Viscous drag in steady state gas flow between rotating cylinders

Abstract

The viscous drag (wall shear-stress) exerted at the interface "gas-rotating cylinder wall" is numerically studied by using the Direct Simulation Monte Carlo (DSMC) method and the continuum model based on the Navier-Stokes-Fourier (NSF) equations for simulation of the cylindrical rarefied gas flow between two concentric cylinders with one of them rotating with a constant velocity and the other being at rest. Different cases were calculated for a set of velocities of rotating inner cylinder and another set for rotating outer one. These studies have been accomplished for several fixed Knudsen numbers. The NSF results have been obtained by setting a local value of Knudsen number in the corresponding first order slip boundary conditions. For the near planar case a typical averaged Knudsen number has been used. The fact of hydrodynamic self-similarity in steady state cylindrical Couette flow is investigated and confirmed. The flow characteristics obtained by both methods are: in an excellent agreement at small Knudsen numbers 0.02 and 0.05 and in a satisfactory agreement at 0.1 and 0.5. The work may be of interest to the analysis of various non-planar micro gas flows.