Optimal performance of actuator disc models for horizontal-axis turbines

This study analyzes actuator disc (AD) models of horizontal-axis turbines to determine optimal performance, defined as the maximum power extracted at any tip speed ratio. We use calculus variations maximize rotor torque relative thrust without making assumptions about loading. The was obtained from angular momentum equation and Kutta-Joukowsky which depends on circumferential velocity optimality requirement is that pitch vorticity exiting must be constant across wake equal ratio thrust. result generalizes classical finding Betz Goldstein lightly-loaded ADs have pitch. Optimizing in far-wake, well downstream rotor, leads same implies an everywhere all ratios. show it not possible for reach its value because distribution wake, propose modifications far-wake. axial velocities are easily determined, were used find those “disc loading equation” also normalized bound circulation rotor. For simplest case a zero ratio, induced linear radius component quadratic, As increases, asymptote familiar Betz-Joukowsky values, become constant. At low ratios, wakes constrained by need avoid breakdown flow high swirl, conventional equation, involving only, inaccurate. found previous studies, coefficient increases monotonically with but reaches slightly above limit two, before decreasing towards limit.