c) At the higher wind speed, a larger region near the root on the windward side remains laminar. 

d) The transition line predicted using the Michel’s transition model in conjunction the Spalart-Allmaras turbulence model has a kink near the 33% radius. The reason for this behavior is not known at this writing.

Figure 6 shows the transition lines on the upper surface at 8m/s.  Eppler’s model predicts that transition will occur near the leading edge, as a result of leading edge separation. Michel’s model, on the other hand, predicts transition around 50% chord, with a considerable radial variation in the transition location, especially near the root. 

The large difference observed in the upper surface transition pattern of the rotor between the 8 m/s and the 6 m/s is attributable to the changes in the operating state of the turbine. For the Phase III rotor at 72 rpm, as the wind speed increase to around 8m/s, the operating state switches from a wind turbine state to a turbulent wake state (Wilson, R. E. et al., 1974).

Yaw Results 

The hybrid code has been modified to account for three yaw effects as described earlier. The Phase III rotor was studied for a 10 m/s wind, and a 20-degree fixed yaw condition. Figure 7 shows the total power generated by all the three blades, taking into account the phase difference among the blades. The instantaneous power curve shows high frequency components superposed on a mean value. The power fluctuations are about 4% of the time-averaged power. The time-averaged values are in good agreement with NREL data.

Figure 7 is the result after Fourier filtering of the present results because the data from the simulation contain numerical noise. For example, in the present simulations, the wake induced velocity is updated once every 10 degrees of azimuth. This produces numerical noise at a wave number of 36, that must be filtered out.

Measurements for the Phase IV rotor of NREL were comparied with results of Hybrid solver. The Phase IV rotor of NREL has the same geometry as the Phase III rotor, but has improved measurement devices. A time series of unsteady measurement lasts 16 seconds, or 18 revolutions of the rotor. The measured data not only includes the effects of yaw and unsteady wind inflow, but also other effects such as the tower shadow and wind shear. Figure 8 shows the unsteadiness of the measured wind. 

Figure 9 compares the present hybrid method results with the measured data at five typical time intervals, each interval correspionding to one blade revolution. Both the computed data and the measurements show comparable  fluctuations in the power, about comparable mean value. 

CONCLUDING REMARKS

The Georgia Tech wind turbine code has been extensively modified. The transition from laminar flow to turbulent flow is now modeled using empirical transition models. Phenomenological one-equation turbulence models have replaced algebraic turbulence models. The code has been modified to model yaw effects. Preliminary calculations done to validate these enhancements show that the predictions are consistent with measurements. 

ACKNOWLEDGEMENTS

The National Renewable Energy Laboratory (NREL) supported this work. Alan Laxson and Scott Schreck of NREL, and Walter Wolfe of Sandia National Laboratory are the technical monitors.

REFERENCES

Tuncer Cebeci, "Essential Ingredients of a Method for Low Reynolds-Number Airfoils," AIAA Journal Vol. 27, No. 12, December 1989, pp. 1680-1685.

Chen, K. K., and Thyson, N. A., "Extension of Emmons' Spot Theory to Flow on Blunt Bodies," AIAA Journal, Vol. 9, 1971, pp. 821-825

Eggleston and Stoddard, Wind Turbine Engineering Design, ISBN 0-442-22195-9

Eppler, R., Airfoil Design and Data, New York, NY, Springer-Verlag, 1990, 562 pp.