单模态RM不稳定性的二维和三维数值计算研究

王涛; 柏劲松; 李平; 陶钢; 姜洋; 钟敏

doi:10.11858/gywlxb.2013.02.016

单模态RM不稳定性的二维和三维数值计算研究

doi: 10.11858/gywlxb.2013.02.016

王涛^1,2, ,,
柏劲松¹,
李平¹,
陶钢²,
姜洋¹,
钟敏¹

1.
中国工程物理研究院流体物理研究所，四川绵阳 621900；
2.
南京理工大学能源与动力工程学院，江苏南京 210094

详细信息

通讯作者:
王涛 E-mail:wtaoxp@21cn.com

计量
- 文章访问数: 7027
- HTML全文浏览量: 281
- PDF下载量: 267
出版历程
- 收稿日期: 2010-12-02
- 修回日期: 2011-05-25
- 刊出日期: 2013-04-15

Two and Three Dimensional Numerical Investigations of the Single-Mode Richtmyer-Meshkov Instability

1.
Institute of Fluid Physics, CAEP, Mianyang 621900, China;
2.
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

摘要

摘要: 发展了可用于可压缩多介质粘性流体动力学问题的数值模拟方法和代码MVPPM（Multi-Viscous-Fluid Piecewise Parabolic Method）。利用MVPPM方法对多个具有不同初始扰动振幅和波长的二维和三维单模态Richtmyer-Meshkov（RM）不稳定性模型进行了数值计算，并和理论模型的计算结果进行了比较。结果显示，扰动界面的发展与扰动的初始条件密切相关。无论二维还是三维情况，当初始扰动强度较小的时候，数值计算的扰动振幅及增长率和理论模型的计算结果一致。对于具有相同初始扰动的情况，三维数值计算结果在线性段与二维计算结果相同，但是在非线性段比二维结果大，说明非线性和三维效应在RM不稳定性发展过程中起着重要作用。
- MVPPM（Multi-Viscous-Fluid Piecewise Parabolic Method）方法 /
- 单模态Richtmyer-Meshkov不稳定性 /
- 非线性
Abstract: A high precision numerical algorithm MVPPM (multi-viscous-fluid piecewise parabolic method) is proposed and applied to the multi-viscous-fluid dynamics problems. Several two and three dimensional single-mode Richtmyer-Meshkov instability models with different amplitude and wavelength are numerically simulated by this method. Comparisons show that the evolving of interface is highly sensitive to the initial conditions of perturbation. Both two and three dimensional calculated amplitudes and growth rates of perturbed interface are consistent with the predictions of theoretical models, while the strength of initial perturbation is small. The three dimensional numerical results are identical with the two dimensional ones at the linear stage and larger than the two dimensional ones at the nonlinear stage for the perturbation with the same wavelength and amplitude. Therefore the effects of nonlinearity and three dimensions play a dominant role in the development of Richtmyer-Meshkov instability.
- multi-viscous-fluid piecewise parabolic method /
- single-mode Richtmyer-Meshkov instability /
- nonlinearity

HTML全文

参考文献(28)

Richtmyer R D. Taylor instability in shock acceleration of compressible fluids [J]. Commun Pur Appl Math, 1960, 13(2): 297-319.

Meshkov E E. Instability of the interface of two gases accelerated by a shock wave [J]. Sov Fluid Dyn, 1969, 4(5): 101-104.

Zhang Q, Sohn S-Ik. Quantitative theory of Richtmyer-Meshkov instability in three dimensions [J]. Z angew Math Phys, 1999, 50(1): 1-46.

Taylor G I. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes [J]. Proc R Soc A, 1950, 201(1065): 192-196.

Zhang Q, Sohn S-Ik. An analytical nonlinear theory of Richtmyer-Meshkov instability [J]. Phys Lett A, 1996, 212(3): 149-155.

Zhang Q, Sohn S-Ik. Nonlinear theory of unstable fluid mixing driven by shock wave [J]. Phys Fluids, 1997, 9(4): 1106-1124.

