Analysis of fluid flow through micro-fluidic devices using characteristic-based-split procedure

Gas flow in micro-electro-mechanical systems can be considered as rarefied since the ratio of free molecular path length to the characteristic length of the device is high. It is possible to analyse these flows using a conventional Navier-Stokes solver with modified boundary conditions to account for temperature-jump and slip-velocity on solid walls. In this study, characteristic-based-split (CBS) algorithm is modified to account for slip-velocity and temperature-jump boundary conditions in order to perform compressible flow analysis for a micro sized geometry. The CBS algorithm is a split procedure which yields a unified solution method valid for both compressible and incompressible flows. To verify the modified CBS solver, straight micro channel and micro step duct geometries are selected as test cases. To reduce the size of the implicit part of the algorithm, pseudo-quadratic velocity/ linear pressure elements (pP2P1) are employed. The results obtained using CBS algorithm, are compared with other analytical and computational results available in the literature. It is shown that this implementation of the CBS algorithm is applicable and effective for micro gas flows. It is also shown that, increasing Knudsen number results in increased temperature-jump and slip-velocity. This effect, however, is limited, especially for high Mach number flows.