numerical analysis of aeroelastic responses of wind turbine under uniform inflow · 2020. 9. 1. ·...

NUMERICAL ANALYSIS OF AEROELASTIC RESPONSES OF WIND

TURBINE UNDER UNIFORM INFLOW

Yang Huang Computational Marine Hydrodynamics Lab (CMHL),

State Key Laboratory of Ocean Engineering, School of

Naval Architecture, Ocean and Civil Engineering,

Shanghai Jiao Tong University, Shanghai, China

Decheng Wan* Computational Marine Hydrodynamics Lab (CMHL),

State Key Laboratory of Ocean Engineering, School

of Naval Architecture, Ocean and Civil Engineering,

Shanghai Jiao Tong University, Shanghai, China *Corresponding author: [email protected]

ABSTRACT

With wind turbine blades becoming longer and slender, the

influence of structural deformation on the aerodynamic

performance of wind turbine cannot be ignored. In the present

work, the actuator line technique that simplifies the wind

turbine blades into virtual actual lines is utilized to simulate the

aerodynamic responses of wind turbine and capture downstream

wake characteristics. Moreover, the structural model based on a

two-node, four degree-of-freedom (DOF) beam element is

adopted for the deformation calculation of the wind turbine

blades. By combing the actuator line technique and linear finite

element theory, the aeroelastic simulations for the wind turbine

blades can be achieved. The aeroelastic responses of NREL-

5MW wind turbine under uniform wind inflow condition with

different wind speeds are investigated. The aerodynamic loads,

turbine wake field, blade tip deformations and blade root

bending moments are analyzed to explore the influence of blade

structural responses on the performance of the wind turbine. It

is found that the power output of the wind turbine decreases

when the blade deformation is taken into account. Significant

asymmetrical phenomenon of the wake velocity is captured due

to the deformation of the wind turbine blades.

INTRODUCTION

In order to improve the economic performance of wind

power generation, the wind turbine is developing towards the

direction of large scale, and the wind turbine blades become

longer and slender [1-3]. This leads to the larger deformation of

the wind turbine blades and more unstable aerodynamic

performance. Structural dynamic responses of the wind turbine

have significant effects on the aerodynamic performance and

the wake behavior, which further alters the inflow condition of

the downstream wind turbine [4]. Moreover, the elastic

deformations of the wind turbine blades result in significant

decrease of the fatigue life [5]. Therefore, it is necessary to take

the aeroelastic effects into consideration for the aerodynamic

analysis of the wind turbine.

To capture the aeroelastic characteristics of the wind

turbine, both aerodynamic loads and the structural deformations

should be considered in the aeroelastic model. For the modeling

of the wind turbine aerodynamics, there are various different

aerodynamic models, such as the blade element momentum

(BEM) model, vortex model, actuator type model and

computational fluid dynamics (CFD) model. The BEM model

[6] has the advantages of simple form and fast calculation.

Accurate results can be obtained when the airfoil aerodynamic

data are available [7]. However, the wake characteristics of the

wind turbine cannot be well predicted by BEM model. The

vortex model [8], which uses the lifting lines or surfaces to

represent the trailing and shed vorticity in the wake, is able to

capture the wake dynamic characteristics. It is noted that the

viscous effects are not taken into consideration in the vortex

model [9]. To reproduce the turbine wake with accepted

computational resource and computational accuracy, the

actuator type model is developed for the modeling of wind

turbine blades [10-12]. The actuator type model can provide a

better insight into the three-dimensional (3D) wake

development. Compared with the above aerodynamic models,

the CFD model can provide more detailed flow information by

solving the governing equations of the flow field, which is

believed to be one of the most accurate approaches to

investigate the 3D flow phenomena around the wind turbine

blades. However, much more computing resources are required

for the CFD simulations of the wind turbine [13].

OMAE2020-18084

1 Copyright © 2020 ASME

Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering

OMAE2020 August 3-7, 2020, Virtual, Online

Attendee Read-Only Copy

The structural model applied for the calculation of the

elastic deformation of the wind turbine blades mainly include

3D finite element method (FEM) and one-dimension (1D)

equivalent beam model [4]. The 3D FEM model can consider

the composite layer characteristics with changeable thickness,

while it is much more complex and time-consuming compared

with the 1D equivalent beam model. To simplify the structural

modeling of wind turbine blades, the 1D equivalent beam model

is widely utilized in the aeroelastic simulations of the wind

turbine. The modal approach, multi-body dynamics and 1D

FEM are usually used for the discretization of the blade in this

model [14-16]. By establishing the aeroelastic model of the

wind turbine, a number of researches have been conducted to

study the aeroelastic responses of the wind turbine. Meng et al.

