Enhanced nozzle design for mitigating the losses arising from non-equilibrium homogeneous condensation

• Investigated non-equilibrium homogeneous condensing flow in modified supersonic Laval nozzles. • Identified key geometric parameters governing supersaturation, nucleation, and droplet growth. • Used a multi-criteria decision approach to select the modified design under independent weighting schemes. • Achieved 72.6% smaller droplets and a 58.4% higher Mach number using the modified SUT de Laval nozzle. Non-equilibrium homogeneous condensation (NHC) significantly affects the efficiency of diverse energy systems, including steam turbines, compressed-air energy storage systems, primary ejector nozzles, and supersonic separator nozzles. In such systems, rapid expansion within supersonic nozzles induces NHC, leading to spontaneous droplet nucleation that detracts from aerodynamic performance and energy efficiency. The nozzle geometry directly affects the local expansion rate and thus plays a critical role in the initiation and severity of the NHC phenomenon. This study proposes and evaluates an effective strategy to mitigate NHC-induced losses and enhance energy efficiency through modified nozzle design. The approach is applied to four representative nozzle configurations: Moore B, Barschdorff, IWSEP (International Wet Steam Experimental Project), and SUT de Laval. Numerical simulations are conducted using an Eulerian–Eulerian framework, incorporating homogeneous nucleation, droplet growth models, and turbulence effects modeled via the shear stress transport ( S S T ) k − ω model. The numerical methodology is validated against available experimental data. A comprehensive dataset is generated to enable multi-criterion performance evaluation, and the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is employed to identify the best modified nozzle configuration. To ensure the robustness and objectivity of the decision-making process, an independent weighting analysis is conducted utilizing five widely adopted weighting methods: equal weight, entropy weight, criteria importance through inter-criteria correlation (CRITIC), analytic hierarchy process (AHP), and standard deviation. The results demonstrate significant performance improvements, with the modified SUT de Laval nozzle achieving a 72.6% reduction in average droplet radius and a 58.4% increase in average Mach number under laboratory conditions.