基于滑移速度壁模型的复杂边界湍流大涡模拟
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摘要
采用滑移速度壁模型实现了浸入边界方法与壁模型相结合的大涡模拟.本文首先分别采用平衡层模型和非平衡壁模型对周期山状流进行数值模拟,以考查在壁模型中考虑切向压力梯度的作用.数值结果表明,流场的压力对本文所采用的壁模型形式并不敏感,但是考虑切向压力梯度可以显著改进壁面摩擦力的计算结果,并且能够准确的预测强压力梯度区以及分离区内的流动平均统计特性.不考虑压力梯度效应的平衡层模型显著低估了壁面摩擦力的分布,同时无法准确预测分离区内的平均速度剖面.非平衡模型的修正项正比于切向压力梯度和壁面法向距离,因此在强压力梯度区或者网格较粗时,计算得到的平均压力和摩擦力分布以及流动的低阶统计量均与参考的实验和计算结果吻合.在此基础上,通过回转体绕流的大涡模拟考查了该方法用于模拟高雷诺数壁湍流的适用性,非平衡壁模型可以准确地捕捉流动的物理结构并较准确地预测其水动力学特性.结果表明,将浸入边界方法与非平衡滑移速度壁模型相结合的大涡模拟,有望成为数值模拟复杂边界高雷诺数壁湍流的工具.
A slip-wall model is combined with the immersed boundary method for large-eddy simulation of flows with complex geometries. Firstly, large eddy simulation of flows over periodic hills are conducted to evaluate the effects of the tangential pressure gradient in wall model. Both the equilibrium stress balance model which based on the assumption of an equilibrium boundary-layer and the non-equilibrium wall model, in which the pressure gradient blend into the simplified thin boundary-layer equations and the RANS-like eddy viscosity in both the procedure of computing the wall-shear stress and reconstructing the wall-slip velocity, are utilized for comparison. The numerical results show that the pressure coefficient is not sensitive to the types of wall model which we considered, especially the strong pressure gradient in front of the hill crest is well catched by both models. However, when taking into account the tangential pressure gradient, the non-equilibrium wall model is superior to the equilibrium one for its ability to improve the prediction of the wall-shear stress and flow separation. When the equilibrium stress balance model is used, the wall-shear stress is heavily underpredicted and remarkable discrepancies of the mean velocity profiles can also be seen in the recirculation region. By comparison, the correction of the non-equilibrium wall model is proportional to both the tangential pressure gradient and the normal distance away from the wall, thus the hydrodynamic coefficients and the mean flow statistics are all in good agreement with the references even on very coarse grids. Secondly, large-eddy simulation of flow around an axisymmetric body is conducted to assess the applicability of current method when applied to high Reynolds number wall-bounded turbulent flows. The flow structures and the hydrodynamic characteristics are well predicted by the non-equilibrium wall model. This work confirms that the immersed boundary method in combination with the non-equilibrium slip-wall model is a possible and promising way to deal with turbulent flows which have complex geometries.
A slip-wall model is combined with the immersed boundary method for large-eddy simulation of flows with complex geometries. Firstly, large eddy simulation of flows over periodic hills are conducted to evaluate the effects of the tangential pressure gradient in wall model. Both the equilibrium stress balance model which based on the assumption of an equilibrium boundary-layer and the non-equilibrium wall model, in which the pressure gradient blend into the simplified thin boundary-layer equations and the RANS-like eddy viscosity in both the procedure of computing the wall-shear stress and reconstructing the wall-slip velocity, are utilized for comparison. The numerical results show that the pressure coefficient is not sensitive to the types of wall model which we considered, especially the strong pressure gradient in front of the hill crest is well catched by both models. However, when taking into account the tangential pressure gradient, the non-equilibrium wall model is superior to the equilibrium one for its ability to improve the prediction of the wall-shear stress and flow separation. When the equilibrium stress balance model is used, the wall-shear stress is heavily underpredicted and remarkable discrepancies of the mean velocity profiles can also be seen in the recirculation region. By comparison, the correction of the non-equilibrium wall model is proportional to both the tangential pressure gradient and the normal distance away from the wall, thus the hydrodynamic coefficients and the mean flow statistics are all in good agreement with the references even on very coarse grids. Secondly, large-eddy simulation of flow around an axisymmetric body is conducted to assess the applicability of current method when applied to high Reynolds number wall-bounded turbulent flows. The flow structures and the hydrodynamic characteristics are well predicted by the non-equilibrium wall model. This work confirms that the immersed boundary method in combination with the non-equilibrium slip-wall model is a possible and promising way to deal with turbulent flows which have complex geometries.
