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Slide 1 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Wind and wake modelling using CFD
Jens A. Melheim
CMR GexCon
Wind Power R&D seminar, 20-21 January 2011, Trondheim
Slide 2 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Outline
• Motivation
• CFD models
– Background
– Turbulence models
– Wind modelling
• Wake models
– Wind deficit models
– Rotor models
• Offshore wind farms
Slide 3 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Motivation
• Wake loss is a large uncertainty when planning wind farms
• Computations of wake losses can be used to:
1. Foresee energy output from a wind farm
2. Optimize wind farm layout
• No industry standard for computation of wake losses in multiple wake cases
Slide 4 / 21.01.2011, Wind Power R&D Seminar, Trondheim
CFD - Computational Fluid Dynamics
• Solve the Navier-Stokes equations on a grid
• Impractical to resolve the smallest time and length scales in a turbulent flow -> solve averaged or filtered Navier-Stokes equations
– Need model for unresolved scales –> turbulence model
• Use a finite volume formulation
• Assume incompressible flow
– Prediction-correction algorithm to obtain pressure field
• Results can not be better than:
1. Models for unresolved physics
2. Boundary conditions
Slide 5 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Turbulence models• Closure for the unknown Reynolds stresses that
appear in the Navier-Stokes equations after averaging/filtering
– RANS: Reynolds Averaged Navier-Stokes
• Turbulent viscosity models
– Use a turbulent viscosity and mean velocity gradients to model the Reynolds stresses
– Solve transport equations for 1 or 2 turbulence parameters
– k-L, k-ε, k-ω
• Reynolds stress models
– Solve transport equations for 6 Reynolds stresses + dissipation rate of turbulent kinetic energy (ε)
• Large eddy models
– Solve filtered N-S eq. using a grid size dependent filter
' 'i ju uρ−
Slide 6 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Characteristics of wind farms
• Large domains (L=1-20 km)
• Large range of time and length scales
• Moving rotors and high tip speeds
• Anisotropic turbulence in wake regions
• Unsteady boundary conditions
Impossible to resolve all physics
Slide 7 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Implications • Large domains (L=1-20 km)
– Only RANS based models applicable without using super computers.
• Large span of time and length scales
– Wall functions at ground / ocean
– Blades cannot be resolved in detail
• Moving rotors with high tip speed
– Average over a rotor swept
• Anisotropic turbulence in wake regions
– Turbulent viscosity models are not accurate in the near wake
• Unsteady boundary conditions
– Assume steady state when planning
Slide 8 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Wake models• Explicit wake models
– Calculate wind speed deficit in the wake
– WaSP, WindSim
• Parabolic models / Eddy viscosity models
– Start ~2D downstream of turbine using Gaussian wake profiles
– Solve simplified Navier-Stokes on axis-symmetric grid or 3D grid
– ECN Wakefarmer, GH Windfarmer, FLaP (Uni Oldenburg)
• Full CFD models
– Model turbine by momentum sink
– NTUA CFD, Ellipsys3D, CENER, CRES, RGU-3D-NS
Slide 9 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Wind turbine models• Actuator Disc models
– Model rotor area by a porous disk
– Momentum sink uniformly distributed
– No mature model for turbulence generation
• Actuator line / Actuator surface models
– Model each blade using a line or a surface
– Use BEM to calculate local forces
– Time step restricted by the tip speed
• Direct methods
– Geometry models of moving blades (moving grid)
– Resolve flow at blade
rdr
Wind Profile
Slide 10 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Summary of wake modelsModel Pre Cons Multiple wakes?
Explict models QuickVery easy to use
Need to tune parametersNo physics solved
No
Parabolic models/ Eddy viscosity
QuickEasy to use
Terrain (2D models)Multiple wakes
Tuning needed
Full CFD with Actuator Disc model
Solve most physicsEasy input
SlowTurbulence productionNot accurate in near wake
Yes
Full CFD with Actuator Line/Surface
Solve most physicsAccurate in near wake
Very slowRequires detailed blade and airfoil data
Maybe
Full CFD with direct blade model
Solve ”all” physicsAccurate in the near wake
Extremely slowMuch work to setup
No
Slide 11 / 21.01.2011, Wind Power R&D Seminar, Trondheim
CFD – Actuator Disc• Momentum sink in control volumes inside the
rotor area – uniformly distributed over disc area
• Turbulence production caused by wind turbine
– No established model for turbulence generation
Slide 12 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Actuator Disc Improvement
cos( ) sin( )sin( ) cos( )
n L D
t L D
dF F FdF F F
φ φφ φ
= += −
• Blade Element Momentum (BEM) Theory yield a better distribution of forces than the traditional AD method.
AD:
BEM:
20
12
0
n t
t
dF C U dA
dF
ρ=
=
Slide 13 / 21.01.2011, Wind Power R&D Seminar, Trondheim
• El Kasmin & Masson (2008):
• Rethoré et al (2009)
• BEM
Turbulence production
( ) 0
1
k n t
k
S dF dF aU
S C Skε ε
αε
= −
=
2
4tPS Ckε ε ρ
=
A. El Kasmin & C. Masson (2008). Journal of Wind Engineering in Industrial Aerodynamics 96:103-122
( )
( )( )( )( )
20
30 0
34 0 5 0
12
1212
U x
k x p d
x p d
S C aU
S C aU kaU
S C C aU C kaUkε ε ε
β β
ε β β
= −
= −
= −
P.-E. Rethore et al. (2009). EWEC 2009
Slide 14 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Sexbierum experiment• West coast of the Netherlands
• Polenko/Holec WPS 30 wind turbine
• Wind 10 m/s at hub height (35 m)
• Turbulence intensity 10%
• Thrust coefficient Ct=0.7
• Measurements 2.5D, 5.5D and 8D downstream at hub height
Slide 15 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Sexbierum experiment
• Wake wind speed deficit:
x=2.5D x=5.5D x=8D
Slide 16 / 21.01.2011, Wind Power R&D Seminar, Trondheim
Conclusions
• The combination of full CFD with RANS based turbulence model and Actuator Disc is a promising technique for modelling of wake losses in wind farms
• Better understanding and modelling of the turbulence in the near-field of the rotor are needed
• Validation and benchmarking are key factors for success
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