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Theoretical and Computational Investigations of Optimized Blade of Horizontal-axis
Wind Turbines for Power Extraction at Wind Farm
By
Suraj Prasad Subedi (Student ID:1707401)
Shuvashis Biswas (Student ID: 1707411)
Prosunto Kumar Biswas (Student ID:1707421)
Muradul Kabir (Student ID:1707436)
A Thesis submitted to the Department of Mechanical Engineering of Hajee Mohammad
Danesh Science and Technology University in partial fulfillment of the requirements for the
degree of Bachelor of Science in Mechanical Engineering.
Under the Supervision of
Sudipta Paul
Lecturer
Department of Mechanical Engineering
Hajee Mohammad Danesh Science and Technology University
Dinajpur-5200
November 14, 2022
ii
DECLARATION
This is to certify that the work presented in this thesis is carried out by the author(s) under the
supervision of Sudipta Paul, Lecturer of Department of Mechanical Engineering, Hajee
Mohammad Danesh Science and Technology University, Dinajpur. No portion of the work
contained in this thesis has been submitted in support of an application for another degree or
qualification of this or any other University or Institution of learning.
Suraj Prasad Subedi Prosunto Kumar Biswas
Student ID: 1707401 Student ID: 1707421
Shuvashis Biswas Muradul Kabir
Student ID: 1707411 Student ID: 1707436
iii
ACKNOWLEDGEMENTS
We would like to offer our sincere thanks to Hajee Mohammad Danesh Science and
Technology University, and the Mechanical Engineering department in specific, for providing
us the opportunity for doing this thesis work. This thesis appears in its current form due to the
assistance and guidance of several people. We would, therefore, like to thank all of them.
We would like to express our deep and sincere gratitude to our honorable thesis supervisor
Sudipta Paul, Lecturer, Department of Mechanical Engineering, Hajee Mohammad Danesh
Science and Technology University, for providing invaluable guidance and technological
support throughout this thesis period. His dynamism, vision, sincerity and motivation have
deeply inspired us. He has taught us the methodology to carry out the work and to present the
thesis work as carefully as possible. It was a great privilege and honor to work under his
guidance.
We are extremely grateful to our parents for their love, prayers, caring and sacrifices for
educating and preparing us for our future. We also express our thanks to all of our friends for
their support and valuable advice.
Finally, our thanks go to all the people who have supported us to complete the thesis directly
or indirectly.
iv
ABSTRACT
Designing horizontal-axis wind turbine (HAWT) blades to achieve satisfactory levels of
performance starts with knowledge of the aerodynamic forces acting on the blades. In this
thesis, SD7080 airfoil was chosen among four standard airfoils with aerodynamic properties
that are specified in the airfoil database and geometry was generated in Q-blade software using
the Schmitz formula. This geometry was investigated theoretically based on the blade-element
momentum (BEM) theory and numerically by using computational fluid dynamics (CFD) to
calculate the rotor power efficiency. Based on these findings, it was concluded that the CFD
results validated the BEM theorem; the differences between the results obtained by these
methods were likely due to the assumptions used when applying the BEM theory. While
comparing annual power output, Commercial wind turbine (Enercon E-30) lagged behind
optimized BEMT blade. Thus, unit cost($/kwh) seemed to be 0.051 USD for SD7080 while
0.076 USD was the unit cost ($/kwh) for Enercon E-30. But land requirement for the wind farm
resulted to be lesser for Enercon E-30 than optimized SD7080 BEMT blade.
v
NOMENCLATURE
B Blade Number
F Combined correction factor
P Power extracted from Windstream
q Dynamic Pressure
r Radius of blade element or collocation point
R Radius of Rotor [m]
T Thrust
w Induced velocity in the z-direction
k Shape parameter
c Scale parameter
v Observing wind speed
h Turbine’s hub height,
a Surface roughness co-efficient
A Projected airfoil area (chord × span)
C Chord length
L Lift force
D Drag force
V Wind velocity
t The pay-off period
A Axial induction factor
a´ Angular induction factor
N Number of blade elements
Q Tip loss correction factor
r Radius and radial direction
D Wind turbine rotor diameter
V Voltage
U Output pitch angle
ƒ(v) Probability density
dΓ Difference in bound circulation between control points
Γ Bound Circulation
𝜃 Blade twist angle
vi
Ω Blade rotational speed
Greek Symbols
α Angle of attack
β Blade pitch angle,
γ Aerofoil inlet angle
ρ Air density
λ Tip Speed Ratio
ω Rotational speed
η Mechanical / Electrical efficiency
Subscripts
Cl Two-dimensional lift coefficient
CQ Torque Coefficient
CT Torque coefficient
Cy Tangential force coefficient
Cx Axial force coefficient
Cp Power coefficient
Cd Drag coefficient
Cp Pressure coefficient
Tm Prime mover input torque
Pm Wind turbine output power
Km Motor gain operator
ωt The angular shaft speed.
A0 Swept area of the wind turbine rotor
Fx Axial force
Fθ Tangential force
Pmr Probability density function
Pwr Mean power density
Cld Design lift coefficient
Comr Operation, Maintenanca and repair cost
dFy Tangential force
𝜎 Total Rotor Solidity
vii
Aeff Effective swept area of the wind turbine rotor
Ptotal Total pressure
Pdynamic Dynamic pressure
Aeff Effective swept area of the wind turbine rotor
ABBREVIATION
STDM Standard deviation method
HAWT Horizontal-axis wind turbines
VAWT Vertical-axis wind turbine
RWM Rigid Wake Method
MLM Maximum likelihood method
PDM Power density method
EEM Equivalent energy method
MOM Method of moments
BEM Blade element momentum
EWM Expanding Wake Method
TSR Tip Speed Ratio
GM Graphical method
viii
Table of Contents
DECLARATION.......................................................................................................................ii
ACKNOWLEDGEMENTS..................................................................................................... iii
ABSTRACT..............................................................................................................................iv
NOMENCLATURE ..................................................................................................................v
ABBREVIATION....................................................................................................................vii
Chapter 1 ..................................................................................................................................1
Introduction..........................................................................................................................1
1.1 Background...............................................................................................................1
1.2 Present Energy Scenario of Bangladesh ...................................................................2
1.3 Motivation of the Research.......................................................................................6
1.4 Research Objectives..................................................................................................7
1.5 Thesis Outline...........................................................................................................8
Chapter 2 ..................................................................................................................................9
Literature Review.................................................................................................................9
2.1 Research on electricity generation and cost estimation ............................................9
2.2 Research on aerodynamic study of horizontal axis wind turbine .............................9
Chapter 3 ................................................................................................................................11
Wind site location...............................................................................................................11
3.1 Nominating wind sites ............................................................................................11
3.2 Geographical and statistical description of Hatiya Island.......................................13
3.3Methodology............................................................................................................14
3.3.1 Wind speed probability density function and cumulative distribution...........14
3.3.2 Shape parameter and scale parameter.............................................................14
3.3.3 wind power density and measurement............................................................16
Chapter 4 ................................................................................................................................17
Extrapolation of wind speed data .....................................................................................17
4.1Methodology............................................................................................................17
4.1.1Data analysis of wind speed and Weibull parameters .....................................18
4.2 Identification and detailed description of nominated wind turbine ........................20
Chapter 5 ................................................................................................................................21
Horizontal axis wind turbine.............................................................................................21
5.1Background..............................................................................................................21
5.2 Horizontal axis wind turbine concepts....................................................................21
5.2.1 Classification of HAWTs................................................................................22
ix
5.2.2 Criteria in HAWT design................................................................................22
5.2.3 Performance parameter of HAWTs ................................................................23
5.3 Aerodynamics of HAWTs ......................................................................................26
5.3.1 Tip-speed Ratio...............................................................................................26
5.3.2 Schmitz formula..............................................................................................27
5.3.3 Blade Element Momentum (BEM) Theory ....................................................28
5.4 HAWT Blade Design..............................................................................................28
5.4.1 Airfoil Selection..............................................................................................28
5.4.2 Analysis of airfoils..........................................................................................29
5.5 Rotor blade design by BEMT method ....................................................................32
5.5.1 Calculation of the Maximum Cl/Cd Ratio......................................................32
5.5.2 Design lift coefficient and angle of attack calculation....................................32
5.5.3 Design Tip Speed Ratio and Blade Count Options.........................................33
5.5.4 Design Power Coefficient Calculation............................................................33
5.5.5 Determination of the Blade Radius.................................................................33
5.5.6 Angle of twist and blade chord calculation.....................................................34
5.6 Rotor Specification .................................................................................................37
5.7 Calculation of Power Coefficient ( BEMT Method ) .............................................38
5.8 Simulation Method..................................................................................................40
Chapter 6 ................................................................................................................................41
CFD simulation...................................................................................................................41
6.1 2D Airfoil Simulation .............................................................................................41
6.2 HWAT 3D Simulation............................................................................................47
Chapter 7 ................................................................................................................................54
Estimation of Wind Farm..................................................................................................54
7.1 Background.............................................................................................................54
7.2 Methodology...........................................................................................................54
Chapter 8 ................................................................................................................................56
Results and Discussion.......................................................................................................56
8.1 Analysis of SD 7080 blade at different Reynolds Number.....................................56
8.2 Power co-efficient analysis of BEMT blade at Re=82000 .....................................57
8.2.1 Variation of Lift and Drag Co-efficient..........................................................59
8.2.2 Determination of Tip-Velocity .......................................................................59
8.2.3 Calculation of co-efficient of power.............................................................60
8.3 Comparison of co-efficient of power.....................................................................60
x
8.4 Annual Power Output ............................................................................................62
8.5 Cost estimation........................................................................................................62
8.6 Required land area for wind farm ...........................................................................65
Chapter 9 ................................................................................................................................66
Conclusion and Future Recommendations......................................................................66
9.1 Conclusion ..............................................................................................................66
9.2 Future Work Recommendations ............................................................................66
References..............................................................................................................................67
.
xi
LIST OF FIGURES
Figure 1: Renewable energy share at Bangladesh ---------------------------------------------------- 3
Figure 2: Monthly mean wind speed in five sites at 10m height (2020) -------------------------11
Figure 3: Wind speed variation based on height at different locations. --------------------------12
Figure 4: Geographical Location of Hatiya island---------------------------------------------------13
Figure 5: Effects of parameters in probability density function -----------------------------------15
Figure 6: Effects of parameters in cumulative distribution function------------------------------16
Figure 7: Monthly mean wind speed variation at different height in Hatiya --------------------19
Figure 8: Monthly scale parameter at different height of Hatiya ---------------------------------20
Figure 9: Parts of Horizontal axis Wind Turbine --------------------------------------------------21
Figure 10:cross-section of a wind turbine blade -----------------------------------------------------24
Figure 11:Airfoil Section--------------------------------------------------------------------------------25
Figure 12:Geometry Shape of different airfoils.-----------------------------------------------------29
Figure 13: Lift coefficient (Cl) for different airfoils at Reynolds no=82000 --------------------30
Figure 14:Lift to drag ratio (Cl/Cd ) for different airfoils at Reynolds no. 82000--------------31
Figure 15:Chord length (Cr) vs. (r/R)------------------------------------------------------------------36
Figure 16:Twist angle (β) vs. (r/R) --------------------------------------------------------------------36
Figure 17: Designed Turbine Blade -------------------------------------------------------------------37
Figure 18:C-mesh flow domain and boundaries -----------------------------------------------------41
Figure 19: Geometry of flow domain and boundaries made in spaceclaim --------------------42
Figure 20: Meshed flow domain -----------------------------------------------------------------------42
Figure 21: Mesh generation for SD7080 utilizing structured grid--------------------------------43
Figure 22: Scaled residuals of calculation of the fluid domain. ----------------------------------45
Figure 23: Velocity contour on blade from CFD ---------------------------------------------------45
Figure 24: Velocity magnitude on blade from CFD------------------------------------------------46
Figure 25: Pressure co-efficient on SD7080 airfoil -------------------------------------------------46
Figure 26: Pressure contour of SD7080 airfoil-------------------------------------------------------47
Figure 27: Blade Geometry made in Solidworks ---------------------------------------------------48
Figure 28: View of blade placement from rotor axis -----------------------------------------------48
Figure 29: Blade placement in fluid domain ---------------------------------------------------------49
Figure 30: Generated Face Mesh of fluid domain --------------------------------------------------49
Figure 31: Generated Volume Mesh of fluid domain ----------------------------------------------50
xii
Figure 32: Scaled residuals of calculation of the fluid domain ------------------------------------52
Figure 33: Integral of pressure along the blade of SD7080 airfoil -------------------------------52
Figure 34: Boundary conditions of the flow domain -----------------------------------------------53
Figure 35: Wall Shear vector on blade of SD7080 -------------------------------------------------53
Figure 36: Lift Coefficient versus tip speed ratio----------------------------------------------------56
Figure 37: Lift Coefficient versus tip speed ratio----------------------------------------------------57
Figure 38: Power Coefficient versus tip speed ratio of SD7080 BEMT-blade. -----------------58
Figure 39:Value of Lift Coefficient--------------------------------------------------------------------58
Figure 40: Drag coefficient of SD7080 airfoil -------------------------------------------------------59
Figure 41: Blade Velocity vector on blade of SD7080---------------------------------------------60
Figure 42:Power Curve of Enercon E-30 -------------------------------------------------------------61
Figure 43: Comparison of Cp for designed blade and Enercon E-30-----------------------------62
xiii
LIST OF TABLES
Table 1.1:Installed capacity and derated capacity of BPDB power plants ...............................2
Table 1.2: Present scenario of Bangladesh power sector ..........................................................3
Table 1.3: Renewable energy installed capacity .......................................................................4
Table 1.4: Details about completed and upcoming wind power plant ......................................5
Table 3.1: Monthly mean wind speed in three sites ...............................................................11
Table 4.1: Extrapolate wind data at 30m altitude ....................................................................18
Table 4.2: Extrapolate wind data at 50m altitude ....................................................................18
Table 4.3: Extrapolate wind data at 60m altitude ....................................................................19
Table 4.4: Datasheet of Enercon E-30 Wind turbine...............................................................20
Table 5.1 : Scale classification of wind turbines ....................................................................22
Table 5.2: Maximum lift coefficient and lift to drag ratio at Reynolds number of 82000 for
selected airfoils. .......................................................................................................................32
Table 5.3: Selection of the number of blades and design tip speed ratio.................................33
Table 5.4: Ideal Blade Sections, Local TSR, Angle of Attack, Blade Setting Angle and Chord
..................................................................................................................................................35
Table 5.5:Specification of blade ..............................................................................................37
Table 6.1: Computational conditions of airfoil simulation .....................................................44
Table 6.2: Boundary conditions of flow domain .....................................................................51
Table 8.1: Calculation of power output and capacity factor....................................................62
Table 8.2: Calculated values of PVC and unit cost .................................................................64
Table 8.3: Calculation of Required land area for two turbines...............................................65
1.1 Background
Energy is fundamental to economic and social development. On the dawn of the 21st century
we are being faced with one of the toughest challenges ever – that of securing energy supply.
We are still heavily dependent on oil resources which will eventually become depleted within
a few decades. An increasing world population, an enlarged global economy and an improved
standard of living all contribute to greater demands for energy. At the same time, we are facing
the greatest threat to our survival on planet earth: global climate change. Climate change is not
just an environmental threat but also an economic threat. Emissions of greenhouse gases, global
warming and fossil fuel combustion have all become major concerns in recent decades.
Nonrenewable energy's finite stock is dwindling every day. The price of crude oil is rising due
to the lack of supply. Electricity generation from renewable energy is the most promising
approach for addressing these issues. Boosting the use of renewable energy can help to bring
down the price of fossil fuels and our reliance on them. Electricity generated from fossil fuels
is produced in a very dirty and environmentally unfriendly manner, whereas renewable energy
is clean and environmentally beneficial. Wind energy is one of the most effective power
technologies that is ready today to be deployed globally on a scale that can aid in tackling this
problem. Wind energy is the fastest-growing clean energy source due to its zero-emission
nature. Wind energy, on the other hand, is regarded as the most abundant source of renewable
energy, with the additional benefit of being more environmentally benign than other
alternatives [1]. China establishes a new global record by generating 52 gigawatts in a single
year. Total wind energy output has achieved a milestone of 733 GW, with a 26 percent growth
rate, however it is declining with time; the maximum growth rate of 64.35 percentage was
found in the year 1999 [2]. The negative marginal impacts of the Covid 19 pandemic affected
electricity generation in 2020. Wind energy is a significant and viable source of renewable
energy in the generation of power in highly developed countries. Denmark, for example, hopes
to use wind energy to provide 50% of its electricity by 2023 [3] .Bangladesh is a country in
South Asia with 35 meteorological stations situated across this land. The Bay of Bengal and
the Ganges of Brahmaputra Meghna, which touches 19 of Bangladesh's 64 districts, are
geomorphologically dominant in the nation's coastal zone. It covers 47,201 km2
, more than
32% of the country's total area [4] . At a height of 30 meters, the wind speed in Bangladesh's
coastal regions is apparent over 5 𝑚𝑠−1
, which is adequate for generating energy [5] .In the
Chapter 1
Introduction
2
world, renewable energy accounts for more than 26% of power whereas Bangladesh accounts
for less than 5% [6], is illustrated in Figure 1. Per capita energy production is 560 kWh [7]
,however global total primary energy consumption is around 23398 kWh [8], which is
substantially more than Bangladesh's per capita energy consumption. Even per capita
generation of Bangladesh is lower than other south Asian countries. Bangladesh generates
about 63 percent of its electricity from national grid gas supplies and imports 1160MW
electricity per year [9] and wind accounts for only 0.04 percent of the 5 percent of renewable
energy (Figure 1). The focus of this study is to demonstrate the installation of a wind turbine
in Hatiya Island after analyzing Three different sites. As Hatiya is a tourist destination, more
electricity is required to install new ideas, innovations, and businesses.
1.2 Present Energy Scenario of Bangladesh
Bangladesh has a population of over 165 million people, making it a densely populated country.
Though Bangladesh has made enormous improvement in the energy sector over the last decade,
a large amount of electricity is required for living and manufacturing. Bangladesh currently has
100% access to electricity, and electrical generation capacity has expanded from 5 Gigawatts
to 26 Gigawatts by end of the year 2021. [10], By 2030, the demand for electricity will exceed
40 Gigawatts. Natural gas produces around 60% of the electricity [11]
Table 1.1: Installed capacity and derated capacity of BPDB power plants [12]
Fuel type Capacity
(MW)
Total (%) Derated capacity
(MW)
Total (%)
Coal 1768 7.91 1688 7.86
Gas 11342 50.75 11007 51.23
HFO 6278 28.09 5833 27.15
HSD 1341 6 1337 6.22
Hydro 230 1.03 230 1.07
Imported 1160 5.19 1160 5.4
Solar 229 1.02 229 1.07
Total 22348 99 21484 100
3
Figure 1: Renewable energy share at Bangladesh
Table1.2: Renewable energy installed capacity [13]
Wind and bio-energy were overlooked in the early years, which is regrettable. The
government has taken some encouraging initiatives to harvest wind energy, as the annual
average wind speed at 30 meters above sea level in the coastal zone exceeds 5 meters per
second. In the divisions of Chittagong, Khulna, and Barisal, there will be 10 new wind power
plants. The 60MW wind power plant at Chakaria upazila in Cox's Bazar is the largest of them
all in terms of capacity.
Technology Off-grid
(MWp)
On-grid
(MWp)
Total (MWp)
Solar 349.57 203.36 552.93
Wind 2 0.9 2.9
Hydro 0 230 230
Biogas to Electricity 0.69 0 0.69
Biomass to Electricity 0.4 0 0.4
Total 352.66 434.26 786.92
69.50%
30%
0.40% 0.10%
Solar
Hydro
wind
Others
4
Table1.3: Present scenario of Bangladesh power sector [12]
For this regard, Bangladesh's government has adopted some intellectual steps to produce that
quantity. Increasing power generation from clean or renewable energy sources such as solar,
wind, hydro, and bio-energy is included. On the renewable side, solar energy and hydropower
plants are producing a significant amount of electricity; electricity from Sapchari waterfall,
Khagrachari, has just been installed.
Headline 2009 2022 Acquisition in last 13 years
Generation capacity
(MW)
4942 25514 20572
Grid substation power
(MVA)
15870 55307 39437
Imported electricity
(MW)
0 1160 1160
Highest generation
(MW)
3268 13792 10524
Power plants(no.) 27 150 123
Expired plants 0 6 6
Total consumers 10800000 42100000 31300000
Transmission lines (Ckt.
