Wake modelling for offshore wind turbine parks. Jens N. Sørensen Department of Wind Energy Technical University of Denmark

Size: px

Start display at page:

Download "Wake modelling for offshore wind turbine parks. Jens N. Sørensen Department of Wind Energy Technical University of Denmark"

Jayson Beasley
5 years ago
Views:

1 Wake modelling for offshore wind turbine parks Jens N. Sørensen Department of Wind Energy Technical University of Denmark

2 Wake and Wind Farm Aerodynamics Basic questions and issues: How important is the dynamics of the vortex system Relationship between strength of the vortices and the blade load Conditions for instability How far downstream do near-wake and far-wake refer to What is the relationship between vortex dynamics and meandering How does the added turbulence intensity relate to the loading Performance predictions of wind farms Life time estimation of turbines in wind farms Influence of stability of the atmospheric boundary layer Estimation of wind resources in wind farm to wind farm interaction

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

4 Development of the wake Scenario: 1. Vortex system formed from circulation 2. Roll-up into center vortex and distinct tip vortices 3. Destabilization of tip vortices 4. Break down into large-scale turbulence 5. Turbulent mixing 6. Interplay with meandering

5 Visualizations of Wind Turbine Wakes Wake development: Stable vortex system Unstable vortex system

6 Modeling of vortex wake behind rotors Far wake model of Joukowski (1912) Observations Felli et al. (2008) Conclusion from stability analysis: The vortex wake behind a wind turbine is unconditional unstable Okulov and Sørensen JFM 576 (2007)

7 Instability Mechanisms Bluff body vortex shedding (Medici and Alfredsson, 2006) Mutual induction instability of the tip vortices (Okulov and Sørensen, 2007) Wake meandering due to ambient turbulence (Larsen et al., 2008) Centrifugal instability of the hub vortex (Viola et al., 2013) Meandering due to vortex/shear interaction (Schröttle et al., 2014)

8 The actuator line technique Basic idea: Replace rotor blades by body forces Determine body forces from aerofoil data Simulate flow domain using LES Inflow Body forces Outflow

9 Actuator disc/line models Basic elements of the model: Flow governed by Navier-Stokes equations Influence of rotor introduced through body forces Body forces determined either from axial drag force or from blade element theory using tabulated airfoil data Needs to be combined with LES No limiting scale restrictions: - Large scales created by body forces - Small scales feeded by larger scales - Small scales die out through dissipatation

10 Comparison with Experiments The NTNU blind-test wake experiment: Rotor diameter: 0.89m Blade airfoil: NREL S826 Krogstad and Eriksen: Renewable Energy 50 (2013)

11 Comparisons with Experiments Cp vs TSR Axial wake velocity Ct vs TSR Axial Reynolds stresses

12 Vortex Structures in the Rotor Wake Nonlinear transition Gaussian Linear amplification l RB X Gaussian l BG l RB X Breakdown X Rotor

13 Vortex pairing as main instability z/r

15 Vortex structures in the wake of a rotor Instability f=2 Instability f=5

16 Spatial growth rate as function of wave number 1/3 domain Full domain

17 Mutual inductance instability of tip vortices : Breakdown position z A e t e Uc A 0 Amplification: h 2h : Distance between vortices U c: Convective velocity : Circulation 2 2 ( Lamb, 1932)

18 Relations between wake and rotor charateristics Geometry of of wake: N h U 2 RU h 2R R N U b c c b o Assuming constant loading: U N 2 o b C T Combining: R NbC T U 16 U / U c 3 c

19 Expression for length of linear amplification Amplitude amplification: l RB Amax ln () t u ln Ao uo Assuming that: u z max Amax C1 Ti ln () t and u Uc Ao o We get the following expression for the length of the linear amplification region: l R RB U U 3 16 c / 0 N C b T ln( C Ti)

20 Expression for length of transition region Correlation coefficient given the correlation between the analytical Gaussian profile and the computed wake deficit profile, computed at different stream-wise positions. corr U, U actual Gaussian R l BG C ln( C Ti) 2 1 C 2 z R / ln( C1 Ti)

21 Expression for total length of near wake Total wake length: l R R R N C 3 l 16 / RB l U BG c U0 C2ln 1 Nearwake b T From simulations we find l 6 Ti 3ln R Nearwake NbCT 3 Typical values for optimum rotor: Ti 0.01 % 0.1% 1% 5% 10% 20% Lrb/R L/R C Ti

22 Wake and Wind Farm Aerodynamics Basic questions and issues: How important is the dynamics of the vortex system Relationship between strength of the vortices and the blade load Conditions for instability How far downstream do near-wake and far-wake refer to What is the relationship between vortex dynamics and meandering How does the added turbulence intensity relate to the loading Performance predictions of wind farms Life time estimation of turbines in wind farms Influence of stability of the atmospheric boundary layer Estimation of wind resources in wind farm to wind farm interaction

23 Wind Turbine Wake Aerodynamics Horns Rev offshore wind farm:

24 Wind Turbine Wake Aerodynamics Horns Rev offshore wind farm:

25 Offshore wind power How much space does wind turbines occupy: Distance between turbines: 10 rotor radii Surface area per wind turbine: S = 100R**2 P/S = 1200*R**2/100*R**2 = 12 W/m**2 Assume 33% ful load hour: P/S = 4 W/m**2 El. consumption in a house keeping: 120W per person Area need: 30 m**2 per person

