Physical insight into transient hydrodynamics and corresponding flow structures of a pitching hydrofoil via boundary vorticity dynamics

The objective of this study is to investigate the hydrodynamic forces acting on a pitching Clark-Y hydrofoil, with a focus on dynamic flow structures such as boundary-layer separation and vortex evolution, which are driven by the interaction between tangential pressure gradients and on-wall vorticity generation. Numerical simulations were conducted using the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations at a Reynolds number of 5 × 10⁴. Proper Orthogonal Decomposition (POD) was applied to identify the energetic flow modes, while Boundary Vorticity Flux (BVF)-based lift decomposition was further employed to explore the dominant lift contribution. The results showed that the time-space evolution of the laminar separation bubble (LSB) and trailing-edge vortices (TEVs) experienced a notable delay in formation during the upstroke as the pitching rate increased. The fluctuating LSB and TEV were extracted as the primary energetic modes. The dominant lift contributions were found to arise from pressure-gradient-induced vorticity generation on the hydrofoil surface. Especially, substantial lift fluctuations were traced to concentrated σ_p peaks downstream of the LSB and alternating peaks at the trailing edge. Moreover, the delayed onset of LSB bursting and an earlier initiation of trailing-edge separation was attributed to variations in the integral magnitude of σ_p in the leading and trailing regions. These insights have direct implications for the design and control of hydrofoil-based systems in marine applications, like underwater control surfaces and hydrokinetic turbines, aiding in the development of strategies to enhance stability and efficiency under dynamic flow conditions.