Kinetic analysis of surface roughness in a microchannel

• Compressible gas flow in a rough channel with triangular obstructions is modeled.
• The implicit scheme for the solution of the S-model equation is applied.
• Wide ranges of Mach and Knudsen numbers are considered.
• The effects of surface roughness, rarefaction and compressibility are discussed.

A flow field numerical simulation was performed for a 2D compressible gas flow through a rough microchannel using the kinetic S-model equation with the Maxwell diffuse reflecting boundary condition at the solid wall. The implicit scheme for the solution of the S-model equation was applied and the algorithm using massive parallelization in both physical and velocities spaces has been optimized. The roughness geometry is modeled as a series of triangular obstructions with the relative roughness ∊ equals to 1.25%, 2.5% and 5%. Wide ranges of Mach and Knudsen numbers were considered. Obtained results are compared with existing expressions and available numerical results. It was found that the surface roughness has an important influence on friction factor. In particular, this effect becomes a more significant with the decrease of the Knudsen number. Compressible gas flow is also sensitive to the height of the wall roughness element. Nevertheless, for a high rarefied gas both compressibility and roughness effects become weak.