Environmental Engineering Reference
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effects. This equation was then solved using a finite difference algorithm [Snel et al . 1994].
Later, Du and Selig [2001] solved a similar equation set in alternative fashion, and captured
key parameter variations in phenomenological relationships. In similar fashion, Eggers and
Digumarthi [1992] began with the Navier-Stokes equations, but applied different criteria to
arrive at a reduced equation set, which was then solved analytically. The approach adopted by
Corten [2001] also began with the Navier-Stokes equations, but diverged from prior approach-
es by excluding the effects of viscosity. Separation over the aft blade surface was introduced
via prescription, permitting emergence and characterization of pronounced radial flows.
Shen and Sørensen [1999] approximated the governing equations for flow over a rotating
blade using an order of magnitude analysis, to efficiently account for rotational and spanwise
flow effects. Resulting quasi-three-dimensional laminar and turbulent computations showed
that rotational influences became more pronounced at locations nearer the rotation axis, re-
ducing the chordwise extent of separation and amplifying aerodynamic forces. Chaviaropou-
los and Hansen [2000] constructed a quasi-three-dimensional computational model, and then
used it in a parametric study that showed orderly trends in three-dimensionality and rotational
effects in response to blade taper ratio and twist distribution. Sorensen et al . [2002] solved the
full Navier-Stokes equations for the Phase VI flow field, without reduction or empiricism.
Dynamic Stall
Dynamic stall initiates when the aerodynamic surface incidence angle (local inflow an-
gle or angle of attack) dynamically exceeds the static stall angle. Soon thereafter, unsteady
boundary layer separation gives rise to a small but energetic dynamic stall vortex, which ap-
pears near the leading edge. This vortex quickly grows, convects rapidly downstream toward
the trailing edge, and soon sheds from the lifting surface.
During this process, the dynamic stall vortex generates a region of low pressure on the
lifting surface, causing dramatic lift amplification beyond static levels, followed by abrupt
deep stall at vortex shedding [McCroskey 1977, Carr 1988]. Surface pressure signatures
confirm that dynamic stall occurs on horizontal-axis wind turbine blades [Shipley et al. 1995,
Robinson et al. 1995, Huyer et al. 1996] and contributes significantly to rotor loads and yaw
dynamics [Hansen et al. 1990].
The complexity of dynamic stall is compounded by three-dimensionality, or nonunfor-
mity of the vortex structure along the length of the vortex. The three-dimensionality of a
dynamic stall vortex has been visualized for a rectangular wing pitching in a wind tunnel
[Freymuth 1988]. Visualizations have been corroborated with time-varying surface pressure
measurements, which also were acquired using rectangular wings pitching in wind tunnels
[Robinson and Wissler 1988, Schreck et al. 1991, Lorber et al. 1992, Schreck and Helin
1994, Piziali 1994]. More recently, dynamic stall vortex three-dimensionality was observed
during yawed turbine operation via analyses of time varying surface pressure data [Schreck
et al. 2000 and 2001].
Inflow Angle Oscillation
With the turbine rotor disc yawed relative to the wind inflow vector, blade incidence
angle (local inflow angle or angle of attack) oscillates in pseudo-sinusoidal fashion as the
blade rotates in azimuth about the rotor axis. Figure 5-52 shows LFA (local inflow angle) as
a function of Y, the blade azimuth angle, at four five-hole probe locations, for U ¥ = 13 m/s
and a rotor yaw angle of 40 deg. At Y = 0 deg, the instrumented blade is situated at the 12
o'clock position, and the period of one rotor revolution is 0.838 s.
These pseudo-sinusoidal oscillation amplitudes with a dominant frequency of one-per-
rotor revolution are largest at 0.34 R and decrease progressively at radial stations farther out-
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