VALIDATION OF A HELICOIDAL VORTEX MODEL WITH THE NREL UNSTEADY AERODYNAMIC EXPERIMENT James M' Halli

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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
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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

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VORTEX STRUCTURE AND TREATMENT OF YAW

• Vortex Structure
• Small Disturbance Treatment of Wake
• Application of Biot-Savart Law
• Blade Element Flow Conditions

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VORTEX STRUCTURE
Vortex sheet constructed as perfect helix with
variable pitch from average power
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SMALL DISTURBANCE TREATMENT OF WAKE
Vorticity is convected along the base helix, not
the displaced helix, a first-order approximation
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APPLICATION OF BIOT-SAVART LAW
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BLADE ELEMENT FLOW CONDITIONS
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EQUATION FOR THE CIRCULATION

• 2-D Viscous Polar
• Kutta-Joukowski Lift Theorem

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2-D VISCOUS POLAR
S809 profile at Re500,000 using XFOIL linear
extrapolation to
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KUTTA-JOUKOWSKI LIFT THEOREM
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NONLINEAR TREATMENT

• Discrete equations
• If
• Where

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NONLINEAR TREATMENT (continued)

• If
• is the coefficient of artificial
  viscosity
• Solved using Newtons method

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CONVECTION IN THE WAKE

• Mesh system stretched mesh from blade
• To x1 where
• Then constant steps to
• Convection equation along vortex filament j
• Boundary condition

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CONVECTION IN THE WAKE (continued)
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RESULTS
Flow velocities and yaw angles analyzed at 30,
47, 63, 80 and 95 span
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STEADY FLOW
Blade working conditions attached/stalled
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STEADY FLOW
Power output comparison
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STEADY FLOW
Comparison of dynamic pressures at specified
spanwise locations
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STEADY FLOW
Normal forces comparison
y30
y47
y63
y80
y95
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STEADY FLOW
Tangential forces comparison
y30
y47
y63
y95
y80
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YAWED FLOW
Blade working conditions for V10 m/s, 20
deg
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YAWED FLOW
Torque versus azimuth angle for V10 m/s,
10 deg
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YAWED FLOW
Time-averaged power versus velocity at different
yaw angles
10 deg
5 deg
20 deg
30 deg
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YAWED FLOW
Force coefficients versus azimuth at 63 span,
V10 m/s, 10 deg
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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.