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In the present paper, the hybrid AUSM-van Leer scheme is extended to solve the governing equations of twophase condensing flows. The method of moments with the classical homogeneous nucleation theory is used to model the non-equilibrium condensation phenomenon. Firstly, the hybrid method is validated using two test cases (i.e. Laval nozzle and rotor-tip cascade) and the results are compared with the MacCormack method. Then the hybrid method is used to solve two other problems (i.e. wavy channel and VKI stage). Based on the numerical results of the paper, the hybrid AUSM-van Leer scheme is an accurate method to simulate twophase transonic flows with nucleation. If the super cooling degree reaches to its maximum value, the nonequilibrium condensation begins and wetness fraction increases suddenly. Also across a shock the wetness fraction decreases due to evaporation of the droplets.

In this paper, effects of non-equilibrium condensation on deviation angle and performance losses of wet stages of steam turbines are investigated. The AUSM-van Leer hybrid scheme is used to solve the two-phase turbulent transonic steam flow around a turbine rotor tip section. The dominant solver of the computational domain is the non-diffusive AUSM scheme (1993), while a smooth transition from AUSM in regions with large gradients (e.g. in and around condensation- and aerodynamic-shocks) to the diffusive scheme by van Leer (1979) guarantees a robust hybrid scheme throughout the domain. The steam is assumed to obey non-equilibrium thermodynamic model, in which abrupt formation of liquid droplets produces a condensation shock. To validate the results, the experimental data by Bakhtar et al. (1995) has been used. It is observed that as a result of condensation, the aerothermodymics of the flow field changes. For example for supersonic wet case with back pressure Pb=30 kPa, the deviation angle and total pressure loss coefficient change by 65% and 200%, respectively, with respect to that in dry case.