A Fast Panel Code for Complex Actuator Disk Flows

Abstract

A fast, linear scaling vortex method is presented to study inviscid incompressible flow problems involving one or more actuator disks. Building upon previous efforts that were limited to axi-symmetric flow cases, the proposed methodology is able to handle arbitrary configurations with no symmetry constraints. Applications include the conceptual study of wake interaction mechanisms in wind farms, and the correction of wind tunnel blockage effects in test sections of arbitrary shape. Actuator disks represent wind turbines through the shedding of a deformable vortex wake, discretized with a plaid of triangular distributed dipole singularities. An iterative method is adopted to align the wake with the local flow field, which is reconstructed from the vorticity field with a Green function approach. Interactions are computed with a Fast Multipole Method (FMM), effectively overcoming the quadratic scaling of computational time associated with traditional panel methods. When compared to direct computation, the use of an FMM algorithm reduced solution time by a factor 30 when studying the wake of a single actuator disk with 60000 panels. In the same case, the mass flux of the actuator streamtube was conserved to 0:002%. Finally, the presence of round and square impermeable walls around the actuator is considered to demonstrate the code applicability to wind tunnel wall interference correction problems.