Refined modelling of the single-mode cylindrical Richtmyer-Meshkov instability

摘要

Evolution of the two-dimensional single-mode Richtmyer-Meshkov (RM) instability in a cylindrical geometry is numerically investigated through direct numerical simulation. A proper decomposition of the measured initial perturbation amplitude is found to be crucial for a comparative study between the numerical simulation and benchmark experiment. A refined compressible model is proposed based on the Bell equation by taking the premixed width of the initial interface into consideration. The modified model can accurately reproduce the development history of a single-mode perturbed gaseous interface between the first shock-interface interaction and reshock based on the evolution data of the unperturbed interface under the same premixing condition. The detailed effects of the RM instability, Rayleigh-Taylor stabilization and compressibility coupled with the Bell-Plesset effect are also specified with the aid of this model. It turns out that the refined Bell model can be further applied to the post-reshock stage of the RM instability before the appearance of strong nonlinearity.