marko horvat, borna Šojat and josip Žužul design and ... · horvat, Šojat i Žužul turbine...

UNIVERSITY OF ZAGREBFACULTY OF MECHANICAL ENGINEERING AND NAVAL

ARCHITECTURE

Marko Horvat, Borna Šojat and Josip Žužul

DESIGN AND NUMERICAL SIMULATION OF THE

TUBERCLE TECHNOLOGY

ON WIND TURBINE BLADES

Zagreb, 2016.

Horvat, Šojat i Žužul

Contents

1 Biomimicry 1

2 Calculation of the Wind Blade Geometry 22.1 Selection of the Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Calculation of the Rotor Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.3 Flow Losses Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3.1 Losses Due to the Drag of an Airfoil . . . . . . . . . . . . . . . . . . . . . 3

2.3.2 Blade Tip Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.3 Wake losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 Chord Length as a Function of Relative Radius . . . . . . . . . . . . . . . . . . . 6

2.5 Calculation of the Twist Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Geometry 7

4 Numerical simulation 94.1 Multiple Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.1.1 Incompressible Navier-Stokes Equations in the Rotating Frame . . . . . . 10

4.2 Numerical Spatial Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.3 Boundary and initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.4.1 Wind Turbine with the Conventional Blade . . . . . . . . . . . . . . . . . 16

4.4.2 Wind Turbine with Tubercles on a 70% of a Blade Length . . . . . . . . . 20

4.4.3 Wind Turbine with Tubercles on a 70% of a Blade Length . . . . . . . . . 25

4.4.4 Distribution of Turbulent Parameters Along the Tubercle Blades . . . . . . 30

4.5 Comparison of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.6 Conclusion of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5 Summary 36

Faculty of Mechanical Engineering and Naval Architecture


List of Figures

1 Humpback whale [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 A flipper [2] and the experimented model of a humpback whale flipper [3] . . . . . 1

3 Model of the free vortex in the downstream flow of the rotor [4] . . . . . . . . . . 5

4 NASA LANGLEY Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 WORTMANN FX 77-W-258 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . 8

6 Three different types of blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7 Numerical domain of a wind turbine with the conventional blades . . . . . . . . . 12

8 The rotor cell zone domain of a wind turbine with the conventional blades . . . . . 13

9 Mesh resolution in the different parts of the mesh of the wind turbine with the

conventional blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

10 Detail of the mesh in a proximity of the conventional rotor blade . . . . . . . . . . 14

11 Mesh resolution in the different parts of the mesh of the wind turbine with the

tubercle blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

12 Detail of the mesh in a proximity of the tubercle rotor blade . . . . . . . . . . . . . 15

13 Power oscillations of a single conventional blade . . . . . . . . . . . . . . . . . . 17

14 Velocity distribution at the wind turbine inlet . . . . . . . . . . . . . . . . . . . . 18

15 Wake behind the wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

16 Detail of the wake behind the wind turbine . . . . . . . . . . . . . . . . . . . . . . 19

17 Velocity and pressure fields at the radius of 1.5 m . . . . . . . . . . . . . . . . . . 19

18 Velocity and pressure fields at the radius of 3 m . . . . . . . . . . . . . . . . . . . 20

19 Velocity and pressure fields at the radius of 6 m . . . . . . . . . . . . . . . . . . . 20

20 Power oscillation of a single blade with tubercles on a 35% of the leading edge . . 21

21 Velocity distribution at the inlet of the wind turbine with tubercles on a 35% of the

leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

22 Wake behind the wind turbine with tubercles on a 35% of the leading edge . . . . . 22

23 Detail of the wake behind the wind turbine with tubercles on a 35% of the leading

edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

24 Velocity and pressure fields at the radius of 1.5 m of the wind turbine with the

tubercles on a 35% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . 24

25 Velocity and pressure fields at the radius of 3 m of the wind turbine with the tuber-

cles on a 35% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . 24



27 Pressure distribution on the suction blade side of the wind turbine with tubercles

on a 35% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

28 Pressure distribution on the pressure blade side of the wind turbine with tubercles

on a 35% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25



29 Power oscillation of a single blade with tubercles on a 35% of the leading edge . . 26

30 Velocity distribution at the inlet of the wind turbine with tubercles on a 70% of the

leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

31 Wake behind the wind turbine with tubercles on a 70% of the leading edge . . . . . 27

32 Detail of the wake behind the wind turbine with tubercles on a 70% of the leading

edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

33 Velocity and pressure fields at the radius of 1.5 m of the wind turbine with the

tubercles on a 70% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . 28





36 Pressure distribution on the suction blade side of a wind turbine with tubercles on

a 70% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

37 Pressure distribution on the pressure blade side of a wind turbine with tubercles on

a 70% of the leading edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

38 Distribution of specific turbulent kinetic energy on the suction side of the tubercle

blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

39 Distribution of specific turbulent kinetic energy on the pressure side of the tubercle

blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

40 Distribution of dissipation of specific turbulent kinetic energy on the suction side

of the tubercle blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

41 Distribution of dissipation of specific turbulent kinetic energy on the pressure side

of the tubercle blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

42 Distribution of turbulent viscosity the on the suction side of the tubercle blade . . . 33

43 Distribution of turbulent viscosity the on the pressure side of the tubercle blade . . 33

44 Vortex in the downstream flow of the wind turbine rotor with tubercle blades . . . . 34



List of Tables

1 Selected Airfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Values of loss coefficient due to the drag for different airfoils . . . . . . . . . . . . 4

3 Chord lengths along the relative radius of the conventional wind turbine blade . . . 7

4 Number of cells for different types of blade . . . . . . . . . . . . . . . . . . . . . 12

5 Conventional wind turbine parameters . . . . . . . . . . . . . . . . . . . . . . . . 16

6 Parameters of the wind turbine with tubercles on a 35% of the leading edge . . . . 20

7 Parameters of a wind turbine with tubercles on a 70% of the leading edge . . . . . 26

8 Comparison of the results obtained by the numerical simulation and the calculation 35



1 Biomimicry

Biomimicry or biomimetics presents us with innovative ways for solving problems humanity faces

today. Those problems can be solved by implementing ideas, systems and solutions that nature

obtained throughout billion years of evolution. Particular idea that will be further discussed is tu-

bercle technology that was observed on flippers of humpback whales. Large knobs on the leading

edge of the flipper is actually evolutionary advantage because they provide humpback whale, an

animal that is 12 - 15 m long, and weights 25 - 40 tonnes, with ability to circle in the water pro-

ducing vortices of just 1.5 m in diameter. By doing so they gather krill and crustaceans on which

they feed upon.

