Large-eddy simulations of the Richtmyer-Meshkov instability of rectangular interfaces accelerated by shock waves

A parallel algorithm and code MVFT (multi-viscous-fluid and turbulence) of large-eddy simulation (LES) is developed from our MVPPM (multi-viscous-fluid piecewise parabolic method), and performed to solve the multi compressible Navier-Stokes (N-S) equations. The effect of the unresolved subgrid-scale (SGS) motions on the large scales is represented by different SGS stress models in LES. A Richtmyer-Meshkov instability experiment of the evolution of a rectangular block of SF6, which occupies half of the height of the shock tube test section, following the interaction with a planar shock wave, is numerically and exhaustively simulated by this code. The comparison between experimental and simulated images of the evolving SF6 block shows that they are consistent. The numerical simulations reproduce the complex developing process of SF6 block, which grows overturningly. The geometric quantities that characterize the extents of SF6 block are also compared in detail between numerical simulations and experiment with good agreements between them, a quantitative demonstration of the developing law of SF6 block. There is an evident discrepancy between the three numerical simulations for the maximum position of the right edge of block at the late stage, because the right interface grows complicated and the dissipation is different for different SGS models. The SGS turbulent dissipation, molecular viscosity dissipation and SGS turbulent kinetic energy have been studied and analyzed. They have a similar distribution to the large eddy structures. The SGS turbulent dissipation is much greater than the molecular viscosity dissipation; the SGS turbulent dissipation of Vreman model is smaller than the Smagorinsky model. In general, the simulated results of Vreman SGS model are better compared with the dynamic viscosity and Smagorinsky SGS model. The vorticity and circulation deposition on the block interface have also been investigated.