各向同性湍流通过正激波的演化特征研究
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摘要
激波与湍流相互作用(shock-turbulence interaction,STI)是空气动力学研究中的一个基础问题.基于格心有限差分法(cell-centered finite difference method,CCFDM)求解器Helios,采用五阶加权紧致非线性格式(weighted compact nonlinear scheme,WCNS)对各向同性湍流通过正激波的情形进行直接数值模拟(direct numerical simulation,DNS).对湍流相关物理量进行统计,分析结果表明,在湍流中波后的密度、温度和压力较无湍流情形下略小,而速度则略大,均在波后呈现短暂过冲然后缓慢向理论值逼近的变化趋势;波后流向雷诺应力突降随之快速增长又衰减,呈现非单调变化趋势,线性相互作用分析(linear interaction analysis,LIA)将其归结为波后能量从声模式转移为涡模式方式,与流向不同,横向雷诺应力突增后单调衰减,波后雷诺应力各向异性明显且随下游距离逐渐增强;波后湍动能突增后呈现非单调变化趋势;泰勒微尺度和Kolmogorov尺度过激波后均明显减小,说明波后湍流长度尺度变小,从而对波后网格的分辨率提出了更高的要求;密度、温度和压力过激波后脉动均方根均增加,密度和压力脉动强度减小,温度脉动强度增大.
Shock-turbulence interaction is a kind of important fundamental problem in aerodynamics.Based on solver Helios which applies cell-centered finite difference method(CCFDM),using fifth-order weighted compact nonlinear scheme(WCNS),we conducted direct numerical simulation(DNS) of the situation where isotropic turbulence passes through a normal shock wave.Turbulence statistics are calculated for analysis.We found after shock,density is a little lower than its non-turbulent value,so do temperature and pressure,on the contrary,longitudinal velocity is a little higher than its non-turbulent value.The commonality is that they all show an overshoot immediately behind the shock,after that they gradually approach towards their non-turbulent values along with downstream distance.Longitudinal Reynolds stress suffers a sudden decrease and increases rapidly followed by decaying.This evolution characteristics is captured in linear interaction analysis(LIA) and a transfer of energy from acoustical to vertical modes behind the shock is thought to be accounted for it according to this analysis.Different from longitudinal Reynolds stress,Transverse Reynolds stress suffers a sudden increase then decay monotonically.Anisotropy of Reynolds stress is apparent after shock,and it gradually increases as downstream distance increases.Turbulent kinetic energy suddenly increases and then evolves non-monotonically.Taylor microscale and Kolmogorov scales apparently decrease after shock,indicating the decrease of turbulent length scales,which leads to a requirement of higher resolution of mesh in this zone to solve the flow field.After shock,the root-mean-squares of density,temperature and pressure fluctuations are enhanced,and intensities of density and pressure decrease while intensity of temperature increases.
Shock-turbulence interaction is a kind of important fundamental problem in aerodynamics.Based on solver Helios which applies cell-centered finite difference method(CCFDM),using fifth-order weighted compact nonlinear scheme(WCNS),we conducted direct numerical simulation(DNS) of the situation where isotropic turbulence passes through a normal shock wave.Turbulence statistics are calculated for analysis.We found after shock,density is a little lower than its non-turbulent value,so do temperature and pressure,on the contrary,longitudinal velocity is a little higher than its non-turbulent value.The commonality is that they all show an overshoot immediately behind the shock,after that they gradually approach towards their non-turbulent values along with downstream distance.Longitudinal Reynolds stress suffers a sudden decrease and increases rapidly followed by decaying.This evolution characteristics is captured in linear interaction analysis(LIA) and a transfer of energy from acoustical to vertical modes behind the shock is thought to be accounted for it according to this analysis.Different from longitudinal Reynolds stress,Transverse Reynolds stress suffers a sudden increase then decay monotonically.Anisotropy of Reynolds stress is apparent after shock,and it gradually increases as downstream distance increases.Turbulent kinetic energy suddenly increases and then evolves non-monotonically.Taylor microscale and Kolmogorov scales apparently decrease after shock,indicating the decrease of turbulent length scales,which leads to a requirement of higher resolution of mesh in this zone to solve the flow field.After shock,the root-mean-squares of density,temperature and pressure fluctuations are enhanced,and intensities of density and pressure decrease while intensity of temperature increases.
