Analytical and Numerical Solutions of the Rotor Flow in Tesla Turbines

Abstract

This paper summarises the numerical and theoretical studies of the incompressible, laminar airflow through a single flow passage of a blade-less radial turbine. Furthermore, it yields the numerical validation of the simplified theoretical model for incompressible rotor flows without the consideration of mechanical losses. It exposes the accuracy of the simplified, analytical performance prediction and flow field for a given geometry, which is based on an optimisation of performance by solving the simplified and incompressible Navier-Stokes-Equations in cylindrical coordinates. The influences of the dimensionless machine parameters on performance and efficiency are obtained from a theoretical analysis. The stream-lines of the bulk flow are derived by analytical means. The inflow conditions for maximum performance and efficiency are theoretically determined and later compared to laminar CFD. In order to quantify the error of the simplified theoretical analysis, different inflow conditions and their influences on shaft power and flow behavior are examined by means of CFD. The de-velopment of the axial velocity distribution at the inlet zone is compared to the one from the theoretical inflow assumption. The influences of Reynolds number and revolution speed on the velocity profiles are investigated. In addition to that, a compressible flow model is introduced. Numerical results are obtained  and compared to the incompressible solution. More-over, compressibility effects on turbine performance are derived.