A non-dimensional study of the flow through co-rotating discs and performance optimization of a Tesla disc turbine

Abstract

This article presents a systematic and comprehensive computational fluid dynamic study for co-rotating discs and, Tesla turbines, in which the full benefit of similitude and scaling is extracted by expressing the results and analyses in terms of carefully formulated non-dimensional numbers—five input parameters and three output parameters. The work formulates a systematic design methodology for the optimum selection of input parameters for the rotor of a Tesla disc turbine that would satisfy practical constraints and deliver high values of power and efficiency. Many subtle flow physics (e.g. the identification of dynamic similarity number, inlet tangential speed ratio and inlet flow angle as the three most important non-dimensional input parameters, the secondary role of aspect ratio as a separate quantity independent of dynamic similarity number, and, the variation in the four fundamental components of the radial pressure difference) are critically explained. The present study establishes, for the first time, that unlike the flow in a conventional turbomachine in which fluid friction plays only a detrimental role, fluid friction plays a dual role in a Tesla disc turbine—a detrimental role in increasing the radial pressure drop (thus tending to decrease the efficiency) and a beneficial role by providing the sole mechanism for power production. This dual role is comprehensively analyzed and quantified in this work. The balance between this dual role of fluid friction gives rise to the optimum values of dynamic similarity number and inlet tangential speed ratio that maximize efficiency.