Heterogeneous condensation reshapes relaxation, losses and efficiency in transonic condensing flows: an OpenFOAM-based moment-method study

Non-equilibrium condensation (NEC) in rapid-expansion devices can intensify irreversibility and alter flow structures. In practical steam systems, entrained impurities necessitate a quantitative assessment of heterogeneous nucleation effects. To address this issue, this study develops an OpenFOAM-based non-equilibrium condensing-flow solver using the Method of Moments, with the SUT de Laval nozzle adopted as a benchmark. The framework is validated against measured centerline pressure and outlet wetness. Thermal and inertial relaxation times are then introduced as local time-scale diagnostics: the former characterizes thermodynamic recovery during phase change, whereas the latter evaluates droplet dynamic response and the applicability of the zero-slip mixture assumption. Both are further decomposed into homogeneous and heterogeneous droplet contributions. Parametric analyses reveal that increasing heterogeneous-particle concentration shifts the two-phase region upstream, transitioning the liquid generation from homogeneous-to heterogeneous-dominated. A competition window appears at intermediate concentrations, where thermal relaxation remains elevated. Across the studied range, the inertial Stokes number consistently satisfies StI≪1, supporting the zero-slip assumption under the present conditions. Combined with entropy-loss and efficiency evaluations, the results show a clear non-monotonic trend: intermediate concentrations increase irreversibility and reduce efficiency, whereas higher concentrations suppress entropy generation and recover performance. Overall, this work establishes a relaxation-time-based diagnostic framework linking local phase-change dynamics to loss formation and efficiency variation in heterogeneous condensing flows.