Compressibility and rarefaction effect on pressure drop in rough microchannels

A numerical analysis of the flow field in rough microchannel is carried out with a finite volume compressible solver, including generalized Maxwell slip flow boundary conditions suitable for arbitrary geometries. Roughness geometry is modeled as a series of triangular obstructions. The relative roughness from 0% to 2.65% was considered. Because for truly compressible flow we have no fully developed flow condition, the simulation is performed over the whole length of the channel. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions. Flow conditions with a Reynolds number up to around 200 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from a very low value to 0.0249. Performance charts are presented in terms of both average and local Poiseuille number as a function of local Knudsen, Mach, and Reynolds numbers. In particular, it appears that roughness strongly decreases the reduction in pressure loss due to rarefaction. Thus, the roughness effect is stronger at a high Knudsen. Furthermore, the compressibility effect has a major effect on pressure drop when the local Mach number exceeds 0.3.