In various engineering applications, the phase change from steam to water droplet during rapid expansion under supersonic flow conditions is inevitable. The occurrence of condensation waves due to the latent heat released during phase change and aerodynamic shocks reduces equipment performance. Given the complexities of two-phase flow, researchers have always been interested in developing an accurate numerical method that can be used in different flow regimes while reducing computation costs. This research has developed a two-dimensional code using the simple low-dissipation advection upstream splitting method (SLAU) and high-resolution simple low-dissipation advection upstream splitting method (HR-SLAU) in the complex geometry of the steam turbine blades and the convergent-divergent nozzles. The performance of these two schemes was examined using the Eulerian-Lagrangian model (ELM) under different boundary conditions. The governing equations are investigated using the Eulerian model, which incorporates the SLAU and HR- SLAU schemes, and the equations for determining the wet flow parameters are solved by the Lagrangian approach to predict the liquid mass in the grid cell. Comparative to the experimental data, regarding the simplicity of these two schemes, and in the absence of any tuning flow-dependent variable, the determination of the position and intensity of shocks has been improved considerably, while the droplet radius prediction has been significantly enhanced. Notably, the HR-SLAU scheme, in which the dissipation component of the pressure flux according to a cell-interface orientation angle and flow characteristics is locally controlled by the dissipation coefficient for modelling two-phase flows, leads to fewer numerical errors.

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