thickness distributions along the blade for one megaâwatt (MW) wind turbine on the basis of ...... 500,000 and 10 million. Generally, in the ..... induced velocity components, we must consider an annular ring of rotor disc with a radius (r) and of a ...
Zagazig University Faculty of Engineering Mechanical Power Engineering Department
The Effect of Blade Geometry and Configuration on Horizontal Axis Wind Turbine Performance A thesis Submitted in Partial Fulfillment for the Requirements of the Degree of Master in Mechanical Power Engineering
by
Mohamed Khaled Mohamed Mohamed Hasanin Supervisors
Prof. Dr. Ahmed Farouk Abdel Gawad Assoc. Prof. Dr. Hesham ElSayed Abdel Hamed Dr. Mostafa Mohamed Mohamed Ibrahim Mechanical Power Engineering Department Faculty of Engineering Zagazig University
2017
Approval Sheet The Effect of Blade Geometry and Configuration on Horizontal Axis Wind Turbine Performance A thesis Submitted in Partial Fulfillment for the Requirements of the Degree of Master in Mechanical Power Engineering
By
Mohamed Khaled Mohamed Mohamed Hasanin Approved by Signature
Examiners: 1- Prof. Dr. Hesham Mohamed Ali Al-Batch Mechanical Power Engineering Department. Faculty of Engineering. Benha University
2- Prof. Dr. Mofreh Melad Nassif Mechanical Power Engineering Department. Faculty of Engineering. Zagazig University
3- Prof. Dr. Ahmed Farouk Abdel Gawad (Supervisor) Mechanical Power Engineering Department. Faculty of Engineering. Zagazig University
4- Assoc. Prof. Dr. Hesham ElSayed Abdel Hamed (Supervisor) Mechanical Power Engineering Department. Faculty of Engineering. Zagazig University
Zagazig University
2017
Affectionately Dedicated To MY BELOVED FATHER AND MOTHER For their patience and encouragement That made this work possible
Acknowledgments Thanks go first and final to Allah who gave me the patience to complete this work. I would like to express my sincere appreciation to my supervisor, Prof. Dr. Ahmed Farouk Abdel Gawad Vice Dean of High Studies and researches, Zagazig University, for his deep interest in the subject of this research, his guidance, invaluable discussions in numerous aspects, and encouragement throughout. I would also like to thank Assoc. Prof. Hesham ElSayed Abdel Hamed, Mechanical power engineering department, Zagazig University, for his help and support throughout this work. I owe so much to Dr. Mostafa Mohamed Mohamed Ibrahim Mechanical power engineering department, Zagazig University for his guidance and support throughout this work. Special thanks to Faculty of Engineering, Ain Shams University for giving opportunity to use air wind tunnel in fluid mechanics laboratory for the experimental work. I am also indebted to my wife for her patience and encouragement, and support throughout the work, and to my son (Luqman) for providing the diversion much needed in many occasions. I would like to express my deep appreciation to my parents, brother (Abdullah) and sisters for their constant encouragement, support, pray, and patience.
i
Abstract The wind turbine blades are the main part of the rotor. Extraction of energy from wind depends on the design of the blade. A design method based on Blade Element Momentum (BEM) theory is explained for small horizontal–axis wind turbine model (HAWT) blades. The method was used to optimize the chord and twist distributions of the wind turbine blades to enhance the aerodynamic performance of the wind turbine and consequently, increasing the generated power. A FORTRAN program was developed to use (BEM) in designing a model of horizontal–axis wind turbine (HAWT). NACA 4412 airfoil was selected for the design of the wind turbine blade. Computational fluid dynamics (CFD) analysis of HAWT blade cross section was carried out at various blade angles with the help of ANSYS Fluent 15 software. Present results are compared with other published results. Power generated from wind turbine increases with increasing blade angle due to the increase in air–velocity impact on the wind turbine blade. For blade angle change from 200 to 600 , the turbine power from wind has a small change and reaches the maximum when the blade angle equals to 900 . Thus, HAWT power depends on the blade profile and its orientation. Three dimensional studies, to demonstrate the effect of winglet dimensions at the tip of the blade on the performance of a small horizontal-axis wind turbine, were introduced experimentally and computationally. The blades with five different configurations of winglets were used for this study. The winglet height was changed from 1% to 5% of the wind turbine rotor with cant angle 900. Different quantities such as power, power coefficient, thrust force, thrust force coefficient, and wind turbine rotational speed were investigated for different winglet heights. This was done for wind speeds from cut-in wind speed (3.12 m/s) to maximum wind speed (9.2 m/s) that was available from the experimental facility. Generally, based on the present experimental and computational results, there are noticed enhancements in power and thrust coefficients in some cases with winglet. Depending on the operating conditions, these enhancements may range from 2% to 3%. ii
Table of Contents Title
Page
ACKNOWLEDGMENTS ………………………………………..…………………
i
ABSTRACT…………………………………………....………..…..…….………......
ii
TABLE OF CONTENTS…………………………………………..………..…….....
iii
LIST OF TABLES………………………………………………..….…….…………
vii
LIST OF FIGURES……………………………………..………..……….……….....
viii
NOMENCLATURE……………………………………..…………………..…….…
xii
……
CHAPTER (1): Introduction 1.1
Introduction………………......…………….........………………....…….. 1
1.2
Wind Turbines................................................….............………….…...
1.3
2
1.2.1
Horizontal Axis Wind Turbines (HAWT) …...........……....……
3
1.2.2
Vertical Axis Wind Turbines (VAWT)........................……..….
4
Small-Scale Wind Turbines………………..…….…........…….....….... 1.3.1
5
Growth of Small Scale Wind Turbines Market............................. 6
1.4
History of wind energy …...................................….....................………..
7
1.5
Modern Wind Turbines……………........................................………
10
1.5.1
Rotor ………………………………....................................……. 12
1.5.2
Drive train...................................................................................... 12
1.5.3
Generator.......................................................................................
1.5.4
Nacelle........................................................................................... 13
1.5.5
Tower and foundation................................................................. 13
1.5.6
Electrical and control system......................................................... 14
13
1.6
Wind Turbine Blade Modification…………..........................………… 14
1.7
Overview of Thesis …………..…………………......................………… 14
CHAPTER (2): Literature
Review
2.1
Introduction……….........…………………………....…………………… 16
2.2
Wind Turbine Rotor …….......................................………………..…….. 16
iii
2.3
2.2.1
Experimental Studies on Wind Turbine Rotor…...................….
16
2.2.2
Computational Studies on Wind Turbine Rotor……..........……
18
Wind Turbine Rotor with Winglet …………….........…………………… 26 2.3.1
Experimental Studies on Wind Turbine Rotor with Winglet...... 26
2.3.2
Computational Studies on Wind Turbine Rotor with Winglet...
28
2.4
General Remarks…………………......................……….…………….
31
2.5
Research Objectives...............................................................................
32
CHAPTER (3): Aerodynamics of Horizontal-Axis Wind Turbines and Present Parametric Case Study 3.1 Introduction……………………………………...………………………. 34 3.2 How blade capture wind power ………........……...........………..………
34
3.3 Blade Twist................................................................................................
36
3.4 Blade Section Shape...................................................................................
37
3.5 Airfoils and General Concepts of Aerodynamics....................................... 38 3.5.1
Airfoil Terminology …………………………...………………
38
3.5.2
Lift, Drag and Non-dimensional Parameters………....………..
39
3.5.3
Airfoils for Wind Turbines.........................................................
42
3.6 Wind Turbine Aerodynamic theories.......................................................... 42 3.6.1
Actuator Disc Theory (Axial Momentum Theory)........................
3.6.2
Wake Rotation................................................................................ 49
3.6.3
Blade Element Theory (BET)......................................................... 51
3.6.4
Blade Element Momentum (BEM) Theory.................................... 54
3.6.5
Tip Loss Correction........................................................................ 59
3.7 Present Parametric Case Study...................................................................
43
62
CHAPTER (4): Numerical Models, Governing Equations, and Computational Aspects 4.1 Introduction…………………….....……………………………………... 70 4.2
ANSYS Fluent CFD…………............…..……..………………………..
70
4.3 Numerical Solvers......................................................................................
70
4.3.1
The Pressure-Based Solver............................................................. 71
iv
4.3.2
Density-Based Solver..................................................................... 73
4.4 Governing Equations…………....................................…..………………
73
4.4.1
Mass conservation equation...........................................................
73
4.4.2
Momentum conservation equation................................................. 74
4.4.3
Auxiliary Equations........................................................................ 75
4.4.4
Turbulence Modeling.....................................................................
75
4.5 Selection of Turbulence Modeling…………....…………….....…………. 78 4.6
Shear Stress Transport SST k Model ……...............................…... 78
4.7 Numerical Simulation................................................................................. 80 4.8 Computational Cases..................................................................................
82
4.8.1
Two Dimensional Wind Turbines.................................................
4.8.2
Three Dimensional Wind Turbines................................................ 84
CHAPTER (5): Experimental
82
Procedure
5.1 Introduction................................................................................................. 93 5.2 Materials of wind turbine blades................................................................. 93 5.3 Wind Turbine Rotor Models....................................................................... 94 5.3.1
Wind Turbine Rotor.......................................................................
94
5.4 Experimental Setup and Procedure............................................................. 101 5.4.1
Experimental Setup........................................................................
101
5.4.2
Experimental Procedure.................................................................
104
CHAPTER (6): Results 6.1
and Discussions
Introduction……………………………………........…………………… 106
6.2 CFD Validation with Experimental Results….......….........….………….
106
6.3 Experimental Results..................................................................................
112
6.3.1
Experimental Results at Design Wind Speed ……....................… 114
6.4 Computational Results ………………………...…………....................… 116 6.4.1
Two Dimensional Results............................................................
116
6.4.2
Three Dimensional wind turbines..................................................
129
v
CHAPTER (7): Conclusions and Future Work 7.1 Introduction…………………………………………………....……….… 137 7.2 Conclusions.................................…………..……………….…….….…
137
7.3 Recommendations for Future Work……...……………………….…...…
138
REFERENCES ……………………………………...…………………….….……
140
APPENDIX (A) …………………………………..………….……………….………
147
vi
List of Tables Table
Title
Page
3.1
NACA 4412 characteristics.………………………..................………….. 62
3.2
Design Parameters for NACA 4412 airfoil ……….……..........…..............
62
3.3
Design blade for NACA 4412 airfoil …………..………….....…..……….
63
3.4
Geometry of wind turbine blade…………..……....……....………………. 63
4.1
Winglet data for CFD …………...................................…...……………… 85
4.2
Mesh statistics for different blade designs…………….…......……………
5.1
Geometry of wind turbine blade ………………....................................….. 95
5.2
Dimensions of wind tunnel components………………….......…...………
102
5.3
Centrifugal Fan specifications …………………..................................….
103
5.4
Performance of wind turbine………......................................................….
105
6.1
Experimental Wind Turbine Blade CP Values.............................................
113
6.2
Average CP Values.......................................................................................
113
6.3
Average power coefficient from experimental and correlation.................... 114
6.4
Experimental power and power coefficient at design wind speed...............
114
6.5
Power coefficient from experimental and correlation.................................
117
6.6
Wind power and maximum power for different blade angle.......................
127
6.7
Computational values of the wind turbine blade CP..................................... 130
6.8
Computational values of the wind turbine blade CT....................................
133
6.9
Computational average CP and CT values....................................................
133
6.10
Computational wind turbine parameters at design wind speed.................... 133
vii
92
List of Figures Figure
Title
Page
1.1
Wind power global capacity[KPMG GLOBAL Renewable Energy, 2016]
2
1.2
Wind power converts to electrical power [29]………………………….
3
1.3
Horizontal axis wind turbine [Wood, D., Springer 2011]……………..
4
1.4
Vertical axis wind turbine categories [To sun, M, 2006]………………
5
1.5
Top ten wind power generating countries [GWEC, 2012]…………..
7
1.6
Smock Mill Wind Turbine [31]…………………................…………….
8
1.7
Growth in size of the rotor diameter of wind turbines since 1980 [32].....
9
1.8
Major components of a horizontal axis wind turbine [Manwell.et
al,2009]
11
1.9
Detailed view of wind turbine components [33].......................................
12
3.1
Flow around airfoil [30]……………………………………………...…
35
3.2
Wind angles and blade angle on airfoil [padmaja, et al 2013]………
36
3.3
NACA 4412 airfoil ………………….................................................…..
37
3.4
Twist at different (r/R) of turbine blade [padmaja, et al 2013]………
37
3.5
Sample airfoils used in wind turbine blade [Hansen and M., 2013] …
38
3.6
Airfoil Nomenclature ………………....................................................…
39
3.7
Forces and moments on an airfoil section.……………..................……..
40
3.8
Wind energy extraction stream tube [Burton et al, 2001]………………
43
3.9
Actuator Disc Stream-tube [Burton et al, 2001]……………………….
44
3.10
Velocity distribution through a wind turbine.……….........……………..
46
3.11
The variation in C P and CT with axial induction factor [Manwell.et al,2009]
49
3.12
Blade Element length dr at radius r.……….....................................……
50
3.13
Wind turbine blade divided into a series number of sections....................
52
viii
3.14
Velocities on blade element [Hansen 2013] ………………….…..…
52
3.15
Forces on blade element [Hansen 2013]……………………………..
53
3.16
Performance curve of wind turbine blade [Jamieson, p, 2011]………….
56
3.17
Optimum chord distribution of wind turbine blade [Manwell.et al,2009]
58
3.18
Optimum twist distribution of wind turbine blade [Manwell.et al,2009]
59
3.19
Span variation of the tip loss factor of a wind turbine blade [To sun, M, 2006]
60
3.20
Flow chart of BEM theory …………………………........………………
61
3.21
NACA 4412 airfoil profile.……………………………......…………….
65
3.22
Lift and drag coefficients.…………………………………….........…….
65
3.23
Ratio of lift coefficient to drag coefficient...............................................
66
3.24
Airfoil chord distribution along the blade length.……….......…………..
66
3.25
Airfoil relative wind angle along the blade length.…………......……….
66
3.26
Airfoil twist angle along the blade length.…………………..............…..
67
3.27
Induction factors along the blade length.……..…….................................
67
3.28
Tip losses correction factor along the blade length.……….........………
67
3.29
Local thrust coefficient along the blade length..........................................
68
3.30
Solidity ratio along the blade length.………............................………….
68
3.31
Power coefficient with tip speed ratio.……………............……………..
68
3.32
Three–dimensional views of wind turbine blade.……................…….….
69
4.1
Flow Chart of the Solution Procedure…………………………………..
81
4.2
Computational domain of NACA 4412 airfoil. (Not to Scale)…............
82
4.3
Mesh Sensitivity......................................................................................
83
4.4
NACA 4412 meshing using structured grid.……............……………….
83
4.5
CFD wind turbine blade profile. …………..…………........…………….
84
4.6
CFD wind turbine blade profile with winglet ………….........…………..
86
ix
4.7
Computational domain and applied boundary conditions …...........…….
88
4.8
Computational Domain Mesh....................................................................
89
4.9
Wind turbine blade mesh...........................................................................
89
4.10
Wind turbine rotor model grid-independency test …………............……
92
5.1
Nose and hub of wind turbine model.……………............………………
94
5.2
Damaged rotor blades after experimental test.……....................………..
96
5.3
Wind turbine blade parts from 3D printer.…………............……………
97
5.4
Fixation method of two parts of blade.…………......................................
98
5.5
Components used for joining the blade parts.….........................………..
98
5.6
Experimental wind turbine blade profile...................................................
99
5.7
Permanent magnet DC motor used as generator. ……......……………
100
5.8
Wind turbine model.……………...................................................….......
99
5.9
Experimental wind turbine blade profile with winglet.................…....…
101
5.10
Wind turbine model with winglet................................................……….
101
5.11
Wind tunnel facility and model.…..............................................………..
102
5.12
Digital portable anemometer device.………….................................……
103
5.13
Arm to control air speeds...........................................................................
104
5.14
The electrical circuit components used in the experimental study............
105
6.1
Power from wind turbine models.……..................................…………...
107
6.2
Computational power validated with experimental power from wind turbine ……...........................................................................................…
109
6.3
Rotational speed for wind turbine models.................……........…………
110
6.4
Computational rotational speed validated with experimental results
112
6.5
Average power coefficient for different cases...........................................
114
6.6
Power coefficient for different cases at design wind speed.......................
115
6.7
Blade Angle = 00 ........................................................................................
117
x
6.8
Blade Angle = 100 .......................................................................………...
118
6.9
Blade Angle = 200 .....................................................................................
119
6.10
Blade Angle = 300 …………………………………………………...…
120
6.11
Blade Angle = 400 .....................................................................................
121
6.12
Blade Angle = 500 ......................................................................................
122
6.13
Blade Angle = 600 ....................................................................................
123
6.14
Blade Angle =700 ……………………………………………………..
124
6.15
………………………………………………………... Blade Angle = 800 .....................................................................................
5 125
6.16
0 0 ………………= ...…….............……………..................................… Blade Angle = 9070 ......................................................................................
126
6.17
…. Air velocity impacts the blade at different blade angles...........................
128
6.18
Power at different blade angles.................................................................
129
6.19
Maximum power that may be generated from wind turbine
[chandrala,et al, 2012]
129
6.20
Thrust force on wind turbine models.........................................................
131
6.21
Contour of static pressure (Pa) and velocity Wind turbine rotor model...
134
xi
Nomenclature Symbol:
Definition
A
Projected area of wind turbine rotor [m2].
a
Axial induction factor
a/
Tangential induction factor
B
Number of wind turbine blades
CD
Drag coefficient
CL
Lift coefficient
CP
Coefficient of power
CT
Coefficient of thrust
c
Chord length [m]
F
Brandt correction factor
Fhub
Hub correction factor
Ftip
Tip correction factor
L/D
Lift/Drag ratio
m
Mass flow rate [ kg s ]
N
Rotational speed [rpm]
P
Power [W]
p
Pressure Pa
Q
Torque N.m
Re
Reynolds number
r
Local blade radius[m]
ST
Source term
S ij
Strain-rate tensor
T
Thrust force N xii
t
Time [s]
U
Wind speed m s
ui
Cartesian velocity component[m/s]
W
Percent of winglet height[m]
Greek Letters:
Angle of attack
Twist angle
Turbulent dissipation
Flow angle
Tip speed ratio
r
Local tip speed ratio
t
Dynamic viscosity [pa.s] Turbulent viscosity [pa.s] Kinematic viscosity [m2/s] Angular speed [RPM] Specific turbulent dissipation rate Density [kg/m3] Blade solidity ij Viscous stress tensor Local pitch angle p Pitch angle Abbreviations: 2D
Two dimensional
3D
Three dimensional
AOA
Angle of Attack
ABS
Acrylonitrile Butadiene Styrene
BEM
Blade Element Momentum
BET
Blade Element Theory
CFD
Computational Fluid Dynamics
HAWT
Horizontal Axis Wind Turbine
LE
Leading Edge xiii
NREL
National Renewable Energy Laboratory
OPT
Optimum blade shape
PLA
Polylactic Acid
PVC
Polyvinyl chloride
RANS
Reynolds Average Navier Stokes
rpm
Revolution Per Minute
SA
Spalart-Allmaras
SST
Shear Stress Transport
TE
Trailing Edge
UOT
untapered and optimum twist blade
UUT
untapered and untwisted blade
VAWT
Vertical Axis Wind Turbine
xiv
Chapter (1) Introduction 1.1 Introduction The need for electricity in present days is of prime importance due to the sort of evolved life mankind needs. The production of power using traditional methods has taken its toll on the environment and the earth has been polluted to degrees beyond imagination. Alternative energy and green energy from natural recourses is the need of the hour. Technology must be used so as to provide human needs and luxuries but still not affect our planet. With increasing awareness about our needs and priorities, one alternative source where we can draw power would be the wind. Wind turbine was invented by engineers in order to extract energy from the wind. Because the energy in the wind is converted to electric energy, the machine is also called wind generator. By the end of 2016, it was reported by the World Wind Energy Association, that there are over 425 GW of wind power capacity in the world, as illustrated in Figure (1.1). According to BTM Consult, a company that specializes in independent wind industry research, the level of annual installed capacity has grown at an average rate of 27.8% per year for the previous five years. [MBT consult, 2012]. These statistics demonstrate that wind energy is already a vital source of energy production around the globe and that the demand for wind energy solutions is increasing. The majority of power generation from wind turbines is currently produced in wind farms, or large fields that have several large commercial wind turbines. From an environmental standpoint, a wind farm is much preferred to a coal burning plant because of carbon emissions and other factors, but both methods of power generation require the consumer buy this power from a utility company.
1
Figure (1.1): Wind power global capacity [KPMG GLOBAL Renewable Energy , 2016] 1.2 Wind Turbine The main concept of a wind turbine system is to convert the kinetic energy of the moving air into mechanical energy and ultimately into an electrical energy via an electrical generator, Figure (1.2). Wind turbines come in many shapes and sizes depending on the environmental location in which it was intended to operate. There are two main categories of wind turbines utilised to extract energy from the wind: Horizontal Axis Wind Turbine (HAWT) and Vertical Axis Wind Turbine (VAWT). It is important to understand the differences between the two as the power output of the turbine can be selected based on the energy available on site which dictates the overall size of the turbine.
2
Figure (1.2): Wind power converts to electrical power [29]
1.2.1 Horizontal Axis Wind Turbine (HAWT) Horizontal axis wind turbines are the most common type of wind turbines employed commercially and domestically. The turbines axis of rotation is parallel to the direction of free-stream flow; hence it is called a horizontal axis wind turbine. Horizontal axis wind turbines work on the fundamental principle of lift. The torque generated to rotate the turbine is produced as a result of the pressure difference on pressure and suction sides of the wind turbine blade. The widely accepted design configuration is the three bladed wind turbines designing as shown Figure (1.3). The advantages of using a horizontal axis wind turbine are as follows: Highly efficient in terms of energy extraction from the wind. Proven reliability as it has been used extensively in the commercial applications. Cost effective.
3
(a) Commercial wind turbine (b) Small domestic scale wind turbine Figure (1.3): Horizontal axis wind turbine [wood, D Springer, 2011]. The underlying factor which continues to over shadow horizontal axis wind turbines is the level of noise it produces. The sound generated from a wind turbine can be divided into mechanical noise and aerodynamic noise. The mechanical noise is generated by different components within a wind turbine system such as the gearbox and the electrical generator housed inside the nacelle. The aerodynamic noise however, is generally the dominant noise source in comparison to the former and it is also very difficult to treat.
