Viscous Vorticity Equation (VISVE) Method Applied to Flow Around Stationary and Rotating Hydrofoils

Over the past few years, the VIScous Vorticity Equation (VISVE) method has developed and become one of the most efficient tools for studying complex fluid flows. The VISVE method focuses on solving the vorticity transport equation, which allows for a more localized and compact representation of the flow field compared to traditional methods. It has been successfully applied to a wide variety of fluid dynamic problems, ranging from two-dimensional (2D) to three-dimensional (3D) flows. Some of its primary areas of application have been in the modeling of hydrofoils and propellers, where the method has consistently demonstrated robust performance. A particularly promising area of application for VISVE is in the analysis of vertical-axis wind turbine (VAWT), where rotating hydrofoils play a fundamental role. Understanding the fluid dynamics around the rotating blades is crucial for optimizing the efficiency and performance of these turbines. Hence, this paper focuses on the application of the VISVE method to investigate viscous flow around both stationary and rotating hydrofoils. Essential flow features including vorticity, velocity, and pressure distributions are obtained and analyzed in detail. To validate the accuracy of VISVE, its results for both stationary and rotating hydrofoils are compared with those obtained from traditional Reynolds-Averaged Navier-Stokes (RANS) simulations. The comparisons show good agreement between the two methods, confirming that VISVE can capture essential flow features with a high degree of accuracy. Beyond accuracy, VISVE results exhibit several advantages over RANS results, particularly in terms of computational efficiency. It requires a significantly smaller computational domain and fewer computational cells, leading to much shorter computation times. As a result, VISVE is proven to be a reliable and efficient method for analyzing hydrofoils.