Tests of the model of the humpback whale flipper in the wind tunnel presented us with stag-

Figure 1: Humpback whale [1]

gering results. It was shown that tubercle technology provides humpback whale with 8% grater lift

and reduces drag up to 32%. Also large knobs on the leading edge of the humpback whale flippers

reduce stall angle for 40% [5].

(a) (b)

Figure 2: A flipper [2] and the experimented model of a humpback whale flipper [3]

Faculty of Mechanical Engineering and Naval Architecture 1


2 Calculation of the Wind Blade Geometry

In the frame of this work calculation is conducted using the BEM (Blade Element-Momentum)

theory and the Betz method [4]. Calculation conducted using Betz method produces values of the

tip-speed ratio and the diameter of a conventional wind turbine. Using the BEM method values of

chord length and twist angle along the relative radius of a blade are obtained.

2.1 Selection of the Airfoil

Wind turbine blade is divided into two characteristic parts depending on the relative radius and in

accordance, two different airfoils are used. In the proximity of the blade root WORTMANN FX

77-W-258 is used and in the proximity of the tip NASA/LANGLEY LS(1)-0241 MOD. Airfoils

from the WORTMANN series are designed especially for the application in wind turbine technol-

ogy and they are characterized with a high curvature [6]. Their thickness is the reason why they

are used in the proximity of the blade root. Desired strength and a smooth transition between the

blade and the hub, as well as between different airfoils is provided. Airfoils from the NASA LS

series are developed for the application in general aviation characterized by a lower wind speeds.

Compared to the WORTMANN series, NASA LS airfoils have lower drag (cD) and higher lift

coefficient (cL) at cruise velocities [7]. Therefore, it can be concluded that NASA LS airfoils have

high ratio of lift and drag coefficients (ε).

Table 1: Selected Airfoils

Airfoil Lift coefficient cL Drag coefficient cD cMWORTMANN FX 77-W-258 1.2876 0.01637 -0.0916NASA/LANGLEY LS(1)-0421 MOD 1.2638 0.01971 -0.0723

2.2 Calculation of the Rotor Diameter

According to the disk theory wind power is calculated as [6]:

P =12

ρR2πu3cp, (1)

where cP is the power coefficient, ρ is the air density and u is the magnitude of the free stream

velocity. In the initial step of the calculation, rotor radius is calculated with the assumption of a

highest theoretically possible power coefficient cP,Betz = 16/27. Wind turbine output power was

set to 30 kW , air density ρ = 1.2 kg/m3 and the magnitude of the free stream velocity u = 10

m/s. After the calculation of the rotor radius, the second step of calculation is conducted using

the information from the initial step. In the second step the tip-speed ratio is calculated as λD = ω

R/u = 4.638. A value of the angular velocity (ω) is calculated from the assumption of the wind



turbine rotational speed equal to 70 rpm. Whole calculation shown in this article is conducted for

an attack angle α = 7o.

2.3 Flow Losses Calculation

Calculation of losses is performed in order to obtain a correction factor of the Betz power coef-

ficient. Using a corrected value of a power coefficient the real value of the wind blade radius is

calculated.

2.3.1 Losses Due to the Drag of an Airfoil

Losses due to an airfoil drag can be calculated using the lift and drag ratio coefficient and an attack

angle. Observing a part of the blade dr, lift and drag forces (dL, dD) that act upon the blade part

can be calculated using following expressions [4]:

dL =ρ

2w2c dr cL(α), (2)

dD =ρ

2w2c dr cD(α), (3)

where w is a relative velocity of a fluid and the coefficients of drag and lift are depending on

the attack angle. Tangential component of a velocity can be derived using an angle between the

absolute and relative velocity γ:

dFT =ρ

2w2c dr [cL(α)cosγ− cD(α)sinγ]. (4)

If the expression (4) is inserted into the following equation:

dP = z dFT ωr, (5)

expression for calculation of power generated by a part of the blade dr is obtained. To calculate

a loss coefficient due to the drag, generated power in an ideal case (without the drag) has to be

calculated as:

dPid = n ωρ

2w2rdr cL(α)cosγ. (6)

Ratio of the generated power with and without the drag taken into an account defines a power loss

due to the drag of an airfoil.

ηair f oil =dP

dPid=

z ρ

2 w2c dr [cL(α)cosγ− cD(α)sinγ]ωrn ω

ρ

2 w2rdr cL(α)cosγ, (7)

ηair f oil = 1− 3 r λD

2 R ε, (8)



where:

ε =cL

cD, (9)

and z is the number of the wind turbine blades.

Table 2: Values of loss coefficient due to the drag for different airfoils

Airfoil ηair f oilWORTMANN FX 77-W-258 0.9768NASA/LANGLEY LS(1)-0421 MOD 0.9417

2.3.2 Blade Tip Losses

Blade tip losses occur as a result of a pressure difference between the pressure and the suction side

of a blade. Thus, a secondary (unwanted) flow from the pressure side to the suction side of a blade

occurs. As a result, pressure difference is lowered, and therefore lower value of a generated power

of a wind turbine can be obtained. In order to take mentioned phenomenon into an account, Betz

has defined an effective diameter D’ [4, 8]:

D′ = D

1− 0.92

z√

(λ 2D + 4

9)

. (10)

Due to the fact that the power is proportional to the squared value of radius for the tip loss coeffi-

cient can be written:

ηtip =

(D′

D

)2

=

1− 0.92

z√

(λ 2D + 4

9)

2

. (11)

For a conventional wind turbine observed in this article calculated tip loss coefficient was set to

ηtip = 0.8724.

