This paper studies the origin and applicability of the traditional Stodola ellipse law and demonstrates its deficiencies when applied in certain conditions. It extends the equation by Cooke and Traupel through the definition of a semi-ellipse law. This new law produces more accurate results as compared to the ellipse law (EL), 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 careful application of nozzle flow equations, correlations were developed to predict the critical pressure ratio of a multistage 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 modeling an axial-flow multistage steam or gas turbine from design base conditions, without requiring a stage-by-stage analysis.
Skip Nav Destination
Article navigation
November 2017
Research-Article
Enhancement to the Traditional Ellipse Law for More Accurate Modeling of a Turbine With a Finite Number of Stages
W. F. Fuls
W. F. Fuls
Department of Mechanical Engineering,
Eskom Power Plant Engineering Institute:
Specialization in Energy Efficiency,
University of Cape Town,
Private Bag X3, Rondebosch,
Cape Town 7701, South Africa
e-mail: wim.fuls@uct.ac.za
Eskom Power Plant Engineering Institute:
Specialization in Energy Efficiency,
University of Cape Town,
Private Bag X3, Rondebosch,
Cape Town 7701, South Africa
e-mail: wim.fuls@uct.ac.za
Search for other works by this author on:
W. F. Fuls
Department of Mechanical Engineering,
Eskom Power Plant Engineering Institute:
Specialization in Energy Efficiency,
University of Cape Town,
Private Bag X3, Rondebosch,
Cape Town 7701, South Africa
e-mail: wim.fuls@uct.ac.za
Eskom Power Plant Engineering Institute:
Specialization in Energy Efficiency,
University of Cape Town,
Private Bag X3, Rondebosch,
Cape Town 7701, South Africa
e-mail: wim.fuls@uct.ac.za
Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 9, 2017; final manuscript received June 11, 2017; published online July 19, 2017. Assoc. Editor: Klaus Dobbeling.
J. Eng. Gas Turbines Power. Nov 2017, 139(11): 112603 (12 pages)
Published Online: July 19, 2017
Article history
Received:
January 9, 2017
Revised:
June 11, 2017
Citation
Fuls, W. F. (July 19, 2017). "Enhancement to the Traditional Ellipse Law for More Accurate Modeling of a Turbine With a Finite Number of Stages." ASME. J. Eng. Gas Turbines Power. November 2017; 139(11): 112603. https://doi.org/10.1115/1.4037097
Download citation file:
Get Email Alerts
Cited By
Image-based flashback detection in a hydrogen-fired gas turbine using a convolutional autoencoder
J. Eng. Gas Turbines Power
Fuel Thermal Management and Injector Part Design for LPBF Manufacturing
J. Eng. Gas Turbines Power
An investigation of a multi-injector, premix/micromix burner burning pure methane to pure hydrogen
J. Eng. Gas Turbines Power
Related Articles
Simulations of the Unsteady Flow Through the Fastrac Supersonic Turbine
J. Turbomach (April,2000)
Unsteady Effect in a Nozzled Turbocharger Turbine
J. Turbomach (July,2010)
Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander
J. Fluids Eng (March,2011)
Design of an Improved Turbine Rim-Seal
J. Eng. Gas Turbines Power (February,2016)
Related Proceedings Papers
Related Chapters
Antilock-Braking System Using Fuzzy Logic
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
A Simple Carburetor
Case Studies in Fluid Mechanics with Sensitivities to Governing Variables
Performance Testing of Combined Cycle Power Plant
Handbook for Cogeneration and Combined Cycle Power Plants, Second Edition