Kinetic Simulation of Nonequilibrium Kelvin-Helmholtz Instability**Supported by the Natural Science Foundation of China under Grant Nos. 91441120, 51806116, 11875001, and 11602162, the China Postdoctoral Science Foundation under Grant No. 2017M620757, the Center for Combustion Energy at Tsinghua University, and the Natural Science Foundation of Hebei Province under Grant Nos. A2017409014, ZD2017001, and A201500111, and the UK Engineering and Physical Sciences

Abstract

The recently developed discrete Boltzmann method (DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability (KHI). It is found that, the relaxation time always strengthens the global nonequilibrium (GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are: (i) Initially, binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate. (ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI. (iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy (light) medium reduces (increases), because the heavy (light) medium has a relatively small (large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.