26 Wake and Wind Farm Aerodynamics Simulation models Momentum theory (Frandsen) Linearized Navier-Stokes (Fuga) Parabolised Navier-Stokes (Ainslie, UMPWAKE) Reynolds Averaged Navier-Stokes (RANS) Detached Eddy Simulation (DES) Large Eddy Simulation (LES) Actuator Disc/Line - LES (AD/L-LES)

27 Scale requirements in wind energy Turbulent scales: Length scale (m) Velocity scale (m/s) Time scale (s) Airfoil boundary layer Airfoil Rotor Cluster Wind farm

28 Aerodynamic Computations Requirements for Navier-Stokes computations: Smallest turbulent length scale: l Largest geometrical length scale: L Estimate based on scales: L/ l Re**(3/4) Reynolds Number: Re=L U/ν, where L: Length of object U: Typical velocity ν: Kinematic viscosity Number of mesh points: N (L/ l)**3 = Re**(9/4) Typically Re = O(10**6) - O(10**7), thus N = O(10**15) Computing performance is generally 10-doubled every 5 years, hence realible aerodynamic computations can be anticipated in about (15-7) x 5 = 40 years Thus, we need to look for simpler models

29 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

30 Actuator disc/line model Extensions of the model: Shear and veer can be introduced through body forces (analogous to immersed boundary conditions) Ambient turbulence introduced as a numerical turbulence lattice through body forces The model is can easily be coupled to an aeroelastic code, e.g. Flex5, enabling detailed aeroelastic computations Atmospheric boundary layer stability can be introduced through the energy equation

31 Actuator disc/line model Mixed-scale sub-grid scale model:

32 The Actuator Line Technique Regular 3D Grid V rz Linear interpolation No tip correction is applied Forces smearing B i i f ( x) F ( s) ( p ) dndt i1 1

33 Evaluation of velocities z n n rel n V V V r V V V r V, ) (, tan Smearing of forces z z p dz e z r z r e p d p p, ), ( ), ( 1 ) (, 2 2 F f f f Aerodynamic Forces cos sin, sin cos,,re) (,Re) ( D L F D L F C C cb V z D D L L rel e e D L Evaluation of aerodynamic forces

34 Wind Shear and Turbulence y h y w y y c y c w y w hub ) ( ) ( t m u u f ) exp( 1 ) (, 2 d d f f Model of wind turbulence Power law wind shear profile Fluid Mechanics

35 Validation of the actuator line technique NextMex project NTNU and DTU experiments WakeBench Comparison between computated and measured wake structures

CFD simulations of wind turbine in sheared inflow The NM80 turbine is simulated using CFD and three different representations of the rotor: a fully resolved geometry

wake Much higher turbulence in the FR simulation Generally good agreement between AL and AD for all downstream position.

36 CFD simulations of wind turbine in sheared inflow The NM80 turbine is simulated using CFD and three different representations of the rotor: a fully resolved geometry (FR), an actuator line (AL) and an actuator disc (AD) Good agreement in near wake axial velocity FR simulation predicts a faster smearing of the mean gradients in the far wake Much higher turbulence in the FR simulation Generally good agreement between AL and AD for all downstream position. 1D FR FR AL AD AL Snapshot of vorticity magnitude contours in horizontal cross-section through rotor center. Mean streamwise velocity 1D and 5D downstream for various azimuth positions Courtesy: Niels N. Sørensen & Troldborg

37 Validation: Nørrekær Enge II Turbulence intensity

38 Simulation of Wind Farms

39 Wind Turbine Wake Aerodynamics Vindeby off-shore wind farm:

40 Modelling of Turbulent Flows in Wind Farms Vorticity shed from 5x5 turbines in a farm computed by actuator disk method

42 Layout of the Lillgrund wind farm

43 LES simulation of the Lillgrund wind farm Comparison between computations and experiments of the Lillgrund wind farm

44 Simulation of Wind Farms Some results of ABL-LES computations: (Porte-Agel et al. (2011)) Flow domain

45 Simulation of Wind Farms Comparison of LES computations with measurements (Porte-Agel et al. (2011))

46 Simulation of Wind Farms Comparison of LES computations with measurements (Porte-Agel et al. (2011))

47 Simulation of Wind Farms Comparison between actuator disc and actuator line models (Porte-Agel et al. (2011)):

48 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.

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

50 Simulation of turbulence inside wind farm Instantaneous slice of axial velocity contours. Dot: Rotor centre. Cross: Centre of mass

51 Simulation of turbulence inside wind farm Wind speed at hub height TKE spectrum

52 Simulation of turbulence inside wind farm PI- controller regulates the tip speed below rated power to achieve maximum performance (Cp=Cp(max)) Tip speed at hub height Wind speed at hub height Power production

53 Simulation of turbulence inside wind farm Wake center motion, computed using centre of mass analogy Question: Is this meandering?

54 Simulation of turbulence inside wind farm Spectra of wake center motion

55 Analytical Modeling of Wind Farms Momentum model: From Frandsen et al.: Wind Energy vol. 9, 2006

56 Simulation of Wind Farms Momentum model:

57 Simulation of Wind Farms Expansion behind single turbine: Generic form of wake expansion equation: Proposal by Jensen and Katic:

58 Simulation of Wind Farms Multiple wakes, single row:

59 Simulation of Wind Farms Momentum model: where is a constant The wake cross-sectional area is expanding linearly with x Frandsen model: where

60 Simulation of Wind Farms Validation of model:

Study on wind turbine arrangement for offshore wind farms

Downloaded from orbit.dtu.dk on: Jul 01, 2018 Study on wind turbine arrangement for offshore wind farms Shen, Wen Zhong; Mikkelsen, Robert Flemming Published in: ICOWEOE-2011 Publication date: 2011 Document