Page 61 - Wind Energy Handbook

TURBULENCE IN WAKES AND WIND FARMS 35

geography and surface roughness conditions in the area surrounding the wind-
s
farm are then modelled by the WA P program (Mortensen et al., 1993). A turbine
wake interaction model PARK (Sanderhoff, 1993) then takes account of wind
direction in relation to the actual turbine positions to calculate wake losses, and
finally a statistical model (as described in the previous section) combines the
meteorological forecasts with recent measurements on the wind farm to give
predictions of the energy output which are good enough to be useful in planning
the deployment of other power stations on the network.

2.10 Turbulence in Wakes and Wind Farms

As it extracts energy from the wind, a turbine leaves behind it a wake characterized
by reduced wind speeds and increased levels of turbulence. Another turbine
operating in this wake, or deep inside a wind farm where the effects of a number of
wakes may be felt simultaneously, will therefore produce less energy and suffer
greater structural loading than a turbine operating in the free stream.
Immediately behind a turbine, its wake can crudely be considered as a region of
reduced wind speed slightly larger in diameter than the turbine itself (Vermeulen,
1980). The reduction in velocity is directly related to the thrust coefficient of the
turbine, since this determines the momentum extracted from the flow. As this
reduced wind speed region convects downstream, the wind speed gradient be-
tween the wake and the free flow outside the wake results in additional shear-
generated turbulence, which assists the transfer of momentum into the wake from
the surrounding flow. Thus the wake and the surrounding flow start to mix, and
the region of mixing spreads inwards to the centre of the wake, as well as outwards
to make the width of the wake increase. In this way, the velocity deficit in the wake
is eroded and the wake becomes broader but shallower until the flow has fully
recovered far downstream. The rate at which this occurs is dependent on the
ambient turbulence level.
In addition to this shear-generated turbulence, the turbine itself generates
additional turbulence directly, as a result of the tip vortices shed by the blades and
the general disturbance to the flow caused by the blades, nacelle and tower. This
‘mechanical’ component of turbulence is of relatively high frequency, and decays
relatively quickly. Bossanyi (1983) develops a theoretical model which describes
how this additional turbulence might decay: large eddies give rise to smaller ones,
and so the turbulent energy moves to higher and higher frequencies until it is
eventually dissipated as heat. The model predicts a faster rate of decay in low
winds and in high ambient turbulence intensities.
Beyond the near wake region, once the shear-generated turbulence has reached
the centre of the wake and started to erode the centreline velocity deficit, the mean
velocity variation in the wake can be described well by an axisymmetric profile
with a Gaussian cross-section. The development of the wake profile downstream of
this point can be reasonably well predicted, for example using an eddy viscosity
model (Ainslie, 1988). This is partly theoretical, derived from the Navier–Stokes
equation of fluid flow, but with some empirical terms.