Numerical modeling of three-dimensional compressible gas flow in microchannnels

Abstract

Nitrogen gas flow in long microchannels with square cross-sections was simulated numerically with a three-dimensional continuum model with slip and no-slip boundary conditions. The governing equations of the model were solved by a control volume method. The numerical model was validated with the available experimental and numerical results. For incompressible flow, it was found that when Dh was less than 60 µm, a slip boundary condition must be applied. An analytical expression for normalized friction coefficients, C*IC, i.e. the ratio of f Re (slip) to f Re (no-slip), was developed on the basis of incompressible flow behavior. For compressible flow, a parametric study was conducted for Dh = 1 µm, L/Dh = 200 and with varying pressure ratios (PR = 1.5–5.0). It was found that as the pressure ratio increased from 1.5 to 5.0, compressibility effects increased while the rarefaction effects started diminishing. Slip effects also played an important role in the friction characteristics of microchannel flows. An analytical expression for normalized friction coefficients, C*C, i.e. the ratio of f Re (compressible) to f Re (incompressible), was developed on the basis of flow behavior for compressible flow. A comparative study of two-dimensional and three-dimensional flows was also conducted, and it was shown that the two-dimensional assumption for the compressible flow was not valid since it predicted 15–45% higher flow velocities, and 7–12% lower friction factors than those predicted by the 3D models.