1-s2.0-S0360319909020175-main.pdf

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 6 0 0 5 – 6 0 1 1

Avai lab le a t www.sc iencedi rec t .com

j ourna l homepage : www.e lsev ier . com/ loca te /he

Numerical simulations of the aerodynamic behavior of largehorizontal-axis wind turbines

C.G. Gebhardt a,c,*, S. Preidikman a,b,c, J.C. Massa a,b

a Departamento de Estructuras, Facultad de Ciencias Exactas Fısicas y Naturales, Universidad Nacional de Cordoba,

Av. Velez Sarsfield N� 1611, CP 5000, Cordoba, Argentinab Departamento de Mecanica, Facultad de Ingenierıa, Universidad Nacional de Rıo, Cuarto, Ruta Nacional 36, Km 601,

CP 5800, Rıo Cuarto, Argentinac Consejo Nacional de Investigaciones Cientıficas y Tecnicas, Avenida Rivadavia 1917, CP C1033AAJ,

Ciudad de Buenos Aires, Argentina

a r t i c l e i n f o

Article history:

Received 23 November 2009

Accepted 17 December 2009

Available online 4 January 2010

Keywords:

Large horizontal-axis

wind turbines

Unsteady aerodynamics

Vortex-lattice method

* Corresponding author. Departamento deCordoba, Av. Velez Sarsfield N� 1611, CP 500

E-mail address: [email protected]/$ – see front matter ª 2009 Profesdoi:10.1016/j.ijhydene.2009.12.089

a b s t r a c t

In the present work, the non-linear and unsteady aerodynamic behavior of large hori-

zontal-axis wind turbines is analyzed. The flowfield around the wind turbine is simu-

lated with the general non-linear unsteady vortex-lattice method, widely used in

aerodynamics. By using this technique, it is possible to compute the aerodynamic loads

and their evolution in the time domain. The results presented in this paper help to

understand how the existence of the land–surface boundary layer and the presence of

the turbine support tower, affect its aerodynamic efficiency. The capability to capture

these phenomena is a novel aspect of the computational tool developed in the present

effort.

ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction turbine, is usually composed of three major parts: the ‘rotor

With increasing environmental concern, and approaching

limits to fossil fuel consumption, alternative and clean sour-

ces of energy have regained interest. Among the several

energy sources being explored, wind energy – a form of solar

energy – shows much promise in selected areas of Argentina

where the average wind speeds are high.

The utilization of the energy in the winds requires the

development of devices which convert that energy into more

useful forms. Wind turbines are used to generate electricity

from the kinetic energy of the wind. In order to capture this

energy and convert it to electrical energy, one needs to have

a device that is capable of ‘touching’ the wind. This device, or

Estructuras, Facultad de0, Cordoba, Argentina. Te

(C.G. Gebhardt).sor T. Nejat Veziroglu. Pu

blades’, the drivetrain (if there is one), and the generator. The

blades are the part of the turbine that touches the wind and

rotates about an axis. Extracting energy from the wind is

typically accomplished by first mechanically converting the

velocity of the wind into a rotational motion of the wind

turbine by means of the rotor blades, and then converting the

rotational energy of the rotor blades into electrical energy by

using a generator. The amount of available energy which the

wind transfers to the rotor depends on the mass density of the

air, the sweep area of the rotor blades, and the wind speed.

The actual amount of energy extracted from the airstream by

the wind turbine strongly depends on its aerodynamic effi-

ciency. In this respect, this paper is going to increase the

Ciencias Exactas Fısicas y Naturales, Universidad Nacional del.: þ54 351 4334141x163.

blished by Elsevier Ltd. All rights reserved.

mailto:[email protected]

http://www.elsevier.com/locate/he

Fig. 1 – Wake evolution neglecting the presence of the

turbine support tower.


capabilities in the area of large horizontal-axis wind turbines

(LHAWT) design by enhancing the ability to accurately predict

their aerodynamic efficiency.

If the rotor blades are considered to be very thin, the speed

very low subsonic, and the Reynolds number large, the

boundary layers on their upper and lower surfaces can be

treated as vortex sheets and merged into a single sheet, which

lies on the camber (i.e., the middle) surface of the rotor blades.