引文
1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))
2冯峰,郭力,王强.高亚声速湍流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))
3周磊,解茂昭,罗开红等.大涡模拟在内燃机中应用的研究进展.力学学报,2013,45(4):467-482(Zhou Lei,Xie Maozhao,Luo Kaihong,et al.Large eddy simulation for internal combustion engines:progress and prospects.Chinese Journal of Theoretical and Applied Mechanics,2013,45(4):467-482(in Chinese))
4安翼,莫晃瑞,刘青泉.高速列车头型长细比对气动噪声的影响.空气动力学学报,2017,49(5):985-996(An Yi,Mo Huangrui,Liu Qingquan.Study on the influence of the slenderness ratio of highspeed train on the aerodynamic noise.Acta Aerodynamica Sinica,2017,49(5):985-996(in Chinese))
5 Choi H,Moin P.Grid-point requirements for large eddy simulation:Chapman’s estimates revisited.Physics of Fluids,2012,24(1):0117026 Larsson J,Kawai S,Bodart J,et al.Large eddy simulation with modeled wall-stress:recent progress and future directions.Mechanical Engineering Reviews,2016,3(1):1-23
7肖志祥,陈海昕,李启兵等.采用RANS/LES混合方法研究分离流动.空气动力学学报,2006,24(2):218-222(Xiao Zhixiang,Chen Haixin,Li Qibing,et al.Simulation of separation flows with RANS/LES hybrid methods.Acta Aerodynamica Sinica,2006,24(2):218-222(in Chinese))
8 Piomelli U,Balaras E.Wall-layer models for large-eddy simulations.Annual Review of Fluid Mechanics,2002,34:349-374
9 Piomelli U.Wall-layer models for large-eddy simulations.Progress in Aerospace Sciences,2008,44:437-446
10 Bose AT,Park GI.Wall-modeled large-eddy simulation for complex turbulent flows.Annual Review of Fluid Mechanics,2018,50:535-56111 Zhang Y F,Chen H X.Aeroacoustic prediction of a multi-element airfoil using wall-modeled large-eddy simulation.AIAA Journal,2017,55:4219-4233
12 Chen S Y,Xia Z H,Pei SY,et al.Reynolds-stress-constrained largeeddy simulation of wall-bounded turbulent flows.Journal of Fluid Mechanics,2012,703:1-28
13尹光,许春晓,黄伟希.近壁湍流的降阶模型及其应用.气体物理,2016,1(2):20-21(Yin Guang,Xu Chunxiao,Huang Weixi.Reduced-order model for near-wall turbulence and its application.Physics of Gases,2016,1(2):20-21(in Chinese))
14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))
15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))
16吴霆,时北极,王士召等.大涡模拟的壁模型及其应用.力学学报,2018,50(3):453-466(Wu Ting,Shi Beiji,Wang Shizhao,et al.Wall-model for large-eddy simulation and its applications.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):453-
466(in Chinese))
17 Cabot W,Moin P.Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow.Flow,Turbulence and Combustion,1999,63:269-291
18 Balaras E,Benocci C.Two-layer approximate boundary conditions for large-eddy simulations.AIAA Journal,1996,34:1111-1119
19 Wang M,Moin P.Dynamic wall modeling for large-eddy simulation of complex turbulent flows.Physics of Fluids,2002,14:2043
20 Duprat C,Balarac G,Metais O,et al.A wall-layer model for large eddy simulations of turbulent flow with/out pressure gradient.Physics of Fluids,2011,23:015101
21 Mittal R,Iaccarino G.Immersed boundary methods.Annual Review of Fluid Mechanics,2005,37:239-261
22 Sotiropoulos F,Yang XL.Immersed boundary methods for simulating fluid-structure interaction.Progress in Aerospace Sciences,2014,65:1-21
23 Liao KP,Hu CH.A coupled FDM-FEM method for free surface flow interaction with thin elastic plate.Journal of Marine Science and Technology,2013,18:1-11
24 Yang JM,Balaras E.An embedded-boundary formulation or largeeddy simulation of turbulent flows interacting with moving boundaries.Journal of Computational Physics,2006,215:12-40
25 Yan C,Huang W X,Cui G X,et al.A ghost-cell immersed boundary method for large eddy simulation of flows in complex geometries.International Journal of Computational Fluid Dynamics,2015,29:12-25
