Robustly Optimal Wind Turbine for Swirl Expansion and Decay

Abstract

The wind turbine optima of propeller actuator disc theories are problematic. The large optimal windmill interference doubles the wake area from the vortex cylinder used to justify the propeller blade element momentum (BEM) theory. The general momentum (GM) theory incorporates expansion, but its optimum windrotor power blows up below a tip speed ratio of about unity where the BEM and experimental optima are low. Even without expansion, the GM and vortex theory optimum can still affect infinitely more gross power flux than in undisturbed wind. The inner massive swirl of their optimal wake is unstable or unrealizable by many indicators. Rather than a cylindrical wake, the BEM is better founded on negligible suction from low swirl in a predominately axial wake expanded after instability and bursting of the hub vorticity outwards to cancel the axial component of the tip vorticity. If moderate swirl at outer high speed ratios can expand first with pressure regain, the optimum local power refines up to 5 per cent higher. Then only as this expanded outer axial vorticity is finally cancelled to relieve the suction from the swirl does the inner BEM flow slow and expand. The inner and outer axial velocities are equal with no radial velocity at local speed ratio 0.57 in the optimal rotor. Direct experimental verification of this dissipated expanded swirl head (DESH) refinement of the BEM is proposed further to support from measurements and computations in the literature. The design blade chord and pitch that make the DESH optimum robust to small changes in windspeed are little changed from the time-proven BEM design, whereas the GM robust chord has a singularity.