Analytical and computational solutions for three-dimensional flow-field and relative pathlines for the rotating flow in a Tesla disc turbine

Abstract

The three-dimensional flow field and the flow pathlines within a Tesla disc turbine have been investigated analytically and computationally. The description of the flow field includes the three-dimensional variation of the radial velocity, tangential velocity and pressure of the fluid in the flow passages within the rotating discs. A detailed comparison between the results obtained from the analytical theory and computational fluid dynamic (CFD) solutions of Navier–Stokes equations is presented in order to establish the reliability of the simplified mathematical model. The present work reveals the dependence of the shape, size and orientation of the pathlines on various operating parameters (such as tangential speed ratio, radial pressure drop, inlet nozzle angle, and position of the exit) and local balance of various forces (viz. inertial, viscous, centrifugal and Coriolis). The relative merits of two possible ways of representing the pathlines in the absolute and relative frame of reference are discussed that provide physical understanding of subtle flow features.