Continuum and DSMC Modeling of Microscale Plane Poiseuille Gas Flows

摘要

This paper derives analytical solutions for the plane Poiseuille flow of a dilute gas based on the continuum theory with three molecular models, including hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS). Computations are conducted by the method of Direct Simulation Monte Carlo (DSMC), with and without Larsen-Borgnakke (L-B) procedures for these three models. The present results compare the performance of various molecular models and provide insights for further understanding of the rarefaction effects on flow characteristics. It is found that for the marginal case of continuum, i.e. Kn = 0.01, the present analytical solutions and DSMC simulations with various molecular models are in reasonable agreement in the velocity and temperature distributions. Comparing the analytic and DSMC solution, the models with L-B procedures yield results with relatively lower values than those of the other cases in temperature distribution, and the deviation may be enlarged with an increase in Kn. For Kn up to 0.1, the discrepancies between analytical and DSMC results of temperature and pressure fields become more noticeable, qualitatively as well as quantitatively.