Transient heat transfer in a rarefied binary gas mixture confined between parallel plates due to a sudden small change of wall temperatures

Transient behavior of the heat transfer through binary gas mixture, confined between two infinite parallel plates, caused by the sudden change of the plates’ temperatures, is studied for two monoatomic gas mixtures: Ne–Ar and He–Ar. The walls’ temperature changes are considered small compared to the equilibrium temperature of the system, so the McCormack kinetic model is used for the numerical simulations. The time evolution of the main macroscopic parameter is investigated for various species concentrations and for different gas rarefactions ranging from near the free molecular to slip flow regime. It is found that the mixture heat flux takes several characteristic times, which is defined by the distance between the plates over the most probable molecular speed, to achieve its new equilibrium state. This time of the steady state flow establishment depends strongly on the gas rarefaction, mixture nature and composition

Unsteady heat transfer in a gas mixture

The time-dependent problem of heat transfer between two parallel plates in a binary gas mixture was investigated on the basis of numerical solution of BGK type kinetic model equation with collision integral taken in the form of McCormack model. The time evolution of the normal heat flux was simulated and time needed to reach the steady state conditions was obtained

GSIS: An efficient and accurate numerical method to obtain the apparent gas permeability of porous media

The apparent gas permeability (AGP) of a porous medium is an important parameter to predict production of unconventional gas. The Klinkenberg correlation, which states that the ratio of the AGP to the intrinsic permeability is approximately a linear function of reciprocal mean gas pressure, is one of the most popular estimations to quantify AGP. However, due to the difficulty in defining the characteristic flow length in complex porous media where the rarefied gas flow is multiscale, the slope in the Klinkenberg correlation varies significantly for different geometries such that a universal expression seems impossible. In this paper, by solving the gas kinetic equation using the general synthetic iterative scheme (GSIS), we compute the AGP in porous media that are represented by Sierpinski fractals and pore body/throat systems. With the abilities of fast convergence to steady-state solution and asymptotic preserving of Navier-Stokes limit, it is shown that GSIS is a promising tool to simulate low-speed rarefied gas flow through complex multiscale geometries. A new definition of the characteristic flow length is proposed as a function of porosity, tortuosity and intrinsic permeability of porous media, which enables to find a unique slope in the Klinkenberg correlation for all the considered geometries. This research also shows that the lattice Boltzmann method using simple wall scaling for the effective shear viscosity is not able to predict the AGP of porous media

A comparative study of discrete velocity methods for low-speed rarefied gas flows

In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. Although various versions of DVM have been developed, their performance, in terms of modeling accuracy and computational efficiency, is yet to be comprehensively studied in all the flow regimes. Here, the traditional third-order time-implicit Godunov DVM (GDVM) and the recently developed discrete unified gas-kinetic scheme (DUGKS) are analysed in finding steady-state solutions of the low-speed force-driven Poiseuille and lid-driven cavity flows. With the molecular collision and free streaming being treated simultaneously, the DUGKS preserves the second-order accuracy in the spatial and temporal discretizations in all flow regimes. Towards the hydrodynamic flow regime, not only is the DUGKS faster than the GDVM when using the same spatial mesh, but also requires less spatial resolution than that of the GDVM to achieve the same numerical accuracy. From the slip to free molecular flow regimes, however, the DUGKS is slower than the GDVM, due to the complicated flux evaluation and the restrictive time step which is smaller than the maximum effective time step of the GDVM. Therefore, the DUGKS is preferable for problems involving different flow regimes, particularly when the hydrodynamic flow regime is dominant. For highly rarefied gas flows, if the steady-state solution is mainly concerned, the implicit GDVM, which can boost the convergence significantly, is a better choice

A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows

Low-speed rarefied gas flow in a lid-driven cavity is chosen as a test case in order to assess the accuracy and efficiency of both the Direct Simulation Bhatnagar-Gross-Krook (DSBGK) method and the Discrete Velocity Method (DVM) for solving the BGK kinetic equation. Various lid-speeds and a broad range of rarefaction levels, from slip to near free-molecular flows, are investigated. The DSBGK and DVM results are in satisfactory agreement for all the examined cases in 2D and 3D. As a statistical method, the stochastic noise of the DSBGK method is much smaller than that of the conventional Direct Simulation Monte Carlo (DSMC) method, and is independent of the Mach number. To achieve the required accuracy, the DSBGK simulations need more CPU time than the DVM simulations, i.e. for the 2D cases, a factor of 2 to 15 times more for convergence, and about 50 to 80 times more overall, including the time-averaging process. However, for 3D cases, the third direction in the DVM velocity grid is needed, so the computational cost of DSBGK is now only 0.16 to 0.51 times that of the DVM for the convergence process, and 1.6 to 5.8 times that of the DVM overall. The efficiency of the DSBGK method can also be expected to be enhanced in large-scale 3D simulations, where the computational cost for time-averaging becomes negligible in comparison with the convergence process. The DSBGK simulations require much less memory, even at low Mach numbers, than the DVM simulations; in the test cases with the required accuracy, about 10 simulated molecules per cell in the DSBGK simulations are sufficient for an arbitrary Kn, while the DVM requires at least 4 × 24 and 4 × 24 × 12 velocity grids for the 2D and 3D cases, respectively, even at Kn=0.1. Finally, we discuss the ray effects in the DVM, which exist in flow problems with a discontinuous boundary and are caused by incompatibility of the velocity grid, the spatial grid, and the order of accuracy of the numerical scheme