Slow Rarefied Gas Flow Past a Cylinder: Analytical Solution in Comparison to the Sphere

摘要

In the variety of approaches to tackle the challenges of rarefied gas flows, the regularized 13-moment equations (R13) have become a very promising contender. The equations are based on moment approximations in kinetic gas theory which can be interpreted as a non-linear discretization of the Boltzmann equation in the velocity space. In order to get a deeper insight into rarefaction effects, an analytic solution for the flow around a sphere has been constructed in [M.Torrilhon, Phys. Fluids. 22, 072001:1-16 (2010)]. In the present work, an analytic solution for the flow past a cylinder is derived, which is another very important text book problem. Again, the investigation is restricted to slow flows (Ma 1), which means a linearized system of the original R13 equations is analyzed. The results for the sphere and the cylinder are then compared and typical rarefaction effects are pointed out.