Mixture-based loss evaluation and critical superheat determination in transonic steam flows for flexible turbine operation: An experimentally validated OpenFOAM approach

Deep peak regulation and flexible operation of steam turbines are imperative for integrating renewable energy into modern power grids. However, operation under low-load conditions frequently drives the last-stage expansion into the unstable non-equilibrium condensation zone, risking significant efficiency penalties and blade erosion. Current loss evaluation methods often rely on simplified single-phase gas assumptions, failing to accurately quantify the thermodynamic irreversibility inherent in these transient two-phase flows. To address this, this study develops a thermodynamically consistent two-phase framework implemented in OpenFOAM. The solver couples non-equilibrium nucleation and droplet growth kinetics and is validated against IWSEP nozzle and transonic stator cascade experiments. Statistical analysis confirms high model fidelity, achieving a coefficient of determination ($R^2$) exceeding 0.98 for static pressure distributions across all configurations and wetness evolution in nozzle benchmarks. Using a reproducible inlet-temperature sweep procedure, a configuration- and operating-condition-specific critical superheat boundary is identified, separating dry expansion from condensation-prone regimes for the examined cases. The results show that increasing inlet superheat shifts the Wilson point downstream, thereby mitigating condensation-induced pressure variations. Furthermore, a mixture-based loss evaluation method is introduced to correct the bias in traditional assessments. Comparative analysis demonstrates that conventional gas-phase formulas systematically overestimate entropy generation by neglecting latent-heat effects, whereas the proposed mixture-based approach remains consistent with the two-phase thermodynamic state. Overall, the proposed framework enables case-specific condensation-risk screening for flexible-operation planning and provides a refined, thermodynamically consistent basis for aerodynamic loss assessment of wet-steam components.