Km)
8000 13213 5213
Distribution line(km) 260000 621000 361000
System loss (%) 13.58 8.50 -5.08
Distribution loss (%) 14.33 8.48 -5.85
Per capita generation
(KWh)
220 560 340
Access electricity (%) 47 100 53
5
Table1.4: Details about completed and upcoming wind power plant [14]
SL. Project
Name
SID Capacity Location RE
Technology
Completion
Date
Present Status
1 1000
KW
capacity
172 1 MWp
Kutubdia,
Cox' Bazar
Wind (Off-
Grid)
2015-12-31
Completed &
Running
2
1000
KW
capacity
171 1 MWp
Kutubdia,
Cox's
Bazar
Wind (Off-
Grid)
2008-12-31
Completed &
Running
3
900KW
Capacity 173
900
KWp
Sonagazi,
Feni
Wind (On-
Grid)
2006-09-27
Completed &
Running
4
2 MW
Capacity
370 2 MWp
Sirajganj
Sadar
Wind (On-
Grid)
2021-08-15
Implementation
Ongoing
5 30
MW
4176 30 MWp
Sonagazi,
Feni
Wind (On-
Grid)
2023-11-22 Under Planning
6
Mongla
50 MW
4173 55 MWp
Mongla,
Bagerhat
Wind (On-
Grid)
2023-11-15 Under Planning
7
50 MW
Grid-
tied
4175 50 MWp Cox'sbazar
Wind (On-
Grid)
2023-10-24 Under Planning
8
50 MW
Grid-
tied
4174 50 MWp
Chandpur
Sadar,
Wind (On-
Grid)
2023-07-12 Under Planning
9
10
MW 155 10 MWp
Kalapara,
Patuakhali
Wind (On-
Grid)
2022-12-31 Under Planning
10 60 MW 158 60 MWp
Chakaria,
Cox's
Bazar
Wind (On-
Grid)
2021-12-31 Under Planning
6
1.3 Motivation of the Research
Many studies and research regarding wind energy potential and aerodynamic investigation of
horizontal axis wind turbine have been conducted before to understand the aerodynamic
properties of airfoil and ways to design blade geometry through different procedures for
extracting maximum [15] power possible. Most recent studies focused on optimization of
turbine blades to investigate the effect of design parameters on rotor efficiency. These studies
confirmed the optimization of turbine blade results in better performance in terms of power
extraction. Along with design, study of possibilities to practically manufacture for required
power extraction and cost analysis for wind farm can add new dimensions to this research. [16]
performed an analysis for OTSR of NACA 65-415 and NACA 64-421 based on BEMT and
CFD and their CFD results validated the BEM theorem, and the results obtained from those
two methods were similar. They showed that the OTSR for low Reynolds number is between
4 and 7 depending on the DTSR and the airfoil. None of the previous studies considered
optimized BEMT blade design for estimating power generation and cost analysis. In our
knowledge this is the first study that compares the power production of designed BEMT blade
with commercial wind turbine and predicts the cost analysis for wind farm. Most of the
previous studies only considered cost analysis through commercial turbine or power co-
efficient of optimized blade. Therefore, in the present study, optimum blade is designed and
studied in CFD simulation for optimum power efficiency.
A very important factor in case of designing a wind farm is the land area it needs. Among
previous studies, only a handful reported the area needed for rated power generation only for
commercial turbines. The present study predicts the land area requirement for wind farm for
optimized BEMT blade.
7
1.4 Research Objectives
In the present study, by numerical and computational fluid dynamics simulation (CFD)
aerodynamic behavior of optimized bemt blade from SD7080 airfoil has been carried out with
(i) different airfoil geometry (ii) different reynolds number (iii) different tip-speed ratio.
The specific objectives and outcomes of the research work are as follows:
• To develop a blade geometry model by Schmitz optimization method from a
selected airfoil based on cl/cd ratio for low Reynold number application.
• To investigate the power and torque on each local radius by dividing the blade into
several elements by BEM theory.
• To simulate the blade model for exploring the power co-efficient at specified wind
speed.
• To validate and compare the power co-efficient of blade by BEMT, Q-blade Rotor
Simulation and CFD simulation.
• To calculate the power generation of BEMT blade in comparison with selected
commercial turbine for specified site.
• To investigate the cost analysis of wind turbine setup and land area required for
wind turbine.
• To calculate the annual energy output and rate of energy per kilowatt comparing
wind turbine through designed blade with commercial turbine.
8
1.5 Thesis Outline
The present thesis focuses on the numerical and computational investigations of the
optimized BEMT blade for maximum possible power generation considering the cost
estimation , land area and energy output . An outline of this thesis is presented below:
Chapter 1: Introduction- discussion about the key elements of this motivation behind
this research work, and research objectives.
Chapter 2: Literature Review- an account of previous research about aerodynamic
behavior, power coefficient and cost analysis of wind
turbine.
Chapter 3: Wind Site- description of geographical location and calculation of
wind power density.
Chapter 4: Extrapolate data- extrapolation of wind speed calculation of data analysis of
wind speed for different hub heights and Weibull parameter
Chapter 5:HAWT Analysis- investigation of optimization process based on BEM theory.
Chapter 6:CFD Simulation- description of elements of computational fluid dynamics.
Chapter 7:Cost Estimation- wind Farm calculation of energy generated and required land
area.
Chapter 8: Results- describes the simulation model, power coefficient, cost
analysis from the results of the study.
Chapter 9: Future Work- summarizes the outcomes of the current research and
provide a framework about the future direction.
9
2.1 Research on electricity generation and cost estimation
Many studies related to wind energy potential and assessment have been performed in various
locations around the world. [17] estimated the wind resources and also wind park design in El-
Kef region, Tunisia. They investigated the characteristic of wind speed using Weibull
distribution function and estimated the capacity factors for different wind turbine
configurations. They performed economic evaluation to examine the feasibility of their project.
[18] utilized different methods for comprehensive study of wind turbine utilization in Zarrineh,
Iran. They used hourly, monthly, seasonal, and yearly wind data analysis. It was concluded that
the location was marginal for harnessing wind energy. Also, the standard deviation and power
density method were performed to determine best method for evaluation of wind power.
[19] evaluated the wind energy potential for coastal locations along the north eastern coasts of
Turkey. They illustrated that the monthly mean wind speed in the region varied between
1.53 m/s and 4.06 m/s. Also, they found that the maximum annual mean wind power density
and wind energy density were 59.96 W/m2
and 525.25 kWh/m2
, respectively. [20] studied
assessment of wind energy potential as a power generation source in the capital of Iran, Tehran.
Long term measured wind speed data at 10 m height was used for this study. They calculated
the annual average wind power densities which were between 74.00 and 122.48 W/m2
. They
concluded that the wind energy potential for Tehran was suitable only for battery charging and
water pumping. [21] investigated the assessment of wind energy potential at Kudat and Labuan,
Malaysia, using Weibull distribution function. They used 10 m height measured wind speed
data and found that highest monthly mean wind speeds were 4.8 m/s and 4.3 m/s at Kudat and
Labuan, respectively. Also, they showed that the maximum wind power densities of Kudat and
Labuan were 67.40 W/m2
and 50.81 W/m2
, respectively. They concluded that the two locations
were suitable only for small-scale wind energy applications.
2.2 Research on aerodynamic study of horizontal axis wind turbine
For horizontal-axis wind turbine (HAWT) blades [22] showed an analysis of 10 different
airfoils to be suited best for low Reynolds numbers. They compared those airfoils on basis of
high-lift, soft stall characteristics in addition to their overall good performance. From their
results, SD7080 was selected as the best airfoil to produce maximum power in low wind speed
applications.
[16] performed an analysis for OTSR of NACA 65-415 and NACA 64-421 based on BEMT
and CFD and their CFD results validated the BEM theorem, and the results obtained from those
two methods were similar. They showed that the OTSR for low Reynolds number is between
4 and 7 depending on the DTSR and the airfoil.
An HWAT was created by [23]to draw 2 kW of power from Kuakata, Bangladesh. They
decided on the NACA 4418 airfoil type, and they correctly determined the design parameters
for the chosen wind sites. They linearized the twist angle and the blade chord while taking into
Chapter 2
Literature Review
10
account the least amount of tip and hub loss of power because it was not viable to produce the
optimum blade form.
[24] provided a description of a design approach based on the notion of blade element
momentum (BEM). The procedure was used to increase the chord and twist distributions in the
blades. A 100kW HAWT rotor was created AND few HAWT blades currently in use were
evaluated using their computer program's aerodynamic efficiency calculations. The blade
profile of a 5 kW HAWT was then constructed using the BEM approach, and CFD was utilized
to assess the designed profile.
For a one-megawatt (MW) wind turbine, [25] used strength and aerodynamics to determine the
blade parameters, such as chord and thickness distributions along the blade. The redesigned
NACA 63-621 and FX 66S-196 series profiles served as the foundation for the blade geometry.
For simple connection with the rotor hub and to ensure structural strength on the inner part of
the blade, the cylindrical profile was chosen close to the blade root.
Three HAWTs were created by [26] with various chord and twist angle distributions along the
blades. The airfoil utilized was NACA 4418, and the rotor had a 0.36 m diameter. Utilizing
three different approaches, namely BEM, CFD, and wind tunnel tests, the power coefficient CP
values of the planned rotors were computed. The ideal blade geometry, which matched that
predicted by the Schmitz formula, was present in one of the proposed rotors. In comparison to
those produced using the BEM theory, the CP values obtained by CFD were lower.
The Reynolds number affects the maximum value of Cl/Cd. The maximum Cl/Cd values are
thought to be related to the Reynolds number since they have a significant impact on the CP.
The chord length of the airfoil, air viscosity, air density, and air relative velocity all affect the
Reynolds number. The Reynolds number is influenced by the length of the blade and the wind
speed because the relative air velocity on the blade airfoil depends on the rotor's rotational
angular velocity. According to the Schmitz formula and other optimum-design methods, the
chord length reduces from hub to tip in opposition to an increase in relative air velocity from
hub to tip, therefore the Reynolds number does not vary along the blade.
Reynolds number is greatly affected by Cl/Cd as they have significant impact on the Cp value.
The chord length of the airfoil, air viscosity, air density, and relative velocity of air all affect
the Reynolds number. The Reynolds number is influenced by the length of the blade and the
wind speed because the relative air velocity on the blade airfoil depends on the rotor's rotational
angular velocity. The Schmitz formula and other optimum-design formulas predict that the
chord length drops from hub to tip inversely as the relative air velocity rises from hub to tip,
resulting in no change in Reynolds number along the blade.
Because the chord lengths of small and big WTs differ, so do their Reynolds numbers, and as
a result, so do their power coefficients and TSR values. But for large Reynolds numbers,
Reynolds number has no effect on the rotor's aerodynamic performance. According to [27], the
optimum TSR and maximum CP values are smaller for smaller WTs than they are for bigger
WTs as they have smaller Reynolds numbers.
11
3.1 Nominating wind sites
The Bay of Bengal and the Ganges of Brahmaputra Meghna, which pass through 19 of
Bangladesh's 64 districts, dominate the country's coastal zone geomorphologically. It covers
47,201 km2
which is almost 32% of whole country [28], Among them we primarily select three
sites from two divisions. where Hatiya, Kutubdia situated in Chittagong division and Sayedpur
situated in Rangpur division. To produce wind energy, speed of wind is most important. We
got wind speed data from Bangladesh meteorological stations at a height of 10 meters.
Table 3.1: Monthly mean wind speed in three sites [29]
Velocity Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg
Hatiya 2.33 2.53 3.57 5.14 5.02 5.81 5.64 4.67 3.38 2.06 1.63 1.65 3.63
Kutubdia 2.52 2.64 3.38 3.88 4.02 5.40 5.40 4.78 3.13 2.19 1.72 1.93 3.43
Sayedpur 2.67 3.14 4.60 4.76 4.00 3.73 3.56 3.05 2.74 2.12 2.04 2.24 3.22
Figure 2: Monthly mean wind speed in three sites at 10m height (2020)
Chapter 3
Wind site location
0
1
2
3
4
5
6
7
JAN FB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC AVG
Sayedpur Hatiya Kutubdia
12
Figure 3: Wind speed variation based on height at different locations.
Hatiya is the best spot for producing more energy based on average wind speed. In this article,
we will offer a statistical study of a wind power plant based on Rayleigh distribution and cost
analysis of that plant.
13
3.2 Geographical and statistical description of Hatiya Island
Hatiya is the largest upazilla in Noakhali district, both in terms of population and area. The
Noakhali district, having an area of 3,600 km2
, consists of six upazillas, including the island
part. Southeast of Bangladesh is where Noakhali is located. The coastal community of Noakhali
has been hampered by seasonal tidal inundation and subsequent salinity intrusions, especially
during the dry winter season when the flow of river water diminishes and the residents are
particularly vulnerable to potential sea level rise. The ground level in Noakhali is lower than
10 m above the mean sea level. The island is a completely isolated territory located in between
22.07° and 22.35° north latitudes and longitudes in between 90.56° and 91.11° east [30].
Figure 4: Geographical Location of Hatiya island
The western border of the island is established by Manpura Upazila, the northern border by
Subarnachar Upazilla, the eastern boundary by the Meghna River, and the southern part by the
Bay of Bengal [30]. The island is 2100 square kilometers in area, and it is inhabited to about
452,463 people. The island is underdeveloped in terms of services and infrastructure compared
to the rest of the nation; the majority of the population works in agriculture and fishing. Only
130 km of Hatiya Island's roads are paved, and another 60 km are semi-paved. There are 216
people per km2
, which is considerably less than the average throughout the country. The island
is not connected to the national electricity grid; the demand is supplied by a local grid. The
island is not connected to the national electrical system; thus, a local grid meets the need. Three
diesel generators with a total capacity of 400 kVA are used to power the island grid, although
right now they can only produce a combined 500 kW. Using sea trucks, the diesel generator
14
fuel is delivered to and stored in the generator facility. The generators run for 12 hours each
day and use about 1400 liters of fuel. From the foregoing description, it is clear that the island
needs better supply and management for supplying (BPDP) with a 2 MW solar/wind hybrid
system and later for a PV-Diesel hybrid system for power generation in the island's total
population with electricity to meet their basic needs. Currently the government of Bangladesh
plans to build a 15MW heavy fuel oil-based power plant. This is the project of BPDB
constructed by Desh Power Ltd. will cost Tk 1,396.65 crore and will last for 15 years.
3.3Methodology
The most effective way to analyze wind energy is to get information from specific
meteorological authorities. Wind speed data was gathered at a height of 10 meters by the
authors. Some frequency distribution methods are useful for obtaining all parameters, co-
efficient, and extrapolation of wind data. Like as Weibull distribution, gamma distribution,
inverse gaussian distribution, log normal distribution, normal square root of wind speed
distribution etc. Here we use Weibull and Rayleigh distribution to analyze the wind parameters.
3.3.1 Wind speed probability density function and cumulative distribution
Probability density function can be described as,
ƒ(v)= (
𝑘
𝑐
)(
𝑣
𝑐
)𝑘−1
𝑒𝑥𝑝[−(
𝑣
𝑐
)𝑘
] (3.1)
here, ƒ(v) is the probability density function of observing speed v
k is the shape parameter which is dimensionless
c denoted as scale parameter
Rayleigh distribution is a special case of the Weibull distribution where k=2. Then the equation
3.1 stands as
ƒ(v)=
2𝑣
𝑐2
𝑒𝑥𝑝[−(
𝑣
𝑐
)𝑘
] (3.2)
The cumulative probability distribution function can be assessed as,
F(v)=1- 𝑒𝑥𝑝[−(
𝑣
𝑐
)𝑘
] (3.3)
3.3.2 Shape parameter and scale parameter
Shape parameter and scale parameter can be calculated by using a lot of methods. Like as
Maximum likelihood method (MLM), Standard deviation method (STDM), power density
method (PDM), equivalent energy method (EEM), graphical method (GM), Method of
moments (MOM). Among all of methods standard deviation and Method of moments is more
preferable to find out the value of shape parameter k. Scaling parameters fits for all methods.
According to standard deviation method,
15
Shape parameter, k=(
𝜎
𝑣
̅
)
−1.086
( 3.4)
Where, σ stands as standard deviation (SD)
SD, σ=√∑ (v𝑖 − 𝑣̅)
𝑛
𝑖=1 (3.5)
𝑣̅ is denoted as mean wind speed
Scale parameter, C=
𝑣
̅
Γ[1+
1
𝑘
]
(3.6)
Where Γ[ ] is the gamma function
According to method of moments,
Shape parameter, K=[
0.9874
𝜎
𝑣
̅
]
1.0983
(3.7)
Scale parameter, C=
𝑣
̅
Γ[1+
1
𝑘
]
(3.8)
Figure 5: Effects of parameters in probability density function
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1 2 3 4 5 6 7 8 9 10 11 12 13
k=2;c=7 k=2;c=9 k=2;c=8
16
Figure 6: Effects of parameters in cumulative distribution function
3.3.3 wind power density and measurement
Wind power density per unit area of a site at any time can be assessed as,
𝑃
𝑤=
1
2
ρc3
Γ [
k+3
k
] (3.9)
Where ρ is stands for mean air density whose value is 1.225 kgm−3
at 15𝑜
𝐶
A negligible error occurs of power density in the time of calculating.
Error (%) =
1
𝑛
∑ (
𝑃𝑤𝑟−𝑃𝑚𝑟
𝑃𝑚𝑟
)
𝑛
𝑖=1 (3.10)
Pmr is the wind power density for the probability density function
Pwr is the mean power density
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14
k=2;c=7 k=2;c=9 k=2;c=8
17
4.1Methodology
Basically, wind speed is lower at the height of 10m.To generate more electricity highly
needed better wind speed. on the other hand, Modern wind turbines designed for higher
heights. To estimate turbine hub height’s Wind speed the following equation:
v
v0
= (
h
h0
)a
(4.1)
Where, h is turbine’s hub height,
h0 is reference height,
v is the wind speed at turbine height,
v0 is the wind speed at reference height
‘a’ is denoted as surface roughness co-efficient which is expressed as following
equation,
a=
0.37−0.088ln(v
̅)
1−0.088ln(
h0
10
)
(4.2)
In this article, the author gathered wind speed data at a height of 10 meters and extrapolated
the wind speed at 30 meters, 50 meters and 60 meters respectively. The comparison of wind
speed data in Hatiya at the heights of 10m, 30, 50m, and 60m is shown in Figure 7
(Histogram).
Shape and scale parameter can also extrapolate by using Weibull distribution.
Estimating shape parameter and scale parameter at turbine height expressed as,
Ch = C0 [
h
h0
]
n
(4.3)
kh =
k0[1−0.088ln(
h0
10
)
[1−0.088ln(
h
10
)
(4.4)
Where n is the law exponent of power and it can be assessed as;
n=
0.37−0.088ln(C0)
1−0.088ln(
h
10
)
(4.5)
Average power output and Capacity factor are the performance parameters of wind turbine.
Capacity factor is the ratio of Average power output and rated electrical power or it can be
mentioned as the average power output over a period to the rated electrical power.
Capacity factor,
Chapter 4
Extrapolation of wind speed data
18
Cf =
Pavg
PR
(4.6)
In this case, PR indicates to rated electrical power.
Average power output, Pavg = PR ∗ [
𝑒
−(
𝑉𝑐
𝑐
)
𝑘
−𝑒
−(
𝑉𝑟
𝑐
)
𝑘
(
𝑉𝑟
𝑐
)
𝑘
−(
𝑉𝑐
𝑐
)
𝑘 − 𝑒
−(
𝑉𝑓
𝑐
)
𝑘
] (4.7)
𝑉
𝑟, 𝑉𝑓, 𝑉
𝑐 are used to represent the terms rated wind speed, cut-off wind speed, and cut-in wind
speed.
Accumulated annual(yearly)energy output,
𝐸𝑜𝑢𝑡 = Pavg*365*24 (4.8)
4.1.1Data analysis of wind speed and Weibull parameters
Author collected the data of Hatiya at 10m height from Bangladesh meteorological authority.
In the month of June, the maximum velocity is 5.81 ms−1
. Wind speed is often higher from
March to August than other seasons. Equation 4.3 and 4.4 are used to calculate scale parameter
and wind power density.in this article, we extrapolate the wind speed data at 30m,50m,60m
height by using the equation no. 4.1, 4.2, 4.3, 4.4 and 4.5
Table 4.1: Extrapolate wind data at 30m altitude
Criteria jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg.