引文
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2 Ribner HS.Convection of a pattern of vorticity through a shock wave.NACA TN 2864,1953
3 Ribner HS.Shock/turbulence interaction and the generation of noise NACA TN 3288,1954
4 Ribner HS.Spectra of noise and amplified turbulence emanating from shock/turbulence interaction.AIAA Journal,1987,35:436-442
5 Lele SK.Shock-jump relations in a turbulent flow.Physics of Fluids A:Fluid Dynamics,1992,4:2900-2905
6 Lee S,Lele SK,Moin P.Direct numerical simulation of isotropic turbulence interacting with a weak shock wave.Journal of Fluid Mechanics,1993,251:533-562
7 Lee S,Lele SK,Moin P.Interaction of isotropic turbulence with shock waves:effect of shock strength.Journal of Fluid Mechanics1997,340:225-247
8 Mahesh K,Lele SK,Moin P.The influence of entropy fluctuations on the interaction of turbulence with shock wave.Journal of Fluid Mechanics,1997,334:353-379
9 Lele SK,Larsson J.Shock-turbulence interaction:what we know and what we can learn from peta-scale simulations.Journal o Physics:Conference Series,2009,180:012032
10 Larsson J,Lele SK.Direct numerical simulation of canonica shock/turbulence interaction.Physics of Fluids,2009,21:126101
11 Larsson J,Bermejo-Moreno I,Lele SK.Reynolds-and Machnumber effects in canonical shock-turbulence interaction.Journal of Fluid Mechanics,2013,717:293-321
12 Ryu J,Livescu D.Turbulence structure behind the shock in canonical shock-vortical turbulence interaction.Journal of Fluid Mechanics,2014,756:R1
13 Livescu D,Ryu J.Vortitity dynamics after the shock-turbulence interaction.Shock Waves,2016,26:241-251
14 Quadros R,Sinha K,Larsson J.Turbulent energy flux generated by shock/homogeneous-turbulence inter-action.Journal of Fluid Mechanics,2016,796:113-157
15 Quadros R,Sinha K.Modeling of turbulent energy flux in canonical shock-turbulence interaction.International Journal of Heat and Fluid Flow,2016,61:626-635
16 Tian YF,Jaberi FA,Livescu D,et al.Numerical simulation of multifluid shock-turbulence interaction.AIP Conference Proceedings,2017,1793:150010
17 Tian YF,Jaberi FA,Li ZR,et al.Numerical study of variable density turbulence interaction with a normal shock wave.Journal of Fluid Mechanics,2017,829:551-588
18 Gao XY,Bermejo-Moreno I,Larsson J.Direct numerical simulation of passive scalar mixing in shock turbulence interaction//70th Annual Meeting of the APS Division of Fluid Dynamics,Denver,Colorado,2017
19 Vemula JB,Sinha K.Reynolds stress models applied to canonical shock-turbulence interaction.Journal of Turbuulence,2017,18:653-687
20 Boukharfane R,Bouali Z,Mura A.Evolution of scalar and velocity dynamics in planar shock-turbulence interaction.Shock Waves,2018,5:1-25
21王国蕾,陆夕云.激波和湍流相互作用的数值模拟.力学进展,2012,42(3):274-281(Wang Guolei,Lu Xiyun.Numerical simulation of shock wave/turbulence interactions.Advances in Mechanics,2012,42(3):274-281(in Chinese))
22崔光耀,潘翀,高琪等.沟槽方向对湍流边界层流动结构影响的实验研究.力学学报,2017,49(6):1201-1212(Cui Guanyao,Pan Chong,Gao Qi,et al.Flow structure in the turbulent boundary layer over directional riblets surfaces.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1201-1212(in Chinese))
23童福林,李欣,于长平等.高超声速激波湍流边界层干扰直接数值模拟研究.力学学报,2018,50(2):197-208(Tong Fulin,Li Xin,Yu Changping,et al.Direct numerical simulation of hypersonic shock wave and turbulent boundary layer interactions.Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):197-208(in Chinese))
