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.

A theory of Tesla disc turbines

“…Solutions are mainly available for incompressible flows although there are some papers containing solutions for compressible flows. 15,16…”

“…Solutions are mainly available for incompressible flows although there are some papers containing solutions for compressible flows. 15,16 Currently the field of micro-turbine is an active research area; the bladeless Tesla turbine because of its simplicity and robustness of structure, low cost and comparatively better operation at high rpm may become a suitable candidate for this application. For this to happen the efficiency of the Tesla turbine, however, has to be improved.…”

Effect of nozzle angle, turbine inlets and mass flow rate on the performance of a bladeless turbine

“…Performance of tesla turbines has been characterized by researchers using analytical models and scarcely through experiments. Both laminar 14–17 and turbulent approaches 18–20 have been reported to model flow in tesla turbines, mostly for the incompressible regime, while compressible modeling was presented in Truman et al. 16 Rice 5 used an overall friction factor to model the viscosity effects.…”