New analytic solutions of the problem of gas flow in a casing with rotating disc

Abstract

We analyse the known approximate analytic solution of the problem of gas flow induced by the disc rotation inside a closed casing. It is shown that this solution is inapplicable because of the negative thickness of the boundary layer in the shaft neighborhood. Several new analytic solutions are obtained for the flow parameters inside the boundary layer of the casing motionless base. To reduce further the discrepancy between the analytic solution and the direct difference solution of three-dimensional Navier-Stokes equations it is proposed to account for the viscous friction force moment on the lateral casing wall. The consideration of this moment has improved considerably the accuracy of the approximate analytic solution. © 2009 Springer Berlin Heidelberg.