Recent years have seen a substantial increase of interest in the flows of granular materials whose rheology is dominated by the physical contact between particles and between particles and the containing walls. Considerable advances in the theoretical understanding of rapid granular material flows have been made by the application of the statistical methods of molecular gas dynamics (e.g., Jenkins and Savage (1983), Lun et al. (1984)) and by the use of computers simulations of these flows (e.g., Campbell and Brennen (1985), Walton (1984)). Experimental studies aimed at measurements of the fundamental rheology properties are much less numerous and are understandably limited by the great difficulties involved in trying to measure velocity profiles, solid fraction profiles, and fluctuating velocities within a flowing granular material. Nevertheless, it has become clear that one of the most severe Measurements of r Bouncing Off Flat Plate problems encountered when trying to compare experimental data with the theoretical models is the uncertainty in the material properties governing particle/particle or particle/wall collisions. Many of the theoretical models and computer simulations assume a constant coefficient of restitution (and, in some cases, a coefficient of friction). The purpose of the present project was to provide some documentation for particle/wall collisions by means of a set of relatively simple experiments in which solid spheres of various diameters and materials were bounced off plates of various thickness and material. The objective was to provide the kind of information on individual particle/wall collisions needed for the theoretical rheological models and computer simulations of granular material flows: in particular, to help resolve some of the issues associated with the boundary condition at a solid wall. For discussion of the complex issues associated with dynamic elastic or inelastic impact, reference is made to Goldsmith (1960) and the recent text by Johnson (1985).

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 at wind speeds 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 compared with the two-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 are 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.

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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.

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