1. Analysis of rotor wake measurements with the inverse vortex wake model Second PhD Seminar on Wind Energy in Europe October 4-5 2006 Risø National Laboratory Roskilde, Denmark Wouter Haans Delft University of Technology Delft, The Netherlands w.haans@lr.tudelft.nl

2. Presentation outline Model wind turbine rotor Rotor wake measurements Inverse vortex wake model The idea Constructing the model Results Conclusions

3. The setup: model rotor in the tunnel View from downwindTop view rotormeasurementsmodelresultsconclusions

4. Characteristics Radius R0.6 m # blades2 airfoilNACA0012 Chord c0.08 m Twist (θ tip – θ root )-4° Solidity σ5.9 % W0W0 θ θ tip = 2° Tunnel radius1.12 m Speed W 0,max 14.5 m/s Turbulence Tu1.2 % @ W 0 = 5.5 m/s 1.4 % @ W 0 = 8.0 m/s rotormeasurementsmodelresultsconclusions

5. Ψ W0W0 Ω c T & smoke visualization Range of yaw angles Ψ, tip pitch angles θ tip and tip speed ratios λ: Ψ = 0°, 30°, 45°; θ tip = 0°, 2°, 4°; λ = 6, 8, 10 Thrust recordings Photos on upwind and downwind side Average tip vortex locations Wake geometry characteristics rotormeasurementsmodelresultsconclusions

6. hot-wire anemometry Ψ = 0°, 30°, 45°; θ tip = 2°; λ = 8 (& 5.5) (Very) near wake measurement planes: z/R = 0.0583, 0.10, 0.15 Resolution: In-plane: Δθ = 15°, Δr/R = 0.1 Temporal: Δθ b = 2° Determined are: Phase-locked average of 3D velocity Phase-locked standard deviation of V eff W0W0 Ψ θbθb θ r z rotormeasurementsmodelresultsconclusions

7. Unsteady near-wake velocity field rotormeasurementsmodelresultsconclusions Axial flow Rotor setting: λ = 8, θ tip = 2°  near maximum power coefficient 5.83 % R downstream of rotor plane Contour: axial velocity Vector: in-plane velocity Contour: standard deviation of effective velocity

8. The idea: an inverse approach Measurements yield wake velocity & geometry Conditions at blade not recorded: no loads, bound circulation, inflow Concept of a vortex wake model  Bound circulation determined from inverse vortex wake models rotormeasurementsmodelresultsconclusions Bound circulation Γ b Trailed circulation Γ t & shed circulation Γ s Induced velocity V Conservation of circulation Vortex wake geometry Biot-Savart law Blade model

9. Constructing the model Inviscid flow  circulation conservation All circulation contributes to induced velocity at point p in rotor wake Bound circulation Γ b Trailed circulation Γ t Shed circulation Γ s At blade: each Γ-contribution expressed in Γ b location & orientation known for all Γ-segments Measured wake convection rotormeasurementsmodelresultsconclusions V0V0 Wake point p ΓbΓb ΓtΓt ΓsΓs

10. Constructing the model - discretizing Discretization of the vortex wake: In radial direction n Γ b(i,j) -segments i = 1, 2, …, n In azimuth direction m Γ b(i,j) -segments j = 1, 2, …, m Trailing circulation: Shed circulation: Per azimuth angle, p points at which induced velocity is computed rotormeasurementsmodelresultsconclusions V∞V∞ Γ b(1,j) Γ b(i,j) Γ b(n,j) Γ t(i,j) Γ t(n+1,j) Γ t(1,j) Γ s(i,j)

11. Constructing the model – discretizing p : number of wake points m : number of blade azimuth angles n : number of radial bound circulation segments System of p*m equations with A : (p*m) x (n*m) aerodynamic influence matrix: measured (+assumed) Γ : (n*m) bound circulation vector: unknown V-V ∞ : (p*m) induced velocity points vector: measured When p<n : over-determined system  Least-Squares solution for Γ b rotormeasurementsmodelresultsconclusions

12. Constructing the model – axial flow Axial flow: steady flow field for rotating observer No shed vorticity Single blade azimuth angle  simplification & size reduction of system of equations: length of unknown Γ-vector is n, instead of (n*m) rotormeasurementsmodelresultsconclusions

13. Constructing the model – axial flow Assumptions used to determine matrix A Wake topology rotormeasurementsmodelresultsconclusions Vortex sheet Tip & root vortex Measured ? Very-near wakeYes Near wakeNoYes Far wakeNoYesNo

14. Constructing the model – axial flow Assumptions used to determine matrix A Root vortex: convection in axial direction only, with V ∞ Tip vortex: Very-near: from smoke visualization & near wake Far wake: constant radius helix Vortex sheet: convection in axial direction only, from wake age rotormeasurementsmodelresultsconclusions

15. Bound circulation distribution Rotor setting: λ = 8, θtip = 2°  near maximum power coefficient Number of bound circulation segments: 7 (unknowns) Number of velocity points: 36 (equations) Bound circulation nearly constant across span To check fit: relative residual This case: rel. res. = 6.46·10 -2 rotormeasurementsmodelresultsconclusions Γ/(V 0 * R) [-]

16. Bound circulation distribution Dependency on size of vortex sheet rolling up into root vortex rotormeasurementsmodelresultsconclusions Indicated with dots V∞V∞ tip root minimum Γ b with minimum relative residual

17. Wake velocity distribution Velocity: computed by inverse wake vortex model versus measured ‘optimal’ bound circulation distribution Comparison: blade passage (inviscid) trends agree wake passage (viscous) trends disagree rotormeasurementsmodelresultsconclusions Wake location: (r, θ,z) = (0.6R, 90°, 5.83·10 -2 R) Axial velocity ○: computed ×: measured Tangential velocity Radial velocity V/V ∞ [-]

18. Inverse vortex wake model: added value Wake measurements: Detailed near wake velocity field description No bound circulation / blade loads Suited for inverse vortex wake model construction Inverse vortex wake model: Based on vortex theory & measurements only Vortex wake geometry definition subject to assumptions Circulation distribution determined for axial flow Yawed flow computations are ongoing! rotormeasurementsmodelresultsconclusions