The Richtmyer-Meshkov Instability On ‘V' Shaped Interface

Richtmyer-Meshkov instability(RMI)occurs when a fluid interface with pertur?bations is impulsively accelerated,and the perturbation on the interface will grow with time and finally turbulent mixing is induced.The RMI has been studied extensively during the last few decades for its significance in many areas of scientific research and engineering application such as supersonic combustion and explosion of the supernova and the process of deflagration to detonation and inertial confinement fusion.Most of the present experimental and theoretical and numerical studies mainly focus on the sin-gle mode interface with small amplitude,while the study about the multi-mode interface with high initial amplitude is inadequate because of the difficulty in forming the initial interface and theoretical analysis and the expensive cost of the numerical simulation.In the present work,RMI of the 'V' shaped interface with different initial amplitudes is experimentally and numerically studied,and the effects of the initial amplitudes on the wave system at the interface and the evolution of the interface are analysed.In the experimental study,a modified soap film technique is adopted to form the initial interface,and the experimental model is specially manufactured to intro-duce thin wires at the cusp of the interface.Experiments are carried in the horizonal shock tube.In the present work,systematic study on the interaction of the 'V' shaped light/heavy(air/sulfur hexafluoride)and heavy/light(air/helium)interface with incident and reflected shock provides benchmark for the analysis of the multi-mode interface with high initial amplitudes.In the study of the interaction between light/heavy interface and incident shock,the initial amplitude has effects on the wave system at the interface and the evolution of the interface.The interface experiences a similar compression,irrespective of the initial amplitude.After the impact of the incident shock,vorticity deposited on the interface varies with different amplitudes,and the smaller the initial amplitude,the less vorticity deposited.The difference in the vorticity affects the subsequent evolution of the interface,and a non-monotonic relationship between the initial amplitude and the growth rate of the mixing width is found.In the study of the interaction between heavy/light interface and incident shock,an obvious spike immediately develops after the impact of the incident shock with dif-ferent wave system at the interface,and subsequently a typical 'phase reversal' in the heavy/light cases occurs.In the heavy/light interface with large amplitude,the veloc-ity induced by the vorticity deposited on the interface is different with the light/heavy cases,thus the discrepancy between the interface and the soap remanent becomes ap-parent.The growth rate after 'phase reversal' and the initial amplitude shows a similar non-monotonic relationship as in the light/heavy cases.In the study of the interaction between light/heavy interface and reflected shock,when the reflected shock impacts the interface which has been evolving after the first impact,different wave systems present at the interface.The interfaces with larger am-plitude evolve more complexly after the first shock,and thus during the second impact the wave system is more complicated and accelerate the flow field to be turbulent.In the theoretical study,a function relationship between the initial amplitude and the growth rate is proposed based on the 'reduction factor theory' and the experimental and numerical results,and the maximum growth rates of the function are found for both light/heav and heavy/light cases.The extreme growth rates from the newly proposed function agree well with the similar former numerical study.In the nonlinear stage,growth rate of the 'V' shaped interface is well predicted by a nonlinear theory model.In the present study,the effects of the intial amplitude on the RMI of the 'V' shaped interface have been systematically studied by a modified soap film technique,and the theory about the RMI of multi-modes interface with high initial amplitudes is refined.The result by the modified soap film technique avoids the effects from membrane and the support and has good symmetry,and can provide benchmark for the theoretical study and numerical validation of the multi-modes RMI with high amplitude.