Compressibility and Rarefaction Effects on Pressure Drop in Rough Microchannels

Abstract

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 shaped obstructions. Relative roughness from 0% to 2.65% were considered. Since 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 number is considered, from nearly incompressible to chocked flow conditions. Flow conditions with Reynolds number up to around 200 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from very low value to 0.0249. Performance charts are presented in terms of both average and local Poiseuille number as a function of local Kn, Ma and Re. In particular, it appears that roughness strongly decreases the reduction in pressure loss due to rarefaction. Thus, roughness effect is stronger at high Kn. Furthermore, compressibility effect has a major effect on pressure drop, as soon as local Mach number exceed 0.3.