Wind speed 3.22 3.47 4.74 6.59 6.45 7.36 7.16 6.04 4.51 2.88 2.33 2.36 4.70
Scale Para. 1.95 2.66 4.44 5.85 5.87 6.77 6.76 6.26 4.13 2.62 1.70 1.71 4.23
Table 4.2: Extrapolate wind data at 50m altitude
Criteria Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg.
Wind speed 3.75 4.02 5.41 7.39 7.25 8.21 8.01 6.81 5.16 3.37 2.76 2.79 5.41
Scale Para. 4.48 4.81 6.41 8.68 8.51 9.62 9.38 8.02 6.12 4.05 3.33 3.36 6.40
19
Table 4.3: Extrapolate wind data at 60m altitude
Criteria Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg
Wind speed 3.96 4.24 5.67 7.71 7.55 8.54 8.33 7.11 5.41 3.57 2.93 2.96 5.66
Scale Para. 4.82 5.15 6.82 9.17 8.99 10.13 9.89 8.48 6.52 4.36 3.61 3.64 6.80
Figure 7: Monthly mean wind speed variation at different height in Hatiya
0
1
2
3
4
5
6
7
8
9
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
10m 30m 50m 60m
20
Figure 8: Monthly scale parameter at different height of Hatiya
4.2 Identification and detailed description of nominated wind turbine
The most important factor in selecting a turbine is the cut-in speed. The mean monthly wind
speeds in November and December at 50 meters height are 2.76 and 2.79 ms−1
. So, the cut-
in speed of the turbine must be less than 3 ms−1
. If not, Power generation will stop in those
months. We selected Enercon E-30 which is manufactured by a German company called
Enercon GmbH. Its rated power is 300KW and cut in speed is 2.5ms−1
. This turbine’s blade
is made of Glass-fiber reinforced material. This turbine used a synchronous generator whose
voltage is 440 Voltage and maximum speed is 48 rpm. The turbine’s tower is made of steel
and conical in shape.
Table 4.4: Datasheet of Enercon E-30 Wind turbine
0
2
4
6
8
10
12
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
10m 30m 50m 60m
Model name
of Turbine
Turbine
Hub
height
(m)
Rotor
diameter
(m)
Swept
Area
(𝑚2
)
Rated
power
𝑃𝑅
(KW)
Cut-in
speed
𝑉
𝑐
(m/s)
Rated
speed
𝑉
𝑟
(m/s)
Cut-off
speed
𝑉𝑓
(m/s)
Enercon E-30 50 29.6 707 300 2.5 13.5 25
21
5.1Background
A wind turbine is a machine which converts the power in the wind into electricity. This is
contrast to a windmill, which is a machine that converts the wind’s power into mechanical
power. There are two great classes of wind turbines, horizontal- and vertical-axis wind turbines.
Conventional wind turbines, horizontal-axis wind turbines (HAWT), spin about a horizontal
axis. As the name implies, a vertical-axis wind turbine (VAWT) spins about a vertical axis.
Today the most common design of wind turbine and the only kind discussed in this thesis in
the view of aerodynamic behavior is the horizontal-axis wind turbines. In this chapter, detail
information about the conventional horizontal-axis wind turbines will be given but before that
some unconventional and innovative horizontal-axis wind turbine concepts will be mentioned.
5.2 Horizontal axis wind turbine concepts
Modern commercial wind turbines frequently employ lift driven force wind turbines because
of their capacity to produce large power coefficients. The horizontal axis wind turbine (HAWT)
and vertical axis wind turbine (VAWT), two different types of lift-driven force wind turbines,
can be distinguished by the orientation of their working axes. Each form of wind turbine has
its own benefits and drawbacks depending on the working axis, enabling it to situations. Over
the past few decades, HAWTs have undergone tremendous development and widespread
application, emerging as the industry standard for contemporary wind energy technologies. The
ability to attain improved energy efficiency is the reason why HAWTs are so widely used.
However, the improved energy efficiency of HAWTs only materialized under conditions of
high energy quality, which included wind flow velocity and flow direction [31]
Figure 9: Parts of Horizontal axis Wind Turbine [32]
The structure of a modern HAWT is shown in Figure 9. The main rotor shaft and the generator
are placed on the top of a tower. To achieve an optimum power output, the yawing mechanism
is required to face the changeable wind directions. The yawing mechanism of HAWTs helps
Chapter 5
Horizontal axis wind turbine
22
the blades take advantage of the wind velocity through a computer-controlled motor in modern
wind farms. The height of a tower also will influence the power output of HAWTs. It was
found that a higher tower can help a wind turbine reach higher wind velocities in higher
altitudes and wind shear [33] However, the tall tower of HAWT cannot have good integration
with urban environments and it also will have a high cost of transportation and installation.
Moreover, the support tower takes the entire load from the blades, rotor, and gear box on the
top and this will cause an increase in the overall cost. Due to many moving parts, HAWTs
require high maintenance [34] .The reason that HAWT cannot be widely used in urban areas
can be concluded as the high cost of transportation and installation, high maintenance, and bad
integration with urban environments.
5.2.1 Classification of HAWTs
Because the interconnection of wind turbines to utilities becomes their principal application,
the average size of HAWTs has grown. The question of ‘size classification’ has been raised, as
well. HAWTs are classified as shown in Table 5.1 according to their diameters and/or their
rated powers.
Table 5.1: Scale classification of wind turbines [35]
Scale Rotor Diameter Power Rating
Small Less than 12m Less than 40kv
Medium 12m-45m 40kw-999kw
Large 46m and larger 1.0mw and larger
5.2.2 Criteria in HAWT design
Before ending this chapter, a few words to be mentioned in about the criteria in HAWT design
and construction include:
• Number of turbine blades
• Rotor orientation; downwind or upwind rotor
• Turbine torque regulation
• Turbine speed; fixed or variable rotor speed
• Blade material, construction method and profile (airfoil section)
• Hub design; rigid, teetering or hinged
• Power control via aerodynamic control (stall control) or variable pitch blades.
• Orientation by self-aligning action (free yaw) or direct control (active yaw)
23
• Types of mechanical transmission and generator; synchronous or induction generator;
gearbox or direct drive transmission
• Type of tower; steel or reinforced –concrete shell or steel truss with tension cables
The design of a rotor is essential to a wind turbine's ability to produce power since the
interaction of the rotor and wind is what generates power in a wind turbine.
5.2.3 Performance parameter of HAWTs
The mean wind flow and turbulent fluctuations are combined to form the wind.
In the 1920s and 1930s, Betz [36] and [37] were the first to analyze the performance of wind
turbine rotors.
Wilson et al. [38] and O Vries then developed and expanded the theory for a solution by digital
computers.
The performance characteristics of a rotor's annular section are determined using a combination
of momentum theory and blade element theory in the analysis of rotor aerodynamic features.
The performance of the whole rotor was determined by integrating the values obtained from
each annular section. [39]
The performance of a wind turbine rotor is usually characterized by power coefficient (Cp),
which is expressed as,
Cp =
P
1
2
ρAV3
(5.1)
As estimated by Betz in 1926, the optimal power output of a wind turbine rotor is around 59.3
percent.
The analysis was conducted under ideal circumstances with the following presumptions:
• 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. In order to produce mechanical forces as a result of the airfoil's relative
motion to a surrounding fluid, it has been integrated into a wind turbine system.
The airfoils on the blades can be used to collect wind energy. The cross-sectional shape is
crucial for wind turbine blades to achieve the specified aerodynamic performances, such as the
maximum desired rotor power, the expected airfoil qualities, and strength considerations.
Figure 10 depicts the cross-section of a wind turbine blade.
The leading and trailing edges, respectively, are where the mean camber line’s greatest forward
and backward points are located. The chord line of length c is the straight line joining the
24
leading and trailing edges. The camber is the distance measured perpendicular to the chord line
between the mean camber line and the chord line.
The thickness is measured perpendicular to the chord line and is the distance between the upper
and lower surfaces. The angle between the chord line and the relative wind id referred to as the
angle of attack. The length of the airfoil measured perpendicular to its cross-section is referred
to as the span of the airfoil.
The leading-edge radius, mean camber line, maximum thickness and thickness distribution of
the profile, and trailing edge angle are all factors that affect an airfoil's ability to move through
the air efficiently.
Figure 10:cross-section of a wind turbine blade [40]
The distribution of forces on a portion of an airfoil while air flows over its surface is based on
the design of wind turbine blades.
low pressure is caused by an increase in velocity in the airfoil convex surface.
The viscous friction between the air and the airfoil surface slows the air flow in the meantime.
Two forces and one momentum can be produced on the chord at a distance of c/4 from the
leading edge by the effects of pressure differences between upper and lower surfaces and
friction forces.
These are the two forces and one moment:
The force perpendicular to the direction of the incoming air flow is known as the lift force. The
pressure difference on the top and lower airfoil surfaces is what generates the lift forces.
The force parallel to the direction of the incoming air flow is known as drag force. The pressure
difference between airfoil surfaces facing toward and away from the approaching flow, as well
as viscous friction forces on the surface of the airfoil, are what generate the drag force.
Pitching moment is described as a moment about an axis that is perpendicular to the cross-
section of an airfoil.
25
Figure 11:Airfoil Section
The two-dimensional lift coefficient, drag coefficient, pitching moment coefficient, and
pressure coefficient can be expressed as Cl, Cd, Cm and Cp respectively. The function of each
coefficient is shown as,
Cl =
L
l
1
2
ρcV3
=
Lift
Dynamic
(5.2)
Cd =
D
l
1
2
ρcV3
=
Drag
Dynamic
(5.3)
Cm =
M
1
2
ρcV3A
=
Pitching moment
Dynamic moment
(5.4)
Cp =
Ptotal−Pdynamic
1
2
ρcV3
=
Static pressure
Dynamic pressure
(5.5)
where ρ is the density of air, V is the velocity of free stream air flow, A is the projected
airfoil area (chord × span), c is the airfoil chord length and l is the airfoil span, L is the lift
force and D is the drag force, Ptotal is total pressure and Pdynamic is dynamic pressure.
26
There are other important dimensionless coefficients of a rotor section, which include power
coefficient, thrust coefficient, tip speed ratio and pressure coefficient:
Cp =
P
1
2
ρAV3
(5.6)
CT =
T
1
2
ρAV3
(5.7)
The airfoils with high maximum lift coefficients, low pitching moment, and low drag are
favored in modern commercial wind turbine blades
For HAWT specifically, a thin form of the same airfoil was used in the design of the blade tip
to achieve a high lift to drag ratio, and a thicker version of the same airfoil was used in the
design of the root region to provide structural support [41].
A general perspective on how to design the blades of unique wind turbines can be gained
through studying wind turbine blades.
5.3 Aerodynamics of HAWTs
Wind turbine power production depends on the interaction between the rotor and the wind.
the wind may be considered to be a combination of the mean wind and turbulent fluctuations
about that mean flow.
Periodic aerodynamic forces caused by wind shear, off-axis winds, rotor rotation, randomly
fluctuating forces induced by turbulence and dynamic effects are the source of fatigue loads
and are a factor in the peak loads experience by a wind turbine. These are, of course,
important, but can only be understood once the aerodynamics of steady state operation has
been understood.
5.3.1 Tip-speed Ratio
The Tip Speed Ratio (TSR) is a crucial element in the design of wind turbines. TSR stands for
the ratio of wind speed and wind turbine blades' tips' speed.
TSR =
speed of rotor tip
wind speed
(5.8)
If the wind turbine's rotor rotates too slowly, the majority of the wind will flow directly through
the space between the blades and leave it with no electricity. The blades, however, will blur
and behave like a solid wall to the wind if the rotor spins too quickly. Turbulence is also
produced by rotor blades as they move through the air. The following blade will strike that
agitated air if it moves too swiftly. Therefore, it can occasionally be beneficial to slow down
your blades. (Calculating the tip-speed ratio of your wind turbine)
27
5.3.2 Schmitz formula
The Betz limit was reached by applying Bernoulli's principle and the conservation of linear
momentum to describe the power that the wind turbine extracts from the air. Schmitz built a
more complete model of the rotor plane flow on the principle of angular momentum
conservation. The most effective chord length and pitch angle distribution around the radius of
the blade is found using this power calculation approach. [42] The Schmitz method starts thin
closest to the hub, reaches a maximum at roughly 15% of the blade length, and then starts to
diminish, whereas the Betz method predicts that the blade should get thicker as it gets closer to
the hub.
Betz and Schmitz are different in that Schmitz accounts for the swirl loss or wake loss that can
be described as,
ηwake =
Cp,schmitz
Cp,Betz
(5.9)
The performance of the wind turbine can be calculated using Blade Element Momentum
(BEM) theory after the chord length and pitch angle distributions have both been established.
Schmitz developed equations describing the conservation of angular momentum in order to
maximize the twist angle and chord length as functions of the blade radius.
Particular Schmitz equations take the airflow behind the rotor into account and call for
assumptions about the TSR and the most effective AOA, which corresponds to the highest lift-
to-drag ratio for any given airfoil.
C(r)=
16πr
B(CL)D
sin2
(
1
3
arctan(
R
rλD
)) (5.10)
β(r) =
2
3
arctan [
R
r
1
λD
] – αD (5.11)
Thus, the HAWT geometry dimensions are obtained using Schmitz formulas. The design Cld
and αD values for respective airfoil were calculated according to the graphs obtained in Q-
blade software. Then, those values were again calculated based on results of 2D CFD
simulations of the airfoils.
Thus, Schmitz formulas are used to get the HAWT geometry dimensions.
28
5.3.3 Blade Element Momentum (BEM) Theory
BEM theory is a compilation of both momentum theory and blade element theory. Momentum
theory, which is useful in predicted ideal efficiency and flow velocity, is the determination of
forces acting on the rotor to produce the motion of the fluid. This theory has no connection to
the geometry of the blade, thus is not able to provide optimal blade parameters. Blade element
theory determines the forces on the blade as a result of the motion of the fluid in terms of the
blade geometry. By combining the two theories, BEM theory, also known as strip theory,
relates rotor performance to rotor geometry. The assumptions made in BEM theory is the
aggregate of the assumptions made for momentum theory and blade element theory. The
following assumptions are made for momentum theory:
• Blades operate without frictional drag.
• A slipstream that is well defined separates the flow passing through the rotor disc from
that outside disc.
• The static pressure in and out of the slipstream far ahead of and behind the rotor are
equal to the undisturbed free-stream static pressure (P1 = P3)
• Thrust loading is uniform over the rotor disc.
• No rotation is imparted to the flow by the disc.
The following assumptions are made in the blade element theory:
• There is no interference between successive blade elements along the blade.
• Forces acting on the blade element are solely due to the lift and drag characteristics of
the sectional profile of a blade element.
5.4 HAWT Blade Design
5.4.1 Airfoil Selection
In this study, 4 airfoils viz, SG6043(10%), NACA 65-415, SD7080 and NACA 4418 were
selected from the literature for low Reynolds number application.
SG6043 profile (10%) has the highest lift coefficient and upgraded lift-to-drag performance for
low Reynolds number applications. Furthermore, SG6043 airfoil yields the best energy capture
in the presence of leading-edge roughness elements applicable for small variable-speed wind
turbine [43].
NACA 65-415 have high lift coefficients, which is favorable to obtain a high-power efficiency
in the HWAT [16]. The maximum lift of the SD7080 profile is slightly lower, and the drag is
fairly low at high Reynolds numbers and low lift coefficients, which makes for good wind
performance. [44]
NACA 4418 is suited for low Reynolds number and low wind speed applications.
29
Figure 12:Geometry Shape of different airfoils.
5.4.2 Analysis of airfoils
The chosen airfoils were tested using the Q Blade software at 82000 Reynolds number and
angles of attack (α) ranging from −150
to 100
with increments of 50
. Based on the variables
of maximum lift coefficient and maximum lift to drag ratio, the chosen airfoils are contrasted
with one another.
From the figure it can be observed that SG 6043 has maximum lift coefficient (Cl)max of 1.61
at α =12.50
followed by SD7080 whose (Cl)max is 1.17 at alpha 110
. (Cl)max of 1.23 occurs
at 150
for NACA 4418 and NACA 65-415 has (Cl)max value of 0.95 at 12.50
Figure illustrates
how the selected airfoils lift coefficients (Cl) changed in relation to various angles of attack
ranging from −150
to 100
.
SG 6043 NACA 65-415
SD 7080 NACA 4418
30
Figure 13: Lift coefficient (Cl) for different airfoils at Reynolds no=82000
31
Figure 14: Lift to drag ratio (Cl/Cd ) for different airfoils at Reynolds no. 82000
From Figure 14, lift to drag ratio for different airfoils are observed and the maximum lift to
drag ratio (Cl/Cd) of 57.7 appeared at α of 7.500
for SG6043 followed by SD 7080 with 46.47
at 𝛼 of 5.50
. NACA 65-415 has maximum lift to drag ratio (Cl/Cd) of 19.32 appeared at 𝛼 of
100
while NACA 4418 has maximum lift to drag ratio (Cl/Cd) of 15.37 appeared at α of 3.00
.
Q-blade software was used to test the selected airfoils at the Reynolds number of 82000 and
the angle of attack ranging from −150
to 100
.
32
Table 5.2: Maximum lift coefficient and lift to drag ratio at Reynolds number of 82000 for
selected airfoils.
Airfoil
Maximum Lift
Coefficient
Maximum Lift to Drag ratio
𝛼(0) (𝐶𝑙)𝑚𝑎𝑥 𝛼(0)
(𝐶𝑙/𝐶𝑑) ratio
SG 6043 12.5 1.61 7.5 57.7
NACA 65-
415
12.5 0.95 10 19.32
SD 7080 11 1.17 5.5 46.47
NACA 4418 15 1.23 3 15.37
Finally, from the obtained results it was found that SD 7080 (9.2%) airfoil has a wide range of
(Cl/Cd) ratios and showed a soft stall behavior in the alpha range of 40
to 90
. Therefore, SD
7080 airfoil is the best profile for small wind turbine to produce maximum power.
5.5 Rotor blade design by BEMT method
5.5.1 Calculation of the Maximum 𝐂𝐥/𝐂𝐝 Ratio
Finding the amount of design lift and design angle of attack from graphs that correlate to the
highest value of Cl/Cd ratio is crucial for the design of a horizontal axis wind turbine. The ratio
of the maximum lift-to-drag coefficient is found from the q-blade for the airfoil section of SD
7080 for the horizontal axis wind turbine blade. Maximum lift to drag ratio (Cl/Cd) of 46.47
appeared at 𝛼 of 5.50
for SD 7080.
5.5.2 Design lift coefficient and angle of attack calculation
Particularly at high tip speed ratios, the highest power coefficients may be obtained. The lift
coefficient and angle of attack values are obtained from the ( Cl − α ) curve corresponding to
the maximum (Cl/Cd) ratio. The design lift coefficient Cld and design angle of attack, αd,
which are represented by the Cld and α values found along the way, respectively, are crucial
design parameters. Cld = 0.88 and αd= 5.5° are the design lift coefficient and angle of attack,
respectively.
33
5.5.3 Design Tip Speed Ratio and Blade Count Options
Table 5.3: Selection of the number of blades and design tip speed ratio
Ratio of design tip speed, 𝜆 Number of blades
1 6-20
2 4-12
3 3-6
4 2-4
5-8 2-3
8-15 1-2
Maximum power coefficient occurs in the region of design tip speed ratio, 5≤ 𝜆𝑑 ≤ 8, for
(Cl/Cd) max= 46.3. Let's take the design tip speed ratio, 𝜆𝑑= 6, into consideration for design
considerations. According to the foregoing Table and the assumption that λd = 6, B = 3
represents the number of blades
5.5.4 Design Power Coefficient Calculation
Through the (Cl/Cd) ratio, the profile drag affects the power coefficient. The tip speed ratio
and the (Cl/Cd) ratio affect the lowering of the maximum power coefficient. In this collection
of maximum power coefficients, it appears that for a range of design tip speed ratios from 5 to
8, the highest theoretically achievable power coefficients fall between 0.30 and 0.50. Choose
the maximum power coefficient, (Cp)max = 0.5, keeping in mind that 𝜆𝑑=6, B=3, and
(Cl/Cd) 𝑚𝑎𝑥= 46.3. Cp= (Cp)maxx 0.8 = 0.5x0.8 = 0.4 for conservative design.
