大涡模拟的壁模型及其应用
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摘要
大涡模拟是研究湍流的非定常特性的重要方法.但解析壁面层的大涡模拟所需的计算量与直接数值模拟相当,是大涡模拟在高雷诺数壁湍流数值模拟中所面临的主要困难.解析壁面层所需的网格尺度与壁面黏性长度同量级,是引起壁湍流大涡模拟计算量增加的主要原因.壁模型通过模化近壁流动避免了完全解析壁面层,可以显著地降低壁湍流大涡模拟的计算量,是克服上述困难的有效方法.本文介绍了大涡模拟壁模型的主要类型;详细讨论了常用的壁面应力模型,特别是平衡层模型和双层模型的构建思路和特点;基于近壁流动的特征讨论了应力边界条件的必要性和适用性;指出了壁面应力模型的局限性以及考虑非平衡效应修正的各种方法;讨论了壁面应力模型的研究历史、最新进展和发展趋势,给出了常用的壁面应力模型的分支与发展关系图;并基于Werner-Wengle模型实现了周期山状流的大涡模拟.
Large-eddy simulation(LES) is an important method to investigate unsteady turbulent flows. The cost of the wall-resolved LES is comparable to that of direct numerical simulation, which prevents the applications of the LES to wallbounded turbulences at high Reynolds numbers. The grid length would be of the order of the viscous length to resolve the near-wall flow structures, which causes the prohibitive computational cost of the wall-resolved LES. Wall-models circumvent the flow details near the wall to avoid resolving all the flow structures near the wall, which significantly reduce the computation cost and have been successfully combined with the LES for turbulent flows. We discuss the basic idea of wall-models for LES and review the wall-stress models with implementation details. The construction and characteristics of the equilibrium models and the two-layer models are discussed in detail. The limitations of the wallstress models and their improvements to account for the non-equilibrium effects are also discussed. We review the state of the art of the wall shear stress models and provide a hierarchical diagram for the current models. Finally, we present the applications of the Werner-Wengle model to the LES of flows over periodic hills.
Large-eddy simulation(LES) is an important method to investigate unsteady turbulent flows. The cost of the wall-resolved LES is comparable to that of direct numerical simulation, which prevents the applications of the LES to wallbounded turbulences at high Reynolds numbers. The grid length would be of the order of the viscous length to resolve the near-wall flow structures, which causes the prohibitive computational cost of the wall-resolved LES. Wall-models circumvent the flow details near the wall to avoid resolving all the flow structures near the wall, which significantly reduce the computation cost and have been successfully combined with the LES for turbulent flows. We discuss the basic idea of wall-models for LES and review the wall-stress models with implementation details. The construction and characteristics of the equilibrium models and the two-layer models are discussed in detail. The limitations of the wallstress models and their improvements to account for the non-equilibrium effects are also discussed. We review the state of the art of the wall shear stress models and provide a hierarchical diagram for the current models. Finally, we present the applications of the Werner-Wengle model to the LES of flows over periodic hills.
引文
1安翼,莫晃锐,刘青泉.高速列车头型长细比对气动噪声的影响.力学学报,2017,49(5):985-996(An Yi,Mo Huangrui,Liu Qingquan.Study on the influence of the nose slenderness ratio of high-speed train on the aerodynamic noise.Chinese Journal of Theoretical and Applied Mechanics,2017,49(5):985-996(in Chinese))
2林孟达,崔桂香,张兆顺等.飞机尾涡演变及快速预测的大涡模拟研究.力学学报,2017,49(6):1185-1200(Lin Mengda,Cui Guixiang,Zhang Zhaoshun,et al.Large eddy simulation on the evolution and the fast-time prediction of aircraft wake vortices.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1185-1200(in Chinese))
3冯峰,郭力,王强.高亚声速喷流气动噪声数值分析.力学学报,2016,48(5):1049-1060(Feng Feng,Guo Li,Wang Qiang.Numerical investigation of noise of a high subsonic turbulent jet.Chinese Journal of Theoretical and Applied Mechanics,2016,48(5):1049-1060(in Chinese))
4王纪,邱翔,罗剑平等.湍流强度对预混燃烧影响的大涡模拟研究.力学季刊,2014(4):548-559(Wang Ji,Qiu Xiang,Luo Jianping,et al.Large eddy simulation of the effects of turbulence intensity on premixed combustion.Chinese Quarterly of Mechanics,2014(4):548-559(in Chinese))
