Wake expansion is necessary to satisfy conservation of mass when induction in flow through a wind turbine rotor disk is substantial. An iterative model is developed to calculate this expansion in an axisymmetric wake generated by an idealized unyawed disk operating at high tip speed ratios. The model satisfies all conservation constraints and boundary conditions, and predicts induction in the wake flow normal to the rotor disk plane due to the sheet of vorticity convected downwind along the surface of the wake. Expansion effects on induction in flow through the rotor disk and in the wake ale noted. The effect of skewing the axis of the wake out of alignment with the axis of a yawed rotor disk is approximated with a simple cross flow model which yields an expanding skewed wake. The sheet of vorticity convected downwind along the surface of this wake is found to significantly alter the induction in flow through the rotor disk from that predicted when wake expansion is neglected with the cylindrical wake approximation. This alteration is in the direction of levelizing the induction and resulting thrust distributions on the yawed disk. This in turn reduces the forward shift of the center of thrust from the axis of a yawed rotor, and this reduction may be very substantial at higher levels of induction and hence wake expansion. The effects of wake expansion on the level of thrust appear to be of second order compared to the effects on center of thrust. These findings are likely to be of particular importance to small wind turbines which are designed to yaw out of the wind as required at higher wind speeds to prevent undesirable overshoots in power and loads.

Two classes of transition modes are examined. The first class involves rotor start-up and shut-down in turbulent winds with rapidly varying mean wind speeds. In the start-up mode, coupling can occur between the mean and cyclic pitch control systems which leads to large peaks in blade flatwise moments. These peaks can substantially increase overall fatigue damage. They can be reduced by controlling blade pitch solely with the closed loop control system. Allowing the rotor to freely rotate at wind speeds below start-up eliminates blade moment peaks in the transition to low speed operation, with the result that closed loop control further increases blade fatigue life. These control alterations reduce power fluctuations but appear to have no significant effect on overall energy capture. Blade pitch control in the shutdown transition mode is restricted solely to mean pitch angle and no control coupling problems are encountered. The second class of transition modes studied is operation from below to above rated wind speed. This transition was previously idealized as an abrupt change from variable to constant rotor speed operation with mean blade pitch angle increased rapidly to hold mean power constant up to rotor shut down. This causes a very sharp peaking of mean moment at rated wind speed which increases blade fatigue damage. This peaking is reduced by smoothing the controlled variation of mean blade pitch angle over a range of wind speeds from below to above rated. As a result, rotor blade fatigue life is substantially increased, and energy capture is somewhat reduced in both open and closed loop operation. Thus there is a trade-off between energy capture and fatigue life which is examined. The comparative effects on blade fatigue life and weight of turbulence induced and 1P gravity loads are examined for large scale rotor blades. The bending strength of each blade in the out-of-plane and in-plane directions at the critical root location was assumed to be the same for full span pitch control requiring a cylindrical cross-section at the root. It is indicated that turbulence induced fatigue damage dominates over that due to gravity for rotor radii up to about 40m and near 2 MW rated power, depending on the number of rotor blades. This open loop result is unaltered in closed loop operation if blade weight is reduced to maintain the same fatigue life. Tradeoffs between rotor blade weight and energy capture in open and closed loop control operation are examined.

The effects of wind shear and turbulence on rotor fatigue and loads control are explored for a large horizontal axis wind turbine in variable speed operation from 4 to 20 m/s. Two and three blade rigid rotors are considered over a range of wind shear exponents up to 1.25 and a range of turbulence intensities up to 17%. RMS blade root flatwise moments are predicted to be very substantially increased at higher wind shear, and resultant fatigue damage is increased by many orders of magnitude. Smaller but similar trends occur with increasing turbulence levels. In-plane fatigue damage is driven by 1P gravity loads and exacerbated by turbulence level at higher wind speeds. This damage is higher by one to two orders of magnitude at the roots of the three blade rotor. Individual blade pitch control of fluctuating flatwise moments markedly reduces flatwise fatigue damage due to this source, and to a lesser degree the in-plane damage due to turbulence. The same is true of fluctuating rotor torque moments driven by turbulence and transmitted to the drive train. Blade root moments out of the plane of rotation aggregate to create rotor pitching and yawing moments transmitted to the turbine structure through the drive train to the yaw drive system and the tower. These moments are predicted to be relatively insensitive to turbulence level and essentially proportional to the wind shear exponent for the two blade rotor. Fluctuating moments are substantially reduced with individual blade pitch control, and addition of a teeter degree of freedom should further contribute to this end. Fluctuating pitching and yawing moments of the three blade rotor are substantially less sensitive to wind shear, more sensitive to turbulence level, and substantially lower than those for the two blade rotor. Mean rotor torque and hence power are essentially the same for both rotors, independent of wind shear, and somewhat reduced with individual blade pitch control of fluctuating flatwise moments. The same is true of mean rotor thrust, however fluctuations in rotor thrust are substantially reduced with individual blade pitch control. It appears, on balance, that higher wind shear coupled with turbulence effects should be accounted for in the fatigue design of large, long life turbines. Much more work is required on this problem.

This assessment of approximate modeling of aerodynamic loads on the UAE rotor indicates that it can be reasonably accurate when it is based on reliable 2D wind tunnel data, and when flow about the rotor blades is unstalled. This includes loads which figure importantly in the yawing of smaller wind turbines out of higher winds to minimize overshoots in power and loads. A welcome but by no means obvious finding is that the assumption of locally two dimensional flow about substantially yawed rotor blades appears to be reasonably valid even in the presence of the complex induction field due to the skewed wake effects. Dynamic stall, expanding skewed wake effects, and effects due to vortices shed inboard into the wake where the onset of deep stalled flow occurs must be accounted for to better predict side force and center of thrust location on the rotor. Rotational effects on rotor thrust, torque, and blade out-of-plane moments must be accounted for in deep stalled flow as it spreads outboard on the blades at higher wind speeds. These effects appear to be more severe at smaller rotor yaw angles, and lower tip speed ratios. Approximate modeling of these effects at zero yaw appears to be improved with the approach to and onset of fully deep stalled flow about the blades when blade aspect ratio and shape effects on non rotating section aerodynamic characteristics are included in the modeling. This matter requires substantial further study.