Computations of Gas Microflows Using Pressure Correction Method with Langmuir Slip Model

Abstract

A Langmuir slip model combined with continuum-based compressible Navier–Stokes equations is proposed and implemented for the purpose of analyzing complex microscale gas flows. For our model, an efficient compressible pressure correction algorithm based on an unstructured grid is developed and modified to be applicable to low Reynolds number slip flows in microgeometries. Gaseous slip flows in a uniform microchannel and compressible flow at backward-facing step are computed for the assessment of the adequacy of the method. Separated flow in a T-shaped micro-manifold is also simulated for the Reynolds number ranging from 10 to 60. In the uniform microchannel flow, the pressure increases nonlinearly in Langmuir slip model as the Knudsen number increases, while it drops nonlinearly in Maxwell slip model. The results from Langmuir slip model have been found to be more compatible with physics. From all the simulation cases, nonlinear behavior owing to both compressibility and rarefaction clearly appears in terms of streamwise velocity, pressure profiles and even reattachment length in the separation-associated flows. These results show that the suggested pressure correction method along with the Langmuir slip model may effectively simulate complex microscale gas flows, thereby offering a sound theoretical and numerical basis and an inexpensive computation procedure.