5刘难生,仲峰泉,陆夕云等.旋转圆管湍流的大涡模拟数值研究.力学学报,2002,34(6):833-846(Liu Nansheng,Zhong Fengquan,Lu Xiyun,et al.Large eddy simulation on turbulent flow in a pipe rotating about its axis.Chinese Journal of Theoretical and Applied Mechanics,2002,34(6):833-846(in Chinese))
6 Moin P,Bodart J,Bose S,et al.Wall-modeling in complex turbulent flows//Braza M,Bottaro A,Thompson M,eds.Advances in FluidStructure Interaction,Berlin:Springer,2016:207-19
7 Park GI,Moin P.Wall-modeled LES:Recent applications to complex flows//Annual Research Briefs 2016.Stanford,CA:Cent.Turbul.Res.,2016:39-50
8 Choi H,Moin P.Grid-point requirements for large eddy simulation:Chapman’s estimates revisited.Phys Fluids,2012,24(1):011702
9 Piomelli U,Balaras E.Wall-layer models for large-eddy simulations.Annu Rev Fluid Mech,2002,34(1):349-374
10 Piomelli U.Wall-layer models for large-eddy simulation.Progress in Aerospace Sciences,2008,44(6):437-446
11 Sagaut P.Large Eddy Simulation for Incompressible Flows:An Introduction.Berlin:Springer,2006
12许春晓.壁湍流相干结构和减阻控制机理.力学进展,2015,45:201504(Xu Chunxiao.Coherent structures and drag-reduction mechanism in wall turbulence.Advances in Mechanics,2015,45:201504(in Chinese))
13 Chaouat B.The state of the art of hybrid RANS/LES modeling for the simulation of turbulent flows.Flow Turbul Combust,2017,99(2):279-327
14 Fu S,Xiao ZX,Chen HX,et al.Simulation of wing-body junction flows with hybrid RANS/LES methods.International Journal of Heat and Fluid Flow,2007,28(6):1379-1390
15 Balin R,Spalart PR,Jansen KE.An investigation into the reduction of log-layer mismatch in wall-modeled LES with a hybrid RANS/LES approach//Bulletin of the American Physical Society,2017,62
16 Bose ST,Park GI.Wall-Modeled Large-eddy simulation for complex turbulent flows.Annu Rev Fluid Mech,2018,50(1):535-561
17 Schumann U.Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli.J Comput Phys,1975,18(4):376-404
18 Gr¨otzbach G.Direct numerical and large eddy simulation of turbulent channel flows.Encyclopedia of fluid mechanics,1987,6:1337-139119 Werner H,Wengle H.Large-eddy simulation of turbulent flow over and around a cube in a plate channel//Werner H,Wengle H,eds.Turbulent Shear Flows 8.Berlin:Springer,1993:155-168
20 Inagaki M,Murata O,Kondoh T,et al.Numerical prediction of fluid-resonant oscillation at low mach number.AIAA Journal,2002,40(9):1823-1829
21 Breuer M,Rodi W.Large eddy simulation of complexturbulent flows of practical interest//Hirschel EH,ed.Flow Simulation with High Performance Computers II.Braunschweig:Vieweg,1996.258-274
22 Rajagopalan S,Antonia RA.Some properties of the large structure in a fully developed turbulent duct flow.Phys Fluids,1979,22(4):614-622
23 Piomelli U,Ferziger J,Moin P,et al.New approximate boundary conditions for large eddy simulations of wall-bounded flows.Physics of Fluids A:Fluid Dynamics,1989,1(6):1061-1068
24 Skote M,Henningson DS.Direct numerical simulation of a separated turbulent boundary layer.J Fluid Mech,2002,471:107-136
25 Larsson J,Kawai S,Bodart J,et al.Large eddy simulation with modeled wall-stress:Recent progress and future directions.Mech Eng Rev,2016,3(1):15-00418
26 Breuer M,Kniazev B,Abel M.Development of wall models for LESof separated flows using statistical evaluations.Computer&Fluids,2007,36:817-837
27 Duprat C,Balarac G,M′etais O,et al.A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient.Phys.Fluids,2011,23(1):015101
28 Yang X,Sadique J,Mittal R,et al.Integral wall model for large eddy simulations of wall-bounded turbulent flows.Phys Fluids,2015,27(2):025112
29 Nicoud F,Baggett JS,Moin P,et al.Large eddy simulation wallmodeling based on suboptimal control theory and linear stochastic estimation.Phys.Fluids,2001,13(10):2968-2984
