Kazuo Aoki (Dept Mechanical Eng. Kyoto) - Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas

The Taylor-vortex flow between two coaxial cylinders rotating at different angular velocities is one of the most fundamental problems in fluid dynamics. In particular, for an incompressible fluid, it is a classical problem that has been investigated extensively. As for a rarefied gas, its study is relatively recent, and some results based on the DSMC method have been reported for the Knudsen numbers (i.e., the mean free path of the gas molecules divided by the characteristic length) of the order of 0.01 and 0.001. However, because of the increase of the computational load, there are few studies of detailed flow structure for small Knudsen numbers. Therefore, the behavior of the flow field when the Knudsen number approaches zero has not been fully understood. In the present study, we revisit this problem with special interest in the structure of the flow field and the magnitude of the velocity slip in the near continuum regime. We investigate it numerically using the DSMC method as well as the compressible Navier-Stokes equations with the correct slip boundary conditions.

The numerical results show that the flow field exhibits a boundary-layer structure as the Knudsen number becomes small. It is also observed that, once the boundary-layer structure is formed, the velocity slip of the circumferential velocity component on the cylinders becomes larger than that of the corresponding cylindrical Couette flow.

This is a joint work with Ryo Kagaya, Shingo Kosuge, and Hiroaki Yoshida.