Li X L, Zhang Q. A comparative numerical study of the Richtmyer-Meshkov instability with nonlinear analysis in two and three dimensions [J]. Phys Fluids, 1997, 9(10): 3069-3077.

Sadot O, Erez L, Alon U, et al. Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability [J]. Phys Rev Lett, 1998, 80(8): 1654-1657.

Meyer K A, Blewett P J. Numerical investigation of the stability of a shock-accelerated interface between two fluids [J]. Phys Fluids, 1972, 15(5): 753-759.

Cloutman L D, Wehner M F. Numerical simulation of Richtmyer-Meshkov instabilities [J]. Phys Fluids A, 1992, 4(8): 1821-1830.

Grove J W, Holmes R H, Sharp D H, et al. Quantitative theory of Richtmyer-Meshkov instability [J]. Phys Rev Lett, 1993, 71(21): 3473-3476.

Holmes R H, Grove J W, Sharp D H. Numerical investigation of Richtmyer-Meshkov instability using front tracking [J]. J Fluid Mech, 1995, 301: 51-64.

Zhang Z Z, Wang J H. Turbulent mixing model and numerical simulation of Richtmyer-Meshkov instability [J]. Explosion and Shock Waves, 1997, 17(3): 199-206. (in Chinese)

张忠珍, 王继海. k-D-a-B模型和Richtmyer-Meshkov不稳定性的数值模拟 [J]. 爆炸与冲击, 1997, 17(3): 199-206.

Srebro Y, Elbaz Y, Sadot O, et al. A general buoyancy-drag model for the evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities [J]. Laser and Particle Beams, 2003, 21(3): 347-353.

Yang M, Wang L L, Zhang S D, et al. The study of turbulent mixing induced by Richtmyer-Meshkov instability using turbulence model [J]. Acta Aerodynamica Sinica, 2010, 28(1): 119-123. (in Chinese)

杨玟, 王丽丽, 张树道, 等. 用湍流模型研究Richtmyer-Meshkov不稳定性诱导的湍流混合 [J]. 空气动力学学报, 2010, 28(1): 119-123.

Hill D J, Pantano C, Pullin D I. Large-eddy simulation and multiscale modeling of a Richtmyer-Meshkov instability with reshock [J]. J Fluid Mech, 2006, 557: 29-61.

Thornber B, Drikakis D. Large-eddy simulation of shock-wave-induced turbulent mixing [J]. Journal of Fluid Engineering, 2007, 129(12): 1504-1513.

Lombardini M, Deiterding R. Large-eddy simulation of Richtmyer-Meshkov instability in a converging geometry [J]. Phys Fluids, 2010, 22(9): 091112.

Schilling O, Latini M, Don W S. Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability [J]. Phys Rev E, 2007, 76(2): 026319(1)-026319(28).

Latini M, Schilling O, Don W S. Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability [J]. J Comput Phys, 2007, 221: 805-836.

Schilling O, Latini M. High-order WENO simulations of three-dimensional reshocked Richtmyer-Meshkov instability to late times: Dynamics, dependence on initial conditions, and comparisons to experimental data [J]. Acta Mathematica Scientia, 2010, 30B(2): 595-620.

Zhang S. Adaptive mesh refinement and visiometrics in accelerated inhomogeneous flows [D]. New Jersey: The State University of New Jersey, 2004.

Nourgaliev R R, Dinh T N, Theofanous T G. Adaptive characteristics-based matching for compressible multifluid dynamics [J]. J Comput Phys, 2006, 213(2): 500-529.

Wang T, Bai J S, Li P, et al. The numerical study of shock-induced hydrodynamic instability and mixing [J]. Chin Phys B, 2009, 18(3): 1127-1135.

Bai J S, Wang T, Zou L Y, et al. Numerical simulation for shock tube and jelly interface instability experiments [J]. Chinese Journal of Applied Mechanics, 2009, 26(3): 418-425. (in Chinese)

柏劲松, 王涛, 邹立勇, 等. 激波管实验和果冻实验界面不稳定性数值计算 [J]. 应用力学学报, 2009, 26(3): 418-425.

施引文献

资源附件(0)

访问统计