pitch angle on the darrieus wind turbine with changes in theno.3(2020)/198-210.pdf ·...

Journal of Mechanical Engineering Research and Developments

ISSN: 1024-1752

CODEN: JERDFO

Vol. 43, No. 3, pp. 198-210

Published Year 2020

198

Pitch Angle on The Darrieus Wind Turbine with Changes In The

Shape of Blade Trailing Edge

Viktus Kolo Koten*, Syukri Himran, Nasaruddin Salam, and Luther Sule

Department of Mechanical Engineering-Atma Jaya University, Department of Mechanical Engineering-

Hasanuddin University, Makassar, Indonesia.

* Email: [email protected]

ABSTRACT: The pitch angle on the Darrieus turbine affects the performance of the turbine. The pitch angle

always changes according to the shape of the blade profile and fluid velocity. This study aims to find the magnitude

of the pitch angle on the NACA 0018 profile blade and its change of the blade edge statically. Model formation,

element division, and analysis of blade characteristics are simulated by CFD. The results show that the pitch angle

in the blade that did not change the trailing edge shape was -12.5o and in the blade that experienced changes in

trailing edge shape by -13o.

KEYWORDS: Wind energy, Darrieus turbine, blade trailing edge shape change, pitch angle.

INTRODUCTION

In accordance with the nature of the wind which often changes direction, turbines that are often used to convert

wind energy into mechanical energy are vertical axis turbines. The types of vertical axis turbines commonly used

to convert wind energy into mechanical energy are turbines of Savonius, Darrieus, and Gorlov. According to

Alexander Gorban et al. [1], the Darrieus turbine has a smaller power coefficient than the Gorlov turbine but is

larger than the Savonius turbine. Nevertheless, Darrieus turbine construction is simpler and easier to develop

further.

Figure 1 shows a Darrius turbine construction which is driven by wind speed V with variations in pitch angle β

and several other parameters. Some characteristics of static turbines can be known through the calculation of drag

force, lift force, and pressure that take places on the blade. The drag force, lift force, and pressure can be calculated

through the drag, lift, and pressure coefficients respectively in equation (1), (2), and (3).

2

21 AV

FC D

D

= (1)

2

21 AV

FC L

L

= (2)

2

21 V

PPCpr

−

= (3)

𝑅𝑒 =𝜌𝑉𝑐

𝜇 =

𝑉𝑐

𝜗 (4)

Calculation of the drag force, lift, and pressure on the blade can be done after determining the type of flow. The

type of flow is known from the calculation of the Reynolds number through equation (4).

Since the Darrieus turbine was discovered in 1931, it has been used as the object of research to improve its

characteristics and for other purposes. Improvements in blade characteristics to establish the performance of the

Darrieus turbine have been carried out by some researchers with various studies. These studies include determining

turbine solidity [2-5], modifying leading edge [6-8], and trailing edge modification [9-12]. In addition, trailing

edge modification has also been carried out by Viktus et al who changed the shape of the NACA 0018 blade

trailing edge to a semicircle and triangle. The results of the study showed that the semicircular trailing edge shape

is better than the triangular trailing edge shape and trailing edge without shape change.

mailto:Email:%[email protected]

Pitch Angle on The Darrieus Wind Turbine with Changes In The Shape of Blade Trailing Edge

199

Another improvement is the positioning of the blade at the end of the turbine arm. The main parameter that

determines the position of the blade at the end of the turbine arm is pitch angle (β); the angle formed between the

blade chord and tangent to the blade path on the circle of turbine pitch diameter (Figure 1). Dynamically, the study

of pitch angle was carried out by Rezaeiha et al [13] who found that the best pitch angle was at -2o with TSR = 4.

In addition, a study of flexible pitch angles as a function of the azimuth angle has been carried out by Sagharichi

et al [4]. This study found that flexible pitch angles are more suitable to be applied to high turbine solidity values.

A study of pitch angle was also carried out by Tummala et al [14] who found differences in pitch angle in each

type of blade profile.