2.3.3 Wake losses

No empirical expressions for calculation of a wake behind the turbine blades have been introduced

by Betz. Wake occurs as a result of the third Newton law, because the fluid is reacting to the torque

of a wind turbine with the reaction force which is acting on the blades at the radius r. From the

following expression it can be concluded that for a higher tip-speed ratio, reactive force (torque) is

lower:

dP = zdFT ωr. (12)

Turbines with high tip-speed ratio (λD) are extracting the power from the fluid at higher angular

velocities ω and therefore, according to the expression (12), torque is lower. On the other side,



turbines with lower values of tip-speed ratio are extracting power from the fluid at lower values of

ω and therefore torque is greater [4].

Figure 3: Model of the free vortex in the downstream flow of the rotor [4]

For the calculation of the conventional blade in this article assumed value of the loss coefficient

due to the wake was set to ηwake = 0.835.

If the values of the loss coefficient presented in previous sections are multiplied, a value of total

efficiency is obtained:

ηtotal = ηwakeηtipηair f oil. (13)

In the frame of this work, another correction factor is used. This factor is introduced to take

into account the losses due to the transition between different airfoils along the blade. Another

reason why this correction factor is used is the fact that the change of the ideal chord length along

the blade (as a function of relative radius) is linearised which is presented in the following section.

Therefore the value of the total efficiency equals:

ηtotal = 0.653. (14)

This factor is used as a correction of the highest theoretically possible power coefficient:

cP = cP,Betzηtotal, (15)

R =

√2P

cPρR2πu3 = 6.5m. (16)



2.4 Chord Length as a Function of Relative Radius

Change of the chord length along the turbine blade is taken into an account by the assumption of

the linear contraction of the chord length, moving from the root to the tip of the blade, using the

BEM method. After the calculation of the chord length along the relative radius, it is recommended

to conduct additional linearisation using the least squares method in order to avoid jumps in the

length values at the transition of the airfoils. Mentioned problem is especially expressed when the

airfoils at the transition point are from different airfoil series. The calculation of chord length is

performed using the following expression [6]:

cr = R[

16π

9zλ 2DcL0.8

(2−

rR

0.8

)]. (17)

2.5 Calculation of the Twist Angles

In order to prevent the change of the attack angle along the radius of the blade, twisting of the blade

in respect to the blade axis is introduced. Circumferential velocity increases with the increasement

of a radius what results in a change of a velocity triangle for a defined radius. Angle at which the

fluid enters the blade (Φ) is defined as:

tanΦ =1−a

λDrR(1+a)

. (18)

Previous expression can be transformed, if the induction factor a is set as a = 1/3 for an optimal

performance of a wind turbine, into:

tanΦoptimal =23

λDrR

(1+ 2

9λ 2D(

rR )

2

) . (19)

In the proximity of the blade root, Φ has the highest value what can cause a stall. In order to

achieve minimal drag coefficient, blade has to be designed with a twist angle which ensures the

optimal attack angle for different types of airfoils along the radius [6]. The twist angle is calculated

using the following expression:

β = Φoptimal−α. (20)



Table 3: Chord lengths along the relative radius of the conventional wind turbine blade

Airfoil Relative radius rR Chord length [mm] Twist angle [◦]

FX 77-W-258 0.2 972.5 22.7FX 77-W-258 0.25 938.8 19.3LS(1)-0421 MOD 0.3 905.1 16.3LS(1)-0421 MOD 0.4 837.7 11.7LS(1)-0421 MOD 0.5 770.3 8.4LS(1)-0421 MOD 0.6 702.9 6.1LS(1)-0421 MOD 0.7 635.6 4.4LS(1)-0421 MOD 0.8 568.2 3.0LS(1)-0421 MOD 0.9 500.8 2.0LS(1)-0421 MOD 1 433.4 1.1

3 Geometry

Generation of geometry is performed in 4 main parts:

1. Generation of conventional blade,

2. generation of tubercles on 35% of the blade leading edge,

3. generation of tubercles on 70% of the blade leading edge,

4. and generation of the hub geometry.

The information required for a geometry generation of the conventional blade are obtained from

the calculation shown in the Chapter 2. Tubercles are generated by changing the straight leading

edge present in the conventional blade into the sine function. The frequency of the sine function

is defined by the distance between the tubercles which is set to 52 mm. This distance represents a

1% of the blade length.

0 0.2 0.4 0.6 0.8 1

coordinate X

-0.2

-0.1

0

0.1

0.2

coord

inate

Y

Figure 4: NASA LANGLEY Airfoil



0 0.2 0.4 0.6 0.8 1

coordinate X

-0.2

-0.1

0

0.1

0.2

coord

inate

YFigure 5: WORTMANN FX 77-W-258 Airfoil

Amplitude of the sine function is defined in such way that the largest airfoil (where the humps

of the tubercles appear) is 10% greater than the smallest airfoil (where the channels created by

the tubercles appear). As mentioned in the previous chapter, blades are designed from 2 different

airfoils. The WORTMANN FX 77-W-258 airfoil takes a part of the blade between the relative

radii (r/R) 0.2 and 0.25, while the NASA LANGLEY LS(1)-0421 MOD takes a part of the blade

from the relative radius 0.25 to the tip of the blade. Airfoils used are shown in the Figure 4 and

the Figure 5. All the axis are representing non-dimensional length, where Y axis can be correlated

to the thickness of the airfoil and X axis to the length of the airfoil. Combination of the hub with

the 3 different types of the turbine blades results in 3 different cases studied in the frame of the

work presented in this article. Studied blades are shown in subfigures of the Figure 6. From the

subfigures, it can be seen that only one third of the full rotor geometry is generated. This is due

to the fact that the numerical simulations are performed with the cyclic boundary conditions at the

edges of the symmetrical domain which is explained in detail in the Chapter 4.

