A two step precedure has been used for modeling yaw effects. The first step simulates axial flow conditions at a given wind speed.  When the hybrid code has converged,  the tip vortex strength, and the wake geometry for the axial flow condition are saved. These quantities serve as the initioal condition for the second step, where the wake geometry is skewed as discussed above, and the edgewise velocity component is applied to the “freestream” velocity. 

At every 10 degree increments in azimuth, the peak bound circulation strength at that azimuthal angle is set to be the strength for all the tip vortex segments that were shed from all the blades when they were at that azimuthal angle.  After two revolutions of the refrence blade, the flow field may be considered to be well-developed and periodic.

Unlike the axial flow condition, the flow properties of the reference blade will not converge to a steady state solution in yaw. Repeatability of the blade loads from one revolution to the next is used as the criterion for convergence.

RESULTS AND DISCUSSION

Transition Model and Turbulence Model Studies: 

The Eppler and Michel transition models, along with the Baldwin-Lomax and the Spalart-Allmaras turbulence models have been fully integrated into the Georgia Tech hybrid code. Figure 3 and Figure 4 show the prediction transition lines on the upper surface and lower surface for a wind turbine known as NREL Phase III rotor (Schepers 1997), operating at a wind speed of 6 m/s.  The rotor operates at 72 rpm. At this low wind speed condition, the flow field behaves nicely, with attached flow over most of the rotor. In these figures, the legends '0 eqn' and '1 eqn' represent the Baldwin-Lomax and the Spalart-Allmaras models, respectively.

On both the upper and the lower surface, Eppler’s model predicts a transition location that is upstream of Michel’s predictions. Eppler’s model, as implemented in the present code, first checks to see if laminar boundary layer has separated. If so, Eppler’s model assumes that transition has occurred. Note that the inflexion point on the separated flow boundary layer will cause Tollmien-Schlichting instability to develop, causing transition. The Michel criterion, on the other hand, bases its transition criterion primarily on the boundary layer thickness. At this wind speed, the boundary layer has to grow up to 55% chord or so, before Michel’s criterion detects transition.

On the lower surface, the pressure gradients tend to be more favorable than on the upper side. This leads to a thinner boundary layer and separation aft of the 40% chord. As a consequence, both these criteria predict that transition will occur aft of the corresponding upper surface locations.

The Reynolds number near the root is less than 105.  Both models predict that the flow will remain laminar all the way to the trailing edge near the root region. It is also observed that the transition line location is relatively insensitive to the turbulence model used.

Figure 5 shows the transition lines on the lower surface of the CER Phase III rotor at 8m/s.  Even though the overall pattern of the transition lines is similar to the 6m/s case, the following differences may be observed:

a) Michel’s model predicts that the transition phenomenon over much of the lower surface is delayed, compared to the 6m/s case. This is attributable to the higher local angle of attack the blade sections operate in, and the favorable pressure gradients that exist on the windward side of the rotor.

b) The Eppler transition model, on the other hand, predicts transition lines that are similar at the 8m/s and 6m/s conditions, presumably because laminar separation is detected in the vicinity of 40% chord at both these wind conditions. Notice that the maximum thickness location for the S-809 airfoil is near 40% chord. The pressure gradient tends to be favorable from the leading edge up to 40% chord, after which it becomes adverse at both these wind conditions.