Figure 1. Darrieus turbine with blade trailing edge shape changes and variation of pitch angle

Determination of pitch angle can also be done statically through a comparison of lift force and drag force. Then,

the comparison of lift force and drag force can also be used to determine the angle of attack on an airfoil.

Determination of angle of attack through comparison of lift and drag force has been carried out by Himran et al

[15] experimentally. They found that the best angle of attack is 7.6o. Although the determination of dynamic pitch

angle has been carried out as described above, a study of static pitch angles has never been done. This study aims

to obtain a pitch angle on the Darrieus turbine with static change of shape on the blade trailing edge.

METHODS

The process of finding the pitch angle was done through determining the maximum comparison value between the

coefficient of the lift and the drag coefficient. Determination of lift and drag coefficient values was done by

computational method. The use of computational method was compared with previous studies [16-20]. This

method was used to determine the pitch angle with several stages. These stages consist of forming a blade and

domain model, division of elements and boundary condition determination, determination of blade characteristics,

and post processing. The activities of each stage are described as follows.

The formation of blade model and domain

The formation of the blade model was carried out on the Autodesk Inventor software because it is more precise.

The spline command on this software can keep the line tracing that forms the blade so that it remains in the desired

coordinates.

The coordinates of the NACA 0018 track points are downloaded from the airfoil tools and adjusted to the study

limits. The downloaded coordinates from the airfoil tools are connected one by one until form blade shape 1 as

shown in Figure 2a. The same points are reconnected and converted into blade shape 2 and blade shape 3 which

are shown respectively in Figures 2b and 2c. The chord length of the blade in this study is 100 mm. The preliminary

study results show that the 4th point of the trailing edge is the best shortening point, the chord shortening for shape

2 and blade shape 3 blade forms is done at this point also.

V

V

FD

FL

R

ω

α θ

u

O

w β

-β

Line of pitch diameter


200

Figure 2. Blade NACA 0018 profile and blade shape changes. a) Blade shape 1; blade that does not change the

shape of the trailing edge. b) Blade shape 2; blade that changes the shape of the semicircular trailing edge. c)

Blade shape 3; blade that changes the shape of triangular trailing edge

The form and size of domains in this study were adapted to previous research studies [21-23]. The domain size in

these studies is greater than this study. There are other studies [20, 24, 25] that have smaller domain sizes than this

study. The form and size of the domain in this study are shown in Figure 4.

Element division and determination of boundary conditions

Figure 3. Mesh around and on the blade trailing edge. a) Overall mesh shape. b) The mesh shape around of the

blade shape 1 trailing edge. c) The mesh shape around around of the blade shape 2 trailing edge. d) The shape of

the mesh around of the blade shape 3 trailing edge

The process of elemental division was carried out bottom-up; the division starts from the mesh edge to the mesh

face. The spacing for the mesh edge is 0.001 and 0.01 for the mesh face. The shape of the element chosen is tri-

pave. Automatically, Gambit cannot form mesh or produce imperfect mesh if there is a discrepancy between the

shape of the element and the size of the selected space. The smallest mesh error factor is 0.4427 and the largest is

0.5366. This mesh error factor is still safe because it is smaller than the allowable mesh error factor; 0.8. The

number of elements divided by 390,075 to 430,483 elements based on the shape and position of the blade. The

overall shape of the mesh is shown in Figure 3a. Figures 3b, 3c, and 3d show mesh on each blade trailing edge

shape.

γ

a b c

0,2c 0,2c 0,04c

(a)

(b) (c) (d) GridFLUENT 6.3 (2d, dp, pbns, ske)

Jan 04, 2009

GridFLUENT 6.3 (2d, dp, pbns, ske)

Jan 04, 2009


Jan 04, 2009


Jan 04, 2009


201

Figure 4. Boundary conditions in the domain and blades

There are two main parts in determination of boundary conditions; domain and blade parts. The domain consists

of three sub-sections; velocity inlet, symmetry, and pressure outlet. The blade only consists of one part; wall.