1.2.2 Vertical Axis Wind Turbine (VAWT) One notable difference of the vertical axis wind turbine (VAWT) is that the axis of rotation is perpendicular to the direction of the free-stream flow. VAWTs are categorized into two distinct categories; Savonius and Darrieus according to the principle used to capture energy from the wind. Savonius type wind turbines operate using the principles of drag whereas Darrieus type wind turbines operate primarily on the principle of lift. Although VAWTs are not as efficient as HAWTs, they are 4
increasingly popular in urban residential areas. This is largely due to the fact that a VAWT possesses fewer moving parts and operates at a low tip speed ratio which makes it significantly quieter and thus well suited for urban residential areas [Eriksson et al, 2008]. HAWTs require a yaw mechanism to redirect itself in the direction of the wind, whereas VAWTs are less sensitive to the changing wind direction and turbulence. Another advantage associated with VAWTs is the simplicity in design. Unlike HAWTs, the gearbox and generator is located at ground level which significantly reduces the complexity of the design and is also relatively easy to maintain and thus lowering the maintenance cost. Figure (1.4) shows the vertical axis wind turbine categories.
(a) Savonius type wind turbine.
(b) Durries type wind turbine.
Figure (1.4): Vertical axis wind turbine categories [To sun, and M thesis, 2005].
1.3 Small-Scale Wind Turbine According to the international standardization body, the International Electro technical Commission (IEC) defines small-scale wind turbines as those having a swept area less than 200 m². The viability of small wind turbines for use in urban areas has 5
generated a growing interest. Small-scale wind turbines have the potential to be integrated on the roofs of houses and buildings and contribute significantly in the reduction of the average house hold electricity costs. The technological improvements of small wind turbines, although not quite as advanced as commercial wind turbines, have contributed to the increase in the overall power output.
1.3.1 Growth of Small-Scale Wind Turbine Market On a global scale, China continues to dominate the rest of the world with a total installed capacity of more than 60,000 MW and closely followed by the USA with an installed capacity of 48,000 MW as shown in Figure (1.5). The success of wind energy as an alternative source of renewable energy is largely due to the use of commercial wind turbines which come in different sizes and configurations. The technological improvement of wind turbines has primarily focused on the commercial use of wind turbines and not so much for the utilization in urban residential environment. However, in recent years the use of small-scale wind turbines in urban residential areas has drawn interest and as a result the small-scale wind turbine market is expanding although the technology is not at the same level maturity as commercial wind turbines. The significant growth of small-scale wind turbines is largely driven by the policies introduced such as tax credits. The overall cost of small wind turbines continues to be one of the main challenges yet be overcome. As the small wind industry is still under developing compared to the commercial industry, the growth of small wind market is essential in order to reduce the costs. Enhancement in aerodynamic efficiency of small wind turbines is essential in order to generate more power.
6
Figure (1.5): Top ten wind power generating countries [GWEC, 2012].
1.4 History of Wind Energy The use of wind energy in getting water out of wells and grinding was a part where this source was of great significance for free power. Older wind capturing machines developed in 200 BC are considered to be the first instance where wind was as a power source for machines. The European countries had built smock mill type of turbines which was mainly used for drawing water from wells and for agricultural purpose, Figure (1.6).
7
Figure (1.6): Smock mill wind turbine [30]
The power of wind if harnessed completely can actually power a whole nation, and if used with other natural alternative energy, we can create a pollution-free green environment. This energy is so important to third world countries where basic electricity is not available. Power of wind turbines has increased 100 times compared to the wind mills those existed a couple of decades ago. In order to harness the wind effectively and for the low costs, the advancement of technology over the last few decades has given rise to not individual turbines but wind farms in general. Advances in materials and composites used for construction of turbines, the analysis for efficiency of aerodynamics and structures, accurate prediction of winds and their direction have provided for cost effective production of power. As 8
technology in every area is advancing, the turbines go higher and grow powerful. Figure (1.7) gives an approximate rotor diameter and years in production. Since its early development in the 1980s, the global market for wind energy has expanded exponentially. In the period between 1990-2007, the world’s total wind electricity capacity has grown 50 times and is predicted to increase over the 2008 level by ten-fold by 2030, and twenty-fold by 2050 [Gsanger.s.pitteloud ,2011]. In order to achieve the expansion expected in this area, there is a need for the development of stronger and lighter materials which will enable manufacturing of blades for larger rotors. The larger the area through which the turbine can extract the wind energy, the more power that can be captured as shown in Figure (1.7). Advanced materials with higher strength to mass ratios could enable larger area rotors to be cost-effective. Nano Carbon tube based composites could enable larger rotor blades.
Figure (1.7): Growth in size of the rotor diameter of wind turbines [31]
The aerodynamic efficiency is lower on a two bladed rotor compared to a three bladed rotor, thus, the rotation speed needs to be higher so as to achieve the same power as that of the three bladed rotor. The two and single bladed rotors need a special kind of arrangement that is hinged or teetering hub. Each time the rotor passes the tower and in 9
order to avoid heavy shocks, the rotor is to tilt away. Also the arrangement can have balance issues and in time the blades are bound to hit the tower during operation. The three bladed rotors are effective to use the yawing mechanism in them. Analysis of blades using wind tunnel would be possible for small scale rotors, but the increase in diameters has called for the use of computational fluid dynamics (CFD) for fluid flow over blades and prediction of loads.
1.5 Modern Wind Turbine Today, the most common design of wind turbine is the horizontal axis wind turbine (HAWT). That is, the axis of rotation is parallel to the ground. The major components of a HAWT are shown in Figure (1.8), for which the most important include: The rotor: blades and hub Drive train: including shafts, gearbox, brake system and generator Nacelle: housing and yaw system Tower and foundation Electrical and control system
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Figure (1.8): Major components of a horizontal axis wind turbine [Manuel, j.F, 2009].
The main options in wind machine design and construction include [Mathew, s, 2006]: Number of blades (commonly two or three) Rotor orientation: downwind or upwind of tower Blade material, construction method, and profile Hub design: rigid, teetering, or hinged Power control via aerodynamic control (stall control) or variable-pitch blades (pitch control) Fixed or variable rotor speed Orientation by self-aligning action (free yaw), or direct control (active yaw) Synchronous or induction generator (squirrel cage or doubly fed) Gearbox or direct drive generator. 11
Figure (1.9): Detailed view of wind turbine components [32] 1.5.1 Rotor The rotor consists of the hub and the blades for the wind turbine. These components are often considered the most important in terms of performance improvement and cost efficiency. Nowadays, most designs have three blades and some manufacturers have included pitch control for the angle of pitch (rotated blade) as it can be observed in Figure (1.9). Some intermediate sized turbines have fixed pitch, especially in Denmark [Man well wileysons, 2009]. The turbine blades are manufactured from composite materials including fiberglass reinforced plastic, epoxy and wood laminates.
1.5.2 Drive train The drive train is composed of the rotating components of the wind turbine. As it can be observed in Figure (1.9), these include the low-speed and high-speed shaft, gearbox, and the generator. Some smaller components are also included such as bearings and couplings. A gearbox is used in order to transfer the mechanical power from the 12
low-speed shaft, which is connected to the rotor to a high-speed shaft, which will have a suitable angular velocity (rpm) to drive a generator. It must be noted that due to the fluctuating nature of the wind, the structural loads are dynamic and loads vary on the components of the drive train.
1.5.3 Generator The vast majority of wind turbines use induction generators. This type of generator operates at a slightly higher range of speeds than synchronous speed, such as a four-phase generator has a 1800 rpm in a 60 Hz grid. Induction generators are solid, inexpensive, and easy to adapt to the electrical grid [Man well wily sons, 2009].
1.5.4 Nacelle The nacelle includes the housing for the wind turbine interior components, as well as the yaw system. The housing cover helps protect the components from weather conditions. As it can be observed in Figure (1.9), the yaw system consists of a gear drive along with a motor. The purpose of this system is to rotate or control the orientation of the wind turbine with respect to the wind direction. The wind direction is specified by a sensor mounted outside, as the wind vane that can be seen in Figure (1.9). Figure (1.9) also shows the brake assembly which is used to keep the nacelle in the desired position.
1.5.5 Tower and foundation Wind turbine towers are manufactured from steel tubes, trusses or concrete towers. The ratio between rotor diameter and tower height is typically 1 to 1.5. It is to be noted that the tower height is also dependent on the geography and weather conditions of the site where it is installed. Moreover, the structural stiffness of the tower is of great importance due to the induced vibrations from the rotor due to unsteady wind loads.
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1.5.6 Electrical and control system The components related to this system are typically the following [Manwell wileysons, 2009]: Sensors: speed, position, flow, temperature, current, voltage, etc.. Controllers: mechanical mechanisms, electrical circuits. Power amplifiers: switches, electrical amplifiers, hydraulic pumps, and valves. Actuators: motors, pistons, magnets, and solenoids. Intelligence: computers, microprocessors.
1.6 Wind Turbine Blade Modification Many wind turbine sites have a restriction on the rotor diameter in one form or Other. In those cases, the only way the power production can be optimized at any specific wind velocity is through maximizing the power coefficient of the wind turbine. Adding a winglet to the wind turbine blade improves the power production without increasing the projected rotor area. This is done by diffusing and moving the wing tip vortex (which rotates around from below the blade), away from the rotor plane, reducing the downwash and thereby the induced drag on the blade the winglet converts some of the otherwise wasted energy in the wingtip vortex to an apparent thrust.
1.7 Overview of Thesis Chapter 1 (Current chapter), reviews the general background of wind energy and wind turbine. Chapter (2) reviews the wind turbine research and the relevant literature. It also presents the research aim and objectives and scope of this research. Chapter (3) describes the fundamental theory of wind turbines. A description of the actuator disc theory and Blade Element Momentum (BEM) theory is also given. Chapter (4) describes the numerical modeling process through CFD simulation of the wind turbine blades. Chapter (5) describes the experimental facilities utilized in this research. It also presents a detailed description of the instrumentation, test equipment, data processing and 14
experimental test setup. Chapter (6) presents and discusses the results obtained from both experimental investigation and computational modeling. Chapter (7) discusses the general and specific conclusions of the research and outlines the recommendations for further study.
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Chapter (2) Literature Review 2.1 Introduction Rotor blades of horizontal axis wind turbine are the most important part in the hub system. The performance of wind turbine depends on the configuration and geometry of blades because it's responsible for extracting kinetic energy from wind. As blades have aerofoil shape and this aerofoil shape gives certain lift and drag coefficients, so, certain power can be extracted from wind. Many researchers have studied the wind turbine rotor aerodynamics. Intense research on the wind turbine rotor aerodynamics was done during the past three decades. A lot of researchers interested in modification of the geometry and shape of blades itself to achieve the best performance of wind turbine.
2.2 Wind Turbine Rotor 2.2.1 Experimental Studies on Wind Turbine Rotor Kamada et al. [2008] conducted field experiments on 10 m diameter horizontal axis wind turbine to measure unsteady aerodynamic loads. The pressure distributions were measured at four radial locations of the rotating wind turbine blade. Sectional aerodynamic forces were analyzed from pressure distribution. Blade root moments were measured simultaneously by a pair of strain gauges. The relation between the aerodynamic moments on the blade root from pressure distribution and the mechanical moment from strain gauges were discussed. Fluctuation in blade root moment for field wind turbines was excited by changes in aerodynamic forces for non-stalled operation. The dominant frequency of the root moment is the same as the rotational frequency. For stalled operation on a local blade section, the dominant frequency of the root moment was the first mode oscillation of the blade. Dan-mei and Zhao-hui [2009] investigated experimentally the properties of the near wake behind the rotor of a horizontal-axis wind turbine (HAWT). 3D velocity was measured at nine axial locations of the wind turbine rotor for various tip speed ratios. In upstream wind along with the axial direction, the radial and circumferential 16
velocities of the free stream would be very small as compared to axial velocity component. Axial velocity ratio at five axial locations behind the horizontal axis wind turbine revealed the expansion and decay of the wake velocity defect. The width of the wake increased with increasing the downstream axial distance. The axial velocity ratio decreased with the increasing downstream axial distance. During the downstream development of the wake, the location of the wake shift was in the positive circumferential direction, as it was opposite to that of the rotor. The turbulence levels in the wake were higher than those in the non-wake region. A significant increase in turbulence intensity was reported in the region of wake centerline. The turbulence levels in the wake were higher than those of in the nonwake region. Adaramola and Krogstad [2011] reported the experimental investigation of the wake effects on wind turbine performance. Two similar model turbines with the same rotor diameter were used. The results presented in their paper showed that the power losses for a turbine operating in the wake of another were significant. The reduction in power and thrust coefficients for the downstream turbine was a result of the velocity deficit in the wake so that the downstream turbine faces a considerable lower free-stream velocity than the upstream turbine and thus, less energy was available in the flow. However, by adjusting the tip speed ratio of the upstream turbine, the power output from the downstream turbine can be substantially increased. Systematically controlling the operating conditions of the upstream wind turbine, the overall performance of a wind farm can be improved significantly. Chen et al. [2011] conducted blockage corrections in wind tunnel test for small horizontal-axis wind turbines. This research provides quantitative results for the effect of tunnel blockage on the power coefficients of small horizontal-axis wind turbines in wind tunnel tests under different tip speed ratios, rotor pitch angles, tunnel blockage ratios and air free-stream velocities. Results indicate that the blockage factor was largely dependent on tip speed ratio, blockage ratio and pitch angle and weakly dependent on free-stream velocity. The blockage effects increase when tip speed ratio and blockage ratio increase, and when rotor pitch angle decreases. The 17
blockage correction of turbine power coefficient was 31% for pitch angle 50 0 and blockage ratio was 28.3%. The tunnel blockage effect was small for small tip speed ratio (TSR), and blockage ratio (BR) approached a constant value at a certain TSR, at which the point blades acted like a solid wall. This study also shows that no blockage correction is necessary for pitch angle 250 and the blockage correction is less than 5% for blockage ratios less than 10% and for tip speed ratio less than 1.5. Kumar et al, [2016] changed the wind turbine blade material from epoxy glass to epoxy carbon to improve the wind turbine performance. The modeling and the static and dynamic structural analysis was carried out by using ANSYS software. The static analysis results indicated that epoxy carbon material undergoes the minimum deformation of 729 mm as compared to the other material epoxy glass. The Minimum Von-misses stress of 0.035 MPa was observed in epoxy carbon material as compared to the other material. From strength and stiffness point of view, epoxy carbon materials performing better than the other material considered in their work Shuwa et al. [2016] studied experimentally the performance of a 1.5 m long horizontal-axis wind turbine blade on a 4 meter tower using 8 o as an angle of attack. They designed the blade using the Blade Element Momentum Theory (BEM), and determined the blade parameters such as the chord length, angle of attack, tip speed ratio, rotor diameter, and lift and drag force. The designed blade profile was developed and tested on an open field at Maiduguri (Nigeria) where the average wind speed was 3.89 m/s. Their results showed that the maximum extractable power was 142.66 W from 5m rotor diameter at a wind relative velocity of 4.8 m/s when the blade was at 8o angle of attack and 3 106 Reynolds Number. The measured power increased consistently with the increase of wind speed.
2.2.2 Computational Studies on Wind Turbine Rotor Kale and Sapali [2009] determined the blade parameters, such as chord and thickness distributions along the blade for one mega–watt (MW) wind turbine on the basis of strength and aerodynamics. The blade geometry was based on the modified NACA 63-621 and FX 66S-196 series profiles. The cylindrical profile was selected 18
near the blade root for easy connection with rotor hub and to assure the structural strength on the inner part of the blade. Kulunk and Yilmaz [2009] explained a design method based on the blade element momentum (BEM) theory for horizontal–axis wind turbine (HAWT) blades. The method was used to optimize the chord and twist distributions of the blades. They applied their method to generate a 100kW HAWT rotor. Their computer program estimated the aerodynamic performance of some existing HAWT blades. Tenguria et al. [2011] designed a horizontal–axis wind turbine blade with the help of Glauert's optimal rotor theory and developed a computer program for getting the chord, thickness and twist distributions while maintaining the lift coefficient constant throughout the blade. The wind turbine blade was divided into 19 sections and each section had the same length. Blade is modeled with ANSYS software with airfoil NACA 634–221. First analysis of the blade was done with the spar of square shape and for the validation of their results; they were compared with experimental work. A new shape of spar of combined shape (box and cross) was used for a second analysis and the results showed that the deflection of cap and web reduced at both root and transition segment. Abdel Gawad [2012] developed a new airfoil with spherical leading-edge tubercles of NACA0012. His study was based on numerical simulation of the effect of tubercles on the flow characteristics around the airfoil using standard k model. The diameter of each tubercle was 10% of the airfoil chord and the spanwise distance between the centerlines of two adjacent tubercles was 20% of the airfoil chord. A wide range of angle of attack was tested; from 00 to 250 and the values of Reynolds number ranged between 65,000 and 1,000,000. The numerical scheme was validated using the well-known results of the standard NACA0012 profile (without tubercles). The results covered pressure distributions, streamline patterns, and lift and drag coefficients. The spherical tubercles were superior in comparison to the wavy tubercles in many aspects of being easier to manufacture, lighter in weight, and ability to control. There was a penalty that may have to be paid when using tubercles that appeared in the increase of values of CD in comparison to regular-airfoils. 19
Chandrala et al. [2012] carried out a study concerning the aerodynamic efficiency of wind turbine blade when tested in wind tunnel. They selected NACA 4420 airfoil for analysis. CFD analysis of HAWT blade was carried out at various blade angles with help of ANSYS CFX software. Their computational results were compared with experimental results. They stated that HAWT efficiency is highly– dependent on the blade profile and its orientation. Prathiban et al. [2014] studied the effect of airfoil thickness on pressure distribution in wind turbine blade. They carried out computational simulation by using commercially available CFD software with the angle of attack ranged from (-40 to 250). Their study was dependent on NACA 4415 as a basic airfoil blade for wind turbine. Other airfoils NACA 23012 and NACA 63-413 were compared with the basic one according to the stall angle and lift to drag ratio. The results showed that NACA 4415 was the best in lift to drag ratio but the best one for stall angle was NACA 63-413 since in the wind turbine blade designs, every cross section was twisted to around 40 degrees. So, optimum performance at higher angle of attack was required. Thus, based on that point, modern low-speed aerofoil series NACA 63-413 was the optimum choice. Srinivas et al [2014] carried out aerodynamic performance of wind turbine blades using computational fluid dynamics (CFD). The wind turbine blade was modeled and several sections were produced from root to tip. The coefficient of Lift and drag was calculated for wind turbine blade for the different angle of attacks 0° to 60. The coefficient of lift increased with the increase in angle of attack up to 140. The drag force began of dominate beyond this angle of attack. The rate of increase in lift was more for angles of attack from 00 to 60 and between zero0 to 60; the rise in lift force was less. They found that the blade with 5° angle of attack had the maximum L/D ratio. Chaudhary and Roy [2015] presented the design and optimization of the rotor blade performance for a 400W small wind turbine at the lower values of operating wind speed based on blade element momentum theory (BEM). The main focus was on the relationship between solidity, pitch angle, tip speed ratio, and maximum power 20
coefficient. In their study, airfoil SG 6043 was selected. Their studies were conducted for variable chord and twisted blade with solidities in the range of 2% to 30% and blade numbers 3, 5, 7, 12, and 15 with rotor diameter of 2 m. These values of blade geometry parameters that were generated in MATLAB were exported to Q–Blade software to give results in terms of power coefficient curve CP . Hence, maximum power coefficient was obtained for the solidity in the range of 3% to 12% for a number of blades of 3, 5, and 7. Derakhshan and Tavaziani [2015] investigated aerodynamic performance of wind turbines. Flow around wind turbine was simulated with Navier-Stokes equations using three different turbulence models (Spalart–Allmaras, K and SST K ) and results were compared with experimental data. According to numerical results, at 5 m s to 10 m s wind speeds (low speeds), the three turbulence models had similar
predictions in power. But at higher wind speeds, K predicted with more accuracy, thus, K was the best between the three models. Based on their results, they suggested K Launder Sharma turbulence model using Hakimi precondition for the prediction of performance of horizontal–axis wind turbines. Hu et al. [2016] studied computationally the feasibility of improving blade power by applying vortex generators to large variable propeller shaft horizontal–axis wind turbines 2 MW . Three different chord wise installation positions of vortex generators were designed according to transition and separation lines at the blade root. Calculation results showed that the blade aerodynamic power increased by 0.6% . It could be seen from the vortices contours in the different downstream span wise position of vortex generators that it was not appropriate to install vortex generators with the same size in different positions of blades. Their results indicated that it was feasible to improve aerodynamic power by applying vortex generators to large variable propeller shaft wind turbines. Mostafa et al. [2016] studied the dynamic behavior of aerodynamic, mechanical and electrical parts of customized variable–speed variable–pitch wind turbine equipped with a permanent magnet synchronous generator. They investigated Aeolos 50 kw wind turbine, drive train, and permanent magnet synchronous 21
generator using simulating software Matlab/simulink. Two controllers for blade pitch angle and torque generator were investigated to guarantee the output power almost constant. Their strategy appeared better than classical approaches according to rotor speed and output power. Nigam et al. [2017] suggested CFD analysis of wind turbine blade using ANSYS Fluent 12.0 software with airfoil NACA 63 -221 profiles. They used k- SST model analysis for obtaining lift coefficient, drag coefficient and pitching moment at different angles of attack. The results obtained from simulation were compared with experimental results. It was found that lift coefficient, drag coefficient and pitching moment increased with the increase in angle of attack. It was also found that the pressure at lower surface of airfoil is more and velocity is higher on the upper surface of airfoil. Henriques et al. [2009] designed a new urban wind turbine airfoil using a pressure load inverse method. The pressure distribution of the designed blade section showed a smooth increase in the blade pressure load, defined as the pressure difference between the upper and lower sides of the section, from the leading edge up to 20% of the axial chord. From 20% up to 80% of the axial chord, the pressure load was almost constant and it reduced smoothly towards, the trailing edge. The experimental testing of the new blade section, as an isolated airfoil, confirmed the high maximum lift and a moderate drag. Their future developments would consider the application of the current design method with an optimization of the thickness distribution for viscous flow. Due to the specification of the blade load, their methodology would reduce the drag without changing the lift. Tenguria et al. [2010] represented investigation of blade performance for a 5 kW horizontal-axis wind turbine based on blade element momentum theory. Two NACA airfoils (NACA 4412 and NACA64-218) were taken for the comparative calculation of elemental power coefficient and other parameters such as chord, thickness and twist distribution. The airfoil taken for designing the blade is the same from root to tip. Stresses are Maximum at the blade root. the blade root was the thickest portion of the blade and twist was maintained such that the angle of attack 22
