,Adami P.Evaluation of RANS and ZDES methods for the prediction of three-dimensional separation in axial flow compressors.Montre′al:ASME;2015.Report No.:GT2015-43975.
7.Liu YW,Yan H,Lu LP.Numerical study of the effect of secondary vortex on three-dimensional corner separation in a compressor cascade.Int J Turbo Jet Eng 2015.Available from:http://dx.doi.org/10.1515/tjj-2014-0039.
8.Guo S,Chen SW,Lu HW,Song YP,Chen F.Enhancing aerodynamic performances of a high-turning compressor cascade via boundary layer suction.Sci China Tech Sci 2010;53(10):2748-55.
9.Gmelin C,Thiele F,Liesner K,Meyer R.Investigations of secondary flow suction in a high speed compressor cascade.Vancouver:ASME;2011.Report No.:GT2011-46479.
10.Choi M.Effects of circumferential casing grooves on the performance of a transonic axial compressor.Int J Turbo Jet Eng2015;32(4):361-71.
11.Liu YW,Sun JJ,Lu LP.Corner separation control by boundary layer suction applied to a highly loaded axial compressor cascade.Energies 2014;7(12):7994-8007.
12.Lakshminarayan B.Fluid dynamics and heat transfer of turbomachinery.New York:A Wiley-Interscience Publication;1996.p.322-7.
13.Spalart PR.Detached-eddy simulation.Annu Rev Fluid Mech2009;41:181-202.
14.Menter F,Egorov Y.The scale-adaptive simulation method for unsteady turbulent flow predictions.Part 1:theory and model description.Flow Turbul Combust 2010;85(1):113-38.
15.Castagna J,Yao YF,Yao J.Direct numerical simulation of a turbulent flow over an axisymmetric hill.Comput Fluids2014;95:116-26.
16.Zhang HD,Yan C,Ye TH,Zhang JM,Chen YL.Large eddy simulation of unconfined turbulent swirling flow.Sci China Tech Sci 2015;58(10):1731-44.
17.Liu J,Sun HS,Liu ZT,Xiao ZX.Numerical investigation of unsteady vortex breakdown past 80°/65°double-delta wing.Chin JAeronaut 2014;27(3):521-30.
18.Wang YF,Chen F,Liu HP,Chen HL.Large eddy simulation of unsteady transitional flow on the low-pressure turbuine blade.Sci China Tech Sci 2014;57(9):1761-8.
19.Spalart PR.Philosophies and fallacies in turbulence modeling.Prog Aerosp Sci 2015;74:1-15.
20.Spalart PR.Strategies for turbulence modelling and simulations.Int J Heat Fluid Flow 2000;21:252-63.
21.Dunham J.CFD validation for propulsion system components.Neuilly-sur-Seine:AGARD;1998.Report No.:AR-355.
22.Liu YW,Yu XJ,Liu BJ.Turbulence models assessment for largescale tip vortices in an axial compressor rotor.J Propul Power2008;24(1):15-25.
23.Vijiapurapu S,Cui J.Performance of turbulence models for flows through rough pipes.Appl Math Model 2010;34:1458-66.
24.Balabel A,Hegab AM,Nasr M,Samy El-Behery M.Assessment of turbulence modeling for gas flow in two-dimensional convergent-divergent rocket nozzle.Appl Math Model 2011;35:3408-22.
25.Liu YW,Lu LP,Fang L,Gao F.Modification of SpalartAllmaras model with consideration of turbulence energy backscatter using velocity helicity.Phys Lett A 2011;375(24):2377-81.
26.Heschl C,Inthavong K,Sanz W,Tu J.Evaluation and improvements of RANS turbulence models for linear diffuser flows.Comput Fluids 2013;71:272-82.
27.Ma L,Lu LP,Fang J,Wang QH.A study on turbulence transportation and modification of Spalart-Allmaras model for shock-wave/turbulent boundary layer interaction flow.Chin JAeronaut 2014;27(2):200-9.
28.Liu YW,Yan H,Lu LP.Investigation of corner separation in a linear compressor cascade using DDES.Montre′al:ASME;2015.Report No.:GT2015-42902.
29.Gbadebo SA,Cumpsty NA,Hynes TP.Three-dimensional separations in axial compressors.J Turbomach 2005;127(2):331-9.
30.Fluent 6.3 User’s Guide.Fluent Documentation,Fluent Inc,2006.
31.Spalart PR,Allmaras SR.A one-equation turbulence model for aerodynamic flows.Reno:AIAA;1992.Report No.:AIAA-92-0439.
32.Spalart PR,Shur M.On the sensitization of turbulence models to rotation and curvature.Aerosp Sci Technol 1997;5:297-302.
33.Launder BE,Spalding DP.The numerical computation of turbulent flows.Comput Method Appl Mech 1974;3:269-89.
