Numerical Study On Interface Instability Caused By Converging Shock Wave

Richtmyer-Meshkov instability is one of the three kinds of typical interface instabilities, which occurs when an interface separating two different fluids is impulsively accelerated. After the shock impact, the interface is hydrodynamically unstable, and eventually the turbulent mixing dominates the flow. The RMI has attracted a lot of researchers all over the world due to the applications in many fields, such as ICF, supersonic combustion, compressible turbulent flow. RMI caused by converging shock gains more and more attention due to its applications in scientific and engineering fields. In the present work, numerical simulations are performed on the interaction of a converging shock wave with the gaseous cylinder.In the work, the well-validated VAS2D code is adopted. Specifically, a finite volume method is used in the VAS2D and MUSCL-Hancock approach is used to achieve second-order accuracy both in space and time. Adaptive grid technology is employed to achieve higher accuracy and lower cost of computing. An approximation of sharp point is needed for polygonal interface generation method. Quantitative numerical study shows that, with this approximation, the interface is nearly the same. Difference between them in size of the main vortex is below five percent from that of ideal rectangular interface, and the approximation can be ignored compared to other factors in the actual experiment. Circulation of the flow field has less difference of below three percent. Therefore this method of interface formation is reliable.The cylinder accelerated by a converging shock is very different from that accelerated by planar shock. The interface accelerated by converging shock of mid-term has a sharp right end while that is smooth under planar shock condition. In the presence of reflection wave from the wall, the interface accelerated by converging shock is different from that under planar shock condition, such as that it moves slower than that under planar shock condition and the cylinder is higher and wider, even more with a greater converging angle. Circulation of the flow field is nearly the same in early stage and becomes different in late stage.A shorter reflection distance makes the right end of the cylinder sharper, and even makes it layered. What’s more, it makes the cylinder move faster, but the reflection shock meets with the interface at later time. The interface becomes higher and narrower, and the circulation of the flow field becomes greater while the reflection distance becomes shorter, but specially, with a too shorter reflection distance, amplitude of circulation is even smaller.