Higher-order Knudsen's permeability correction model for rarefied gas in micro-scale channels

Abstract

Rarefaction effect appears when gas flows in micro/nano channels, so it is difficult to accurately predict real gas flow rate by using the classical theory. It is necessary to establish a more accurate and universal permeability correction model to describe the flow behavior of rarefied gas. In this work, the gas flow in a plate micro-scale channel was numerically simulated using R26 moment method, and the simulation results were compared with those of the direct simulation Monte Carlo method (DSMC method) and R13 moment method. Then, a gas permeability correction model for plate micro-scale channels and circular micro-scale channels was established based on the simulation results of the R26 moment method, and used to describe the flow behavior of rarefied gas in micro-scale channels. Finally, the gas permeability correction coefficient for different Knudsen numbers was calculated and compared with the prediction results of the Tang model, the available experimental data and the solution of linearized Boltzmann equation. The following research results were obtained. First, when the R26 moment method is used to describe the rarefaction effect of gas, its result is accordant with the calculation result of the DSMC method, and its calculation accuracy is higher than that of R13 moment method. Second, the gas permeability correction coefficient which is calculated by using the higher-order Knudsen's gas permeability correction model for plate micro-scale channels is in accordance with the experimental data and the solution of linearized Boltzmann equation. Third, the gas permeability correction coefficient which is calculated by using the higher-order Knudsen's gas permeability correction model for circular micro-scale channels is accordant with the solution of linearized Boltzmann equation. In conclusion, this higher-order Knudsen's gas permeability correction model is advantageous with high prediction precision and universality, and it can be used to describe the rarefaction effect of gas in micro/nano-scale channels.