二维激波与剪切层相互作用的直接数值模拟研究

刘旭亮; 张树海

doi:10.6052/0459-1879-12-106

二维激波与剪切层相互作用的直接数值模拟研究

刘旭亮,
张树海^,

中国空气动力研究与发展中心, 空气动力学国家重点实验室, 四川绵阳621000

基金项目: 国家自然科学基金(11172317, 91016001) 和国家重点基础研究发展计划(973 计划)(2009CB724104) 资助项目.

详细信息

通讯作者:
张树海

中图分类号: V211.3
计量
- 文章访问数: 02053
- HTML全文浏览量: 0160
- PDF下载量: 01295
出版历程
- 收稿日期: 2012-04-18
- 修回日期: 2012-10-22
- 刊出日期: 2013-01-17

DIRECT NUMERICAL SIMULATION OF THE INTERACTION OF 2D SHOCKWAVE AND SHEAR LAYER

Liu Xuliang,
Zhang Shuhai^,

State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Sichuan Mianyang 621000, China

Funds: The project was supported by the National Natural Science Foundation of China (11172317, 91016001) and Major State Basic Research Development Program of China (2009CB724104).

摘要

摘要: 采用五阶weighed esseritially non-oscillatory (WENO) 格式和三阶total variation diminishing (TVD) Runge-Kutta 格式, 通过求解二维非定常Navier-Stokes 方程, 直接数值模拟了激波与剪切层相互作用, 目的在于揭示激波与剪切层相互作用过程中噪声产生的机理. 研究发现:(1) 当入射激波穿过剪切层时, 剪切层中心位置向下层区域偏移;(2) 入射激波穿过剪切层产生小激波, 在小激波与剪切层接触点处产生声波并向外辐射;(3) 反射激波穿过剪切层后形成了分段弧状激波;(4) 当反射激波穿过剪切层时, 激波在鞍点处泄漏并向外辐射声波, 这是一种激波泄漏机制.
- 激波 /
- 剪切层 /
- 直接数值模拟 /
- 激波噪声
Abstract: Direct numerical simulation (DNS) of the interaction of shock wave and shear layer was performed. The compressible unsteady two-dimensional Navier-Stokes equations were solved using the fifth-order WENO scheme combined with the third-order TVD Runge-Kutta scheme. The purpose of this paper is to reveal the mechanism of sound generation in the interaction of shock wave and shear layer. The results show that: (1) When incident shock wave is passing through the shear layer, the center of the vortex cores is shifted towards the lower side; (2) The interaction of incident shock wave and shear layer generates shocklet, and then acoustic wave is generated and radiated at the locus of contact of shocklet and shear layer; (3) Several arc-shocks are formed after reflected shock wave passing through shear layer; (4) When reflected shock wave is passing through shear layer, shock wave is leaking in the braid region and shock-associated noise is generated at the saddle points between vortices. This is a form of shock leakage mechanism.
- shock wave /
- shear layer /
- DNS /
- shock-associated noise

HTML全文

参考文献(38)

1 Wang M, Freund JB, Lele SK. Computational prediction of flowgenerated sound. Annual Review of Fluid Mechanics, 2006, 38:483-512

2 Mitchell BE, Lele SK, Moin P. Direct computation of the sound from a compressible co-rotating vortex pair. Journal of Fluid Mechanics,1995, 285: 181-202

3 Colonius T, Lele SK, Moin P. Sound generation in a mixing layer. Journal of Fluid Mechanics, 1997, 330: 375-409

4 Mitchell BE, Lele SK, Moin P. Direct computation of the sound generated by vortex pairing in an axisymmetric jet. Journal of Fluid Mechanics, 1999, 383: 113-142

5 Manning TA. A numerical investigation of sound generation in supersonic jet screech. [PhD Thesis]. Stanford: Department of Aeronautics and Astronautics, Stanford University, 1999

6 Freund JB, Lele SK, Moin P. Numerical simulation of a Mach 1.92 turbulent jet and its sound field. AIAA Journal, 2000, 38: 2023-2031

7 Mohseni K, Colonius T, Freund JB. An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet. Physics of Fluids, 2002, 14(10): 3593-3600

8 Suzuki T, Lele SK. Shock leakage through an unsteady vortex-laden mixing layer: Application to jet screech. Journal of Fluid Mechanics,2003, 490: 139-167

9 Lui CCM. A numerical investigation of shock-associated noise. [PhD Thesis]. Stanford: Department of Mechanical Engineering, Stanford University, 2003

10 Cheung LC, Lele SK. Linear and nonlinear processes in twodimensional mixing layer dynamics and sound radiation. Journal of Fluid Mechanics, 2009, 625: 321-351

11 Bogey C, Bailly C, Juve D. Numerical simulation of sound generated by vortex pairing in a mixing layer. AIAA Journal, 2000, 38:2210-2218

12 Bogey C, Bailly C, Juve D. Computation of flow noise using source terms in linearized Euler’s equations. AIAA Journal, 2002, 40: 235-243

