Linear Rayleigh-Taylor Instability Analysis of a Double-Shell Kidder’s Self-Similar Implosion
-
摘要: 将单层Kidder自相似解推广到双层，使得两层壳体的交界面两侧存在密度跳跃，使得轻流体向重流体加速产生Rayleigh-Taylor不稳定性；通过采用Lagrange坐标下的Godunov方法进行一维直接数值模拟，将模拟解与双层Kidder自相似基本解进行比较，验证了双层Kidder自相似解的可靠性；最后，通过编制球形内爆的三维扰动的线性稳定性分析程序，对双层Kidder自相似解的Rayleigh-Taylor不稳定性进行了分析计算．计算结果表明：初始扰动越集中于交界面,会造成后期扰动增长得越快，越不稳定；扰动波数越大，扰动增长得越快，越不稳定；从扰动在空间上的发展来看，可压缩性研究表明内外壳体的可压缩性对扰动增长起着相反的作用，外层壳体的可压缩性对Rayleigh-Taylor不稳定起失稳作用，而内层壳体的可压缩性对Rayleigh-Taylor不稳定起致稳作用．
-
关键词:
- 双层Kidder自相似解 /
- Rayleigh-Taylor不稳定性 /
- 内爆压缩
Abstract: By generalizing the single-shell Kidder's self-similar solution to double-shell with a discontinuity for density across the interface,an isentropic implosion model was constructed to study the Rayleigh-Taylor instability for the miplosion compression.A Godunov-type method in Lagrangian coordinates was used to compute the one-dmiensional Euler equation with the initial conditions and boundary conditions of the double-shell Kidder's self-similar solution in spherical geometry,and numerical results were obtained to validate the double-shell miplosion model. By programming and using the linear perturbation code,a linear stability analysis on the Rayleigh-Taylor instability for the double-shellisen tropic miplosion model was performed.It is found that when the initial perturbation concentrates much closer to the inter face of the two shells,or when the spherical wave number becomes much smaller,the interface modal radius grows much faster,i.e.more unstable.In addition,from the spatial point of view for the compressibility effect on the perturbation evolution,it is found that the compressibility of the outer shell has destabilization effect on Rayleigh-Taylor instability,while the compressibility of the inner shell has stabilization effect. -
[1] Rayleigh L. Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density[J]. Proc London Math Soc, 1883, 14:170-177. [2] Taylor G I. The instability of liquid surface when accelerated in a direction perpendicular to their planes[J]. Proc R Soc London, Ser A, 1950, 201: 192-196. [3] Richtmyer R D. Taylor instability in shock acceleration of compressible fluids[J]. Commun Pure Appl Math，1960， 13(2)： 297-319. doi: 10.1002/cpa.3160130207 [4] Meshkov E E. Instability of the interface of two gases accelerated by a shock wave[J]. Sov Fluid Dyn,1969, 4(5): 151-157. [5] Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability[M]. London: Oxford University Press, 1961. [6] Kidder R E. Laser-driven compression of hollow shells: power requirements and stability limitations[J]. Nuclear Fusion,1976, 16(1): 3-14. doi: 10.1088/0029-5515/16/1/001 [7] Breil J, Hallo L, Maire P H,et al. Hydrodynamic instabilities in axisymmetric geometry self-similar models and numerical simulations[J]. Laser and Particle Beams, 2005, 23(2): 155-160. [8] Jaouen S. A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry[J]. Journal of Computational Physics, 2007, 225(1): 464-490. doi: 10.1016/j.jcp.2006.12.008 [9] 水鸿寿.一维流体力学差分方法[M].北京：国防工业出版社，1998. [10] Després B. Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition[J]. Numer Math, 2001, 89(1): 99-134. doi: 10.1007/PL00005465 [11] Livescu D. Compressible effects on the Rayleigh-Taylor instability growth between immiscible fluids[J]. Phys Fluids, 2004, 16(1): 118-127. doi: 10.1063/1.1630800 -
点击查看大图
计量
- 文章访问数: 1482
- HTML全文浏览量: 78
- PDF下载量: 838
- 被引次数: 0
下载:
