Informes Técnicos Ciemat 910diciembre, 1999

CFD Calculations of the Flow AroundaWindTurbineNacelle

J. VárelaD. Bercebal

Departamento de Energías Renovables

Toda correspondenica en relación con este trabajo debe dirigirse al Servicio de

Información y Documentación, Centro de Investigaciones Energéticas, Medioambientales y

Tecnológicas, Ciudad Universitaria, 28040-MADRID, ESPAÑA.

Las solicitudes de ejemplares deben dirigirse a este mismo Servicio.

Los descriptores se han seleccionado del Thesauro del DOE para describir las materias

que contiene este informe con vistas a su recuperación. La catalogación se ha hecho

utilizando el documento DOE/TIC-4602 (Rev. 1) Descriptive Cataloguing On-Line, y la

clasificación de acuerdo con ei documento DOE/TIC.4584-R7 Subject Categories and Scope

publicados por el Office of Scientific and Technical Information del Departamento de Energia

de los Estdos Unidos.

Se autoriza la reproducción de los resúmenes analíticos que aparecen en estapublicación.

Depósito Legal: M -14226-1995ISSN: 1135-9420ÑIPO: 238-99-003-5

Editorial CIEMAT

CLASIFICACIÓN DOE Y DESCRIPTORES

170600

CALCULARON METHODS; ANEMOMETERS; FLOWMETERS; WIND TURBINES;AERODYNAMICS; FLUID MECHANICS

"CFD Calculations of the Flow Around a Wind Trubine Nacelle"

Várela, J.; Bercebal, D.

41 pp. 38 fig. 5 refs.

Abstract:

The purpose of this work is to identify the influence of a MADE AE30 wind turbine nacelle on the site calibrationaiiemometer placed on the upper back of the nacelle by means of flow simulations around the nacelle usingFLUENT, a Commercial Computational Fluid Dynamics code (CFD), which provides modeling capabilities forthe simulation of wide range laminar and turbulent fluid flow problems. Different 2D and 3D simulations wereaccomplished in order to estimate the effects of the complex geometry on the flow behavior. The speed up andbraking valúes of the air flow at the anemometer position are presented for different flow conditions. Finally someconclusiones aboutthe accuracy of results are mentioned.

"Cálculos con CFD del Flujo Alrededor de una Góndola de un Aerogenerador"

Várela, J.¡ Berceba!, D.

41 pp. 38 fig. 5 refs.

Resumen:

El Propósito de este trabajo es la identificación de la influencia de la góndola de un aerogenerador MADEAE-30 sobre el anemómetro de calibración del emplazamiento situado en lo alto de la parte posterior de lagóndola, mediate simulaciones del flujo alrededor de ésta, usando FLUENT, un código de FluidodinámicaComputacional (CFD), que es capaz de modelizar simulaciones fuidodinámicas laminares y turbulentas. Serealizan diferentes simulaciones en 2D y 3D para poder estimar los efectos de la geometría compleja de lagóndola en el comportamiento del flujo.También se presentan los valores de aceleración y deceleración delflujo en la posición del anemómetro de calibración para diferentes condiciones del flujo. Finalmente se men-cionan algunas conclusiones sobre la exactitud de los resultados.

Contents

1 Introduction 3

2 Methodology 3

3 Physical Models 53.1 Transport Equations 53.2 Türbulence models 73.3 Near-Wall treatment 8

4 Numerical Simulation 9

5 Results of the CFD calculations 105.1 2-D calculations 10

5.1.1 Different domains 105.1.2 Different velocities 20

5.2 3-D calculations 275.2.1 Different velocities 275.2.2 Different vertical inclination 295.2.3 Different horizontal inclination 34

6 Conclusions 39

List of Figures

1 The nacelle 42 Enclosure for case A (2-D) 113 Enclosure for case B (2-D) 124 Enclosure for case C (2-D) 125 Velocity magnitude. Case A (2-D) 136 Velocity magnitude. Case B (2-D) 137 Velocity magnitude. Case C (2-D) 148 Turbulent viscosity ratio. Case A (2-D) 149 Turbulent viscosity ratio. Case B (2-D) 1510 Turbulent viscosity ratio. Case C (2-D) 1511 Turbulent kinetic energy. Case A (2-D) 1612 Turbulent kinetic energy. Case B (2-D) 1613 Turbulent kinetic energy. Case C (2-D) 1714 Wind profiles with different domains (2-D) 1915 Velocity magnitude. V¿n¡eí = 4 m/s (2-D) 2016 Velocity magnitude. Viniet = 8 m/s (2-D) 2117 Velocity magnitude. Vini&t = 12 m/s (2-D) 2118 Velocity magnitude. Viniet = 16 m/s (2-D) 22

19 Turbulent viscosity ratio. Viníet = 4 m/s (2-D) 2220 Turbulent viscosity ratio. Viniet = 8 m/s (2-D) 2321 Turbulent viscosity ratio. Viniet = 12 m/s (2-D) 2322 Turbulent viscosity ratio. Vinlet = 16 m/s (2-D) 2423 Turbulent kinetic energy. Viniet = 4 m/s (2-D) 2424 Turbulent kinetic energy. Viniet = 8 m/s (2-D) 2525 Turbulent kinetic energy. Vin\et = 12 m/ s (2-D) 2526 Turbulent kinetic energy. V¿n¿eí = 16 m/s (2-D) 2627 Contours of velocity difierence (2-D) 2828 Comparison of the wind profiles between 2-D and 3-D cases . 3029 Velocity vectors. 10° of vertical inclination. (3-D) 3130 Velocity vectors. 30° of vertical inclination. (3-D) 3131 Wind profiles with different vertical inclination (3-D) 3232 Contours of velocity difierence, 10°of vertical inclination . . . 3333 Contours of velocity difierence, 30°of vertical inclination . . . 3334 Velocity vectors. 10° of horizontal inclination. (3-D) 3535 Velocity vectors. 30° of horizontal inclination. (3-D) 3536 Wind profiles with different horizontal inclination (3-D). . . . 3737 Contours of velocity difference, 10°of horizontal inclination . 3838 Contours of velocity difference, 30°of horizontal inclination . 38

1 Introduction

During September 1998 and March 1999 a power performance mea-surement according to standard IEC 61400-12 [1] was carried out on aMADE E30 wind turbine at the 'A Capelada', a wind farm in Galicia,Northwest of Spain. The orographic complexity of the terrain surround-ing the wind turbine led to perform a calibration of the site, using the windturbine itself as second wind mast.

The purpose of this paper is to identify the influence of the wind turbinenacelle on the site calibration anemometer placed on the upper back of thenacelle by means of flow simulations around the nacelle using FLUENT,a commercial Computational Fluid Dynamics code (CFD), which providesmodeling capabilities for the sknulation of wide range laminar and turbulentfluid flow problems.

These simulations were performed at the Renewable Energy Departmentof CIEMAT.

2 Methodology

A site calibration is usually done with two meteomasts, one of them atthe turbine position, to obtain the correlation factors for the correction ofthe power performance measurement. Because the turbulence was alreadyinstalled at the wind farm, the second anemometer was placed on a sepáratesmall mast on the top of the nacelle's back. The wind turbine was stoppedand yawing downwind during site calibration procedure.

The influence of the turbine nacelle on the site calibration anemome-ter are determined by means of CFD calculations simulating the air flowaround the MADE AE30 nacelle using real manufacturing geometry. TheCFD simulations identify the speed up or deceleration factors of the flowat the anemometer position due to the nacelle in comparison to the undis-turbed air flow.Two different kind of simulations were accomplished by means of FLUENT;first they were carried out 2-D calculations in order to estimate the amountof space surrounding the nacelle necessary to achieve accuracy valúes ofwind profiles while providing a number of cells as least as possible, trying todecrease the computational effort. Later they were made 3-D calculationsto consider the effects of the complex geometry in the simulations.

A view of the nacelle is shown in figure 1 on page 4.The dimensions of the nacelle are grossly 3 m of height, 2 m of depth

and 5 m of length. In all the simulations the nacelle's rear end was orientedupwind, and the blades were not modeled. The speeds of interest in this

Figure 1: The nacelle

study ranges from 4 m/s to 16 m/s, therefore the Reynolds number is veryhigh and the effects of turbulence must be considered.

The adimensional numbers that characterize the flow are:

Re = ^ i ^ ~ 3.89v

feThe height of the boundary layer is

H

- 0 . 7 2

- 3

And the Kohnogorov scale isH

Re§

T ~ 2.4 • Wó m

~ 5.4 • 1(T5 m

In the next section it will be shown how FLUENT solves the Navier-Stokes equations and how turbulence is modeled.

3 Physical Models

3.1 Transport Equations

FLUENT solves the Navier-Stokes equations for conservation of mass,momentum and energy. Additiona! conservation equations for 'jfc' and 'e' aresolved when the flow is turbulent.

Mass conservation

The equation for conservation of mass or continuity equation can bewritten as:

^ O (i)

Momentum conservation

Conservation of momentum in each component 'i' is described by [2]:

^L w i t h ¿ = 1,2,3 (2)

where r¿j is the stress tensor, given by:

The first term on the right is the volunae dilation and ¡i is the molecularviscosity.

Energy conservation

The energy equation can be written in terms of the sensible enthalpy has (neglecting the effects of viscous heating):

| W + V • (PW) = V • (AVT, + ¿ (± £K — i. vi — i-

where A is the thermal conductivity.The sensible enthalpy is defined as:

h= I CpdT= íJTref

Equations 1, 2, 4 contain v, p, T, p as unknown dependent variables, so onefurther scalar equation is needed to make possible the determination of theflow field. This additional relationship is provided by the equation of state,which may be written generally as:

f(p,T,p)=0

where the functional form of the equation of state, depends on the natureof the fluid.

Equation of State

The pressure valué used in the code is a gauge pressure, relative to thereference pressure: p = pabs —pref, henee the equation of state has the form:

(P+Pref)W9 RT

FLUENT has an approximation denoted incompressible ideal gas law fordensity. In this approximation the overpressure p is very small comparedwith pref, henee its contribution to density is ignored, and pressure onlyaffeets density through the reference pressure:

_ PrefWP RT

This approximation implies that pressure fluctuations are ignored in theequation of state, cutting out sound waves. In fact, it is assumed:

dpc

In all the simulations it was assumed that the flow is incompressible andisotherm, so the valué of p at the pressure of reference (1 atm) is 1.225 kg/m3.

3.2 Turbulence models

In this problem the concept of boundary layer, turbulent flow and walleffects will play a dominant role. The turbulent model used in all the simu-lations was the Standard fe-e model.Proposed by Jones and Launder [3], it is a two-equation model based on anisotropic eddy-viscosity concept, derived from the Reynolds-Average Navier-Stokes equations, based on the assumption that the flow is fully turbulentand the effects of molecular viscosity are negligible. It is a semi-empiricalmodel and provides a reasonably accuracy for a wide range of turbulentflows.In the Reynolds averaging, all the solution variables in the original Navier-Stokes equations are decomposed into the mean (ensemble-averaged or time-averaged) and fluctuating components. For an scalar <j>:

cf) = (f) -f (jj where:

_ i rt+6t

¿ot Jt-st

where St is a time scale larger than the turbulent fluctuations and smallerthan the time scale we want to resolve. Substituting the expressions ofthis form for the flow variables into the instantaneous continuity and mo-mentum equations 1, 2; the "Reynolds averaged" Navier-Stokes equationscan be written (dropping the bars from Reynolds averaged mean quantitiesfor all primitive variables except averages involving products of fluctuatingquantities) as:

^ 0 (5)

—pVjV1) with i =

The effects of turbulence are represented by the "Reynolds stresses": — pv^v'j,this term arise from the non-linear convective térra in the un-averaged equa-tions, and need to be modeled in order to cióse equation 2. In the Standardfe-e model, Reynolds stresses are modeled using the boussinesq hypothesis:

-pon = IH ^ + e¿¡) - 3 [Pk + /t^TJ

Now ¡ieff = ¡i + fif, where /x¿ is the turbulent viscosity and is computedusing the turbulent kinetic energy 'fe' and its rate of dissipation 'e'from:

fe2

C

And k and e are obtained from the solutions of their "modeled" transportequations:

^(pk) + V-(pkv)=V

~(pe) + V-(pev) = V

^~) Vfc] + Gfc + Gb - pe (7)

where G^ and G& is the generation of k due to turbulent stress and buoyancy:

T—r 9Vn \

3.3 Near-Wall treatmentThe near-wall modeling significantly impacts the fidelity of the numérica!

solution, due to walls are the main source of mean vorticity and turbulence.The near-wall región can be subdivided into three layers:

1. The viscous sublayer, it is the inner región, where the flow is almostlaminar üke.

2. The fully turbulent layer, it is the outer región, and where turbulentplays the main role.

3. The buffer layer, between both, where the effect of molecular viscosityand turbulent are equally important.

There are two approaches to model the near-wall región:

Near-Wall modeling

The viscosity-affected región is solved, including the viscous sublayer.In the near-wall model the viscosity-affected región is solved all the wayto the viscous sublayer. The whole domain is subdivided into two zones:a viscosity affected región and a fully turbulent región; the limit betweenthem is established considering the turbulent Reynolds number:

Rey =pVky

where y is the normal distance from the wall to the cell center.When Rey > 200 the cell belongs to the fully turbulent región, and the

turbulence model is employed.When Rey < 200 the cell belongs to the viscosity affected near-wall región,and the one-equation model of Wolfstein is employed, where the turbulentviscosity nt and the e field are computed from:

MÍ = pC

__ A;3/4

where ZM and le are length scales, and they are function of the turbulentReynolds number.

Wall-function approach

Where the viscosity-affected layers (the viscous sublayer and the bufferlayer) are not solved, instead semi-empirical functions are used to link theviscosity affected and the fully turbulent regions. The standard wall-functionin the code is based on the proposa! of Launder an Spaiding, and has beenmost widely used for industria! flows.The law of the waü for mean velocity yields:

U* = ~ln(Ey*)

where k is the Von Karman's constant and E is an empírica! constant. Thelogarithmic law for mean velocity is valid for y* > 30 — 60, while in the codeis used when y* > 11.225. When y* < 11.225 at the wall-adjacent cells, theyapply the laminar stress-strain relationship:

4 Numerical Simulation

In order to conduct a CFD analysis it is necessary to créate a suitabledomain around the nacelle, where it will be generated the mesh on theoutside of the nacelle, therefore it will be created a brick around the nacelleto represent the flow domain.The scheme selected in the solver was initially of first order, and when it wasachieved a converged solution it was substituted by a second order schemein all the equations, and was run again until it reached the new convergedsolution. In all the simulations the velocity is very low compared with theMach number, so it could be assumed that the flow is incompressible andisotherm, henee it is not necessary to solve the equation of energy.

Mesh considerationsThe approach of an standard wall-function was used in all the cases

considered, this was taken into account when meshing the volume, so the gridis very fine neax the surface of the nacelle, and more coarse as it approachesthe boundaries. Specifically the mesh near the surface was meshed usingthe model of boundaxy layer provided by GAMBIT (the mesh generator ofFLUENT), so it could be achieved a valué of y+ very cióse to 20, enough tohave an accurate simulation according to [5].

The grid was generated using the pave model of GAMBIT, with trian-gular cells in the cases of 2-D and with tetrahedral cells in the 3-D cases.This unstructured mesh was selected because it is the simplest to adapt tothe complex geometry, while providing accurate results.

5 Results of the CFD calculations

5.1 2-D calculations

In these simulations the boundaxy conditions were:

• Velocity inlet, for the boundaxy in front of the nacelle's reax end, witha constant valué in each simulation.

• Pressure-Outlet, for the boundaxy in front of the nacelle, with a refer-ence pressure of 101325 Pa.

• Wall boundaxy, for all the walls comprising the geometry of the nacelle.

o Symmetry, for the top and bottom of the enclosure considered.

For all the simulations the turbulent parameters were:

• Intensity of turbulence, I = 12%. This valué was estimated analyzingthe chaxacteristics of the wind typical of the emplacement.

@ Turbulent viscosity ratio, /¿t//i = 10. This input valué is enough forthe code to consider that turbulence is fully developed.

5.1.1 Different domains

First they were carried out three simulations in other to consider howthe amount of space surrounding the nacelle affected the wind profiles andhow much CPU time was needed to achieve a converged solution.

Three cases with different grid surrounding the nacelle were studied:

1. Case A. In the first case the size of the grid is 13 m x 15 m, with 25725cells.

10

2. Case B. In the second case the size of the grid is 19 m x 15 m, with36551 cells.

3. Case C. In the third case the size of the grid is 25 m x 15 m, with45821 cells.

For all the cases the velocity at the inlet was 12 m/s. The problems to beconsidered and the position of the anemometer are shown schematically infigures on page 11.

The contours of velocity, kinetic energy and turbulent viscosity ratio for

Grid

Figure 2: Enclosure for case A (2-D).

all the cases are shown in figures on page 13

11

Grid

Grid

Figure 3: Enclosure for case B (2-D).

Figure 4: Enclosure for case C (2-D).

12

... .2.58e+O1

2.33e+01 :

2.07e+01

1.81e+01 ;

:•• 1.55etO1 '.

'•; . 1.29&+01 ;

J •

•1.03B+01 :

7.75ertO :

5.17&f00

| • ; 2 . 58e+O0 :

í • I :

LjO.OOe+00 •

Contours of Velocity Magnitude (m/s)

Figure S: Vtíacly magnitude. Gasc Al

2.4Se+01

.2.20B+01

1-96etO1

1.71&+01

1.47e+0i

g.79e+oo . ••

7.35e+00 ;

4.90e+00 :

. 2.4Se+00 ; .

