The Flutterwing WindPumps: Design, NonLinearities, & Measurements

Abstract

A preceding linear stability analysis showed that the pitch and roll flutter of a wing can stop in high winds. The built-in protection and variable stroke motivated development of a flutterwing windpump, because rotors pumping with a fixed stroke usefully convert only 10% of the Betz limit of the wind's annual power. Here the stroke has to be negligible at small roll not to stiffle the start of flutter in the lightest of winds, but ultimately must increase fast to safely limit the roll amplitude by absorbing all the power of the strongest oscillation. It must be largely single-acting, just as for a piston pump down a deep well, to allow a suddenly-becalmed wing to return to vertical and then restart with a new wind. The more non-linear the pump's stroke, the larger its stiffening side effect. Other non-linearities at large amplitude include the apparent wind, the centrifuging effects of roll speed and the saturation of pitch. Smoke observation of light wind flow at full +/−90° tangent pitch shows remarkable stall delay until at the end of the roll swing the leading edge sheds a massive vortex to completely reverse the wing circulation. Such a wide vortex street maximises the swept area in the actuator limit where tangent blades of constant chord keep the circulation constant between stalls. Runaway of frequency and amplitude with wind speed is avoided by static gravity imbalance replacing some dynamic imbalance and the inertia and softening of a gravity pendulum, both as favoured by large scale and low design wind speed. Also helpful are not too high pitch inertia centrifuging and an aircushion on the output pipeline which reduces the stresses and pipe frictional loss as well as the pump stiffening. Then in moderate winds, the pitch can unsaturate and the wing start to feather at lower reduced frequency, containing the power and especially the downwind bending moment. In higher wind the wing then becomes stable just leaning with the wind veer. The niche is pumping as much as the prairie rotary windpumps of diameter equalling the wing length, but with only 1/2 of the mean wind or 1/8 the mean windpower density, and with much less material. Both floating and well bases and pumps have been developed for the same pendulum, wing, and nonlinear pump winch.