Although the vorticity is generated in the boundary layers by

viscous stresses, there is a kinematic relationship between

vorticity and the velocity field that surrounds it, which is valid

whether viscous effects are explicitly modeled or not. This

relationship enables one to express the disturbance velocity in

terms of the vorticity. These hypotheses allow predicting the

aerodynamic loads by using the unsteady and non-linear

version of the vortex-lattice method (UVLM).

The main objective of this work is to develop a funda-

mental understanding of the non-linear and unsteady aero-

dynamic behavior of large horizontal-axis wind turbines. To

accomplish this objective, the authors have developed

comprehensive computational tools that can be used for

predicting the uncontrolled and controlled responses of

LHAWT. These numerical tools will provide the accuracy

needed during the design, development, testing, and deploy-

ment of LHAWT.

Fig. 2 – Wake evolution considering the presence of the

turbine support tower.

2. The aerodynamic model

2.1. The mathematical problem

Consider a 3D incompressible flow of an inviscid fluid gener-

ated due to the unsteady motion of the rotor blades. The

absolute velocity of a fluid particle which occupies the posi-

tion R at instant t is denoted by V(R;t). Since the flow is irro-

tational outside the boundary layers and the wakes, the

velocity field can be expressed as the gradient of a total

velocity potential FðR; tÞ as follows:

VðR; tÞ ¼ VFðR; tÞ (1)

The spatial/temporal evolution of the total velocity poten-

tial is governed by the continuity equation for incompressible

flows.

V2Fðr; tÞ ¼ 0 (2)

A set of boundary conditions (BCs) must be added [1–3]. The

location of the body’s surface is known, possibly as a function

of time, and the normal component of the fluid velocity is

prescribed on this boundary. The first BC requires the normal

component of the velocity of the fluid relative to the body to be

zero at the boundaries of the body. This BC, commonly called

the ‘‘no-penetration or impermeability’’ BC (on the surface of

the solid surface), becomes:

ðV�VSÞ$bn ¼ ðVF�VSÞ$bn ¼ 0 (3)

where VS is the velocity of the boundary surface S, and bn is the

unit normal vector. In general, VS and bn vary in space and

time. A regularity condition at infinity must also be imposed.

This second BC requires that the flow disturbance, due to the

motion of the body (or bodies) through the fluid, should

diminish far from the body. This is usually called the regu-

larity condition at infinity and is given by

limjRj/N

jVðR; tÞj ¼ limjRj/N

jVFðR; tÞj ¼ 0 (4)

Since the disturbance velocity field is computed according

to the Biot-Savart law, the regularity condition at infinity is

satisfied identically. For incompressible potential flows, the

velocity field is determined from the continuity equation,

and hence, it may be established independently of the

pressure. Once the velocity field is known, the pressure is

calculated from the unsteady Bernoulli equation. Moreover,

since the speed of sound is assumed to be infinite, the

influence of the BCs is immediately radiated across the

whole fluid region; therefore, the instantaneous velocity field

is obtained from the instantaneous BCs. In addition to the

BCs, the Kelvin–Helmholtz theorems [4] and the unsteady

Kutta condition are used to determine the strength and

position of the wakes.

The integral representation of the velocity field V(R;t) in

terms of the vorticity field UðR; tÞ ¼ V�VðR; tÞ, is an extension

Fig. 3 – Detailed view of the process of wake rupture.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 6 0 0 5 – 6 0 1 1 6007

of the well-known Biot-Savart law. For 3D flows, it takes the

following form:

VðR; tÞ ¼ 14p

Z ZSðR0 ;tÞ

UðR0; tÞ � ðR� R0ÞjR� R0j2

dSðR0; tÞ (5)

where R0 is a position vector on the compact region S(R0;t) of

the fluid domain. The integrand in the surface integral (5) is

zero wherever U(R;t) vanishes. Thus, the region where the

flow is irrotational does not contribute to V anywhere. V can

be evaluated explicitly at each point, i.e., independently of the

evaluation of V at neighboring points. As a consequence of

this feature, which is absent in finite difference methods, the

evaluation of V can be confined to the viscous region; the

vorticity distribution in the viscous region determines the flowfield in

both, the viscous and inviscid regions.

