An Unsteady Panel (Boundary Element) Model for the Prediction of Performance of Vertical Axis Water Turbine Blades

Optimization algorithms are key approaches for enhancing hydrofoil performance in Vertical Axis Wind/Water Turbines (VAWTs). These algorithms provide accurate results at the cost of large training datasets. Given the high computational cost of the commonly applied RANS solvers, this study aims to explore the potential of more computationally efficient alternatives, specifically Quasi-steady Hydrofoil Theory (QHT) and the Unsteady Boundary Element Method (UBEM) or Panel Method, through comparative analysis with SST k-ω Reynolds-averaged Navier-Stokes (RANS) simulations. QHT is derived from a classic hydrofoil theory for VAWT. According to the geometry and periodic motion of VAWT system, QHT formulates the relative inflow and angle of attack of the hydrofoil based on the azimuth angle, while disregarding the memory and wake effect of the flow field. The torque performance is accessed based on the lift and drag coefficient from an external database (XFOIL), which depends on the hydrofoil type. Reduce frequency is reviewed to evaluate the performance of quasi-steady formulation, which measures the residence time of a particle convecting over the hydrofoil chord compared to the period of motion. It is found that the reduced frequency of a system constrains the performance of its corresponding QHT, and QHT is considered insufficient to describe the complexity of VAWT systems. UBEM is an analytical model based on potential flow theory, which reduces the dimension of the problem by refining the problem to the hydrofoil boundary instead of the entire flow domain. It solves the Laplace equation for the velocity potential based on the kinematic boundary conditions along the hydrofoil surface and the pressure Kutta condition at the trailing edge. By modeling the continuous dipole/vortex wake sheet behind the trailing edge, UBEM accounts for the wake effect. In this study, the singularity caused by foil-wake intersection is avoided by retaining the latest generated wake sheet to allow continuous revolutions. The results of UBEM have shown that it can effectively predict the hydrofoil pressure distribution and torque performance results from RANS, with significantly less computation time. Additionally, the wake sheet generated by UBEM aligns well with the wake development seen in RANS vorticity contours.