24高天达,孙姣,范赢等.基于PIV技术分析颗粒在湍流边界层中的行为.力学学报,DOI:10.6052/0459-1879-18-211(PIV experimental investigation on the behavior of particle in the turbulent boundary layer.Chinese Journal of Theoretical and Applied Mechanics,DOI:10.6052/0459-1879-18-211
25 Liao F,Ye ZY,Zhang LX.Extending geometric conservation law to cell-centered finite difference methods on stationary grids.Journal of Computational Physics,2015,284:419-433
26 Liao F,Ye ZY.Extending geometric conservation law to cellcentered finite difference methods on moving and deforming grids.Journal of Computational Physics,2015,303:212-221
27 Deng XG,Zhang HX.Developing high-order weigh-ted compact nonlinear schemes.Journal of Computational Physics,2000,165:22-44
28刘昕,邓小刚,毛枚良等.高阶精度非线性格式WCNS-E-5在二维流动中的应用研究.空气动力学报,2004,22(2):206-210(Liu Xin,Deng Xiaogang,Mao Meiliang,et al.Weighted compact high-order nonlinear scheme WCNS-E-5 applied to two dimensional flows.Chinese Journal of Theoretical Applied Mechanics,2004,22(2):206-210(in Chinese))
29 Mahesh K,Moin P,Lele SK.The interaction of a shock wave with a turbulent shear flow.AFSOR TF-69,1996
30 Rogallo RS.Numerical experiments in homogeneous turbulence NASA,Technical Report 81315,1981
31秦泽聪,方乐.一种改进的均匀各向同性湍流初始化方法.力学学报,2016,48(6):1319-1325(Qin Zecong,Fang Le.An improved method for initializing homogeneous isotropic turbulent flows.Chinese Journal of Theoretical and Applied Mechanics,2016,48(6)1319-1325(in Chinese))
32 Samtaney R,Pullin DI,Kosovic B.Direct numerical simulation of decaying compressible turbulence and shocklet statistics.Physics of Fluids,2001,13:1415-1430
33 Pope SB.Turbulent Flows.Cambridge:Cambridge University Press,2000
2 Ribner HS.Convection of a pattern of vorticity through a shock wave.NACA TN 2864,1953
3 Ribner HS.Shock/turbulence interaction and the generation of noise NACA TN 3288,1954
4 Ribner HS.Spectra of noise and amplified turbulence emanating from shock/turbulence interaction.AIAA Journal,1987,35:436-442
5 Lele SK.Shock-jump relations in a turbulent flow.Physics of Fluids A:Fluid Dynamics,1992,4:2900-2905
6 Lee S,Lele SK,Moin P.Direct numerical simulation of isotropic turbulence interacting with a weak shock wave.Journal of Fluid Mechanics,1993,251:533-562
7 Lee S,Lele SK,Moin P.Interaction of isotropic turbulence with shock waves:effect of shock strength.Journal of Fluid Mechanics1997,340:225-247
8 Mahesh K,Lele SK,Moin P.The influence of entropy fluctuations on the interaction of turbulence with shock wave.Journal of Fluid Mechanics,1997,334:353-379
9 Lele SK,Larsson J.Shock-turbulence interaction:what we know and what we can learn from peta-scale simulations.Journal o Physics:Conference Series,2009,180:012032
10 Larsson J,Lele SK.Direct numerical simulation of canonica shock/turbulence interaction.Physics of Fluids,2009,21:126101
11 Larsson J,Bermejo-Moreno I,Lele SK.Reynolds-and Machnumber effects in canonical shock-turbulence interaction.Journal of Fluid Mechanics,2013,717:293-321
12 Ryu J,Livescu D.Turbulence structure behind the shock in canonical shock-vortical turbulence interaction.Journal of Fluid Mechanics,2014,756:R1
13 Livescu D,Ryu J.Vortitity dynamics after the shock-turbulence interaction.Shock Waves,2016,26:241-251
14 Quadros R,Sinha K,Larsson J.Turbulent energy flux generated by shock/homogeneous-turbulence inter-action.Journal of Fluid Mechanics,2016,796:113-157
