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and complex. Empirical models normally rely on time averaged
velocity deficit wake models producing quasistatic 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 poststall operating environment producing transient
effects. Both threedimensional quasistatic 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
360 010 1020 2030 3040 4050 5060 6070 7080 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
threebladed, 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 “10min.”). The 10minute average...
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 Spring '11
 O.Uzol
 Aerodynamics, Wind turbine, tower shadow, yaw error, Unsteady Aerodynamics Experiment

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