13 Berland J, Bogey C, Bailly C. Numerical study of screech generation in a planar supersonic jet. Physics of Fluids, 2007, 19(075105):1-14

14 Schaupp C, Sesterhenn J, Friedrich R. On a method for direct numerical simulation of shear layer/compression wave interaction for aeroacoustics investigations. Computers and Fluids, 2008, 37: 463-474

15 Pao SP, Salas MD. A numerical study of two-dimensional shock vortex interaction. AIAA Paper 1981-1205, 1981

16 Ellzey JL, Henneke MR, Picone JM, et al. The interaction of a shock with a vortex: Shock distortion and the production of acoustic waves. Physics of Fluids, 1995, 7: 172-184

17 Meadows KR. A study of fundamental shock noise mechanisms. NASA Technical Paper 3605, 1997

18 Inoue O, Hattori Y. Sound generation by shock-vortex interactions. Journal of Fluid Mechanics, 1999, 380: 81-116

19 Zhang SH, Zhang YT, Shu CW. Multistage interaction of a shock wave and a strong vortex. Physics of Fluids, 2005, 17(116101): 1-13

20 Zhang SH, Zhang YT, ShuCW. Interaction of an oblique shock wave with a pair of parallel vortices: Shock dynamics and mechanism of sound generation. Physics of Fluids, 2006, 18(126101): 1-21

21 Zhang SH, Jiang SF, Zhang YT, et al. The mechanism of sound generation in the interaction between a shock wave and two counterrotating vortices. Physics of Fluids, 2009, 21(076101): 1-9

22 Sandham ND, Yee HC. Performance of low dissipative high order shock-capturing schemes for shock-turbulence interactions. RIACS Technical Report 98.10, NASA Ames Research Center, 1998

23 Yee HC, Sandham ND, Djomehri MJ. Low-dissipative high-order shock-capturing methods using characteristic-based filters. Journal of Computational Physics, 1999, 150: 199-238

24 Yee HC, Vinokur M, Djomehri MJ. Entropy splitting and numerical dissipation. Journal of Computational Physics, 2000, 162: 33-81

25 Kim D, Kwon JH. A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis. Journal of Computational Physics, 2005, 210: 554-583

26 Shen YQ, Yang GW. Hybrid finite compact-WENO schemes for shock calculation. International Journal for Numerical Methods in Fluids, 2007, 53: 531-560

27 Shen YQ, Zha GC. Generalized finite compact difference scheme for shock/complex flowfield interaction. Journal of Computational Physics, 2011, 230: 4419-4436

28 Chaudhuri A, Hadjadj A, Chinnayya A, et al. Numerical study of compressible mixing layers using high-order WENO schemes. Journal of Scientific Computing, 2011, 47: 170-197

29 Jiang GS, Shu CW. E cient implementation of weighted ENO schemes. Journal of Computational Physics, 1996, 126: 202-228

30 Zhang SH, Shu CW. A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solutions. Journal of Scientific Computing, 2007, 31: 273-305

31 Zhang SH, Jiang SF, Shu CW. Improvement of convergence to steady state solutions of Euler equations with the WENO schemes. Journal of Scientific Computing, 2011, 47: 216-238

32 Shu CW, Osher S. E cient implementation of essentially nonoscillatory shock capturing schemes. Journal of Computational Physics, 1988, 77: 439-471

33 Zhang SH, Zhang HX, Shu CW. Topological structure of shock induced vortex breakdown. Journal of Fluid Mechanics, 2009, 639:343-372

34 傅德薰, 马延文. 平面混合流拟序结构的直接数值模拟. 中国科学A 辑, 1996, 26(7): 657-664 (Fu Dexun, Ma Yanwen. Direct numerical simulation of coherent structure in the compressible mixing layer. Science in China, Series A, 1996, 26(7): 657-664 (in Chinese))

35 李启兵. 应用BGK 格式对可压缩混合层的数值研究. [博士论文]. 北京: 清华大学, 2002 (Li Qibing. Numerical study of compressible mixing layer with BGK scheme. [PhD Thesis]. Beijing: Tsinghua University, 2002 (in Chinese))

36 时晓天. 基于间断有限元的可压缩混合层数值模拟及其结构系综分析. [博士论文]. 北京: 北京大学, 2010 (Shi Xiaotian. Numerical simulations of compressible mixing layers with a Discontinuous Galerkin method and structural ensemble study. [PhD Thesis]. Beijing: Peking University, 2010 (in Chinese))

37 李虎, 张树海. 可压缩各向同性衰减湍流直接数值模拟研究. 力学学报, 2012, 44(4): 673-686 (Li Hu, Zhang Shuhai. Direct numerical simulation of decaying compressible isotropic turbulence. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(4): 673-686 (in Chinese))

38 Samtaney R, Pullin DI, Kosovic B. Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Physics of Fluids, 2001, 13(5): 1415-1430