15 Quadros R,Sinha K.Modeling of turbulent energy flux in canonical shock-turbulence interaction.International Journal of Heat and Fluid Flow,2016,61:626-635
16 Tian YF,Jaberi FA,Livescu D,et al.Numerical simulation of multifluid shock-turbulence interaction.AIP Conference Proceedings,2017,1793:150010
17 Tian YF,Jaberi FA,Li ZR,et al.Numerical study of variable density turbulence interaction with a normal shock wave.Journal of Fluid Mechanics,2017,829:551-588
18 Gao XY,Bermejo-Moreno I,Larsson J.Direct numerical simulation of passive scalar mixing in shock turbulence interaction//70th Annual Meeting of the APS Division of Fluid Dynamics,Denver,Colorado,2017
19 Vemula JB,Sinha K.Reynolds stress models applied to canonical shock-turbulence interaction.Journal of Turbuulence,2017,18:653-687
20 Boukharfane R,Bouali Z,Mura A.Evolution of scalar and velocity dynamics in planar shock-turbulence interaction.Shock Waves,2018,5:1-25
21王国蕾,陆夕云.激波和湍流相互作用的数值模拟.力学进展,2012,42(3):274-281(Wang Guolei,Lu Xiyun.Numerical simulation of shock wave/turbulence interactions.Advances in Mechanics,2012,42(3):274-281(in Chinese))
22崔光耀,潘翀,高琪等.沟槽方向对湍流边界层流动结构影响的实验研究.力学学报,2017,49(6):1201-1212(Cui Guanyao,Pan Chong,Gao Qi,et al.Flow structure in the turbulent boundary layer over directional riblets surfaces.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1201-1212(in Chinese))
23童福林,李欣,于长平等.高超声速激波湍流边界层干扰直接数值模拟研究.力学学报,2018,50(2):197-208(Tong Fulin,Li Xin,Yu Changping,et al.Direct numerical simulation of hypersonic shock wave and turbulent boundary layer interactions.Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):197-208(in Chinese))
24高天达,孙姣,范赢等.基于PIV技术分析颗粒在湍流边界层中的行为.力学学报,DOI:10.6052/0459-1879-18-211(PIV experimental investigation on the behavior of particle in the turbulent boundary layer.Chinese Journal of Theoretical and Applied Mechanics,DOI:10.6052/0459-1879-18-211
25 Liao F,Ye ZY,Zhang LX.Extending geometric conservation law to cell-centered finite difference methods on stationary grids.Journal of Computational Physics,2015,284:419-433
26 Liao F,Ye ZY.Extending geometric conservation law to cellcentered finite difference methods on moving and deforming grids.Journal of Computational Physics,2015,303:212-221
27 Deng XG,Zhang HX.Developing high-order weigh-ted compact nonlinear schemes.Journal of Computational Physics,2000,165:22-44
28刘昕,邓小刚,毛枚良等.高阶精度非线性格式WCNS-E-5在二维流动中的应用研究.空气动力学报,2004,22(2):206-210(Liu Xin,Deng Xiaogang,Mao Meiliang,et al.Weighted compact high-order nonlinear scheme WCNS-E-5 applied to two dimensional flows.Chinese Journal of Theoretical Applied Mechanics,2004,22(2):206-210(in Chinese))
29 Mahesh K,Moin P,Lele SK.The interaction of a shock wave with a turbulent shear flow.AFSOR TF-69,1996
30 Rogallo RS.Numerical experiments in homogeneous turbulence NASA,Technical Report 81315,1981
31秦泽聪,方乐.一种改进的均匀各向同性湍流初始化方法.力学学报,2016,48(6):1319-1325(Qin Zecong,Fang Le.An improved method for initializing homogeneous isotropic turbulent flows.Chinese Journal of Theoretical and Applied Mechanics,2016,48(6)1319-1325(in Chinese))
32 Samtaney R,Pullin DI,Kosovic B.Direct numerical simulation of decaying compressible turbulence and shocklet statistics.Physics of Fluids,2001,13:1415-1430
33 Pope SB.Turbulent Flows.Cambridge:Cambridge University Press,2000