Figure 6: Three different types of blades



4 Numerical simulation

Simulation of a flow around the turbine blades can be performed using Computational Fluid Dy-

namics (CFD). With the aid of CFD, behaviour of a flow around the wind turbine rotor can be

studied without using expensive experiments. However numerical simulations are always an ap-

proximation of the real flow and an error in results is always present. For the purposes of showing

advantages of tubercle blades, Multiple Reference Frame (MRF) model with the Generalized Grid

Interface (GGI) is used. Different mathematical models affect the CPU time required and the result

accuracy and the chosen model should be the compromise between the two. MRF model results in

a faster convergence compared to transient simulation with a dynamic mesh because the rotation

of the rotor cell zone is taken into account with additional term in the momentum equation.

4.1 Multiple Reference Frame

Multiple Reference Frame (MRF) model is a steady-state approach for turbomachinery simula-

tions. In this model, each zone can be assigned different rotational velocity. The flow for each

moving zone is solved using the moving reference frame equations. If the zone is assigned velocity

equal to zero, the equations are reduced to their stationary form in the inertial frame of reference.

Regardless of the assigned velocity, numerical mesh remains fixed for the whole domain. This is

analogous to "freezing" the motion of the moving part in a specific position and observing the flow

for that position. Because of that, MRF model is often called "frozen rotor approach".

Despite the MRF being only an approximation of transient flow, it can provide reasonable

numerical results of a flow in turbomachinery. Another potential use of the MRF model is to

compute a flow field that can be used as an initial condition for a transient flow simulation with

a dynamic mesh. However, if it is necessary to simulate transient phenomena that may occur in

rotor-stator interactions, transient simulation with a dynamic mesh should be performed.

4.1.1 Incompressible Navier-Stokes Equations in the Rotating Frame

For every cell zone that has been assigned a rotational velocity different from zero, Navier-Stokes

equations used to solve an incompressible flow have to be modified [9]. For a general vector A in

the inertial reference frame, following can be expressed:[dAdt

]I=

[dAdt

]R+ω×A, (21)

where ω is the angular velocity vector. If general vector A is substituted with the position vector

r, (21) is transformed into: [drdt

]I=

[drdt

]R+ω× r. (22)



Differentiation of position vector equals velocity and (22) can be written in following way:

uI = uR +ω× r. (23)

Further differentiation of (22) results in an expression for acceleration in inertial reference frame.

This expression in standard form is shown by (24).[duI

dt

]I=

[duR

dt

]R+

dω

dt× r+2ω×uR +ω×ω× r (24)

Three characteristic terms are present on the right hand side of (24):

• term dω

dt × r is the tangential acceleration,

• term 2ω×uR is the Coriolis acceleration,

• and term ω×ω× r is the centrifugal acceleration.

By taking into account (24) for the acceleration term, Navier-Stokes equations for incompressible

flow with kinematic viscosity and with respect to inertial reference frame can be written:

duI

dt+∇ · (uI⊗uI) =−∇p+∇ · (ν∇uI) (25)

∇ ·uI = 0, (26)

where (25) represents the momentum equation and (26) the continuity equation. If this set of

equations is adjusted for a relative reference frame the set of equations used in the MRF model is

obtained:

duR

dt+ω×uI +∇ · (uR⊗uI) =−∇p+∇ · (ν∇uI), (27)

∇ ·uI = 0. (28)

Coupling interface between the rotor and farfield zone is GGI used to couple multiple non-

conformal regions where the patch nodes on each side of the interface do not match. It is commonly

used in turbomachinery simulations due to the fact that 3D numerical meshes of such cases are

mostly made of several domains which are not connected. After joining of rotor and stator cell

zone into a single computational mesh, interfaces between non-conformal parts require special

attention. Interfaces are handled using pairs of GGIs, whose purpose is passing of information

from one patch of GGI pair to another using direct interpolation.



4.2 Numerical Spatial Domain

Numerical meshes of different wind turbine blades are generated on the geometry presented in

the previous section. Geometry of each blade type is made clean. This means that the geometry

consists only of parts that significantly affect fluid flow and is ready for the meshing process. Each

numerical mesh is made manually in the software called Pointwise [10]. The process of manual

mesh generation is time intensive, but user has greater control over the meshing process compared

to the automatic mesh generation. Additionally, the lack of working experience in this software

can lead to a generation of an unusable mesh.

The surface mesh is made structured, except for the part on tubercles which is made unstruc-

tured due to the complex geometry. The whole volume mesh grown from the surface mesh is made

unstructured. Advantage of an unstructured mesh is that the meshing process requires less time

than the equivalent meshing process of a structured mesh. To reduce result error which occurs

when the mesh is made unstructured, anisoTropic tetRahedral EXtrusion (T-Rex) is used to make

structured boundary layer mesh [11]. This feature enables combining of tetrahedral and pyramidal

finite volumes into the hexahedral and prism cells. In such way, structured finite volume layers

are obtained in the proximity of the blade geometry what increases the accuracy of results. To

significantly reduce the number of cells, only a third of the rotor is meshed with cyclic boundary

conditions on the edges of the domain. In Table 4 finite volume numbers of each cell zone for the

different types of wind turbine blades are shown.

Table 4: Number of cells for different types of blade

Type of the blade Rotor cell zone Farfield cell zoneConventional blade 2 230 178 3 022 607Tubercles on 35% of the leading edge 3 597 186 3 022 607Tubercles on 70% of the leading edge 3 109 689 3 022 607

Figure 7 is showing a spatial domain of a wind turbine with the conventional blade. It can be

seen that the farfield cell zone is multiple times longer than the cell zone around the rotor blade.

