Environmental Engineering Reference
In-Depth Information
where t is in seconds and
R
is in meters. It can be seen that the time scale associated with
shed vorticity is much shorter than that associated with trailing vorticity, and that both scales
increase linearly with rotor size. From this example, it is evident that the first focus on
aerodynamic transients should be on the trailing vorticity process. Further, the second focus
should be to determine the nature of t
g
, and t
b
.
The way in which an aerodynamic force approaches its steady-state value during a tran-
sient can be discussed qualitatively using an example in which a blade initially at pitch angle
b
1
is suddenly brought to pitch angle b
2
< b
1
. Since decreasing pitch increases angles of
attack, the aerodynamic force then goes from one positive value to a higher positive value.
The shed vorticity effect dies out in a time period of 2t
sv
to 3t
sv
. This leaves the blade with
the final pitch angle but the
initial
induced velocity, since t
tv
(which is also the time scale of
induction changes) is much longer than t
sv
. Hence, the aerodynamic forces will first exceed
the final forces and then decrease to them asymptotically as the added induced velocity de-
velops from the wake vorticity. In every case of sudden pitch change, transient forces will
go outside the range of the initial and final forces. Similar arguments can be used to examine
gust responses.
Dynamic Stall
Transient aerodynamics has another facet called dynamic stall, which is related to chang-
es in the lift curve near its peak and in the first stages of stall, resulting from oscillations in the
angle of attack. These changes often produce a
hysteresis loop
in the lift coefficient which
can, in turn, lead to cyclic pressure loadings that are not predictable from conventional lift
and drag data obtained at steady angles of attack. Increased excitation of blade structural-
dynamic modes becomes a possibility during dynamic stall. Analytical investigations of the
potential scope of these cyclic loads have been conducted using the
Gormont
model [1973]
and more recently the Leishman-Beddoes [1986, 1989] method. Dynamic stall effects have
been measured and analyzed for HAWT rotors by Hansen [1992] and Hansen and Butterfield
[1993], and these have also been analyzed by Berg [1983] for VAWT rotors.
The AeroDyn
Theory Manual
[Moriarty
et al.
2005] discusses the treatment of dynamic stall used in current
aero-structural dynamic codes
.
Vortex Generators
Faced with a tradeoff between thin airfoils with superior performance but inferior
strength and moderately thick airfoils with superior strength but inferior performance, wind
turbine designers have recognized the benefit from some sort of
boundary-layer control
to
increase the resistance of the boundary layer on a thicker airfoil to
adverse pressure gradi-
ents
. This delays separation and stall, and allows a moderately-thick airfoil to reach a higher
lift coefficient without a large drag penalty.
Re-energizing the boundary layer on a wind turbine blade can be achieved by mixing
the boundary layer air with faster-moving air from the free stream. This mixing occurs natu-
rally in a
turbulent boundary layer
, and one simple “fix” used to extend the performance of
a number of airfoils is to add a
trip strip
(a small step or band of roughness perpendicular to
the flow direction) to the low-pressure surface, to force the transition of a previously laminar
boundary layer to a turbulent one. However, the rate of momentum transfer in a turbulent
boundary layer is limited by the magnitude of the turbulence. If the turbulence could be
increased, the mixing rate would also increase, and there would be the potential for perfor-
mance improvements greater than those possible with trip strips.
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