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 nonlinear 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 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.

Modeling of a Steam Turbine Including Partial Arc Admission for Use in a Process Simulation Software Environment

“…The Stodola equation, as described by Cooke [2], is used to define the pressure ratio to flow relationship for a group of stages, nor mally eight or more. Plotted in Fig.…”

“…Plotted in Fig. Cooke [2] states that if the Stodola equation is used only for the last stage (the 6:1 pressure ratio), then it will not be as accurate for "choked" conditions, but a modification is suggested as a good approximation. Since the initial pressure ratio assumed will change the results for the Stodola equation (via the flow coefficient),-the way it should be used is ambiguous.…”

“…The objectives of this paper are (1) to describe steam turbine entrance admission design; (2) to describe different types of steam turbine governing (first) stages and give a simple model for this; (3) to describe a model for the last stage of a steam tur bine that is just upstream of a condenser; and (4) to demonstrate the implementation of the models in Aspen Dynamics, showing appropriate partial arc steam turbine behavior over an operating range.…”

Efficiency enhancement in a Rankine cycle power plant: Combined cycle approach

“…The saturated liquid from the condenser In the bottoming cycle, the wet steam from the turbine exhaust gives up its latent heat to the ammonia-water liquid coming out of the high temperature recuperator (HTR). The ammonia-water liquid (13) utilizes the latent heat and transforms to vapour (14) in the vapourizer (VAP). The AWM exits from the VAP and is split into two streams (15,17).…”

“…Cooke [14] tried to predict off-design multistage turbine pressures using the law of the ellipse. In a multistage turbine expansion for any extraction group, a nozzle analogy may be developed, which treats each entire group expansion as if it were a single nozzle.…”