5.5.5 Determination of the Blade Radius
Equation 5.6, has been used to compute the blade radius:
Cp =
𝑃𝑒
1
2
𝜌𝜋𝑅2𝑉𝛼3
(5.12)
R=√
2𝑃𝑒
𝜌𝜋𝑉𝛼
3
𝐶𝑝
(5.13)
Where air density is 1.225 kg/m3, at the wind speed 5.4 m/s. Using the provided data, the rotor
radius is now calculated to be 14m. The turbine's speed is N = 60 rpm for a design tip speed
ratio of λd = 6 (determined using the formula λd(Rω/Vα) )
34
5.5.6 Angle of twist and blade chord calculation
The ideal blade, which has been divided into 7 cross sections of equal length along the radius,
is examined in this section in order to determine several characteristics, including the local
design speed, the angle of relative wind velocity, the twist angle, and the blade chord.
The equations given are used to compute the local speed ratio (λr), flow angle (ϕ), twist angle
(βT) and chord (Cr) of each section for the blade design.
Re =
ρVc
μ
(5.14)
Where, Re stands for Reynolds number, c is an airfoil's chord length, V is wind speed, and ρ
and μ are fluid's density and dynamic viscosity. In comparison to large-scale wind turbines,
small-scale wind turbines perform better with reduced Reynolds numbers because these two
components have extremely low values. Additionally, when the Reynolds number decreases,
the maximum lift coefficient decreases while the drag coefficient marginally rises. It shows
that as Reynolds number decreases, the lift to drag ratio drops precipitously, which leads to the
small horizontal axis wind turbine performing poorly.
PT = Cp
1
2
ρV3
A (5.15)
Where A = rotor swept area =, Cp = power coefficient, V = wind velocity, 𝜌 = air density, and
R signifies the radius of the rotor blades. With respect to a particular wind turbine, the power
coefficient (Cp) varies with tip speed ratio (λ). The tip speed ratio (λ), which is determined by
the Equation 5.16, is the ratio of the rotor blade tip speed to the wind speed.
λ =
λr
R
(5.16)
The chord and twist distribution of the blades were two key factors that the wind turbine's
maximum power coefficient took into account. Large values of the chord and twist at the root
of the wind turbine blade provide improved performance when there is less wind.
tan ϕ =
2
3λr
(5.17)
By increasing the blade size and quantity, the wind turbine's power production and beginning
performance are enhanced. [45] Schmitz formula is used for calculating chord length and twist
angle.
C(r)=
16πr
B(CL)D
sin2
(
1
3
arctan(
R
rλD
)) (5.18)
35
β(r) =
2
3
arctan [
R
r
1
λD
] – αD (5.19)
Where, c and r stand for the blade's chord length and local radius, respectively. λr stands for
the local tip speed ratio; B stands for the number of blades; and Twist angle = β. Chord length
and twist angle are calculated for every blade element (r) thus represented as C(r) and β(r).
Above Table shows the chord length and twist angle at different radius of the blade. Graph of
chord length and twist angle versus (r/R) are shown in figure below.
Table 5.4: Ideal Blade Sections, Local TSR, Angle of Attack, Blade Setting Angle and Chord
Cross
Section
No.
Local
radius
of
rotor,
r
Local
design
speed,
λr
=
λ
∗
r/R
Relative wind speed
angle
ϕ =
2
3
arc tan(
1
λr
)
Angle
of
Attack,
α
d
Twist
angle
β
T
=
ϕ
−
α
d
Chord,
Cr
m Degree Degree Degree m
1 1 0.43 44.53 5.5 39.034 2.734
2 3 0.8 25.25 5.5 19.750 2.729
3 5 1.2 16.68 5.5 11.178 2.002
4 7 1.6 12.29 5.5 6.79 1.527
5 9 2.0 9.69 5.5 4.190 1.222
6 11 2.4 7.98 5.5 2.484 1.015
7 13 2.8 6.78 5.5 1.284 0.866
36
Figure 5.7 Chord Length (Cr) vs. (r/R)
Figure 15:Chord length (Cr) vs. (r/R)
Figure 5.8: Twist Angle (β) vs. (r/R)
Figure 16:Twist angle (β) vs. (r/R)
37
From the calculated chord length and twist angle, blade was designed on Q-blade software
which was further designed on Ansys for CFD simulation.
Figure 17: Designed Turbine Blade
5.6 Rotor Specification
The specification of the rotor blade for the design of small horizontal axis wind turbine is
listed in table
Table 5.5: Specification of blade
Parameter Range
Rotor radius, R 14 m
Number of blades, B 3
Axis of rotation Horizontal
Tip Speed Ratio, 6
Rated Wind Velocity, V 5.4 m/s
Root Chord Length, Cr 2.734 m
Tip Chord Length, Ct 0.866 m
38
5.7 Calculation of Power Coefficient ( BEMT Method )
According to BEM theory, the blade is broken up into smaller components that work
independently of one another and perform aerodynamically as 2D airfoils with calculate
aerodynamic forces based on regional flow conditions.
For every blade element, the flow angle φ, AOA α, tangential force coefficient Cy, axial force
coefficient Cx , tip loss factor F, solidity rate 𝜎, and induction values ɑ and ɑ’ are calculated
iteratively.
The axial and angular changes are denoted by the a and a’ respectively, in the wind speed as
the wind passes through the rotor axis.
Following the discovery of these numbers, the axial force dFx, tangential force dFy, and power
dP for each blade element are separately determined. Integrating dFx, dFy, and dP yields the
rotor's total values Fx , Fx , and P.
The value of Cp is calculated for the rotor. These operations are applied as an algorithm in the
order given below:
The induction coefficients ɑ and ɑ’ are set initially to zero.
The flow angle φ is calculated as
φ = tan−1
(
(1−a)V1
(1+a′)ωr
) (5.20)
The AOA a is calculated as
α = ϕ − β (5.21)
Where,
the pitch angle β is known from the blade geometry.
The values of Cl and Cd for the chosen blade-section geometry at this AOA α are kept as
design lift coefficient and design drag coefficient.
The tangential force coefficient, which rotates the blade, is obtained as
Cy = Cl sin φ - CD cos φ (5.21)
The axial force coefficient, which affects the blade, is obtained as
Cx = Cl cos φ + CD sin φ (5.22)
The tip loss factor F is calculated as
F =
2
𝜋
cos−1(𝑒−𝑓) (5.23)
39
Where,
f=
𝐵
2
𝑅−𝑟
𝑟−sin 𝜑
(5.24)
The solidity factor is found for the blade element as
σ =
cB
2πr
(5.25)
The axial induction factor ɑ is calculated as
a=
1
4Fsin2φ
σCx
+1
(5.26)
If the calculated value of ɑ is less than ɑc (the critical value of ɑ), Step 10 is not applied.
However, if ɑ exceeds ɑc (ɑc may be accepted as 0.2), the Glauert correction is made as
a =
1
2
a[2 + 𝐾(1 − 2𝑎𝑐)]√[𝐾(1 − 2𝑎𝑐) + 2]2 + 4(𝐾𝑎𝑐
2 − 1) (5.27)
The tangential induction factor ɑ’ is calculated as
a′
=
1
4F sin φ cos φ
σCy
−1
(5.28)
The ɑ and ɑ’ can be calculated by using following equations:
|𝑎𝑛+1 − 𝑎𝑛| < 0.001 𝑎𝑛𝑑 |𝑎𝑛+1
′
− 𝑎𝑛
′ | < 0.001 (5.29)
Once the values of ɑ and ɑ’ have converged, the relative speed W is calculated as,
W= √[(1 − 𝑎)𝑉1]2 + [(1 + 𝑎′)𝜔𝑟]2 (5.30)
The values calculated thus far (W, 𝐶𝑥, and 𝐶𝑦) are used to calculate the axial force on a blade
element as
d𝐹
𝑥 = (
1
2
ρW2
cdr) Cx (5.31)
The tangential force on a blade element as
d𝐹
𝑦 = (
1
2
ρW2
cdr) Cy (5.31)
40
The torque on a blade element as
dT=rdFy (5.32)
and the power of a blade element as,
dP = 𝜔𝑑𝑇 (5.33)
By considering the blade number B, the total tangential force on the rotor is calculated as,
Fy = B ∑ (dFy)
i
N
i=1 (5.34)
the axial force as,
Fx = B∑ (dFx)i
N
i=1 (5.35)
and the power as,
P = B∑ (𝑑𝑃)𝑖
𝑁
𝑖=1 (5.36)
Finally, the power coefficient is calculated
Cp =
p
1
2
ρAV1
3
(5.37)
Thus obtained Cp is the power coefficient of designed turbine for 3 blades.
5.8 Simulation Method
All the necessary equations required to predict the performance of a particular blade section
through BEM simulation have been discussed lately.
As each element is assumed independent from the others, the power produced by each element
are calculated separately. Then finally the overall power is found by integrating results from
individual sections which then leads for the calculation of overall power coefficient of the
blade. A MATLAB code is generated to perform the BEM simulation and the stages listed
below are followed by the computation process.
41
6.1 2D Airfoil Simulation
Given that the blades created for this study's study had a chord length of 1 m.
We performed aerodynamic evaluations on the SD 7080 airfoil for AOA of 5.50
. Given that
the blades created for this study had a chord length of 1 m, Cl and Cd were derived after an
investigation of the pressure and velocity variations around airfoils. This is how these analyses
were carried out:
Design Modeler program was used to generate 2D geometries using the wing-section
geometries coordinates. The boundaries of the flow area surrounding the wing section
geometry were drawn using a C-mesh flow field geometry, as illustrated in Figure 18. The
boundary locations of the input (curve F) and output (line C) layers were established, and the
wing section (airfoil curve G) was set as wall. Asymmetrical edges AB and DE were drawn.
[46]
Figure 6.1.1: C-mesh flow domain and boundaries. [46]
Figure 18:C-mesh flow domain and boundaries
Chapter 6
CFD simulation
42
Figure 19: Geometry of flow domain and boundaries made in space claim [46]
This geometry was broken up into cells to create a mesh, incorporating the wing section and
flow area, as seen in Figure 19. A total of 288411 cells were placed for the mesh domain and
where small cells were utilized on the surface of the wing portion, while gradually massive
cells were utilized elsewhere. In order to solve the conservation equations, each cell can be
thought of as a very small control volume. The number of nodes on the structured mesh was
found to be 289677. [46] [47]
Figure 20: Meshed flow domain
43
Figure 21: Mesh generation for SD7080 utilizing structured grid
The pressure gradient at the boundary layer is precisely captured by a large number of grids
surrounding the airfoil surface. This is because flow separation is caused by the unfavorable
pressure gradient. When the separating region widens, a stall will happen. Since the flow
gradients are becoming closer to zero in the far-field region, the mesh resolution can get
gradually coarser. In Figure 20, the meshing overview is displayed.
The leading and trailing edges of the airfoil should be maximum. It is preferable for the
transition of mesh size to change gradually because a sharp change could reduce the numerical
precision.
The flow domain geometry was imported into Setup in the CFD simulation (ANSYS) when
the meshing procedure was finished. All cells underwent iterative solutions of the conservation
and turbulence model equations starting from the initial values. The K-epsilon standard model
was used as Viscous Model. [46]
44
Table 6.1: Computational conditions of airfoil simulation [46]
We selected inlet for standard initialization. As observed from figure 22, 650 iteration were
enough for precise calculation as the convergence was happening gradually.
Conditions Data
Airfoil SD7080
Simulation Type Steady Simulation
Fluid Material Air
Boundary condition Pressure far field
Stationary wall with no slip shear condition
Interpolating scheme Pressure (Standard)
Density (Second Order Upwind)
Momentum (Second Order Upwind)
Modified Turbulent Viscosity (Second Order
Upwind)
Pressure 101325 pa
Density 1.2 kg/m3
Kinematic Viscosity 1.4607 10-5 m2/s
Velocity Magnitude 5.4m/s
Angle of attack 5.5
X Component Flow Direction 0.99539619836
Y Component Flow Direction 0.09584575252
Turbulent Viscosity Ratio 1
Outlet Pressure Outlet Gauge Pressure 0 Pa
45
Figure 22: Scaled residuals of calculation of the fluid domain.
Velocity changes along lower surface and upper surface from the velocity contour & velocity
magnitude contour can be seen in Figure 23 & Figure 24.
Figure 23: Velocity contour on blade from CFD
46
Figure 24: Velocity magnitude on blade from CFD
According to the Bernoulli equation, the varying velocities at various positions around the
airfoil lead to changes in the pressure distribution at each location around the item. According
to the Bernoulli equation, the pressure decreases further as air velocity increases.
Figure 25: Pressure co-efficient on SD7080 airfoil
47
Figure 26: Pressure contour of SD7080 airfoil
As a result, there is an increase in the pressure difference between the top and lower surfaces,
producing a lift force. Figures shows the pressure coefficients along the upper and lower
surfaces of airfoil at AOAs of 5.50
6.2 HWAT 3D Simulation
In Solidworks2019, Blade geometry was generated. The design dimensions of the geometry
were integrated using Schmitz technique. Only one of the rotor blades of the turbine was
modeled; a periodic condition was imposed to account for the other two blades.
The rotational axis was chosen as the z-axis, with the blade extending along the negative x-
axis. The blades were placed in the fluid domain exactly as in the examples shown in Figure
27.
48
Figure 27: Blade Geometry made in Solidworks
The designed blade geometry was then prepared for CFD analysis. [46] Airfoil was imported
into Space claim from the Workbench of ANSYS and a flow domain was created around the
blade.
Figure 28: View of blade placement from rotor axis
49
The cylindrical figure displays the boundary parameters for the computational fluid domain's
surface. The computational flow's inlet and outlet diameter was set at 3R. For the rotor, the
domain is expanded to the 3R of the blade in the front-stream direction and 6R of the blade in
the back-stream direction.
Figure 29: Blade placement in fluid domain
For meshing purposes, we used Fluid Flow (Fluent with Fluent Meshing). Geometry was
imported from the workbench and added local sizing to the blade wall. For generating the
surface mesh, we kept a minimum size of 0.06 and a maximum size of 0.6, with a growth rate
of 1.2. Face Mesh was generated as seen in the Figure 30.
Figure 30: Generated Face Mesh of fluid domain
50
Geometry consisting of only fluid regions with no voids was kept with no topology shared.
After updating boundaries and periodic boundaries.
Figure 31: Generated Volume Mesh of fluid domain
Geometry consisting of only fluid regions with no voids was kept with no topology shared.
After updating boundaries and periodic boundaries, Volume Mesh was generated as seen in
Figure 31.
After completing the meshing process, the meshed geometries were imported into the solution
part, and the boundary conditions were chosen as those given in Table 6.2
51
Table 6.2: Boundary conditions of flow domain
Boundary Condition Choice
Simulation type Steady simulation
Fluid material Air
Flow type Incompressible flow
Temperature 300 K
Kinematic viscosity 1.7894e-05 m2/s
Pressure 101,325 Pa
Wind speed 5.4 m/s
CFD algorithm SIMPLE
Viscous model SST k–omega
Solution methods Pressure–velocity coupling
Least-squares cell based
Pressure(standard);density
(second-order upwind) Momentum
(second-order upwind) Turbulent kinetic energy
(first-order upwind) Specific dissipation rate
(first-order upwind)
Solution controls Pressure: 0.5
Momentum: 0.5
Density: 1.225 kg/m3
Turbulent kinetic energy: 0.75
Boundary
Conditions Velocity inlet (5.4 m/s); Velocity inlet top
(5.4m/s)
pressure outlet (gauge
pressure: 0)
Moving wall with no-slip shear condition
Cell Zone Condition Frame Motion
Rotational Velocity 6.3 rad/s
Number of mesh cells About 1270000
In the solution part, we plotted the Integral of pressure. Then initialized the solution with
Standard Solution, and computed from Inlet. For iteration, we kept 1000 iterations as our data
did not change gradually after that. From the residuals in Figure 32, we can see that the
solution did not vary appreciably after 250 iterations and that the variables approached the
convergence factor. Therefore, 1000 iterations were conducted in this study [46]. Integral of
pressure did not show change after 90 iterations as it converged.
In the CFD post, we rotated the flow domain 3 times to make a full circle around the Z-Axis,
as it was our principal axis. Full domain circle can be seen in Figure 34.
52
Figure 32: Scaled residuals of calculation of the fluid domain
Figure 33: Integral of pressure along the blade of SD7080 airfoil.
Then we created a Blade Velocity vector on the blade wall and kept the factor of 50, shown
in results. [46]Wall Shear vector on the blade wall was created and kept the factor of 50 as
shown in Figure 35.
53
Figure 34: Boundary conditions of the flow domain
Figure 35: Wall Shear vector on blade of SD7080
54
7.1 Background
The most major downside of many forms of renewable sources, aside from higher capital costs,
is that the energy source is widely distributed. This is an inherent issue with producing big
amounts of wind energy because it takes a lot of land to generate power adequate for a utility.
Having a way to rapidly determine how much space a wind farm will take up is important and
beneficial. This presents some challenges because wind farms are frequently placed along
ridgelines, making it challenging to determine how much area they actually occupy. The land
between turbines can frequently still be used for other purposes, including farming, even if they
may need a site with a lot of square meters.
7.2 Methodology
Power density of wind (ideal) ,
Pdensity= 1
2
⁄ ρAV3
Annual average power output,
Pavg = 0.5 ∗ Cp ∗ ρ ∗ v3
*A
= Cp*Pdensity*A
= Cp*Pdensity*
π
4
D2
(7.1)
Each turbine will need 64D2
rotor diameters of land area (Larea), with a rotor diameter spacing
of around (8D*8D).
So, Larea can be assessed as,
Larea =64D2
Now equation (1) stands as,
Chapter 7
Estimation of Wind Farm
55
Pavg = Cp*Pdensity*
π
4
D2
*
Larea
64
(7.2)
By simplifying equation (2),
Pavg
Larea
=
Pdensity
320
Or, Pavg m2
⁄ =
Pdensity
320
(7.3)
56
8.1 Analysis of SD 7080 blade at different Reynolds Number
Numerical simulation of SD7080 blade which was carried out at various Re values and
variation of the lift coefficient with respect to the different angle of attack are shown in Figure
36. From the results, It was found that the maximum values of Cl = 0.81, 1.15, 1.17, 1.18 and
1.2 were reached for Re = 30000, 60000, 82000, 10000 and 125000 respectively.
Figure 36: Lift Coefficient versus tip speed ratio
Also, from figure 37, It was found that the maximum values of Cl/Cd = 12.5, 39.7, 46.47, 53.4
and 59.8 were reached for Re = 30000, 60000, 82000, 10000 and 125000 respectively.
Finally, It was found that SD 7080 blade starts to produce the maximum power coefficient (Cp)
values from lower Re value of 60000 due to the aerodynamic shape of blade which produced
maximum Lift to Drag ratio (Cl/Cd) than Re value 30000. A high maximum Cl/Cd value
produces a high-power coefficient and a high OTSR. The maximum Cl/Cd values have a
significant impact on those values.
Chapter 8
Results and Discussion
57
Figure 37: Lift Coefficient versus tip speed ratio
8.2 Power co-efficient analysis of BEMT blade at Re=82000
The performance of a wind turbine is evaluated by determining its power coefficient or
coefficient of performance (Cp). The power coefficient as a function of the tip speed ratio
depicts the response of BEMT-blades at Re=82000.
From MATLAB code generated to perform the BEM simulation through computation process
as described previously in Chapter 5.8, Cp of BEMT-blade was found to be 0.3962.
Also, Cp from Q-blade simulation as shown was found to be 0.412, close to Cp of BEMT-blade.
From figure 38, it can be observed that the Cp values initially increase with the increase in the
value of tip speed ratio (λ), reaches the maximum, and then decreases. Furthermore, the blade
rotors with a wider range of tip speed ratios offer high power coefficients.
58
Figure 38: Power Coefficient versus tip speed ratio of SD7080 BEMT-blade.
Figure 39:Value of Lift Coefficient
From the graphical representation, the BEMT-blade SD 7080 generates Cp values of 0.412 at
λ = 6 respectively. A high maximum Cl/Cd value produces a high-power coefficient and a
high OTSR. The maximum Cl/Cd values have a significant impact on those values.
