The phenomenon of water–jet pump stall can be ascribed to the development of blade boundary layer separation with the transition process playing a significant role in this separation. The hydrofoil is usually used as a simplified model of the water–jet pump impeller blade, and its flow field characteristics have important reference values for analyzing the impeller flow. Based on the transition model and the dynamic mode decomposition method, this article presents the results of a study that was carried out on the stall characteristics of the NACA0009 blunt trailing edge hydrofoil. The transition characteristics of hydrofoil surfaces at different angles of attack (AoA)and Chord-based Reynolds numbers (ReL) are obtained. The hydrofoil boundary layer transition is dominated by natural transition as the AoA is less than 4°, while the transition is dominated by leading-edge separation-induced transition as the AoA is greater than 4°. The investigation yields the dynamic properties of the LSB (Laminar Separation Bubble) as the AoA is varied. The phenomenon known as the deep stall is distinguished by the movement of the stall vortex toward the upstream direction near the trailing-edge region, where it merges with the LSB in the leading-edge region. This phenomenon leads to oscillations in the lift and drag coefficients. The relationship between the LSB and the trailing-edge stall vortex is established using DMD (Dynamic Mode Decomposition) methods. As the phenomenon of the deep stall occurs, it can be observed that the modal energy of the leading-edge LSB is comparatively higher than the modal energy of the trailing-edge stall vortex, inducing the dominant role of the LSB and the movement toward the trailing-edge region and, consequently, the phenomenon of trailing-edge vortex shedding in the hydrofoil. The findings of this study could be guidance for the design of fluid machinery blades.

The Bradshaw assumption, that the ratio of Reynolds shear stress to turbulence kinetic energy (TKE) is a constant roughly equal to 0.3, is introduced into eddy viscosity and TKE dissipation term of the shear stress transport turbulence model (SST). This constant is calibrated by the zero-pressure-gradient plate boundary layer test. This is not applicable to rotating separation flows in hydraulic machinery, while its dynamic effects are usually ignored. In this article, a comprehensive evaluation of the dynamic Bradshaw coefficient (DBC) in SST is conducted. First, theoretical analyses of the existing typical DBCs are carried out, and a suitable expression form driven by a single turbulence Reynolds number is adopted in view of its well-reflected dynamic effects and high robustness. According to the equation structures of SST, three dynamic strategies are proposed, including only introducing DBC into eddy viscosity (SST-M1), only introducing DBC into TKE dissipation term (SST-M2), and introducing DBC both into eddy viscosity and TKE dissipation term (SST-M1 + M2). Second, the classical case of flows around a hydrofoil is employed to evaluate the application effects of these three dynamic strategies. The results show that SST-M1 exhibits severe lift/drag oscillations at large angles of attack accompanied by the eddy viscosity fluctuations, indicating poor numerical stability and potential risk of this strategy. In contrast, both SST-M2 and SST-M1 + M2 can effectively improve the deficiencies of SST in overestimating lift and underestimating drag at large angles of attack, which is attributed to the promotion of earlier and larger flow separation. The consistency between these two strategies implies that introducing DBC into the TKE dissipation term plays a key role in enhancing the prediction of SST. Therefore, the dynamic strategy SST-M2 is recommended to extend the applicability of SST for rotating separation flows in hydraulic machinery.