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Actuator cylinder theory is an effective approach for analyzing theaerodynamic performance of vertical axis wind turbines at a conceptual designlevel. Existing actuator cylinder theory can analyze single turbines, butanalysis of multiple turbines is often desirable because turbines may operatein near proximity within a wind farm. For vertical axis wind turbines, whichtend 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 ofaerodynamic loading for any number of turbines. We also extended the theoryto handle thrust coefficients outside of the momentum region and explicitlydefined the additional terms needed for curved or swept blades.  While the focus of this paper is a derivation of an extended methodology, anapplication of this theory was explored involving two turbines operating inclose proximity. Comparisons were made against two-dimensional unsteadyReynolds-averaged Navier–Stokes (URANS) simulations, across a full360° of inflow, with excellent agreement. The counter-rotatingturbines produced a 5–10 % increase in power across a wide range ofinflow conditions. A second comparison was made to a three-dimensional RANSsimulation with a different turbine under different conditions. While onlyone data point was available, the agreement was reasonable, with thecomputational fluid dynamics (CFD) predicting a 12 % power loss, ascompared to a 15 % power loss for the actuator cylinder method. Thisextended theory appears promising for conceptual design studies of closely spaced vertical axis wind turbines (VAWTs), but further development and validation is needed

Actuator cylinder theory for multiple vertical axis wind turbines