59
8.2.1 Variation of Lift and Drag Co-efficient
the polar curve of the lift coefficient: the horizontal-axis is the value of iteration times and the
vertical-axis represents the value of the lift coefficient. Initially, the value of lift coefficient
was going down, the lowest value is 0.7 when the simulation was iterated 500 times. Then, it
climbs to 1.1. [48]
Figure 40: Drag coefficient of SD7080 airfoil
According to CFD, the lift and drag forces for airfoil is less than the data provided in airfoil
database for wind turbines. This is most likely due to the various Reynolds numbers taken into
account in this investigation. [48]
8.2.2 Determination of Tip-Velocity
The velocity measurement made by ANSYS in Figure 41, shows how the rotation of the blades
causes the local wind turbine blade velocity to rise with radius. The tip's velocity, which is the
greatest velocity, is around 85.08 m/s. [46]
60
Figure 41: Blade Velocity vector on blade of SD7080
8.2.3 Calculation of co-efficient of power
A torque is a force that spins or twists something. It is the same as the force times the distance
for a wind turbine. This implies that longer blades can produce higher torque.
Through Function Calculator present in the result section of CFD,
Torque in the blade wall was found (T ) = 3665.6 [N m] (one blade )
Applying equation
Average Power = 69.094 kW
The values of the power coefficient of SD7080 obtained by CFD is smaller than the values of
the pressure coefficient obtained by BEM.
The results for the power coefficient CP of the HAWT in BEMT, Q-blade simulation and CFD
are compared one by one.
8.3 Comparison of co-efficient of power
As discussed in Chapter 5.8 and Chapter 8.3, Power Co-efficient of designed blade through
BEM Theory was found to be 0.3962 and while simulated the designed blade in Q-blade’s
Rotor BEM, Cp was found to be 0.412 previously shown in Figure 38.
61
Figure 42: Power Curve of Enercon E-30
And from Chapter 8.3.1, Cp of designed blade through CFD was found to be 0.3878.
From above shown figure 42, Maximum Power Coefficient for Enercon E-30 Turbine provided
in is seen to be 0.4.
Figure 43, shows the comparison of Cp among designed blade through 3 different procedure
and Enercon E-30. From figure, it can be observed that the Cp of the blade simulated in
Q-blade V2 has highest while CFD result shows lowest Cp.
The reason for the difference in power coefficient with CFD and BEM may be due to the
differences between the 2D case (BEM) and the 3D case (CFD). The lift/drag ratio in the 2D
airfoil aerodynamics data was taken at a low Reynolds number, thus resulting in a lower power
coefficient in BEM.
To identify the cause of the previously mentioned difference, it could be assumed that there
was negligible interference between the neighboring blade elements and that only lift and drag
forces were acting on the blade elements.
And finally, through the graph, it is observed that the selected turbine Enercon E-30 while
working at full efficiency have similar power coefficient as the power coefficient of designed
blade but has less power generation than the designed blade.
62
Figure 43: Comparison of Cp for designed blade and Enercon E-30.
8.4 Annual Power Output
For the purpose of evaluating wind turbine performance and determining the amount of energy
that could be gathered from wind turbines in the Hatiya area,
Enercon E-30 has been chosen. The wind turbines chosen are considered for operation at
standard hub heights of 50m. We calculate average power output, annual energy power output
and capacity factor.
8.5 Cost estimation
The cost of the electricity produced by wind turbines is usually relevant to the economic
viability of wind turbine projects. The project should be adjusted in this way to produce energy
at the lowest cost per kWh possible. The price of electricity generated by wind turbines depends
on a variety of elements, including wind speed, taxes, installation, operation, and maintenance.
0.375
0.38
0.385
0.39
0.395
0.4
0.405
0.41
0.415
Q-Blade BEM CFD Enercon E-30
Cp
Turbine
63
The cost of wind turbines is the only one that varies by location. Wind turbine prices can differ
depending on the manufacturer.
Table 8.1: Calculation of power output and capacity factor
Present value of cost can be assessed as follows:
PVC=I +𝐶𝑜𝑚𝑟 (
1+𝑖
𝑟−𝑖
) ∗ {1 − (
1+𝑖
1+𝑟
)
𝑛
} − 𝑠 (
1+𝑖
1+𝑟
)
𝑛
(8.1)
The Cost estimation (kWh) of energy produced by the nominated three turbines at Hatiya
region has been done under the following assumptions [n] Investment (I) includes the turbine
price and its 20% for the civil work and other belongings. Operation maintenance and repair
cost (Comr) is considered to be 25% of the annual cost of the turbine (machine price/lifetime).
The lifetime of the machine (n) is assumed to be 20 years.
The interest rate (r) and inflation rate (i) are taken to be 15 and 12%, respectively. Scrap value
S was taken to be 10% of the turbine price and civil work.
Serial Terms Values
1. Cut-in speed, 𝑉
𝑐 2.5 (𝑚𝑠−1
)
2. Cut-off speed, 𝑉𝑓 13.5 (𝑚𝑠−1
)
3. Rated speed, 𝑉
𝑟 25 (𝑚𝑠−1
)
4. Scale factor, c 6.39
5. Shape parameter, k 2
6. Average power output,𝑃
𝑎𝑣𝑔 59.22 KW
7. Annual energy power output (𝐸𝑜𝑢𝑡) 174.3 MWh
8. Capacity factor, Cf 19.74%
64
The cost of each kWh produced by the turbine in $/kWh, within the pay-off period, t, is
calculated from the following equation 8.2,
Costkwh=
PVC
Eout
(8.2)
Table 8.2 : Calculation of PVC and and unit cost
Serial Terms SD7080 Enercon E-30
1. Investment, I 317400 USD 414000 USD
2. Pay back period, n 10 years 10 years
3. Lifetime,T 20 years 20 Years
4. Comr 3306.3 USD 4312.5USD
5. Inflation rate,i 0.12 0.12
6. Interest rate,r 0.15 0.15
7. Scrap value,s 31740 USD 41400 USD
8. PVC 101389.6 USD 132246.7 USD
9. Eout 198.5 MWh 174.3 MWh
10. Unit cost($/KWh) 0.051 USD 0.076 USD
65
8.6 Required land area for wind farm
Table 8.3: Calculation of Required land area for two turbines
Serial Terms SD7080 Enercon E-30
1. Wind speed 5.41 ms-1
5.41 ms-1
2. Power density 96.984 Watt/m2
96.984 Watt/m2
3. Power available per
square meter
2.63 Kwh/year/m2
2.63 Kwh/year/m2
4. Annual power
output
198.5MWh 174.3MWh
5. Land area 75475.29 m2
66282.89 m2
Power extraction from wind energy..pptx
Power extraction from wind energy..pptx
Power extraction from wind energy..pptx
Power extraction from wind energy..pptx
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Power extraction from wind energy..pptx

  • 1. Theoretical and Computational Investigations of Optimized Blade of Horizontal-axis Wind Turbines for Power Extraction at Wind Farm By Suraj Prasad Subedi (Student ID:1707401) Shuvashis Biswas (Student ID: 1707411) Prosunto Kumar Biswas (Student ID:1707421) Muradul Kabir (Student ID:1707436) A Thesis submitted to the Department of Mechanical Engineering of Hajee Mohammad Danesh Science and Technology University in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering. Under the Supervision of Sudipta Paul Lecturer Department of Mechanical Engineering Hajee Mohammad Danesh Science and Technology University Dinajpur-5200 November 14, 2022
  • 2. ii DECLARATION This is to certify that the work presented in this thesis is carried out by the author(s) under the supervision of Sudipta Paul, Lecturer of Department of Mechanical Engineering, Hajee Mohammad Danesh Science and Technology University, Dinajpur. No portion of the work contained in this thesis has been submitted in support of an application for another degree or qualification of this or any other University or Institution of learning. Suraj Prasad Subedi Prosunto Kumar Biswas Student ID: 1707401 Student ID: 1707421 Shuvashis Biswas Muradul Kabir Student ID: 1707411 Student ID: 1707436
  • 3. iii ACKNOWLEDGEMENTS We would like to offer our sincere thanks to Hajee Mohammad Danesh Science and Technology University, and the Mechanical Engineering department in specific, for providing us the opportunity for doing this thesis work. This thesis appears in its current form due to the assistance and guidance of several people. We would, therefore, like to thank all of them. We would like to express our deep and sincere gratitude to our honorable thesis supervisor Sudipta Paul, Lecturer, Department of Mechanical Engineering, Hajee Mohammad Danesh Science and Technology University, for providing invaluable guidance and technological support throughout this thesis period. His dynamism, vision, sincerity and motivation have deeply inspired us. He has taught us the methodology to carry out the work and to present the thesis work as carefully as possible. It was a great privilege and honor to work under his guidance. We are extremely grateful to our parents for their love, prayers, caring and sacrifices for educating and preparing us for our future. We also express our thanks to all of our friends for their support and valuable advice. Finally, our thanks go to all the people who have supported us to complete the thesis directly or indirectly.
  • 4. iv ABSTRACT Designing horizontal-axis wind turbine (HAWT) blades to achieve satisfactory levels of performance starts with knowledge of the aerodynamic forces acting on the blades. In this thesis, SD7080 airfoil was chosen among four standard airfoils with aerodynamic properties that are specified in the airfoil database and geometry was generated in Q-blade software using the Schmitz formula. This geometry was investigated theoretically based on the blade-element momentum (BEM) theory and numerically by using computational fluid dynamics (CFD) to calculate the rotor power efficiency. Based on these findings, it was concluded that the CFD results validated the BEM theorem; the differences between the results obtained by these methods were likely due to the assumptions used when applying the BEM theory. While comparing annual power output, Commercial wind turbine (Enercon E-30) lagged behind optimized BEMT blade. Thus, unit cost($/kwh) seemed to be 0.051 USD for SD7080 while 0.076 USD was the unit cost ($/kwh) for Enercon E-30. But land requirement for the wind farm resulted to be lesser for Enercon E-30 than optimized SD7080 BEMT blade.
  • 5. v NOMENCLATURE B Blade Number F Combined correction factor P Power extracted from Windstream q Dynamic Pressure r Radius of blade element or collocation point R Radius of Rotor [m] T Thrust w Induced velocity in the z-direction k Shape parameter c Scale parameter v Observing wind speed h Turbine’s hub height, a Surface roughness co-efficient A Projected airfoil area (chord × span) C Chord length L Lift force D Drag force V Wind velocity t The pay-off period A Axial induction factor a´ Angular induction factor N Number of blade elements Q Tip loss correction factor r Radius and radial direction D Wind turbine rotor diameter V Voltage U Output pitch angle ƒ(v) Probability density dΓ Difference in bound circulation between control points Γ Bound Circulation 𝜃 Blade twist angle
  • 6. vi Ω Blade rotational speed Greek Symbols α Angle of attack β Blade pitch angle, γ Aerofoil inlet angle ρ Air density λ Tip Speed Ratio ω Rotational speed η Mechanical / Electrical efficiency Subscripts Cl Two-dimensional lift coefficient CQ Torque Coefficient CT Torque coefficient Cy Tangential force coefficient Cx Axial force coefficient Cp Power coefficient Cd Drag coefficient Cp Pressure coefficient Tm Prime mover input torque Pm Wind turbine output power Km Motor gain operator ωt The angular shaft speed. A0 Swept area of the wind turbine rotor Fx Axial force Fθ Tangential force Pmr Probability density function Pwr Mean power density Cld Design lift coefficient Comr Operation, Maintenanca and repair cost dFy Tangential force 𝜎 Total Rotor Solidity
  • 7. vii Aeff Effective swept area of the wind turbine rotor Ptotal Total pressure Pdynamic Dynamic pressure Aeff Effective swept area of the wind turbine rotor ABBREVIATION STDM Standard deviation method HAWT Horizontal-axis wind turbines VAWT Vertical-axis wind turbine RWM Rigid Wake Method MLM Maximum likelihood method PDM Power density method EEM Equivalent energy method MOM Method of moments BEM Blade element momentum EWM Expanding Wake Method TSR Tip Speed Ratio GM Graphical method
  • 8. viii Table of Contents DECLARATION.......................................................................................................................ii ACKNOWLEDGEMENTS..................................................................................................... iii ABSTRACT..............................................................................................................................iv NOMENCLATURE ..................................................................................................................v ABBREVIATION....................................................................................................................vii Chapter 1 ..................................................................................................................................1 Introduction..........................................................................................................................1 1.1 Background...............................................................................................................1 1.2 Present Energy Scenario of Bangladesh ...................................................................2 1.3 Motivation of the Research.......................................................................................6 1.4 Research Objectives..................................................................................................7 1.5 Thesis Outline...........................................................................................................8 Chapter 2 ..................................................................................................................................9 Literature Review.................................................................................................................9 2.1 Research on electricity generation and cost estimation ............................................9 2.2 Research on aerodynamic study of horizontal axis wind turbine .............................9 Chapter 3 ................................................................................................................................11 Wind site location...............................................................................................................11 3.1 Nominating wind sites ............................................................................................11 3.2 Geographical and statistical description of Hatiya Island.......................................13 3.3Methodology............................................................................................................14 3.3.1 Wind speed probability density function and cumulative distribution...........14 3.3.2 Shape parameter and scale parameter.............................................................14 3.3.3 wind power density and measurement............................................................16 Chapter 4 ................................................................................................................................17 Extrapolation of wind speed data .....................................................................................17 4.1Methodology............................................................................................................17 4.1.1Data analysis of wind speed and Weibull parameters .....................................18 4.2 Identification and detailed description of nominated wind turbine ........................20 Chapter 5 ................................................................................................................................21 Horizontal axis wind turbine.............................................................................................21 5.1Background..............................................................................................................21 5.2 Horizontal axis wind turbine concepts....................................................................21 5.2.1 Classification of HAWTs................................................................................22
  • 9. ix 5.2.2 Criteria in HAWT design................................................................................22 5.2.3 Performance parameter of HAWTs ................................................................23 5.3 Aerodynamics of HAWTs ......................................................................................26 5.3.1 Tip-speed Ratio...............................................................................................26 5.3.2 Schmitz formula..............................................................................................27 5.3.3 Blade Element Momentum (BEM) Theory ....................................................28 5.4 HAWT Blade Design..............................................................................................28 5.4.1 Airfoil Selection..............................................................................................28 5.4.2 Analysis of airfoils..........................................................................................29 5.5 Rotor blade design by BEMT method ....................................................................32 5.5.1 Calculation of the Maximum Cl/Cd Ratio......................................................32 5.5.2 Design lift coefficient and angle of attack calculation....................................32 5.5.3 Design Tip Speed Ratio and Blade Count Options.........................................33 5.5.4 Design Power Coefficient Calculation............................................................33 5.5.5 Determination of the Blade Radius.................................................................33 5.5.6 Angle of twist and blade chord calculation.....................................................34 5.6 Rotor Specification .................................................................................................37 5.7 Calculation of Power Coefficient ( BEMT Method ) .............................................38 5.8 Simulation Method..................................................................................................40 Chapter 6 ................................................................................................................................41 CFD simulation...................................................................................................................41 6.1 2D Airfoil Simulation .............................................................................................41 6.2 HWAT 3D Simulation............................................................................................47 Chapter 7 ................................................................................................................................54 Estimation of Wind Farm..................................................................................................54 7.1 Background.............................................................................................................54 7.2 Methodology...........................................................................................................54 Chapter 8 ................................................................................................................................56 Results and Discussion.......................................................................................................56 8.1 Analysis of SD 7080 blade at different Reynolds Number.....................................56 8.2 Power co-efficient analysis of BEMT blade at Re=82000 .....................................57 8.2.1 Variation of Lift and Drag Co-efficient..........................................................59 8.2.2 Determination of Tip-Velocity .......................................................................59 8.2.3 Calculation of co-efficient of power.............................................................60 8.3 Comparison of co-efficient of power.....................................................................60
  • 10. x 8.4 Annual Power Output ............................................................................................62 8.5 Cost estimation........................................................................................................62 8.6 Required land area for wind farm ...........................................................................65 Chapter 9 ................................................................................................................................66 Conclusion and Future Recommendations......................................................................66 9.1 Conclusion ..............................................................................................................66 9.2 Future Work Recommendations ............................................................................66 References..............................................................................................................................67 .
