Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

Abstract

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model. Technically, two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes. One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures; the other is to evaluate the growth rate of KHI from the slopes of morphological functionals. Physically, it is found that the time histories of width of mixing layer, TNE intensity, and boundary length show high correlation and attain their maxima simultaneously. The viscosity effects are twofold, stabilize the KHI, and enhance both the local and global TNE intensities. Contrary to the monotonically inhibiting effects of viscosity, the heat conduction effects firstly refrain then enhance the evolution afterwards. The physical reasons are analyzed and presented.

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

“…The whole kinetic (internal) energy becomes only a bit smaller (larger) with the increasing thermal conductivity. It is concluded that both heat conduction and temperature exert slight influences on the formation and evolution of the KHI, which is absolutely different from previous studies [40][41][42][43][44]. It is noteworthy that previous works are based upon physical models suitable for single-component fluids [40][41][42][43][44], while the present research is on the base of our reliable kinetic model for multicomponent mixtures.…”

“…As an essential physical mechanism in turbulence and fluids mixing process, the KHI has been studied extensively with experimental [55][56][57], theoretical [40,41,58], and computational [42][43][44][45] methods during the past decades. In this section, we further utilize the DBM to simulate and investigate the compressible KHI with both hydrodynamic and thermodynamic nonequilibriun effects.…”

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

“…From a computational resource perspective, the remarkable merits are brevity of programming, numerical potency, inherent parallelism, and ease treatment of intricate boundary conditions. This kind of method has comprehensive capacities in quite several fields, from phonon transport [13] to approximate incompressible flows [14][15][16][17][18][19][20][21][22][23][24][25], full compressible flows [26][27][28][29][30][31][32][33][34][35][36][37], dendrite growth [38,39] and thermal multiphase flows [40]. Recently, the mesoscopic kinetics method is also becoming increasingly popular in computational mathematics and engineering science for solving certain NPDEs, including Burgers' equations [41,42], Korteweg-de Vries equation [43], Gross-Pitaevskii equation [44], convection-diffusion equation [45][46][47][48][49][50][51], Kuramoto-Sivashinsky equation [52], wave equation [53,54], Dirac equation [55], Poisson equation…”

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

“…In 2019, Gan et al studied the effects of viscosity and heat conduction on the Kelvin–Helmholtz (KH) instability through the DBM. The authors found the viscosity effects stabilize the KH instability and enhance both the local and global TNE intensities [ 69 ]. Lin et al employed the DBM to investigate the KH instability and found the relaxation time always strengthens the global non-equilibrium, entropy of mixing, and free enthalpy of mixing [ 70 ].…”