High specific speed Francis turbine for small hydro purposes - Design methodology based on solving the inverse problem in fluid mechanics and the cavitation test experience

The paper is a result of a research and development project aimed at developing a series of types of high specific speed (90 < n(sQ) < 100) Francis turbines. The inverse flow analysis approach based on the hodograph theory has been employed in order to develop the blading geometry of quality high enough to minimize the subsequent CFD based optimization process. The three-dimensional turbine blades are developed on meridional stream surfaces determined using the VLM methodology. The mass and momentum conservation equations are written in a curvilinear coordinate system, which is adjusted to the streamlines by means of the Christoffel symbols. The solution is found using the method of characteristics. The developed geometry is optimized by means of the genetic algorithm implemented in CFD software. Model tests were conducted in the Institute of Fluid-Flow Machinery of the Polish Academy of Sciences. Satisfactory coincidence between design assumptions, the CFD based performance assessments and those based on the model test results attained, shows reliability of the methodology adopted. Critical cavitation numbers as established according to different criteria have been applied to plot the sigma permissible isolines on top of the efficiency hill diagram. Physical interpretation of some irregularities in diagnostic characteristics is provided. (C) 2021 Elsevier Ltd. All rights reserved.