Viscosity, heat conductivity, and Prandtl number effects in the Rayleigh–Taylor Instability

et al. 2017

Phys. Rev. E

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

Lin

et al. 2017

Phys. Rev. E

Discrete ellipsoidal statistical BGK model and Burnett equations

et al. 2018

Front. Phys.

Self Cite

A new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed to simulate non-equilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in Burnett level, two kinds of discrete velocity model are introduced; the relations between non-equilibrium quantities and the viscous stress and heat flux in Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, based on the Navier-Stokes, the Burnett equations, etc.Key words: discrete Boltzmann model, ellipsoidal statistical BGK, Burnett equations, non-equilibrium quantities, actual distribution function. boundary conditions), but it fails to provide the correct viscous stress and heat flux in transitional regime. The reason for the inapplicability of NS equations in transitional flow is that the constitutive equations, i.e. Newton's viscosity law and the Fourier heat conduction law, are assumed to be linear which is inapposite when the non-equilibrium (or rarefaction) effect is significant. The Burnett equations [3,6], which are obtained from the Boltzmann equation through Chapman-Enskog (CE) expansion, have a modified constitutive equations and can work in part of the transition flow zones. However, the Burnett equations often encounter numerical instabilities because of the high order derivatives in the viscosity and heat flux terms [6].It has been known that Boltzmann equation is applicable for all of the four flow regimes mentioned above. Unfortunately, the original Boltzmann equation is too complicated to be solved directly [7]. The multidimensional nature of distribution function and collision operator pose a great challenge for its numerical solution. Realistic numerical computations of the Boltzmann equation are based on probabilistic methods, such as direct simulation Monte Carlo (DSMC) method[8], or deterministic fast numerical methods, such as fast spectral method (FSM) [7]. In general, however, the computation cost is still too expensive for the direct solution of the Boltzmann equation. So, a variety of simplified methods have been developed to approximate the solution of the Boltzmann equation, such as the unified gas-kinetic scheme(UGKS)[9,10], the discrete velocity method (DVM) [11], the discrete unified gas-kinetic scheme (DUGKS) [12,13], the lattice Boltzmann method (LBM) [14][15][16][17][18], and the discrete Boltzmann method(DBM) [19][20][21].Recently, DBM has been developed as a non-equilibrium flow simulation tool and has been widely used in various flow conditions including high speed compressible flow, multiphase flow [22], flow instability [23][24], combustion and detonation [25][26], etc. Besides the values and evolutions of conserved kineti...

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

Gan

et al. 2019

Front. Phys.

Self Cite

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.