Determination of the boundary conditions of each part and size of the domain and blade is shown in Figure 4. In

the section area between domain and blade is defined as air fluid

Determination of blade characteristics

This stage was carried out with four main processes; greed processing, defining the model and determining the

type of material, iteration process, and determining the reference value. Greed processing is done to look back at

the number of elements, number of vertices, shape of elements, size of domain, and position of the blade in the

domain.

Defining the model can be done after determining the flow properties through the calculation of the Reynolds

number. The Reynolds number calculated based on this study boundary is 4.45 x 104. Fluent provides several

completion models based on the number of equations and flow properties. Because the Reynolds number shows

the turbulent flow properties, the k-epsilon model is chosen to analyze the external flow characteristics of the

blade. Determination of this completion model has been compared with previous studies [20, 26]. Although there

are other studies [27-29] that use the k-omega model, this study only looks at the difference pitch angle for each

blade shape. The shape of the element, the model of completion, the fluid properties, and other things which are

related to them are assumed to be the same or constant. The type of material used is an air temperature of 300 K

with a velocity of 7.5 m/s. Air properties such as density and viscosity are adjusted for air temperature.

The iteration process was began with determining the residual monitor convergence. Residual monitor

convergence in this study is 1 x 10-5. The magnitude of the residual value of this monitor convergence was

compared with previous studies [13, 29-31]. The smaller the residual monitor convergence, the more accurate the

results obtained but the longer the fluent operation time. In this study, even though the reduction in the residual

value of the monitor convergence continues, fluent produces a constant blade characteristic. This shows that the

choice of the residual monitor convergence value is appropriate. The number of iterations in this study varies for

each type of blade and the position of the pitch angle analyzed. The highest number of iterations is 2.578 in blade

shape 1 in pitch angle 16o. The smallest number of iterations is 1.900 in the form of blade shape 2 on pitch angle

0o. Automatically, fluent asks for an increase in the number of iterations if the number of inputted iterations is not

enough. Automatically, fluent stops the calculation if there has been a calculation even though the number of

inputted iterations has not been reached.

Reference values are chosen based on the condition of the study boundary and reference zone. Study boundary

conditions are adjusted for fluid properties and domain conditions. Although this study was carried out in 2

dimensions, fluent continued to provide space as part of the accuracy of the calculations. The space is formed

based on the function of the size of the domain that is formed, the depth of the domain, and the area covered by

fluid. Because the area covered by fluid is 1 m2, the depth of the domain is calculated based on the area and width

of the domain. The depth of the domain in Figure 4 is 0,5 m.

Post processing

3/4L

Symetri

Symetri

Vel

oci

ty I

nle

t

Pre

ssu

re O

utl

et

Wall

c

L = 30 c

1/4L

3/4c W =

20

c


202

This process is the final part of determining blade characteristics. This process is carried out to see the flow

characteristics and blade characteristics at different pitch angles. Pressure and velocity distribution, pressure and

speed counters, drag and lift coefficients, moment coefficients, path lines, greed displays, and others which are

related them can be shown in this process.

Data validation

Data validation of this study was carried out with data from previous studies [32]. Although this study only looks

at changes in pitch angle to lift and drag coefficient on different blade trailing edge shapes, research data validation

can be done on the relationship between angle of attack and lift coefficient and drag on different airfoils. Data

validation is only done on the NACA 0018 symmetrical airfoil. The results of the data validation show the same

graph pattern for both the lift coefficient and the drag coefficient. Figure 5 and Figure 6 show the relationship

between angle of attack and the lift coefficient and the relationship between angle of attack and drag coefficient,

respectively.

Figure 5. Relationship of azimuth angle Vs lift coefficient

Figure 5 shows the minimum lift coefficient occurring at angle of attack 0o, 90o, and 180o. The maximum lift

coefficient occurs in the range of angle of attack 45o and 135o. Although Figure 5 shows the lift coefficient graph

line between the previous studies and this study coincide, the actual coefficient of lift is different. The lift

coefficient value from the previous study can read only one decimal number while this study up to four decimal.

Estimates of the lift coefficient value of the previous study were based solely on the graph of the research results

while the lift coefficient value of this study was obtained by a more complete study.

