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Motivations Vortex Structure and Treatment of Yaw Equation for the Circulation

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.

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Motivations Vortex Structure and Treatment of Yaw Equation for the Circulation

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  1. VALIDATION OF A HELICOIDAL VORTEX MODEL WITH THE NREL UNSTEADY AERODYNAMIC EXPERIMENTJames M. Hallissy and Jean-Jacques ChattotUniversity of California DavisOUTLINE • 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 • Vortex Structure • 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 =10 deg =5 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, 0 20 deg • The vortex model will be used as far field condition with a near field Navier-Stokes simulation.

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