[17] proposed an elastic actuator line (EAL) model that

combines the actuator line model and a finite difference

structural model, which was employed to study the influence of

wake induced fatigue loads on the downstream wind turbine. A

two-way coupling approach was adopted in the EAL model. Ma

et al. [18] developed an aeroelastic analysis tool ALFEM to

investigate the dynamic wake development of the wind turbine.

The aerodynamic performance of the wind turbine was

predicted by the actuator line mode, and the structural

deformation was solved based on the nonlinear finite beam

theory. Moreover, the CFD approach coupled with MBD code

or 1D FEM were applied to the aeroelastic modeling of the

wind turbine [19, 20]. However, the computational cost of the

CFD simulations increases significantly.

To reduce the requirement of computational resources, the

actuator line technique is employed in the present work. We

combine the actuator line model and the 1D FEM to establish a

coupled analysis tool. Aeroelastic responses of the wind turbine

under various wind speeds are investigate in detail. The actuator

line technique that simplifies the wind turbine blades into

virtual actual lines is utilized to simulate the aerodynamic

responses of the wind turbine and capture the downstream wake

characteristics. A structural model based on a two-node, four

degree-of-freedom (DOF) beam element is developed for the

deformation calculation of the wind turbine blades. Based on

the simulation results, the aerodynamic loads and structural

dynamic responses including the blade tip displacement and

blade root bending moment are analyzed to explore the

influence of structural deformation on the performance of the

wind turbine.

NUMERICAL METHODS

Aerodynamic Governing Equations

The three-dimensional (3D) Reynolds-averaged Navier-

Stocks (RANS) equations are selected to describe the transient

and viscous airflow. The PISO solver is utilized to decouple

velocity and pressure fields. Due to the low rotational speed of

the wind turbine, the air is regarded as the incompressible fluid.

The aerodynamic governing equations are defined by the

following equations:

0U (1)

21( )

UU U p U f

t

(2)

where U is the velocity field; donates the density of air;

is the kinematic viscosity coefficient; f represents the body

forces calculated from the actuator line model. To solve the

RANS equations, the two-equation turbulence model k-ω SST

is selected. The turbulent kinetic energy k and the turbulent

dissipation rate are determined by the following equations:

( U ) ( )k k k k

kk k G Y S

t

(3)

( U ) ( ) G Y D St

(4)

where Г is the effective diffusion coefficient, G donates

turbulence generation term, Y is the turbulent dissipation term,

S represents the source terms, D is the cross-diffusion term. It

should be noted that the full-scale Reynolds number in the

present simulation is about 7.6×106. RANS is employed in

computations to reduce the computational time. Aerodynamic

loads can be well predicted in RANS simulation.

Figure 1. Velocity vector components at the blade section

The actuator line technique [11] is applied to calculate the

aerodynamic loads in the present work. Virtual actuator lines

are utilized to replace wind turbine blades in this model. Thus,

the blade geometry layer does not require solved, and

computation loads can be greatly reduced. Body forces are

calculated based on local relative wind speed and local attack

angle at the blade section. As shown in Figure 1, a cross-

sectional element is defined at the (θ, z) plane. To reflect the

impacts of structural deformation, an additional velocity SU

induced by the blade deformation is taken into consideration.

The local relative wind speed relU is defined by the following

equation:

rel z sU U r U U (5)

where U and zU are the tangential and axial velocity in the

inertial frame, respectively. represents the rotational speed

of the turbine rotor. The attack angel can also be calculated by

the following equation:

t (6)

where represents the inflow angle, which can be calculated


according to the magnitude of velocity vector along different

directions. t donates the local twist angle. Based on the local

attack angle and two-dimensional airfoil aerodynamic

parameters, the lift coefficient LC and drag coefficient

DC

can be calculated by linear interpolation. Then body forces

acting on the blade can be determined.

2

rel| U |

2 d d

b

L L D D

cNC C

r z

f e e (7)

where c represents the chord length; Nb is the number of blades;

eL and eD denote the unit vectors in the directions of the lift and

the drag, respectively.