  • 11. xi LIST OF FIGURES Figure 1: Renewable energy share at Bangladesh ---------------------------------------------------- 3 Figure 2: Monthly mean wind speed in five sites at 10m height (2020) -------------------------11 Figure 3: Wind speed variation based on height at different locations. --------------------------12 Figure 4: Geographical Location of Hatiya island---------------------------------------------------13 Figure 5: Effects of parameters in probability density function -----------------------------------15 Figure 6: Effects of parameters in cumulative distribution function------------------------------16 Figure 7: Monthly mean wind speed variation at different height in Hatiya --------------------19 Figure 8: Monthly scale parameter at different height of Hatiya ---------------------------------20 Figure 9: Parts of Horizontal axis Wind Turbine --------------------------------------------------21 Figure 10:cross-section of a wind turbine blade -----------------------------------------------------24 Figure 11:Airfoil Section--------------------------------------------------------------------------------25 Figure 12:Geometry Shape of different airfoils.-----------------------------------------------------29 Figure 13: Lift coefficient (Cl) for different airfoils at Reynolds no=82000 --------------------30 Figure 14:Lift to drag ratio (Cl/Cd ) for different airfoils at Reynolds no. 82000--------------31 Figure 15:Chord length (Cr) vs. (r/R)------------------------------------------------------------------36 Figure 16:Twist angle (β) vs. (r/R) --------------------------------------------------------------------36 Figure 17: Designed Turbine Blade -------------------------------------------------------------------37 Figure 18:C-mesh flow domain and boundaries -----------------------------------------------------41 Figure 19: Geometry of flow domain and boundaries made in spaceclaim --------------------42 Figure 20: Meshed flow domain -----------------------------------------------------------------------42 Figure 21: Mesh generation for SD7080 utilizing structured grid--------------------------------43 Figure 22: Scaled residuals of calculation of the fluid domain. ----------------------------------45 Figure 23: Velocity contour on blade from CFD ---------------------------------------------------45 Figure 24: Velocity magnitude on blade from CFD------------------------------------------------46 Figure 25: Pressure co-efficient on SD7080 airfoil -------------------------------------------------46 Figure 26: Pressure contour of SD7080 airfoil-------------------------------------------------------47 Figure 27: Blade Geometry made in Solidworks ---------------------------------------------------48 Figure 28: View of blade placement from rotor axis -----------------------------------------------48 Figure 29: Blade placement in fluid domain ---------------------------------------------------------49 Figure 30: Generated Face Mesh of fluid domain --------------------------------------------------49 Figure 31: Generated Volume Mesh of fluid domain ----------------------------------------------50
  • 12. xii Figure 32: Scaled residuals of calculation of the fluid domain ------------------------------------52 Figure 33: Integral of pressure along the blade of SD7080 airfoil -------------------------------52 Figure 34: Boundary conditions of the flow domain -----------------------------------------------53 Figure 35: Wall Shear vector on blade of SD7080 -------------------------------------------------53 Figure 36: Lift Coefficient versus tip speed ratio----------------------------------------------------56 Figure 37: Lift Coefficient versus tip speed ratio----------------------------------------------------57 Figure 38: Power Coefficient versus tip speed ratio of SD7080 BEMT-blade. -----------------58 Figure 39:Value of Lift Coefficient--------------------------------------------------------------------58 Figure 40: Drag coefficient of SD7080 airfoil -------------------------------------------------------59 Figure 41: Blade Velocity vector on blade of SD7080---------------------------------------------60 Figure 42:Power Curve of Enercon E-30 -------------------------------------------------------------61 Figure 43: Comparison of Cp for designed blade and Enercon E-30-----------------------------62
  • 13. xiii LIST OF TABLES Table 1.1:Installed capacity and derated capacity of BPDB power plants ...............................2 Table 1.2: Present scenario of Bangladesh power sector ..........................................................3 Table 1.3: Renewable energy installed capacity .......................................................................4 Table 1.4: Details about completed and upcoming wind power plant ......................................5 Table 3.1: Monthly mean wind speed in three sites ...............................................................11 Table 4.1: Extrapolate wind data at 30m altitude ....................................................................18 Table 4.2: Extrapolate wind data at 50m altitude ....................................................................18 Table 4.3: Extrapolate wind data at 60m altitude ....................................................................19 Table 4.4: Datasheet of Enercon E-30 Wind turbine...............................................................20 Table 5.1 : Scale classification of wind turbines ....................................................................22 Table 5.2: Maximum lift coefficient and lift to drag ratio at Reynolds number of 82000 for selected airfoils. .......................................................................................................................32 Table 5.3: Selection of the number of blades and design tip speed ratio.................................33 Table 5.4: Ideal Blade Sections, Local TSR, Angle of Attack, Blade Setting Angle and Chord ..................................................................................................................................................35 Table 5.5:Specification of blade ..............................................................................................37 Table 6.1: Computational conditions of airfoil simulation .....................................................44 Table 6.2: Boundary conditions of flow domain .....................................................................51 Table 8.1: Calculation of power output and capacity factor....................................................62 Table 8.2: Calculated values of PVC and unit cost .................................................................64 Table 8.3: Calculation of Required land area for two turbines...............................................65
  • 14. 1.1 Background Energy is fundamental to economic and social development. On the dawn of the 21st century we are being faced with one of the toughest challenges ever – that of securing energy supply. We are still heavily dependent on oil resources which will eventually become depleted within a few decades. An increasing world population, an enlarged global economy and an improved standard of living all contribute to greater demands for energy. At the same time, we are facing the greatest threat to our survival on planet earth: global climate change. Climate change is not just an environmental threat but also an economic threat. Emissions of greenhouse gases, global warming and fossil fuel combustion have all become major concerns in recent decades. Nonrenewable energy's finite stock is dwindling every day. The price of crude oil is rising due to the lack of supply. Electricity generation from renewable energy is the most promising approach for addressing these issues. Boosting the use of renewable energy can help to bring down the price of fossil fuels and our reliance on them. Electricity generated from fossil fuels is produced in a very dirty and environmentally unfriendly manner, whereas renewable energy is clean and environmentally beneficial. Wind energy is one of the most effective power technologies that is ready today to be deployed globally on a scale that can aid in tackling this problem. Wind energy is the fastest-growing clean energy source due to its zero-emission nature. Wind energy, on the other hand, is regarded as the most abundant source of renewable energy, with the additional benefit of being more environmentally benign than other alternatives [1]. China establishes a new global record by generating 52 gigawatts in a single year. Total wind energy output has achieved a milestone of 733 GW, with a 26 percent growth rate, however it is declining with time; the maximum growth rate of 64.35 percentage was found in the year 1999 [2]. The negative marginal impacts of the Covid 19 pandemic affected electricity generation in 2020. Wind energy is a significant and viable source of renewable energy in the generation of power in highly developed countries. Denmark, for example, hopes to use wind energy to provide 50% of its electricity by 2023 [3] .Bangladesh is a country in South Asia with 35 meteorological stations situated across this land. The Bay of Bengal and the Ganges of Brahmaputra Meghna, which touches 19 of Bangladesh's 64 districts, are geomorphologically dominant in the nation's coastal zone. It covers 47,201 km2 , more than 32% of the country's total area [4] . At a height of 30 meters, the wind speed in Bangladesh's coastal regions is apparent over 5 𝑚𝑠−1 , which is adequate for generating energy [5] .In the Chapter 1 Introduction
  • 15. 2 world, renewable energy accounts for more than 26% of power whereas Bangladesh accounts for less than 5% [6], is illustrated in Figure 1. Per capita energy production is 560 kWh [7] ,however global total primary energy consumption is around 23398 kWh [8], which is substantially more than Bangladesh's per capita energy consumption. Even per capita generation of Bangladesh is lower than other south Asian countries. Bangladesh generates about 63 percent of its electricity from national grid gas supplies and imports 1160MW electricity per year [9] and wind accounts for only 0.04 percent of the 5 percent of renewable energy (Figure 1). The focus of this study is to demonstrate the installation of a wind turbine in Hatiya Island after analyzing Three different sites. As Hatiya is a tourist destination, more electricity is required to install new ideas, innovations, and businesses. 1.2 Present Energy Scenario of Bangladesh Bangladesh has a population of over 165 million people, making it a densely populated country. Though Bangladesh has made enormous improvement in the energy sector over the last decade, a large amount of electricity is required for living and manufacturing. Bangladesh currently has 100% access to electricity, and electrical generation capacity has expanded from 5 Gigawatts to 26 Gigawatts by end of the year 2021. [10], By 2030, the demand for electricity will exceed 40 Gigawatts. Natural gas produces around 60% of the electricity [11] Table 1.1: Installed capacity and derated capacity of BPDB power plants [12] Fuel type Capacity (MW) Total (%) Derated capacity (MW) Total (%) Coal 1768 7.91 1688 7.86 Gas 11342 50.75 11007 51.23 HFO 6278 28.09 5833 27.15 HSD 1341 6 1337 6.22 Hydro 230 1.03 230 1.07 Imported 1160 5.19 1160 5.4 Solar 229 1.02 229 1.07 Total 22348 99 21484 100
  • 16. 3 Figure 1: Renewable energy share at Bangladesh Table1.2: Renewable energy installed capacity [13] Wind and bio-energy were overlooked in the early years, which is regrettable. The government has taken some encouraging initiatives to harvest wind energy, as the annual average wind speed at 30 meters above sea level in the coastal zone exceeds 5 meters per second. In the divisions of Chittagong, Khulna, and Barisal, there will be 10 new wind power plants. The 60MW wind power plant at Chakaria upazila in Cox's Bazar is the largest of them all in terms of capacity. Technology Off-grid (MWp) On-grid (MWp) Total (MWp) Solar 349.57 203.36 552.93 Wind 2 0.9 2.9 Hydro 0 230 230 Biogas to Electricity 0.69 0 0.69 Biomass to Electricity 0.4 0 0.4 Total 352.66 434.26 786.92 69.50% 30% 0.40% 0.10% Solar Hydro wind Others
  • 17. 4 Table1.3: Present scenario of Bangladesh power sector [12] For this regard, Bangladesh's government has adopted some intellectual steps to produce that quantity. Increasing power generation from clean or renewable energy sources such as solar, wind, hydro, and bio-energy is included. On the renewable side, solar energy and hydropower plants are producing a significant amount of electricity; electricity from Sapchari waterfall, Khagrachari, has just been installed. Headline 2009 2022 Acquisition in last 13 years Generation capacity (MW) 4942 25514 20572 Grid substation power (MVA) 15870 55307 39437 Imported electricity (MW) 0 1160 1160 Highest generation (MW) 3268 13792 10524 Power plants(no.) 27 150 123 Expired plants 0 6 6 Total consumers 10800000 42100000 31300000 Transmission lines (Ckt. Km) 8000 13213 5213 Distribution line(km) 260000 621000 361000 System loss (%) 13.58 8.50 -5.08 Distribution loss (%) 14.33 8.48 -5.85 Per capita generation (KWh) 220 560 340 Access electricity (%) 47 100 53
  • 18. 5 Table1.4: Details about completed and upcoming wind power plant [14] SL. Project Name SID Capacity Location RE Technology Completion Date Present Status 1 1000 KW capacity 172 1 MWp Kutubdia, Cox' Bazar Wind (Off- Grid) 2015-12-31 Completed & Running 2 1000 KW capacity 171 1 MWp Kutubdia, Cox's Bazar Wind (Off- Grid) 2008-12-31 Completed & Running 3 900KW Capacity 173 900 KWp Sonagazi, Feni Wind (On- Grid) 2006-09-27 Completed & Running 4 2 MW Capacity 370 2 MWp Sirajganj Sadar Wind (On- Grid) 2021-08-15 Implementation Ongoing 5 30 MW 4176 30 MWp Sonagazi, Feni Wind (On- Grid) 2023-11-22 Under Planning 6 Mongla 50 MW 4173 55 MWp Mongla, Bagerhat Wind (On- Grid) 2023-11-15 Under Planning 7 50 MW Grid- tied 4175 50 MWp Cox'sbazar Wind (On- Grid) 2023-10-24 Under Planning 8 50 MW Grid- tied 4174 50 MWp Chandpur Sadar, Wind (On- Grid) 2023-07-12 Under Planning 9 10 MW 155 10 MWp Kalapara, Patuakhali Wind (On- Grid) 2022-12-31 Under Planning 10 60 MW 158 60 MWp Chakaria, Cox's Bazar Wind (On- Grid) 2021-12-31 Under Planning
  • 19. 6 1.3 Motivation of the Research Many studies and research regarding wind energy potential and aerodynamic investigation of horizontal axis wind turbine have been conducted before to understand the aerodynamic properties of airfoil and ways to design blade geometry through different procedures for extracting maximum [15] power possible. Most recent studies focused on optimization of turbine blades to investigate the effect of design parameters on rotor efficiency. These studies confirmed the optimization of turbine blade results in better performance in terms of power extraction. Along with design, study of possibilities to practically manufacture for required power extraction and cost analysis for wind farm can add new dimensions to this research. [16] performed an analysis for OTSR of NACA 65-415 and NACA 64-421 based on BEMT and CFD and their CFD results validated the BEM theorem, and the results obtained from those two methods were similar. They showed that the OTSR for low Reynolds number is between 4 and 7 depending on the DTSR and the airfoil. None of the previous studies considered optimized BEMT blade design for estimating power generation and cost analysis. In our knowledge this is the first study that compares the power production of designed BEMT blade with commercial wind turbine and predicts the cost analysis for wind farm. Most of the previous studies only considered cost analysis through commercial turbine or power co- efficient of optimized blade. Therefore, in the present study, optimum blade is designed and studied in CFD simulation for optimum power efficiency. A very important factor in case of designing a wind farm is the land area it needs. Among previous studies, only a handful reported the area needed for rated power generation only for commercial turbines. The present study predicts the land area requirement for wind farm for optimized BEMT blade.
  • 20. 7 1.4 Research Objectives In the present study, by numerical and computational fluid dynamics simulation (CFD) aerodynamic behavior of optimized bemt blade from SD7080 airfoil has been carried out with (i) different airfoil geometry (ii) different reynolds number (iii) different tip-speed ratio. The specific objectives and outcomes of the research work are as follows: • To develop a blade geometry model by Schmitz optimization method from a selected airfoil based on cl/cd ratio for low Reynold number application. • To investigate the power and torque on each local radius by dividing the blade into several elements by BEM theory. • To simulate the blade model for exploring the power co-efficient at specified wind speed. • To validate and compare the power co-efficient of blade by BEMT, Q-blade Rotor Simulation and CFD simulation. • To calculate the power generation of BEMT blade in comparison with selected commercial turbine for specified site. • To investigate the cost analysis of wind turbine setup and land area required for wind turbine. • To calculate the annual energy output and rate of energy per kilowatt comparing wind turbine through designed blade with commercial turbine.
  • 21. 8 1.5 Thesis Outline The present thesis focuses on the numerical and computational investigations of the optimized BEMT blade for maximum possible power generation considering the cost estimation , land area and energy output . An outline of this thesis is presented below: Chapter 1: Introduction- discussion about the key elements of this motivation behind this research work, and research objectives. Chapter 2: Literature Review- an account of previous research about aerodynamic behavior, power coefficient and cost analysis of wind turbine. Chapter 3: Wind Site- description of geographical location and calculation of wind power density. Chapter 4: Extrapolate data- extrapolation of wind speed calculation of data analysis of wind speed for different hub heights and Weibull parameter Chapter 5:HAWT Analysis- investigation of optimization process based on BEM theory. Chapter 6:CFD Simulation- description of elements of computational fluid dynamics. Chapter 7:Cost Estimation- wind Farm calculation of energy generated and required land area. Chapter 8: Results- describes the simulation model, power coefficient, cost analysis from the results of the study. Chapter 9: Future Work- summarizes the outcomes of the current research and provide a framework about the future direction.
  • 22. 9 2.1 Research on electricity generation and cost estimation Many studies related to wind energy potential and assessment have been performed in various locations around the world. [17] estimated the wind resources and also wind park design in El- Kef region, Tunisia. They investigated the characteristic of wind speed using Weibull distribution function and estimated the capacity factors for different wind turbine configurations. They performed economic evaluation to examine the feasibility of their project. [18] utilized different methods for comprehensive study of wind turbine utilization in Zarrineh, Iran. They used hourly, monthly, seasonal, and yearly wind data analysis. It was concluded that the location was marginal for harnessing wind energy. Also, the standard deviation and power density method were performed to determine best method for evaluation of wind power. [19] evaluated the wind energy potential for coastal locations along the north eastern coasts of Turkey. They illustrated that the monthly mean wind speed in the region varied between 1.53 m/s and 4.06 m/s. Also, they found that the maximum annual mean wind power density and wind energy density were 59.96 W/m2 and 525.25 kWh/m2 , respectively. [20] studied assessment of wind energy potential as a power generation source in the capital of Iran, Tehran. Long term measured wind speed data at 10 m height was used for this study. They calculated the annual average wind power densities which were between 74.00 and 122.48 W/m2 . They concluded that the wind energy potential for Tehran was suitable only for battery charging and water pumping. [21] investigated the assessment of wind energy potential at Kudat and Labuan, Malaysia, using Weibull distribution function. They used 10 m height measured wind speed data and found that highest monthly mean wind speeds were 4.8 m/s and 4.3 m/s at Kudat and Labuan, respectively. Also, they showed that the maximum wind power densities of Kudat and Labuan were 67.40 W/m2 and 50.81 W/m2 , respectively. They concluded that the two locations were suitable only for small-scale wind energy applications. 2.2 Research on aerodynamic study of horizontal axis wind turbine For horizontal-axis wind turbine (HAWT) blades [22] showed an analysis of 10 different airfoils to be suited best for low Reynolds numbers. They compared those airfoils on basis of high-lift, soft stall characteristics in addition to their overall good performance. From their results, SD7080 was selected as the best airfoil to produce maximum power in low wind speed applications. [16] performed an analysis for OTSR of NACA 65-415 and NACA 64-421 based on BEMT and CFD and their CFD results validated the BEM theorem, and the results obtained from those two methods were similar. They showed that the OTSR for low Reynolds number is between 4 and 7 depending on the DTSR and the airfoil. An HWAT was created by [23]to draw 2 kW of power from Kuakata, Bangladesh. They decided on the NACA 4418 airfoil type, and they correctly determined the design parameters for the chosen wind sites. They linearized the twist angle and the blade chord while taking into Chapter 2 Literature Review
  • 23. 10 account the least amount of tip and hub loss of power because it was not viable to produce the optimum blade form. [24] provided a description of a design approach based on the notion of blade element momentum (BEM). The procedure was used to increase the chord and twist distributions in the blades. A 100kW HAWT rotor was created AND few HAWT blades currently in use were evaluated using their computer program's aerodynamic efficiency calculations. The blade profile of a 5 kW HAWT was then constructed using the BEM approach, and CFD was utilized to assess the designed profile. For a one-megawatt (MW) wind turbine, [25] used strength and aerodynamics to determine the blade parameters, such as chord and thickness distributions along the blade. The redesigned NACA 63-621 and FX 66S-196 series profiles served as the foundation for the blade geometry. For simple connection with the rotor hub and to ensure structural strength on the inner part of the blade, the cylindrical profile was chosen close to the blade root. Three HAWTs were created by [26] with various chord and twist angle distributions along the blades. The airfoil utilized was NACA 4418, and the rotor had a 0.36 m diameter. Utilizing three different approaches, namely BEM, CFD, and wind tunnel tests, the power coefficient CP values of the planned rotors were computed. The ideal blade geometry, which matched that predicted by the Schmitz formula, was present in one of the proposed rotors. In comparison to those produced using the BEM theory, the CP values obtained by CFD were lower. The Reynolds number affects the maximum value of Cl/Cd. The maximum Cl/Cd values are thought to be related to the Reynolds number since they have a significant impact on the CP. The chord length of the airfoil, air viscosity, air density, and air relative velocity all affect the Reynolds number. The Reynolds number is influenced by the length of the blade and the wind speed because the relative air velocity on the blade airfoil depends on the rotor's rotational angular velocity. According to the Schmitz formula and other optimum-design methods, the chord length reduces from hub to tip in opposition to an increase in relative air velocity from hub to tip, therefore the Reynolds number does not vary along the blade. Reynolds number is greatly affected by Cl/Cd as they have significant impact on the Cp value. The chord length of the airfoil, air viscosity, air density, and relative velocity of air all affect the Reynolds number. The Reynolds number is influenced by the length of the blade and the wind speed because the relative air velocity on the blade airfoil depends on the rotor's rotational angular velocity. The Schmitz formula and other optimum-design formulas predict that the chord length drops from hub to tip inversely as the relative air velocity rises from hub to tip, resulting in no change in Reynolds number along the blade. Because the chord lengths of small and big WTs differ, so do their Reynolds numbers, and as a result, so do their power coefficients and TSR values. But for large Reynolds numbers, Reynolds number has no effect on the rotor's aerodynamic performance. According to [27], the optimum TSR and maximum CP values are smaller for smaller WTs than they are for bigger WTs as they have smaller Reynolds numbers.
  • 24. 11 3.1 Nominating wind sites The Bay of Bengal and the Ganges of Brahmaputra Meghna, which pass through 19 of Bangladesh's 64 districts, dominate the country's coastal zone geomorphologically. It covers 47,201 km2 which is almost 32% of whole country [28], Among them we primarily select three sites from two divisions. where Hatiya, Kutubdia situated in Chittagong division and Sayedpur situated in Rangpur division. To produce wind energy, speed of wind is most important. We got wind speed data from Bangladesh meteorological stations at a height of 10 meters. Table 3.1: Monthly mean wind speed in three sites [29] Velocity Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg Hatiya 2.33 2.53 3.57 5.14 5.02 5.81 5.64 4.67 3.38 2.06 1.63 1.65 3.63 Kutubdia 2.52 2.64 3.38 3.88 4.02 5.40 5.40 4.78 3.13 2.19 1.72 1.93 3.43 Sayedpur 2.67 3.14 4.60 4.76 4.00 3.73 3.56 3.05 2.74 2.12 2.04 2.24 3.22 Figure 2: Monthly mean wind speed in three sites at 10m height (2020) Chapter 3 Wind site location 0 1 2 3 4 5 6 7 JAN FB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC AVG Sayedpur Hatiya Kutubdia
  • 25. 12 Figure 3: Wind speed variation based on height at different locations. Hatiya is the best spot for producing more energy based on average wind speed. In this article, we will offer a statistical study of a wind power plant based on Rayleigh distribution and cost analysis of that plant.