Figure 6. Relationship of azimuth angle Vs drag coefficient

The minimum drag coefficient in Figure 6 occurs at the angle of attack 0o and 180o while the maximum drag

coefficient occurs at an angle of attack 90o. Unlike the lift coefficient which has a negative coefficient, the drag

coefficient is only positive. An explanation of the coincidence of the graph line between the previous research and

this study is the explanation of the coefficient of lift.

RESULT AND DISCUSION

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

Lif

t co

effi

cien

t

Azimuth angle (deg)

Alessandro Bianchini et al

Numerical present

0

0.5

1

1.5

2

2.5

0 30 60 90 120 150 180

Dra

g co

effi

cien

t

Azimuth angle (deg)

Alessandro Bianchini et al

Numerical present


203

Velocity of fluid V that flowing from the left side of the turbine on the Figure 1 produces a velocity distribution

in the blade. The distributed types of velocity consist of the relative velocity w and the tangential velocity of the

turbine u. At the critical turbine position, the azimuth angle θ in Figure 1 = 0o with the radius perpendicular to the

blade, this results in a very small lift force. The small lift force causes the Darrieus turbine to lack thrust.

Increasing or decreasing the lift force can be done by changing the pitch angle at a certain position. Pitch angles

that are too small or too large do not produce optimal thrust. The variation of pitch angle in this study is chosen

after conducting a preliminary study of various range pitch angles examined by previous researchers.

Determination of pitch angle is done after making a comparison between the lift and drag coefficient which results

in a ratio of maximum ε.

The label data shown on the graph lines formed by changes in pitch angle to the lift coefficient, drag coefficient,

and ratio ε are labeled data for blade shape 2 and blade shape 3. This is done because the difference in the two

values is very small which results in the graph line coincides. The label data listed at the top of the graph line is

the data label for the blade shape 2 and the bottom is the label data for the blade shape 3.

Lift

Figure 7 shows the relation between pitch angle with lift coefficient. Overall, an increase in the pitch angle towards

a positive β or a decrease in pitch angle towards -β is always directly proportional to the value of the lift coefficient.

The greater the pitch angle, the greater the coefficient of the lift; vice versa. The decrease in the lift coefficient

value in Figure 7 only shows the change in direction of the lift force because the lift force still has a certain

magnitude. At 0o pitch angle, the three blade shapes show similarities in the lift coefficient value of zero.

Figure 7. The relationship between pitch angle and lift coefficient

Overall, the lift coefficient of blade shape 1 is always greater than the blade shape 2 and 3 on each change in the

pitch angle. This can be seen from the graph lines formed. On the overall change in pitch angle, the lift coefficient

value of blade shape 1 averaged 5,2687% on the blade shape 2 and 4,8943% on blade shape 3 respectively. The

amount of difference in lift coefficient values on blade shape 1 with blade shapes 2 and 3 shows that the difference

in blade trailing edge has an impact on changes in the lift coefficient in each pitch angle position. For blade shape

2 and 3, the average lift coefficient for each shape 2 pitch angle blade change is 0,405% greater than that of blade

shape 3. Because of the small difference in lift coefficient values on blade shapes 2 and 3 it can be said that the

difference in trailing edge shape for both types of blades; semicircle and triangle, does not have an impact on the

dimensions of the lift coefficient. The effect of changing shape shapes 2 and 3 blades on the lift coefficient at the

pitch angle range is assumed to be the same.

Drag

Figure 8 shows the relation between pitch angle and drag coefficient for all three blade shapes. In contrast to the

lift coefficient value that has a positive and negative value as a function of the change in pitch angle, the drag

coefficient value does not change even though the pitch angle changes the sign. Unlike the lift coefficient which

produces a coefficient value equal to zero because the blade changes position, the drag coefficient value is never

equal to zero. In this study, the drag coefficient value is only close to zero. The drag coefficients on the left side

or on the right side of the vertical line have almost the same value. The similarity of this value illustrates that the

-0.0431

-0.0338

-0.0232

0.0114

0.0230

0.0335

0.0433

-0.04295

-0.03363

-0.02302

0.01180

0.02310

0.03373

0.04289

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

-16 -12 -8 -4 0 4 8 12 16

Lif

t C

oef

fici

ent

Pitch angle (deg)

Blade shape 1

Blade shape 2

Blade shape 3


204

drag value is not a function of the blade ± β position. As explained in Figure 1, when the leading edge is outside

or inside the circle line pitch diameter, the drag coefficient is not subject to change in sign. The magnitude of the

drag value is a function of the cross-sectional area facing the fluid flow.

