Wet Steam Flow Modeling in a General CFD Flow Solver

Abstract

The focus of this paper is on the implementation of a two-phase wet-steam model in a general-purpose CFD flow solver. The formation of liquid-droplets in a homogeneous non-equilibrium condensation process is defined by a phase-change model which is based on classical nucleation theory. The conservation equations for the mixture flow and the equations describing the droplet formation and interphase heat and mass transfer are treated in a fully-Eulerian approach. Numerical results are presented for steam condensation in an inviscid flow inside a Laval nozzle geometry and for turbulent flow in a turbine cascade. The results from these two test cases show good agreement with available experimental measurements. I. Introduction During the rapid expansion of steam, a condensation process takes place shortly after the state path crosses the vapor-saturation line. The expansion process causes the super-heated dry steam to first subcool and then nucleate to form a two-phase mixture of saturated vapor and fine liquid droplets known as wet steam. Modeling wet steam is very important in the analysis and design of steam turbines. The increase in steam turbine exit wetness can cause severe erosion of the turbine blades at the low-pressure stages, and a reduction in aerodynamic efficiency of the turbine stages operating in the wet steam region. 1 Since a large segment of the total power output is produced by the low-pressure stages of the turbine, accurately predicting steam condensation and stage efficiency is of paramount importance. In the past, the effect of wetness in low-pressure turbine stages was accounted for by single-phase flow modeling combined with empirical correlations. However, with recent advances in numerical methods for multiphase flows and the availability of powerful computers, modeling steam turbines with phase-change is becoming more attractive. In general, the wet-steam models fall into two categories. The first category are the Eulerian-Lagrangian approaches, where droplet tracking, nucleation, condensation, and growth are modeled in a Lagrangian framework, while the mixture conservation equations are defined in an Eulerian framework. Yeoh and Young 2 used a streamline curvature technique combined with one-dimensional wet steam theory to predict non-equilibrium condensation effects in low-pressure steam turbines. Later, Young 3 extended the work to solve the mixture flow using two-dimensional Euler equations in a time-marching scheme while the wetnesss calculation were performed in a Lagrangian framework by integrating the droplet growth equation along the flow streamlines . This solution approach was based on similar methods in earlier works of Moheban and Young, 4 and Bakhtar and Tochai. 5 The second category consists of fully-Eulerian approaches. Here, the droplet nucleation, condensation, growth, and the mixture conservation equations are all modeled in the Eulerian framework. Ishizaka 6 presented a high-resolution numerical method for capturing condensation shock waves on steam turbine cascade while using a body-fitted structured grid. Ishizaka coupled the main flow equations with the equations describing the droplet formation and interphase change. In this work, a fully-Eulerian approach has been developed for modeling wet steam flow in a general unstructuredgrid based CFD flow solver. The equations describing droplet formations and interphase change are not solved in a