would be maximum at every station of the blade. In the designed blade, the elemental power coefficient was Maximum in transition segment where r/R varies from 0.3 to 0.6. Their method was useful for predicting the performance of the wind turbine blade. Cao [2011] studied the aerodynamic characteristics of small horizontal- axis wind turbine blades using 2D and 3D CFD modeling. In this study, the SpalartAllmaras turbulent viscosity, the dimensionless lift, drag and pitching moment coefficients were calculated for wind-turbine blade at different angles of attack. In three-dimensional wind turbine modeling, the innovated root design gave a significant power output increase and tapered tip design had a better ability for noise reduction. Wind turbine rotational effect could be simulated by using sliding mesh approach and the wake could be reported once the wind turbine rotated. In the far field, aerodynamic noise could be simulated by using large eddy simulation (LES) approach. This turbulent model gave a better physical representation of the eddy dynamics than Reynolds-Average Navier-Stocks (RANS). Dai et al. [2011] studied the aerodynamic loads for large wind turbine based on modified BEM theory with dynamic stall model. A set of coordinate system was established to describe larger scale wind turbines. Then, combining BEM modified theory with dynamic stall model, the calculation models of blade aerodynamic loads for MW scale wind turbines were proposed, including edgewise moment, flap wise moment, pitch moment, edgewise force and flap wise force, etc. A practical way of calculation and analysis for aerodynamic loads was proposed in their work. The aerodynamic loads were influenced by many factors such as tower shadow, wind shear, dynamic stall, tower and blade vibration, etc, with different degree; the single blade endures periodical changing loads but the variations of rotor shaft power caused by all blade aerodynamic loads was very small. Wu and Porté-Agel [2011] presented some efforts to develop and validate a large-eddy simulation (LES) framework for wind energy applications. Three types of models were used to parameterize the turbine induced forces: a standard actuator disk model without rotation that computed an overall thrust force and distributed it 23
uniformly over the rotor disk area; an actuator disk model with rotation that computed the local lift and drag forces and distributed them on the rotor disk area; and an actuator line model that distributed those forces along lines that followed position of the blades. The proposed LES framework was validated against high resolution velocity measurements collected in the wake of a miniature wind turbine placed in a wind tunnel boundary layer flow. The model overestimated the average velocity in the center of the wake, while underestimating the turbulence intensity at the top tip level, where turbulence levels were high due to the presence of a strong shear layer. The actuator-disk model with rotation (ADM-R) yields more accurate predictions of the different turbulence statistics in the near wake region. In the far wake, all three models produced reasonable results. Kwon et al. [2012] developed a numerical optimization technique to enhance the wind turbine aerodynamic performance. Considering very long and slender horizontal-axis wind turbine rotor blades, the effect of three-dimensional aerodynamic features was neglected, and the blade airfoil section configuration was optimized at selected span-wise stations of the blade. Their design frame work was applied to optimize the blade airfoil section of the NREL phase IV rotor blade. The optimized airfoil sections were reconfigured to reconstruct a three-dimensional rotor blade, and the performance of the optimized rotor blade was predicted by using a three-dimensional flow solver. Their results were compared with those of the original baseline rotor blade to demonstrate the capability of their methodology. It was found that approximately 11% of the torque enhancement was obtained from their aerodynamic shape design optimization. Bai et al. [2013] designed a horizontal-axis wind turbine (HAWT) blade with 10,000 Watt power output using the blade element momentum theory using S822 blade profile. The design conditions of the turbine blade in order to display the linear distributions of pitch angle in each section include the rated wind speed, design tip speed ratio and design angle of attack that were set to 10 m/s, 6 and 6°, respectively. They developed an improved BEM theory including Viterna Corrigan stall model, tip-loss factor and stall delay model for predicting the performance of the designed 24
turbine blade. Their investigations of aerodynamic characteristics were performed by three-dimensional CFD simulation using the Reynolds-Averaged Navier-Stokes (RANS) equations combined with the Spalart-Allmaras turbulence model. The simulation results were compared with the improvd BEM theory at rated wind speed of 10 m/s and showed that the CFD was a good method on aerodynamic investigation of a HAWT blade. Hsiao et al. [2013] studied the performance of three different shapes of horizontal-axis wind turbine blade by using experimental and computational methods. The model that was studied had 0.72 m diameter with airfoil profile of NACA 4418. The three different shapes of blade were tested as, first shape, optimum blade shape (OPT) using blade element momentum theory (BEM), second shape, untapered and optimum twist (UOT) blade shape with the same twist distribution as the OPT blade, third shape, un-tapered and untwisted (UUT) blade. The experimental data referred that both (OPT) and (UOT) blades performed the same power coefficient of 0.428 but it located at different speed ratio as (OPT) at tip speed ratio of 4.92 and (UOT) at tip speed ratio of 4.32 but (UUT) blade had maximum of 0.21 at tip speed ratio=3.86. Also, three-dimensional simulation applied for optimization by using CFD (k-ω) SST turbulence model. The results referred that the best shape was (OPT) and the lowest performance shape was (UUT) because it worked at stall conditions. Kumar et al. [2013] studied experimentally and computationally a single rotor and a counter rotor wind turbine using NACA 0012 and NACA 4415. Computational calculations used standard K- SST turbulence model. A parametric study on axial distance between two rotors was also investigated by CFD. It was founded that when axis distance increased to the rotor, the performance of (HAWT) and its power would increase for a counter rotor, so, it lead to increase efficiency. It was observed that for 0.65 d (d was the diameter of the primary rotor) the power increased by 10% for a wind velocity of 10 m/s. Kale and Varma [2014] represented functional design and aerodynamic design of an 800 mm long blade of 600 W horizontal-axis micro wind turbine using 25
NACA4412 profile. They determined the blade parameters such as chord and twist angle distributions of the preliminary blade design. They carried out optimization of enhancement of power performance and low-speed starting behavior. They developed MATLAB programming for the blades and drawn the power coefficients curves for the optimized wind turbine. The chord of optimized blade was reduced by 24% and thickness was reduced by 44%. Coefficient of power of optimized blade was increased significantly up to 30% than that of normal blade. Sessarego and Wood [2015] described a computer method to allow the design of small wind turbine blades for the multiple objectives of rapid starting, efficient power extraction, low noise, and minimal mass. Four materials were used for chosen model that were blades of 1.1 m length were designed to match a permanent magnet generator with a rated power of 750 W at 550 rpm. The materials considered were (i) traditional E-glass and polyester resin; (ii) flax and polyester resin; (iii) a typical rapid prototyping plastic, ABS-M30; and Timber. Two airfoils SG6043, and SD7062 were chosen with thicknesses 10% and 14%, respectively. They founded that the blade chord and twist increased as starting was given greater importance. Materials (I), (ii), and (IV) were better suited to the SG6043 airfoil whereas ABS-M30 benefited from the thicker SD7062 section.
2.3 Wind Turbine Rotor with Winglet 2.3.1 Experimental Studies on Wind Turbine Rotor with Winglet Gertz and Johnson [2011] investigated the 3.3 m diameter variable speed wind turbine with exchangeable blade tip capability. Power produced by the blades was determined as a function of the input wind speed. The coefficient of power was determined as a function of the tip speed ratio. Peak power coefficient was found to approach 0.42 at the design tip speed ratio of 6.7. At the design shaft speed of 200 rpm, the maximum power produced was 1.45 kW at 11 m/s. Experimental results were compared with model predictions and the model predicted the performance fairly accurately for tip speed ratio greater than 6.5, whereas the model was less successful at predicting power coefficient accurately at low tip speed ratio. This 26
region corresponded to the airfoil post-stall region where prediction was known to be challenging. Saravanan et al. [2012] studied experimentally the effect of the winglets at the blade tip of the wind turbine. They found that the pressure difference between the pressure and suction surfaces increased in the presence of winglet. Also, they stated that the pressure difference increased as the winglet height increased or the curvature radius of winglet decreased. The winglet with height 4% of the rotor radius and radius of curvature 25% of winglet height gave more pressure difference at the tip region of the blade which can improve power output. Belferhat et al. [2013] performed an experimental study for the flow around an isolated wing equipped by a winglet and profiled with NACA 0012. They tested several cases of winglets according to the cant angle of 0°, 55°, 65°, and 75° with velocity of 20, 30, and 40 m/s. They observed that the aerodynamic performance of the winglet with the cant angle 55° differs favorably for positive angle of incidence compared to the other cases. Saravanan et al. [2013] studied experimentally the power performance of small horizontal-axis wind turbine rotor with winglets at the tip of the blade. The blades with four different configurations of winglets, with and without load conditions in the wind tunnel for various conditions, were investigated. The maximum power coefficient obtained for an effective winglet configuration was about 0.43. They observed that the presence of winglet improved the power coefficient for low wind speed regions. They recommended that the smaller curvature radius with sufficient winglet height captured more wind energy in low wind speed region in comparison to wind turbine rotors without winglets. Aravindkumar [2014] investigated experimentally and computationally the power performance and noise level of a small wind turbine blade with and without winglet. In the experiments, the output power of generator was increased by about 2.01% and noise level was reduced by 25% in the winglet blade compared with the blade without winglet. The winglet was designed using Pro/E software and 27
experimental performances of the blades were compared with the results of CFD analysis using fluent software. Tobin et al. [2015] performed wind tunnel experiments to investigate the effects of downstream-facing winglets on the wake dynamics, power and thrust of a model wind turbine. Two similar turbines with and without winglets were operated under the same conditions. Results showed an increase in the power and thrust coefficients of 8.2% and 15.0% , respectively, for the winglet case. 2.3.2 Computational Studies on Wind Turbine Rotor with Winglet Imamura et al. [1998] investigated computationally the effect of winglets on a wind turbine rotor. They changed the cant angle from 80 0 to a 00 (equivalent to a radial extension). Their results showed that a winglet positioned close to 90 0 from the plane of the rotor was most effective at increasing power coefficient. Elfarra et al. [2014] investigated the aerodynamically design and optimization of a winglet for a wind turbine blade by using computational fluid dynamics and its effect on the power production. For validation and as a baseline rotor, the National Renewable Energy Laboratory Phase VI wind turbine rotor blade was used. The numerical results showed a considerable agreement with the experimental data. The genetic algorithm was used as the optimization technique with the help of artificial neural network (ANN) to reduce the computational cost. In the winglet design, the variable parameters are the cant and twist angles of the winglet and the objective was the torque. The final optimized winglet showed around 9% increase in the power production. Johansen and Sørensen [2006] investigated the aerodynamics around a wind turbine rotor with winglets numerically by using computational fluid dynamics (CFD). Ten different winglet configurations were designed and their mechanical power and thrust production were investigated. Adding winglet to the existing blade can change the downwash distribution leading to increased power, but a load analysis was necessary to verify whether the increased thrust can be accepted. Finally, they reported that mechanical power and thrust increased as curvature radius decreased 28
and winglet height increased. Sweeping the winglet 30° backwards did not increase mechanical power and small dependence on winglet tip twist was reported. Jian-Wen et al. [2007] simulated the effects of pressure distribution of wind turbine blade with a tip vane numerically. The tip vane brought the great influence on the pressure distribution of the wind turbine. The pressure difference between pressure surface and suction surface was increased. The tip vane increased the pressure on the pressure surface and decreased the pressure on the suction surface. More pressure difference increase was found at the tip and no difference was noticed at the root. The position of the maximum thickness of airfoil, the pressure difference between the pressure and suction surface were found to be maximum. The pressure difference between the pressure surface and the suction surface of the blade increased the force, so that the blade could absorb more wind energy. Ferrer and Munduate [2007] discussed the effects of wind turbine blade tip geometry which was analyzed numerically using CFD. Three tip geometries were investigated based on changes along with the radius and a change for a fixed radial station. The tip shape modifies the radial flow leading to 3D effects which were affecting the local loading. A higher suction for the outboard part due to higher momentum was being moved towards the inboard sections, which could lead to a local transfer of momentum. At the sweptback tip, increased normal force component was reported due to the presence of span-wise flow component towards inboard part. Lanzafame and Messina [2009] proposed a mathematical model for a double pitch wind turbine with non-twisted blades. The simulated results were compared using NREL data from the NASA-Ames wind tunnel tests and simulated power coefficient was in good agreement with experimental power coefficient. The mathematical model enabled the wind turbine power coefficient in the design wind speed to be maximized and the wind turbine performance in all the off-design operating conditions to be evaluated. The two blade parts were connected using a plate shaped like an aeronautical winglet to Minimise tip vortex. Chattot [2009] studied the effects of blade tip modifications on a wind turbine performance using vortex model. The sweep, dihedral, and winglet were used. The 29
backward sweep had increased more power capture than forward sweep. The forward dihedral was very efficient to increase power than backward dihedral. Winglets were efficient in increasing the power capture up to 3.5%. Sivaraj and Raj [2012] investigated computationally the effect of pointing the winglet towards the suction side (downstream). They designed a rectangular modification of the original blade tip and compared it with the winglet cases. This blade modification produced power more than the original blade and less than winglets. All upwind pointing winglets had lower thrust compared to the rectangular blade tip, while the downwind pointing winglet had higher thrust. Based on their investigation, the best overall power performance was that of the upwind pointing winglets with the increase in power of about 1.3% for wind speeds larger than 6 m/s and the increase in thrust of about 1.6%. Manikandan and Stalin [2013] used Pro/E hypermesh software to design wind turbine blade using NACA 63-215 airfoil profile. They used the design parameters of the winglet as height, radius, and cant angle. They considered a range of variation for the cant angle from 10° to 90°. The radius between the turbine blade and the winglet varied from 10% to 100% of the height of the winglet. The height of the winglet changed from 1% to 2% of the rotor radius. The original turbine blade and the modified blade with the winglet were compared for their designs. Sanke and Sawadi [2015] investigated computationally the aerodynamic performance of the wind turbine by adding winglets at the tip of the blade using ANSYS Fluent 14.5. NACA 4415 airfoil profile was considered for the analysis of the wind turbine blade. The modified blades decreased the total drag force, the generation pressure, and the vortex created at the tip of the blade. According to thier results, the best winglet angle was 45°. Sawadi and snake [2015] investigated computationally the performance of wind turbine with and without winglet at the tip of the blade. The calculation showed that when using blades with winglet 45° at air velocity 8 m/s, the pressure was decreased by 2% compared to blade without winglet. The force at blade tip with 30
winglet was decreased by 27 N compared to the blade without winglet and the velocity at the tip blade of wind turbine was approximately the same in both cases. Devit [2016] investigated the design and analysis of winglets for wind turbine rotor blade with varying the sweep and cant angles of the attached winglets. Thereby, employing the winglet, wingtip vortices can be reduced to a great extent. Winglets were designed and placed at different angles. He showed that winglets can effectively improve the performance of a conventional wind turbine blade. Premalatha and Rajakumar [2016] studied computationally the aerodynamic characteristics for small wind turbine rotor blades with and without winglet using ANSYS Fluent 14.5 software. The results showed that increasing winglets height and decreasing curvature radius increase the power coefficient. Zhu et al. [2017] studied computationally the extraction of energy of a horizontal-axis wind or marine current turbine model with a fusion winglet. They deduced that added winglet generally promised a positive influence on the turbine energy extraction performance, and its effectiveness was enhanced with the increase of turbine's tip speed ratio. They stated that the design of winglet facing to both sides of the blade can produce much more power than that of the winglet facing only one side for different blade hub pitch angles and vast majority of tip speed ratios. Also, they mentioned that the optimization of the winglet design parameters may further increase the horizontal-axis turbine performance.
2.4 General Remarks It is observed from the above literatures that there is not much work that was done on winglets for wind turbines. Only few researchers had reported that they carried out the work on tip vanes for horizontal-axis wind turbine. Johansen et al. [2006] investigated the aerodynamics around the wind turbine rotor with winglets numerically by using computational fluid dynamics (CFD). Adding winglet to the existing blade can change the downwash distribution leading to increased power. Also, he reported that mechanical power and thrust increases as curvature radius decreases and winglet height increases. Ferrer et al. [2007] discussed that the three 31
different rotating blade tip effects of wind turbine blade tip geometry was analyzed numerically using computational fluid dynamics (CFD). Lanzafame et al. [2009] outlined the wind turbine blade connected using a plate shape like an aeronautical winglet to Minimise tip vortex. Chattot [2009] developed a design code to study the effects of blade tip modifications on a wind turbine blade and also reported that winglets were efficient in increasing the power capture up to 3.5%. Johansen [2010] described the numerical investigation of the aerodynamics around a wind turbine rotor with winglets using computational fluid dynamics (CFD). The present work included both experimental and computational studies for the same turbine. The dimensionless parameters such as power coefficient and thrust coefficient of wind turbine blades with and without winglets are estimated. Correlations for power coefficient with and without winglet are deduced and plotted.
2.5 Present Research Objectives From an examination of the prior work undertaken in this area, one may conclude that there are significant gaps in understanding of winglet geometry on aerodynamic efficiency of small-scale wind turbine blades. Thus, the main objectives of this study are to: 1. Design a small horizontal-axis wind turbine blade using blade element momentum (BEM) theory. 2. Analyze the flow field around the horizontal-axis wind turbine by numerically solving the governing equations using a finite-volume method and ReynoldsAveraged Navier-Stokes (RANS) approach. 3. Calculate the power extracted by the wind turbine computationally and experimentally. 4. Understand the effect of winglet geometric configuration on aerodynamic efficiency (lift to drag ratio) of small-scale HAWT. 5. Investigate the impact of winglet height and cant angles on aerodynamic performance. 6. Develop power curve for small-scale wind turbine with and without winglet. 32
In order to achieve the aforementioned objectives, a comprehensive work would be undertaken using experimental investigation and computational modeling.
33
Chapter (3) Aerodynamics of Horizontal-Axis Wind Turbine And Present Parametric Case Study 3.1 Introduction Wind turbine blades are shaped to generate the maximum power from the wind at the minimum cost. Primarily the design is driven by the aerodynamic requirements, but economics mean that the blade shape is a compromise to keep the cost of construction reasonable. In particular, the blade tends to be thicker than the aerodynamic optimum close to the root, where the stresses due to bending are the greatest. The blade design process starts with a “best guess” compromise between aerodynamic and structural efficiency. The choice of materials and manufacturing process will also have an influence on how thin (hence aerodynamically ideal) the blade can be built. For instance, prepared carbon fiber is stiffer and stronger than infused glass fiber. The chosen aerodynamic shape gives rise to loads, which are fed into the structural design. Problems identified at this stage can then be used to modify the shape if necessary and recalculate the aerodynamic performance
3.2 How Blade Capture Wind Power Just like an aero-plane wing, wind turbine blades work by generating lift due to their shape. The more curved side generates low air pressure while high pressure air pushes on the other side of the aerofoil. The net result is a lift force perpendicular to the direction of flow of the air, as shown in Figure (3.1a). The lift force increases as the blade is turned to present itself at a greater angle to the wind. This is called the angle of attack. At very large angles of attack, the blade “stalls” and the lift decreases again. So, there is an optimum angle of attack to generate the maximum lift as shown Figure (3.1b).
34
(a) Lift and Drag on airfoil.
(b) Different angle of attack. Figure (3.1): Flow around airfoil [30].
There is, unfortunately, also a retarding force on the blade; the drag. This is the force parallel to the wind flow, and also increases with angle of attack. If the aerofoil shape is good, the lift force is much bigger than the drag, but at very high angles of attack, especially when the blade stalls, the drag increases dramatically. So, at an angle slightly less than the maximum lift angle, the blade reaches its maximum lift/drag ratio. The best operating point will be between these two angles. Since the drag is in the downwind direction, it may seem that it wouldn‟t matter for a wind turbine as the drag would be parallel to the turbine axis, so, wouldn‟t slow the rotor down. It would just create “thrust”, the force that acts parallel to the turbine axis hence has no tendency to speed up or slow down the rotor. When the rotor is stationary (e.g., just before start-up), this is indeed the case. However, the blade‟s own movement through the air means that, as far as the blade is concerned, 35
the wind is blowing from a different angle. The relative wind velocity is higher than the wind velocity and has another direction angle, so, lift and drag forces based on the relative wind speed different from that forces based on wind speed in magnitude and direction. It also means that the lift force contributes to the thrust on the rotor as shown in Figure (3.2). The result of this is that, to maintain a good angle of attack, the blade must be turned further from the true wind angle.
Figure (3.2): Wind angles and blade angle on airfoil [padmaja et.al,2013]
3.3 Blade Twist For some modern wind turbines, the blade tips are designed using a thin airfoil for high lift to drag ratio, and the root region is designed using a thick version of the same airfoil for structural support. The crucial factors for choosing airfoil are; maximum lift to drag ratio and low pitch moment. Note that in order to achieve the maximum lift and efficiency for some long blades, not only the chord length, thickness and twisted angle change, but also the shape of airfoil varies along the blade. Manufacturing difficulty needs to be taken into account as well. Previously, the most popular aerofoil of certain rotor diameter wind turbine blade was NACA4412 shown in Figure (3.3) since the lower surface of this aerofoil is flat which is easy to manufacture with glass fiber, although it does not
36
have a good air performance. Nowadays, many practical airfoils have been designed for different wind turbines such as NREL, DU and BE series.
Figure (3.3): NACA 4412 airfoil The closer to the tip of the blade you get, the faster the blade is moving through the air and so the greater the apparent wind angle is. Thus the blade needs to be turned further at the tips than at the root, in other words it must be built with a twist along its length. Generally, the twist in wind turbine blade is around 10-20° from root to tip. The requirement to twist the blade has implications on the ease of manufacture. Figure (3.4) shows the mean of twisted sections in turbine blades.
