Aerodynamics and aeroelastics of wind turbines - Wind Power Generation and Wind Turbine Design - page 102

of CPU time and terrabytes of data. After Large Eddy Simulation (LES), the next
stage of simplifi cation is Reynolds averaged Navier Stokes equations (RANS). An
ensemble average, which is assumed to be a time average by an ergodic hypothesis
is carried out for all fl ow quantities.
Turbulence then emerges as a never ending hierarchy of higher correlations
which has to be truncated by the so-called closure assumption. In wind-turbine
applications at the present time the k - w shear stress transport (SST) extension of
Menter isfrequently used. k is the turbulent kinetic energy (per unit mass) and w is
a local frequency scale. Unfortunately all these empirical turbulence models
describe only fully developed turbulent fl ow and are not able to resolve the transi-
tional region from laminar to turbulent fl ow. There are good reasons to believe that
parts of the blade must be laminar because otherwise the large L2D ratio cannot be
achieved for c P of the order of 0.5.
At UAS Kiel from 2000-2003 a program [65] comparing 2D-CFD simulation
with measurements was carried out. A 30% thick airfoil from Delft University was
chosen: DU-W-300-mod. For including transitional fl ow properties to e N - method
of Stock was included in DLR's structured CFD-Code FLOWer. The main fi ndings
of this project were as follows:

• Mesh generation with mostly orthogonal grids is very important. Therefore a

hyperbolic type of generating equation, namely

xx + yy = 0,

( 37)

xh xh

xy − yy = Δ A .

( 38 )

xh xh

was chosen. For details see [62].

e N method has to be parameterized with an N (usually between 6 and 9)
which is related to a surrounding turbulence intensity by Mack's correlation.
Comparison with wind tunnel measurements was diffi cult because the turbu-
lence intensity was not known exactly.
Prediction of

• The

•

ma c , meaning computation of fl ow separation (stall) was also
diffi cult, because the fl ow started to become unsteady.
Transition points were predicted correctly as long as only laminar separation or

L

•

Tollmien Schlichting (TS) instabilities triggered transition.
In addition, drag effects for example from Carborundun or Zig-Zag band were •

diffi cult to predict [ 28 ].

The situation becomes more complicated when whole blades are investigated.
Correct prediction of overall power curves is seen to be very diffi cult. The picture
is uneven [37] but parametric studies such as for wings including winglets [35]
give valuable insight into the fl ow fi eld and comparative changes. This is especially
important when discussing performance enhancements.
Much better results can be achieved when no turbulence has to be included in
the discussion. This is always the case, when basic studies have been performed