To avoid singular behavior in the simulation, the body

forces need to be distributed smoothly on the mesh points near

the actuator points. This is accomplished by taking convolution

of the computed local load f and a regularization kernel

function:

f f (8)

2

3 3/2

1exp

d

(9)

where d represents the distance between the actuator point and

measured point in flow field. ε is a constant parameter to adjust

the strength of regularization function. Finally, the body force

term introduced into the momentum equation can be written as:

ε /( , , , ) (x ,y ,z , ) exp

N

i i i

i

dx y z t t

f f

2

3 3 21

1 (10)

Structural Governing Equations

Considering that the wind turbine blade is slender, one-

dimensional equivalent beam model is adopted in the present

work. Moreover, the shear deformation effects can be ignored

due to the thin and slender structure of the wind turbine blades.

Therefore, Euler-Bernoulli beam model is applied to calculate

the dynamic structural deformation. In addition, 1D FEM is

used to discretise the blade into a series of beam elements, as

shown in Figure 2. It is noted that only the displacement along

flap-wise and edge-wise directions are taken into consideration.

A two-node, four degree-of-freedom (DOF) beam element is

selected to calculate the deformation of the wind turbine blades.

Figure 2. The schematic diagram of the structural model

The structural governing equations of the blade are defined

by the following second-order ordinary differential equations:

[ ] [ ] [ ]x x xM x C x K x F (11)

[ ] [ ] [ ]y y yM y C y K y F (12)

where [M], [C] and [K] are the mass, damping and stiffness

matrices, respectively. [x] and [y] represent the structural

displacement in flap-wise direction and edge-wise direction.

respectively. It should be noted that the stiffness of each wind

turbine blade along flap-wise direction and edge-wise direction

has great difference. The [Fx] and [Fy] donate the aerodynamic

forces acting the blade along flap-wise and edge-wise directions,

respectively. Moreover, the gravity force and the centrifugal

force are both added into the right-hand item of the force matrix.

Besides, the damping matrix can be obtained according to

Rayleigh damping, which is defined by the following equation: [ ] [ ] [ ]C M K (13)

where and are the damping coefficients of the mass

matrix and the damping coefficient, respectively, which are

determined by the damping ratio and the natural frequency of

the wind turbine blades. The MCK equations are solved by the

Newmark-beta method.

Coupled Aeroelastic Analysis Method

The aeroelastic model for the wind turbine blades is

established by combining the actuator line model and the 1D

equivalent beam model. It is noted that the aerodynamic model

based on the actuator line technique has been developed in the

previous work [21], while the structural model based on the 1D

FEM is developed in the present work. On the base of existing

code, the coupled aeroelastic analysis tool is developed to

investigate the influence of structural deformation. In order to

achieve the coupling between the structural deformation and the

aerodynamic calculation, the influence of the structural

deformation on the local attack angle and the impacts of the

aerodynamic loads on the structural model are both considered

in the aeroelastic simulations.

The solving procedure of aeroelastic simulations for the

wind turbine is shown in Figure 3. It can be seen that the

additional velocity induced by the structural deformation is

considered in the calculation of relative wind speed, which

further alters the local attack angle and aerodynamic force

coefficients. In return, the aerodynamic forces calculated from

the ALM obviously affect the structural deformation of the wind

turbine blades. Besides, a wake-coupling approach is selected in

the present work. It means that structural vibration velocity

considered in the calculation of local relative wind speed is

induced by the deformation calculated from the last time step.


Initialize

Start time step

Read blade structural parameters

Inputs for structural Model: position &

velocities of time t-Δt

Apply the aerodynamic force, gravity

and centrifugal force to structural

model

Calculate the deformation of time t

Generate the geometric configuration

of time t

t=t+Δt

Aerodynamic

forces

Inputs for ALM: position &

velocities of time t-Δt

t>T

End

Read wind turbine parameters

Calculate relative speed of

Actuator element

Calculate angle of attack

Calculate drag and lift

coefficients via Interpolation

Calculate body forces

Update wind turbine

No

Yes

Structural

solver Fluid

solver

Update structural information

Structural

vibration

velocity

No

Figure 3. Solving procedure of the coupled aeroelastic

simulation

SIMULATION DESCRIPTIONS

Wind Turbine Model

The NREL 5-MW wind turbine, which is a respective

utility-scale multi-megawatt wind turbine, is employed in the

present work to perform aeroelastic analyses and investigate the

effects of structural deformation on the aerodynamic

performance. The nacelle, hub and tower are all ignored, and

only the wind turbine blades are modelled. Besides, the control

strategy including the blade-pitch regulator and yaw-control is

not taken into account. The main properties of the wind turbine

are listed in Table 1, and more detailed information can be

found in the Reference [22].

