Wind Turbine Aerodynamics Part A: Basic Principles - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 319

Transient Aerodynamics

Current state-of-the-art approaches use steady-state aerodynamics to determine aero-
dynamic forces, although the transient processes are well known. When aerodynamic tran-
sients occur during blade pitch changes, large-scale gusts or coherent turbulence (enveloping
the whole rotor), or small-scale turbulence (smaller than the swept area) the question arises
as to the time history of aerodynamic forces experienced by the rotor. If the initial force is
F 1 and the final force is F 2 , do transient forces ever fall outside the range between F 1 and F 2 ?
The answer this question if yes, because several processes are at work. First, pitch motion
and/or gusts will induce a circulation (and, therefore, a force) which varies with the pitch rate
and/or the gust strength . Second, during a transient, vorticity is shed parallel to the blade
that interacts with the blade to dampen the forced response. Finally, there is vorticity trail-
ing the blade, perpendicular to the span, which induces a flow that alters the angle of attack
experienced by the blade.

Time Scales

Some insight into the relative importance of these force-producing processes can be
inferred from their time scales. Let t g , t b , t sv , and t tv be the time scales associated with gusts ,
pitch changes , shed vorticity , and trailing vorticity , respectively. The gust time scale, t g , is a
function of the site (through its turbulence scale ) and the size of the rotor. The pitch-change
time scale, t b , is specific to a particular control system. The change in lift coefficient induced
by a pitch change at the rate d b/ dt is as follows:

c
r

d / dt
W

b

D C L , B » p
2

While the time scale t b is a significant parameter, the induced change in lift coefficient ap-
pears to be small, since c << r and d b/ dt << W.
The third time scale, t sv , is associated with the shed vorticity that is convected down-
stream. This vorticity is initially parallel to the blade-pitch axis and yields a force response of
the type [ 1 - exp (- t /t sv )], as exhibited by the classical Wagner gust function . In broad terms,
t sv = 5c / V r , so it can be seen that it varies with rotor size, tip-speed ratio, and position on the
blade, since blades are usually tapered and

V r » R W

The fourth time scale, t tv , is associated with vorticity trailing downstream from the rotor. A
simple actuator disk model of this process yields t tv = R / V , where V is the wake velocity near
the rotor.
Sample calculations of t sv and t tv , will illustrate their relative durations. Assume a
HAWT of radius R operating in a free-stream wind speed of 20 m/s, with a tip-speed ratio of
5.7, an axial induction factor of 0.2, and a chord-to-radius ratio of 0.045. Evaluating the shed
vorticity time scale at 3/4 span, the results are as follows:

Shed vorticity : t sv = 0.0026 R

Trailing vorticity : t tv = 0.0625 R