Two Phase Flow

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A comparative study of treatment of two-dimensional two-phase flows of steam by a Runge-Kutta and by Denton’s methods Q1

F Bakhtar1∗ , M Y Zamri2 , and J M Rodriguez-Lelis3 1 Department of Mechanical and Manufacturing Engineering, University of Birmingham, Edgbaston, Birmingham, UK 2 Department of Mechanical Engineering, College of Engineering, Universiti Tenaga Nasional, Kajang, Selangor, Malaysia 3 Departamento de Ingenieria Mechanica, Interior Internado Palmera, Cuernevaca, Mexico The manuscript was received on 17 August 2006 and was accepted after revision for publication on 21 March 2007. DOI: 10.1243/0954406JMES477

Abstract: This paper describes a comparative study of the treatment of two-dimensional nucleating flows of steam using two different time-marching numerical schemes. A treatment based on Denton’s scheme but a refined grid has been available from earlier work. To compare with this a treatment based on the Runge-Kutta scheme has been developed, which is described. Solutions using this scheme and a simple mesh are compared with experimental results and with solutions using the earlier treatment. The agreement obtained between the two schemes and with the experimental results is satisfactory. Oscillating flows in a convergent–divergent nozzle are also examined and excellent agreement obtained with experimental measurements. Keywords: steam turbines, two-phase flows, non-equilibrium flow, time marching, cascades of blades, fluid dynamics, nucleation, wet steam

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INTRODUCTION

In the course of expansion of steam in turbines the state path crosses the saturation line and some of the stages have to operate on a two-phase mixture. The design of the stages operating on superheated steam has benefited considerably from work on aircraft gas turbines and very high efficiencies can be achieved. In contrast, the problems associated with two-phase effects in the wet stages have been comparatively neglected. Generally, there is loss of performance experienced in these stages and the phenomena underlying the additional losses are imperfectly understood. An appreciable proportion of the power is generated in these stages and economic rewards for improved designs resulting from better understating are considerable.

∗ Corresponding

author:

Manufacturing

Engineering,

Department

of

University

Mechanical of

and

Birmingham,

PO Box 363, Edgbaston, Birmingham B15 2TT, UK. email: [email protected]

JMES477 © IMechE 2007

Many experimental investigations of wet steam flows in steam turbines have been reported in the literature and these highlight the problems experienced [1–20]. The state of progress in the studies of wetness problems in steam has been reviewed in a two part special issue of the journal of mechanical engineering science recently [21, 22]. There has been reasonable progress in the understanding of some of the underlying problems but much work still remains to be done and the effort devoted to the study of these problems is small in comparison with their practical significance. An important aspect of the subject is analysis of these flows. To treat two-phase flows of steam in turbine blading, the equations describing droplet nucleation and growth are combined with the gas dynamic field conservation equations and the set treated numerically. A feature of flows in the low pressure stages of steam turbines is that they are generally transonic with appreciable supersonic zones and often contain shock waves. For this reason the most suitable method of treating the equations is the time marching technique. A number of treatments of two-phase flows of steam using this technique have

Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science