(a) (b)

(c) (d)

Figure 4. Structural properties of the NREL 5-MW wind turbine

blade: (a) mass; (b) twist angle; (c) stiffness along flap-wise

direction; (d) stiffness along edge-wise direction

Table 1 Main properties of the NERL 5-MW turbine

Rotor, Hub Diameter 126 m, 3 m

Hub Height 90 m

Cut-in, Rated, Cut-out

Wind Speed 3 m/s, 11.4 m/s, 25 m/s

Cut-in, Rated Rotor Speed 6.9 rpm, 12.1 rpm

Overhang, Shaft Tilt,

Precone Angle 5 m, 5°, 2.5°

Rotor Mass 110,000 kg

Nacelle Mass 240,000 kg

Tower Mass 347,460 kg

Coordinate Location of CM

(center of mass) ( -0.2 m, 0.0 m, 64.0 m)

The structural properties of the NREL 5-MW wind turbine

are presented in Figure 4. It can be found that the stiffness of

wind turbine blade varies dramatically along span-wise

direction. The density of each turbine blade also significantly

changes with the distance from the turbine hub. To simplify the

simulations, it should be noted that the influence of the twist

angle on structural deformation is not taken into consideration.

Computation Set Up

A cuboid domain with the dimension of 6D(x)×3D (y)×3D

(z) (D = 126m is the diameter of the turbine rotor) is generated

as the computational domain, as shown in Figure 5. The wind

turbine is located in the origin of the computational domain.

Different mesh resolutions are generated to reduce the

computational loads. The gird size of background mesh is 8m×

8m×8m. Figure 6 shows the grid distribution in horizontal and

cross section. The grids in the region behind the wind turbine

are refined with the grid size of 2m×2m×2m to capture the

turbine wake. The total grid number is 3.2 million.

Figure 5. Computational domain (D = 126m is the diameter of

the turbine rotor)


(a) (b)

Figure 6. Grid distribution: (a) cross section; (b) horizontal

section

Uniform inflow boundary condition is adopted as the inlet

boundary. Two different wind speeds of 8 m/s and 11.4 m/s are

both considered in order to study the influence of the magnitude

of wind speed on the aeroelastic responses of the wind turbine.

The output boundary condition is zero gradient boundary

condition, and symmetrical boundary condition is applied to

surrounding walls. Considering that the bottom boundary is no

the ground, the bottom and tip boundaries both adopt slip

boundary condition. In addition, detailed information of

simulation cases is summarized in Table 2.

Table 2 Simulation cases description

Case number Structural deformation Wind speed

Case #1 consider 11.4 m/s

Case #2 ignore 11.4 m/s

Case #3 consider 8 m/s

Case #4 ignore 8 m/s

RESTLTS AND DISCUSSIONS

Validation Simulation

The aeroelastic model is composed of the structural model

and the actuator line model. The accuracy of ALM has been

validated in the previous work [23]. Thus, only the structural

model is validated in the present work. The dynamic structural

deformation of a typical cantilever beam under a ramp-infinite

duration load is chosen to perform the validation simulation.

Structural properties of the cantilever beam and the load acting

on the free end of beam are both presented in Figure 7.

(a) (b)

Figure 7. The set-up of the validation test: (a) cantilever beam

geometry; (b) load history.

Figure 8. Time histories of the deflection of the cantilever beam

for different numerical methods.

According to the reference [24], a time step of 0.01s and

40 beam elements are selected in the present structural model to

calculate the dynamic structural deformation. Figure 8 shows

the time history of the deflection of the cantilever beam. It is

shown that the structural deflection of the cantilever beam

calculated by the present structural model has good agreements

with the theoretical value, which prove the accuracy of the

structural model.

