On Prediction of Off-Design Multistage Turbine Pressures by Stodola’s Ellipse

Abstract

The variation of extraction pressures with flow to the following stage for high backpressure, multistage turbine designs is highly non-linear in typical cogeneration applications where the turbine nozzles are not choked. Consequently, the linear method based on Constant Flow Coefficient, which is applicable for uncontrolled expansion with high vacuum exhaust as is common in utility power cycles, cannot be used to predict extraction pressures at off-design loads. The paper presents schematic examples and brief descriptions of cogeneration designs, with background and theoretical derivation of a more generalized “nozzle analogy” which is applicable in these cases. This method is known as the Law of the Ellipse. It was originally developed experimentally by Professor Stodola and published in English in 1927. The paper shows that the Constant Flow Coefficient method is really a special case of the more generalized Law of the Ellipse. Graphic interpretation of the Law of the Ellipse for controlled and uncontrolled expansions, and variations for sonic choking and reduced number of stages (including single stage) are presented. The derived relations are given in computer codable form, and methods of solution integral with overall heat balance iteration schemes are suggested, with successful practical experience. The pressures predicted by the relations compare favorably with manufacturers’ data on four high-backpressure, cogeneration cycle turbines and three large utility low-pressure ends.

CAES Systems Integrated into a Gas-Steam Combined Plant: Design Point Performance Assessment

“…Heat transfer devices (HRSG tube bundles and condenser) have been modeled adopting the ε-NTU approach. The steam turbine has been modeled by scaling suitable efficiency curves on the basis of reference design data and by adopting a modified Stodola ellipse law [28]. The expected GSCC steam section performance enhancement previously discussed has been evaluated.…”

Development of a model for the prediction of the fuel consumption and nitrogen oxides emission trade-off for large ships

“…The relationship between mass flow rate (ṁ), pressure in and out (P i and P o ) and inlet temperature (T i ) for the T/C turbine is governed by the Stodola [31] turbine constant (C T ):…”

“…∆ symbolises the difference between inlet and outlet. The relationship between expander pressures, temperatures and mass flow rates is governed by the law of the ellipse by Stodola [31] (Eq. 1).…”

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“…This is primarily because of the presence of a distillation-condensation subsystem, at least three pressure levels and several heat exchangers. In applications such as solar power plants where the heat input fluctuates throughout the day, and over the year, it is essential to include the part-load performance of the power cycle to assess the plant performance in a thorough 35 manner. Similarly, it is also necessary to evaluate the part-load performance of the power cycle in other cases such as waste heat recovery from diesel engines or other fluctuating sources of energy input.…”

“…27) to calculate the turbine constant [35], and the off-design isentropic efficiency (Eq. 28) as described in Ray [36]:…”