The fluid dynamics of the rotating flow in a Tesla disc turbine

The flow induced by rotating discs has attracted some of the greatest minds in fluid dynamics like von Kármán and Batchelor, and still is a vigorously active research area. In comparison, the available analysis of the rotating flow in the narrow gaps among closely-spaced co-axial multiple discs of a Tesla turbine, which produces power, is limited. In this paper a simple theory has been presented that describes the three-dimensional fields of velocity and pressure in the Tesla disc turbine. The theory gives the torque and power output which have been verified by comparing the theoretical predictions with recently published experimental results. The governing conservation equations have been cast in a form that makes it possible to formulate analytical solutions and to develop clear physical interpretation for each term in the equations. Thus the roles of each of the centrifugal, Coriolis, inertial and viscous forces in generating torque and power, and in establishing the pressure field have been comprehensively investigated and explained here. This physical exposition of the rotating flow in a Tesla disc turbine has been achieved for the first time in the present paper. Several subtle flow physics and fluid dynamic behaviors have been elucidated. As an example, it is shown here that a Tesla disc turbine may generate net torque and power even when the tangential fluid speed at the disc periphery is less than the local tangential speed of the disc. The subtle role of the Coriolis acceleration in establishing such flow conditions, which involve flow reversal and complex pathlines, has been explained.