Actuator cylinder theory for multiple vertical axis wind turbines

Abstract

Actuator cylinder theory is an effective approach for analyzing the aerodynamic performance of vertical axis wind turbines at a conceptual design level. Existing actuator cylinder theory can analyze single turbines, but analysis of multiple turbines is often desirable because turbines may operate in near proximity within a wind farm. For vertical axis wind turbines, which tend to operate in closer proximity than do horizontal axis turbines, aerodynamic interactions may not be strictly confined to wake interactions. We modified actuator cylinder theory to permit the simultaneous solution of aerodynamic loading for any number of turbines. We also extended the theory to handle thrust coefficients outside of the momentum region and explicitly defined the additional terms needed for curved or swept blades. While the focus of this paper is a derivation of an extended methodology, an application of this theory was explored involving two turbines operating in close proximity. Comparisons were made against two-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, across a full 360° of inflow, with excellent agreement. The counter-rotating turbines produced a 5-10% increase in power across a wide range of inflow conditions. A second comparison was made to a three-dimensional RANS simulation with a different turbine under different conditions. While only one data point was available, the agreement was reasonable, with the computational fluid dynamics (CFD) predicting a 12% power loss, as compared to a 15% power loss for the actuator cylinder method. This extended theory appears promising for conceptual design studies of closely spaced vertical axis wind turbines (VAWTs), but further development and validation is needed.