Modeling of Thermal Transpiration Flows for Knudsen Compressor Optimization

Rarefied gas flows through two-dimensional finite length capillaries are studied numerically with the goal of performance optimization of a nanomembrane-based Knudsen compressor. Both density and temperature gradient driven flows are considered in a wide range of Knudsen numbers from 0.05 to 75. The length-to-height ratios from 5 to 30 were examined. Three different wall temperature distributions were considered, namely, linear, step-wise, and a non-monotonic profile typical for a radiantly heated Knudsen compressor membrane. The direct simulation Monte Carlo method was used for shorter channels, and a discrete ordinate method for the solution of the BGK model equation is utilized for a longer channel. The mechanism for the Knudsen minimum in flow conductance is quantitatively explained, the short channel end effects are characterized, and the sensitivity of the mass flow rate to a non-monotonic temperature distribution is shown.