Figure 8. The relationship between pitch angle and drag coefficient

Overall, the smallest drag coefficient occurs at pitch angle 0o but there is an increase in the drag coefficient along

with the increase or decrease in pitch angle. The drag coefficient on the blade shape 1 is always smaller than drag

coefficients of the blade shape 2 and 3. The difference in drag coefficient in this study is only reviewed in the pitch

angle range of -16o ≤ 0o ≤ 16o. On the overall change in pitch angle, the drag coefficient value on average blade

shape 1 was smaller by 3.8437% on the blade shape 2 and 4.0874% on the blade sahe 3. The difference in the

value of drag coefficient on blade shape 1 with blade shape 2 and 3 show that the difference in blade trailing edge

shape affects the change in the drag coefficient at various pitch angles. For blade shape 2 and blades shape 3, the

average drag coefficient for each change in pitch angle shows a bigger the blade shape 2 of 0.2234% than the blade

shape 3. Because of the small difference in the drag coefficient values on blade shapes 2 and 3, the different trailing

edge shape on both types of blade does not affect the drag coefficient changes. The effect of changing the trailing

edge on the blade shape 2 and 3 to the drag coefficient at this pitch angle range is assumed to be the same.

Comparison Lift and Drag Coefficient.

Figure 9. The relationship between pitch angle and ratio ε (lift coefficient/drag coefficient)

Figure 9 shows a graph of the relation between the pitch angle with the ratio ε (ratio that obtained from the

comparison between the lift coefficient with the drag coefficient). The maximum value of the ratio ε that obtained

is in the range of pitch angle +12o and minimum at pitch angle -12o. Changes in the direction of β outside the

trajectory of the turbine pich diameter line produce a positive lift coefficient and changes in the direction of β in

the trajectory of the turbine pitch diameter line produce negative lift coefficients. Just as the lift coefficient

0.0149

0.0116

0.0090 0.0089

0.0115

0.0150

0.01490

0.01157

0.00902 0.00900

0.01156

0.01489

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

0.015

-16 -12 -8 -4 0 4 8 12 16

Dra

g co

effi

cien

tPitch angle (deg)

Blade shape 1

Blade shape 2

Blade shape 3

-2.889 -2.919

-2.590

-1.554

1.538

2.579

2.908 2.886

-2.882 -2.907

-2.551

-1.574

1.590

2.565

2.9172.881

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

-16 -12 -8 -4 0 4 8 12 16

ԑ (l

ift/

dra

g co

effi

cien

t)

Pitch angle (deg)

Blade shape 1

Blade shape 2

Blade shape 3


205

increases with the increase in pitch angle in Figure 7, an increase in drag coefficient also occurs together with an

increase in the pitch angle in Figure 8. Determination of pitch angle cannot be done based on the maximum lift

coefficient because in this condition the drag coefficient also increases. The large drag coefficient value on the

Darrieus turbine causes the turbine to lose its thrust. Decreasing the drag coefficient together with the decrease in

pitch angle in Figure 8 is followed by decrease the lift coefficient along with the decrease in pitch angle in Figure

7. The determination of pitch angle also cannot be done based on the smallest drag coefficient because in this

condition the minimum lift coefficient occurs. The small lift coefficient value on the Darrieus turbine causes the

turbine to lack thrust. Determination of pitch angle cannot be done based on minimum drag coefficient or

maximum lift coefficient.