!íü0.O0e+O0 :

Contours of Velocity Magnttude (m/s)

Figure 6: Velaaüby magnafcude. Gase B (2-D)

13

:2.176+01

1.936+01

1.696+01

. 1.45e+01 :

: 1.21e+01 :

: -9.67e+00

7.25e+00

: 4.836+00

i ¡2.42&+00

LjO.OOe+OO '••-

Contours of Velocity Magnitude (m/s)

Figure 7: Vbfacity magnitude. Qase C (¡2-DJ

._ ,9.576+03

8.61 e+03

7.65e+03

6.70S+03

5.74e+03

' '4.786+03

! 3.836+03

2.87e+03

1.91e+03

.. ; 9.57e+02

LJi.24e-01 • - - -

Contours of Turbulent Viscosity Ratio

Figure 8: Ttabiulenfc víscxjsity ratio. Case A (2-D)

14

2.05e+O3

,'i.03e+03

I í 1.33e-01

Contours of Turbulent Viscosity Ratio

Figure 9: Ttaibuñenifc visaasilty ratio. Qaisc B flZ-D]

•1.07 " i '

Ü1.1. 0- " - -

Contours of Turbulent Visoosity Ratio

Figure 10: Ttonbufeoii vLacosity natio. Case C (2-D)

15

; 6.72e+00

6.05e+00

5.37e+00

4.70e+00

- 4.03e+00

'. 3.366+00

'• 2.69e+00

2.02e+00

1.346+00

¡6.72e-01

EJ 1.97604

Contours of Turbulent Kinetic Energy (k) (m2/s2)

Figure 11: Tunbullent kinetic ensngyj. OEIBC A p-D]

6.73e+00

6.056+00

5.38e+00

4.71e+00

. 4.046+00

! ,3.36e+00

• 2.696+00

. ,2.02e+00

1.3Se+00

'• ' ¡6.73&ÍI1

í i

Lj1.35e-04

Contours of Turbulent Kinetic Energy (k) (m2/s2)

Figure 12: TtaiMeat kiiaetic eruengy. Case B (2-D)

16

Contours of Turbulent Kinetic Energy (k) (m2/s2)

Figure 13: Tuxbuilent kinetic energy. Oase C (2-D)

17

The wind profiles along the y-axis (perpendicular to the velocity inlet)at the position of the anemometer are shown in figure on page 19 (the po-sition of the anemometer in the y-axis is represented by a red line), whereL = 2.7 Tn is the height of the nacelle and the origin of H is taken at themiddle of the nacelle.

Erom these it can be stated that the lower is the domain surrounding thenacelle, lower is the change in the velocity at the same point; this is clear,because when the grid is shorter, the wind has less space to adapt to thegeometry of the nacelle.And the differences can be very significant, specially at the middle of thenacelle, reaching a düference of 7% between the cases A and C.

Another interesting point is that at positions not very cióse to the na-celle, in particular near the anemometer, the difference is negligible, as it isshown in the next table, so it can be inferred that the speed-up due to thenacelle is 4.7% approximately.

CaseABC

Va(m/s)12.51812.58512.569

Vdiff(%)4.34.94.7

Table 1: Velocity magnitude and difference in per cent at the anemometer

However, compaxing the number of iterations, it is clear that diminishingthe space surrounding the nacelle doesn't mean a significant improvement inthe computational effort, because it is needed a greater number of iterations.Therefore in the next simulations it was used the same grid as in case C.

CaseABC

Iterations413342302

Table 2: Iterations needed to achieve a converged solution

18

Figure 14: Wind profiles with different domains (2-D).

19

5.1!.2 Diffenent veliocities

Tlhcn. tüeyi were períbrmedi anotlier- four ualculationia witU dífFcrcTit vclac-ities rangíng franx 4 m/s io 16 m/\s. tu watdi liow the wind apeed obangedat aaemometer position and cx>mpar.e laten wifih. thJe 3-D oalnuiations.Thie uontouirs of velocítyj, kinetlic energy and turbufant víscosity; ratio WCTOJ

. 8.03B+00

6.42e+00

5.626+00

. 4.82e+O0

4.O1B+O0

3.218+00

'. 2.41 e+00

1.61e+00

! • 8.03&O1

LJo.oos+oo

Contours of Velocity MagnHude (m/s)

Figure 15J Velocity magnitude. V¡niet = 4 m/s (2-1

20

1.45e+Q1

1-298+01 :

1.13e+01

9.65e+00

•8.056400 ¡

6.44e+oo

4.83e+00

3.Z2e+00

"; . ; 1.61&+0Q

i lO.OOS+00

Contours of Vetocity Magnitude (m/s)

Figura 16: Veíocity magnifcude. Viniet ~ 8 m/s (.2-DJ.

1.936+01

1.59S+01

1.45e+01 :

. -1¿1e+01

' 9.67tH0Q

7.256+00

4.83e+O0

! J2.42e+00

SlJo.OOe+00

Contours of Velocity Magnitude (m/s)

CD*

Figure 17: Vdooity. magnitude. Viniet — 12 mfa (2-D)

21¡

3.22e+01

2.90&+01

2.58e+01 .

