小扰动界面形态对RM不稳定性影响的数值分析

蒋华; 董刚; 陈霄

doi:10.6052/0459-1879-13-347

小扰动界面形态对RM不稳定性影响的数值分析

蒋华¹,
董刚^1,2,
陈霄¹

1.
南京理工大学瞬态物理重点实验室, 南京 210094
2. 北京理工大学爆炸科学与技术国家重点实验室, 北京 100081

基金项目: 国家自然科学基金（11372140）和爆炸科学与技术国家重点实验室（北京理工大学）开放基金（KFJJ12-04Y）资助项目.

详细信息

作者简介:
董刚，研究员，主要研究方向：计算流体力学.E-mail：dgvehicle@yahoo.com

中图分类号: O354.5
计量
- 文章访问数: 1422
- HTML全文浏览量: 125
- PDF下载量: 972
出版历程
- 收稿日期: 2013-10-15
- 修回日期: 2013-12-20
- 刊出日期: 2014-07-17

NUMERICAL STUDY ON THE EFFECTS OF SMALL-AMPLITUDE INITIAL PERTURBATIONS ON RM INSTABILITY

1.
Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, China
2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Funds: The project was supported by the National Natural Science Foundation of China (11372140) and the Open Foundation of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (KFJJ12-04Y).

摘要

摘要: 采用Navier-Stokes 方程对入射激波及其反射激波连续诱导小振幅扰动界面的Richtmyer-Meshkov 不稳定性增长过程进行了二维数值模拟，分析了单模和随机多模两种不同初始形态的界面上钉结构和泡结构在反射激波作用前后的发展特性. 研究结果发现：单模扰动的初始界面形态对反射激波前、后界面的扰动增长都有影响，反射激波前的界面形态信息可以通过钉和泡结构之间的反转传递到反射激波过后. 扰动界面上钉结构的发展速度控制了界面混合区总体的发展速度，反射激波前界面上发展成具有完整冠部形态的钉，在反射激波后会反转成复杂的泡结构，此泡结构对反射激波后钉的发展不利. 随机多模界面显示了与单模界面类似的发展规律，但随机多模界面上的复杂泡结构分布的不对称性使得其对钉结构增长的拖曳效应相对要弱，这导致了相似扰动波长下多模随机界面的扰动发展相对单模界面扰动发展要快.
- RM不稳定性 /
- 激波 /
- 单模扰动 /
- 随机多模扰动 /
- 钉和泡
Abstract: Two-dimensional simulations of Richtmyer-Meshkov (RM) instability of small-amplitude initial perturbed interface induced by shock waves are performed by using Navier-Stokes equations. The evolution of interface mixing zone, which is considered as a combination of a bubble and a spike before and after the passages of reshock wave, is analyzed under the single-mode and random multi-mode initial perturbed conditions. The results show that the perturbation growth is influenced by the initial patterns of interface before and after the passages of reshock wave. The information of initial perturbed interface pattern can be transmitted to that of the interface after reshock wave by transforming between the bubble and spike. The growth rate of spike on the interface dominates the whole growth rate of the mixing zone. The developed spike with crown shape before the passage of reshock is transformed into the complex bubble structure that drags the development of spike after the passage of reshock wave. The evolution of random multi-mode perturbed interface shows the similar behavior as that of single-mode perturbed interface. However, the asymmetric feature of complex bubble structure on random multi-mode interface weakens the drag effect on the development of spike, and thus gives rise to the faster growth of the random multi-mode interface than that of the single-mode interface, under the conditions of similar initial wave length for both interfaces.
- RM instability /
- shock wave /
- single-mode perturbation /
- random multi-mode perturbation /
- spike and bubble

HTML全文

参考文献(19)

Lindl JD, McCrory RL, Campbell EM. Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today, 1992, 45: 32-40

Maran SP, Sonneborn G, Pun CSJ, et al. Physical conditions in circumstellar gas surrounding SN 1987 A 12 years after outburst. Astrophys. J., 2000, 545: 390-398

Yang J, Kubota T, Zukoski EE. Applications of shock-induced mixing to supersonic combustion. AIAA J., 1994, 31: 854-862

Oran ES, Gamezo VN. Origin of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame, 2007, 148: 4-47

Vetter M, Sturtevant B. Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface. Shock Waves, 1995, 4(5): 247-252

Erez L, Sadot O, Oron D, et al. Study of the membrane effect on turbulent mixing measurements in shock tubes. Shock Waves, 2000, 10: 241-251

Leinov E, Malamud G, Elbaz Y, et al. Experimental and numerical investigation of the Richtmyer-Meshkov instability under re-shock conditions. J. Fluid Mech., 2009, 626: 449-475

严长林, 孙德军, 尹协远, 等. Richtmyer-Meshkov不稳定性的数值模拟. 计算物理, 2001, 18(1): 27-32 (Yan Changlin, Sun Dejiang, Yin Xieyuan, et al. Numercial simulations of Richtmyer-Meshkov instability. Chinese Journal of Computational Physics, 2001, 18(1):27-32 (in Chinese))

欧阳良琛, 马东军, 孙德军, 等. 单模大扰动的Richtmyer-Meshkov不稳定性. 爆炸与冲击, 2008, 28(5): 407-414 (Ou-yang Liangchen, Ma Dongjun, Sun Dejun, et al. High-amplitude single-mode perturbation evolution of Richtmyer-Meshkov instability. Explosion and Shock Wave, 2008, 28(5): 407-414 (in Chinese))

Bai JS, Wang B, Wang T, et al. Numerical simulation of the Richtmyer-Meshkov instability in initially nonuniform flows and mixing with reshock. Phys. Rev. E, 2012, 86: 066319

王显圣, 司廷, 罗喜胜, 等. 反射激波冲击重气柱的 RM 不稳定性数值研究. 力学学报, 2012, 44(4): 664-672 (Wang Xiansheng, Si Ting, Luo Xisheng, et al. Numerical study on the RM instability of a heavy-gas cylinder interacted with reshock. Acta Mechanica Sinica, 2012, 44(4): 664-672 (in Chinese))

Thornber B, Drikakis D, Youngs DL, et al. Growth of a Richtmyer-Meshkov turbulent layer after reshock. Physics of Fluids, 2011, 23: 095107

Ukai S, Balakrishnan K, Menon S. Growth rate predictions of single-and multi-mode Richtmyer-Meshkov instability with reshock. Shock Waves, 2011, 21: 533-546

Balasubramanian S, Orlicz G C, Prestridge K P, et al. Influence of initial conditions on turbulent mixing in shock driven Richtmyer-Meshkov flows. In: Proc. 41st AIAA Fluid Dynamics Conf. (Honolulu, Hawaii, 27-30 June 2011). 2011: 1-11

Bagabir A, Drikakis D. Mach number effects on shock-bubble interaction. Shock Waves, 2001, 11: 209-218

Chakravarthy S R, Osher S. A new class of high accuracy TVD schemes for hyperbolic conservation laws. AIAA paper, 1985, 85-0363

Zhu Y J, Dong G, Fan B C, et al. Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble. Shock Waves, 2012, 22(6): 495-509

Zhu Y, Dong G, Liu Y. Three-dimensional numerical simulations of spherical flame evolutions in shock and reshock accelerated flows. Combustion Science and Technology, 2013, 185(10): 1415-1440

Latini M, Schilling O, Don W S. Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability. Journal of Computational Physics, 2007, 221(2): 805-836