26 Cristallo A,Verzicco R.Combined immersed boundary/large-eddysimulations of in compressible three dimensional complex flows.Flow,Turbulence and Combustion,2006,77:3-26
27 Roman F,Armenio V,Frohlich J.A simple wall-layer model for large eddy simulation with immersed boundary method.Physics of Fluids,2009,21:101701
28 Tessiciniy F,Iaccarino G,Fatica M,et al.Wall modeling for largeeddy simulation using an immersed boundary method.CTR,Annual Research Briefs,2002,23:181-187
29 Choi JI,Oberoi RC,Edwards JR,et al.An immersed boundary method for complex incompressible flows.Journal of Computational Physics,2007,224:757-784
30 Ji C,Munjiza A,Williams,JJR.A novel iterative direct-forcing immersed boundary method and its finite volume applications.Journal of Computational Physics,2012,231:1797-1821
31 Shi BJ,He GW,Wang SZ.A slip-wall model in combination with the immersed boundary method for large-eddy simulations.Under Review
32 Nicoud F,Ducros F.Subgrid-scale stress modelling based on the square of the velocity gradient tensor.Flow,Turbulence and Combustion,1999,62:183-200
33 Wang SZ,Vanella M,Balaras E.A hydrodynamic stress model for simulating turbulence/particle interactions with immersed boundary methods.Journal of Computational Physics,2019,382:240-263
34 Vanella M,Wang SZ,Balaras E.Direct and Large-Eddy Simulation X.Berlin Heidelberg:Springer,2018:43-51
35 Balaras E.Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations.Computer and Fluids,2004,33:375-404
36 Vanella M,Balaras E.A moving-least-squares reconstruction for embedded-boundary formulations.Journal of Computational Physics,2009,228:6617-6628
37 van Driest ER.On turbulent flow near a wall.Journal of the Aeronautical Sciences,1956,23:1007
38 Breuer M,Peller N,Rapp Ch,et al.Flow over periodic hills-numerical and experimental study in a wide range of Reynolds numbers.Computer and Fluids,2009,38:433-457
39 Temmerman L,Leachziner MA,Mellen CP,et al.Investigation of wall-function approximations and subgrid-scale model in large eddy simulation of separated flow in a channel with streamwise periodic constrictions.International Journal of Heat and Fluid Flow,2003,24:157-180
40 Frere A,Hillewaert K,Chatelain P,et al.High Reynolds number airfoil:from wall-resolved to wall-modeled LES.Flow,Turbulence and Combustion,2018,101:457-476
41 Bose ST,Moin P.A dynamic slip boundary condition for wallmodeled large-eddy simulation.Physics of Fluids,2014,26:015104
42 Chang PH,Liao CC,Hsu HW,et al.Simulations of laminar and turbulent flows over periodic hills with immersed boundary method.Computers&Fluids,2014,92:233-243
43 Groves NC,Huang TT,Chang MS.Geometric Characteristics of the DARPA SUBOFF Models.Technical Report No.DTRC/SHD-1298-01,David Taylor Research Center,Bethesda,MD,1989
44 Posa A,Balaras E.A numerical investigation of the wake of an axisymmetric body with appendages.Journal of Fluid Mechanics,2016,792:470-498
45 Huang T,Liu HL,Groves N,et al.Measurements of flows over an axisymmetric body with various appendages in a wind tunnel:the DARPA SUBOFF experimental program//Proceedings of the 19th Symposium on Naval Hydrodynamics,Korea:National Academy Press,1994
46 Shi BJ,Yang XL,Jin GD,et al.Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuseinterface immersed boundary method.Journal of Applied Mathematics and Mechanics-English Edition,2019,40(3):305-320
47 Bae HJ,Lozano-Duran A,Bose ST,et al.Turbulence intensities in large-eddy simulation of wall-bounded flows.Physical Review Fluids,2018,3:014610
