Numerical simulation of pulsed planar evaporation into background gas based on direct Monte Carlo simulation and solution of the BGK model kinetic equation

A numerical study of the planar gas expansion under pulsed evaporation into the background gas is carried out. The chosen conditions are typical for nanosecond laser deposition of thin films and nanostructure synthesis, with the saturated gas pressure at the surface of 5.4 MPa and the background pressure of 50 and 500 Pa. The problem is solved based on the direct simulation Monte Carlo method and direct numerical solution of the BGK model kinetic equation. A generally good agreement was obtained for all computed macroscopic quantities, with the exception of the higher density peak in the compressed layer and a wider shock front in the background gas for the BGK model.

Rarefied Poiseuille Flow in a Circular Tube

An isothermal rarefied gas flow through a long circular tube due to longitudinal pressure gradient (a three-dimensional Poiseuille problem) was studied using the linearized Bhatnagar-Gross-Krook model kinetic equation over the whole range of the Knudsen numbers covering both free molecular and hydrodynamic regimes. The solution of the model kinetic equation with the diffuse boundary condition is obtained by the collocation method. This approach is based on the Chebyshev polynomials and rational Chebyshev functions. Choosing the zeros of Chebyshev polynomials in the multivariate range of integration for the collocation points, we reduce this problem to a set of algebraic equations. Based on the proposed approach, we have calculated the mass and the heat fluxes through the tube. The obtained results have also been compared with other studies. The developed approach may also be applied to a more general class of problems of rarefied gas flows in microand nanotubes.

Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter δ, ratios of hotter to cooler surface temperatures T, and inner to outer radii ratio R. The results of S-model kinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T=1.1 and large radius ratios R≥0.5; however, for large temperature ratio, a pronounced disagreement is observed.