  • 26. 13 3.2 Geographical and statistical description of Hatiya Island Hatiya is the largest upazilla in Noakhali district, both in terms of population and area. The Noakhali district, having an area of 3,600 km2 , consists of six upazillas, including the island part. Southeast of Bangladesh is where Noakhali is located. The coastal community of Noakhali has been hampered by seasonal tidal inundation and subsequent salinity intrusions, especially during the dry winter season when the flow of river water diminishes and the residents are particularly vulnerable to potential sea level rise. The ground level in Noakhali is lower than 10 m above the mean sea level. The island is a completely isolated territory located in between 22.07° and 22.35° north latitudes and longitudes in between 90.56° and 91.11° east [30]. Figure 4: Geographical Location of Hatiya island The western border of the island is established by Manpura Upazila, the northern border by Subarnachar Upazilla, the eastern boundary by the Meghna River, and the southern part by the Bay of Bengal [30]. The island is 2100 square kilometers in area, and it is inhabited to about 452,463 people. The island is underdeveloped in terms of services and infrastructure compared to the rest of the nation; the majority of the population works in agriculture and fishing. Only 130 km of Hatiya Island's roads are paved, and another 60 km are semi-paved. There are 216 people per km2 , which is considerably less than the average throughout the country. The island is not connected to the national electricity grid; the demand is supplied by a local grid. The island is not connected to the national electrical system; thus, a local grid meets the need. Three diesel generators with a total capacity of 400 kVA are used to power the island grid, although right now they can only produce a combined 500 kW. Using sea trucks, the diesel generator
  • 27. 14 fuel is delivered to and stored in the generator facility. The generators run for 12 hours each day and use about 1400 liters of fuel. From the foregoing description, it is clear that the island needs better supply and management for supplying (BPDP) with a 2 MW solar/wind hybrid system and later for a PV-Diesel hybrid system for power generation in the island's total population with electricity to meet their basic needs. Currently the government of Bangladesh plans to build a 15MW heavy fuel oil-based power plant. This is the project of BPDB constructed by Desh Power Ltd. will cost Tk 1,396.65 crore and will last for 15 years. 3.3Methodology The most effective way to analyze wind energy is to get information from specific meteorological authorities. Wind speed data was gathered at a height of 10 meters by the authors. Some frequency distribution methods are useful for obtaining all parameters, co- efficient, and extrapolation of wind data. Like as Weibull distribution, gamma distribution, inverse gaussian distribution, log normal distribution, normal square root of wind speed distribution etc. Here we use Weibull and Rayleigh distribution to analyze the wind parameters. 3.3.1 Wind speed probability density function and cumulative distribution Probability density function can be described as, ƒ(v)= ( 𝑘 𝑐 )( 𝑣 𝑐 )𝑘−1 𝑒𝑥𝑝[−( 𝑣 𝑐 )𝑘 ] (3.1) here, ƒ(v) is the probability density function of observing speed v k is the shape parameter which is dimensionless c denoted as scale parameter Rayleigh distribution is a special case of the Weibull distribution where k=2. Then the equation 3.1 stands as ƒ(v)= 2𝑣 𝑐2 𝑒𝑥𝑝[−( 𝑣 𝑐 )𝑘 ] (3.2) The cumulative probability distribution function can be assessed as, F(v)=1- 𝑒𝑥𝑝[−( 𝑣 𝑐 )𝑘 ] (3.3) 3.3.2 Shape parameter and scale parameter Shape parameter and scale parameter can be calculated by using a lot of methods. Like as Maximum likelihood method (MLM), Standard deviation method (STDM), power density method (PDM), equivalent energy method (EEM), graphical method (GM), Method of moments (MOM). Among all of methods standard deviation and Method of moments is more preferable to find out the value of shape parameter k. Scaling parameters fits for all methods. According to standard deviation method,
  • 28. 15 Shape parameter, k=( 𝜎 𝑣 ̅ ) −1.086 ( 3.4) Where, σ stands as standard deviation (SD) SD, σ=√∑ (v𝑖 − 𝑣̅) 𝑛 𝑖=1 (3.5) 𝑣̅ is denoted as mean wind speed Scale parameter, C= 𝑣 ̅ Γ[1+ 1 𝑘 ] (3.6) Where Γ[ ] is the gamma function According to method of moments, Shape parameter, K=[ 0.9874 𝜎 𝑣 ̅ ] 1.0983 (3.7) Scale parameter, C= 𝑣 ̅ Γ[1+ 1 𝑘 ] (3.8) Figure 5: Effects of parameters in probability density function 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 1 2 3 4 5 6 7 8 9 10 11 12 13 k=2;c=7 k=2;c=9 k=2;c=8
  • 29. 16 Figure 6: Effects of parameters in cumulative distribution function 3.3.3 wind power density and measurement Wind power density per unit area of a site at any time can be assessed as, 𝑃 𝑤= 1 2 ρc3 Γ [ k+3 k ] (3.9) Where ρ is stands for mean air density whose value is 1.225 kgm−3 at 15𝑜 𝐶 A negligible error occurs of power density in the time of calculating. Error (%) = 1 𝑛 ∑ ( 𝑃𝑤𝑟−𝑃𝑚𝑟 𝑃𝑚𝑟 ) 𝑛 𝑖=1 (3.10) Pmr is the wind power density for the probability density function Pwr is the mean power density 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8 10 12 14 k=2;c=7 k=2;c=9 k=2;c=8
  • 30. 17 4.1Methodology Basically, wind speed is lower at the height of 10m.To generate more electricity highly needed better wind speed. on the other hand, Modern wind turbines designed for higher heights. To estimate turbine hub height’s Wind speed the following equation: v v0 = ( h h0 )a (4.1) Where, h is turbine’s hub height, h0 is reference height, v is the wind speed at turbine height, v0 is the wind speed at reference height ‘a’ is denoted as surface roughness co-efficient which is expressed as following equation, a= 0.37−0.088ln(v ̅) 1−0.088ln( h0 10 ) (4.2) In this article, the author gathered wind speed data at a height of 10 meters and extrapolated the wind speed at 30 meters, 50 meters and 60 meters respectively. The comparison of wind speed data in Hatiya at the heights of 10m, 30, 50m, and 60m is shown in Figure 7 (Histogram). Shape and scale parameter can also extrapolate by using Weibull distribution. Estimating shape parameter and scale parameter at turbine height expressed as, Ch = C0 [ h h0 ] n (4.3) kh = k0[1−0.088ln( h0 10 ) [1−0.088ln( h 10 ) (4.4) Where n is the law exponent of power and it can be assessed as; n= 0.37−0.088ln(C0) 1−0.088ln( h 10 ) (4.5) Average power output and Capacity factor are the performance parameters of wind turbine. Capacity factor is the ratio of Average power output and rated electrical power or it can be mentioned as the average power output over a period to the rated electrical power. Capacity factor, Chapter 4 Extrapolation of wind speed data
  • 31. 18 Cf = Pavg PR (4.6) In this case, PR indicates to rated electrical power. Average power output, Pavg = PR ∗ [ 𝑒 −( 𝑉𝑐 𝑐 ) 𝑘 −𝑒 −( 𝑉𝑟 𝑐 ) 𝑘 ( 𝑉𝑟 𝑐 ) 𝑘 −( 𝑉𝑐 𝑐 ) 𝑘 − 𝑒 −( 𝑉𝑓 𝑐 ) 𝑘 ] (4.7) 𝑉 𝑟, 𝑉𝑓, 𝑉 𝑐 are used to represent the terms rated wind speed, cut-off wind speed, and cut-in wind speed. Accumulated annual(yearly)energy output, 𝐸𝑜𝑢𝑡 = Pavg*365*24 (4.8) 4.1.1Data analysis of wind speed and Weibull parameters Author collected the data of Hatiya at 10m height from Bangladesh meteorological authority. In the month of June, the maximum velocity is 5.81 ms−1 . Wind speed is often higher from March to August than other seasons. Equation 4.3 and 4.4 are used to calculate scale parameter and wind power density.in this article, we extrapolate the wind speed data at 30m,50m,60m height by using the equation no. 4.1, 4.2, 4.3, 4.4 and 4.5 Table 4.1: Extrapolate wind data at 30m altitude Criteria jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg. Wind speed 3.22 3.47 4.74 6.59 6.45 7.36 7.16 6.04 4.51 2.88 2.33 2.36 4.70 Scale Para. 1.95 2.66 4.44 5.85 5.87 6.77 6.76 6.26 4.13 2.62 1.70 1.71 4.23 Table 4.2: Extrapolate wind data at 50m altitude Criteria Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg. Wind speed 3.75 4.02 5.41 7.39 7.25 8.21 8.01 6.81 5.16 3.37 2.76 2.79 5.41 Scale Para. 4.48 4.81 6.41 8.68 8.51 9.62 9.38 8.02 6.12 4.05 3.33 3.36 6.40
  • 32. 19 Table 4.3: Extrapolate wind data at 60m altitude Criteria Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg Wind speed 3.96 4.24 5.67 7.71 7.55 8.54 8.33 7.11 5.41 3.57 2.93 2.96 5.66 Scale Para. 4.82 5.15 6.82 9.17 8.99 10.13 9.89 8.48 6.52 4.36 3.61 3.64 6.80 Figure 7: Monthly mean wind speed variation at different height in Hatiya 0 1 2 3 4 5 6 7 8 9 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 10m 30m 50m 60m
  • 33. 20 Figure 8: Monthly scale parameter at different height of Hatiya 4.2 Identification and detailed description of nominated wind turbine The most important factor in selecting a turbine is the cut-in speed. The mean monthly wind speeds in November and December at 50 meters height are 2.76 and 2.79 ms−1 . So, the cut- in speed of the turbine must be less than 3 ms−1 . If not, Power generation will stop in those months. We selected Enercon E-30 which is manufactured by a German company called Enercon GmbH. Its rated power is 300KW and cut in speed is 2.5ms−1 . This turbine’s blade is made of Glass-fiber reinforced material. This turbine used a synchronous generator whose voltage is 440 Voltage and maximum speed is 48 rpm. The turbine’s tower is made of steel and conical in shape. Table 4.4: Datasheet of Enercon E-30 Wind turbine 0 2 4 6 8 10 12 Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 10m 30m 50m 60m Model name of Turbine Turbine Hub height (m) Rotor diameter (m) Swept Area (𝑚2 ) Rated power 𝑃𝑅 (KW) Cut-in speed 𝑉 𝑐 (m/s) Rated speed 𝑉 𝑟 (m/s) Cut-off speed 𝑉𝑓 (m/s) Enercon E-30 50 29.6 707 300 2.5 13.5 25
  • 34. 21 5.1Background A wind turbine is a machine which converts the power in the wind into electricity. This is contrast to a windmill, which is a machine that converts the wind’s power into mechanical power. There are two great classes of wind turbines, horizontal- and vertical-axis wind turbines. Conventional wind turbines, horizontal-axis wind turbines (HAWT), spin about a horizontal axis. As the name implies, a vertical-axis wind turbine (VAWT) spins about a vertical axis. Today the most common design of wind turbine and the only kind discussed in this thesis in the view of aerodynamic behavior is the horizontal-axis wind turbines. In this chapter, detail information about the conventional horizontal-axis wind turbines will be given but before that some unconventional and innovative horizontal-axis wind turbine concepts will be mentioned. 5.2 Horizontal axis wind turbine concepts Modern commercial wind turbines frequently employ lift driven force wind turbines because of their capacity to produce large power coefficients. The horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT), two different types of lift-driven force wind turbines, can be distinguished by the orientation of their working axes. Each form of wind turbine has its own benefits and drawbacks depending on the working axis, enabling it to situations. Over the past few decades, HAWTs have undergone tremendous development and widespread application, emerging as the industry standard for contemporary wind energy technologies. The ability to attain improved energy efficiency is the reason why HAWTs are so widely used. However, the improved energy efficiency of HAWTs only materialized under conditions of high energy quality, which included wind flow velocity and flow direction [31] Figure 9: Parts of Horizontal axis Wind Turbine [32] The structure of a modern HAWT is shown in Figure 9. The main rotor shaft and the generator are placed on the top of a tower. To achieve an optimum power output, the yawing mechanism is required to face the changeable wind directions. The yawing mechanism of HAWTs helps Chapter 5 Horizontal axis wind turbine
  • 35. 22 the blades take advantage of the wind velocity through a computer-controlled motor in modern wind farms. The height of a tower also will influence the power output of HAWTs. It was found that a higher tower can help a wind turbine reach higher wind velocities in higher altitudes and wind shear [33] However, the tall tower of HAWT cannot have good integration with urban environments and it also will have a high cost of transportation and installation. Moreover, the support tower takes the entire load from the blades, rotor, and gear box on the top and this will cause an increase in the overall cost. Due to many moving parts, HAWTs require high maintenance [34] .The reason that HAWT cannot be widely used in urban areas can be concluded as the high cost of transportation and installation, high maintenance, and bad integration with urban environments. 5.2.1 Classification of HAWTs Because the interconnection of wind turbines to utilities becomes their principal application, the average size of HAWTs has grown. The question of ‘size classification’ has been raised, as well. HAWTs are classified as shown in Table 5.1 according to their diameters and/or their rated powers. Table 5.1: Scale classification of wind turbines [35] Scale Rotor Diameter Power Rating Small Less than 12m Less than 40kv Medium 12m-45m 40kw-999kw Large 46m and larger 1.0mw and larger 5.2.2 Criteria in HAWT design Before ending this chapter, a few words to be mentioned in about the criteria in HAWT design and construction include: • Number of turbine blades • Rotor orientation; downwind or upwind rotor • Turbine torque regulation • Turbine speed; fixed or variable rotor speed • Blade material, construction method and profile (airfoil section) • Hub design; rigid, teetering or hinged • Power control via aerodynamic control (stall control) or variable pitch blades. • Orientation by self-aligning action (free yaw) or direct control (active yaw)
  • 36. 23 • Types of mechanical transmission and generator; synchronous or induction generator; gearbox or direct drive transmission • Type of tower; steel or reinforced –concrete shell or steel truss with tension cables The design of a rotor is essential to a wind turbine's ability to produce power since the interaction of the rotor and wind is what generates power in a wind turbine. 5.2.3 Performance parameter of HAWTs The mean wind flow and turbulent fluctuations are combined to form the wind. In the 1920s and 1930s, Betz [36] and [37] were the first to analyze the performance of wind turbine rotors. Wilson et al. [38] and O Vries then developed and expanded the theory for a solution by digital computers. The performance characteristics of a rotor's annular section are determined using a combination of momentum theory and blade element theory in the analysis of rotor aerodynamic features. The performance of the whole rotor was determined by integrating the values obtained from each annular section. [39] The performance of a wind turbine rotor is usually characterized by power coefficient (Cp), which is expressed as, Cp = P 1 2 ρAV3 (5.1) As estimated by Betz in 1926, the optimal power output of a wind turbine rotor is around 59.3 percent. The analysis was conducted under ideal circumstances with the following presumptions: • 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. In order to produce mechanical forces as a result of the airfoil's relative motion to a surrounding fluid, it has been integrated into a wind turbine system. The airfoils on the blades can be used to collect wind energy. The cross-sectional shape is crucial for wind turbine blades to achieve the specified aerodynamic performances, such as the maximum desired rotor power, the expected airfoil qualities, and strength considerations. Figure 10 depicts the cross-section of a wind turbine blade. The leading and trailing edges, respectively, are where the mean camber line’s greatest forward and backward points are located. The chord line of length c is the straight line joining the
  • 37. 24 leading and trailing edges. The camber is the distance measured perpendicular to the chord line between the mean camber line and the chord line. The thickness is measured perpendicular to the chord line and is the distance between the upper and lower surfaces. The angle between the chord line and the relative wind id referred to as the angle of attack. The length of the airfoil measured perpendicular to its cross-section is referred to as the span of the airfoil. The leading-edge radius, mean camber line, maximum thickness and thickness distribution of the profile, and trailing edge angle are all factors that affect an airfoil's ability to move through the air efficiently. Figure 10:cross-section of a wind turbine blade [40] The distribution of forces on a portion of an airfoil while air flows over its surface is based on the design of wind turbine blades. low pressure is caused by an increase in velocity in the airfoil convex surface. The viscous friction between the air and the airfoil surface slows the air flow in the meantime. Two forces and one momentum can be produced on the chord at a distance of c/4 from the leading edge by the effects of pressure differences between upper and lower surfaces and friction forces. These are the two forces and one moment: The force perpendicular to the direction of the incoming air flow is known as the lift force. The pressure difference on the top and lower airfoil surfaces is what generates the lift forces. The force parallel to the direction of the incoming air flow is known as drag force. The pressure difference between airfoil surfaces facing toward and away from the approaching flow, as well as viscous friction forces on the surface of the airfoil, are what generate the drag force. Pitching moment is described as a moment about an axis that is perpendicular to the cross- section of an airfoil.
  • 38. 25 Figure 11:Airfoil Section The two-dimensional lift coefficient, drag coefficient, pitching moment coefficient, and pressure coefficient can be expressed as Cl, Cd, Cm and Cp respectively. The function of each coefficient is shown as, Cl = L l 1 2 ρcV3 = Lift Dynamic (5.2) Cd = D l 1 2 ρcV3 = Drag Dynamic (5.3) Cm = M 1 2 ρcV3A = Pitching moment Dynamic moment (5.4) Cp = Ptotal−Pdynamic 1 2 ρcV3 = Static pressure Dynamic pressure (5.5) where ρ is the density of air, V is the velocity of free stream air flow, A is the projected airfoil area (chord × span), c is the airfoil chord length and l is the airfoil span, L is the lift force and D is the drag force, Ptotal is total pressure and Pdynamic is dynamic pressure.
  • 39. 26 There are other important dimensionless coefficients of a rotor section, which include power coefficient, thrust coefficient, tip speed ratio and pressure coefficient: Cp = P 1 2 ρAV3 (5.6) CT = T 1 2 ρAV3 (5.7) The airfoils with high maximum lift coefficients, low pitching moment, and low drag are favored in modern commercial wind turbine blades For HAWT specifically, a thin form of the same airfoil was used in the design of the blade tip to achieve a high lift to drag ratio, and a thicker version of the same airfoil was used in the design of the root region to provide structural support [41]. A general perspective on how to design the blades of unique wind turbines can be gained through studying wind turbine blades. 5.3 Aerodynamics of HAWTs Wind turbine power production depends on the interaction between the rotor and the wind. the wind may be considered to be a combination of the mean wind and turbulent fluctuations about that mean flow. Periodic aerodynamic forces caused by wind shear, off-axis winds, rotor rotation, randomly fluctuating forces induced by turbulence and dynamic effects are the source of fatigue loads and are a factor in the peak loads experience by a wind turbine. These are, of course, important, but can only be understood once the aerodynamics of steady state operation has been understood. 5.3.1 Tip-speed Ratio The Tip Speed Ratio (TSR) is a crucial element in the design of wind turbines. TSR stands for the ratio of wind speed and wind turbine blades' tips' speed. TSR = speed of rotor tip wind speed (5.8) If the wind turbine's rotor rotates too slowly, the majority of the wind will flow directly through the space between the blades and leave it with no electricity. The blades, however, will blur and behave like a solid wall to the wind if the rotor spins too quickly. Turbulence is also produced by rotor blades as they move through the air. The following blade will strike that agitated air if it moves too swiftly. Therefore, it can occasionally be beneficial to slow down your blades. (Calculating the tip-speed ratio of your wind turbine)
  • 40. 27 5.3.2 Schmitz formula The Betz limit was reached by applying Bernoulli's principle and the conservation of linear momentum to describe the power that the wind turbine extracts from the air. Schmitz built a more complete model of the rotor plane flow on the principle of angular momentum conservation. The most effective chord length and pitch angle distribution around the radius of the blade is found using this power calculation approach. [42] The Schmitz method starts thin closest to the hub, reaches a maximum at roughly 15% of the blade length, and then starts to diminish, whereas the Betz method predicts that the blade should get thicker as it gets closer to the hub. Betz and Schmitz are different in that Schmitz accounts for the swirl loss or wake loss that can be described as, ηwake = Cp,schmitz Cp,Betz (5.9) The performance of the wind turbine can be calculated using Blade Element Momentum (BEM) theory after the chord length and pitch angle distributions have both been established. Schmitz developed equations describing the conservation of angular momentum in order to maximize the twist angle and chord length as functions of the blade radius. Particular Schmitz equations take the airflow behind the rotor into account and call for assumptions about the TSR and the most effective AOA, which corresponds to the highest lift- to-drag ratio for any given airfoil. C(r)= 16πr B(CL)D sin2 ( 1 3 arctan( R rλD )) (5.10) β(r) = 2 3 arctan [ R r 1 λD ] – αD (5.11) Thus, the HAWT geometry dimensions are obtained using Schmitz formulas. The design Cld and αD values for respective airfoil were calculated according to the graphs obtained in Q- blade software. Then, those values were again calculated based on results of 2D CFD simulations of the airfoils. Thus, Schmitz formulas are used to get the HAWT geometry dimensions.
  • 41. 28 5.3.3 Blade Element Momentum (BEM) Theory BEM theory is a compilation of both momentum theory and blade element theory. Momentum theory, which is useful in predicted ideal efficiency and flow velocity, is the determination of forces acting on the rotor to produce the motion of the fluid. This theory has no connection to the geometry of the blade, thus is not able to provide optimal blade parameters. Blade element theory determines the forces on the blade as a result of the motion of the fluid in terms of the blade geometry. By combining the two theories, BEM theory, also known as strip theory, relates rotor performance to rotor geometry. The assumptions made in BEM theory is the aggregate of the assumptions made for momentum theory and blade element theory. The following assumptions are made for momentum theory: • Blades operate without frictional drag. • A slipstream that is well defined separates the flow passing through the rotor disc from that outside disc. • The static pressure in and out of the slipstream far ahead of and behind the rotor are equal to the undisturbed free-stream static pressure (P1 = P3) • Thrust loading is uniform over the rotor disc. • No rotation is imparted to the flow by the disc. The following assumptions are made in the blade element theory: • There is no interference between successive blade elements along the blade. • Forces acting on the blade element are solely due to the lift and drag characteristics of the sectional profile of a blade element. 5.4 HAWT Blade Design 5.4.1 Airfoil Selection In this study, 4 airfoils viz, SG6043(10%), NACA 65-415, SD7080 and NACA 4418 were selected from the literature for low Reynolds number application. SG6043 profile (10%) has the highest lift coefficient and upgraded lift-to-drag performance for low Reynolds number applications. Furthermore, SG6043 airfoil yields the best energy capture in the presence of leading-edge roughness elements applicable for small variable-speed wind turbine [43]. NACA 65-415 have high lift coefficients, which is favorable to obtain a high-power efficiency in the HWAT [16]. The maximum lift of the SD7080 profile is slightly lower, and the drag is fairly low at high Reynolds numbers and low lift coefficients, which makes for good wind performance. [44] NACA 4418 is suited for low Reynolds number and low wind speed applications.