2冯峰,郭力,王强.高亚声速湍流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))
3周磊,解茂昭,罗开红等.大涡模拟在内燃机中应用的研究进展.力学学报,2013,45(4):467-482(Zhou Lei,Xie Maozhao,Luo Kaihong,et al.Large eddy simulation for internal combustion engines:progress and prospects.Chinese Journal of Theoretical and Applied Mechanics,2013,45(4):467-482(in Chinese))
4安翼,莫晃瑞,刘青泉.高速列车头型长细比对气动噪声的影响.空气动力学学报,2017,49(5):985-996(An Yi,Mo Huangrui,Liu Qingquan.Study on the influence of the slenderness ratio of highspeed train on the aerodynamic noise.Acta Aerodynamica Sinica,2017,49(5):985-996(in Chinese))
5 Choi H,Moin P.Grid-point requirements for large eddy simulation:Chapman’s estimates revisited.Physics of Fluids,2012,24(1):0117026 Larsson J,Kawai S,Bodart J,et al.Large eddy simulation with modeled wall-stress:recent progress and future directions.Mechanical Engineering Reviews,2016,3(1):1-23
7肖志祥,陈海昕,李启兵等.采用RANS/LES混合方法研究分离流动.空气动力学学报,2006,24(2):218-222(Xiao Zhixiang,Chen Haixin,Li Qibing,et al.Simulation of separation flows with RANS/LES hybrid methods.Acta Aerodynamica Sinica,2006,24(2):218-222(in Chinese))
8 Piomelli U,Balaras E.Wall-layer models for large-eddy simulations.Annual Review of Fluid Mechanics,2002,34:349-374
9 Piomelli U.Wall-layer models for large-eddy simulations.Progress in Aerospace Sciences,2008,44:437-446
10 Bose AT,Park GI.Wall-modeled large-eddy simulation for complex turbulent flows.Annual Review of Fluid Mechanics,2018,50:535-56111 Zhang Y F,Chen H X.Aeroacoustic prediction of a multi-element airfoil using wall-modeled large-eddy simulation.AIAA Journal,2017,55:4219-4233
12 Chen S Y,Xia Z H,Pei SY,et al.Reynolds-stress-constrained largeeddy simulation of wall-bounded turbulent flows.Journal of Fluid Mechanics,2012,703:1-28
13尹光,许春晓,黄伟希.近壁湍流的降阶模型及其应用.气体物理,2016,1(2):20-21(Yin Guang,Xu Chunxiao,Huang Weixi.Reduced-order model for near-wall turbulence and its application.Physics of Gases,2016,1(2):20-21(in Chinese))
14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))
15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))
16吴霆,时北极,王士召等.大涡模拟的壁模型及其应用.力学学报,2018,50(3):453-466(Wu Ting,Shi Beiji,Wang Shizhao,et al.Wall-model for large-eddy simulation and its applications.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):453-
466(in Chinese))
17 Cabot W,Moin P.Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow.Flow,Turbulence and Combustion,1999,63:269-291
18 Balaras E,Benocci C.Two-layer approximate boundary conditions for large-eddy simulations.AIAA Journal,1996,34:1111-1119
19 Wang M,Moin P.Dynamic wall modeling for large-eddy simulation of complex turbulent flows.Physics of Fluids,2002,14:2043
20 Duprat C,Balarac G,Metais O,et al.A wall-layer model for large eddy simulations of turbulent flow with/out pressure gradient.Physics of Fluids,2011,23:015101
21 Mittal R,Iaccarino G.Immersed boundary methods.Annual Review of Fluid Mechanics,2005,37:239-261
22 Sotiropoulos F,Yang XL.Immersed boundary methods for simulating fluid-structure interaction.Progress in Aerospace Sciences,2014,65:1-21
23 Liao KP,Hu CH.A coupled FDM-FEM method for free surface flow interaction with thin elastic plate.Journal of Marine Science and Technology,2013,18:1-11
24 Yang JM,Balaras E.An embedded-boundary formulation or largeeddy simulation of turbulent flows interacting with moving boundaries.Journal of Computational Physics,2006,215:12-40
25 Yan C,Huang W X,Cui G X,et al.A ghost-cell immersed boundary method for large eddy simulation of flows in complex geometries.International Journal of Computational Fluid Dynamics,2015,29:12-25