2.2&3+01 : "

' 1.93e+01

; 1.61e+01

; 1.29S+01 :

9.67e+00 !

6.45S+00 ;

i i 3.22e+00

t_jo.00e+00

Contours of Velocity Magnitude (m/s)

Figura 18: Vblbcíty magnitjude. Vjrafeí = 16 m/s ('2-D).

. . ,3.76e+03

3.398+03

3.01 e+03

2.63e+03

- 2.26e+03

; 1.88e+03

• 1.51 e+03

1.136+03

7.53e+02

: 3.77B+02

l_J5.08e-01

Ü•*fSv"5• • Í-.-Í

Conlours of Turbulent Viscosity Ratio

* ; • . • . " • * " . •

- . , . - • ; _ • : >

Figure 1S: Huvbuilent viscosity ratita. — 4' m¡/|s (2-D].

22

, 7.25B+03

6.53e*03

S.80e+03

5.08e+O3

4.35e+03

3.03e+03

2.90&+O3

2.1Be+03

1.4Se+03

' 7.26e+02

LJ2.07e-01

Contours of Turbulent Viscosity Ratio

Figure 20: Turbulent visoositly ratiio. V¡nlet =• 8 m/s (¡2-D).

. 1.07e+04

9.67e+03

8.603+03

7.S2S+03

6.45&+O3

. 5.37&+O3

• 4.30B+03

3.22e+03

2.1Se+03 --

. :1.07e+O3

I li.12e-01

Contours of Turbulent Viscosity Ratio

Figure 21: Ibrbulent vjisoosity ratiiu. Vini^ = 12 m,/s (2-Dj

1.41e+O4

1.27e+04

1.136+04

9.87e+03

8.46e+03

7.0SS+03

5.64e+03

4.23e+í)3

2.82e+03

;i.41e+03

Contours of Turbulent Viscosity Ratio

Figure 22: Tuiitxulent viscrositly rat'io. V¡niBt => 1G m/s (¡2-D).

5.54B-01

4.85e-01

4.156-01

;3.46e-01

¡2.77e-01

2.086-01

1.38e-01

;6.93e-02

LJ4.49e-O5

Contours of Turbulent Kinetio Energy (k) (m2/s2)

Figure 23: TlirbudeQt Icinetiio encrgy:. Vlnia = 4 m(\s. (2-D]

24

, ,2.816+00

2-53B+00

255B+O0

1.97e+00

1.69&+00

1.40e+O0

. :i.12e+00

B.43&-01

5.62e-01

: :2.81e-01

LJ7.23&ÍI5

Contours of Turbulent Kinetic Energy (k) (m2/s2)

Figure 243 Tuibudent ki'netio enengy;. V¡niet ^ 8 m¡s (Í2-DJ.

. ...6.46e+00

5.81 e+00

5.17e+00

4.526+00

3.87e+00

•2.58S+00

1.94e+00

1.29e+00

; ; 6.46e-01

i !LJi.01e-04

Contours oí Turbulent Kinetic Energy (k) (m2/s2)

Figure 25: Tlurhulent lci'nelilc en:ergy. Viniet = 12 m,/s (2-D]j

25

—.. 1-I6e+Oi

1.04e+01

9.28e+00

8.126+00

6.956+00

5.806+00

'• 4.64e+00

3.48S+00

2.32e+00

; ,¡1.16e+00

LJi.29e-04

Contours of Turbulent Kinetic Energy (k) (m2/s2)

. . r í i . ' '?;-••.•:.-..* i > i í»,•

Figura 28¡ Turbwlcnt kinatic enengy — 16 m/s (2-D).

26

And the difference between the velocity at any point and the velocityinlet have all the same appearance, and it is shown on page 28.

The next table shows the velocity and the velocity difference in % at theanemometer position.

V;niet(m/s)

481216

Va(m/s)4.18838.378112.568816.7591

Vdiff(%)4.704.734.744.74

Table 3: Velocities at the anemometer in the 2-D cases

Therefore the change in velocity is insignificant, ant it can be stated thatthe velocity inlet doesn't impact the speed-up at the anemometer, whichremains constant at 4.7% for all the cases.

5.2 3-D calculations

5.2.1 Different velocities

They were studied again the four cases analyzed in 2-D, to determinehow the complex geometry of the nacelle affects the wind profiles. Theenclosure that contains the nacelle is 20m x 12m x lOm (20 m along thewind dixection, 12 m of height, and 10 m of width), these dimensions werechosen taking into account the results of the 2-D calculations with differentdomains. Also it was considered the symmetry plañe of the nacelle, heneeit was only necessary to mesh 5 m of width.

