Master equation, design equations and runaway speed of the Kaplan turbine

Abstract

To make the Kaplan turbine technology comparable to both the Pelton and the Francis turbine, the master equation for the Kaplan turbine has been established by analyses similar to that-for the Francis turbine. The analysis begins with the descriptions of free vortex flows at the runner inlet and the swirl flow at the impeller exit. By considering the Euler equation for specific work and by further evaluating the most significant shock and swirling losses, the first and the second energy equations in the form of hydraulic efficiency were formulated. The master equation is then established by combining both energy equations. In addition, three design equations and a new design parameter are presented. The master equation relates the turbine hydromechanics to the geometrical design of both the runner and the guide-vane parameters. It enables the complete hydraulic characteristics of a given Kaplan turbine to be analytically and simply computed. A computation example demonstrates the functionality and applicability of the method. With the reconstructed master equation, the runaway speed of the Kaplan turbine and its dependence on the guide-vane setting can be easily and precisely computed. For bulb turbines with guide vanes directly ahead of the turbine runner in the same tube, all computations are also applicable using another equivalent control parameter.