Fig (3.4) : Twist at different (r/R) of turbine blade [padmaja et.al,2013]
3.4 Blade Section Shape Apart from the twist, wind turbine blades have similar requirements to aeroplane wings, so, their cross-sections are usually based on a similar family of shapes that shown in figure (3.5). In general, the best lift/drag characteristics are obtained by an aerofoil that is fairly thin: its thickness might be only 10-15% of its “chord” length (the length across the blade, in the direction of the wind flow). 37
Figure (3.5): Sample airfoils used in wind turbine blade [Hansen, M, 2013].
3.5 Airfoils and General Concepts of Aerodynamics Airfoils are structures with specific geometric shapes that are used to generate mechanical forces due to the relative motion of the airfoil and a surrounding fluid. Wind turbine blades use airfoils to develop mechanical power. The cross-sections of wind turbine blades have the shape of airfoils. The width and length of the blade are functions of the desired aerodynamic performance, the maximum desired rotor power, the assumed airfoil properties, and strength considerations. Before the details of wind turbine power production are explained, aerodynamic concepts related to airfoils need to be discussed.
3.5.1 Airfoil Terminology A number of terms are used to characterize an airfoil, as shown in Figure (3.6). The mean camber line is the locus of points halfway between the upper and lower surfaces of the airfoil. The most forward and rearward points of the mean camber-line are on the leading and trailing edges, respectively. The straight line connecting the leading and trailing edges is the chord line of the airfoil, and the distance from the leading to the trailing edge measured along the chord line is designated the chord, c, of the airfoil. The camber is the distance between the mean camber line and the chord line, measured perpendicular to the chord line. The thickness is the distance between the upper and lower surfaces, also measured perpendicular to the chord line. Finally,
38
the angle of attack, , is defined as the angle between the relative wind U rel and the chord line [50].
Figure (3.6): Airfoil Nomenclature.
Not shown in the figure is the span of the airfoil, which is the length of the airfoil perpendicular to its cross-section. The geometric parameters that have an effect on the aerodynamic performance of an airfoil include: the leading edge radius, mean camber line, maximum thickness and thickness distribution of the profile, and the trailing edge angle.
3.5.2 Lift, Drag and Non-dimensional Parameters Air flow over an airfoil produces a distribution of forces over the airfoil surface. The flow velocity over airfoils increases over the convex surface resulting in lower average pressure on the „suction‟ side of the airfoil compared with the concave or „pressure‟ side of the airfoil. Meanwhile, viscous friction between the air and the airfoil surface slows the air flow to some extent next to the surface.
39
Figure (3.7): Forces and moments on an airfoil section.
As shown in Figure (3.7), the resultant of all of these pressure and friction forces is usually resolved into two forces and a moment that act along the chord at a distance of c 4 from the leading edge (at the „quarter chord‟) [Manwell etal, 2009] Lift force: defined to be perpendicular to direction of the incoming air flow. The lift force is a consequence of the unequal pressure on the upper and lower airfoil surfaces. Drag force: defined to be parallel to the direction of the incoming air flow. The drag force is due both to viscous friction forces at the surface of the airfoil and to unequal pressure on the airfoil surfaces facing toward and away from the incoming flow. Pitching moment: defined to be about an axis perpendicular to the airfoil crosssection. Theory and research have shown that many flow problems can be characterized by non- dimensional parameters. The most important non-dimensional parameter for defining the characteristics of fluid flow conditions is the Reynolds number. The Reynolds number Re is defined by: Re
U c U c
(3.1)
Where: the fluid density The fluid viscosity
40
The fluid kinematic viscosity,
c The airfoil chord U The wind speed
Additional non–dimensional zed force and moment coefficients, which are functions of the Reynolds number, can be defined for two–or three–dimensional objects, based on wind tunnel tests. Three–dimensional airfoils have a finite span and force and moment coefficients are affected by the flow around the end of the airfoil. Two-dimensional airfoil data, on the other hand, are assumed to have an infinite span (no end effects). Rotor design usually uses two-dimensional coefficients, determined for a range of angles of attack and Reynolds numbers, in wind tunnel tests. The two-dimensional lift coefficient is defined as: CL
L
(3.2)
1 U2 A 2
The two-dimensional drag coefficient is defined as: CD
D
(3.3)
1 U2 A 2
The pitching moment coefficient is: Cm
M
(3.4)
1 U2 Ac 2
Where: L Lift Force D Drag Force M Pitching Moment
c Airfoil chord A Airfoil Area Chord Span
Under ideal conditions, all symmetric airfoils of finite thickness would have similar theoretical lift coefficients. This means that lift coefficients would increase with increasing angles of attack and continue to increase until the angle of attack reached 90 degrees. 41
3.5.3 Airfoils for Wind Turbines Modern HAWT blades have been designed using airfoil „families‟. That is, the blade tip is designed using a thin airfoil, for high lift to drag ratio, and the root region is designed using a thick version of the same airfoil for structural support. Typical Reynolds numbers found in wind turbine operation are in the range of 500,000 and 10 million. Generally, in the 1970s and early 1980s, wind turbine designers felt that minor differences in airfoil performance characteristics were far less important than optimizing blade twist and taper. For this reason, little attention was paid to the task of airfoil selection. Thus, airfoils that were in use by the aircraft industry were chosen because aircraft were viewed as similar applications. Aviation airfoils such as the NACA 44xx and NACA 230xx were popular airfoil choices because they had high maximum lift coefficients, low pitching moment, and low minimum drag [Manwell etal, 2009]
3.6 Wind Turbine Aerodynamic theories The primary function of a wind turbine is to extract the kinetic energy from the wind. From the laws of physics, any object in motion possesses a kinetic energy. It is apparent that not all of the kinetic energy of the air can be extracted as this would indicate that there is no flow downstream of the wind turbine. If we were to separate the mass flow of air passing through the turbine from the mass flow which is not affected by the presence of the turbine, a boundary surface can be drawn containing the affected mass. This boundary is extended both upstream and downstream which forms a long stream tube as shown in Figure (3.8).
42
Figure (3.8): Wind energy extraction stream tube [Burton etal, 2001]
Between 1922 and 1925 German Physicist Albert Bertz, formulated a theory which predicted the maximum output that can be achieved by an ideal wind turbine. This theory has its limitation in terms of predicting the maximum power output. A number of assumptions is made to simplify the theory such as: (1) The flow is considered in viscid, incompressible and steady flow. (2) Velocity changes in the direction of rotor axis and is considered uniform flow in one dimensional. (3) There is no rotational flow or swirl in the wake. Like Albert Bertz, Glauert [Burton etal, 2001] introduced the Blade Element Momentum (BEM) theory which combines the momentum theory and the blade element theory [Burton etal, 2001] this theory allows the user to predict the performance characteristics of an annular section of the rotor.
3.6.1 Actuator Disc Theory (Axial Momentum Theory) The actuator disc model (theory) is the simplest form of analytical tool to determine the aerodynamic behavior of a wind turbine. It is based on the linear momentum theory and widely used to predict the performance of ship propellers. The control volume under this one-dimensional model shown in figure (3.9) comprises of a surface stream tube and two cross sections of the stream tube. The airflow is assumed to move across the ends of the stream tube. The turbine in this model is represented as a circular disc stationed in the middle of the stream tube. This model is 43
purely used to assess the overall efficiency of wind turbines. Note that this analysis is not limited to any particular type of wind turbine. This analysis uses the following assumptions: homogenous, incompressible, steady state fluid flow no frictional drag an infinite number of blades uniform thrust over the disc or rotor area a non–rotating wake the static pressure far upstream and far downstream of the rotor is equal to the undisturbed ambient static pressure
Figure (3.9): Actuator disc stream-tube[Burton etal, 2001]
Upstream of the disc, the stream-tube has a cross-sectional area smaller than that of the disc and an area larger than the disc downstream. The expansion of the stream-tube is because the mass flow rate must be the same everywhere. The mass of air which passes through a given cross-section of the stream-tube in a unit length of time is U A, where the air density is, A is the cross-sectional area and U is the flow velocity. The mass flow rate must be the same everywhere along the stream tube and so:
m1 m2 m3 m4
(3.5)
1 U1 A1 2 U 2 A2 3 U 3 A3 4 U 4 A4
(3.6)
44
Where: U1 The wind velocity As the total energy is different for both upstream and downstream, the Bernoulli‟s equation is applied to derive the equations. Bernoulli‟s equation states that the total energy in the flow which is made up of, kinetic energy, static pressure energy, and gravitational potential energy, remains constant given that there is no work done by the fluid [Manwell etal, 2009]. . Applying Bernoulli‟s theory at the upstream section of the stream tube ignoring the losses, we have: P1
1 1 U12 P2 U 22 2 2
(3.7)
The downstream section of the stream tube is given as: P3
1 1 U 32 P4 U 42 2 2
(3.8)
By applying the conservation of linear momentum to the control volume, we can determine the net force on the turbine. This force is equal and opposite to the thrust, T . Thrust is equivalent to the rate of change of momentum of the air stream. This can be written as: T U1 UA1 U 4 UA4
(3.9)
Assuming that P1 P4 , U 2 U 3 Thrust can be expressed as the net sum of forces on each side of the actuator disc: T A2 P2 P3
(3.10)
To obtain the pressure difference at both ends of actuator disc we have: P2 P1
1 1 U12 U 22 2 2
(3.11)
P3 P4
1 1 U 42 U 32 2 2
(3.12)
The pressure difference from the front and back of the turbine can be obtained and is given as: P2 P3
1 U12 U 42 2
(3.13)
45
If we substitute equation (3.13) into (3.10) we obtain: T
1 A2 U12 U 42 2
(3.14)
If we equate equation (3.14) to (3.9), we have: T mU1 U 4
1 A2 U12 U 42 2
(3.15)
A2U 2 U1 U 4
1 A2 U1 U 4 U1 U 4 2
(3.16)
U2
1 U1 U 4 2
(3.17)
The actuator disc induces a velocity in the stream tube which is represented by the axial induction factor a and is defined as the fractional decrease in wind velocity between the free-stream and the turbine plane. This is expressed as: a
U1 U 2 U1
(3.18)
U 2 U1 1 a
(3.19)
From equation (3.17) and (3.19), 1 U1 U 4 U1 1 a 2
(3.20)
U 4 U1 1 2a
(3.21)
The velocity distribution through a wind turbine as a function of wind speed can be shown in Figure (3.10)
Figure (3.10): Velocity distribution through a wind turbine. 46
The term U1a is referred to as the induced velocity at the turbine. The velocity of the wind comprises two velocities, the free-stream velocity and the induced velocity of the wind. An increase in the induction factor will result in the speed at the wake to slow down significantly. As the induction approaches a maximum value of 0.5, the wind speed at downstream of the disc is zero. Therefore, in order for the actuator disc theory to work, the speed of at the wake must be greater than zero. The power output produced by the turbine is equivalent to the thrust times the velocity at the disc. P
1 A2 U12 U 42 U 2 2
P
1 A2U 2 U1 U 4 U1 U 4 2
(3.22)
By substituting equation (3.19) and (3.21) into (3.22): P
1 A2U13 4a1 a 2 2
P
1 AU 3 4a1 a 2 2
(3.23)
Where: A the turbine swept area U The free stream velocity
The coefficient of power is non-dimensional value which is used to measure the efficiency of any particular turbine. It is obtained from dividing the power available in the wind by the power extracted by the turbine. The turbine power coefficient can be defined as: CP
CP
Turbine Power output Power in the wind
P
(3.24)
1 AU 3 2
Since C P represents the ratio of the turbine power output and the available power in the wind, we can express the power coefficient as: CP 4a 1 a
2
(3.25) 47
The maximum power coefficient can be determined when:
d CP 0 da
CP 4a 1 a
2
d CP 2 41 a 4a 21 a 1 0 da 12a 4
a
1 3
Then maximum power coefficient is: CP 4a 1 a
2
1 1 C P max 4 1 3 3 C P max
2
16 0.5926 27
(3.26)
From equation (3.26), the maximum power coefficient that can be achieved by an ideal turbine is known as Betz limit, named after the German aerodynamicist, Albert Betz. To achieve a power coefficient of 59%, the axial induction factor a must be equal to 1 3 . This means that the downstream wind velocity must be reduced to a third of the upstream wind velocity. The coefficient of thrust is also expressed as non-dimensional value. CT CT
Thrust Force Dynamic Force T
(3.27)
1 AU 2 2
Figure (3.11) represents both the power coefficient of an ideal turbine and the non-dimensional downstream wind speed or axial induction factor. The graph illustrates that the maximum efficiency of an ideal turbine is nearly 59% . This emphasizes that maximum efficiency can only be achieved if the axial induction factor is less than 0.4 . However, in real life, the maximum efficiency of a welldesigned turbine is quite lower than Betz limit. As for the thrust created, in practice, the thrust coefficient can exceed the ideal maximum. There are a number of effects which contribute to the decrease in efficiency of a wind turbine that is not taken into 48
account. This includes the fact that there is some drag which is present and is induced by the blades and losses at the tip.
Figure (3.11): The variation in C P and CT with axial induction factor [Manwell etal, 2009]. 3.6.2 Wake Rotation The linear momentum theory assumes that there is no rotation of flow at the wake of the turbine. However, in reality flow exiting from the turbine has constant rotation and gradually moves downstream. The torque applied on the turbine by the air moving through it requires an equal and opposite torque imposed upon the air. This causes the air to rotate in the opposite direction of the turbine. As the air flow gains momentum, the air particles move at downstream of the turbine consists of a velocity component not only in the axial direction but also in the tangential direction relative to the rotation of the turbine. The existence of a rotational flow in the wake results in less energy being extracted by the turbine and as a result losses in kinetic energy occur. The most vulnerable wind turbines with large kinetic energy losses that cannot be recovered are those operating at low rotational speed and high torque [Eggleston etal, 1987]. There are minimal losses however, for wind turbines which have a higher rotational speed and lower torque.
49
Fig. (3.12): Blade Element length dr at radius r.
Since the tangential velocity is not the same for all radial positions, the axial induced velocity varies. In order for changes to occur for both the tangential and axial induced velocity components, we must consider an annular ring of rotor disc with a radius (r) and of a radial width of r is considered as shown in Figure (3.12). It is also important to know that the angular velocity of the air relative to the blades increases from to where be the angular velocity of the turbine blade and is the angular velocity of the air flow in the wake.
The torque on the ring is equal to the rate of angular momentum of the air passing through the ring. Therefore: Torque mass flow rate change of tangential velocity radius Q A U 1 a 2 a / r 2
The
angular induction factor is defined as: a/
(3.29)
2
The induced velocity at the rotor comprises of the axial component Ua and r a / . Therefore thrust can be expressed as [Eggleston et al, 1987]. 1 dT 4a / 1 a 2 r 2 2 rdr 2
(3.30)
From linear momentum, the thrust of the rotor as a function of the axial induction factor is: 1 dT 4a 1 a ρ U 2 2π rdr 2
(3.31) 50
Equating equation (3.30) and (3.31) yields: a 1 a 2 r 2 2r a / 1 a / U 2
(3.32)
The tip speed ratio is defined as the ratio of the blade tips speed to the free stream wind speed and is expressed as:
R a(1 a) a (1 a) U
(3.33)
3.6.3 Blade Element Theory (BET) The Blade Element Theory is used to predict the forces acting on a blade through lift and drag forces generated at span wise of the blade sections. In this theory, the blade is divided into a number of sections in the span wise direction. Each section of the blade is independent of the other and operates aerodynamically as a 2D aerofoil. Using the local flow condition, the aerodynamic forces are calculated on each aerofoil at every section of the blade. The sums of all forces at each section are then accumulated to calculate the forces and moments that have been exerted on the turbine blade. There are a number of assumptions taken into account for the blade element theory. It is important to consider that there is no aerodynamic interaction between each element of the blade allowing no radial flow. It is also assumed that the forces on the blades are only determined by the lift and drag characteristics of the aerofoil shape of the blade. Figure (3.13) shows the sequence of the wind turbine blade divided into a series number of sections.
Figure (3.13): Wind turbine blade divided into a series number of sections. 51
In order to calculate the relative wind velocity at a section of the blade, both the axial and tangential velocities are combined. The resultant velocity is then used to calculate the lift and drag forces of each blade section. From Figure (3.14), a section of the wind turbine with (N) number of blades with a tip radius (R) and chord (c) is considered. Assuming that the blades are rotating at an angular velocity of , Let U be the wind speed and angle is the angle between the relative wind speed and the plane of rotation.
Figure (3.14): Velocities on blade element [Hansen ,2013] From the diagram shown in Figure (3.14), the velocity vector is represented as: U A U 1 a
(3.34)
U T r 1 a /
(3.35)
Where: U A Axial velocity of the wind U T Tangential velocity of the wind
The relative wind velocity can then be given as: W
U 1 a 2 Ω r1 a / 2
(3.36)
52
The angle at which the relative wind velocity coincides with the plane of rotation is given by: 1 a U 1 a tan 1 / / r 1 a 1 a r
tan 1
(3.37)
The angle of attack, which is defined as the angle between the chord line and the relative wind velocity and is given by:
(3.38)
Figure (3.15): Forces on blade element [Hansen ,2013]
As lift is the force produced that is perpendicular to the relative wind velocity and drag is the force parallel to the relative wind velocity. The relative wind velocity is utilized to calculate each of these forces acting on the aerofoil. The lift and drag forces are given as: 1 2
(3.39)
1 2
(3.40)
L C L A W 2 c r D CD A W 2 c r
The lift and drag forces acting on the aerofoil as depicted in Figure (3.15) is broken down into two components. The first component is the force in the plane of rotation and the other being the force perpendicular to the plane of rotation. The force in the plane of rotation yields the torque on the turbine and the forces perpendicular to the plane of rotation will result in thrust. The forces in both the plane of rotation and perpendicular to the plane of rotation are given us: FA L cos D sin
(3.41)
FT L sin D cos
(3.42) 53
3.6.4 Blade Element Momentum (BEM) Theory Blade element momentum theory is a combination of the blade element theory and momentum theory. This theory lays the foundation for an iterative process that calculates the induced velocities and aerodynamic forces of a wind turbine. Although the BEM theory is used in many applications, there are limitations which are made in order to make the theory simpler. It is assumed that the airflow around an aerofoil will always be in equilibrium and that the flow will accelerate to adjust to the changes in vortices at the wake region. The combination of equations (3.39) and (3.40) into equation (3.41) will result in total thrust of the turbine and is given as [Ali, 2014] T
1 W 2 B cCL cos CD sin dr 2
(3.43)
Like thrust, the total torque can be found by also combining equation (3.39) and (3.40) into (3.42) and this is given as: δQ
1 ρW 2 B c CL sin φ CD cos φ rdr 2
(3.44)
If we consider thrust to be the rate of change of linear momentum of the flow passing through an annulus at radius r of width dr and a tip loss factor of F , thrust is expressed as: dT 4π ρ r U 2 a1 a Fdr
(3.45)
As mentioned previously, torque is equal to the rate of change of angular momentum, with tip loss correction factor is given as: dQ 4π ρ r3 U a / 1 a Fdr
(3.46)
In order to obtain the values of both the induction factors a and a / , an iterative process using equation (3.45) and (3.46) must be solved. The right hand side of the equation below is evaluated using existing values of the flow induction factors. To solve for both the axial a and tangential a / velocities, we utilize equation (3.37) into both the torque and thrust equations. This will give us: C L C D tan a 1 a 4 F tan sin
(3.47)
C L C D tan a/ / 1 a 4 F tan sin
(3.48) 54
The blade solidity is defined as the total blade area divided by the rotor disc area and is equal to:
Bc 2 r
(3.49)
It is important to note that the BEM theory can only be applied if the blades have uniform circulation, that is if a is uniform. For a non-uniform circulation, there is a radial interaction and exchange of momentum between flows through adjacent elemental annular rings. 3.6.4.1 Power and Torque The extrapolation of both the power and torque depends on the flow induction factors. This can be obtained from the above equations of (3.47) and (3.48). The process of determining the induction factors is usually carried out through an iterative process. This iterative process is initiated by assuming both the induction factors a and a / to be zero. The first iterative process results in determining , C P and C D . This process is repeated many times until convergence is reached. Figure (3.16) shows a typical performance curve for a modern high tip speed ratio wind turbine. The graph illustrates that the maximum power coefficient occurs at a tip speed ratio of about 7. This corresponds to an axial induction factor that is closer to a value of 1 3 [Jamieson, 2011].
Figure (3.16): Performance curve of wind turbine blade [Jamieson, 2011].
55
3.6.4.2 Blade Geometry An important design feature of a wind turbine is the blade geometry as it is responsible for the extraction of kinetic energy from the wind. Optimising wind turbine blades is to maximize power output and efficiency. An optimal blade design is influenced by many factors such as its mode of operation. It is essential to determine whether the turbines would be operating as a fixed rotational speed or variable rotational speed, depending on the terrain. For a high tip-speed-ratio wind turbine, the geometry of the blade would require a long, slender blade. However, a low tip-speed-ratio wind turbine would be the opposite. It requires a short, thicker blade. Wind turbines cannot always operate at optimum tip-speed-ratio all the time but for a range of wind speeds, the turbines operate at different tip-speed-ratios. If the wind turbine were to operate at a tip-speed-ratio other than the optimum tip speed ratio, then the performance of the turbine would significantly be less than the optimum performance for which the turbine is designed for. To determine the distribution of the cross-sectional shape on the blade, a number of design parameters are required to satisfy the requirements of the BEM theory equation. Design parameters such as: tip-speed-ratio, the desired number of blades, the radius of the blade and an aerofoil for which the lift and drag characteristics are known as a function of angle of attack. Once these parameters are selected, it will result in the extrapolation of chord distribution and twist distribution of a blade which closely resembles the Betz limit power production ideal blade. If we assume that the axial and angular induction factors are a function of the radius r , from equation (3.31), applying the conservation of linear momentum, we can further express thrust as [Manwell etal, 2009]: dT U 2 4a 1 a rdr
(3.50)
The design goal of any wind turbine blade, even though it is impossible, is to try and replicate the Betz limit power production. To achieve Betz limit, the axial induction factor a must be equal to 1 3 . Therefore, it is assumed that the axial induction factor a is equal to 1 3 . By substituting the value of the axial induction factor a into equation (3.46), the result becomes: 56
1 1 8 dT U 2 4 1 rdr U 2 rdr 3 3 9
(3.51)
From equation (3.44), if we assume that C D is equal to zero, the equation becomes: dQ
1 2 U rel B c C L sin r dr 2
(3.52)
The relative velocity can be expressed in terms of other variables and is given as: W
U 1 a 2U sin 3sin
(3.53)
Determining the performance of wind turbine blades requires the combination of momentum theory and blade element theory equations. By equating equations (3.51) and (3.52) and utilizing equation (3.53), this yields: CL B c tan sin 4 r
(3.54)
To solve for the geometrical shape of the blade, we must first consider that equation (3.37) which relates to both axial induction and tangential factor. If we assume a 1 3 and a / 0 , then equation (3.37) becomes: tan
2
(3.55)
3 r
Where: r the tip speed ratio at fraction of rotor radius r R . CL B c 2 sin 4 r 3 r
(3.56)
Rearranging equations (3.55) and (3.54), we solve now for both the angle relative to the wind and the chord distribution along the radius of the blade. 2 3 r
tan 1 c
(3.57)
8 r sin 3B C L r
(3.58)
B Number of blades
C L Lift coefficient
Both equations (3.57) and (3.58) can be utilized to solve for the twist and chord distributions for a given angle of attack which corresponds to the highest lift to drag ratio. Figures (3.17) and (3.18) illustrate the optimum chord and twist distribution, 57
respectively, for a particular wind turbine in a non-dimensional form. It is worth noting that the chord at the root is significantly higher than at the tip. This enables the turbine to generate more torque at the root, thus, provide more power. The twist distribution in Figure (3.18) shows that the twist at the root is significantly high. This would represent a great deal of complexity in the manufacturing process. Therefore, the twist at the root would need to be decreased to a more reasonable value that would not complicate the manufacturing of the blade.