The grid was again meshed with GAMBIT, refining the mesh near thesurface, producing a total of 305804 tetrahedral cells. The boundary condi-tions were the same as in the 2-D cases, but with the condition of symmetryin the plañe of symmetry of the nacelle:

a Velocity inlet, for the boundary in front of the nacelle's rear end, witha constant valué in each simulation.

• Pressure-Outlet, for the boundary in front of the nacelle, with a refer-ence pressure of 101325 Pa.

• Wall boundary, for all the waJls comprising the geometry of the nacelle.

a Symmetry, for the top, bottom of the enclosure considered and for theplañe of symmetry of the nacelle.

27

o pcó

pC\¡

po

p p

Figure 27: Canitours of velooiity] difference (2-D].

The velocity differences at the anemometer position in % were:

Vintet(m/s)481216

Va(m/s)4.04808.095512.142916.1902

Vdiff(%)1.201.191.191.19

Table 4: Velocities at the anemometer in the 3-D cases without inclination

Henee, again the velocity inlet didn't affect the velocity difference in percent, but there is a significant decrease in the speed-up valué, from 4.7% inthe 2-D cases to 1.2% in the 3-D's. This can be explained considering thatin the 2-D simulations the extrapolation to a tree dimensional problem isconsidering an infinitely long nacelle in the new 3-D axis, and that couldproduce a greater interaction with the wind resulting in a greater speed-up.In the figure on page 30 it is shown how the wind profiles changed betweenthe 2-D and 3-D cases.

5.2.2 Different vertical inclination

It was analyzed how the vertical inclination of the wind impact the windspeed at the anemometer. Six different cases were run, in tree of them thevertical inclination was 10°, while on the other tree it was 30° (always posi-tive, oriented to the top of the enclosure). Also it was analyzed the influenceof the velocity, for this reason it was varied the velocity at the inlet, from4 m/s to 16 m/s. The mesh used was the same as in the case before, chang-ing the boundary condition of symmetry of the bottom to velocity inlet.Taking a vertical section at the middle of the nacelle, on page 31 is repre-sented the velocity vectors colored by velocity magnitude, for the cases with

= 16 m/s and with 10 and 30 degrees of vertical inclination.

29

Figure 28: Comparison of the wind profiles between 2-D and 3-D cases

30

_30.9

27.8

24.8

21.7

18.6

15.5

12.4

9.3

6.3

3.2

0.1

Figura 29: Velocity vectars. 10° of vertical ínclination. (3-D)

30.8

27.7

24.7

21.6

18.6

.15.5

•12.4

:9.4

6.3

;3.3

i

Figure 30: Vblocily. ver.tors. 30Q of vertical incMoaticui. (3-Q)j

The vekicity magnífcude albng the y-axás (perpendicular to thé velacityInletj at thc positrón of thte anwtrDometer aire shown ÍIÍ figure on¡ page 32 (théposltlcm of. the aTiemomateiF in thc y-axis is represented hy a red Une].

•((j-g) uoxyexiípm iAv sa¡Tjoid p x n ^ :jg

Velocity difference %

o OÍ

hfl contuuns uf: differeniue btetwaen thte velocitv at any point and thcvek>.ciüy inlet fon the cases with 10. and 30 degnees of vertical iacíinatlan

were:

... 80.0

69.5

59.0

485

38.0

' 27.5

''• 1 7 . 0

: 6.5

-4.0

1-14.5

-25.0

Figure 32: Confluirrs of velooityj differen.ee. 10°of verticaí inclinatiort

... . 50.00

40.00

30.00

20.00

10.00

. . 0.00

: ;-lo.oo

: -20.00

-30.00

! :-4o.ool ' i

1.00

Figure 33: Contours of veíooityj diifl'eraniue, 30°of vertioal in:clinatiioa

33:

And the resulting velocities at the anemometer were:

V¡niet(m/s)444888161616

Degrees010300103001030

Va(m/s)4.04804.04304.13238.09558.08598.263916.190216.171616.5268

vdiff(%)1.201.073.311.191.073.291.191.073.29

Table 5: Velocities at the anemometer in the 3-D cases with vertical incli-nation

As in the other 2-D and 3-D cases, the variation of the velocity differencein % with velocity inlet is negligible, but in contrast there are significantchanges with the vertical inclination of the wind. The velocity differencechanges in a complex way, decreasing with low inclination and later increas-ing when the inclination reaches 30°.

