Robustly Optimal Contra-Rotating HAWT

Abstract

The contra-torquing Horizontal Axis Wind Turbine (HAWT) is optimised. The two rotor actuator discs are sheets of equal and opposite bound vorticity which induce a swirl crosswind flow between them, halved at the discs and nil outside them. The optimal circulation is constant radially and the power is the Betz limit. Aft at blade speed of 1/3 windspeeed, the optimum apparent wind is straight ahead; the axial velocity change and thrust both reverse; and the product of lift coefficient by solidity is 2. If this aft value is realistically held at 2 for lower speed ratios, then the product climbs to 2 for the front rotor which becomes identical to the optimum single HAWT at zero speed ratio, where the contra combination has 3.56 times the starting torque and zero net thrust. The design lift coefficients that robustly maintain the optimum as the windspeed varies slightly are given for a typical stalling blade section for the single HAWT, as well as the greater ones for the aft contra rotor and smaller for the fore rotor above the 1/3 speed ratio of reversing aft thrust. But the apparent wind difference dominates to make the aft robust design pitch considerably greater than the fore (and single) towards the 1/3 ratio. A contra-torquing stator is shown to best follow a rotor.