1. VALIDATION OF A HELICOIDAL VORTEX MODEL WITH THE NREL UNSTEADY AERODYNAMIC EXPERIMENT James M. Hallissy and Jean-Jacques Chattot University of California Davis OUTLINE
Motivations
Vortex Structure and Treatment of Yaw
Equation for the Circulation
Convection in the Wake
Results
Conclusion
43rd AIAA Aerospace Sciences Meeting and Exhibit
24th ASME Wind Energy Symposium, Reno, NV, Jan.10-13, 2005

2. MOTIVATIONS
Assess the Prediction Capabilities of Model in “Stand-alone” Mode
Analyze the Effect of Yaw as Source of Unsteadiness
Validate the Model as Far-Field Boundary Condition for Navier-Stokes Simulation

3. VORTEX STRUCTURE AND TREATMENT OF YAW
Small Disturbance Treatment of Wake
Application of Biot-Savart Law
Blade Element Flow Conditions

4. VORTEX STRUCTURE
Vortex sheet constructed as perfect helix with variable pitch from average power:

5. SMALL DISTURBANCE TREATMENT OF WAKE
Vorticity is convected along the base helix, not the displaced helix, a first-order approximation

6. APPLICATION OF BIOT-SAVART LAW

7. BLADE ELEMENT FLOW CONDITIONS

8. EQUATION FOR THE CIRCULATION
2-D Viscous Polar
Kutta-Joukowski Lift Theorem

9. 2-D VISCOUS POLAR S809 profile at Re=500,000 using XFOIL
+ linear extrapolation to

10. KUTTA-JOUKOWSKI LIFT THEOREM

11. NONLINEAR TREATMENT
Discrete equations: If
Where

12. NONLINEAR TREATMENT (continued)If
is the coefficient of artificial viscosity
Solved using Newton’s method

13. CONVECTION IN THE WAKE Mesh system: stretched mesh from blade
To x=1 where
Then constant steps to
Convection equation along vortex filament j:
Boundary condition

14. CONVECTION IN THE WAKE (continued)

15. RESULTS
Flow velocities and yaw angles analyzed at 30, 47, 63, 80 and 95% span

16. STEADY FLOW
Blade working conditions: attached/stalled

17. STEADY FLOW
Power output comparison

18. STEADY FLOW
Comparison of dynamic pressures at specified spanwise locations

19. STEADY FLOW
Normal forces comparison
y=30%
y=47%
y=63%
y=80%
y=95%

20. STEADY FLOW
Tangential forces comparison
y=30%
y=47%
y=63%
y=95%
y=80%

21. YAWED FLOW
Blade working conditions for V=10 m/s, =20 deg

22. YAWED FLOW
Torque versus azimuth angle for V=10 m/s, =10 deg

23. YAWED FLOW Time-averaged power versus velocity at different yaw angles
=5 deg
=10 deg
=20 deg
=30 deg

24. YAWED FLOW
Force coefficients versus azimuth at 63% span, V=10 m/s, =10 deg

25. CONCLUSIONS
The helicoidal vortex model is accurate in steady flow when flow attached (V 8 m/s) and for partially separated flow (V 10 m/s)
The effect of yaw is well accounted for in the range V 10 m/s, deg
The vortex model will be used as far field condition with a near field Navier-Stokes simulation.