A theory of Tesla disc turbines

Abstract

In the present article, a mathematical theory for the flow field within a Tesla disc turbine has been formulated in the appropriate cylindrical co-ordinate system. The basis of the theory is the Navier–Stokes equations simplified by a systematic order of magnitude analysis. The presented theory can compute three-dimensional variation of the radial velocity, tangential velocity and pressure of the fluid in the flow passages within the rotating discs. Differential equations as well as closed-form analytical relations are derived. The present mathematical theory can predict torque, power output and efficiency over a wide range of rotational speed of the rotor, in good agreement with recently published experimental data. The performance of the turbine is characterized by conceptualizing the variation of load through the non-dimensional ratio of the absolute tangential velocity of the jet and the peripheral speed of the rotor. The mathematical model developed here is a simple but effective method of predicting the performance of a Tesla disc turbine along with the three-dimensional flowfield within its range of applicability. A hypothesis is also presented that it may be possible to exploit the effects of intelligently designed and manufactured surface roughness elements to enhance the performance of a Tesla disc turbine.