34.Launder BE,Sharma BI.Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc.Lett Heat Mass Transfer 1974;1:131-8.
35.Shih TH,Liou WW,Shabbir A.A new k-e eddy-viscosity model for high Reynolds number turbulent flows-model development and validation.Comput Fluids 1995;24(3):227-38.
36.Wilcox DC.Turbulence modeling for CFD.San Diego:DCWIndustries;2006.p.124-36.
37.Menter FR.Two-equation eddy-visocity turbulence models for engineering applications.AIAA J 1994;32(8):1598-605.
38.Durbin PA.Near-wall turbulence closure modeling without damping functions.Theor Comput Fluid Dyn 1991;3:1-13.
39.Durbin PA.Separated flow computations with the k-e-v2model.AIAA J 1995;33(4):659-64.
40.Behnia M,Parneix S,Shabany Y.Numerical study of turbulent.Int J Heat Fluid Flow 1999;20:1-9.
41.Launder BE,Reece GJ,Rodi W.Progress in the development of a Reynolds-stress turbulence closure.J Fluid Mech 1975;3(68):537-66.
42.Gibson MM,Launder BE.Ground effects on pressure fluctuations in the atmospheric boundary layer.J Fluid Mech1978;86:491-511.
43.Smirnov PE,Menter FR.Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term.J Turbomach 2009;131:0410104.
44.Gbadebo SA,Cumpsty NA,Hynes TP.Interaction of tip clearance flow and three-dimensional separations in axial compressors.J Turbomach 2007;129(4):679-85.
45.Gbadebo SA,Cumpsty NA,Hynes TP.Control of three-dimensional separations in axial compressors by tailored boundary layer suction.J Turbomach 2008;130(1):011004-8.
46.Gbadebo SA,Hynes TP,Cumpsty NA.Influence of surface roughness on three-dimensional separation in axial compressors.JTurbomach 2004;126(4):455-63.
47.Lumely J.Computational modeling of turbulent flows.Adv Appl Math 1978;18:123-76.
2.Denton JD.Loss mechanisms in turbomachines.J Turbomach1993;115:621-56.
3.Schulz HD,Gallus HE.Experimental investigation of the threedimensional flow in an annular compressor cascade.J Turbomach1988;110(4):467-78.
4.Guo S,Lu HW,Chen F,Wu CJ.Vortex control and aerodynamic performance improvement of a highly loaded compressor cascade via inlet boundary layer suction.Exp Fluids 2013;54:1570.
5.Zhang HD,Wu Y,Li YH,Lu HW.Experimental investigation on a high subsonic compressor cascade flow.Chin J Aeronaut 2015;28(4):1034-43.
6.Scillitoe AD,Tucker PG,Adami P.Evaluation of RANS and ZDES methods for the prediction of three-dimensional separation in axial flow compressors.Montre′al:ASME;2015.Report No.:GT2015-43975.
7.Liu YW,Yan H,Lu LP.Numerical study of the effect of secondary vortex on three-dimensional corner separation in a compressor cascade.Int J Turbo Jet Eng 2015.Available from:http://dx.doi.org/10.1515/tjj-2014-0039.
8.Guo S,Chen SW,Lu HW,Song YP,Chen F.Enhancing aerodynamic performances of a high-turning compressor cascade via boundary layer suction.Sci China Tech Sci 2010;53(10):2748-55.
9.Gmelin C,Thiele F,Liesner K,Meyer R.Investigations of secondary flow suction in a high speed compressor cascade.Vancouver:ASME;2011.Report No.:GT2011-46479.
10.Choi M.Effects of circumferential casing grooves on the performance of a transonic axial compressor.Int J Turbo Jet Eng2015;32(4):361-71.
11.Liu YW,Sun JJ,Lu LP.Corner separation control by boundary layer suction applied to a highly loaded axial compressor cascade.Energies 2014;7(12):7994-8007.
12.Lakshminarayan B.Fluid dynamics and heat transfer of turbomachinery.New York:A Wiley-Interscience Publication;1996.p.322-7.
13.Spalart PR.Detached-eddy simulation.Annu Rev Fluid Mech2009;41:181-202.
14.Menter F,Egorov Y.The scale-adaptive simulation method for unsteady turbulent flow predictions.Part 1:theory and model description.Flow Turbul Combust 2010;85(1):113-38.
15.Castagna J,Yao YF,Yao J.Direct numerical simulation of a turbulent flow over an axisymmetric hill.Comput Fluids2014;95:116-26.
16.Zhang HD,Yan C,Ye TH,Zhang JM,Chen YL.Large eddy simulation of unconfined turbulent swirling flow.Sci China Tech Sci 2015;58(10):1731-44.
