Laminar Compressible Flow Between Rotating Disks

Abstract

An integral method is used to obtain a solution for laminar flow of a compressible Newtonian fluid between rotating disks. The solution method is based on a Galerkin approach to the solution of the Navier-Stokes (radial, tangential, and axial momentum) equations, continuity, and on approximation of the energy equations. Four parameters are necessary to specify the flow: tangential inlet velocity, Reynolds number, a flowrate parameter, and Mach number of the disk tip. The solution is developed for turbine flow with uniform admission of the fluid at the outer boundary. The method can easily be extended to consider pump flow. Velocity profiles as well as turbine efficiencies are presented. Good agreement with published results for the incompressible regime is demonstrated. Short computational time and acceptable accuracy were obtained with a small number of terms in the velocity expansions.