Fig. (3.17): Optimum chord distribution of wind turbine blade [Manwell etal, 2009].
Fig. (3.18): Optimum twist distribution of wind turbine blade [Manwell etal, 2009].
3.6.5 Tip Loss Correction The losses which occur at the tip of the blade cannot be ignored. The losses at the tip occur as a result of the pressure difference that is present between the lower 58
surface of the aerofoil and the upper surface of the aerofoil. The air particles generally have a tendency to move from the high pressure region to the lower region. At the tip of the blade this phenomenon takes effect and generally creates a vortex which dissipates into the wake. As a result of this vortex created at the tip, there are losses in the overall power output of the blade. In BEM theory, there are a number of methods which are applied to account for the losses. The most widely used method is the Prandt method which introduces a tip-loss correction factor. The correction factor is a function of the angle relative to the wind, number of blades and also the position of the blade. As the circulation of flow varies from root to tip, the tip-loss correction factor allows us to understand the reduction in forces along the blade. Figure (3.19) shows the tip loss factor of the radial blade from root to tip. The tip loss correction factor varies from 0 to 1. From the root of the blade to about 85 per cent of the blade radius, a constant factor of 1 is maintained.
Figure (3.19): Span variation of the tip loss factor of a wind turbine blade [To sun ,2005] However, at the tip the tip-loss factor sharply decreases as it approaches the tip. This corresponds to the fact that the induction factor increases dramatically near the tip. As a result, the relative wind speed for a given blade sections decreases as well as the angle of attack. This means the lift and drag forces generated at the tip must also decrease as they are a function of relative wind speed and angle of attack. The blade loss correction factor developed by Ludwig Brandt is given as [To sun, 2005]. Tip loss correction;
B2 r Rsinr 2 1 Ftip cos e
59
(3.59)
Hub loss correction;
B2 1sinr 2 1 Fhub cos e
(3.60)
r R
Where local radius;
Blade losses correction;
F Ftip Fhub
(3.61)
F is always between 0 and 1 . This tip loss correction factor characterizes the
reduction in the forces at a radius r along the blade that is due to the tip loss at the end of the blade. Figure (3.20) shows the iterative process involved in the BEM theory by an illustrative flow chart. Initially, both the axial and tangential induction factors are assumed zero. The flow angle is then calculated. This is the angle at which the relative wind velocity coincides with the plane of rotation. Using the flow angle, local angle of attack can be determined. In the BEM theory, the blade is divided into a number of segments and these segments are independent of each other and analyzed individually. Based on the 2D aerofoil type selected, both the lift and drag coefficients can be determined. The forces on each segment of the blade along the span are summed up to calculate the forces and moments subjected on the turbine.
60
From Qblade Software:
Inputs to FORTRAN
αdesign,CL , CD
Program: B, Ω, Ωair , dr, U, λ
Calculate from:
Choose guess values For a and a / (Guess=0)
1 a
1 a r
tan 1
No
\
Calculate the Solidity
Calculate from:
From:
Calculate a and a / from:
If values of a and a /
C L C D tan a 1 a 4 F tan sin
have changed by more than the target % from previous a and a
Bc 2 r
C L C D tan a/ 1 a/ 4 F tan sin
/
Yes
Calculate the local forces on each segment of the blade
Figure (3.20): Flow chart of BEM theory
61
3.7 Present Parametric Case Study The first step of wind blade design is to select the airfoil profile and obtain its design parameters. Figure (3.21) shows the NACA 4412 airfoil which is selected as an airfoil profile for a small wind turbine. The number 4412 corresponds to distinct characteristics of the foil, these characteristics are tabulated in Table (3.1) [Marten etal, 2013] Table (3.1): NACA 4412 characteristics NACA-4412 Maximum Thickness location
12% of the chord (Airfoil length)
Maximum Camber
4% of the chord (Airfoil length)
Location of maximum camber
40% of the chord (Airfoil length)
Lift and drag coefficients for NACA 4412 aerofoil are shown in Figure (3.22) and the ratio of lift coefficient to drag coefficient CL CD is shown in Figure (3.23). This plot obtained from Q–blade software which shows that for small values of angle of attack the aerofoil successfully produces a large amount of lift with little drag. At around 150 , a phenomenon known as stall occurs where there is a massive increase in drag and a sharp reduction in lift. The design point must be selected to achieve maximum lift coefficient and minimum drag coefficient. So, select the design point at maximum ratio of lift coefficient to drag coefficient CL CD max imum. From Figure (3.23), choose the design point for NACA 4412 airfoil as shown in table (3.2). Table (3.2) Designed parameters of NACA 4412 airfoil. Parameter Design Value Angle of attack design 5.850 CL, design 1.1106 Lift coefficient CD, design 0.00828 Drag coefficient CL CD design 134.13 Ratio between lift and drag coefficient In the previous section, the design of a HAWT blade was explained and the solution method was illustrated via the derived equations from BEM theory for NACA 4412 airfoil blade. The method of determining blade shape for optimum 62
performance of a turbine was developed using FORTRAN program, see Appendix (A). The geometry and configuration of the designed rotor is summarized in table (3.3) which shows that the rotor uses NACA 4412 airfoil profile at inboard, mid-span and outboard stations of the blades. The NACA 4412 profile is also uniquely defined by its coordinates. Table (3.3): Designed blade for NACA 4412 airfoil. Parameter Hub radius Tip radius Blade length Airfoil profile Mid–span airfoil Tip airfoil The blade is divided
Value Parameter Value 0.035 m Maximum chord 0.068710 m 0.35 m Maximum chord station 0.073293 m 0.315 m Number of blades 3 NACA 4412 Designed wind speed 6 m/s NACA 4412 Output power 27 W NACA 4412 Tip speed ratio 5 into 25 sections and geometry of airfoil parameters, which are
obtained at each section by FORTRAN program, is shown in Table (3.4). Table (3.4): wind turbine blade Geometry. r/R 0 .10000 0.13600 0.17200 0.20800 0.24400 0.28000 0.31600 0.35200 0.38800 0.42400 0.46000 0.49600 0.53200 0.56800 0.60400 0.64000 0.67600 0.71200 0.74800 0.78400 0.82000 0.85600 0.89200 0.94800 1.00000
r(cm) 3.5000 4.7600 6.0200 7.2800 8.5400 9.8000 11.060 12.320 13.580 14.840 16.100 17.360 18.620 19.880 21.140 22.400 23.660 24.920 26.180 27.440 28.700 29.960 31.220 33.080 35.000
Chord/R 0.196 0.208 0.207 0.200 0.189 0.178 0.166 0.155 0.146 0.137 0.128 0.121 0.114 0.108 0.102 0.097 0.092 0.087 0.082 0.077 0.072 0.066 0.059 0.049 0.036 63
Twist Angle 36.439 31.339 27.019 23.401 20.377 17.841 15.703 13.886 12.329 10.985 9.815 8.790 7.885 7.081 6.364 5.719 5.137 4.609 4.129 3.690 3.287 2.917 2.575 2.258 1.963
Figures (3.24) – (3.26) show the blade geometry at the wind speed of 6 m/s and the output power of 27W. Figure (3.24) shows the change of the airfoil chord length relative to the rotor tip radius from blade hub to blade tip. It is clear that the airfoil chord length is decreased from hub radius (hub chord=0.068710 m) to tip radius (tip chord=0.003 m). Figure (3.25) shows the change of relative wind angle through the blade length. The relative wind angle changes from hub radius (42.290) to tip radius (7.610). Figure (3.26) shows the change of blade twist angle of blade through the blade length. The blade twist angle changes from hub radius (36.440) to tip radius (1.720). Figure (3.27) shows both axial and radial induction factors along the blade length. Axial induction factor has a small increase from (0.298) at blade hub to (0.332) at blade tip. Angular induction factor decreases from (0.543) at blade hub to (0.009121) at blade tip. Figure (3.28) shows tip-losses correction factor along the blade length. Tip losses correction factor is almost constant (its value equal unity) along the blade from hub to 80% of blade height. But near blade tip, it decreases from (0.920) at 80% to (0.395) at blade tip. Figure (3.29) shows local thrust coefficient along the blade length. Local thrust coefficient is almost constant (its value equals 0.8) along the blade from hub to 80% of blade height. But near blade tip, it decreases from (0.8) at 80% to (0.350624) at blade tip. Figure (3.30) shows solidity ratio along the blade length. It is clear that the solidity ratio is decreased from (0.937) at blade hub to (0.0127) at blade tip. Figure (3.31) shows power coefficient with tip-speed ratio. The power coefficient is increased with increase of the tip-speed ratio till it reaches the maximum value (0.537) at tip-speed ratio (5), then power coefficient decreases with increase of the tip-speed ratio. Figure (3.32) shows three views for three–dimensional wind turbine blade profile.
64
0.25 0.2 0.15
Y(i) /Chord
0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
X(i) /Chord
Fig. (3.21): NACA 4412 airfoil profile. 0.28 Lift Coefficient Drag Coefficient
1.6
0.24
1.4
0.2
1 0.16 0.8 0.12 0.6
Drag Coefficient
Lift Coefficient
1.2
0.08
0.4 0.2
0.04
0 -4
-2
0
2
4
6
8
10
12
14
16
18
0 20
Angle of Attack (Degree)
Fig. (3.22): Lift and drag coefficients. 140 130 120
Gluide Ratio (CL/CD)
110 100 90 80 70 60 50 40 30 20 10 0 -4
-2
0
2
4
6
8
10
12
14
16
18
20
Angle of Attack (Degree)
Fig. (3.23): Ratio of lift coefficient to drag coefficient.
65
0.13 0.12 0.11
Chord Ratio (C(i)/Rtip)
0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.24): Airfoil chord distribution along the blade length. 44
Relative Flow Angle (Degree)
40 36 32 28 24 20 16 12 8 4 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.25): Airfoil relative wind angle along the blade length. 40
Twist Blade Angle (Degree)
36 32 28 24 20 16 12 8 4 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.26): Airfoil twist angle along the blade length.
66
0.55 Axial Induction Factor Angular Induction Factor
0.5 0.45
Induction Factors
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.27): Induction factors along the blade length. 1
Tip Losses Correction Factor
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.28): Tip losses correction factor along the blade length. 1 0.9
Local Thrust Coefficient
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.29): Local thrust coefficient along the blade length. 67
1 0.9 0.8
Solidity
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Radius Ratio (r(i)/Rtip)
Fig. (3.30): Solidity ratio along the blade length. 0.55 0.5
Power Coefficient (Cp)
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
1
2
3
4
5
6
7
8
9
10
Tip Speed Ratio (TSR)
Fig. (3.31): Power coefficient with tip speed ratio.
68
Fig. (3.32): Three–dimensional views of wind turbine blade.
69
Chapter (4) Governing Equations, Numerical Models, and Computational Aspects 4.1 Introduction In this chapter, the numerical study is conducted to simulate a three-dimensional wind turbine. The steady, viscous, and 3D governing equations (continuity and momentum) are described and solved together with SST k turbulence model. Moreover, numerical simulation for the wind turbine is explained. ANSYS Fluent 15 software provided by FLUENT Inc. is used to simulate the problem under consideration.
4.2 ANSYS Fluent (Finite -Volume Approach) The commercial code ANSYS Fluent solves the governing equations for the conservation of mass and momentum, and (when appropriate) for energy and other scalars, such as turbulence and chemical species. In both cases a control-volumebased technique is used [Van Bussel etal, 2005]. Discretization steps are as follows: • Division of domain into discrete control volumes using computational grid. • Integration of governing equations on the individual control volumes to construct algebraic equations for the discrete dependent variables (unknowns), such as velocities, pressure, temperature, and conserved scalars. • Linearization of the discredited equations and solution of the resultant linear equation system, to yield updated values of the dependent variables.
4.3 Numerical Solvers Fluent is a commercial 2D/3D mesh solver, which adopts multi grid solution algorithms. Two numerical solver technologies are available in Fluent: • Pressure-based solver • Density-based solver The first solver was developed for low-speed incompressible flows, whereas, the second was created for the high-speed compressible flows solution. In the present 70
study, which involves incompressible flows, the pressure-based approach was preferred. Both approaches are now applicable to a broad range of flows (from incompressible to highly compressible), but the origins of the density-based formulation may give it an accuracy (i.e., shock resolution) advantage over the pressure-based solver for high-speed compressible flows.
4.3.1 The Pressure-Based Solver The pressure-based solver employs an algorithm which belongs to a general class of methods called the projection method. In the projection method, the constraint of mass conservation (continuity) of the velocity field is achieved by solving a pressure (or pressure correction) equation. The pressure equation is derived from the continuity and the momentum equations in such a way that the velocity field, corrected by the pressure, satisfies the continuity. Since the governing equations are nonlinear and coupled to one another, the solution process involves iterations wherein the entire set of governing equations is solved repeatedly until the solution converges [FluentANSYS, 2009]. Fluent provides three different solver formulations: • Segregated • Coupled implicit • Coupled explicit The manner in which the governing equations are linear zed may take an "implicit'' or "explicit'' form with respect to the dependent variable (or set of variables) of interest. By implicit or explicit we mean the following: • Implicit: For a given variable, the unknown value in each cell is computed using a relation that includes both existing and unknown values from neighboring cells. Therefore, each unknown will appear in more than one equation in the system, and these equations must be solved simultaneously to give the unknown quantities [Fluent ANSYS, 2009]. • Explicit: For a given variable, the unknown value in each cell is computed using a relation that includes only existing values. Therefore, each unknown will appear in only one equation in the system and the equations for the unknown value in 71
each cell can be solved one at a time to give the unknown quantities [Fluent ANSYS, 2009]. All three solver formulations will provide accurate results for a broad range of flows. In some cases, one formulation may perform better (i.e., yield a solution more quickly) than others. The segregated pressure-based solver uses a solution algorithm where the governing equations are solved sequentially (i.e., segregated) from one another. The segregated algorithm is memory-efficient, since the discredited equations need only be stored in the memory one at a time. However, the solution convergence is relatively slow, in as much as the equations are solved in a decoupled manner. The pressure-based coupled algorithm solves a coupled system of equations comprising the momentum equations and the pressure-based continuity equation. The remaining equations (i.e., scalars) are solved in a decoupled fashion as in the segregated algorithm. Since, the momentum and continuity equations are solved in a closely coupled manner, the rate of solution convergence significantly improves when compared to the segregated algorithm. However, the memory requirement increases by 1.5 – 2 times that of the segregated algorithm since the discrete system of all momentum and pressure-based continuity equations needs to be stored in the memory when solving for the velocity and pressure fields (rather than just a single equation, as is the case with the segregated algorithm). By default, Fluent uses the segregated solver, but for high-speed compressible flows, highly coupled flows with strong body forces (e.g., buoyancy or rotational forces), or flows being solved on very fine meshes, one may want to consider the coupled implicit solver instead. For cases where the use of the coupled implicit solver is desirable, but your machine does not have sufficient memory, the segregated solver or the coupled explicit solver can be used instead. The coupled explicit solver also couples the flow and energy equations, but it requires less memory than the coupled implicit solver. It will, however, usually take longer to reach a converged solution than the coupled implicit solver. For this flow simulation, the coupled explicit pressure-based solver has been used. Scheme is a preferable choice for single phase implementation for steady flows [Fluent ANSYS, 2009]. 72
4.3.2 Density-Based Solver The density-based solver solves the governing equations of continuity, momentum, and (where appropriate) energy and species transport simultaneously (i.e., coupled together). Governing equations for additional scalars will be solved afterward and sequentially (i.e., segregated from one another and from the coupled set). In density-based solution method, one can solve the coupled system of equations (continuity, momentum, energy and species equations if available) using, either coupled-explicit formulation or the coupled implicit formulation. If you choose the implicit option of the density-based solver, each equation in the coupled set of governing equations is linear zed implicitly with respect to all dependent variables in the set. In the explicit option of the density-based solver, each equation in the coupled set of governing equations is linear zed explicitly [Fluent ANSYS, 2009].
4.4 Governing Equations The basic equations are conservation of mass, conservation of momentum, and conservation of energy. In addition to these basic equations, there are some other auxiliary equations. The basic equations are expressed in a fixed frame of reference. Accordingly, they are based on the absolute velocity formulation over the whole domain. These differential equations, for laminar flows, are expressed as follows[Fluent ANSYS, 2009]: 4.4.1 Mass conservation equation The mass conservation equation for steady flow is given by: ( Vi ) 0 xi
(4.1)
Where: Vi
: velocity in the i th direction
xi
: Coordinate in the i th direction
: air density.
i
:
tensor indicating 1, 2, 3. 73
The relative velocity Vr ,i in the rotating frame can be obtained by: For i =1
, j=1 , k= 1, 2, 3
J=2 , k=1, 2, 3
J=3 , k=1, 2, 3
Vr1 = v1- {e111 1x1+ e121 1x2+ e131 1x3+ e211 2x1+ e221 2x2+ e231 2x3+ e311 3x1+ e321 3x2+ e331 3x3} = v1 – [- 3x2- 2x3] = v1+ 3x2+ 2x3 = vx + z y+ yz For i =2
j=1 , k= 1, 2, 3
J=2 , k=1, 2, 3
J=3 , k=1, 2, 3
Vr2 = v2- {e112 1x1+ e122 1x2+ e132 1x3+ e212 2x1+ e222 2x2+ e232 2x3+ e312 3x1+ e322 3x2+ e332 3x3} = v2 – [- 1x3- 3x1] = v2+ 1x3+ 3x1 = vy + x z+ yx For i =3
, j=1 , k= 1, 2, 3
J=2 , k=1, 2, 3
J=3 , k=1, 2, 3
Vr3 = v3- {e113 1x1+ e123 1x2+ e133 1x3+ e213 2x1+ e223 2x2+ e233 2x3+ e313 3x1+ e323 3x2+ e333 3x3} = v3 – [ 1x2- 2x1] = v3- 1x2+ 2x1 = vz + x y+ yx
Vr ,i Vi e jki j xk
(4.2)
Where: j
: the angular velocity for the rotating frame in the j direction
xk
: coordinates in the rotating frame in the k direction.
j, k , i
: tensors indicating 1, 2, 3.
e jki
: the permutation symbol given by:
1 e jki 1 0
If j, k , i are in a repeating order as 1, 2, 3. If j, k , i are in different repeating order. If any two of j, k , i are equal.
4.4.2 Momentum conservation equation The conservation of momentum equation in the i th direction for unsteady flow can be written as follows [Fluent ANSYS, 2009] ij p ( ViV j ) g j x j xi x j
(4.3)
Where: p is the static pressure, and ij is the viscous stress tensor given by
74
Vi
ij
x j
V j xi
23 ij
Vl xl
(4.4)
where:
: is the absolute viscosity.
i, j , l
: are tensor indices indicating 1, 2, 3. 1 0
ij
if if
i j i j
g is the gravitational body force.
4.4.3 Auxiliary Equations The air viscosity is computed according to the Sutherland viscosity law. Sutherland’s law is expressed as follows [Fluent ANSYS, 2009]: T 0 T0
3/ 2
T0 S
(4.5)
T S
Where, = the viscosity in kg/m-s
T = the static temperature in K
0 = reference value in kg/m-s
T0 = reference temperature in K
S = an effective temperature in K (Sutherland constant)
For air at moderate temperatures and pressures, 0 1.7894 *10 5 Pa.s T0 273.11 K , S 110.56 K .
4.4.4 Turbulence Modeling Turbulent flow is characterized by fluctuating velocity field. The fluctuation mixes transported quantities such as momentum and energy, and causes the independent parameters fluctuate as well. The instantaneous governing equations can be time averaged to remove the small scales resulting in a modified set of equations that are computationally less expensive to solve. These modified equations contain additional unknown terms. The Navier–Stokes equations can be transformed to such a modified form by using Reynolds's averaging.
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4.4.4.1 Reynolds Averaging Of the Conservation Equations In Reynolds averaging, each solution variable in the instantaneous Navier– Stokes equations is decomposed into the mean (time averaged) and fluctuating components. Mathematically, it can be expressed as
\
(4.6)
Where is the time averaged value of , which is defined as
1 t t dt t t
(4.7)
And t is a time scale much larger than the largest time scale of turbulent fluctuations. The turbulent fluctuations are assumed to be random such that
\ 0
(4.8)
By substituting in the instantaneous continuity and momentum equations (4.1) and (4.3) and time integration over a sufficient time interval, yields the ReynoldsAveraged Navier-Stokes (RANS) equations. The continuity and momentum equations can be rearranged to take the following forms, respectively [FluentANSYS, 2009]: ( Vi ) 0 xi
(4.9)
p Vi V j 2 Vl ( ViV j ) g j ij Vi \V j\ x j xi x j x j xi 3 xl x j
(4.10)
The last two equations are the same as the instantaneous continuity and NavierStokes equations (4.1) and (4.3), with variables representing time averaged values instead of instantaneous values. An additional term representing the effect of turbulence, namely the Reynolds stresses
V V \
i
\ j
appeared in Navier-Stokes
equation (4.10). The main task of the turbulence model is to provide expressions or closure models that allow the evaluation of these Reynolds stresses in terms of mean flow quantities.
