Numerical study on thermal transpiration flows through a rectangular channel

Abstract: Gaseous thermal transpiration flows through a rectangular micro-channel are simulated by the direct simulation BGK (DSBGK) method. These flows are rarefied, within the slip and transitional flow regimes, which are beyond many traditional computational fluid dynamic simulation schemes, such as those based on the continuum flow assumption. The flows are very slow and thus many traditional particle simulation methods suffer large statistical noises. The adopted method is a combination of particle and gas kinetic methods and it can simulate micro-flows properly. The simulation results of mass flow rates have excellent agreement with experimental measurements. In another case of 2D channel, the DSBGK comparisons with the DSMC result and the solution of Shakhov equation are also in very good agreement. Another finding from this study is that numerical simulations by including two reservoirs at the channel ends lead to appreciable differences in simulation results of velocity and pressure distributions within the micro-channel. This is due to the inhaling and exhaling effects of reservoirs at the channel ends. Even though excluding those reservoirs may accelerate the simulations significantly by using a single channel in simulations, special attentions are needed because this treatment may over-simplify the problem, and some procedures and results may be questionable. One example is to determine the surface momentum accommodation coefficient by using analytical solution of the mass flow rate obtained in a single-channel problem without the confinement effect of reservoirs at the two ends.