30 Bae HJ,Lozano-Dur′an A,Bose ST,et al.Turbulence intensities in large-eddy simulation of wall-bounded flows.Phys Rev Fluids,2018,3(1):014610
31 Bae HJ,Lozano-Dur′an A,Moin P.Investigation of the slip boundary condition in wall-modeled LES//Annual Research Briefs 2016.Stanford,CA:Cent.Turbul.Res.2016:75-86
32 Yang X,Bose ST,Moin P.A physics-based interpretation of the slipwall LES model//Annual Research Briefs 2016.Stanford,CA:Cent.Turbul.Res.2016:65-74
33 Lozano-Dur′an A,Bae HJ,Bose ST,et al.Dynamic wall models for the slip boundary condition//Annual Research Briefs 2017.Stanford,CA:Cent.Turbul.Res.2017.In press
34 Balaras E,Benocci C,Piomelli U.Two-layer approximate boundary conditions for large-eddy simulations.AIAA Journal,1996,34(6):1111-1119
35 Wang M,Moin P.Dynamic wall modeling for large-eddy simulation of complex turbulent flows.Phys Fluids,2002,14(7):2043-2051
36 Kawai S,Larsson J.Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers.Phys Fluids,2013,25(1):015105
37 Park GI,Moin P.An improved dynamic non-equilibrium wall-model for large eddy simulation.Phys.Fluids,2014,26(1):37-48
38 Park GI,Moin P.Numerical aspects and implementation of a twolayer zonal wall model for LES ofcompressible turbulent flows on unstructured meshes.J Comput Phys,2016,305:589-603
39张兆顺,崔桂香,许春晓.湍流大涡数值模拟的理论与应用.北京:清华大学出版社,2008:194-196(Zhang Zhaoshun,Cui Guixiang,Xu Chunxiao.Theory and Application of Large-Eddy Simulation of Turbulent Flows.Beijing:Tsinghua University Press,2008:194-196(in Chinese))
40崔桂香,许春晓,张兆顺.湍流大涡数值模拟进展.空气动力学学报,2004,22(2):121-129(Cui Guixiang,Xu Chunxiao,Zhang Zhaoshun.Progress in large eddy simulation of turbulent flows.Acta Aerodynamica Sinica,2004,22(2):121-129(in Chinese))
41 Tunstall R,Laurence D,Prosser R,et al.Towards a generalised dual-mesh hybrid LES/RANS framework with improved consistency.Computers&Fluids,2017,157:73-83
42 Kumar G,Lakshmanan SK,Gopalan H,et al.Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS-LES models for predicting flow fields with separation and reattachment.International Journal for Numerical Methods in Fluids,2017,83(12):917-939
43 Kadoch B,Reimann T,Schneider K,et al.Comparison of a spectral method with volume penalization and a finite volume method with body fitted grids for turbulent flows.Computers&Fluids,2016,133:140-150
44 Wu JL,Wang JX,Xiao H,et al.A priori assessment of prediction confidence for data-driven turbulence modeling.Flow Turbul Combust,2017,99(1):25-46
45 Smagorinsky J.General circulation experiments with the primitive equations.Monthly Weather Review,1963,91(3):99-164
46 Germano M,Piomelli U,Moin P,et al.A dynamic subgrid-scale eddy viscosity model.Physics of Fluids A:Fluid Dynamics,1991,3(7):1760-1765
47 Lilly DK.A proposed modification of the Germanosubgrid-scale closure method.Physics of Fluids A:Fluid Dynamics,1992,4(3):633-635
48 You D,Ham F,Moin P.Discrete conservation principles in largeeddy simulation with application to separation control over an airfoil.Phys Fluids,2008,20(10):101515
49 Temmerman L,Leschziner MA,Mellen CP,et al.Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions.Int J Heat Fluid Flow,2003,24(2):157-180
50 Fr¨ohlich J,Mellen CP,Rodi W,et al.Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions.J Fluid Mech,2005,526:19-66
51 Breuer M,Peller N,Rapp C,et al.Flow over periodic hillsnumerical and experimental study in a wide range of Reynolds numbers.Computers&Fluids,2009,38(2):433-457
52 He GW,Jin GD,Yang Y.Space-time correlations and dynamic coupling in turbulent flows.Annu Rev Fluid Mech,2017,49:51-70
2林孟达,崔桂香,张兆顺等.飞机尾涡演变及快速预测的大涡模拟研究.力学学报,2017,49(6):1185-1200(Lin Mengda,Cui Guixiang,Zhang Zhaoshun,et al.Large eddy simulation on the evolution and the fast-time prediction of aircraft wake vortices.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1185-1200(in Chinese))