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4.4.4.2 Eddy-Viscosity Turbulence Models In the eddy-viscosity turbulence models, the Reynolds stresses are assumed to be proportional to the mean velocity gradients with the constant of proportionality being the turbulent viscosity this assumption, known as Boussinesq hypothesis. The Boussinesq hypothesis is employed to relate the Reynolds stresses to the mean velocity gradients by the following expression [FluentANSYS, 2009]: V V j 2 Vl 2 Vi \V j\ K ij t i 3 ij 3 xi xl x j
(4.11)
Where; k is the turbulent kinetic energy given by k
1 Vi \ 2 i
(4.12)
Equation (4.9) for Reynolds stresses is analogous to that describing the instantaneous shear stresses (equation (4.4)) with the turbulent viscosity t instead of the viscosity . Therefore, the form of the Reynolds averaged momentum equation; equation (4.10) remains identical to the form of laminar momentum equation (equation 4.3) except that is replaced by an effective viscosity eff , which can be expressed as a sum of both absolute and turbulent viscosities as: eff t
(4.13)
Then, equation (4-10) can take its final form as [FluentANSYS, 2009]: p ij eff ( ViV j ) g j x j xi x j
(4.14)
The stress tensor ij eff is calculated using effective viscosity eff and is given by
ij eff
V V 2 V eff i j eff l ij x j xi 3 xl
(4.15)
Eddy-Viscosity models include a number of classes. All of these models approximate the effect of the turbulence on the mean motion by introducing the effective viscosity as given in equation (4.13). The different classes of eddy viscosity models are distinguished by the number of additional differential equations that are solved to determine the turbulent viscosity. Dimensional analysis suggests that the 77
turbulent viscosity is the product of the density, a velocity scale and a length scale. The turbulent kinetic energy is used to obtain the velocity scale. A commonly used approach to determine the length scale is to develop a transport equation for the dissipation rate of the turbulent kinetic energy that is defined as
Vi\ Vi\ x j x j
(4.16)
Where: υ is the kinematic viscosity 4.5 Selection of Turbulence Modeling The available turbulence models in this version of ANSYS Fluent are: • Spalart -Allmaras model • K-ε models (standard, renormalization-group (RNG), realizable) • K-ω models (standard, sheer-stress transport (SST)) • Reynolds Stress models (RSM) • Large eddy simulation (LES) model The choice of turbulence model significantly affects the accuracy of the solution. Extensive research has been done to evaluate the turbulence models for the prediction of wind turbine aerodynamics. It was observed that the k SST turbulence model is one of the most suitable models for capturing the flow physics around the wind turbine blades because of its capability of considering all threedimensional secondary flow effects. Good predictions for the adverse pressure gradients and separating flow have been reported by researchers who employ k SST model. Based on these advantages this model was deployed. For the present
study the k SST model was chosen for all the simulations performed for the various blade designs. 4.6 Shear Stress Transport SST k Model The k turbulence model is again a two equation model one equation for the kinetic turbulent energy k while the second equation is for the specific turbulent dissipation rate . Similar to k , the k model has many versions. One of the most known one is the Wilcox k model [Versteeg et al, 1995].The Wilcox model 78
has Superior numerical stability to the k model especially in the viscous sub layer near the wall. However, the big disadvantage of the Wilcox model is that its results are extremely sensitive to the free-stream value of in free shear layer and adverse pressure gradient boundary layer flows. Therefore, the k does not seem to be an ideal model for applications in the wake region of the boundary layer. On the other hand, the k model behaves better in the outer portion and wake regions of the boundary layer. So a combination or blending of both of the models including the best feature of each one has been sought for. One of the results was the Shear Stress Transport SST k model [Elfarra, 2011] The two transport equations of the SST model are defined below: x j
k * k t Pk k x j
x j
1 k 2 k t Pk 21-F1 ρσ ω 2 x j k x j x j
(4.17)
And (4.18)
The constant * has value 0.09. The last term on the right-hand side of Equation (4.18) is a cross diffusion term that is activated only outside the boundary layer. F1 is the blending function which is designed to blend the model coefficients of the
original k model in the boundary layer zones with the transformed k model in free shear layer and free-stream zones. The constants appearing in Equations (4.17) and (4.18) are expressed in a general compact form as: F11 1 F1 2
(4.19)
where 1 represents the constants associated with the k model (when F1 1 ), and 2 represents the constants associated with the k model (when F1 0 ). Now, , k and defined by blending the coefficients as: Inner model constants: 1 0.5532 , 1 0.075 , k1 0.5 , 1 0.5 Outer model constants: 2 0.4403 , 2 0.0828 , k 2 1.0 , 2 0.856 The blending function F1 is defined by: 79
k 500 4 2 k , F1 tanhmin max * , 2 2 d d CDk d
(4.20)
1 k CDk max 2 2 , 1.0 e 20 x j x j
(4.21)
with:
and d being the distance to the nearest surface. For the k model, the boundary condition on the solid wall is as follow: Wall
16 1 d 2
(4.22)
kWall 0
(4.23)
4.7 Numerical Simulation The previous models for fluid flow are solved in this study using the commercial code ANSYS Fluent 15. This code is a general purpose computer program for modeling fluid flow, heat transfer and chemical reactions.
Fluent solves the
governing differential equations for the conservation of mass, momentum, energy and turbulence using a control-volume-based technique that consists of [Fluent ANSYS, 2009] 1. Division of the domain into discrete control volumes using an arbitrary computational grid. 2. Integration of the governing equations on the individual control volumes to construct algebraic equations for the discrete dependent variables such as velocities, pressure, temperature, and conserved scalars. 3. Linearization of the discredited equations and solution of the resultant linear equation system to yield updated values of the dependent variables. The Pressure-based segregated solver in the fluent software is selected to solve the air flow field .Each iteration consists of the steps illustrated in Figure (4.1) and outlined below. 1. Fluid properties are initialized and successively updated, based on the current solution.
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2. The momentum equation is solved in turn using current values for pressure and face mass fluxes, in order to update the velocity field. 3. Since the velocities obtained in Step 2 may not satisfy the continuity equation locally, an equation for the pressure correction is derived from the continuity equation and the linear zed momentum equations.
This pressure correction
equation is then solved to obtain the necessary corrections to the pressure and the face mass fluxes such that continuity is satisfied. 4. Equations for scalar quantities such as energy and turbulence are solved using the previously updated values of the other variables. 5. A check for convergence of the equation set is made Start
Read the geometry and grid Set the boundary conditions Initialization Solve the momentum equation and update the velocity field Solve the pressure correction equation and update velocity, pressure and face mass flux
Solve the turbulence, other scalar equations Update the flow field properties No Yes
Converged ?
Stop
Figure (4.1) the solution procedure flow chart. 81
4.8 Computational Cases Computations were performed using the ANSYS Fluent 15 software assuming a steady, incompressible and isothermal flow. 4.8.1 -Two Dimensional Wind Turbine Aerofoil NACA 4412 was modeled with chord length equal unity. Structured grids (C – type) were used in airfoil modeling for comparing of the accuracy of the simulation results. To allow the air flow to be fully expanded, the length of computational domain using structured grid was determined at 32.5 times that of the chord length, and the width was determined at 25 times that of the chord length as shown in figure (4.2).
Figure(4.2): Computational domain of NACA 4412 airfoil.(Not to Scale) To ensure grid – independency of the solution, computations were carried out for a wide range of the grid sizes (from 90,000 to 500,000 cells) at zero blade angle. The judging parameters were the lift and drag coefficients. From figure (4.3), it is clear that there is no change of the values of the lift and drag coefficients after the grid size of 450,000 cells.
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0.5
0.02 Lift Coefficient Drag Coefficient
0.48
0.019
0.46 0.018 0.017
0.42 0.4
0.016
0.38
0.015
0.36 0.014 0.34 0.013
0.32 0.3
Drag Coefficient (CD)
Lift Coefficient (CL)
0.44
0.012
0.28
0.011
0.26 100000
200000
300000
400000
0.01 500000
Mesh Size
Figure (4.3): Mesh Sensitivity.
Thus, the grid consisted of 450,000 quadrilateral cells. A large number of grid cells was concentrated around the aerofoil surface to capture the flow characteristics gradient accurately in the boundary layer. This is because the adverse pressure gradient induces flow separation. Stall occurs when separation region extends. In the far–field region, the mesh resolution becomes progressively coarser since the flow gradients approach zero. The meshing overview is shown in figure (4.4).
Air foil NACA4412 2
Pressure far filed
Inlet
Figure (4.4): NACA 4412 meshing using structured grid. 83
Pressure far-field boundary condition was used in the computational domain which is large enough. Aerofoil was treated as stationary–wall boundary condition with no slip shear condition. Steady simulations were carried out with viscosity 1.7894 105 kg m.s , air density 1.225 kg m3 , and wind speed 6 m s .
Shear-
stress transport SST K model was used because it absorbs both the property of good accuracy in the near-wall region of standard K model and nice precision in the far field region of K model.
4.8.2 Three-Dimensional Wind Turbine 4.8.2.1 Wind Turbine Rotor The chosen physical model of a horizontal axis turbine simulated in this thesis was designed using Blade Element Momentum theory as explained in chapter (3). The rotor radius is 350 mm with a hub radius of 35 mm, and the number of blades is three with design wind speed of 6 m/s. Figure (4.5) shows the wind turbine blade profile created by Gambit software to simulate wind turbine by CFD.
Figure (4.5): CFD wind turbine blade profile 84
4.8.2.2 Winglet Blade Model Many wind turbine sites have a restriction on the rotor diameter in one form or the other. In those cases, the only way the power production can be optimized at any specific wind velocity is through maximizing the power coefficient (C P) of the wind turbine. Adding a winglet to the wind turbine blade improves the power production without increasing the projected rotor area. This is done by diffusing and moving the wing tip vortex (which rotates around from below the blade), away from the rotor plane, reducing the downwash and thereby the induced drag on the blade. The winglet converts some of the otherwise wasted energy in the wing tip vortex to an apparent thrust. Five winglets with the same thickness of wind turbine blade tip airfoil were designed and analyzed based on the increase in produced power and thrust compared to the original rotor without winglets. Based on the results of the initial winglet design, each of the winglet parameters was varied for obtaining the most efficient winglet configuration. For all winglets, the curvature radius is equal to 1 mm with zero twist angle. The resulting design matrix is given in Table (4.1) with cant angle (the angle between the wind turbine blade and the winglet) is 90 0 for all cases of winglet. Table (4.1): Winglet data for CFD Case No.
Winglet name
1 2 3 4 5 6
Rotor W1 W2 W3 W4 W5
Winglet Height (% Radius) 0 1.0 2.0 3.0 4.0 5.0
Figure (4.6) shows the wind turbine blade profile with winglet at 90 0 created by Gambit software to simulate wind turbine by CFD.
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Figure (4.6): CFD wind turbine blade profile with winglet.
4.8.2.3 Computational Domain and Boundary Conditions 4.8.2.3.1 Computational Domain A complete three-dimensional computational fluid dynamic (CFD) analysis was performed for a rotor with three blades of 350 mm each. Because of similarity and for simplification, only one blade was considered. This was done for all cases without and with winglet. The goal for this CFD investigation was to find the torque generated due to the flow driving the wind turbine blade, which was used to determine the power output using the following equation: P T . . B
(4.1)
Where: P = the power generated in Watts T = the torque generated per blade in N.m = the angular velocity in radians/seconds
B = the number of blades of the wind turbine.
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A simplified computational domain was considered for the simulations with only one-third of the actual flow domain (120 degrees sector). This domain consisted of a single blade attached to the hub, as described in Figure (4.7). The computational domain was elongated to 5 times the radius in the upstream, which was equivalent to 1.75 m from the blade location and 5 times the radius in the downstream, which was equivalent to 1.75 m both the inlet and the outlet regions at upstream and downstream, which had a radius of 3R. The computational domain has been given uniform different axial velocity from inlet to the turbine and starting from turbine and extended to outlet was given a rotational speed, different for each wind velocity, about the axial direction. By keeping the blade at rest and setting the complete fluid volume to motion, this has the same effect as when the blade was in rotation, and is referred to as flow induced motion. This was done to avoid the complexity of dynamic meshing, which involves more computational power.
4.8.2.3.2 Boundary Conditions (BC) Once 3-D model for the wind turbine rotor and computational domain is created, the flow boundary conditions have to be specified. For obtaining accurate simulation results, it is very critical that these boundary conditions are specified properly. The following boundary conditions were used in the model:
Wall (no-slip) Wall boundary conditions (BC) are used to bound fluid and solid region. In our case the wall was considered as solid walls with no-slip and no-penetration conditions.
Velocity-inlet BC is used to specify the defined air flow velocity, along with all relevant scalar properties of the flow, like turbulent model at flow inlets. The total pressure is not fixed but will rise to whatever value is necessary to give the necessary velocity distribution. In Fluent this boundary condition is intended for incompressible flows 87
and it has to be kept as far away from a solid obstruction as possible. When a velocity inlet boundary condition is defined, Fluent computes the mass flow rate. Outflow Boundary conditions are used to model flow exits where the details of the flow velocity and pressure are not known prior to solving the flow problem. This boundary condition is appropriate where the exit flow is close to fully-developed condition. It assumes that there is a zero stream-wise pressure gradient for all flow variables except pressure.
Periodic Periodic boundary conditions are used when the physical geometry of interest and the expected pattern of the flow/thermal solution have a periodically repeating nature. By using a periodic boundary the number of grids can be reduced enabling finer grids.
Figure (4.7): Computational domain and applied boundary conditions.
4.8.2.4 Mesh Generation The accuracy of the CFD solution depends on the quality of the grid used to perform the calculations. Unstructured mesh was deployed along the computational domain, and a mesh refinement took place near the blade. Figure (4.8) shows the mesh constructed for the computational domain. Figure (4.9) shows the mesh generated for wind turbine blade without and with winglet.
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Figure (4.8): Computational domain mesh.
Figure (4.9a): Wind turbine blade without winglet.
Figure (4.9b): Wind turbine blade with winglet. Figure (4.9): Wind turbine blade mesh. 89
4.8.2.5 Mesh Sensitivity The grid-independency test was performed on all cases for wind turbine blade with and without winglet. The torque generated was selected as a factor to judge the grid-independency test results. Figure (4.10) shows the test results for the wind turbine blade for different test cases. The mesh statistics for different cases can be seen in Table (4.2).
0.1 0.098 0.096
Torque (N.m)
0.094 0.092 0.09 0.088 0.086 0.084 0.082 0.08
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Mesh Size (by million)
Figure (4.10a): Wind turbine rotor model grid-independency test (case1). 0.1 0.098 0.096
Torque (N.m)
0.094 0.092 0.09 0.088 0.086 0.084 0.082 0.08
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Mesh Size (by million)
Figure (4.10b): Wind turbine W1 model grid-independency test (case2).
90
0.1 0.098 0.096
Torque (N.m)
0.094 0.092 0.09 0.088 0.086 0.084 0.082 0.08
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Mesh Size (by million)
Figure (4.10c): Wind turbine W2 model grid-independency test (case3). 0.1 0.098 0.096
Torque (N.m)
0.094 0.092 0.09 0.088 0.086 0.084 0.082 0.08
1.6
1.8
2
2.2
2.4
2.6
2.8
Mesh Size (by million)
Figure (4.10d): Wind turbine W3 model grid-independency test (case4). 0.1 0.098 0.096
Torque (N.m)
0.094 0.092 0.09 0.088 0.086 0.084 0.082 0.08
1.6
1.8
2
2.2
2.4
2.6
2.8
Mesh Size (by million)
Figure (4.10e): Wind turbine W4 model grid-independency test (case5). 91
0.1 0.098 0.096
Torque (N.m)
0.094 0.092 0.09 0.088 0.086 0.084 0.082 0.08
1.6
1.8
2
2.2
2.4
2.6
2.8
Mesh Size (by million)
Figure (4.10f): Wind turbine W5 model grid-independency test (case6).
Table (4.2): Mesh statistics for different blade designs. Case
Number of mesh cells
Rotor
2,233,121
W1
2,592,230
W2
2,641,935
W3
2,666,655
W4
2,678,893
W5
2,687,321
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Chapter (5) Experimental Procedure 5.1 Introduction In this chapter, the details of the experimental procedures done to complete this study are explored. Manufacturing blade of horizontal-axis wind turbine represents the most important and difficult process in producing turbine. Manufacturing process depends on material selection, technique of manufacturing, durability, life time of blade and cost, etc. Techniques that are used in producing blades of (HAWT) are affected with size of turbine as for large wind turbines designing and producing blades can be easier than small-scale and models of wind turbine. Also, adding pitch control or twist for large scale (HAWT) blades has defined way than small-scale and models of wind turbine. Also, choosing suitable generator for large wind turbine may be easy in large scale wind turbines. As this study introduces experimental performance for model of (HAWT) and for achieving good performance, it's important to choose suitable manufacturing method to produce this model. In this study, Solid works software was used to draw the profiles and isometric of the blade models. Three-dimensional printer was used to manufacture these blade models.
5.2 Materials of wind turbine blades For large wind turbines certain materials can be used for manufacturing blades. Material selection seeks to durable and lighter material as weight has big effect on the blade inertia and stiffness of material affects the fatigue and shear loads on turbine blades. The most common material used in producing turbine blades in market is glass fiber due to its good mechanical properties. For small-scale models of wind turbines, several materials can be used for turbine blades like wood, PVC plastic, carbon glass, epoxy glass, aluminum, and galvanized steel or composite between different types of those materials. Three-dimensional printing is a new technology used for producing blade with correct design. In this technology, different types of material can be used like ABS, PLA, rubber, and
93
nylon. These materials are the most common material that can be used in threedimensional printing as each material has certain mechanical and thermal proprieties.
5.3 Wind Turbine Rotor Models 5.3.1 Wind Turbine Rotor The chosen physical model of a horizontal-axis turbine simulated in this section was designed using Blade Element Momentum theory as mentioned in chapter (3). The rotor radius is 350 mm with a hub radius of 35 mm, and the number of blades is three with design wind speed of 6 m/s. The main components of the wind turbine can be listed as follows: (1) Nose The nose has a hemispherical profile with radius 35 mm and was made from nylon material using three-dimensional (3D) printer. It enhances the aerodynamic performance over the turbine body and prevents stagnation at the turbine head. (2) Hub It is a straight shaft with radius 35 mm (10% rotor radius) and length of 10.5 cm. The hub has slots to fix the turbine blades and was made from nylon material. The 3D printer created the hub and nose as one piece as shown in figure (5.1).
Figure (5.1): Nose and hub of wind turbine model.
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(3) Blades The turbine model is equipped with three tapered twisted blades with length 31.5 cm. The profile shape was developed based on the widely used airfoil series NACA4412. The applied geometric airfoil parameters are shown in Table (5.1).
Table (5.1):- Wind turbine blade Geometry. r/R 0 .10000 0.13600 0.17200 0.20800 0.24400 0.28000 0.31600 0.35200 0.38800 0.42400 0.46000 0.49600 0.53200 0.56800 0.60400 0.64000 0.67600 0.71200 0.74800 0.78400 0.82000 0.85600 0.89200 0.94800 1.00000
r(cm) 3.5000 4.7600 6.0200 7.2800 8.5400 9.8000 11.060 12.320 13.580 14.840 16.100 17.360 18.620 19.880 21.140 22.400 23.660 24.920 26.180 27.440 28.700 29.960 31.220 33.080 35.000
Chord/R
Twist Angle
0.196 0.208 0.207 0.200 0.189 0.178 0.166 0.155 0.146 0.137 0.128 0.121 0.114 0.108 0.102 0.097 0.092 0.087 0.082 0.077 0.072 0.066 0.059 0.049 0.036
36.439 31.339 27.019 23.401 20.377 17.841 15.703 13.886 12.329 10.985 9.815 8.790 7.885 7.081 6.364 5.719 5.137 4.609 4.129 3.690 3.287 2.917 2.575 2.258 1.963
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For manufacturing wind turbine, there is a lot of material to do this. So, some trials were done to obtain a suitable material. First trial to choose material was PLA, which had good mechanical and excellent properties in printing diffusion. The produced rotor was very light with very good surface smoothing but with weak stiffness of blade tip. Small parts from the tip of the two blades broke due to centrifugal force and the test failed. ABS material was used for the second trial of manufacturing process of rotor hub and blades. Also, the same technique of joining rotor parts was used in the second trial. There were some problems at the tip of this rotor but its stiffness and surface quality after painting made it suitable for the experimental test. Parts of the blade were joined together and each blade was joined with the hub. When the wind speed reached to 5 m/s, a small part of one blade tip broke. Then due to centrifugal force and unbalanced rotor, all blades of rotor were broken and test failed as shown in Figure (5.2).
Figure (5.2): Damaged rotor blades after experimental test.
It was decided to repeat manufacturing process and choose more suitable material for these rotor blades. The values of forces calculated with dependence centrifugal, tangential and axial forces, components and static simulation applied by using solid works software to decide the best material that can be used. Four materials were selected for this static simulation. Three of them were materials that can be manufacturing on 3D printer. The other one was wood as a final 96
decision in case of repeated rotor damage in the experimental tests. The three materials that were chosen were PLA, ABS, and nylon. Nylon was the chosen material especially at the tip due to its flexibility to withstand the force components due to wind speed. The blades were made of nylon material. Each blade was created by the 3D printer as three parts to be suitable to the printer size. The three parts were joined together to form the complete blade as shown in figure (5.3).
Figure (5.3): Wind turbine blade parts from 3D printer.
