Mixed-flow vertical tubular hydraulic turbine: determination of proper design duty point

Abstract

A new vertical single-regulated mixed-flow turbine with conical guide apparatus and without spiral casing is presented in this paper. Runner blades are fixed to the hub and runner band and resemble to the Francis type runner of extremely high specific speed. Due to lack of information and guidelines for the design of a new turbine, a theoretical model was developed in order to determinate the design duty point, i.e. to determine the optimum narrow operation range of the turbine. It is not necessary to know the kinematic conditions at the runner inlet, but only general information on the geometry of turbine flow-passage, meridional contour of the runner and blading, the number of blades and the turbine speed of rotation. The model is based on the integral tangential lift coefficient, which is the average value over the entire runner blading. The results are calculated for the lift coefficient 0.5 and 0.6, for the flow coefficient range from 0.2 to 0.36, for the number of the blades between 5 and 13, and are finally presented in the Cordier diagram (specific speed vs. specific diameter). Calculated results of the turbine optimum operation in Cordier diagram correspond very well to the adequate area of Kaplan turbines with medium and low specific speed and extends into the area of Francis turbines with high specific speed. Presented model clearly highlights the parameters that affect specific load of the runner blade row and therefore the optimum turbine operation (discharge—turbine head). The presented method is not limited to a specific reaction type of the hydraulic turbine. The method can therefore be applied to a wide range from mixed-flow (radial-axial) turbines to the axial turbines. Applicability of the method may be considered as a tool in the first stage of the turbine design i.e. when designing the meridional geometry and selecting the number of blades according to calculated operating point. Geometric and energy parameters are generally defined to an extent that these parameters are considered in detailed design using turbulent viscous flow CFD solver.