Determination of pitch angle is done based on the relationship between changes in pitch angle with a maximum

value of ε. The value of the maximum ε ratio in Figure 9 is obtained in the range of pitch angle ±12o ≤ β ≤ ±16o

for all blade shapes. In smaller pitch angles 12o or greater 16o, the comparison value ԑ indicates decrease. In the

pitch angles greater than -12o to 0o or smaller -16o, the comparison value ԑ also indicates decrease. Darrieus turbines

do not provide maximum work at a ratio of smaller or minimum.

The ratio ε = 0 that obtained at pitch angle 0o, it increases and decreases gradually until reaches its peak point in

the range of pitch angle ±12o ≤ β ≤ ±16o but decrease again after ±16o pitch angle. This condition indicates that

static determination of the pitch angle can be done at this pitch angle range; ±12o ≤ β ≤ ±16o.

Based on the graph lines formed and changes in values on the vertical and horizontal axis, the static pitch angle is

recommended at ±12.5o for blade shape 1 and ±13o for blade shape 2 and blade shape 3. In relation to studies

conducted by Tummala et al [14] who found that pitch angle is a function of airfoil profile, the results of this study

showed that changes in the shape of the trailing edge on the NACA 0018 blade profile also affected static pitch

angle changes. There are two positions for choosing the pitch angle that can be done; -β or +β, because it has the

same value ԑ even though the sign is different. Based on a study conducted by Rezaeiha et al [13], the selection of

pitch angle in this study is -β. Therefore, the static pitch angle found in this study is –β = 12.5o for blade shape 1

and 13o for blade shape 2 and 3.

Overall, the blade shape 1 produces the ε ratio that is greater than the blade shape 2 and 3 in each pitch angle

position. The blade shape 1 average ratio is greater by 8.7474 % for blade shape 2 and 8.4755% for blade shapes

3 respectively. For blade shape 2 and blades shape 3, the ratio ε on the each change in the pitch angle shows the

blade shape 2 is 0.2366 % larger than the blade shape 3. Because of the small difference in the ratio of the blade

shape 2 and 3, the difference in the trailing edge shape in the two types of blade does not have an impact on the

change in pitch angle. Blade shape 2 is the same as blade shape 3.

Pressure Distribution.

The pressure distribution on the turbine blade shape 1 is shown at pitch angle β = -12.5o and β = -13o for blades

shape 2 and 3. Figure 10, 11, and 12 show the pressure distribution on the overall blade, blade leading edge, and

blade trailing edge for all blades types respectively. The color difference in the overall domain shows the difference

in pressure in each part of the domain. In addition, the color differences around the blade also indicate the boundry

layer of maximum and minimum pressure. The level of density or estrangement of the pressure line depends on

the number of elements formed in the mesh process in gambit. The more number of elements divided, the smaller

the degree of estrangement of the line of pressure that occurs; and vice versa. However, after the process on the

fluent is complete, the density and estrangement of the pressure line can be adjusted again by zoom out or zoom

in the scale of the image without changing the number of elements. The density of the pressure line can be seen in

Figures 10a, 11a, and 12a while the estrangement can be seen in figures 10b, 10c, 11b, 11c, 12b, and 12c.


206

Figure 10. Pressure distribution on (a) the overall blade shape 1, (b) the blae leading edge, (c) the blade trailing

edge

The magnification of the image scale shows each arrow with certain line characteristics. Each arrow is located in

each element that has been divided. The length of arrows shown in Figures 10b, 10c, 11b, 11c, 12b, and 12c do

not determine the amount of pressure occured. The length of the arrow is determined by the size of the space and

the type of mesh selected in the process in gambit. Changing the direction of the arrow does not indicate a change

in pressure in the direction of x or y. Every arrow has two limits of magnitude; upper and lower limit. The upper

and lower limits read in each of the arrows represent the counter level on the left side of each 10, 11, and 12. In

this study there are 20 counter levels; starting from counter level 0 to counter level 19.

