Improvement of the SST γ-Reθt transition model for flows along a curved hydrofoil

The transition in the boundary-layer flow affects the hydrodynamic performances of hydraulic machineries, as the key components in the ship propulsion system. The shear stress transfer (SST) γ-Reθt transition model is an important prediction tool in the boundary layer simulation for hydrofoils. The present paper improves the prediction accuracy of the SST γ-Reθt model for the boundary layers along a curved hydrofoil. The SST γ-Reθt transition model for the flows along a curved hydrofoil is improved by introducing a correction to the transition onset Reynolds number Reθt. First, the transition onset locations for the flows along the hydrofoils of different curvatures are obtained by the large eddy simulation and by using the SST γ-Reθt model. Then, the transition onset Reynolds numbers Reθt in the SST γ-Reθt model is modified to ensure that the predicted boundary layer parameters are consistent with the large eddy simulation (LES) results. The correlation function between the curvature ratio and the modified transition onset Reynolds number is obtained and subsequently used as a correction function in the original SST γ-Reθt model. Three test cases are used to evaluate the performance of the improved SST γ-Reθt model. For the NACA0035 hydrofoil with a large curvature, the predicted results obtained by using the improved SST γ-Reθt model are quite consistent with the experimental data, which indicates the advantages of the improved model in predicting the boundary layer transition along a hydrofoil. In the test cases of the NACA0016 hydrofoil with a mild curvature and the NACA66(mod)-312 hydrofoil, the prediction results of the improved model are in good agreement with the experimental results in terms of the wake region and the boundary layer parameters, which indicates that the improved SST γ-Reθt model can serve as a powerful tool in the design and the optimization of hydraulic machineries such as the waterjet pumps or the naval propellers.