In order to formulate the no-penetration BC given by

Equation (3) it is convenient to divide the total velocity potential

FðR; tÞ into two parts, due to the bound-vortex sheet FB and

Fig. 4 – Time evolution of the axial force. I

another due to the free-vortex sheet FW. Hence, Eq. (3) can be

rewritten as:

ðVFB þ VFW � VSÞ$bn ¼ 0 (6)

2.2. The unsteady vortex-lattice method

In the UVLM, the continuous bound-vortex sheets are dis-

cretized into a lattice of short, straight vortex segments of

constant circulation GiðtÞ. These segments divide the surface of

the body into a number of elements of area. The model is

completed by joining free-vortex lines, representing the

continuous free-vortex sheets, to the bound-vortex lattice

along the edges of separation; such as the trailing edges and

tips of the rotor blades. Experience with the vortex-lattice

method suggests that the geometric shape of the elements in

the lattice affects the accuracy and the rate of convergence. It

was found that rectangular elements work better than other

shapes. Consequently, as much as possible we use rectangular,

or nearly rectangular, elements everywhere except in those

places where we are forced to use triangular elements: for

example, at the hub of the windmill. Each element of area in

the lattice is enclosed by a loop of vortex segments. To reduce

the size of the problem, we can consider each element to be

enclosed by a closed loop of vortex segments having the same

circulation. Then the requirement of spatial conservation of

circulation is automatically satisfied. These loop circulations

are denoted by Gi(t). Because the vortex sheets are approxi-

mated by a lattice, the no-penetration condition given by Eqs.

(3) or (6) can be satisfied at only a finite number of points, the

so-called control points. The control points are the centroids of

the corner points (aerodynamic nodes). The problem consists

of finding the circulations Gi(t) around the discrete vortices on

the bound-lattice such that the velocity field V satisfies condi-

tions (3) or (6) at the control points. In order to find these

circulations, we construct a matrix of aerodynamic influence

coefficients Aij for i; j ¼ 1;2;.;NP where NP is the number of

elements (closed loops of constant vorticity) in the bound-

lattice. The coefficient Aij represents the normal component of

the velocity at the control point of the ith element associated

with a unit circulation around the vortex of element jth, and is

nfluence of the turbine support tower.

Fig. 5 – Time evolution of the produced power. Influence of the turbine support tower.

Fig. 6 – Wake evolution neglecting the land–surface

boundary layer.


in general a function of time. In terms of the coefficients Aij

[6,5], the no-penetration condition given by Equation (6) can be

written as follows:

XNP

j¼1

AijGjðtÞ ¼ �½VFW �VB�i$bni; i ¼ 1;2;.;NP (7)

The linear algebraic system of equations given by Eq. (7) is

used to compute the unknown circulations Gj(t). At the end of

each time step, to satisfy the Kutta condition, vorticity is shed

into the flowfield and become part of the grids that approxi-

mate the free-vortex sheets of the wake. Because the vorticity

in the wake now was generated on, and shed from, the body at

an earlier time, the flowfield is history-dependent and so the

current distribution of vorticity on the surface of the body

depends to some extent on the previous distributions of

vorticity. The vorticity distribution in and the shape of the

wake are determined as part of the solution so the history of

the motion is stored in the wake. We say that the wake is the

‘‘historian’’ of the flow. As time passes and the vorticity in the

wake convects far downstream, its associated velocity field

does not have any appreciable influence on the flow around

the body; thus, the historian has a fading memory. In the

numerical method, this means that only the wake near to the

body is important; the rest can be safely neglected.