The fixation method of blade parts It was decided to manufacture the blades of wind turbine by using 3D printing as this method can achieve perfect dimensions, geometry, and configuration. The available 3D printer had dimensions (23 14 15 cm3). These dimensions represent respectively length, width, and height. This machine called "dreamer" with double extruder and closed working space. So, it was decided to divide blade into three parts. It's important to realize that structural strength is very important for wind turbines. To achieve that, holes were done in the each part of the blade and steel pins were used to join parts together then, super glue was used to complete the joints by filling the clearance in the joint as shown in Figure (5.4). After joining the three parts of blade together, super glue added again above the regions of joints. Then, hardener and resin glue was putted above these jointed regions. Finally, spray paint was used to coat all the blade surfaces to achieve very smooth surface and support the joints. Between each process, it was very important to leave each chemical process at least five hours. 97
Figure (5.4): Fixation method of two parts of blade. Figure (5.5) shows the components used for joining the blade parts. Number (1) represents the main filling and adhesive chemical material that was used for joining parts together. Number (2) represents the adhesive super glue that used above jointed region after fixation with pins and super glue (1). Number (3) represents chemical material used for bonding jointed region as this material consists of hardener and resin that are mixed with each other to give very strong glue. This material was putted also above jointed regions. Number (4) represents steel pins used for joining blade parts. Finally, all surface of blade coating with painting.
Figure (5.5): Components used for joining the blade parts.
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Figure (5.6) shows two pictures of the wind turbine blade that was made by 3D printer
Figure (5.6): Experimental wind turbine blade. (4) Generator The wind turbine was connected directly to the generator. In this experiment, because the scale of this model is very small, there was a problem to find a small AC generator suitable for this application. So, a permanent magnet DC motor was used as generator. It has a rated voltage of about 30 volts as shown in Figure (5.7). Figure (5.8) shows the assembly of the wind turbine model which consists of nose, hub, three blades, and generator.
Figure (5.7): Permanent magnet DC motor used as generator.
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Figure (5.8): Wind turbine model.
Figure (5.9) shows two views of wind turbine blade with winglet that was fabricated by 3D printer. Figure (5.10) shows the assembly of the wind turbine model which consists of nose, hub, three blades with winglet, and generator.
Figure (5.9): Experimental wind turbine blade profile with winglet.
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Figure (5.10): Wind turbine model with winglet.
5.4 Experimental Setup and Procedure 5.4.1 Experimental Setup The experiments were carried out in a low-speed wind tunnel facility in Ain Shames University, Egypt, as shown in figure (5.11). This tunnel consists of centrifugal fan, diffuser, duct, air box, holder, and nozzle, table (5.4). The motor of the centrifugal fan is three-Phase AC motor with power factor equals 0.87 and rotational speed 1460 rpm with rated power of 40 hp, table (5.2). The nozzle exit cross-section is 100cm 100cm and its center is above the ground by 134 cm. The wind turbine blades are attached to the hub and this rotor-hub assembly is connected to the rotating horizontal shaft by roller bearings.
Figure (5.11): Wind tunnel facility and model. 101
Table (5.2): Dimensions of wind tunnel components Part specification
Cross section
Length
Air box
Surface area =150 150 cm2
b=203cm
Ducts (5)
Surface area =100 100 cm2
b=80cm
Diffuser
Exit=100 100 cm2
b=90cm
Inlet=50 70 cm2 Leather
Area= 50 70 cm2
b=12cm
Nozzle
Exit=100 100 cm2
b=80cm
Inlet= 150 150 cm2 Belt
Center length= 85 cm
Table (5.3): Specifications of the motor of the centrifugal fan type
Induction squirrel cage
Number of poles
4poles
Number of phase
3 phase
System of operation
delta
Volt (Δ/Υ)
380/660
Rated rotational speed
1460 rpm
frequency
50 HZ
Slip speed
0.028
Code
VDE 0530 (Germany)
Shaft has
2pully and 2 belt
Rated power
40 HP
The rotational speed of the turbine was monitored using a digital tachometer device (DT-6234B) [35]. This device uses a laser beam which is pointed at a refractor sheet. This sheet repels the laser beam per rotation and is monitored by an optical sensor. The tachometer was placed on the outside wall of the test section, at a constant location throughout the study. The refractor sheet was placed on the wind 102
turbine hub to reduce the experimental error. The air velocity in the wind tunnel test section was measured using a digital portable anemometer device, Figure (5.12) [34].
Figure (5.12): Digital portable anemometer device. 5.4.2 Experimental Procedure First, wind tunnel air was allowed to flow to the wind turbine blades that were connected directly with the generator. The wind speed that exits from the wind tunnel is controlled by a gate. In turn, the gate is controlled manually by a metal arm, Figure (5.13). The positions of the arm were calibrated to give certain amounts of wind speed. Usually, the wind tunnel was kept running for a period of time that was sufficient to reach steady state operation.
Figure (5.13): Arm to control air speeds.
103
Output of DC motor had two connections, one to the voltmeter to measure the output volt and the other to an electrical load. The electrical load was connected to an ammeter to measure the electric current. The electrical circuit components are shown in Figure (5.14).
Figure (5.14a): Drawing the electrical circuit components connected to the wind turbine.
Figure (5.14b): The electrical Figure (5.14c): Zoomed view of the electrical circuit components connected to circuit components. the wind turbine. Figure (5.14): The electrical circuit components used in the experimental study.
104
The test was applied for the wind turbine and data was tabulated in table (5.6) to obtain the performance of the wind turbine.
Table (5.4): wind turbine performance. U
m s
Current (I)
Volt (v)
P V I Watt
0.00
0
0
0
0
1.50
0
0
0
0
2.70
0
0
0
0
3.12
0.42
5.3
2.20
412
4.25
0.98
6.9
6.80
568
5.82
1.65
12.2
20.13
782
6.00
1.77
12.5
22.125
807
6.70
2.20
13.8
30.36
902
7.83
3.51
14
49.14
1055
8.00
3.67
14.2
52.16
1080
9.20
4.95
16.35
80.93
1240
105
N
rpm
Chapter (6) Results and Discussions 6.1 Introduction This chapter represents the results of the experimental and computational investigations for all cases. First, CFD validation with experimental results is presented, then, experimental results are illustrated, and finally, CFD results are presented. 6.2 CFD Validation with Experimental Results Figure (6.1) shows the power output from wind turbine rotor model (all cases) for both experimental and computational investigations. For the experiments, the output electrical power from the wind turbine was calculated from the relation: Pelec V I
(6.1)
Where V is the voltage and I is the current. It is clear, from Figure (6.1a) that the power output from the wind turbine increases by increasing the wind speed. From experimental curve, the wind turbine power is zero until the wind speed reaches (3.12 m/s) which is the cut-in speed. Calculations are stopped at wind speed of (9.2 m/s) which is the maximum air velocity that can be obtained from the wind tunnel. Figures from (6.1b) to (6.1f) show the power output from the wind turbine at different wind speeds for experimental and computational results at different winglet heights. In each case, the cut-in speed is still the same (3.12 m/s). From these figures, at a certain wind speed, both experimental and computational power is increased by increasing the winglet height. It is noticed that the computational results are slightly higher than the experimental results. This may be attributed to the operating losses of the experiments. Figure (6.2) shows the power output from the wind turbine for the six cases on the same graph from both the experimental and computational results. The computational power is within an error of 15% from the experimental power at the same wind speed expect before cut-in speed. Before cut-in speed (3.12m/s), the wind turbine power output from experimental is zero, so, the predicted computational 106
power is away from this value. This error ( 15% ) decreases considerably as the wind speed increases away from the cut-in speed. Figure (6.3a) shows variation of the rotational speed with wind speed of the wind turbine rotor model for both the experimental and computational investigations. After cut-in speed (3.12 m/s), the rotational speed from experiments is approximately similar to that of computations. Figures from (6.3b) to (6.3f) show the rotational speed of the wind turbine at different wind speeds of the experimental and computational. It's noticed in experimental measurements that RPM values have been measured but in the computational the value of RPM was been entered to CFD as a previous known data as the domain in CFD treated as rotating frame domain. Results for different winglet height attached at the blade tip. From these figures, it is clear that at any wind speed, the experimental rotational speed is increased by increasing winglet height. Figure (6.4) shows the rotational speed of wind turbine for the six cases on the same graph from both the experimental and computational results. The computational rotational speed is within an error 5% from the experimental rotational speed at the same wind speed expect before cut-in speed. Before cut-in speed (3.12m/s), the wind turbine rotational speed from experiments is zero, so, the predicted computational rotational speed is away from this value. This may be attributed to the fact that computations did not consider the inertial effect of the turbine mass. 90 Experimental Power Computational Power
80 70
Power (W)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.1a): Power from wind turbine rotor model (case1).
107
90 Experimental Power Computational Power
80 70
Power (W)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.1b): Power from wind turbine W1 model (case2). 90 Experimental Power Computational Power
80 70
Power (W)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.1c): Power from wind turbine W2 model (case3). 90 Experimental Power Computational Power
80 70
Power (W)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.1d): Power from wind turbine W3 model(case4). 108
90
Experimental Power Computational Power
80 70
Power (W)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.1e): Power from wind turbine W4 model (case5). 90
Experimental Power Computational Power
80 70
Power (W)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.1f): Power from wind turbine W5 model (case6). 100
80 5%
70
+1
5%
60 50
-1
Computational Power (W)
90
40 30 20 10 0
0
10
20
30
40
50
60
70
80
90
100
Experimental Power (W)
Figure (6.2): Computational power validated with the experimental power from wind turbine. 109
1300 Experimental Rotational Speed Computational Rotational Speed
Turbine Rotational Speed (rpm)
1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.3a): Rotational speed for wind turbine rotor model (case1). 1300 Experimental Rotational Speed Computational Rotational Speed
Turbine Rotational Speed (rpm)
1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.3b): Rotational speed for wind turbine W1 model (case2). 1300 Experimental Rotational Speed Computational Rotational Speed
Turbine Rotational Speed (rpm)
1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.3c): Rotational speed for wind turbine W2 model (case3). 110
1300 Experimental Rotational Speed Computational Rotational Speed
Turbine Rotational Speed (rpm)
1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.3d): Rotational speed for wind turbine W3 model (case4). 1300 Experimental Rotational Speed Computational Rotational Speed
Turbine Rotational Speed (rpm)
1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.3e): Rotational speed for wind turbine W4 model (case5). 1300 Experimental Rotational Speed Computational Rotational Speed
Turbine Rotational Speed (rpm)
1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.3f): Rotational speed for wind turbine W5 model (case6). 111
1200 1100 1000 900 %
800 +5 %
700
-5
Computational Rotational Speed (rpm)
1300
600 500 400 300 200 100 0
0
125
250
375
500
625
750
875 1000 1125 1250
Experimental Rotational Speed (rpm)
Figure (6.4): Computational rotational speed validated with experimental results.
6.3 Experimental Results For the experimental study, all cases of the wind turbine were investigated with wind velocity from cut-in speed (3.12 m/s) to the maximum speed (9.2 m/s) that can be obtained from the wind tunnel. The experimental work done for this study is tabulated here, comparing the behavior of the wind turbine without and with winglet. Define the power coefficient Cp by the relation: CP
P 1 2 AU 3
(6.2)
Where P is the power, is the air density, A is the wind turbine projected area, U is the wind speed. Table (6.1) represents CP values for different wind turbine cases at different wind speeds from cut-in speed (3.12 m/s) to the maximum speed (9.2m/s) that can be obtained from the wind tunnel. At each case, the average power coefficient was calculated for this case which included the minimum value for the case of wind turbine without winglet. Table (6.2) shows that the average power coefficient increases by using the winglet at cant angle 900. By increasing the winglet height, the average power coefficient increases.
112
Table (6.1): Experimental CP values for wind turbine. Wind Speed (m/s) 9.20
Average
0.3796 0.4364 0.4395 0.4325 0.4383 0.4366
0.4455
0.4149
0.3185
0.3688 0.4418 0.4429 0.4402 0.4422 0.4418
0.4512
0.4184
Coefficient W2 CP W3
0.3384
0.3710 0.4378 0.4450 0.4386 0.4460 0.4386
0.4480
0.4202
0.3660
0.3721 0.4380 0.4475 0.4342 0.4348 0.4353
0.4451
0.4216
W4
0.3676
0.3731 0.4394 0.4504 0.4343 0.4367 0.4361
0.4458
0.4229
W5
0.3702
0.3742 0.4402 0.4522 0.4344 0.4388 0.4382
0.4472
0.4244
Power
Case
3.12
4.25
Rotor
0.3104
W1
5.82
6.00
6.70
7.83
8.00
Table (6.2):- Average values of CP. Case Rotor W1 W2 W3 W4 W5
Average CP 0.4149 0.4184 0.4202 0.4216 0.4229 0.4244
Increase % 0.0 0.8436 1.2774 1.6148 1.9282 2.2897
The average value of power coefficient can be correlated to the winglet height as shown in equation (6.3) by the technique of curve fitting. CP 0.4149 0.0042 W 0.0009 W 2 0.0001W 3
Where:
(6.3)
W percentage of winglet height
Figure (6.5) shows the average power coefficient from the experiments and from correlation (6.3). Table (6.3) shows the error of the correlation for average C P from the experiments. The maximum error reaches 0.353%. This error is very small. So, the correlation can be used with confidence to predict the average value of C P for the wind turbine without and with winglet. It's important to rely that this formula available for this model with this specified diameter and geometry and it couldn’t be available for all wind turbine models. Also it's important to apply uncertainty measurements on any results obtained from computational or experimental data.
113
0.43 Experimental Power Coefficient Correlation Power Coefficient
Average Power Coefficient
0.428 0.426 0.424 0.422 0.42 0.418 0.416 0.414 0.412 0.41
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Winglet Height (%)
Figure (6.5): Average power coefficient for different cases. Table (6.3): Average power coefficient from experimental and correlation. Case Rotor W1 W2 W3 W4 W5
Experimental CP 0.4149 0.4184 0.4202 0.4216 0.4229 0.4244
Correlation CP 0.4149 0.4183 0.4205 0.4221 0.4237 0.4259
Error % 0.0 0.024 0.072 0.119 0.189 0.353
6.3.1 Experimental Results at Design Wind Speed Table (6.4) shows the power and power coefficient at the design wind speed (6 m/s) for all cases of the wind turbine. By increasing the winglet height, the power and power coefficient increase. The power increases from (22.154W) for wind turbine without winglet to (22.7943 W) by (2.89%) for wind turbine with winglet height of (5%). Table (6.4): Experimental power and power coefficient at design wind speed. Case Rotor W1 W2 W3 W4 W5
Power (W) 22.1540 22.3246 22.4287 22.5572 22.7034 22.7943
CP 0.4395 0.4429 0.4450 0.4475 0.4504 0.4522 114
Increase % 0.0 0.77 1.24 1.82 2.48 2.89
The value of power coefficient at design wind speed may be plotted and a correlation with the winglet height can be obtained as shown in equation (6.4). CP 0.4396 0.0031W 0.0002 W 2 9 106 W 3
Where:
(6.4)
W percentage of winglet height
Figure (6.6) shows the power coefficient from the experiments and from correlation (6.4). Table (6.5) shows the error of the correlation for CP from the experiments. The maximum error reaches 0.222%. This error is very small. So, the correlation can be used to predict the values of Cp for the wind turbine without and with winglet at design wind speed. 0.456 Experimental Power Coefficient Correlation Power Coefficient
Power Coefficient at Design Speed
0.454 0.452 0.45 0.448 0.446 0.444 0.442 0.44 0.438 0.436 0.434
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Winglet Height (%)
Figure (6.6): Power coefficient for different cases at design wind speed.
Table (6.5): Power coefficient from experimental and correlation Case Rotor W1 W2 W3 W4 W5
Experimental CP 0.4395 0.4429 0.4450 0.4475 0.4504 0.4522
Correlation CP 0.4396 0.4424 0.4451 0.4473 0.4494 0.4512
115
Error % 0.023 0.113 0.016 0.047 0.222 0.221
6.4 Computational Results and Discussions 6.4.1 Two-Dimensional Results Figures (6.7) – (6.16) show the vortices, velocity, and pressure coefficient contours for the profile of the wind turbine blade at different blade angles compared with velocity contours of [Chandrala et al,2012] Figure (6.7) shows the vortices, velocity, and pressure coefficient contours for the airfoil profile of the wind turbine blade at zero blade angle. The vortex generated behind the airfoil is very thin due to zero blade angles. As expected, pressure on the upper surface is less than the pressure on the lower surface but velocity on the upper surface is higher than the velocity on the lower surface of the airfoil. Figure (6.7d) shows the counters of velocity at zero blade angles for NACA 4420 airfoil [Chandrala et al,2012] .Comparing figure (6.7b) with figure (6.7d), the change of velocity has the same trend and results of NACA 4412 are really acceptable in comparison to the result of NACA 4420 [Chandrala et al,2012]. Figure (6.8) shows the vortices, velocity, and pressure coefficient contours for the airfoil profile of the wind turbine blade at 100 blade angle. The vortex that appears behind the airfoil is bigger than that of zero blade angles. The change of pressure and velocity around the airfoil is more than that of zero blade angles. Figure (6.9) shows the vortices, velocity, and pressure coefficient contours for the airfoil profile of the wind turbine blade at 200 blade angle. The vortex generated behind the airfoil covers a large area. Figure (6.9d) shows the counters of velocity at 22.50 blade angle for NACA 4420 airfoil [Chandrala et al, 2012]. Comparing Figure
(6.9b) with Figure (6.9d), the distribution of velocity has the same trend and results of NACA 4412 that are generally acceptable in comparison to the results of NACA 4420. For Figures (6.10) – (6.16), the vortex generated behind the airfoil is covers a larger area as the blade angle increases. By increasing the blade angle, the change of pressure and velocity around the airfoil increases. Comparing the results with the results of NACA 4420 airfoil, the change of velocity has the same trend and results of
116
NACA 4412 that are acceptable in comparison to the result of NACA 4420[Chandrala et al,2012] . It's noticed that NACA4412 with constant step 100 and this didn’t occur for NACA4420 so at certain angle there is no comparison between NACA4412 and NACA4420.
(a) Vorticity contours
(b) Velocity contours
(c) Pressure coefficient contours
(d) Velocity contours at zero blade angle [Chandrala et al,2012] Figure (6.7): Blade Angle = 00 .
117
(a) Vorticity contours.
(b) Velocity contours.
(c) Pressure coefficient contours. Figure (6.8): Blade Angle = 100 .
118
(a) Vorticity contours.
(b) Velocity contours.
(d) Velocity contours at 22.50 blade angle [Chandrala et al,2012] Figure (6.9): Blade Angle = 200 .
(c) Pressure coefficient contours.
119
(a) Vorticity contours
(b) Velocity contours
(d) Velocity contours at 300 blade angle [Chandrala et al,2012] Figure (6.10): Blade Angle = 300 .
(c) Pressure coefficient contours
120
(a) Vorticity contours
(b) Velocity contours
(d) Velocity contours at 37.50 blade angle[Chandrala et al,2012] Figure (6.11): Blade Angle = 400 .
(c) Pressure coefficient contours
121
(a) Vorticity contours
(b) Velocity contours
(d) Velocity contours at 450 blade angle [Chandrala et al,2012] Figure (6.12): Blade Angle = 500 .
(c) Pressure coefficient contours
122
(a) Vorticity contours
(b) Velocity contours
(d) Velocity contours at 600 blade angle [Chandrala et al,2012]. Figure (6.13): Blade Angle = 600 .
(c) Pressure coefficient contours
123
(a) Vorticity contours
(b) Velocity contours
(c) Pressure coefficient contours Figure (6.14): Blade Angle = 700 .
124
(a) Vorticity contours
(b) Velocity contours
(c) Pressure coefficient contours Figure (6.15): Blade Angle = 800 .
125
(a) Vorticity contours
(b) Velocity contours
(d) Velocity contours at 900 blade angle [Chandrala et al,2012] Figure (6.16): Blade Angle = 900 .
(c) Pressure coefficient contours
126
From Figures (6.7) – (6.16), velocities are obtained for different blade angles. Power produced from the wind is given by the following: (1) Wind power can be calculated from the following equation: PW
1 V 3A 2
(6.5)
where: PW power produced from the wind Air density is taken as 1.225 kg m3
A Wind turbine projected area = Rt2 Rh2 0.35 0.035 0.381 m2 2
2
Vw Wind speed is taken as 6 m s .
(2) Maximum generated power may be obtained from the wind turbine can be calculated from the following equation [man well etal, 2013]: Pmax
1 16 ρ U3A 2 27
(6.6)
Table (6.6) was obtained from the calculations of wind power and maximum generated power may be obtained from the turbine with respect to velocity.
Table (6.6) shows Wind power and maximum power for different blade angle. Blade Angle [0]
Velocity [m/s]
Wind Power [W]
Maximum Generated Power [W]
0 10 20 30 40 50 60 70 80 90
5.835 5.910 6.000 6.025 6.045 6.053 6.10 6.31 6.43 6.70
46.360 48.172 50.406 51.039 51.549 51.754 52.969 58.630 62.039 70.187
27.473 28.546 29.870 30.245 30.548 30.669 31.389 34.744 36.764 41.592
Figure (6.17) shows the change of air velocity impacts the blade at different blade angles. It is clear that the air velocity increases with the increase in blade angle from 5.835 m s at 00 to 6.7 m s at 900 . From angle 200 to 600 , the increase in velocity is small; from 6 m s to 6.1 m s , then, air velocity increases sharply with the
127
increase of the blade angle. The air velocity reaches the maximum value when the blade angle equals to 900 . Figure (6.18) shows the change of wind power at different blade angles. It is clear that the wind power increases with the increase in blade angle from (46.36 W) at
0 0
to (70.187 W) at 900 . From angle 200 to 600 , the increase in wind power is
small; from (50.406 W) to (52.969 W), then, wind power increases sharply with the increase of the blade angle. The wind power reaches the maximum value when the blade angle equals to 900 . Figure (6.19) shows the maximum power that may be generated by the turbine [Chandrala et al,2012] which has the hub diameter of 0.3375 m , blade length of 10.7 m , NACA 4420 airfoil profile and wind speed of 16 m s .
Comparing Figures (6.18) and (6.19), the present study gives the power at different angles which increases with the increase of the blade angle. For blade angle change from 200 to 600 , the wind power has a small increase and reaches the maximum when the blade angle equals to 900 . This change of power with the blade angle is close to that of the other published data [Chandrala et al,2012]. 6.8 6.7 6.6
Velocity (m/s)
6.5 6.4 6.3 6.2 6.1 6 5.9 5.8 5.7 5.6
0
10
20
30
40
50
60
70
80
90
Blade Angle (degree)
Figure (6.17): Air velocity impacts the blade at different blade angles.
