Analytical and numerical study of gas flow in a casing with a rotating disk

Abstract

The known approximate analytic solution to the problem of gas flow induced by the disc rotation inside a closed casing ia analyzed. It is shown that this solution is inapplicable because of a negative thickness of the boundary layer near the shaft. Several new analytic solutions are obtained for the flow parameters inside the boundary layer of the casing motionless base. To further reduce the discrepancy between the analytic solution and the direct difference solution to the three-dimensional Navier-Stokes equations, it is proposed to account for the viscous friction force moment on the lateral wall of the casing. The consideration of this moment considerably improves the accuracy of the approximate analytic solution.