Numerical Analysis of a Two-Phase Turbine: A Comparative Study Between Barotropic and Mixture Models

Two-phase turbines offer the potential to significantly enhance the performance of power generation and refrigeration systems. However, their development has been hindered by comparatively lower efficiencies resulting from additional loss mechanisms absent in single-phase turbines. In this context, Computational Fluid Dynamics (CFD) emerges as a crucial tool to predict the performance of two-phase turbines and guide the design process towards higher efficiency. To date, most multiphase CFD studies on turbomachinery have focused on condensation in the final stages of steam turbines, and on cavitation in hydraulic pumps and turbines. These applications, however, are not representative of the conditions in two-phase turbines, where a liquid-dominated mixture undergoes a large expansion ratio, leading to a significant increase in the gas phase volume fraction throughout the entire flow. Recognizing the lack of an established modeling approach, this paper aims to identify a suitable modeling methodology for two-phase turbines. Our evaluation is centered around two models: the mixture model and the barotropic model. The validity and accuracy of these two modeling approaches is assessed using existing experimental data from a single-stage impulse turbine operating with several mixtures of water and nitrogen as working fluid. The results indicate that both the mixture and barotropic models are consistent and accurately predict the nozzle mass flow rate, yet, both models systematically overpredict the nozzle exit velocity and rotor torque. Adding correction terms for windage and unsteady pumping losses significantly improves the torque predictions, bringing them within the uncertainty range of the experimental data. In addition, refining the models to account for the effect of slip presents a promising avenue to enhance the prediction of nozzle exit velocity and overall performance of two-phase turbines.