Empirical models normally rely on time averaged

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Unformatted text preview: dy and complex. Empirical models normally rely on time averaged velocity deficit wake models producing quasi-static α changes through the tower wake. Unsteady Aerodynamics Experiment data [6] have shown tower wake flow to be strongly vortical. Given the time varying vortical flow in the tower wake, even with all other parameters remaining constant, it is unlikely that two subsequent blade rotation cycles through the tower wake would produce the same transient aerodynamic response. These authors are unaware of detailed rotating blade/wake interaction investigations that have quantified this effect in sufficient detail to support comprehensive model validation. These blade/inflow/tower wake interactions can elicit substantial dynamic alterations in α, generating appreciable transient aerodynamic responses. Under certain conditions, α variations are sufficient to produce dynamic stall over portions of the rotating blade. The readers are referred to extensive reviews of dynamic stall from unsteady pitching and plunging lifting surfaces [7,8]. For horizontal wind turbines operating at high tip speed ratios, rapid inflow changes create the same dynamic α variation and transient aerodynamic response. However, dynamic stall is only one of several effects in the near and post-stall operating environment producing transient effects. Both three-dimensional quasi-static and unsteady effects from tower shadow and the stochastic inflow will be shown to play a role as significant as dynamic stall on the transient loads. The complex interrelationships between α variation, turbine geometry, and inflow are shown in Fig. 3 for the Phase IV (twisted blade) rotor. The three plots show the variation in local angle (α) over the blade span with blade rotation through a full cycle (φ = 0° to 360°). The three plots top to bottom correspond to yaw errors (ϕ) of +20°, 0°, and –20° at a single uniform inflow velocity (V∞ = 20 m/sec). All of the data were generated using YawDyn, and include a turbine wake model and tower shadow effect. Local angle (α) is extremely sensitive to the axial induction factor as well as to the other parameters noted earlier. Very different results can be produced with different models, and the principal intent is to demonstrate the 0.3 360 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Figure 3: Local angle of attack (αi) cyclic variation with blade azimuth angle (φ), span (r i), yaw error (ϕ). Yaw errors of 20° (upper panel), 0° (middle panel), and -20° (lower panel). DATA DENSITY AND INFLOW CONDITIONS The Unsteady Aerodynamics Experiment turbine is a three-bladed, downwind, free yaw machine. Of all the data collected for the two geometries (Table 1), the largest data sets are for pitch angles of 12° and 3° for the untwisted (Phase II) and twisted (Phase IV) geometries, respectively. The data 4 densities for Phase IV are presented graphically as the number of cycles binned according to cycle mean values of wind speed and yaw error in Fig. 4. Bin dimensions are 2.0 m/s for wind speed and 5° for yaw error. In the upper plot, the entire Phase IV data set corresponding to a 12° pitch angle is included and plotted using a contour increment of 100 cycles. In the lower plot, to better resolve data distribution at the extremes of V∞ and ϕ, bins containing 100 or more cycles were omitted, and the remaining bins were contour plotted with a contour interval of 10 cycles. During field tests, engineers had noted the propensity for the turbine to remain at slightly negative ϕ’s under steady winds. Consistent with these observations, the upper plot in Fig. 4 shows that, between 6 and 17 m/s, ϕ most frequently assumed a value between -5° and -10°. computed for 10 minute data records and binned according to the 10 minute mean velocity (identified in the legend as “10min.”). Second, standard deviations were computed for each cycle and binned according to the cycle average velocity (all traces not identified as “10-min.”). The 10-minute average...
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