Cylindrical Couette flow with fixed outer cylinder: Rarefied effects

Abstract

We consider the rarefied cylindrical Couette flow. The inner cylinder rotates at the constant angular velocity and the outer cylinder is at rest. We investigate the momentum and energy fluxes transferred to the cylinders and show that this flow is fundamentally different from the rarefied Couette flow with the fixed inner cylinder. For the free molecular mode, we derive the explicit analytical expressions for the fluxes. We find that momentum and energy fluxes transferred to the inner cylinder have a maximum with respect to the ratio of radii. The influence of the rarefaction on the energy and momentum transfer in the transitional regime is studied using the direct simulation Monte Carlo method. The shear stress and energy flux transferred to the inner cylinder increase with an increase in the angular velocity of the inner cylinder rather than tend to zero at high velocities, as in the Couette flow with the fixed inner cylinder with an increase in the angular velocity of the outer cylinder. In the transitional mode, for the flow with the fixed outer cylinder, the absolute value of the normal momentum flux transferred to the inner cylinder has a minimum as a function of the angular velocity of the inner cylinder. On the other hand, in the Couette flow with the fixed inner cylinder, this flux tends to zero at high angular velocities of the outer cylinder. The fundamental difference between these two flows at high velocities is associated with the degree of influence of dissipation on the flows.