Numerical mesh is made in such way because the wake requires space to resolve behind the rotor

of a wind turbine. In Figure 8 it can be seen the position of the rotor blade in the rotor cell zone.

Even though the rotor cell zone is smaller than the farfield cell zone, it consists from approximately

the same number of finite volumes.



Figure 7: Numerical domain of a wind turbine with the conventional blades

Figure 8: The rotor cell zone domain of a wind turbine with the conventional blades

In Figure 9 and Figure 10 details of the mesh around the rotor blade can be seen. Figure 9

shows the difference of the mesh resolution around the rotor blade and in the farfield cell zone,

while the figure 10 shows the part of the mesh in which is expected for boundary layer to occur.

It can be seen that this part is made structured and with the finest mesh resolution. Figure 11 and

Figure 12 are showing the same for the wind turbine with the tubercle blades.



Figure 9: Mesh resolution in the different parts of the mesh of the wind turbine with the conven-tional blades

Figure 10: Detail of the mesh in a proximity of the conventional rotor blade



Figure 11: Mesh resolution in the different parts of the mesh of the wind turbine with the tubercleblades

Figure 12: Detail of the mesh in a proximity of the tubercle rotor blade

4.3 Boundary and initial conditions

Boundary and initial conditions are required for partial differential equations, which are solved

within the mathematical model, to be solvable. Inlet boundary condition for velocity is defined

with the velocity magnitude of 10 ms and the direction of a rotor rotation axis. On the outlet patch

velocity boundary condition is set as zero gradient. Boundary conditions for pressure are defined in

a similar way as for velocity. Inlet boundary condition is defined with the zero gradient boundary

condition, while the boundary condition on the outlet patch is defined with the constant uniform

value of 0. Outlet value of pressure is assumed to be equal to the value of an undisturbed flow.

Hence, every obtained value of pressure field is relative to the value set on the outlet patch. It is

important to take into account that the pressure obtained by a simulation is kinematic pressure and



to get the real value of pressure, pressure field has to be multiplied with the fluid density.

Initial condition for velocity is set for every cell in the same way as for boundary condition on

the inlet patch, while the initial condition for pressure is defined in the same way as for the outlet

patch. Because the temporal derivative in a mathematical model is set to zero (stationary simula-

tion) final solution of a simulation does not depend on a set initial conditions. Initial conditions

only affect CPU time required to perform a steady-state simulation.

To define cyclic boundary conditions, which enable simulation of only third of the wind turbine

rotor, cyclicGGI is used.

4.4 Results

Numerical simulations are performed in a community driven fork of OpenFOAM, foam-extend-

3.2. Simulations are performed on three different wind turbine geometries:

• the wind turbine with the conventional blade,

• the wind turbine with the tubercle blade where tubercles cover the leading edge of the blade

from 0.65 r to r (35% of a leading edge)

• and the wind turbine with the tubercle blade where tubercles cover the leading edge of the

blade from 0.3 r to r (70% of a leading edge).

The main goal of performed numerical simulations is to prove that the wind turbine with tubercles

on a leading edge of a blade has better aerodynamic properties than the equivalent blade without

them. It is also presented that the higher coverage of a turbine blade with tubercles yields higher

lift and therefore higher power of a wind turbine.

4.4.1 Wind Turbine with the Conventional Blade

As a convergence indicator a wind turbine power is monitored and the convergence is assumed

to be achieved if oscillations in power are lower than 1%. In Figure 13, graphs of wind turbine

power is shown. Both figures are presenting the same graph with the difference that the upper

subfigure is showing the power graph for every iteration of a simulation, while the lower subfigure

is showing only the ending detail of the graph. Simulation is assumed to be over in the 3045th

iteration for which the relative oscillation in power equals 0.56%. From obtained fields of velocity

and pressure are further calculated forces and moments of forces that act upon a wind turbine

blade, power which is generated for a given flow parameters and a power coefficient. Calculation

is performed using function object called turboPerformance and the results are shown in a Table 5.



(a) Oscillation graph

(b) Detail of the oscillation graph

Figure 13: Power oscillations of a single conventional blade

Table 5: Conventional wind turbine parameters

Parameter ValueForce on a single blade [N] (1617.87 46.06 358.86)Force moment on a single blade [Nm] (1221.25 -295 -6734.74)Power generated by a single blade [W ] 8952.2Total power [W ] 26775.6Wind power [W ] 79639.5Coefficient of power 0.337



Presented data in the Table 5 are describing the behaviour of a wind turbine for the design operating

point. Power of a single blade is calculated as a product of force moment around the rotation axis

and the angular velocity of a rotor:

P = Mxω. (29)

Due to the fact that the simulated geometry represents only the third of a complete geometry, to

obtain the power of a whole wind turbine, power of a single blade has to be multiplied by three.

Power coefficient represents the amount of a power generated by a wind turbine for a unit of a

wind power available. Wind power is calculated as follows:

Pwind =ρu2

2A u, (30)

where the term ρu2

2 is the kinetic energy of the wind flow which has a defined velocity magnitude

u of 10 m/s and the constant density ρ . The term A u is the volumetric flux through the rotor in

the direction of the rotation axis.

Pressure and Velocity Fields

In following figures pressure and velocity field details which give an idea of a flow behaviour

around the wind turbine blade are shown.

Figure 14: Velocity distribution at the wind turbine inlet



Figure 15: Wake behind the wind turbine

Figure 16: Detail of the wake behind the wind turbine

Figure 14 shows a velocity field over a domain cross-section perpendicular to the rotation axis.

