Citation: | WANG Zhen, WANG Tao, BAI Jingsong, XIAO Jiaxin. Numerical study of non-uniformity effect on Richtmyer-Meshkov instability induced by non-planar shock wave[J]. Explosion And Shock Waves, 2019, 39(4): 041407. doi: 10.11883/bzycj-2018-0342 |
Based on the Navier-Stokes equations, the large-eddy simulation code MVFT (multi-viscous-flow and turbulence) was applied to numerically study the Richtmyer-Meshkov instability (i.e. RMI) for a perturbed interface, which is driven by a non-planar shock wave with Ma=1.25 in uniform and non-uniform flows with Gaussian distribution of the initial density. The simulation results show that the interface evolution of the RMI induced by non-planar shock wave is affected by the non-uniformity of the initial flows. Before reshock, the growth of the disturbed interface increases with the increasing of the non-uniformity flow field for either φ=0 or φ=π. However, these discrepancies are reduced as the flow enters the turbulent mixing. Further quantitative analysis of the circulations and high-order fluctuating velocity correlation in the flow field reveal the mechanisms for the aforementioned regulations. In addition, it is found that the interface evolution of the RMI induced by non-planar shock wave is different from that driven by planar shock wave. The mechanism for the difference is the influence of the initial vorticity of non-planar shock wave and the vorticity generated by the shock-interface.
[1] |
RICHTMYER R D. Taylor instability in shock acceleration of compressible fluids [J]. Communications on Pure and Applied Mathematics, 1960, 13(2): 297–319. DOI: 10.1002/cpa.3160130207.
|
[2] |
ARNETT D. The role of mixing in astrophysics [J]. The Astrophysical Journal Supplement Series, 2000, 127(2): 213–217. DOI: 10.1086/313364.
|
[3] |
YANG J, KUBOTA T, ZUKOSKI E E. Applications of shock-induced mixing to supersonic combustion [J]. AIAA Journal, 1993, 31(5): 854–862. DOI: 10.2514/3.11696.
|
[4] |
AMENDT P, COLVIN J D, TIPTON R E, et al. Indirect-drive noncryogenic double-shell ignition targets for the national ignition facility: Design and analysis [J]. Physics of Plasmas, 2002, 9(5): 2221–2233. DOI: 10.1063/1.1459451.
|
[5] |
ZOU L Y, LIU C L, TAN D W, et al. On interaction of shock wave with elliptic gas cylinder [J]. Journal of Visualization, 2010, 13(4): 347–353. DOI: 10.1007/s12650-010-0053-y.
|
[6] |
BAI J S, ZOU L Y, WANG T, et al. Experimental and numerical study of shock-accelerated elliptic heavy gas cylinders [J]. Physical Review E, 2010, 82(2): 056318. DOI: 10.1103/PhysRevE.82.056318.
|
[7] |
BAI J S, LIU J H, WANG T, et al. Investigation of the Richtmyer-Meshkov instability with double perturbation interface in nonuniform flows [J]. Physical Review E, 2010, 81(2): 056302. DOI: 10.1103/PhysRevE.81.056302.
|
[8] |
XIAO J X, BAI J S, WANG T. Numerical study of initial perturbation effects on Richtmyer-Meshkov instability in nonuniform flows [J]. Physical Review E, 2016, 94(1): 013112. DOI: 10.1103/PhysRevE.94.013112.
|
[9] |
肖佳欣, 柏劲松, 王涛. 密度非均匀流场中冲击加载双模态界面失稳现象的数值模拟 [J]. 高压物理学报, 2018, 32(1): 82–90. DOI: 10.11858/gywlxb.20170501
XIAO Jiaxin, BAI Jingsong, WANG Tao. Numerical study of shock wave impacting on the double-mode interface in nonuniform flows [J]. Chinese Journal of High Pressure Physics, 2018, 32(1): 82–90. DOI: 10.11858/gywlxb.20170501
|
[10] |
BAI J S, WANG B, WANG T, et al. Numerical simulation of the Richtmyer-Meshkov instability in initially nonuniform flows and mixing with reshock [J]. Physical Review E, 2012, 86(2): 066319. DOI: 10.1103/PhysRevE.86.066319.
|
[11] |
ISHIZAKI R, NISHIHARA K, SAKAGAMI H, et al. Instability of a contact surface driven by a nonuniform shock wave [J]. Physical Review E, 1996, 53(6): R5592. DOI: 10.1103/PhysRevE.53.R5592.
|
[12] |
KANE J O, ROBEY H F, REMINGTON B A, et al. Interface imprinting by a rippled shock using an intense laser [J]. Physical Review E, 2001, 63(2): 055401. DOI: 10.1103/PhysRevE.63.055401.
|
[13] |
ZOU L Y, LIU J H, LIAO S F, et al. Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave [J]. Physical Review E, 2017, 95(1): 013107. DOI: 10.1103/PhysRevE.95.013107.
|
[14] |
ZHAI Z G, LIANG Y, LIU L L, et al. Interaction of rippled shock wave with flat fast-slow interface [J]. Physics of Fluids, 2018, 30(4): 046104. DOI: 10.1063/1.5024774.
|
[15] |
柏劲松, 李平, 王涛, 等. 可压缩多介质粘性流体的数值计算 [J]. 爆炸与冲击, 2007, 27(6): 515–521. DOI: 10.11883/1001-1455(2007)06-0515-07
BAI Jingsong, LI Ping, WANG Tao, et al. Computation of compressible multi-viscosity-fluid flows [J]. Explosion and Shock Waves, 2007, 27(6): 515–521. DOI: 10.11883/1001-1455(2007)06-0515-07
|
[16] |
王涛, 柏劲松, 李平, 等. 再冲击载荷作用下流动混合的数值模拟 [J]. 爆炸与冲击, 2009, 29(3): 243–248. DOI: 10.11883/1001-1455(2009)03-0243-06
WANG Tao, BAI Jingsong, LI Ping, et al. Numerical simulation of flow mixing impacted by reshock [J]. Explosion and Shock Waves, 2009, 29(3): 243–248. DOI: 10.11883/1001-1455(2009)03-0243-06
|
[17] |
柏劲松, 王涛, 邹立勇, 等. 可压缩多介质粘性流体和湍流的大涡模拟 [J]. 爆炸与冲击, 2010, 30(3): 262–268. DOI: 10.11883/1001-1455(2010)03-0262-07
BAI Jingsong, WANG Tao, ZOU Liyong, et al. Large eddy simulation for the multi-viscosity-fluid and turbulence [J]. Explosion and Shock Waves, 2010, 30(3): 262–268. DOI: 10.11883/1001-1455(2010)03-0262-07
|
[18] |
王涛, 李平, 柏劲松, 等. 低密度流体界面不稳定性大涡模拟 [J]. 爆炸与冲击, 2013, 33(5): 487–493. DOI: 10.11883/1001-1455(2013)05-0487-07
WANG Tao, LI Ping, BAI Jingsong, et al. Large-eddy simulation of interface instability of low-density fluids [J]. Explosion and Shock Waves, 2013, 33(5): 487–493. DOI: 10.11883/1001-1455(2013)05-0487-07
|
[19] |
VREMAN A W. An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications [J]. Physics of Fluids, 2004, 16(10): 3670–3681. DOI: 10.1063/1.1785131.
|
[20] |
BAI J S, WANG T, LI P, et al. Numerical simulation of the hydrodynamic instability experiments and flow mixing [J]. Science in China Series G: Physics, Mechanics & Astronomy, 2009, 52(12): 2027–2040. DOI: 10.1007/s11433-009-0277-9.
|