Grid Convergence Test and Time Step Dependence Study

In order to ensure the accuracy of simulation results, grid

dependence test is firstly performed. Three sets of grids with

different mesh resolutions are generated to perform the grid

convergence test. Total grid number of different mesh can be

found in Table 3. In the grid convergence test, a time step of

0.02 s is selected. At this time step, the blades rotate about 1.4

degree at rated angular speed pre time step, which is small

enough to satisfies the accuracy of computations. Mean

aeroelastic responses including aerodynamic loads and

structural deformation are summarized in Table 3. The

differences of aerodynamic loads between the medium mesh

and fine mesh are both below 2%. Besides, the differences of

blade tip deformation along flap-wise and edge-wise directions

between the medium mesh and fine mesh are 1.5% and 2.4%,

respectively. It indicates that the aeroelastic responses of wind

turbine can be well predicted with the medium mesh.

In addition, the time step dependence study is also

conducted. Three different time step sizes (0.01 s, 0.02 s, 0.03

s) are chosen in computations. Averaged aeroelastic responses

of NREL 5-MW wind turbine under rated wind speed of 11.4

m/s are presented in Table 4. It can be found that the

aerodynamic loads and structural deformation both gradually

convergence with the decrease of time step size. The differences

of aerodynamic loads and structural deformations between

medium time step and small tine step are all below 1%. Thus,


the medium time step size of 0.02s is selected to perform later

computations in order to reduce the computational time.

Table 3 Mean aeroelastic responses of the wind turbine in grid

convergence test.

Case

Grid

number Power Thrust

Flap-

wise

Edge-

wise

(million) (MW) (kN) (m) (m)

coarse 1.6 5.35 719 5.2586 0.2177

medium 3.2 5.10 706 5.1296 0.2017

fine 6.4 5.03 701 5.0556 0.1969

Table 4 Mean aeroelastic responses of the wind turbine under

different time step sizes.

Case

Time

step Power Thrust

Flap-

wise

Edge-

wise

(s) (MW) (kN) (m) (m)

small 0.01 5.09 705 5.1282 0.2011

medium 0.02 5.10 706 5.1296 0.2017

large 0.03 5.15 710 5.1486 0.2032

Aerodynamic Loads

The influence of structural deformation of wind turbine

blades on the aerodynamic loads including the rotor power and

thrust is discussed herein. As Figure 9 shows, the aerodynamic

loads with considering structural deformation are compared

with that without blade deformation. Only the time history

curves of aerodynamic loads under wind speed of 11.4 m/s are

present in the picture. The red line represents the aerodynamic

loads considering the blade deformation, and the blue dotted

line donates the aerodynamic loads without the structural

deformation.

(a)

(b)

Figure 9. Time history curves of aerodynamic loads under

uniform wind speed of 11.4 m/s: (a) rotor power; (b) thrust.

The aerodynamic loads in different cases all reach steady

values after about 20 s. It is observed that the mean values of

the rotor power and thrust considering the wind turbine

deformation are all smaller than those without structural

deformation, while the dynamic responses of the aerodynamic

loads show little discrepancy for different cases. It suggests that

the structural deformation of the wind turbine blades have

adverse effects on the aerodynamic loads under uniform inflow

condition. To illustrate the reason for this phenomenon, the

local attack angle and local relative wind speed of a typical

blade section are discussed. As shown in Figure 10, the

comparison of the aerodynamic parameters at the selected blade

section in Case 1 and Case 2 are achieved. The relative wind

speeds in different cases are almost the same, while the local

angles show great difference. The mean value of the local attack

angle in Case 2 is about 0.2 degree larger than that in Case 1.

However, the structural deformation results in the significant

increase of the variation range of the local attack angle. The

fluctuating amplitude of local attack angle in Case 1 is about 2

times that in Case 2. The change of local attack angle leads to

the smaller lift forces acting on the blades with a result of the

decrease of the aerodynamic forces.

