Laminar Boundary Layer on a Finite Disk in a Rotating Compressible Isothermal Flow

Abstract

An improved momentum integral method for the solution of shrouded rotating disk problems is presented. The method admits compressibility and accounts for the radial variation of the velocity profiles within the boundary layer, to reproduce the correct asymptotic behavior. For the incompressible case, the integral solution is in agreement with an exact numerical solution of the boundary layer equations. Compressibility effects, controlled by the azimuthal Mach number of the outer flow, are shown to increase the boundary layer thickness and the axial velocity at the edge of the boundary layer and to decrease its radial mass flux. The method of solution can be applied to the solution of the interaction between an outer rotating flow—not necessarily rigid body like—and the boundary layer on a finite rotating disk in closed configurations.