Flow Past a Micro-Sphere in a Pipe: Effects of Rarefaction

Abstract

Abstract The canonical problem of rarefied gas flow past a sphere in a pipe has been studied in a wide range of Knudsen number (Kn), covering the continuum, slip, and transitional flow regimes. The blockage effects are studied by varying the pipe to sphere diameter ratio H/D, as well as the Knudsen number. The numerical results in the continuum and slip flow regimes are obtained by ΝεκΤαr and μFlow, based on spectral element algorithms for incompressible continuum, and for compressible continuum/slip flows, respectively. The transitional flow regime is investigated by the code F3, based on the direct simulation Monte Carlo (DSMC) method of Bird. Our results show that the drag coefficient CD is inversely proportional to Kn, the Reynolds number Re and H/D. The blockage effects are shown to become negligible for high Knudsen number regime (Kn ≥ 3.5) even for small values of H/D. The sphere in a pipe configuration can be used in designing electro-magnetically driven micro-valve systems.