17.Liu J,Sun HS,Liu ZT,Xiao ZX.Numerical investigation of unsteady vortex breakdown past 80°/65°double-delta wing.Chin JAeronaut 2014;27(3):521-30.
18.Wang YF,Chen F,Liu HP,Chen HL.Large eddy simulation of unsteady transitional flow on the low-pressure turbuine blade.Sci China Tech Sci 2014;57(9):1761-8.
19.Spalart PR.Philosophies and fallacies in turbulence modeling.Prog Aerosp Sci 2015;74:1-15.
20.Spalart PR.Strategies for turbulence modelling and simulations.Int J Heat Fluid Flow 2000;21:252-63.
21.Dunham J.CFD validation for propulsion system components.Neuilly-sur-Seine:AGARD;1998.Report No.:AR-355.
22.Liu YW,Yu XJ,Liu BJ.Turbulence models assessment for largescale tip vortices in an axial compressor rotor.J Propul Power2008;24(1):15-25.
23.Vijiapurapu S,Cui J.Performance of turbulence models for flows through rough pipes.Appl Math Model 2010;34:1458-66.
24.Balabel A,Hegab AM,Nasr M,Samy El-Behery M.Assessment of turbulence modeling for gas flow in two-dimensional convergent-divergent rocket nozzle.Appl Math Model 2011;35:3408-22.
25.Liu YW,Lu LP,Fang L,Gao F.Modification of SpalartAllmaras model with consideration of turbulence energy backscatter using velocity helicity.Phys Lett A 2011;375(24):2377-81.
26.Heschl C,Inthavong K,Sanz W,Tu J.Evaluation and improvements of RANS turbulence models for linear diffuser flows.Comput Fluids 2013;71:272-82.
27.Ma L,Lu LP,Fang J,Wang QH.A study on turbulence transportation and modification of Spalart-Allmaras model for shock-wave/turbulent boundary layer interaction flow.Chin JAeronaut 2014;27(2):200-9.
28.Liu YW,Yan H,Lu LP.Investigation of corner separation in a linear compressor cascade using DDES.Montre′al:ASME;2015.Report No.:GT2015-42902.
29.Gbadebo SA,Cumpsty NA,Hynes TP.Three-dimensional separations in axial compressors.J Turbomach 2005;127(2):331-9.
30.Fluent 6.3 User’s Guide.Fluent Documentation,Fluent Inc,2006.
31.Spalart PR,Allmaras SR.A one-equation turbulence model for aerodynamic flows.Reno:AIAA;1992.Report No.:AIAA-92-0439.
32.Spalart PR,Shur M.On the sensitization of turbulence models to rotation and curvature.Aerosp Sci Technol 1997;5:297-302.
33.Launder BE,Spalding DP.The numerical computation of turbulent flows.Comput Method Appl Mech 1974;3:269-89.
34.Launder BE,Sharma BI.Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc.Lett Heat Mass Transfer 1974;1:131-8.
35.Shih TH,Liou WW,Shabbir A.A new k-e eddy-viscosity model for high Reynolds number turbulent flows-model development and validation.Comput Fluids 1995;24(3):227-38.
36.Wilcox DC.Turbulence modeling for CFD.San Diego:DCWIndustries;2006.p.124-36.
37.Menter FR.Two-equation eddy-visocity turbulence models for engineering applications.AIAA J 1994;32(8):1598-605.
38.Durbin PA.Near-wall turbulence closure modeling without damping functions.Theor Comput Fluid Dyn 1991;3:1-13.
39.Durbin PA.Separated flow computations with the k-e-v2model.AIAA J 1995;33(4):659-64.
40.Behnia M,Parneix S,Shabany Y.Numerical study of turbulent.Int J Heat Fluid Flow 1999;20:1-9.
41.Launder BE,Reece GJ,Rodi W.Progress in the development of a Reynolds-stress turbulence closure.J Fluid Mech 1975;3(68):537-66.
42.Gibson MM,Launder BE.Ground effects on pressure fluctuations in the atmospheric boundary layer.J Fluid Mech1978;86:491-511.
43.Smirnov PE,Menter FR.Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term.J Turbomach 2009;131:0410104.
44.Gbadebo SA,Cumpsty NA,Hynes TP.Interaction of tip clearance flow and three-dimensional separations in axial compressors.J Turbomach 2007;129(4):679-85.
45.Gbadebo SA,Cumpsty NA,Hynes TP.Control of three-dimensional separations in axial compressors by tailored boundary layer suction.J Turbomach 2008;130(1):011004-8.
46.Gbadebo SA,Hynes TP,Cumpsty NA.Influence of surface roughness on three-dimensional separation in axial compressors.JTurbomach 2004;126(4):455-63.
47.Lumely J.Computational modeling of turbulent flows.Adv Appl Math 1978;18:123-76.
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