The cross-section is positioned at the inlet of the wind turbine rotor. It can be seen that the blade

introduces a wake in the flow behind the blade. Figure 15 shows the length of a wake behind the

wind turbine. It can be concluded that the wake length is greater than 200 m due to the fact that the

computational spatial domain behind the rotor is exactly 200 m long. This is an important infor-

mation because of the increased turbulence in a wake which results in additional dynamic stresses

on a wind turbine blade and a non-optimal flow around the blade. Therefore, the wind turbine

manufacturer wants to avoid placing a wind turbine in a wake of another wind turbine. Figure 16

is showing a detail of a wake in proximity of the blade. It can be seen that the velocity field behind

the blade is significantly lower due to the fact that the kinetic energy of a wind has to be reduced

in order for a wind turbine to generate power.



Figure 17 shows velocity and pressure distribution over an airfoil which occurs at the radius of 1.5

m. Figure 18 shows velocity and pressure distribution over an airfoil which occurs at the radius of

3 m. Higher values of pressure and velocity are result of a higher tangential velocity of the blade

at greater radii. At the radius of 6 m, as shown in Figure 19 this effect has even greater influence.

Figure 17: Velocity and pressure fields at the radius of 1.5 m

Figure 18: Velocity and pressure fields at the radius of 3 m

Figure 19: Velocity and pressure fields at the radius of 6 m

4.4.2 Wind Turbine with Tubercles on a 70% of a Blade Length

As a convergence indicator a wind turbine power is monitored and the convergence is assumed to

be achieved if oscillations in power are lower than 1%. In Figure 20 graphs of wind turbine power

is shown. Both figures are presenting the same graph with the difference that the upper subfigure is

showing the power graph for every iteration of the simulation, while the lower subfigure is showing

only the ending detail of the graph. Simulation is assumed to be over in the 2465th iteration



for which the relative oscillation in power equals 0.19%. Important parameters describing the

behaviour of the wind turbine are presented in the Table 6.



Figure 20: Power oscillation of a single blade with tubercles on a 35% of the leading edge



Table 6: Parameters of the wind turbine with tubercles on a 35% of the leading edge

Parameter ValueForce on a single blade [N] (1674.67 45.1 385.75)Force moment on a single blade [Nm] (1399.44 -301.83 -7034.51)Power generated by a single blade [W ] 10258.4Total power [W ] 30775.2Wind power [W ] 79639.5Coefficient of power 0.386

By a comparison between parameters shown in Table 5 and Table 6 it can be concluded that the

power of the wind turbine with tubercle blades is greater than the power of the wind turbine with

conventional blades. Greater power of the turbine with the same velocity magnitude of an undis-

turbed flow results in the higher power coefficient. Power generated by the turbine with tubercles

on a 35% of the leading edge is 15% higher than the power generated by the wind turbine with

conventional blades.


In following figures pressure and velocity field details which give an idea of the flow behaviour


Figure 21: Velocity distribution at the inlet of the wind turbine with tubercles on a 35% of theleading edge



Figure 22: Wake behind the wind turbine with tubercles on a 35% of the leading edge

Figure 23: Detail of the wake behind the wind turbine with tubercles on a 35% of the leading edge


The cross-section is positioned at the inlet of a wind turbine rotor. It can be seen that the blade

introduces a wake in a flow behind the blade. Figure 22 shows the length of a wake behind the

wind turbine. Figure 23 is showing a detail of a wake in proximity of the blade.

Figure 24 shows velocity and pressure distribution over an airfoil which occurs at the radius of 1.5

m. Figure 25 shows velocity and pressure distribution over an airfoil which occurs at the radius of 3

m. Higher values of pressure and velocity are the result of a higher tangential velocity of the blade

at greater radii. At the radius of 6 m, as shown in Figure ?? this effect has even greater influence.

Figure 27 shows a pressure distribution over the suction side of a blade with the tubercles. It can be

seen that between the tubercles lower values of pressure occur due to the jet streams generated by

the tubercles. Figure 28 shows a pressure distribution over the pressure blade side with tubercles.



Figure 24: Velocity and pressure fields at the radius of 1.5 m of the wind turbine with the tubercleson a 35% of the leading edge

Figure 25: Velocity and pressure fields at the radius of 3 m of the wind turbine with the tubercleson a 35% of the leading edge




Figure 27: Pressure distribution on the suction blade side of the wind turbine with tubercles on a35% of the leading edge

Figure 28: Pressure distribution on the pressure blade side of the wind turbine with tubercles on a35% of the leading edge

4.4.3 Wind Turbine with Tubercles on a 70% of a Blade Length

As a convergence indicator a wind turbine power is monitored and the convergence is assumed to

be achieved if oscillations in the power are lower than 1%. In Figure 29 graphs of wind turbine

power are shown. Both figures are presenting the same graph with the difference that the upper

subfigure is showing the power graph for every iteration of the simulation, while the lower subfig-

ure is showing only the ending detail of the graph. Simulation is assumed to be over in the 2620th

iteration for which the relative oscillation in power equals 0.96%. Important parameters describing

the behaviour of the wind turbine are presented in the Table 7.





Figure 29: Power oscillation of a single blade with tubercles on a 35% of the leading edge

Table 7: Parameters of a wind turbine with tubercles on a 70% of the leading edge

Parameter ValueForce on a single blade [N] (1708.36 51.32 408.4)Force moment on a single blade [Nm] (1429.22 -307.16 -7147.31)Power generated by a single blade [W ] 10476.7Total power [W ] 31430.1Wind power [W ] 79639.5Coefficient of power 0.395



By a comparison between parameters shown in Table 5 and Table 6 and Table 7 it can be concluded

that the higher percentage of a blade covered with tubercles results in a generation of a greater

power. From presented parameters it can be seen that the power generated by a wind turbine

with tubercles on 70% of the leading edge is 17% greater than the power with the conventional

blades. This is additional increase of a 2% in power generation compared to the wind turbine with

tubercles on a 35% of the leading edge. Power coefficient is also increased for 17% compared to

the wind turbine with conventional blades and for 2% compared to the wind turbine with tubercles

on a 35% of the leading edge.


