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摘要
A high-order weighted essentially non-oscillatory scheme is employed to investigate the stability of a rapidly expanding material interface produced by a spherical shock tube. The flow structure is characterized by a forward moving primary shock, a backward moving secondary shock, and a spherical contact interface in-between. We consider herein the linear inviscid regime and focus on the development of the three-dimensional perturbations around the contact interface by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the effects of the contact interface's density discontinuity on the growth of the disturbances for various spherical wave numbers. In a spherical shock tube the instability is influenced by various mechanisms which include classical Rayleigh-Taylor (RT) effects, Bell-Plesset or geometry/curvature effects, the effects of impulsively accelerating the interface, and compressibility effects. Henceforth, the present instability will be referred to as non-classical RT instability to distinguish it from classical RT instability. For an extended intermediate time period, it can be shown that the small disturbances grow exponentially as in the classical RT instability. During this stage, the exponential growth rate increases with the spherical wave number, until it saturates for very large wave numbers due to the finite thickness limitation of the numerical representation of the contact interface. The results compare favorably with previous theoretical models; but indicate that in addition to compressibility, the space-time evolution of the contact interface's thickness plays a significant role. A parametric study is performed that varies the pressure and density ratios of the initial spherical container. The characteristics of the contact interface and the applicability of various instability theories is investigated for these regimes. Furthermore, varying the pressure and density ratios aids in understanding significance of compressibility effects on the instability at different operating conditions.
- 出版日期2012-3
