Enhancement to the traditional ellipse law for more accurate modelling of a turbine with a finite number of stages

[+] Author and Article Information
W.F. Fuls

Eskom Power Plant Engineering Institute: Specialization in Energy Efficiency Department of Mechanical Engineering University of Cape Town Private Bag X3 Rondebosch Cape Town 7701 South Africa

1Corresponding author.

ASME doi:10.1115/1.4037097 History: Received January 09, 2017; Revised June 11, 2017


This paper studies the origin and applicability of the traditional Stodola ellipse law, and demonstrates it deficiencies when applied in certain conditions. It extends the equation by Cooke and Traupel through the definition a semi-ellipse law. This new law produces more accurate results as compared to the ellipse law, especially for turbines with a low number of stages. It does however require knowledge of the choking behavior of the turbine, as well as an appropriate pressure ratio exponent. Through numerical studies and the careful application of nozzle flow equations, correlations were developed to predict the critical pressure ratio of a multi-stage turbine, taking nozzle and blade efficiency into account. Correlations are also presented to obtain an appropriate pressure ratio exponent to use in the semi-ellipse law. A methodology is proposed through which the necessary semi-ellipse law terms can be calculated using only design base conditions, and estimates of efficiencies. This was successfully validated on a steam turbine. The semi-ellipse law is believed to be the most accurate way of modelling an axial-flow multi-stage steam or gas turbine from design base conditions, without requiring a stage-by-stage analysis.

Copyright (c) 2017 by ASME
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