5.2.3 Different horizontal inclination

There were also studied two different cases with different horizontal in-clination of the wind. For these cases it was necessary to consider the totalvolume in 3-D, because the wind inclination broke the symmetry of theproblem. So an enclosure analogous to the before cases, 20m x 12m x lOmwas meshed again, resulting in 333484 tetrahedral cells.In the fixst case the inclination with respect to the horizontal plañe was 10degrees, while in the last was 30 degrees. On both cases the velocity mag-nitude was 12 m/s and there was no inclination in the vertical direction.Taking an horizontal section at the middle of the nacelle, on page 35 it isshown the velocity vectors colored by velocity magnitude, for the cases with10 and 30 degrees of horizontal inclination.

34

,—,22.6

, 20.3

18.1

15.8

13.6

r ,11.3: ii i 9 .1

' i 6.8

.4.6

: i! !2-3 U

Fíguna 34: Velocity, vecüors. 10° of htonizontaí incBnatJion. (3-D)

.. ..25.7

¿32

20.6

18.0

15.5

12.9

i '

: ;10.3

7.8

, ¡52

'• 21

\A

Figure 35: Velacltiy, vectora. 30° of Hunizanital inclination. (3-D)

The velocity magnitude along the y-axis (perpendicular to the velocityinlet) at the position of the aaemometer are shown in figure on page 37 (theposition of the anemometer in the y-axis is represented by a red line).

The contours of difference between the velocity at any point and thevelocity inlet for the cases with 10 and 30 degrees of horizontal mclinationare shown on page 38. And the velocity magnitude at the anemometerposition is shown in the next table:

Degrees01030

Va(m/s)12.142912.17212.026

vdiff(%)1.191.440.22

Table 6: Velocities at the anemometer in the 3-D cases with horizontalinclination

Erom these results we can see that when the inclination reaches high val-úes (30°) the speed-up at the anemometer is lower, while at low inclination(10°) the speed-up is a little greater.

36

Velocity difference %

:gg 8JtiSt¿[

en 01

r _ , 40.0

30.0

20.0

10.0

0.0

:-10.0

Ii-20.0

I-30.0

I -40.0

i -50.0

LJ-60.0

Fligume 37: Contours of vefcncity; differenca, Ii0aof hon*íaantal ioalinafcion

.__ 40.0

33.0

26.0

19.0

12.0

5.0

i . -2.0

• :-9.o

-16.0

i ¡-2 3-0

LJ-30.0

Figure 38: Cant0urs ai veliacüKy difíercnae, 3fl°afi horiizoníali ünalínatian

38

6 Conclusions

The code FLUENT has been used to asses the speed-up due to the nacellein a variety of cases.

Comparing the 2-D and the 3-D cases, there is a clear diminution of thespeed-up due to the nacelle, from 4.7% in the 2-D's to 1.2% in the 3-D's.This can be interpreted taking into account that when the simulation is in2-D, in fact the extrapolation to 3-D assumes a nacelle which is infinitelylong in the other direction, and these could result in a raise in the speed-up,due to a greater interaction with the nacelle.

Also it has been shown that this speed-up remains ahnost constant, for awide range of velocities (from 4 m/s to 16 m/s) in both 2-D and 3-D cases.This is due to the approximation of incompressible and isotherm flow, whichallowed to not solve the equation of energy.

Greater importance has the inclination in the vertical plañe, with a com-plex variation of the differences in %, decreasing at low inclination and in-creasing quickly at greater inclination. The inclination in the horizontalplañe resulted in a different behavior, increasing a little at low inclinationand decreasing quickly at high valúes of inclination. Both behaviors couldbe produced due to the influence of the complex geometry.

However, all these results must be considered as approximations within arange of error, not exact valúes, because there are a lot of uncertainties in thesimulation: influence of the enclosure selected, the number and type of cells,the model of turbulence, the mesh quality near the boundary layer, ... andof course the influence of the blades, not included in these simulations.More simulations will have to be done to understand how the inclusión of theequation of energy affects the speed-up at different velocities (not observedin this paper), and another set of simulations will be necessary to understandhow the quality of the mesh near the surface of the nacelle affects the windprofiles.

39

References

[1] IEC 61400-12: Wind Turbine Generator Systems. Part 12: Power Per-formance Testing, 1998.

[2] G. K. Bathelor. An Introduction to Fluid Dynamics. Cambridge Univ.Press, England 1967.

[3] B. E. Launder and D.B. Spalding. Lectures in Mathematical Models ofTurbulence. Academic Press, London, England, 1972.

[4] V. Yakhot and S. A. Orszag. Renormalization Group Analysis of Tur-bulence: I. Basic Theory. J. Scientific Computing, 1986.

[5] FLUENT User's Guide. FLUENT Inc., 1998.

40