Wind and wake modelling using CFD - SINTEF · Wind and wake modelling using CFD Jens A. Melheim CMR GexCon Wind Power R&D seminar, 20 -21 January 2011, Trondheim. ... • Polenko/Holec

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


Outline

• Motivation

• CFD models

– Background

– Turbulence models

– Wind modelling

• Wake models

– Wind deficit models

– Rotor models

• Offshore wind farms


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


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


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−


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


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


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


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


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


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


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=

=


• 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


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


Sexbierum experiment

• Wake wind speed deficit:

x=2.5D x=5.5D x=8D


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

Documents

Wind and wake modelling using CFD - SINTEF · Wind and wake modelling using CFD Jens A. Melheim CMR GexCon Wind Power R&D seminar, 20 -21 January 2011, Trondheim. ... • Polenko/Holec