Velocity Vectors Colored By Static Pressure (pascal)FLUENT 6.3 (2d, dp, pbns, ske)

Jan 18, 2009

6.33e+01

5.75e+01

5.17e+01

4.59e+01

4.02e+01

3.44e+01

2.86e+01

2.28e+01

1.71e+01

1.13e+01

5.52e+00

-2.56e-01

-6.03e+00

-1.18e+01

-1.76e+01

-2.34e+01

-2.91e+01

-3.49e+01

-4.07e+01

-4.64e+01

-5.22e+01


Jan 17, 2009

6.33e+01

5.75e+01

5.17e+01

4.59e+01

4.02e+01

3.44e+01

2.86e+01

2.28e+01

1.71e+01

1.13e+01

5.52e+00

-2.56e-01

-6.03e+00

-1.18e+01

-1.76e+01

-2.34e+01

-2.91e+01

-3.49e+01

-4.07e+01

-4.64e+01

-5.22e+01


Jan 17, 2009

6.33e+01

5.75e+01

5.17e+01

4.59e+01

4.02e+01

3.44e+01

2.86e+01

2.28e+01

1.71e+01

1.13e+01

5.52e+00

-2.56e-01

-6.03e+00

-1.18e+01

-1.76e+01

-2.34e+01

-2.91e+01

-3.49e+01

-4.07e+01

-4.64e+01

-5.22e+01

(a)

(b) (c)

N/m2


Jan 17, 2009

6.32e+01

5.75e+01

5.17e+01

4.60e+01

4.02e+01

3.45e+01

2.87e+01

2.30e+01

1.73e+01

1.15e+01

5.78e+00

3.52e-02

-5.71e+00

-1.14e+01

-1.72e+01

-2.29e+01

-2.87e+01

-3.44e+01

-4.02e+01

-4.59e+01

-5.16e+01


Jan 17, 2009

6.32e+01

5.75e+01

5.17e+01

4.60e+01

4.02e+01

3.45e+01

2.87e+01

2.30e+01

1.73e+01

1.15e+01

5.78e+00

3.52e-02

-5.71e+00

-1.14e+01

-1.72e+01

-2.29e+01

-2.87e+01

-3.44e+01

-4.02e+01

-4.59e+01

-5.16e+01


Jan 17, 2009

6.33e+01

5.75e+01

5.17e+01

4.59e+01

4.02e+01

3.44e+01

2.86e+01

2.28e+01

1.71e+01

1.13e+01

5.52e+00

-2.56e-01

-6.03e+00

-1.18e+01

-1.76e+01

-2.34e+01

-2.91e+01

-3.49e+01

-4.07e+01

-4.64e+01

-5.22e+01

(a)

(b) (c)

N/m2


207

Figure 11. Pressure distribution on (a) the overall blade shape 2, (b) the blade leading edge, (c) the blade trailing

edge

Figures 10a, 11a, and 12a show pressure distributions in blade shape 1, blade shape 2, and blade shape 3

respectively. Maximum pressure occurs on the surface of the upper leading edge of the blade. This pressure

gradually decreases following the path of the blade profile with a certain pattern. The farther the fluid from the

blade leading edge surface, the smaller the pressure that occurs. The pressure decreases until it reaches the same

pressure as the pressure on the inlet velocity. The maximum pressure in Figures 10, 11 and 12 are 63.3 N/m2, 63.2

N/m2, and 63.4 N/m2 respectively. Pressure drops in the next stage are 57.47 N/m2, 57.5 N/m2, and 57.7 N/m2

respectively for blade shape 1, 2, and 3. This pressure continues to decrease until it reaches the minimum limit on

the outermost parts of the maximum pressure boundry layer is 11.3 N/m2, 5.78 N/m2, and 6.09 N/m2 respectively

for blade shape 1, blade shape 2, and blade shape 3.

