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

• Published in: Renewable energy Vol. 169; pp. 1210 - 1228
• Main Authors: Krzemianowski, Zbigniew, Steller, Janusz
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2021
• Subjects: algorithms; Cavitation; computer software; Curvilinear coordinate system; development projects; fluid mechanics; geometry; High specific speed francis turbine; Inverse problem in fluid mechanics; isogenic lines; Model tests; momentum; renewable energy sources; research and development; Runner blade optimization using CFD analysis; streams; Model tests; Inverse problem in fluid mechanics; Curvilinear coordinate system; Runner blade optimization using CFD analysis; Cavitation; High specific speed francis turbine
• ISSN: 0960-1481
• DOI: 10.1016/j.renene.2021.01.095

The paper is a result of a research and development project aimed at developing a series of types of high specific speed (90 < nsQ < 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. •A high specific speed Francis turbine is proposed for some applications.•Genetic algorithm is used to optimize a Francis runner blade.•VLM and inverse problem method is used to design initial shape of runner blade.•A high specific speed runner with high efficiency has been developed.•Multi-aspect experimental approach is used to derive the permissible Thoma number.