Simulation and Modelling of Wakes and Turbulence in Wind Farms

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1 Simulation and Modelling of Wakes and Turbulence in Wind Farms Jens N. Sørensen, Niels Troldborg, Robert Mikkelsen, Dan Henningson and Stefan Ivanell Mechanical Engineering Technical University of Denmark

2 Wake Aerodynamics Wake development: Near wake? Far wake : Axial velocity : Turbulence intensity

3 Wake Aerodynamics Basic questions: How important is the dynamics of the vortex system How does the strength of the vortices depend on the blade load How does roll-up take place Can we determine the conditions for instability How far does far-wake refer to How far downstream can BEM be applied What is the relationship between vortex dynamics and meandering How does the added turbulence intensity relate to the loading

4 Single Wind Turbine Wake development: Stable vortex system Unstable vortex system

5 The actuator line technique Basic idea: Replace rotor blades by body forces Determine body forces from aerofoil data Simulate flow domain using DNS or LES Computing code: EllipSys3D Inflow Body forces Outflow

6 EllipSys3D Developed in close collaboration between DTU J. Michelsen and Risø N.N. Sørensen Incompressible Navier-Stokes, 2D and 3D Block structured Multi block / Multi grid Parallelized using MPI Up to 50 mill. mesh points Turbulence models: K-ε, K-ω, DES, LES, 3D Transition Computer facility: 210 CPU-node cluster

7 The Actuator Line Technique Regular 3D Grid V rθz Linear interpolation No tip correction is applied Forces smeared out B + + i i f x = F s η p dndt i= 1 1 MEK Fluid Mechanics Section Technical University of Denmark

8 Vortex structures in the wake of a rotor

9 Vortex structures in the wake of a rotor

10 Vortex structures in the wake of a rotor

11 Stability analysis of vortex structures

12 Vortex structures in the wake of a rotor TSR=11.8; V=6m/s TSR=7.1; V=10m/s TSR=5.0; V=14m/s TSR=3.2; V=22m/s

13 Vortex structures in the wake of a rotor TSR=11.8; V=6m/s TSR=7.1; V=10m/s TSR=5.0; V=14m/s TSR=3.2; V=22m/s

14 Wind Shear and Turbulence > Δ Δ + = y h y w y y c y c w y w hub α t m + = u u f ρε & exp 1, 2 = = ε π ε η η ε ε ε d d f f Model of wind turbulence Power law wind shear profile Fluid Mechanics

15 Sexbierum wind farm Mean axial velocity Turbulence intensity of axial velocity component

16 Vortex structures in the wake of a row of rotors Development of wake behind three rotors in a row at W 0 = 10 m/s; Turbine spacing 6 rotor radii. A Constant inflow; B Turbulent inflow.

17 Simulation of turbulence inside wind farm Basic idea: Replace rotor blades by body forces Determine body forces from aerofoil data Simulate an infinite row of turbines using cyclic boundary conditions Cyclic b.c. Body forces Cyclic b.c.

18 Simulation of turbulence inside wind farm Cross sectional turbulent flow fields: Iso-vorticity contours in the final stage

19 Proper Orthogonal Decomposition Galerkin projection on the Navier-Stokes equations: Reconstruction of velocity field: = + = N i k i i k k x t a x V t x V 1, r r r φ k j ijk j ij i i a a a t a γ β α + + = t a a i i = x k i r φ Amplitude function for mode i at time t: Spatial mode i :

20 Reconstruction of turbulence inside wind farm Proper Orthogonal Decompositon: POD Mode 1 POD Mode 2 POD Mode 3 POD Mode 8 = + = N i k i i k k x t a x V t x V 1, r r r φ

21 Horns Rev wind farm

22 Simulation of performance in Horns Rev wind farm

23 Simulation of performance in Horns Rev wind farm

24 Wind Turbine Wake Structures Summary A numerical wake model based on the actuator line technique and body forces has been developed The model enables to study single wake behaviour as well as the interaction of wakes from a multiplicity of wind turbines Computational results have been compared to experimental data. The agreement is generally very good. A turbulence generator based on POD reconstruction of computed wake structures has been developed The technique has been utilized to simulate the Horns Rev wind farm The next step is to carry out a systematic parametrical study on turbine spacing, wind shear and free stream turbulence