Wind Energy

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48 Numerical Computations of Wind Turbine Wakes 261
Frame 001 ⏐ 27 Jan 2005 ⏐ volume solution
Fig. 48.2. x = 0-plane, pressure distribution; y = 0-plane, streamwise velocity; iso
surface, constant vorticity with a surface of a contour pressure distribution
block side. The total number of node points are then: 5.5×10 5 , 1.3×10 6 , 2.6×
10 6 , and 4.4 × 10 6 .
The sensitivity of the Gaussian smearing and the Reynolds number has
also been studied.
An evaluation method to extract values of the circulation from the wake
flow field is developed. When the circulation is evaluated in the wake, an
integration is performed around a loop, enclosing the vortex. Each vortex is
evaluated in terms of its circulation in a plane perpendicular to the turbine
disc. The vortex created at the tip, or at least close to the tip, is evaluated
every 30 ◦ behind the blade. The root vortex is evaluated in the same manner
but since the vortices tend to be smeared out further downstream, because of
diffusion, it is more difficult to evaluate the circulation further downstream in
this case. The circulation is integrated at a specific value of the vorticity.
The sensitivity of the circulation with respect to the grid resolution has
been evaluated. The evaluation was performed with three different grid sizes,
64, 80, and 96 node points at each side of the blocks. The solution converges
with greater grid size.
Some wiggles appear at some distance downstream and can probably be
explained by a too few number of grid points when the circulation is integrated
and because of increasing smearing of the cores further downstream. When
using a finer grid, the vortices become more concentrated and the integration
can be performed further downstream without large fluctuations in the result.