Numerical Study On The Influence Of Initial Conditions On Non-classical Rickettmyer-Meshkov Instability

Richtmyer-Meshkov instability(RMI)and its induced turbulent mixing play an important role in academia due to their wide applications.However,the research in this area has focused primarily on the effect of initial conditions on the RMI of perturbed interface impacted by planar shock wave with uniform intensity distribution(hereinafter referred to as the standard RMI).In this paper,non-planar shock wave with sinusoidal function and shock wave of non-unifonrm strength are constructed.The evolution of RMI induced by these two kinds of shock waves under different initial conditions,such as incident shock,perturbed interface and flow,is analyzed numerically.In addition,the instability of free surface with defects of the condensed medium is simulated,considering the strength properties of the condensate.In this paper,the three interface instabilities mentioned above are collectively referred to as non-standard RMI for comparison.As for the RMI caused by non-planar shock wave,the influences of the phase and initial amplitude of the non-planar shock wave,the initial amplitude of the material interface and the non-uniformity of the initial flows are analyzed.The simulated results show that the vortex pairs appear in the region of the disturbed interface after the initial passage of the non-planar shock wave.The RMI induced by non-planar shock wave is dramatically different from the standard RMI due to the effect of vortex pairs,especially before reshock.When the initial phase of the non-planar shock wave is 0,the vortex pairs promote the development of the interface disturbance.As the phase of the non-planar shock wave increases from 0 to ?,the perturbation amplitude decreases due to the prominent suppression effect of the vortex pairs.With the increase of the initial amplitude of the non-planar shock wave,the local total circulation near the interface increases(or decreases)as well as the perturbation amplitude for the phase ?=0(or ?).As the initial amplitude of the material interface increases,the vorticity and circulation deposited at the interface increase,which lead to the increase of the perturbation amplitude.The smaller the non-uniformity coefficient of the flows is,the larger the perturbation amplitude is.The influences of the initial phase and amplitude of non-planar shock wave and non-uniformity of flows are gradually weakened after reshock,but the initial amplitude of material interface still has some influence on the evolution of interface.Besides,the effects of intensity distribution function of non-uniform shock wave,initial amplitude and wavelength of material interface,and initial distance between incident shock wave and material interface on the evolution of disturbance are analyzed in term of the RMI driven by shock wave of non-uniform strength.The results show that the evolution law of such RMI is obviously different from that of the standard RMI before reshock.As the initial amplitude of material interface increases or the wavelength of material interface decreases,perturbation amplitude increases.The influence of intensity distribution function of non-uniform shock wave on the growth of the disturbed interface is not obvious.When the reshock hits the disturbed interface,the effect of intensity distribution function of non-uniform shock wave becomes gradually significant,while the influences of the initial disturbance amplitude and wavelength of the material interface weaken.In the whole calculation time,the influence of the initial distance between the incident shock wave and material interface on the interface evolution is not obvious.At last,the influences of defect shape and constitutive models of free surface on its instability are preliminarily analyzed.The results show that the instability of condensate free surface can still be explained by baroclinic mechanism.The analysis of the interface instability,fracture and ejection distribution calculated by two different initial defects shows that the research of material initial defect shapes is significant.However the evolution of the condensate free surface instability is more complex than that of gas material due to the strength property of the condensate medium.So this instability is affected by the material constitutive model.