Open AccessAnalysis and improvement of a mathematical turbine model
Author(s) -
A. F. Reines,
B. Svingen
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1608/1/012001
Subject(s) - generality , turbine , correctness , computer science , flow (mathematics) , mathematical model , francis turbine , point (geometry) , transient (computer programming) , turbulence , dissipation , control theory (sociology) , engineering , mathematics , mechanical engineering , algorithm , mechanics , psychology , statistics , psychotherapist , operating system , physics , geometry , control (management) , artificial intelligence , thermodynamics
A mathematical turbine model is necessary for dynamic and transient analysis of hydro power plants, also in the early stages of a project. Such models can be based on a first principles approach or on empirical data, many models are a combination. A first principles approach is practical when specific laboratory data are unavailable, for example in the design phase of a new plant. These models can easily be simplified and linearized without losing physical correctness or generality, even though accuracy may vary when applied to a specific system. The model studied in this work, was developed several years ago from the Euler turbine equation and the opening degree definition, and has later been modified and linearized for simple implementation into simulation software. The model captures losses for varying rotational speed quite well, but struggles to capture losses for varying flow rate. The hydraulic efficiency is over-predicted for flow far off the design point, because irreversible hydraulic loss phenomena such as 3D turbulence and dissipation are not inherently included in this 1D model. Empirical relations or Hill charts for exact fit to a measured turbine can be included, however generality is then lost. This paper analyzes and discusses the mathematical model compared to laboratory measurements, highlighting its performance in predicting the efficiency off best efficiency point (BEP). A mathematical improvement based on turbine data is presented and implemented for three specific Francis turbines. The possibility to generalize the procedure is also discussed.