An examination of the Throughflow of Nucleating Steam in a Turbine Stage by a Time-Marching Method

Author(s):  
F Bakhtar ◽  
B O Bamkole

The paper describes a theoretical treatment for nucleating throughflow of steam in a turbine stage. The conservation equations governing the overall behaviour of the fluid are combined with those describing droplet behaviour and treated by a time-marching method. The computer program developed has been applied to some test cases and comparisons are presented between solutions allowing for non-equilibrium effects and those in which steam has been assumed to remain in thermodynamic equilibrium.

Author(s):  
F Bakhtar ◽  
R Mohsin

In the course of expansion in turbines, steam first supercools and then nucleates to become a two-phase mixture. The fluid then consists of a very large number of extremely small droplets which are carried by and interact with the parent vapour. The formation and subsequent behaviour of the liquid phase cause problems which lower the performance of the wet stages of steam turbines. To treat such flows the general conservation equations governing the whole field are combined with those describing droplet nucleation and growth and the set treated numerically. The article examines the solution of throughflows of nucleating steam in a turbine stage using a time-marching technique. The treatment which is the refinement of an earlier one has been applied to the flow in a turbine stage. Comparisons are presented between the results of theoretical solutions and direct measurements upstream and downstream of the nucleating stage and the agreement obtained is good.


1977 ◽  
Vol 99 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Jean-Pierre Veuillot

The equations of the through flow are obtained by an asymptotic theory valid when the blade pitch is small. An iterative method determines the meridian stream function, the circulation, and the density. The various equations are discretized in an orthogonal mesh and solved by classical finite difference techniques. The calculation of the steady transonic blade-to-blade flow is achieved by a time marching method using the MacCormack scheme. The space discretization is obtained either by a finite difference approach or by a finite volume approach. Numerical applications are presented.


2003 ◽  
Vol 125 (1) ◽  
pp. 25-32 ◽  
Author(s):  
W. Ning ◽  
Y. S. Li ◽  
R. G. Wells

A multistage frequency domain (time-linearized/nonlinear harmonic) Navier-Stokes unsteady flow solver has been developed for predicting unsteady flows induced by bladerow interactions. In this paper, the time-linearized option of the solver has been used to analyze unsteady flows in a subsonic turbine test stage and the DLR transonic counter-rotating shrouded propfan. The numerical accuracy and computational efficiency of the time-linearized viscous methods have been demonstrated by comparing predictions with test data and nonlinear time-marching solutions for these two test cases. It is concluded that the development of efficient frequency domain approaches enables unsteady flow predictions to be used in the design cycles to tackle aeromechanics problems.


1965 ◽  
Vol 5 (02) ◽  
pp. 160-166 ◽  
Author(s):  
A.M. Rowe ◽  
I.H. Silberberg

Abstract A computer program was written to predict the phase behavior generated by the enriched-gas-drive process. This program is based, in part, on a new concept of convergence pressure, which is then used to select vapor-liquid equilibrium ratios (K-factors) for performing a series of flash calculations. The results of these calculations are the equilibrium vapor and liquid phase compositions which define the phase envelopes. The program was used to predict phase envelopes for 11 different hydrocarbon systems on which published experimental data were available. The predicted and experimental results compare favorably. Introduction The reservoir engineer is frequently faced with the problem of predicting what will happen if gas is injected into a reservoir. One aspect of this general problem is predicting the phase changes that will occur when a non-equilibrium gas displaces a reservoir fluid. In particular, a "dry" gas, upon displacing a volatile oil will pick up intermediate components from the oil. On the other hand, a "wet" gas, containing a high concentration of intermediates, will lose some of these components to a relatively low-gravity, non-equilibrium crude. It is this latter process, occurring in the enriched-gas displacement, which is treated in this paper. In the past, these phase changes have been determined experimentally and the results incorporated into various modifications of the Buckley-Leverett analysis. Such experimental work is time consuming, and the results are sensitive to numerous experimental errors. With the wide availability of high-speed digital computing equipment and numerous correlations pertaining to the vapor-liquid equilibria of hydrocarbon systems, it is now practical to calculate such phase behavior. This paper describes a computer program for performing these calculations. THE ENRICHED GAS DISPLACEMENT PROCESS Experimental results have shown that oil recovery can be significantly increased by enriching the displacing gas with intermediate hydrocarbon components. The essential features of the phase behavior generated by this enriched-gas-drive process are commonly illustrated with ternary diagrams such as Fig. 1. In this figure, Gas D, which contains a high concentration of intermediate hydrocarbons with respect to the undersaturated Crude A, is injected into the reservoir. When D contacts A, gas goes into solution until the oil becomes saturated (Point. B). Further contacting of Gas D and saturated Oil B results in a Mixture C which separates into Vapor Y(c) and Liquid X(c). Liquid X(c) is contacted by additional Gas D, resulting in Mixture E which separates into Vapor Y(e) and Liquid X(e). Repeated contacts of the liquid by the injected gas will eventually result in Liquid X(d) of maximum enrichment existing in equilibrium with Gas Y(d). The equilibrium tie-line X(d) Y(d), when extended, passes through the Point D representing the enriched injection gas. For systems of more than three components, the predicted equilibrium states are dependent upon not only reservoir temperature and pressure, but also the compositions of the crude oil and injected gas. If the gas is sufficiently enriched, a miscible displacement is generated. Line is tangent to the phase envelope at the critical point (Point Z) and represents the limiting slope of the tie-lines as the critical state is approached. Point I therefore represents the minimum enrichment of injection gas required to generate a miscible displacement. Point G represents the minimum enrichment required for initial miscibility of the injection gas with Crude A.Attra has presented a method to be used for prediction of oil recovery by the enriched gas displacement process. To develop the phase behavior data needed, he designed the experimental procedure described in the following quotation from his paper SPEJ P. 160ˆ


1994 ◽  
Author(s):  
F. Pommel

A procedure for blade design, using a time marching method to solve the Euler equations in the blade-to-blade plane is presented. This procedure uses an Office Nationale d’Etude et de Recherches Aeronautique flow solver. The classical slip conditions (no normal velocity component along the blade profile) has been replaced by another boundary conditions in such a way that the required pressure may be imposed directly. The orignal direct code was therefore transformed into an inverse solver. The unknows are calculated on the blade wall using the so-called compatibility relations. The blade geometry is then modified by resetting the wall parallel to the new flow field. The results obtained with this design process for a supersonic turbine blade of a space turbopump is presented.


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