Efficient DSBGK simulations of the low speed thermal transpiration gas flows through micro-channels

Low speed thermal transpiration gas flows through micro-channels are simulated by the direct simulation BGK (DSBGK) method that is based on the Bhatnagar-Gross-Krook model equation. Different from the ordinary application of BGK equation having the viscosity matched, we selected its relaxation time according to the thermal conductivity coefficient and thus significantly improved the accuracy. In comparing the detailed flow field solutions of a 2D Knudsen pump, the validation by the standard direct simulation Monte Carlo (DSMC) method shows that the improved BGK equation has about the same accuracy as the Shakhov equation that is solved by the well-developed gas kinetic unified algorithm (GKUA). We also present the ordinary application of BGK equation with noticeable error to clearly show the difference made in our study. Then, the efficient DSBGK method is applied to simulate the low-speed rarefied gas flows in 3D real-size thermal transpiration problem to show its applicability and its validity is verified by comparing with the experimental measurement of mass flow rates. The DSBGK simulation results have excellent agreement with experimental data for three types of gases over a wide range of Knudsen number. Additionally, the channel end effect is also studied and discussed as a prerequisite for high-fidelity modeling, otherwise it will be mistakenly interpreted as the variation of accommodation coefficients of the molecular reflection process on the solid boundary.