Influence of Knudsen and Mach numbers on Kelvin-Helmholtz instability (original) (raw)
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Entropy, 2020
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 sid...
Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients
2010
A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate gamma\gammagamma for the KHI decreases with increasing the width of velocity transition layer Dv{D_{v}}Dv but increases with increasing the width of density transition layer Drho{D_{\rho}}Drho. After the initial transient period and before the vortex has been well formed, the linear growth rates, gammav\gamma_vgammav and gammarho\gamma_{\rho}gammarho, vary with Dv{D_{v}}Dv and Drho{D_{\rho}}Drho approximately in the following way, lngammav=a−bDv\ln\gamma_{v}=a-bD_{v}lngammav=a−bDv and gammarho=c+elnDrho(Drho<DrhoE)\gamma_{\rho}=c+e\ln D_{\rho} ({D_{\rho}}<{D_{\rho}^{E}})gammarho=c+elnDrho(Drho<DrhoE), where aaa, bbb, ccc and eee are fitting parameters and DrhoE{D_{\rho}^{E}}DrhoE is the effective interaction width of density transition layer. When Drho>DrhoE{D_{\rho}}>{D_{\rho}^{E}}Drho>DrhoE the linear growth rate gammarho\gamma_{\rho}gammarho does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma \textbf{17}, 042103 (2010)].
An in-house, fully parallel compressible Navier-Stokes solver was developed based on an implicit, non-dissipative, energy conserving, finite-volume algorithm. PETSc software was utilized for this purpose. To be able to handle occasional instances of slow convergence due to possible oscillating pressure corrections on successive iterations in time, a fixing procedure was adopted. To demonstrate the algorithms ability to evolve a linear perturbation into nonlinear hydrodynamic turbulence, temporal Kelvin-Helmholtz Instability problem is studied. KHI occurs when a perturbation is introduced into a system with a velocity shear. The theory can be used to predict the onset of instability and transition to turbulence in fluids moving at various speeds. In this study, growth rate of the instability was compared to predictions from linear theory using a single mode perturbation in the linear regime. Effect of various factors on growth rate was also discussed. Compressible KHI is most unstable in subsonic/transonic regime. High Reynolds number (low viscosity) allows perturbations to develop easily, in consistent with the nature of KHI. Higher wave numbers (shorter wavelengths) also grow faster. These results match with the findings of stability analysis, as well as other results presented in the literature.