128
75 Wind Power Maximum Generated Power
70 65
Power (W)
60 55 50 45 40 35 30 25
0
10
20
30
40
50
60
70
80
90
Blade Angle (degree)
Figure (6.18): Power at different blade angles. 2200
Maximum Generated Power (kW)
2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000
0
10
20
30
40
50
60
70
80
90
Angle of Blade (degree)
Figure (6.19): Maximum power that may be generated from wind turbine [Chandrala et al, 2012].
6.4.2 Three-Dimensional Wind Turbine For CFD study, all cases of wind turbine were investigated with wind velocities from (0 m/s) to (9.2 m/s). Table (6.7) represents CP values for different wind turbine cases at different wind speeds from cut-in speed (3.12 m/s) to speed (9.2m/s). At each case, the average power coefficient was calculated for this case which included the minimum value for the case of wind turbine without winglet. This table shows that average power 129
coefficient increases by increasing the winglet height. Figure (6.20a) shows the thrust force exerted on the wind turbine by air for the wind turbine rotor without winglet at different wind speeds. The thrust force increases by increasing the wind speed. Figures (6.20b) - (6.20f) show the thrust force exerted on the wind turbine by air for the wind turbine with winglet at wind speeds from (0 m/s) to (9.2 m/s). In each case, the thrust force increases by increasing the wind speed. Table (6.8) represents the thrust coefficient (CT) values for different wind turbine cases at different wind speeds from cut-in speed (3.12 m/s) to speed (9.2m/s). Define the thrust coefficient as: CT
Thrust Force 1 2 ρAU 2
(6.7)
At each case of the wind turbine, the average thrust coefficient was calculated for this case which has minimum value for case of the wind turbine without winglet. Table (6.8) is showing that the average thrust coefficient increases by increasing the winglet height. Table (6.9) shows the average power coefficient and average thrust coefficient for different cases of the wind turbine models. It is clear that the average power coefficient and average thrust coefficient increase with increasing the winglet height. Table (6.7): Computational values of the wind turbine blade CP. Wind Speed (m/s) Case
3.12
Rotor
0.4898
Power
W1
Coefficient CP
4.25
5.82
9.20
Average
0.4845 0.4805 0.4876 0.4758 0.4746 0.4728
0.4656
0.4789
0.4752
0.4963 0.4915 0.4927 0.4864 0.4782 0.4729
0.4765
0.4837
W2
0.4874
0.4964 0.4844 0.4953 0.4862 0.4801 0.4775
0.4764
0.4855
W3
0.4938
0.4896 0.4868 0.4980 0.4866 0.4820 0.4828
0.4814
0.4876
W4
0.4942
0.4908 0.4880 0.5010 0.4862 0.4830 0.4840
0.4848
0.4890
W5
0.4948
0.4932 0.4901 0.5024 0.4875 0.4842 0.4848
0.4886
0.4907
130
6.00
6.70
7.83
8.00
18 16
Thtust Force (N)
14 12 10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.20a): Thrust force on wind turbine rotor model (case1). 18 16
Thrust Force (N)
14 12 10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.20b): Thrust force on wind turbine W1 model (case2). 18 16
Thrust Force (N)
14 12 10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.20c): Thrust force on wind turbine W2 model (case3).
131
18 16
Thrust Force (N)
14 12 10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.20d): Thrust force on wind turbine W3 model (case4). 18 16
Thrust Force (N)
14 12 10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.20e): Thrust force on wind turbine W4 model (case5). 18 16
Thrust Force (N)
14 12 10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Wind Speed (m/s)
Figure (6.20f): Thrust force on wind turbine W5 model (case6).
132
Table (6.8): Computational values of the wind turbine blade CT Wind Speed (m/s) Case
3.12
Thrust
Rotor
0.9028
Coefficient
W1
CT
4.25
5.82
6.00
6.70
7.83
8.00
9.20
Average
0.8888 0.8675 0.8649 0.8558 0.8488 0.8478
0.8396
0.8645
0.9015
0.8962 0.8762 0.8725 0.8596 0.8512 0.8472
0.8498
0.8693
W2
0.9145
0.8976 0.8688 0.8783 0.8660 0.8568 0.8562
0.8524
0.8738
W3
0.9152
0.9048 0.8812 0.8837 0.8706 0.8622 0.8514
0.8446
0.8767
W4
0.9160
0.9014 0.8860 0.8876 0.8740 0.8672 0.8642
0.8462
0.8800
W5
0.9182
0.9112 0.8836 0.8907 0.8732 0.8684 0.8652
0.8464
0.8821
Table (6.9): average Computational values CP and CT. Case Rotor W1 W2 W3 W4 W5
Average CP 0.4789 0.4837 0.4855 0.4876 0.4890 0.4904
Increase % 0.0 1.0023 1.3781 1.8167 2.1090 2.4640
Average CT 0.8645 0.8693 0.8738 0.8767 0.880 0.8821
Increase % 0.0 0.5552 1.0758 1.4112 1.7929 2.0358
6.4.2.1 Computational Results at Design Wind Speed Table (6.10) shows the power, power coefficient, thrust force, and thrust coefficient at the design wind speed (6 m/s) for all cases of wind turbine. By increasing the winglet height, the power, power coefficient, thrust force, and thrust coefficient increase. The power increases from (24.5804W) for wind turbine without winglet to (25.3244 W) by (3.03%) for wind turbine with winglet height of (5%). The thrust force increases from (7.266 N) for wind turbine without winglet to (7.4824 N) by (2.978%) for wind turbine with winglet height of (5%).
Table (6.10): Computational wind turbine parameters at design wind speed. Case Rotor W1 W2 W3 W4 W5
Power (W) 24.5804 24.8357 24.9658 25.1030 25.2547 25.3244
CP 0.4876 0.4927 0.4953 0.4980 0.5010 0.5024
Increase % 0.0 1.04 1.57 2.13 2.74 3.03 133
Thrust (N) 7.2660 7.3297 7.3785 7.4242 7.4567 7.4824
CT 0.8649 0.8725 0.8783 0.8837 0.8876 0.8907
Increase % 0.000 0.877 1.548 2.177 2.624 2.978
Figures (6.21a) - (6.21f) show the static pressure and velocity contours on the blade surface for the wind turbine models at design wind speed (6 m/s). It is clear that by increasing winglet height, the maximum blade velocity increased from (30.1 m/s) for wind turbine rotor model to (34.2 m/s) for wind turbine W5 model. The maximum static pressure at the blade surface increased with increasing the winglet height from (366 Pa) for wind turbine rotor model to (625 Pa) for wind turbine W5 model. It is clear that the pressure on suction side is decrease and velocity is increased with increasing the winglet height. So, this is reducing the effect of the vortex at the blade tip which leads to improve the wind turbine performance and increase the power extracted by the wind turbine.
Static pressure (Pa)
Velocity (m/s)
Figure (6.21a): Wind turbine rotor model (case 1), U=6 m/s.
Static pressure (Pa)
Velocity (m/s)
Figure (6.21b): Wind turbine W1 model (case 2), U=6 m/s.
134
Static pressure (Pa)
Velocity (m/s)
Figure (6.21c): Wind turbine W2 model (case 3), U=6 m/s.
Static pressure (Pa)
Velocity (m/s)
Figure (6.21d): Wind turbine W3 model (case 4), U=6 m/s.
Static pressure (Pa)
Velocity (m/s)
Figure (6.21e): Wind turbine W4 model (case 5), U=6 m/s.
135
Static pressure (Pa)
Velocity (m/s)
Figure (6.21f): Wind turbine W5 model (case 6), U=6 m/s.
136
Chapter (7) Conclusions and Future Work 7.1 Introduction In this thesis a small horizontal-axis wind turbine blade of 0.35 m in radius at a design wind speed of 6 m/s was designed using the blade element moment theory where the chord length and twist angle at each section determined the blade taper and twist. Parameters such as thrust, torque and power were calculated in both experimental and computational studies for wind turbine with and without winglet. 7.2 Conclusions In this thesis, a two dimensional horizontal–axis wind turbine blade with NACA 4412 profile was designed and analyzed for different blade angles and wind speeds. CFD analysis was carried out using ANSYS Fluent software. The vortices, velocity and pressure distributions at various blade angles were discussed. The present results are coinciding with the published data of others. From results, it is seen that the wind power is increased by increasing the blade angle due to the increase in air velocity impacting the wind turbine blade. For blade angle change from 200 to 600 , the wind power has a small increase and reaches the maximum when blade angle equals to 900 . Thus, HAWT output power depends on the blade profile and its orientation. In three-dimensional case, the present study indicates a relation between powers, power coefficient, thrust force, thrust force coefficient and wind turbine rotational speed with winglet height. This study is done using both experimental and computational investigations for wind speeds from cut-in speed (3.12 m/s) to maximum speed (9.2 m/s) that can obtained from the wind tunnel. For experimental results, as the winglet height increased, the average power coefficient increased from (0.4149) for wind turbine rotor to (0.4244) by (2.2897%) for wind turbine W5 model. The power at design wind speed (6 m/s) increased by increasing the winglet height. The power increased from (22.154W) for wind turbine 137
rotor model to (22.7943 W) by (2.89%) for wind turbine W5 model. The power coefficient at design wind speed (6 m/s) increased by increasing the winglet height. The power coefficient increased from (0.4395) for wind turbine rotor model to (0.4522) by (2.89%) for wind turbine W5 model. For computational results, as the winglet height increased the average power coefficient increased from (0.4789) for wind turbine rotor to (0.4907) by (2.464%) for wind turbine W5 model. By increasing the winglet height, the average thrust coefficient increased from (0.8645) for wind turbine rotor to (0.8821) by (2.0358%) for wind turbine W5 model. The power at design wind speed (6 m/s) increased by increasing the winglet height. The power increased from (24.5804W) for wind turbine rotor model to (25.3244 W) by (3.03%) for wind turbine W5 model. The power coefficient at design wind speed (6 m/s) increased by increasing the winglet height. The power coefficient increased from (0.4876) for wind turbine rotor model to (0.5024) by (3.03%) for wind turbine W5 model. The thrust force at design wind speed (6 m/s) increased by increasing the winglet height. The thrust force increased from (7.266 N) for wind turbine rotor model to (7.4824N) by (2.978%) for wind turbine W5 model. The thrust force coefficient at design wind speed (6 m/s) increased by increasing the winglet height, the thrust force coefficient increased from (0.8649) for wind turbine rotor model to (0.8907) by (2.978%) for wind turbine W5 model. It is clear that by increasing winglet height, power, power coefficient, thrust force, thrust force coefficient, and wind turbine rotational speed increased.
7.3 Recommendations for Future Work After conducting the work presented here and reviewing the literature review available in the public domain, the following areas have been identified for future work:
138
1. The performance curve obtained in this study is based on the mechanical power output and not the electrical power by construct complete turbine part like nacelle and gear train also it would be extremely useful to evaluate the power generation capabilities of the turbine using an electric generator. 2. Winglets are highly sensitive devices that can influence the aerodynamic forces and the performance of wind turbines. Further optimization of the winglet is required that evaluates the effects of sweep angle, toe angle, and twist. 3. For the winglet optimization, more design variables are to be considered such as different airfoils 4. More comprehensive CFD modeling is imperative in order to understand better and establish an accurate correlation with the experimental findings.
139
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Appendix (A) Fortran Program to design wind turbine blade using BEM theory C ============================================================= C PROGRAM TO CALCULATE A WIND TURBINE BLADE SHAPE USING C BLADE ELEMENT THEORY C ============================================================= IMPLICIT DOUBLE PRECISION (A-H, O-Z) DIMENSION R (900), CORD (900), PHI (900), THETA (900), ALAMDAR (900) DIMENSION PHIDEG (900), THETADEG (900), F (900), SEGMA (900) OPEN (2, FILE='PLOTS.DAT', STATUS='UNKNOWN') OPEN (3, FILE='CHROD.DAT', STATUS='UNKNOWN') OPEN (4, FILE='FACTORS.DAT', STATUS='UNKNOWN') C ---------------------------------------------------------------------C INPUT DATA FOR WIND TURBINE C ---------------------------------------------------------------------C NACA 4412 C ---------------------------------------------------------------------PI=4.0*ATAN (1.0) WINDSPEED=6 RHO=1.225 NBLADE=3 N=25 ALAMDA=5.0 ALPHAD=5.85 CL=1.1106 CD=0.00828 X=0.10 RTIP=0.35 RHUB=X*RTIP C -----------------------------------------------------------------------C STARTING LOOP OVER THE BLADE ELEMENTS C -----------------------------------------------------------------------DR= (RTIP-RHUB)/N SUMCP=0 DO I=1, N R (I) =RHUB+float (I-1)*DR ALAMDAR (I) =(R (I)/RTIP)*ALAMDA PHI (I) = (2.0/3.0)*ATAN (1.0/ALAMDAR (I)) THETA (I) =PHI (I)-ALPHAD*PI/180 PHIDEG (I) =PHI (I)*180.0/PI 149
THETADEG (I) =PHIDEG (I)-ALPHAD C -------------------------------------------------------------------------SINPHI=SIN (PHI (I)) COSPHI=COS (PHI (I)) RATIO=R (I)/RTIP CORD (I) =8.0*PI*R (I)*(1.0-COSPHI)/ (NBLADE*CL) SEGMA (I) =NBLADE*CORD (I)/ (2.0*PI*R (I)) AOLD =1.0/ (1.0+ ((4.0*SINPHI**2)/ (SEGMA (I)*CL*COSPHI))) ADOLD=1.0/ ((4.0*COSPHI)/ (SEGMA (I)*CL)-1.0) C ============================================================ 200 PHIN=ATAN ((1.0-AOLD)/ ((1.0+ADOLD)*ALAMDAR (I))) C ------------------------------------------------------------------------C CALCULATE THE TIP LOSS FACTOR F C ------------------------------------------------------------------------SINPHIN=SIN (PHIN) COSPHIN=COS (PHIN) TERMEXP= (FLOAT (NBLADE)/2.0)*(1.0-RATIO)/ (RATIO*SINPHIN) F (i) = (2.0/PI)*ACOS (EXP (-TERMEXP)) CORD (I) =8.0*PI*R (I)*F(I)*SINPHIN*(COSPHIN-ALAMDAR(I)*SINPHIN) 1 /(NBLADE*CL*(SINPHIN+ALAMDAR(I)*COSPHIN)) SEGMA (I)=NBLADE*CORD(I)/(2.0*PI*R(I)) CTR=SEGMA (I)*(1.0AOLD)**2*(CL*COSPHIN+CD*SINPHIN)/(SINPHIN**2) ANEW =1.0/(1.0+((4.0*F(I)*SINPHI**2)/(SEGMA(I)*CL*COSPHI))) ADNEW=1.0/((4.0*F(I)*COSPHI)/(SEGMA(I)*CL)-1.0) C ------------------------------------------------------------------------C CALCULATE THE TOLERANCE C ------------------------------------------------------------------------TOL1=ABS (ANEW-AOLD) TOL2=ABS(ADNEW-ADOLD) TOL = DMAX1(TOL1,TOL2) IF(TOL.GT.0.000001)THEN AOLD=ANEW ADOLD=ADNEW GO TO 200 ELSE PHI(I)=PHIN THETA(I)=PHIN-ALPHAD*PI/180.0 PHIDEG(I)=PHIN*180.0/PI THETADEG(I)=PHIDEG(I)-ALPHAD ENDIF WRITE(2,100)R(I)/RTIP,CORD(I)/RTIP, PHIDEG(I), THETADEG(I) 150
WRITE(3,300)R(I),CORD(I), THETADEG(I) C ------------------------------------------------------------------------------C CALCULATE THE POWER COEFFICIENT C ------------------------------------------------------------------------------SINPHI=SIN(PHI(I)) COSPHI=COS(PHI(I)) COTPHI=1.0/TAN(PHI(I)) TERM2=F(I)*SINPHI**2*(COSPHI-ALAMDAR(I)*SINPHI)* 1 (SINPHI+ALAMDAR(I)*COSPHI)*(1.0(CD/CL)*COTPHI)*ALAMDAR(I)**2 SUMCP=SUMCP+TERM2 WRITE (4,300)R(I)/RTIP,ANEW,ADNEW,F(I),CTR,SEGMA(I) ENDDO 300 FORMAT (1X,6(F10.6)) C -------------------------------------------------------------------------------C END THE MAIN LOOP C -------------------------------------------------------------------------------CP=8.0*SUMCP/(ALAMDA*N) POWERN=0.5*RHO*WINDSPEED**3*PI*(RTIP**2-RHUB**2)*CP OMEGA=ALAMDA*WINDSPEED/RTIP CT=CP/ALAMDA THRUST=0.5*RHO*WINDSPEED**2*PI*(RTIP**2-RHUB**2)*CT TORQUE=THRUST*RTIP WRITE (*,*)'CP =', CP WRITE (*,*)'THE POWER IS EQUAL TO', POWERN WRITE (*,*)'THE ROTATIONAL SPEED=', OMEGA WRITE (*,*)'THE TORQUE=', TORQUE WRITE (*,*)'THE THRUST FORCE=', THRUST WRITE (*,*)'THE THRUST COEFFICIENT=', CT CLOSE (2) 101 FORMAT (1X, I5, 1X,2(F10.5,1X))
151
جامعة الزقازيق كمية الهندسة قسم هندسة القوى الميكانيكية
دراسة تأثير الشكل الهنذسى لريشة التىربين الهىائى رو المحىر األفقى على أدائه رسالة مقدمة من المهندس
محمد خالد محمد محمد حسانين معيد بقسم هندسة القوى واآلالت الكهربية بالمعهد العالى لمهندسة -أكاديمية الشروق -القاهرة ضمن متطمبات الحصول عمى درجة الماجستير فى الهندسة الميكانيكية المشرفون
أ.د /.أحمد فاروق عبد الجواد أ.د.م/.هشام السيد عبد الحميد د/مصطفى محمد محمد إبراهيم قسم هندسة القوى الميكانيكية كمية الهندسة -جامعة الزقازيق الزقازيق 1027
ٳهـــــــــّّّ ــــــــذاء ٳلـــى أبي الغــــالي و ٳلـــى أمي الحـــبيبة
دراسة تأثير الشكل الهنذسى لريشة التىربين الهىائى رو المحىر األفقى على أدائه رسالة مقدمة من المهندس
محمد خالد محمد محمد حسانين معيد بقسم هندسة القوى واألالت الكهربية بالمعهد العالى لمهندسة -أكاديمية الشروق -القاهرة ضمن متطمبات الحصول عمى درجة الماجستير فى الهندسة الميكانيكية
التوقيع
لجنة الحكم والمناقشة
-١أ.د/هشام محمذ على البطش كليت الٌِذست -جاهعت بٌِا
-٢أ.د/مفرح ميالد نصيف قسم هندسة القوى الميكانيكية كلية الهندسة – جامعة الزقازيق
-٣أ.د /أحمد فاروق عبد الجواد (مشرفاً) قسم هندسة القوى الميكانيكية كلية الهندسة – جامعة الزقازيق
-٤أ.د.مُ/شام السيذ عبذ الحويذ (هششفا) قسم هندسة القوى الميكانيكية كلية الهندسة – جامعة الزقازيق
جامعة الزقازيق 1027
ملخص الرسالة حعخبش سيشت حْسبيٌت الشياا ُأ الءاضأل اسساسأ هاي ه ًْااث الخْسبيٌات ّالخأ ًعخواذ عليِاا فأ اسخخالص الطاقت الوْجْدة فٔ الِْاأل .حن حصوين سيشت حْسبيٌت صغيشة هي الٌْع راث الوحْس اسفقأ بإسااخخذام ًيشياات ال ا ) .Blade Element Momentum (BEMحيااذ حاان الحصااْأ علاأ أبعاااد الشيشات ّوااْأ الوقطااو ّصاّياات دّساًااَ ّرلار هااي مااالأ بشًاااهل حاان عولاَ بلغاات ال ااْسحشاى هااو امخياااس هقطو الشيشت هي الٌْع .NACA 4412فٔ البذايت حوج دساست حسابيت بإسخخذام بشًااهل ANSYS Fluent 15لوقطو سيشت رٌائٔ اسبعاد ّرلر لوعشفت حاريش صاّيت هيل الشيشت علأ القاذسة الوسخخلصات هي الخْسبيي ّهقاسًت ُازٍ الٌخاائل هاو الٌخاائل الوٌشاْسة .هاي ماالأ ُازٍ الذساسات حبايي أى عٌاذها ح اْى صاّيت هيل الشيشت هي 02دسجت الٔ 02دسجت فاإى الخغياش فأ القاذسة ي اْى ماعين هقاسًات بالضاّيات 02دسجت حيذ كاًج القذسة أكبش ها يو يّ .بالخالٔ فإى القذسة الوسخخلصات هاي حْسبيٌات الشياا حعخواذ بش ل أساسٔ علٔ صاّيت هيل الشيشت. بعذ رلر حوج دساست رالريت اسبعاد لٌ س حْسبيٌت الشياا ّل اي الذساسات كاًاج هعوليات ّحساابيت فأ حالت ّجْد ّعذم ّجْد جٌا وشفٔ .wingletالذساست الحسابيت حوج بإسخخذام بشًااهل ANSYS .Fluent 15كلخا الذساسخيي حواج للخْسبيٌات فقاع هاو مواس حااىث اماشٓ فأ حالات ّجاْد winglet بطْأ هي %1الٔ %5هي ًصان قطاش الخْسبيٌات بضياادة كال هاشة ّ %1بضاّيات هيال 02دسجات فأ جويو الحاىثّ .حن حساب هخغيشاث القذسة ّهعاهل القذسة ّقْة الذفو ّهعاهل قْة الذفو ّكزلر ساشعت دّساى الخْسبيٌاات فاأ جويااو الحاااىث .حوااج ُاازٍ الذساساات فاأ سااشعاث الشيااا حبااذأ هااي سااشعت القطااو 2.10م/د ّحخٔ سشعت سيا 0.0م/د ُّٔ أكبش سشعت هخاحت هي الخءشبت العوليت. بٌاأل علٔ كل هي الذساست الوعوليت ّالحسابيت فإى كل هي القذسة ّهعاهل القذسة ّقْة الذفو ّهعاهل قْة الذفو حخحسي بضيادة وْأ ال ّ wingletاى ُزا الخحسي فٔ حذّد هي %0الٔ .%2
