Theoretical and numerical studies of two rarefied gas flow problems.

摘要

This work analyzes two rarefied gas flow problems: rarefied plume impingement on a flat plate, and compressible gaseous slip flow through a straight three-dimensional microchannel with a uniform rectangular cross-section. For both problems, due to the rarefication effects we must use non-traditional analysis methods. The first problem analyzes rarefied jet flows impinging on a flat plate. In this work, we investigate three cases of rarefied jet gas flows and impinging on a flat plate with a gaskinetic method: 1). two dimensional nozzle, 2). three dimensional round jet and 3). three dimensional annular jet. With a relation between velocity-directions and geometry-positions, we obtain the corresponding analytical solutions of free plume pressure, temperature, shear stress and heat flux. Then we obtain several sets of analytical solutions for the density, slip velocity, temperature, pressure, shear stress and heat flux on locations very close or right on the flat plate. Numerical simulation results obtained with the direct simulation Monte Carlo Method (DSMC) validate these analytical solutions. In general, the comparisons between the complex exact analytical solutions and the numerical results are virtually identical. The second problem is compressible gaseous slip flow through a straight three-dimensional microchannel with a uniform rectangular cross-section, we report a complete set of first order asymptotic solutions. By comparing the magnitudes of different forces in the compressible gas flow, we obtain proper estimations for Reynolds and Mach numbers at the channel exit. Based on these estimations, we obtain asymptotic analytical solutions of velocities, pressure, and mass flow rate inside the microchannel with a relaxation of the isothermal assumption, which was previously used by many researchers. Detailed solutions with first order and second order velocity slip boundary conditions and no-slip boundary conditions are examined in this work. Numerical simulations of compressible flows through microchannels with the direct simulation Monte Carlo Method are performed and the results are compared with the asymptotic solutions. We further compare our results with the available numerical and experimental results in the literature.