In following figures pressure and velocity field details which give an idea of the flow behaviour


Figure 30: Velocity distribution at the inlet of the wind turbine with tubercles on a 70% of theleading edge

Figure 31: Wake behind the wind turbine with tubercles on a 70% of the leading edge



Figure 32: Detail of the wake behind the wind turbine with tubercles on a 70% of the leading edge


The cross-section is positioned at the inlet of the wind turbine rotor. It can be seen that the blade

introduces a wake in the flow behind the blade. Figure 31 shows the length of a wake behind the

wind turbine. Figure 32 is showing a detail of a wake in proximity of the blade.

Figure 33 shows velocity and pressure distribution over an airfoil which occurs at the radius of

1.5 m. Figure 34 shows velocity and pressure distribution over an airfoil which occurs at the radius

of 3 m. Higher values of pressure and velocity are result of a higher tangential velocity of a blade

at greater radii. At the radius of 6 m, as shown in Figure 35 this effect has even greater influence.

Figure 36 shows a pressure distribution over the suction side of a blade with the tubercles. It can

be seen that between tubercles lower values of pressure occur due to the jet streams generated by

the tubercles. Figure 37 shows a pressure distribution over the pressure blade side with tubercles.

Figure 33: Velocity and pressure fields at the radius of 1.5 m of the wind turbine with the tubercleson a 70% of the leading edge



Figure 36: Pressure distribution on the suction blade side of a wind turbine with tubercles on a70% of the leading edge

Figure 37: Pressure distribution on the pressure blade side of a wind turbine with tubercles on a70% of the leading edge

4.4.4 Distribution of Turbulent Parameters Along the Tubercle Blades

Turbulence model used in the frame of the work presented in the previous chapters is k−ω SST .

This model consists of two differential equations which are solved to obtain k and ω turbulence

parameters. K stands for the turbulent kinetic energy and ω stands for the dissipation of turbulent

kinetic energy. K−ω SST model combines the best properties of both k−ω and k− ε models.

Mentioned equations for turbulent parameters are connected with the system of Navier-Stokes

equations by the turbulent viscosity which is calculated from the values of k and ω [12].



Figure 38: Distribution of specific turbulent kinetic energy on the suction side of the tubercle blade

Figure 39: Distribution of specific turbulent kinetic energy on the pressure side of the tubercleblade

Distribution of turbulent kinetic energy along the suction and pressure side of the tubercle blade is

shown in Figure 38 and Figure 39. In places where the turbulent kinetic energy is higher turbulent

vortices with higher energy occur in real flow. From the figures it can be seen that vortices with

higher energy occur in the channels between the tubercles with maximum values around the blade

tip due to the highest magnitude of the circumferential velocity.



Figure 40: Distribution of dissipation of specific turbulent kinetic energy on the suction side of thetubercle blade

Figure 41: Distribution of dissipation of specific turbulent kinetic energy on the pressure side ofthe tubercle blade

Distribution of the dissipation of turbulent kinetic energy along the suction and pressure side of the

tubercle blade is shown in Figure 40 and Figure 41. This parameter is higher in the areas where

the energy of vortices are higher due to their rapid decay.



Figure 42: Distribution of turbulent viscosity the on the suction side of the tubercle blade

Figure 43: Distribution of turbulent viscosity the on the pressure side of the tubercle blade

Distribution of the turbulent viscosity along the suction and pressure side of the tubercle blade

is shown in Figure 42 and Figure 43. This parameter takes into account dissipation of the flow

energy affecting the effective viscosity in the momentum equation of the Navier-Stokes system of

equations. Turbulent viscosity is proportional to the specific kinetic turbulent energy and inversely

proportional to the dissipation of specific turbulent kinetic energy [12].



Figure 44: Vortex in the downstream flow of the wind turbine rotor with tubercle blades

Figure 44 is showing a vortex which is left behind the rotor due to the disturbance of flow caused

by the wind turbine operation. Two characteristic parts of the vortex can be seen in the Figure 44:

1. Vortex at the highest relative radius that occurs due to the secondary flow from the pressure

to the suction blade side around the blade tip.

2. Vortices behind the trailing edge of the blade due to the physical phenomena in the wake of

the blade.

4.5 Comparison of the Results

Due to the fact that the calculation of the conventional wind turbine blade is done according to

the BEM theory and the Betz method, inaccuracy in the results were expected. Inaccuracy of the

results are present because to assume the correction factors of total efficiency accurately, a long-

time engineering experience and knowledge are required. Therefore, the values of coefficients

presented in the Chapter 2 are not optimal. Relative error of power obtained by the CFD simulation

and the assumed power of the turbine at the start of the calculation is 10% for the conventional wind

turbine as shown in the Table 8.



Table 8: Comparison of the results obtained by the numerical simulation and the calculation

Wind turbine type Power, P [kW ] Torque, Mx [Nm] Power coefficient, cPConventional(Calculation) 30 4092.6 0.377

Conventional(CFD) 26.8 3652.7 0.337

Tubercles on 35%of the leading edge 30.8 4198.3 0.386

Tubercles on 70%of the leading edge 31.4 4287.7 0.395

In the Table 8 all the results obtained by numerical simulations and the results of the calculation are

shown. It can be concluded that by the use of the biomimicry, imitating the solutions from nature,

efficiency of wind turbines can be significantly increased by the use of the passive technology.

4.6 Conclusion of the results

Results of the performed and presented simulations match the facts from the scientific articles

which deal with the topics of modifying the leading edge of the wind turbine blade in order to

create tubercles. Increase of the power and efficiency of the wind turbine is directly connected

to the percentage of the blade covered with tubercles. Therefore, it can be concluded that the

higher the percentage of the covered blade with tubercles the higher the lift acting upon the blade.

Numerical simulations are performed for 3 different cases:

1. the wind turbine with conventional blades,

2. the wind turbine with tubercles on 35% of the leading edge,

3. and the wind turbine with tubercles on 70% of the leading edge.

