A High-Order Flux Reconstruction Actuator-Line Framework for Rotating-Blade Aerodynamics on Fixed Cartesian Grids

Abstract

This work couples a high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) solver with a rotating actuator-line model (ALM) to simulate rotating-blade aerodynamics on fixed Cartesian grids. Blade loading is represented by volumetric body force source terms projected through an isotropic Gaussian kernel in a blade-attached frame, eliminating the need to resolve blade geometry. Vertical-axis wind turbines (VAWTs) serve as the demonstration configuration, with a modified Boeing-Vertol dynamic stall model incorporated to capture unsteady lift and drag. A mesh-resolution criterion for the Gaussian projection kernel on reasonably coarse meshes is derived. It shows that cost-effective coarse meshes can operate in a mesh-controlled regime with negligible induction feedback, motivating a Double Multiple Streamtube (DMST) correction to recover the physical inflow. Simulations are carried out over a range of tip-speed ratios at a chord-based Reynolds number of Re_c ~ 3.6 x 10^5. The framework is validated against experimental near-wake measurements and previously reported LES-ALM results, and the mean wake profile shows good agreement. The predicted power-coefficient curve matches high-fidelity three-dimensional LES-ALM data to within 6% around the optimal VAWT operation conditions. The framework also captures the regime-dependent influence of dynamic stall, azimuthal blade loading, lift hysteresis, and characteristic wake structures. These results demonstrate that the FR/CPR-ALM framework provides an accurate and computationally efficient geometry-free approach for VAWT analysis, making it well suited for parametric studies and large-scale wind energy applications.