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.

References

References
1.
Steag, 2012, “
EBSILON® Professional
,” STEAG Energy Services GmbH, Essen, Germany, accessed June 24, 2017, http://www.steag-systemtechnologies.com/ebsilon_professional.html
2.
GP Stragtegies, 2017, “
EtaPRO™ VirtualPlant™
,” GP Stragtegies, Columbia, MD, accessed June 24, 2017, https://www.gpstrategies.com/solution/performance-condition-monitoring-etapro
3.
CURTISS WRIGHT, 2016, “
PEPSE
,” Curtiss-Wright Nuclear Division, Idaho Falls, ID, accessed June 24, 2017, http://famos.scientech.us/PEPSE.html
4.
FLOWNEX, “
Flownex Simulation Environment
,” FLOWNEX SE, Potchefstroom, South Africa, accessed June 24, 2017, http://www.flownex.com/
5.
Thermoflow, 2017, “
Steam Master
,” Thermoflow Inc., Southborough, MA, accessed June 24, 2017, https://www.thermoflow.com/convsteamcycle_STM.html
6.
Stodola
,
A.
,
1945
,
Steam and Gas Turbines
, Vol.
1
,
Peter Smith
,
New York
.
7.
Cooke
,
D. H.
,
1985
, “
On Prediction of Off Design Multistage Turbine Pressure by Stodola's Ellipse
,”
ASME J. Eng. Gas Turbines Power
,
107
(
3
), pp.
596
606
.
8.
Traupel
,
W.
, 1982,
Thermische Turbomachinen
,
3rd ed.
,
Springer-Verlag
,
Berlin
.
9.
Cooke
,
D. H.
,
1983
, “
Modeling of Off-Design Multistage Turbine Pressures by Stodola's Ellipse
,”
Energy Incorporated PEPSE User's Group Meeting
, Richmond, VA, Nov. 2–3, pp. 205–226.http://famos.scientech.us/Papers/1983/1983section11.pdf
10.
Ray
,
A.
,
1980
, “
Dynamic Modelling of Power Plant Turbines for Controller Design
,”
Appl. Math. Modell.
,
4
(
2
), pp.
109
112
.
11.
Church
,
E. F.
,
1928
,
Steam Turbines
,
McGraw-Hill
, New York.
12.
Kearton
,
W. J.
, 1931,
Steam Turbine Theory and Practice
,
7th ed.
,
Sir Isaac Pitman and Sons
,
London
.
13.
Fuls
,
W. F.
,
2017
, “
Accurate Stage-by-Stage Modelling of Axial Turbines Using an Appropriate Nozzle Analogy With Minimal Geometric Data
,”
Appl. Therm. Eng.
,
116
, pp.
134
146
.
You do not currently have access to this content.