Numerical Solution of Transonic Wet Steam Flow in Blade-to-Blade Cascade with Non-equilibrium Condensation and Real Thermodynamics

¹ Department of Technical Mathematics, FME CTU Prague, Karl. nám. 13, CZ-12135, Prague 2, Czech Republic
² Institute of Thermomechanics, AS CR, Dolejškova 5, CZ-18200, Prague 8, Czech Republic

^a e-mail: vladimir.hric@fs.cvut.cz
^b e-mail: jan.halama@fs.cvut.cz

Published online: 6 May 2015

Abstract

We present an engineering approach to mathematical modeling and numerical solution of 2D inviscid transonic flow of wet steam in a steam turbine cascade channel of penultimate stage at rotor tip section in full Eulerian framework. Our flow model consists of the Euler system for the mixture (dry steam + homogeneously dispersed water droplets) and transport equations for moments of droplet number distribution function known as method of moments. Thermodynamic properties of vapor steam are provided by set of IAPWS equations. For equation of state for vapor phase valid both in superheated and wet (meta-stable) region we adopted recently developed equation in CFD formulation for low pressures provi1ded by Hrubý et al. [9], [8], [10]. For extraction of vapor parameters from the mixture ones we implemented simple relations in polynomial form describing thermodynamic properties of saturated liquid state. Nucleation model is resorting to modified classical nucleation theory. Linear droplet growth model is implemented for calculation of liquid sources. Numerical method is simple: cell-centered finite volume approach, 1st-order AUSM+ scheme for spatial derivatives, symmetrical fractional step method for separation of convection and condensation part, explicit 2-stage 2nd-order Runge-Kutta method for time integration. Geometry of blade profile and experimental results are provided by Bakhtar’s work [22], [23]. Results were obtained for one subsonic inlet/subsonic outlet regime and gave quite reasonable accordance with experiment.