Semi-analytical techniques for investigating thermal non-equilibrium effects in wet steam turbines

This paper describes a semi-analytical solution of the polydispersed wet stream equations, valid in regions where the nucleation rate is negligible. The solution can be used in conjunction with any conventional turbomachinery calculation procedure to obtain estimates of the magnitude of departures from thermal equilibrium. For example, from an initial estimate of the pressure distribution, it is a simple matter to calculate the distribution of supercooling and wetness fraction, together with the thermodynamic losses incurred by the flow.The method differs from the usual numerical approach by providing general results which give considerable physical insight. Computational time and effort is also dramatically reduced. The controlling parameters emerge naturally from the analysis, and information concerning the fundamental fluid mechanics of wet steam is revealed. In particular, the analysis demonstrates the role played by the thermal relaxation time and the rate of expansion in controlling the deviation from equilibrium.The versatility and usefulness of the technique in furnishing results for the turbine designer are demonstrated by a number of applications including one-dimensional nozzle flows and two-dimensional blade-to-blade and hub-to-tip flows. In each case it is shown how the droplet size and expansion rate influence the thermodynamic losses and other flow variables of interest.