Nonlinear oscillatory fully-developed rarefied gas flow in plane geometry

Abstract

The nonlinear oscillatory fully developed rarefied gas flow between parallel plates due to an external harmonic force is investigated by the Direct Simulation Monte Carlo (DSMC) method in terms of the parameters characterizing the flow, namely, the gas rarefaction and oscillation parameters, and the force amplitude. The results are in dimensionless form and include the axial velocity, temperature, pressure, wall shear stress, and heat flow vector, as well as the flow rate, cycle-averaged wall shear stress, space-averaged axial heat flow, and pumping power. Even with large force amplitudes, all macroscopic distributions have a sinusoidal pattern with their fundamental frequency being the same with the driving frequency of the external force without the appearance of other harmonics, except of the axial heat flow where the nonlinearities are responsible for generating oscillatory motion containing several harmonics. Nonlinear effects are becoming more significant in highly rarefied flows and low oscillation frequencies. The temperature profile, including the bimodal shape encountered in steady-state flows in the continuum limit, strongly depends on the gas rarefaction and oscillation parameters. The DSMC results have been compared with the corresponding linear oscillatory results, available in the literature, to find out that at small and moderate external forces, the agreement between DSMC and linear flow rates is very good and always remain less than 10%, while at large external forces, the deviation in the flow rate amplitude reaches about 25%. The cycle-averaged oscillatory pumping power is not zero and smaller than the corresponding linear one, following the trend of the flow rates.