26 Cristallo A,Verzicco R.Combined immersed boundary/large-eddysimulations of in compressible three dimensional complex flows.Flow,Turbulence and Combustion,2006,77:3-26
27 Roman F,Armenio V,Frohlich J.A simple wall-layer model for large eddy simulation with immersed boundary method.Physics of Fluids,2009,21:101701
28 Tessiciniy F,Iaccarino G,Fatica M,et al.Wall modeling for largeeddy simulation using an immersed boundary method.CTR,Annual Research Briefs,2002,23:181-187
29 Choi JI,Oberoi RC,Edwards JR,et al.An immersed boundary method for complex incompressible flows.Journal of Computational Physics,2007,224:757-784
30 Ji C,Munjiza A,Williams,JJR.A novel iterative direct-forcing immersed boundary method and its finite volume applications.Journal of Computational Physics,2012,231:1797-1821
31 Shi BJ,He GW,Wang SZ.A slip-wall model in combination with the immersed boundary method for large-eddy simulations.Under Review
32 Nicoud F,Ducros F.Subgrid-scale stress modelling based on the square of the velocity gradient tensor.Flow,Turbulence and Combustion,1999,62:183-200
33 Wang SZ,Vanella M,Balaras E.A hydrodynamic stress model for simulating turbulence/particle interactions with immersed boundary methods.Journal of Computational Physics,2019,382:240-263
34 Vanella M,Wang SZ,Balaras E.Direct and Large-Eddy Simulation X.Berlin Heidelberg:Springer,2018:43-51
35 Balaras E.Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations.Computer and Fluids,2004,33:375-404
36 Vanella M,Balaras E.A moving-least-squares reconstruction for embedded-boundary formulations.Journal of Computational Physics,2009,228:6617-6628
37 van Driest ER.On turbulent flow near a wall.Journal of the Aeronautical Sciences,1956,23:1007
38 Breuer M,Peller N,Rapp Ch,et al.Flow over periodic hills-numerical and experimental study in a wide range of Reynolds numbers.Computer and Fluids,2009,38:433-457
39 Temmerman L,Leachziner MA,Mellen CP,et al.Investigation of wall-function approximations and subgrid-scale model in large eddy simulation of separated flow in a channel with streamwise periodic constrictions.International Journal of Heat and Fluid Flow,2003,24:157-180
40 Frere A,Hillewaert K,Chatelain P,et al.High Reynolds number airfoil:from wall-resolved to wall-modeled LES.Flow,Turbulence and Combustion,2018,101:457-476
41 Bose ST,Moin P.A dynamic slip boundary condition for wallmodeled large-eddy simulation.Physics of Fluids,2014,26:015104
42 Chang PH,Liao CC,Hsu HW,et al.Simulations of laminar and turbulent flows over periodic hills with immersed boundary method.Computers&Fluids,2014,92:233-243
43 Groves NC,Huang TT,Chang MS.Geometric Characteristics of the DARPA SUBOFF Models.Technical Report No.DTRC/SHD-1298-01,David Taylor Research Center,Bethesda,MD,1989
44 Posa A,Balaras E.A numerical investigation of the wake of an axisymmetric body with appendages.Journal of Fluid Mechanics,2016,792:470-498
45 Huang T,Liu HL,Groves N,et al.Measurements of flows over an axisymmetric body with various appendages in a wind tunnel:the DARPA SUBOFF experimental program//Proceedings of the 19th Symposium on Naval Hydrodynamics,Korea:National Academy Press,1994
46 Shi BJ,Yang XL,Jin GD,et al.Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuseinterface immersed boundary method.Journal of Applied Mathematics and Mechanics-English Edition,2019,40(3):305-320
47 Bae HJ,Lozano-Duran A,Bose ST,et al.Turbulence intensities in large-eddy simulation of wall-bounded flows.Physical Review Fluids,2018,3:014610