Numerical simulation of nucleating flow and shock capturing in steam turbines by a simple low-dissipation upwind scheme using an Eulerian-Lagrangian model

Abstract

The rapid expansion of steam leads to non-equilibrium condensation of steam in the supersonic region which the performance of the turbines is reduced. The achievement of an accurate numerical method in a wide range of regimes to capture the aerodynamic and condensation shocks with minimum computation and numerical errors has always been of interest to researchers. Therefore, in this research, an in-house code is developed with a version of Advection Upstream Splitting Methods (AUSM), named Simple Low-dissipation AUSM (SLAU). The results of the SLAU scheme for condensing flow in three convergent-diverging nozzles are presented and compared with experimental data to validate the scheme. Then the SLAU scheme's performance in condensation and aerodynamic shock capturing for two-dimensional turbine blades is evaluated using an Eulerian-Lagrangian approach under different outlet conditions. The governing equations of flow are solved by the Eulerian approach using the SLAU scheme, and to accurately calculate wet parameters of the solution field, the corresponding equations are solved in Lagrangian form. Comparing the results of the SLAU scheme with experimental data, it was found that, despite the simplicity of the SLAU scheme, in the absence of tuning variables, it provided suitable predictions, even within shock zones. The results of the SLAU scheme for modeling steam nucleating flows and the prediction of the droplet radius are in better agreement with the experimental data and the results are improved considerably for the supersonic outlet cascade.