Development of the Richtmeyer-Meshkov instability during interaction of the mixing diffusion layer of two gases with transmitted and reflected shock waves

Abstract

Development of instability in the region of mixing of fast-moving gases of different densities is a topical problem for energy-commuting facilities. Conventionally, the mixing layer is considered as a surface of the continuity break, i.e., as the contact break. The interaction of the shock wave with a perturbed contact discontinuity generates the Richtmeyer‐Meshkov instability. At the final stage, in the region of the initial contact break, the region of turbulent mixing separating the flows of compressed gases is formed. Numerous works on numerical modeling of the development of the Richtmeyer‐Meshkov instability based on the Euler equations did not take into account the influence of processes of mutual penetration of gases. Therefore, it is of interest to investigate this problem based on the equations of the double-speed two-temperature gas mixture, where each component has its own velocity and temperature. This approach allows one to describe the development of instability at various stages allowing for mutual penetration of gases. The necessity of applying models of multicomponent systems to describe the destruction of the contact boundary and formation of the region of the mixture was, e.g., pointed out in [1]. In [2], a semiempirical model of turbulent mixing of a multicomponent medium based on the use of its own velocity for each component is constructed. In this model, it is assumed that turbulent mixing appears instantly. Below, based on the equations of the double-speed two-temperature gas dynamics of the mixtures, we investigate the processes at the initial stages of mixing. We previously [4] investigated the interaction of the mixing layer with the incident shock wave and compression wave [5]. In this work, on the basis of equations of the doublespeed two-temperature gas dynamics of the mixtures [3], we investigate the processes of development of the Richtmeyer‐Meshkov instability during the interaction of the incident shock wave with the perturbed mixing layer allowing for the further repeated interaction of the layer with the waves reflected from the end. The initial sinusoidally perturbed diffusion layer of mixing was formed on the basis of the solution suggested in [4] with the perturbation amplitude a 0 , the perturbation wavelength λ , and the initial layer width δ 0 . The interaction of the mixing layer with the incident shock wave, which transfers from the light gas into the heavy gas and from the heavy gas into the light gas, is considered. The parameters of the mixture in the layer are described by the equations of the double-speed two-temperature gas dynamics of the mixtures [3], which transform to the Euler equations for pure gas out of the layer. The method of calculation of the starting set of equations is described in [4, 5]. The shock wave moved from upward to downward. At the upper boundary, the condition that derivatives were equal to zero was given, and the lower boundary is a solid wall. Symmetry conditions were given at the side boundaries. We considered the incidence of the shock wave on the mixing layer with the reflection angle in a onedimensional approximation in the absence of perturbations in the initial mixing layer. The results of these investigations are in complete agreement with the conclusions of [6].