3冯峰,郭力,王强.高亚声速喷流气动噪声数值分析.力学学报,2016,48(5):1049-1060(Feng Feng,Guo Li,Wang Qiang.Numerical investigation of noise of a high subsonic turbulent jet.Chinese Journal of Theoretical and Applied Mechanics,2016,48(5):1049-1060(in Chinese))
4王纪,邱翔,罗剑平等.湍流强度对预混燃烧影响的大涡模拟研究.力学季刊,2014(4):548-559(Wang Ji,Qiu Xiang,Luo Jianping,et al.Large eddy simulation of the effects of turbulence intensity on premixed combustion.Chinese Quarterly of Mechanics,2014(4):548-559(in Chinese))
5刘难生,仲峰泉,陆夕云等.旋转圆管湍流的大涡模拟数值研究.力学学报,2002,34(6):833-846(Liu Nansheng,Zhong Fengquan,Lu Xiyun,et al.Large eddy simulation on turbulent flow in a pipe rotating about its axis.Chinese Journal of Theoretical and Applied Mechanics,2002,34(6):833-846(in Chinese))
6 Moin P,Bodart J,Bose S,et al.Wall-modeling in complex turbulent flows//Braza M,Bottaro A,Thompson M,eds.Advances in FluidStructure Interaction,Berlin:Springer,2016:207-19
7 Park GI,Moin P.Wall-modeled LES:Recent applications to complex flows//Annual Research Briefs 2016.Stanford,CA:Cent.Turbul.Res.,2016:39-50
8 Choi H,Moin P.Grid-point requirements for large eddy simulation:Chapman’s estimates revisited.Phys Fluids,2012,24(1):011702
9 Piomelli U,Balaras E.Wall-layer models for large-eddy simulations.Annu Rev Fluid Mech,2002,34(1):349-374
10 Piomelli U.Wall-layer models for large-eddy simulation.Progress in Aerospace Sciences,2008,44(6):437-446
11 Sagaut P.Large Eddy Simulation for Incompressible Flows:An Introduction.Berlin:Springer,2006
12许春晓.壁湍流相干结构和减阻控制机理.力学进展,2015,45:201504(Xu Chunxiao.Coherent structures and drag-reduction mechanism in wall turbulence.Advances in Mechanics,2015,45:201504(in Chinese))
13 Chaouat B.The state of the art of hybrid RANS/LES modeling for the simulation of turbulent flows.Flow Turbul Combust,2017,99(2):279-327
14 Fu S,Xiao ZX,Chen HX,et al.Simulation of wing-body junction flows with hybrid RANS/LES methods.International Journal of Heat and Fluid Flow,2007,28(6):1379-1390
15 Balin R,Spalart PR,Jansen KE.An investigation into the reduction of log-layer mismatch in wall-modeled LES with a hybrid RANS/LES approach//Bulletin of the American Physical Society,2017,62
16 Bose ST,Park GI.Wall-Modeled Large-eddy simulation for complex turbulent flows.Annu Rev Fluid Mech,2018,50(1):535-561
17 Schumann U.Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli.J Comput Phys,1975,18(4):376-404
18 Gr¨otzbach G.Direct numerical and large eddy simulation of turbulent channel flows.Encyclopedia of fluid mechanics,1987,6:1337-139119 Werner H,Wengle H.Large-eddy simulation of turbulent flow over and around a cube in a plate channel//Werner H,Wengle H,eds.Turbulent Shear Flows 8.Berlin:Springer,1993:155-168
20 Inagaki M,Murata O,Kondoh T,et al.Numerical prediction of fluid-resonant oscillation at low mach number.AIAA Journal,2002,40(9):1823-1829
21 Breuer M,Rodi W.Large eddy simulation of complexturbulent flows of practical interest//Hirschel EH,ed.Flow Simulation with High Performance Computers II.Braunschweig:Vieweg,1996.258-274
22 Rajagopalan S,Antonia RA.Some properties of the large structure in a fully developed turbulent duct flow.Phys Fluids,1979,22(4):614-622
23 Piomelli U,Ferziger J,Moin P,et al.New approximate boundary conditions for large eddy simulations of wall-bounded flows.Physics of Fluids A:Fluid Dynamics,1989,1(6):1061-1068
24 Skote M,Henningson DS.Direct numerical simulation of a separated turbulent boundary layer.J Fluid Mech,2002,471:107-136
25 Larsson J,Kawai S,Bodart J,et al.Large eddy simulation with modeled wall-stress:Recent progress and future directions.Mech Eng Rev,2016,3(1):15-00418
26 Breuer M,Kniazev B,Abel M.Development of wall models for LESof separated flows using statistical evaluations.Computer&Fluids,2007,36:817-837
27 Duprat C,Balarac G,M′etais O,et al.A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient.Phys.Fluids,2011,23(1):015101