(a)


(b)

Figure 10. Dynamic responses of the local attack angle and

local relative wind speed at a typical blade section (0.8r from

the blade root, r is the radius of the turbine rotor) under uniform

wind speed of 11.4 m/s: (a) local attack angle; (b) local relative

wind speed

The mean values of the aerodynamic loads under different

inflow wind speeds are also summarized in Table 5. Obviously,

the aerodynamic loads under rated wind speed (11.4 m/s) are

larger than those under lower wind speed (8 m/s). It is observed

that the rotor power with structural deformation are 96% of that

without considering the deformation of the blades at rated wind

speed, while this ratio increases up to 98% at low wind speed. It

suggests that the structural deformation of the wind turbine

blades have more significant effects on the aerodynamic loads

at high wind speed. Besides, the thrust of the wind turbine with

blade deformation is found to be 98% of that without

considering the structural deformation under wind speed of 11.4

m/s. It is larger than the ratio of the rotor power under the same

wind inflow condition. It indicates that the rotor power is more

sensitive to the structural deformation of the wind turbine

blades compared with the thrust.

Table 5 Mean values of the aerodynamic loads in different cases

No. Rotor power

(MW) ratio

Thrust

(kN) ratio

Case 1 5.10 -- 710 --

Case 2 5.30 96% 722 98%

Case 3 1.97 -- 382 --

Case 4 2.00 98% 385 99%

Turbine Wake Field

Based on the above analyses, the influence of the structural

deformation of the wind turbine blades on the aerodynamic

performance of the wind turbine are more significant compared

with low wind speed. Therefore, the wake field characteristics

obtained from case 1 and case 2 are analyzed in order to further

detect the influence of the structural deformation on the wake

field of the wind turbine.

The turbine wake is significantly affected by the body

forces acting on the wind turbine blades, while the aerodynamic

forces are obviously affected by the structural deformation. In

order to detect the influence of structural deformation on the

turbine wake, the instantaneous body force distribution on the

rotor plane is plotted in Fig. 11. It is shown that body forces

along different directions distributed on the blade tip in case 1

are much smaller than those in case 2 due to the large structural

deformation. This further leads to the change of turbine wake

characteristics.

(a)

(b)

Figure 11. Instantaneous body force distribution on the rotor

plane: (a) forces along stream-wise direction; (b) forces along

vertical direction.

(a)


(b)

Figure 12. Wake velocity at horizontal plane with a height of

hub height: (a) Case 1; (2) Case 2.

(a)

(b)

Figure 13. Wake velocity at horizontal plane (xz plane) in

different cases: (a) Case 1; (b) Case 2

The wake velocity at horizontal plane with a height of hub

height is presented in Figure 12. In Case 2, the velocity deficit

region is almost symmetrical to yz plane, while obvious

asymmetrical velocity deficit is found in Case 1. The wake

velocity in left half plane is smaller than that in right half plane,

which will lead to the asymmetrical loads acting the rotor plane

and further increase the yawing moment of wind turbine.

Moreover, the asymmetrical phenomenon of the wake speed is

also captured in vertical plane, as shown in Figure 13. The wake

velocity in upper half plane are much smaller than that in lower

half plane. This significant asymmetrical distribution of the

wake velocity is a comprehensive result of the structural

deformation and the shift-tile of the wind turbine. To clearly

illustrate the difference between the velocities in the vertical

plane, the profiles of the wake velocity at different stream-wise

cross sections in Case 1 and Case 2 are compared in Figure 14.

In the near wake region (x=1D, 2D, 3D), the wake velocity in

Case 1 is obviously smaller than that in Case 2. Besides, it is

clearly observed that the velocity deficit in upper half plane is

more serious than that in the lower half plane in Case 1.

Overall, the velocity deficit becomes more serious when the

structural deformation is taken into account. However, the

power output of the wind turbine has a decrease due to the

blade deformation.

Figure 14. Mean wake velocity profile at different stream-wise

cross sections (D=126 m is the rotor diameter), in which the red

dotted line and blue solid line represent the wake velocities in

Case 1 and Case 2, reprehensively.

Structural Dynamic Responses

The blade tip displacement and blade root bending

moment are obtained from the simulation results and analyzed

in detail to investigate the structural dynamic responses of the

wind turbine blades under different uniform wind inflow

conditions.

