Knudsen Number Effects on Two-Dimensional Rayleigh-Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method.

Haiyan Ye,Yanbiao Gan,Huilin Lai,Aiguo Xu,Chuandong Lin,Demei Li,Lu Chen

doi:10.3390/e22050500

Abstract

Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh–Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is found that the Knudsen number effects strongly inhibit the RT instability but always enormously strengthen both the global hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. Moreover, when Knudsen number increases, the Kelvin–Helmholtz instability induced by the development of the RT instability is difficult to sufficiently develop in the later stage. Different from the traditional computational fluid dynamics, the discrete Boltzmann method further presents a wealth of non-equilibrium information. Specifically, the two-dimensional TNE quantities demonstrate that, far from the disturbance interface, the value of TNE strength is basically zero; the TNE effects are mainly concentrated on both sides of the interface, which is closely related to the gradient of macroscopic quantities. The global TNE first decreases then increases with evolution. The relevant physical mechanisms are analyzed and discussed.

Highlights

Rayleigh–Taylor (RT) instability is widespread in nature and industry
Based on previous work [74], in the following, we focus on the hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE)
Knudsen number H2 when the compressibility doesn’t change. 2D HNE and TNE effects are demonstrated in detail

Summary

Introduction

Rayleigh–Taylor (RT) instability is widespread in nature and industry. It arises that, when a light fluid supports or pushes a heavy one (that is, when there are acceleration points from a heavy density fluid to a light one), a physical phenomenon in which disturbances at the interface increase with time [1]. Used the finite difference method to simulate the late-time evolution of single-mode RT instability for isothermal stratification to study effects of compressibility and Atwood number [35]. These studies provide a lot of useful information for understanding the physical mechanism of RT instability [36,37]. Chen et al used a multi-relaxation-time DBM to investigate the effects of viscosity, heat conductivity, and Prandtl number on the 2D RT instability from macroscopic and non-equilibrium viewpoints, and found that viscosity and heat conduction suppress RT instability mainly by suppressing the re-acceleration phase KH instability [75]. The research conclusions of this paper have been summarized and its further studies forecasted

Discrete Boltzmann Model

Numerical Simulations

Conclusions