Minimum pressure occurs on the surface of the lower blade leading edge in Figures 10a, 11a, and 12a. In contrast

to the maximum pressure that experiences a decrease in pressure when away from the surface of the blade, this

minimum pressure increases gradually following the profile of the blade with a certain pattern when the fluid

moves away from the blade. The farther the fluid from the blade's leading edge surface, the greater the pressure

that occurs. The pressure increases until it reaches the same pressure as the air pressure on the velocity inlet. The

minimum pressure in Figures 10, 11, and 12 are -52.2 N/m2, -51.6 N/m2, and -51.2 N/m2 respectively. The pressure

increase in the next stage is -46.6 N/m2, -45.9 N/m2, and -45.6 N/m2 respectively for the blade shape 1, blade shape

2, and blade shape 3. This pressure continues increased to reach the maximum limit on the parts of minimum

pressure boundry layer of -25.6 N/m2, -5.71 N/m2, and -5.38 N/m2, respectively for blade shape 1, blade shape 2,

and blade shape 3.

Figure 12. Pressure distribution on (a) the overall blade shape 3, (b) the blade leading edge, (c) the blade trailing

edge

Figures 10c, 11c, and 12c show the pressure distribution on the trailing edge of the blade shape 1, blade shape 2,

and blade shape 3 respectively. Unlike trailing edge of the blade shape 1, trailing edge of the blade shape 2 and 3

show fortex pressure on the trailing edge blade. In relation to pitch angle, changes in trailing edge shape and the

effect of fortex pressure on the trailing edge blade cause a decrease in ratio ε for each change in pitch angle.

Decreasing the value of the ε ratio causes a decrease in pitch angle of 3.85% from the pitch angle in the blade


Jan 17, 2009

6.33e+01

5.75e+01

5.17e+01

4.59e+01

4.02e+01

3.44e+01

2.86e+01

2.28e+01

1.71e+01

1.13e+01

5.52e+00

-2.56e-01

-6.03e+00

-1.18e+01

-1.76e+01

-2.34e+01

-2.91e+01

-3.49e+01

-4.07e+01

-4.64e+01

-5.22e+01


Jan 17, 2009

6.34e+01

5.77e+01

5.19e+01

4.62e+01

4.05e+01

3.47e+01

2.90e+01

2.33e+01

1.76e+01

1.18e+01

6.09e+00

3.54e-01

-5.38e+00

-1.11e+01

-1.68e+01

-2.26e+01

-2.83e+01

-3.40e+01

-3.98e+01

-4.55e+01

-5.12e+01


Jan 17, 2009

6.34e+01

5.77e+01

5.19e+01

4.62e+01

4.05e+01

3.47e+01

2.90e+01

2.33e+01

1.76e+01

1.18e+01

6.09e+00

3.54e-01

-5.38e+00

-1.11e+01

-1.68e+01

-2.26e+01

-2.83e+01

-3.40e+01

-3.98e+01

-4.55e+01

-5.12e+01

(a)

(b) (c)

N/m2


208

shape 1 which is -12.5o. The graph in Figure 9 shows a decrease in the ratio ε on the vertical axis causes a shift in

the peak point of the meeting between the pitch angle and the ratio ε.

CONCLUSION

Based on the results of this study, it can be concluded that the pitch angle is a function of the blade profile and

changes in the shape of the trailing edge. Changes in the shape of a semicircular trailing edge (blade shape 2) and

a triangle (blade shape 3) does not affect the change in pitch angle. The pitch angle for each type of blade is -12.5o

for blade shape 1 and -13o for blade shape 2 and 3. Chord shortening in the blade causes a decrease in pitch angle.

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Nomenclature.

Anonyms

VAWT = Vertical Axis Wind Turbine.

NACA = The National Advisory Committe for Aeronautics.

CFD = Computer Fluids Dynamic

TSR = Tip Speed Rasio

Symbols

c = Chord length, mm.

A = Area of blade square, m2.

P = The pressure of the point, Pa

P∞ = The pressure of the wind undisturbed, Pa.

V∞ = Inlet velocity, m/s.

FL = Lift force, N.

FD = Drag force, N.

FT = Tangensial force, N.

FN = Normal force, N.

α = Angle of attack, deg.

β = Pitch angle, deg

θ = Azimut angle, deg.

ρ = Fluid density, kg/m3.

υ = Kinematic viscosity, m2/s.

µ = Dynamic viscosity, m2/s.

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