非理想流体中Rayleigh-Taylor和Richtmyer-Meshkov不稳定性气泡速度研究

霍新贺; 王立锋; 陶烨晟; 李英骏

doi:10.7498/aps.62.144705

摘要

在随气泡顶端运动的坐标系中, 通过将理想流体模型推广到非理想流体的情况, 研究了流体黏性和表面张力对Rayleigh-Taylor (RT)和Richtmyer-Meshkov (RM)不稳定性气泡速度的影响. 首先得到了RT和RM不稳定性气泡运动的控制方程 (自洽的微分方程组); 其次给出了二维平面坐标和三维柱坐标中气泡速度的数值解和渐近解, 并定量分析了流体黏性和表面张力对RT和RM气泡速度和振幅的影响. 结果表明: 从线性阶段到非线性阶段的全过程中, 非理想流体中的气泡速度和振幅小于理想流体中的气泡速度和振幅. 也就是说, 流体黏性和表面张力对RT和RM不稳定性的发展都具有致稳作用.

关键词:

Abstract

In a reference system moving with the bubble vertex we investigate the effects of fluid viscosity and surface tension on the bubble velocity in the nonlinear Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, by extending the ideal fluid model [Goncharov V N, Phys. Rev. Lett. 88 134502 (2002)] to the non-ideal fluid case. First of all, the governing equation (i.e. self-consistent differential equations) describing the dynamic of the bubble front in RT and RM instabilities is obtained. Then, the numerical and asymptotic solutions of the bubble velocity in two-dimensional planar geometry and three-dimensional cylindrical geometry are obtained. Moreover, we quantitatively study the effects of fluid viscosity and surface tension on the RT and RM bubble velocities. It is found that in the fully nonlinear evolutions of RT and RM instabilities, the bubble velocity and amplitude in the non-ideal fluid are both less than those in its ideal fluid counterpart. That is to say, the effects of fluid viscosity and surface tension tend to stabilize the RT and RM instabilities.

Keywords:

作者及机构信息

1.
中国矿业大学, 深部岩土力学与地下工程国家重点实验室, 北京 100083;

2.
北京大学应用物理与技术研究中心, 高能量密度物理数值模拟教育部重点实验室, 北京 100871

基金项目: 国家自然科学基金(批准号: 11074300, 11274026, 11275031)和国家重点基础研究发展计划(批准号: 2013CBA01504)资助的课题.

Authors and contacts

1.
State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, China;

2.
HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074300, 11274026, 11275031) and the National Basic Research Program of China (Grant No. 2013CBA01504).

参考文献

[1]	Taylor G I 1950 Proc. R. Soc. London A 201 192
[2]	Ramaprabhu P, Andrews M J 2004 J. Fluid Mech. 502 233
[3]	Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[4]	Meshkov E E 1969 Sov.Fluid Dyn. 4 101
[5]	Ye W H, Wang L F, He X T 2010 Phys. Plasmas 17 122704
[6]	Wang L F, Ye W H, He X T, Zhang W Y, Sheng Z M, Yu M Y 2012 Phys. Plasmas 19 100701
[7]	Layzer D 1955 Astrophys. J. 122 1
[8]	Zufiria J 1988 Phys. Fluids 31 440
[9]	Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J, He X T 2010 Phys. Plasmas 17 122706
[10]	Wang L F, Ye W H, Li Y J 2010 Phys. Plasmas 17 052305
[11]	Wang L F, Ye W H, Fan Z F, Li Y J 2010 EPL. 90 15001
[12]	Liu W H, Wang L F, Ye W H, He X T 2012 Phys. Plasmas 19 042705
[13]	Wang L F, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025203
[14]	Zhang Q 1998 Phys. Rev. Lett. 81 3391
[15]	Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[16]	Karnig O Mikaelian 2010 Phys. Rev. E 81 016325
[17]	Young Y N, Ham F E 2006 J. Turbul. 7 1
[18]	Niebling M J, Flekkoy E G, Måloy K J, Toussaint R 2010 Phys. Rev. E 82 051302
[19]	Garnier J 2003 Phys. Rev. E 68 036401
[20]	Sohn S I 2004 Phys. Rev. E 70 045301
[21]	Sohn S I 2009 Phys. Rev. E 80 055302(R)
[22]	Oron D, Arazi L, Kartoon D, Rikanati A, Alon U, Shrarts D 2001 Phys. Plasmas 8 2883
[23]	Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 物理学报 61 075207]

施引文献

[1]	Taylor G I 1950 Proc. R. Soc. London A 201 192
[2]	Ramaprabhu P, Andrews M J 2004 J. Fluid Mech. 502 233
[3]	Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[4]	Meshkov E E 1969 Sov.Fluid Dyn. 4 101
[5]	Ye W H, Wang L F, He X T 2010 Phys. Plasmas 17 122704
[6]	Wang L F, Ye W H, He X T, Zhang W Y, Sheng Z M, Yu M Y 2012 Phys. Plasmas 19 100701
[7]	Layzer D 1955 Astrophys. J. 122 1
[8]	Zufiria J 1988 Phys. Fluids 31 440
[9]	Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J, He X T 2010 Phys. Plasmas 17 122706
[10]	Wang L F, Ye W H, Li Y J 2010 Phys. Plasmas 17 052305
[11]	Wang L F, Ye W H, Fan Z F, Li Y J 2010 EPL. 90 15001
[12]	Liu W H, Wang L F, Ye W H, He X T 2012 Phys. Plasmas 19 042705
[13]	Wang L F, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025203
[14]	Zhang Q 1998 Phys. Rev. Lett. 81 3391
[15]	Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[16]	Karnig O Mikaelian 2010 Phys. Rev. E 81 016325
[17]	Young Y N, Ham F E 2006 J. Turbul. 7 1
[18]	Niebling M J, Flekkoy E G, Måloy K J, Toussaint R 2010 Phys. Rev. E 82 051302
[19]	Garnier J 2003 Phys. Rev. E 68 036401
[20]	Sohn S I 2004 Phys. Rev. E 70 045301
[21]	Sohn S I 2009 Phys. Rev. E 80 055302(R)
[22]	Oron D, Arazi L, Kartoon D, Rikanati A, Alon U, Shrarts D 2001 Phys. Plasmas 8 2883
[23]	Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 物理学报 61 075207]

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