28 Yang X,Sadique J,Mittal R,et al.Integral wall model for large eddy simulations of wall-bounded turbulent flows.Phys Fluids,2015,27(2):025112
29 Nicoud F,Baggett JS,Moin P,et al.Large eddy simulation wallmodeling based on suboptimal control theory and linear stochastic estimation.Phys.Fluids,2001,13(10):2968-2984
30 Bae HJ,Lozano-Dur′an A,Bose ST,et al.Turbulence intensities in large-eddy simulation of wall-bounded flows.Phys Rev Fluids,2018,3(1):014610
31 Bae HJ,Lozano-Dur′an A,Moin P.Investigation of the slip boundary condition in wall-modeled LES//Annual Research Briefs 2016.Stanford,CA:Cent.Turbul.Res.2016:75-86
32 Yang X,Bose ST,Moin P.A physics-based interpretation of the slipwall LES model//Annual Research Briefs 2016.Stanford,CA:Cent.Turbul.Res.2016:65-74
33 Lozano-Dur′an A,Bae HJ,Bose ST,et al.Dynamic wall models for the slip boundary condition//Annual Research Briefs 2017.Stanford,CA:Cent.Turbul.Res.2017.In press
34 Balaras E,Benocci C,Piomelli U.Two-layer approximate boundary conditions for large-eddy simulations.AIAA Journal,1996,34(6):1111-1119
35 Wang M,Moin P.Dynamic wall modeling for large-eddy simulation of complex turbulent flows.Phys Fluids,2002,14(7):2043-2051
36 Kawai S,Larsson J.Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers.Phys Fluids,2013,25(1):015105
37 Park GI,Moin P.An improved dynamic non-equilibrium wall-model for large eddy simulation.Phys.Fluids,2014,26(1):37-48
38 Park GI,Moin P.Numerical aspects and implementation of a twolayer zonal wall model for LES ofcompressible turbulent flows on unstructured meshes.J Comput Phys,2016,305:589-603
39张兆顺,崔桂香,许春晓.湍流大涡数值模拟的理论与应用.北京:清华大学出版社,2008:194-196(Zhang Zhaoshun,Cui Guixiang,Xu Chunxiao.Theory and Application of Large-Eddy Simulation of Turbulent Flows.Beijing:Tsinghua University Press,2008:194-196(in Chinese))
40崔桂香,许春晓,张兆顺.湍流大涡数值模拟进展.空气动力学学报,2004,22(2):121-129(Cui Guixiang,Xu Chunxiao,Zhang Zhaoshun.Progress in large eddy simulation of turbulent flows.Acta Aerodynamica Sinica,2004,22(2):121-129(in Chinese))
41 Tunstall R,Laurence D,Prosser R,et al.Towards a generalised dual-mesh hybrid LES/RANS framework with improved consistency.Computers&Fluids,2017,157:73-83
42 Kumar G,Lakshmanan SK,Gopalan H,et al.Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS-LES models for predicting flow fields with separation and reattachment.International Journal for Numerical Methods in Fluids,2017,83(12):917-939
43 Kadoch B,Reimann T,Schneider K,et al.Comparison of a spectral method with volume penalization and a finite volume method with body fitted grids for turbulent flows.Computers&Fluids,2016,133:140-150
44 Wu JL,Wang JX,Xiao H,et al.A priori assessment of prediction confidence for data-driven turbulence modeling.Flow Turbul Combust,2017,99(1):25-46
45 Smagorinsky J.General circulation experiments with the primitive equations.Monthly Weather Review,1963,91(3):99-164
46 Germano M,Piomelli U,Moin P,et al.A dynamic subgrid-scale eddy viscosity model.Physics of Fluids A:Fluid Dynamics,1991,3(7):1760-1765
47 Lilly DK.A proposed modification of the Germanosubgrid-scale closure method.Physics of Fluids A:Fluid Dynamics,1992,4(3):633-635
48 You D,Ham F,Moin P.Discrete conservation principles in largeeddy simulation with application to separation control over an airfoil.Phys Fluids,2008,20(10):101515
49 Temmerman L,Leschziner MA,Mellen CP,et al.Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions.Int J Heat Fluid Flow,2003,24(2):157-180
50 Fr¨ohlich J,Mellen CP,Rodi W,et al.Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions.J Fluid Mech,2005,526:19-66
51 Breuer M,Peller N,Rapp C,et al.Flow over periodic hillsnumerical and experimental study in a wide range of Reynolds numbers.Computers&Fluids,2009,38(2):433-457
52 He GW,Jin GD,Yang Y.Space-time correlations and dynamic coupling in turbulent flows.Annu Rev Fluid Mech,2017,49:51-70