The method developed in this effort treats the position of,

and the distribution of vorticity in, the wakes as unknown and

they are determined as part of the solution. The present

method employs an explicit routine for generating the

unsteady wake (instead of the iterative scheme that was used

previously by some investigators), providing efficiency

without a loss of accuracy and even providing solution for

some cases where the iterative methods did not converge. To

generate the wakes the discrete vortex segments at the trail-

ing edge an the tip of each rotor blade are convected at the

local particle velocity, V½RðtÞ�, calculated from the Biot-Savart

law. The updated positions, Rðtþ DtÞ, of the vortex points are

computed according to

Rðtþ DtÞ ¼ RðtÞ þ DRðtÞzRðtÞ þV½RðtÞ�Dt (8)

This approximation for the value of DRðtÞ does not need iter-

ations and is stable [7].

2.3. Loads computation

The aerodynamics loads acting on the lifting surfaces (rotor

blades) are computed as follows: (i) the pressure jump at the

control point of each element is computed from the unsteady

version of Bernoulli Equation (9); (ii) the force at each area

element is computed as the product among the pressure jump

times the area of the element times the unit normal vector;

(iii) the resultant force and moment are computed as the

vector addition of the forces and moments produced by each

element, respectively.

vF

vtþ 1

2V$Vþ p

r¼ 1

2VN$VN þ

pN

rN

(9)

The details of each term of Eq. (9) are shown in references

[6, 8, 9].

Fig. 7 – Wake evolution considering the land–surface

boundary layer.


3. Results

The results obtained using the computational tool developed

in this effort are presented in this section. First, in Section 3.1

the influence of the turbine support tower is presented; then,

in Section 3.2, the incidence of the land–surface boundary

layer is shown.

3.1. Influence of the turbine support tower

During the rotational cycle, the blades of a horizontal-axis

wind turbine encounter a region of disturbed inflow when

they pass near the azimuthal position of the turbine support

tower. For upwind rotor configurations this effect is due to the

slowdown and deflection of the flow upstream of the tower

and so its severity depends on the proximity of the rotor disk

to the support tower. If the rotor is far enough upstream of the

tower, the interference effect becomes negligible.

The time and spatial evolution of the wakes, neglecting

and including the presence of the turbine support tower is

Fig. 8 – Time evolution of the axial force. Influ

presented in Figs. 1 and 2, respectively. In Fig. 2, it is possible

to note how the wakes brake when they impact the turbine

support tower.

Vorticity cannot be created or destroyed in the interior of

a homogeneous fluid under normal conditions, and is

produced (or destroyed) only at the boundaries, where

‘‘normal conditions’’ excludes the merger of two streams with

different velocities. For an inviscid fluid, vorticity is convected

with the fluid in the sense that the flux of vorticity associated

with each surface element moving with the fluid remains

constant for all times. When the wakes impact the turbine

support tower, they break because they cannot penetrate the

solid (See Fig. 3). A readjustment of the circulation occurs at

the solid surface.

Fig. 4 shows the time history of the axial force that acts in

a direction perpendicular to the rotor; this load is responsible

for bending effects on the turbine support tower. It is possible

to note that the presence of the turbine support tower

produces an alternating variation in the axial force (dashed

blue line) respect to the value obtained with the model where

the presence of the tower is neglected (solid black line). In both

curves, after the transient, the value of the axial reaches

a constant value. When the turbine support tower is included,

the variation of the axial force undergoes three periods per

revolution of the rotor. This fact is explained because the

blades pass in front of the tower three times per revolution of

the rotor.

The time history of the produced power is shown in Fig. 5.

The situation is similar to that of the axial force.

When designing, we must take these loads variations into

account because they can either produce fatigue in some of

the LHAWT components and/or produce significant dynamic

effects that can compromise the structural integrity of the

wind turbine structure.

3.2. Incidence of the land–surface boundary layer

Figs. 6 and 7 show the time history of the wakes neglecting

and including the presence of the of the land–surface

boundary layer.

Comparing these two figures, it is possible to note the

difference in the shape of the wakes. When the land–surface

ence of the land–surface boundary layer.

Fig. 9 – Time evolution of the produced power. Influence of the land–surface boundary layer.


boundary layer is neglected, the wake moves uniformly

almost parallel to the land–surface. On the other hand, when

the land–surface boundary layer is included, the wake moves

and deforms in the vertical direction copying the velocity

profile associated to the land–surface boundary layer.