(a)


(b)

Figure 15. Blade tip displacement along different directions: (a)

flap-wise direction; (b) edge-wise direction

(a)

(b)

Figure 16. Blade root bending moment along different

directions: (a) flap-wise direction; (b) edge-wise direction

The tip displacements of blade #1 along the flap-wise and

edge-wise directions are shown in Figure 15. It is seen that

mean value of the blade-tip displacement along flap-wise

direction under rated wind speed is about 5m, which is close to

the published data in previous study [17]. In addition, the blade

tip displacements in different conditions all periodically vary

with the azimuth angle, and the variation period is nearly equal

to the rotational period of the wind turbine. Considering that the

structural deformation is dominated by the forces acting on the

blade, the main reason for this periodical variation of the blade

tip displacement is that the aerodynamic forces vary with the

azimuth angle. Obviously, the tip displacement increases with

the inflow wind speed, resulting from the larger aerodynamic

forces. The mean value of the blade tip displacement along flap-

wise direction with rated wind speed of 11.4 m/s is about 1.7

times that with a wind speed of 8 m/s. The mean blade tip

displacement along edge-wise direction at rated wind speed is

about 0.1 m larger than that under a low wind speed condition.

Besides, it is found that the mean value of the blade tip

displacement along flap-wise direction is much larger than that

along edge-wise direction, while the variation amplitude of the

blade deformation along flap-wise direction is smaller than that

along edge-wise direction. At rated wind speed of 11.4 m/s, the

variation of blade tip deformation along edge-wise direction is

about 5 times that along flap-wise direction, and this ratio

further increase up to 11 times at the wind speed of 8 m/s. The

periodical variation of the blade deformation will result in the

increase of fatigue loads and further leads to accelerated

damage of the wind turbine blades. In addition, the blade root

bending moments along different directions are presented in

Figure 16. It is shown that the mean blade root bending

moments become smaller when the blade deformation is taken

into account, resulting from reduced aerodynamic forces. The

variation amplitudes of the bending moments along flap-wise

direction in Case 1 and Case 3 are also smaller than that without

considering blade formation. However, the variation amplitudes

of the blade root bending moments along edge-wise direction

significant increase with blade deformation. It indicates that the

edge-wise bending moment is more sensitive to the blade

deformation compared with the flap-wise bending moment.

CONCLUSIONS

In this paper, the actuator line technique is applied to

calculate the aerodynamic loads of the wind turbine. A one-

dimensional equivalent beam model based on a two-node, four

degree-of-freedom (DOF) beam element is developed to predict

the structural deformation of the wind turbine blades. A coupled

aeroelastic model is established for the wind turbine by

combing a modified actuator model and a 1D equivalent beam

model. The structural model is firstly validated, and gird

convergence test and time step dependence study are both

conducted to determine proper suitable computational

parameters. Then aeroelastic simulations for the wind turbine


under different uniform inflow wind speeds are performed using

this coupled aeroelastic analysis model. The aerodynamic loads,

turbine wake field and structural dynamic responses are

obtained from the simulation results and analyzed in detail.

Several conclusions can be drawn from the discussion. It is

found that the structural deformation of the wind turbine blades

has adverse effects on the aerodynamic loads by altering the

local attack angle. At high wind speed, the influence of blade

deformation on the aerodynamic loads will be more significant.

The rotor power is more sensitive to the structural deformation

of the wind turbine blades compared with the thrust. Besides,

significant asymmetrical phenomenon of the wake velocity is

captured. This is mainly induced by the blade deformation and

the shift tilt of wind turbine. The velocity deficit becomes more

serious when the structural deformation of the wind turbine

blade is considered. In addition, the mean value of the blade tip

displacement along flap-wise direction is much larger than that

along edge-wise direction, while the variation amplitude of the

blade deformation along flap-wise direction is smaller than that

along edge-wise direction. The variation amplitude of the blade

root bending moment along edge-wise direction has a

significant increase when blade deformation is taken into

account, which results in the increase of fatigue loads and

further leads to accelerated damage of the wind turbine blades.

It is noted that the gird in present work is relatively coarse, and

the turbine wake characteristics are not well predicted with

RANS. Fine mesh and LES simulations are needed in the later

work to further study the aeroelastic responses of the wind

turbine. Atmospheric boundary flow condition is also

considered in order to obtain the realistic aeroelastic responses

of the wind turbine.

ACKNOWLEDGMENTS

This work is supported by the National Natural Science

Foundation of China (51879159), The National Key Research

and Development Program of China (2019YFB1704200,

2019YFC0312400), Chang Jiang Scholars Program

(T2014099), Shanghai Excellent Academic Leaders Program

(17XD1402300), and Innovative Special Project of Numerical

Tank of Ministry of Industry and Information Technology of

China (2016-23/09), to which the authors are most grateful.

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