Numerical investigation of thermally generated gas flow between saw-tooth like surfaces

Abstract

The two-dimensional thermally generated gas flow between two saw-tooth like surfaces is numerically investigated using the kinetic approach based on the S-model of the Boltzmann kinetic equation. An implicit scheme for the solution of the S-model kinetic equation is applied and the algorithm is optimized for the use of massive parallelization in both physical and velocity spaces. Both surfaces are assumed to be isothermal and kept at different temperatures. Top peaks are shifted with respected to bottom peaks in the x-direction. The perpendicular to surfaces temperature gradient and the asymmetric distribution of saw tooth along surfaces may lead to an occurrence of temperature gradients tangential to surfaces causing a thermal creep flow in the x-direction. The rarefaction effect on the thermal transportation flow is estimated by varying Knudsen number from 0.02 to 40, i.e. covering slip, transition and free-molecular regimes. The influence of the surface geometry, such as the distribution of top and bottom peaks, the inclination angle of saw-tooth structure, on flow is analyzed. It is found that rarefaction, as well as geometry configuration, have a crucial effect on the occurrence and strength of gas flow.