Analysis of rotor wake measurements with the inverse vortex wake model Second PhD Seminar on Wind Energy in Europe October Risø National Laboratory Roskilde, Denmark Wouter Haans Delft University of Technology Delft, The Netherlands

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

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

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

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

hot-wire anemometry Ψ = 0°, 30°, 45°; θ tip = 2°; λ = 8 (& 5.5) (Very) near wake measurement planes: z/R = , 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

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

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

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

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)

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

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

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

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

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) [-]

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

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 ∞ [-]

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