From the presented results it can be seen that the power for the wind turbine with tubercles on

35% of the leading edge is 15% higher than the power of conventional wind turbine. The case

with the tubercles on 70% of the leading edge shows that the increase of the power is equal to 17%

compared to the conventional wind turbine. Non-linearity of the power increase with the increase

in percentage of the blade coverage with tubercles is due to the fact that the most of the power

extracted from the fluid is done on the higher relative radii. Therefore, it is recommended to put

tubercles on higher radii in order to achieve higher profit of the described technology. Taking into

account price of the electricity, the amount of energy that can be extracted from the wind and the

cost of the tubercle technology optimal coverage of the blade with tubercles can be calculated from

the economical aspect.



5 Summary

Mankind has always been searching for the inspiration for their technological achievements imitat-

ing the certain phenomena found in the nature. One such example is the recent discovery of Cana-

dian company Whale power, whose observations and study of the humpback whale’s behaviour in

the ocean resulted in conclusion that the tubercles on their fins are improving their aerodynamic

characteristics. Therefore, in accordance to the findings, company modified the conventional wind

turbine blade using the embedded sinusoidal tubercles on the leading edge of the blade, which

consequently increases the lift and the output power with same design parameters compared to the

equivalent conventional wind turbine. Due to the fact that the observation of this phenomena hap-

pened in the recent past, a very few scientific papers on this subject exist despite its great potential.

With that in mind, the basic idea of this paper imposes confirmation or refutation of the thesis that

the existence of tubercles on the leading edge increases the output power.

Instead of the expensive and limited experiments in the wind tunnels, the answer to the pre-

sented idea was attempted to be resolved by the aid of numerical simulations (CFD). Numerical

CFD simulations provide an opportunity to solve and visualize the complex fluid flows in nature

by implementing the mathematical models of basic conservative laws, where the only limit is the

available computing resources. Thus, the wind flow around the conventional and modified wind

turbine has been simulated and their respective operating characteristics and output powers were

compared.

The main part of the study is divided into several sections. In the first section, the basic calcu-

lation of wind turbine blade is given according to the design parameters, which completely define

the conventional wind turbine geometry. Second section describes the generation of the geometry.

Mentioned geometry is used to generate a grid of finite volumes in the process called meshing

for each analysed case in the manual meshing software. The process of the mesh generation is

described in detail in the third chapter. Last chapter deals with the set-up and the conduction of

the numerical simulations. After the generation of spatially discretized grid of finite volumes, the

initial and boundary conditions for numerical simulations are set. Numerical simulations are per-

formed in a community driven fork of OpenFOAM, foam-extend-3.2. Finally, obtained results

which confirmed the greater power output of the tubercle wind turbine compared to the equivalent

conventional wind turbine at the same incoming wind velocity are presented.

Key words: computational fluid dynamics, wind turbine, tubercle blade, biomimicry, renewable

energy sources.



References

[1] Wikipedia - Humpback whale (last access: 23.12.2016.).

URL http://en.wikipedia.org/wiki/Humpback_whale#/media/File:Humpback_

Whale_underwater_shot.jpg

[2] Wikipedia - Experimental model (last access: 23.12.2016.).

URL https://upload.wikimedia.org/wikipedia/commons/9/9a/Tubercle_model_

Humpback_whale_flipper.jpg

[3] Wikipedia - Whale flipper (last access: 23.12.2016.).

URL https://upload.wikimedia.org/wikipedia/commons/9/9a/Humpback_

flipper.jpg

[4] Gasch R., Twele J., Wind Power Plants - Fundamentals, Design, Construction and Operation

(2002).

[5] Flippers provide lift, reduce drag (last access: 23.12.2016.).

URL http://www.asknature.org/strategy/3f2fb504a0cd000eae85d5dcc4915dd4

[6] I. Hrgovan, Vjetroturbina za pogon elektricnog generatora, Master’s thesis, Fakultet stro-

jarstva i brodogradnje (2011).

[7] McGhee R.J., Beasley W.D., Whitcomb R.T., NASA Low- and Medium-Speed Airfoil De-

velopment (1979).

[8] G. S., Wind Turbines (2009).

[9] See the MRF development (2009, last access 23.12.1016.).

URL http://openfoamwiki.net/index.php/See_the_MRF_development

[10] Pointwise V17.3R5 (last access: 23.12.2016.).

URL http://www.pointwise.com/library/pw_ReleaseNotes.pdf

[11] T-Rex Hybrid Meshing in Pointwise (last access: 23.12.2016.).

URL http://www.pointwise.com/theconnector/July-2011/

T-Rex-Hybrid-Meshing-in-Pointwise.shtml

[12] SST k-omega model (last access: 23.12.2016.).

URL http://www.cfd-online.com/Wiki/SST_k-omega_model#Turbulence_

Kinetic_Energy


http://en.wikipedia.org/wiki/Humpback_whale#/media/File:Humpback_Whale_underwater_shot.jpg



https://upload.wikimedia.org/wikipedia/commons/9/9a/Tubercle_model_Humpback_whale_flipper.jpg



https://upload.wikimedia.org/wikipedia/commons/9/9a/Humpback_flipper.jpg



http://www.asknature.org/strategy/3f2fb504a0cd000eae85d5dcc4915dd4

http://www.asknature.org/strategy/3f2fb504a0cd000eae85d5dcc4915dd4

http://openfoamwiki.net/index.php/See_the_MRF_development

http://openfoamwiki.net/index.php/See_the_MRF_development

http://www.pointwise.com/library/pw_ReleaseNotes.pdf

http://www.pointwise.com/library/pw_ReleaseNotes.pdf

http://www.pointwise.com/theconnector/July-2011/T-Rex-Hybrid-Meshing-in-Pointwise.shtml



http://www.cfd-online.com/Wiki/SST_k-omega_model#Turbulence_Kinetic_Energy



marko horvat, borna Šojat and josip Žužul design and ... · horvat, Šojat i Žužul turbine...

Documents