Fig. 8 shows the time evolution of the axial force. It is clear

that the existence of the land–surface boundary layer

produces a reduction in the magnitude of that load (dashed

blue line) with respect to the case where the effect of the land–

surface boundary layer is neglected (solid black line). When

the steady state is reached, the reduction in the magnitude of

the axial force is around 3%.

The time history of the produced power is shown in Fig. 9.

The situation is similar to that of the axial force. When the

steady state is reached, the reduction in the produced power is

around 2%.

Figs. 8 and 9 show the variations originated by the presence

of the turbine support tower. This case, which includes the

presence of both the turbine support tower and the land–

surface boundary layer, was the most complex situation

analyzed in the present work.

The adopted wind profile to model the land–surface

boundary layer follows the CIRSOC 102 standard [10] where the

wind velocity is a function of altitude and terrain ruggedness.

4. Concluding remarks

Several results obtained by using the computational tool

developed in this work were presented. The main objective of

this effort was to simulate, in the time domain, the non-linear

and unsteady aerodynamic behavior of large horizontal-axis

wind turbines.

Some important conclusions can be drawn from these

results. Though the aerodynamic behavior is usually not fully

understood, the results presented here help to understand the

aerodynamic behavior associated to LHAWTs, whose

complexity is well-known and accepted.

The aerodynamic interference due to the presence of the

turbine support tower has been satisfactorily captured and in

agreement with results from wind tunnel experiments.

Although the presence of the turbine support tower does not

change the aerodynamic performances of the windmill, this

interference originates alternating load components, which

can produce fatigue in the LHAWT components and/or non–

desirable dynamic effects. These aspects were no studied in

detail in the present effort.

The effects produced by the land–surface boundary layer

were also satisfactorily captured. It was shown, that the pres-

ence of the land–surface boundary layer reduces the aero-

dynamic efficiency of the windmill.

Although the computational tool developed in this effort

establishes a good starting point towards a better under-

standing of the aerodynamic behavior of LHAWTs, it will be

necessary to carry out simulations that include structural

dynamics, control systems, and highly complex environ-

mental conditions that usually take place in the regions where

these machines are installed.

r e f e r e n c e s

[1] Gebhardt CG, Preidikman S, Massa JC, Aerodinamicainestacionaria y no-lineal de generadores eolicos de granpotencia y de eje horizontal. Primer Congreso Argentino deIngenierıa Aeronautica; 2008a.

[2] Gebhardt CG, Preidikman S, Massa JC, Weber GG,Simulaciones numericas de la aerodinamica no estacionariade generadores eolicos de eje horizontal y gran potencia.Primer Congreso Argentino de Ingenierıa Mecanica; 2008b.

[3] Gebhardt CG, Preidikman S, Massa JC, Weber GG.Comportamiento aerodinamico y aeroelastico de rotores degeneradores eolicos de eje horizontal y de gran potencia.Mecanica Computacional 2008c;17:519–39.

[4] Lugt H. Vortex flow in nature and technology. John Wiley &Sons; 1983.

[5] Katz J, Plotkin A. In: Low-speed aerodynamics. 2nd ed.Cambridge University Press; 2001.

[6] Konstandinopoulos P, Mook DT, Nayfeh AH, 1981.A numerical method for general, unsteady aerodynamics.AIAA-81-1877.


[7] Kandil OA, Mook DT, Nayfeh AH. Non-linear prediction of theaerodynamic loads on lifting surfaces. Journal of Aircraft1976;13:22–8.

[8] Preidikman S, Numerical simulations of interactions amongaerodynamics, structural dynamics, and control systems.Ph.D. Thesis, Virginia Polytechnic Institute and StateUniversity; 1998.

[9] Preidikman S, Mook DT. Modelado de fenomenosaeroelasticos lineales y no-lineales: los modelosaerodinamico y estructural. Modelizacion Aplicada ala Ingenierıa, Regional Bs. As, UTN. I; 2005.pp. 365–388.

[10] CIRSOC 102 Standard. Accion dinamica del viento sobre lasconstrucciones. INTI-CIRSOC; 1982.

Documents

1-s2.0-S0360319909020175-main.pdf