摘要
The interaction of a planar shock with SF_(6)/Ar/He dual interfaces(SF_(6)/Ar interface is sinusoidal and Ar/He interface is unperturbed)is numerically studied with a compressible multi-component flow solver that is capable of simultaneously capturing discontinuities and resolving small-scale smooth structures.Six cases with different interface distances and incident shock strengths are considered.For all cases,after the shock impact,the amplitude of the first interface reduces gradually to zero(i.e.,phase inversion)and then increases continuously in the negative direction.The rarefaction wave(RW2)reflected from the second interface promotes or suppresses the development of the first interface depending on the interface distance(D).Specifically,if D is small,RW2 arrives at the first interface at a time before phase inversion,and thus promotes the instability growth at the first interface.If D is large,RW2 encounters the first interface at a time after phase inversion,and thus suppresses the instability growth.A theoretical model for the critical distance,under which the first interface just completes phase inversion at the arrival time of RW2,is developed.With this model,one can regulate the instability growth at the first interface by giving a desired D.The development of the second interface belongs to non-standard Richtmyer-Meshkov instability,which depends heavily on the phase of the rippled transmitted shock.It is found that the model of Ishizaki(Phys.Rev.E 53,R5592,1996)fails to predict the perturbation growth of the second interface for cases where the transmitted shock is at phase 2 due to the ignorance of baroclinic vorticity.A new model considering the combined effects of baroclinic vorticity,velocity perturbation,and pressure disturbance is proposed,which gives a reasonable prediction of perturbation growth at the second interface.
采用可压缩多组分流动高精度求解器数值研究平面激波冲击SF_(6)/Ar/He双层界面(SF_(6)/Ar界面有正弦扰动,Ar/He界面无扰动)的不稳定性问题,重点考察激波强度和界面间距对不稳定性发展的影响.结果表明,在入射激波冲击后第一道界面振幅会逐渐减小到零(反相),随后在相反的方向上持续增长.从第二道界面上反射回来的稀疏波促进或抑制第一道界面的扰动发展,这取决于界面间距D.具体地说,如果D很小,稀疏波在到达第一道界面时界面还没有完成反相,那么会促进第一道界面的扰动发展;如果D很大,稀疏波到达时第一道界面已完成反相,那么会抑制第一道界面的扰动发展.对于任意初始条件,存在一个临界距离,在此距离下稀疏波作用第一道界面时界面刚好完成反相.本文提出了计算这一临界距离的理论模型,为调控第一道界面的扰动增长速率提供了理论支撑.第二道界面的失稳是由扰动透射激波冲击无扰动界面引起的,属于非标准Richtmyer-Meshkov(RM)不稳定性问题,其扰动增长速率强依赖于冲击界面时扰动激波的相位.本文发现Ishizaki模型由于忽略斜压涡量的影响,不能准确预测第二道界面上的扰动增长.综合考虑斜压涡量、速度扰动和压力扰动的影响,本文提出了一个修正的非标准RM不稳定性理论模型,可以对第二道界面的扰动发展给予有效预测.
基金
This work was supported by the National Natural Science Foundation of China(Grant Nos.12122213,12072341,and 91952205).