  • 42. 29 Figure 12:Geometry Shape of different airfoils. 5.4.2 Analysis of airfoils The chosen airfoils were tested using the Q Blade software at 82000 Reynolds number and angles of attack (α) ranging from −150 to 100 with increments of 50 . Based on the variables of maximum lift coefficient and maximum lift to drag ratio, the chosen airfoils are contrasted with one another. From the figure it can be observed that SG 6043 has maximum lift coefficient (Cl)max of 1.61 at α =12.50 followed by SD7080 whose (Cl)max is 1.17 at alpha 110 . (Cl)max of 1.23 occurs at 150 for NACA 4418 and NACA 65-415 has (Cl)max value of 0.95 at 12.50 Figure illustrates how the selected airfoils lift coefficients (Cl) changed in relation to various angles of attack ranging from −150 to 100 . SG 6043 NACA 65-415 SD 7080 NACA 4418
  • 43. 30 Figure 13: Lift coefficient (Cl) for different airfoils at Reynolds no=82000
  • 44. 31 Figure 14: Lift to drag ratio (Cl/Cd ) for different airfoils at Reynolds no. 82000 From Figure 14, lift to drag ratio for different airfoils are observed and the maximum lift to drag ratio (Cl/Cd) of 57.7 appeared at α of 7.500 for SG6043 followed by SD 7080 with 46.47 at 𝛼 of 5.50 . NACA 65-415 has maximum lift to drag ratio (Cl/Cd) of 19.32 appeared at 𝛼 of 100 while NACA 4418 has maximum lift to drag ratio (Cl/Cd) of 15.37 appeared at α of 3.00 . Q-blade software was used to test the selected airfoils at the Reynolds number of 82000 and the angle of attack ranging from −150 to 100 .
  • 45. 32 Table 5.2: Maximum lift coefficient and lift to drag ratio at Reynolds number of 82000 for selected airfoils. Airfoil Maximum Lift Coefficient Maximum Lift to Drag ratio 𝛼(0) (𝐶𝑙)𝑚𝑎𝑥 𝛼(0) (𝐶𝑙/𝐶𝑑) ratio SG 6043 12.5 1.61 7.5 57.7 NACA 65- 415 12.5 0.95 10 19.32 SD 7080 11 1.17 5.5 46.47 NACA 4418 15 1.23 3 15.37 Finally, from the obtained results it was found that SD 7080 (9.2%) airfoil has a wide range of (Cl/Cd) ratios and showed a soft stall behavior in the alpha range of 40 to 90 . Therefore, SD 7080 airfoil is the best profile for small wind turbine to produce maximum power. 5.5 Rotor blade design by BEMT method 5.5.1 Calculation of the Maximum 𝐂𝐥/𝐂𝐝 Ratio Finding the amount of design lift and design angle of attack from graphs that correlate to the highest value of Cl/Cd ratio is crucial for the design of a horizontal axis wind turbine. The ratio of the maximum lift-to-drag coefficient is found from the q-blade for the airfoil section of SD 7080 for the horizontal axis wind turbine blade. Maximum lift to drag ratio (Cl/Cd) of 46.47 appeared at 𝛼 of 5.50 for SD 7080. 5.5.2 Design lift coefficient and angle of attack calculation Particularly at high tip speed ratios, the highest power coefficients may be obtained. The lift coefficient and angle of attack values are obtained from the ( Cl − α ) curve corresponding to the maximum (Cl/Cd) ratio. The design lift coefficient Cld and design angle of attack, αd, which are represented by the Cld and α values found along the way, respectively, are crucial design parameters. Cld = 0.88 and αd= 5.5° are the design lift coefficient and angle of attack, respectively.
  • 46. 33 5.5.3 Design Tip Speed Ratio and Blade Count Options Table 5.3: Selection of the number of blades and design tip speed ratio Ratio of design tip speed, 𝜆 Number of blades 1 6-20 2 4-12 3 3-6 4 2-4 5-8 2-3 8-15 1-2 Maximum power coefficient occurs in the region of design tip speed ratio, 5≤ 𝜆𝑑 ≤ 8, for (Cl/Cd) max= 46.3. Let's take the design tip speed ratio, 𝜆𝑑= 6, into consideration for design considerations. According to the foregoing Table and the assumption that λd = 6, B = 3 represents the number of blades 5.5.4 Design Power Coefficient Calculation Through the (Cl/Cd) ratio, the profile drag affects the power coefficient. The tip speed ratio and the (Cl/Cd) ratio affect the lowering of the maximum power coefficient. In this collection of maximum power coefficients, it appears that for a range of design tip speed ratios from 5 to 8, the highest theoretically achievable power coefficients fall between 0.30 and 0.50. Choose the maximum power coefficient, (Cp)max = 0.5, keeping in mind that 𝜆𝑑=6, B=3, and (Cl/Cd) 𝑚𝑎𝑥= 46.3. Cp= (Cp)maxx 0.8 = 0.5x0.8 = 0.4 for conservative design. 5.5.5 Determination of the Blade Radius Equation 5.6, has been used to compute the blade radius: Cp = 𝑃𝑒 1 2 𝜌𝜋𝑅2𝑉𝛼3 (5.12) R=√ 2𝑃𝑒 𝜌𝜋𝑉𝛼 3 𝐶𝑝 (5.13) Where air density is 1.225 kg/m3, at the wind speed 5.4 m/s. Using the provided data, the rotor radius is now calculated to be 14m. The turbine's speed is N = 60 rpm for a design tip speed ratio of λd = 6 (determined using the formula λd(Rω/Vα) )
  • 47. 34 5.5.6 Angle of twist and blade chord calculation The ideal blade, which has been divided into 7 cross sections of equal length along the radius, is examined in this section in order to determine several characteristics, including the local design speed, the angle of relative wind velocity, the twist angle, and the blade chord. The equations given are used to compute the local speed ratio (λr), flow angle (ϕ), twist angle (βT) and chord (Cr) of each section for the blade design. Re = ρVc μ (5.14) Where, Re stands for Reynolds number, c is an airfoil's chord length, V is wind speed, and ρ and μ are fluid's density and dynamic viscosity. In comparison to large-scale wind turbines, small-scale wind turbines perform better with reduced Reynolds numbers because these two components have extremely low values. Additionally, when the Reynolds number decreases, the maximum lift coefficient decreases while the drag coefficient marginally rises. It shows that as Reynolds number decreases, the lift to drag ratio drops precipitously, which leads to the small horizontal axis wind turbine performing poorly. PT = Cp 1 2 ρV3 A (5.15) Where A = rotor swept area =, Cp = power coefficient, V = wind velocity, 𝜌 = air density, and R signifies the radius of the rotor blades. With respect to a particular wind turbine, the power coefficient (Cp) varies with tip speed ratio (λ). The tip speed ratio (λ), which is determined by the Equation 5.16, is the ratio of the rotor blade tip speed to the wind speed. λ = λr R (5.16) The chord and twist distribution of the blades were two key factors that the wind turbine's maximum power coefficient took into account. Large values of the chord and twist at the root of the wind turbine blade provide improved performance when there is less wind. tan ϕ = 2 3λr (5.17) By increasing the blade size and quantity, the wind turbine's power production and beginning performance are enhanced. [45] Schmitz formula is used for calculating chord length and twist angle. C(r)= 16πr B(CL)D sin2 ( 1 3 arctan( R rλD )) (5.18)
  • 48. 35 β(r) = 2 3 arctan [ R r 1 λD ] – αD (5.19) Where, c and r stand for the blade's chord length and local radius, respectively. λr stands for the local tip speed ratio; B stands for the number of blades; and Twist angle = β. Chord length and twist angle are calculated for every blade element (r) thus represented as C(r) and β(r). Above Table shows the chord length and twist angle at different radius of the blade. Graph of chord length and twist angle versus (r/R) are shown in figure below. Table 5.4: Ideal Blade Sections, Local TSR, Angle of Attack, Blade Setting Angle and Chord Cross Section No. Local radius of rotor, r Local design speed, λr = λ ∗ r/R Relative wind speed angle ϕ = 2 3 arc tan( 1 λr ) Angle of Attack, α d Twist angle β T = ϕ − α d Chord, Cr m Degree Degree Degree m 1 1 0.43 44.53 5.5 39.034 2.734 2 3 0.8 25.25 5.5 19.750 2.729 3 5 1.2 16.68 5.5 11.178 2.002 4 7 1.6 12.29 5.5 6.79 1.527 5 9 2.0 9.69 5.5 4.190 1.222 6 11 2.4 7.98 5.5 2.484 1.015 7 13 2.8 6.78 5.5 1.284 0.866
  • 49. 36 Figure 5.7 Chord Length (Cr) vs. (r/R) Figure 15:Chord length (Cr) vs. (r/R) Figure 5.8: Twist Angle (β) vs. (r/R) Figure 16:Twist angle (β) vs. (r/R)
  • 50. 37 From the calculated chord length and twist angle, blade was designed on Q-blade software which was further designed on Ansys for CFD simulation. Figure 17: Designed Turbine Blade 5.6 Rotor Specification The specification of the rotor blade for the design of small horizontal axis wind turbine is listed in table Table 5.5: Specification of blade Parameter Range Rotor radius, R 14 m Number of blades, B 3 Axis of rotation Horizontal Tip Speed Ratio, 6 Rated Wind Velocity, V 5.4 m/s Root Chord Length, Cr 2.734 m Tip Chord Length, Ct 0.866 m
  • 51. 38 5.7 Calculation of Power Coefficient ( BEMT Method ) According to BEM theory, the blade is broken up into smaller components that work independently of one another and perform aerodynamically as 2D airfoils with calculate aerodynamic forces based on regional flow conditions. For every blade element, the flow angle φ, AOA α, tangential force coefficient Cy, axial force coefficient Cx , tip loss factor F, solidity rate 𝜎, and induction values ɑ and ɑ’ are calculated iteratively. The axial and angular changes are denoted by the a and a’ respectively, in the wind speed as the wind passes through the rotor axis. Following the discovery of these numbers, the axial force dFx, tangential force dFy, and power dP for each blade element are separately determined. Integrating dFx, dFy, and dP yields the rotor's total values Fx , Fx , and P. The value of Cp is calculated for the rotor. These operations are applied as an algorithm in the order given below: The induction coefficients ɑ and ɑ’ are set initially to zero. The flow angle φ is calculated as φ = tan−1 ( (1−a)V1 (1+a′)ωr ) (5.20) The AOA a is calculated as α = ϕ − β (5.21) Where, the pitch angle β is known from the blade geometry. The values of Cl and Cd for the chosen blade-section geometry at this AOA α are kept as design lift coefficient and design drag coefficient. The tangential force coefficient, which rotates the blade, is obtained as Cy = Cl sin φ - CD cos φ (5.21) The axial force coefficient, which affects the blade, is obtained as Cx = Cl cos φ + CD sin φ (5.22) The tip loss factor F is calculated as F = 2 𝜋 cos−1(𝑒−𝑓) (5.23)
  • 52. 39 Where, f= 𝐵 2 𝑅−𝑟 𝑟−sin 𝜑 (5.24) The solidity factor is found for the blade element as σ = cB 2πr (5.25) The axial induction factor ɑ is calculated as a= 1 4Fsin2φ σCx +1 (5.26) If the calculated value of ɑ is less than ɑc (the critical value of ɑ), Step 10 is not applied. However, if ɑ exceeds ɑc (ɑc may be accepted as 0.2), the Glauert correction is made as a = 1 2 a[2 + 𝐾(1 − 2𝑎𝑐)]√[𝐾(1 − 2𝑎𝑐) + 2]2 + 4(𝐾𝑎𝑐 2 − 1) (5.27) The tangential induction factor ɑ’ is calculated as a′ = 1 4F sin φ cos φ σCy −1 (5.28) The ɑ and ɑ’ can be calculated by using following equations: |𝑎𝑛+1 − 𝑎𝑛| < 0.001 𝑎𝑛𝑑 |𝑎𝑛+1 ′ − 𝑎𝑛 ′ | < 0.001 (5.29) Once the values of ɑ and ɑ’ have converged, the relative speed W is calculated as, W= √[(1 − 𝑎)𝑉1]2 + [(1 + 𝑎′)𝜔𝑟]2 (5.30) The values calculated thus far (W, 𝐶𝑥, and 𝐶𝑦) are used to calculate the axial force on a blade element as d𝐹 𝑥 = ( 1 2 ρW2 cdr) Cx (5.31) The tangential force on a blade element as d𝐹 𝑦 = ( 1 2 ρW2 cdr) Cy (5.31)
  • 53. 40 The torque on a blade element as dT=rdFy (5.32) and the power of a blade element as, dP = 𝜔𝑑𝑇 (5.33) By considering the blade number B, the total tangential force on the rotor is calculated as, Fy = B ∑ (dFy) i N i=1 (5.34) the axial force as, Fx = B∑ (dFx)i N i=1 (5.35) and the power as, P = B∑ (𝑑𝑃)𝑖 𝑁 𝑖=1 (5.36) Finally, the power coefficient is calculated Cp = p 1 2 ρAV1 3 (5.37) Thus obtained Cp is the power coefficient of designed turbine for 3 blades. 5.8 Simulation Method All the necessary equations required to predict the performance of a particular blade section through BEM simulation have been discussed lately. As each element is assumed independent from the others, the power produced by each element are calculated separately. Then finally the overall power is found by integrating results from individual sections which then leads for the calculation of overall power coefficient of the blade. A MATLAB code is generated to perform the BEM simulation and the stages listed below are followed by the computation process.
  • 54. 41 6.1 2D Airfoil Simulation Given that the blades created for this study's study had a chord length of 1 m. We performed aerodynamic evaluations on the SD 7080 airfoil for AOA of 5.50 . Given that the blades created for this study had a chord length of 1 m, Cl and Cd were derived after an investigation of the pressure and velocity variations around airfoils. This is how these analyses were carried out: Design Modeler program was used to generate 2D geometries using the wing-section geometries coordinates. The boundaries of the flow area surrounding the wing section geometry were drawn using a C-mesh flow field geometry, as illustrated in Figure 18. The boundary locations of the input (curve F) and output (line C) layers were established, and the wing section (airfoil curve G) was set as wall. Asymmetrical edges AB and DE were drawn. [46] Figure 6.1.1: C-mesh flow domain and boundaries. [46] Figure 18:C-mesh flow domain and boundaries Chapter 6 CFD simulation
  • 55. 42 Figure 19: Geometry of flow domain and boundaries made in space claim [46] This geometry was broken up into cells to create a mesh, incorporating the wing section and flow area, as seen in Figure 19. A total of 288411 cells were placed for the mesh domain and where small cells were utilized on the surface of the wing portion, while gradually massive cells were utilized elsewhere. In order to solve the conservation equations, each cell can be thought of as a very small control volume. The number of nodes on the structured mesh was found to be 289677. [46] [47] Figure 20: Meshed flow domain
  • 56. 43 Figure 21: Mesh generation for SD7080 utilizing structured grid The pressure gradient at the boundary layer is precisely captured by a large number of grids surrounding the airfoil surface. This is because flow separation is caused by the unfavorable pressure gradient. When the separating region widens, a stall will happen. Since the flow gradients are becoming closer to zero in the far-field region, the mesh resolution can get gradually coarser. In Figure 20, the meshing overview is displayed. The leading and trailing edges of the airfoil should be maximum. It is preferable for the transition of mesh size to change gradually because a sharp change could reduce the numerical precision. The flow domain geometry was imported into Setup in the CFD simulation (ANSYS) when the meshing procedure was finished. All cells underwent iterative solutions of the conservation and turbulence model equations starting from the initial values. The K-epsilon standard model was used as Viscous Model. [46]
  • 57. 44 Table 6.1: Computational conditions of airfoil simulation [46] We selected inlet for standard initialization. As observed from figure 22, 650 iteration were enough for precise calculation as the convergence was happening gradually. Conditions Data Airfoil SD7080 Simulation Type Steady Simulation Fluid Material Air Boundary condition Pressure far field Stationary wall with no slip shear condition Interpolating scheme Pressure (Standard) Density (Second Order Upwind) Momentum (Second Order Upwind) Modified Turbulent Viscosity (Second Order Upwind) Pressure 101325 pa Density 1.2 kg/m3 Kinematic Viscosity 1.4607 10-5 m2/s Velocity Magnitude 5.4m/s Angle of attack 5.5 X Component Flow Direction 0.99539619836 Y Component Flow Direction 0.09584575252 Turbulent Viscosity Ratio 1 Outlet Pressure Outlet Gauge Pressure 0 Pa
  • 58. 45 Figure 22: Scaled residuals of calculation of the fluid domain. Velocity changes along lower surface and upper surface from the velocity contour & velocity magnitude contour can be seen in Figure 23 & Figure 24. Figure 23: Velocity contour on blade from CFD
  • 59. 46 Figure 24: Velocity magnitude on blade from CFD According to the Bernoulli equation, the varying velocities at various positions around the airfoil lead to changes in the pressure distribution at each location around the item. According to the Bernoulli equation, the pressure decreases further as air velocity increases. Figure 25: Pressure co-efficient on SD7080 airfoil
  • 60. 47 Figure 26: Pressure contour of SD7080 airfoil As a result, there is an increase in the pressure difference between the top and lower surfaces, producing a lift force. Figures shows the pressure coefficients along the upper and lower surfaces of airfoil at AOAs of 5.50 6.2 HWAT 3D Simulation In Solidworks2019, Blade geometry was generated. The design dimensions of the geometry were integrated using Schmitz technique. Only one of the rotor blades of the turbine was modeled; a periodic condition was imposed to account for the other two blades. The rotational axis was chosen as the z-axis, with the blade extending along the negative x- axis. The blades were placed in the fluid domain exactly as in the examples shown in Figure 27.
  • 61. 48 Figure 27: Blade Geometry made in Solidworks The designed blade geometry was then prepared for CFD analysis. [46] Airfoil was imported into Space claim from the Workbench of ANSYS and a flow domain was created around the blade. Figure 28: View of blade placement from rotor axis
  • 62. 49 The cylindrical figure displays the boundary parameters for the computational fluid domain's surface. The computational flow's inlet and outlet diameter was set at 3R. For the rotor, the domain is expanded to the 3R of the blade in the front-stream direction and 6R of the blade in the back-stream direction. Figure 29: Blade placement in fluid domain For meshing purposes, we used Fluid Flow (Fluent with Fluent Meshing). Geometry was imported from the workbench and added local sizing to the blade wall. For generating the surface mesh, we kept a minimum size of 0.06 and a maximum size of 0.6, with a growth rate of 1.2. Face Mesh was generated as seen in the Figure 30. Figure 30: Generated Face Mesh of fluid domain
  • 63. 50 Geometry consisting of only fluid regions with no voids was kept with no topology shared. After updating boundaries and periodic boundaries. Figure 31: Generated Volume Mesh of fluid domain Geometry consisting of only fluid regions with no voids was kept with no topology shared. After updating boundaries and periodic boundaries, Volume Mesh was generated as seen in Figure 31. After completing the meshing process, the meshed geometries were imported into the solution part, and the boundary conditions were chosen as those given in Table 6.2
  • 64. 51 Table 6.2: Boundary conditions of flow domain Boundary Condition Choice Simulation type Steady simulation Fluid material Air Flow type Incompressible flow Temperature 300 K Kinematic viscosity 1.7894e-05 m2/s Pressure 101,325 Pa Wind speed 5.4 m/s CFD algorithm SIMPLE Viscous model SST k–omega Solution methods Pressure–velocity coupling Least-squares cell based Pressure(standard);density (second-order upwind) Momentum (second-order upwind) Turbulent kinetic energy (first-order upwind) Specific dissipation rate (first-order upwind) Solution controls Pressure: 0.5 Momentum: 0.5 Density: 1.225 kg/m3 Turbulent kinetic energy: 0.75 Boundary Conditions Velocity inlet (5.4 m/s); Velocity inlet top (5.4m/s) pressure outlet (gauge pressure: 0) Moving wall with no-slip shear condition Cell Zone Condition Frame Motion Rotational Velocity 6.3 rad/s Number of mesh cells About 1270000 In the solution part, we plotted the Integral of pressure. Then initialized the solution with Standard Solution, and computed from Inlet. For iteration, we kept 1000 iterations as our data did not change gradually after that. From the residuals in Figure 32, we can see that the solution did not vary appreciably after 250 iterations and that the variables approached the convergence factor. Therefore, 1000 iterations were conducted in this study [46]. Integral of pressure did not show change after 90 iterations as it converged. In the CFD post, we rotated the flow domain 3 times to make a full circle around the Z-Axis, as it was our principal axis. Full domain circle can be seen in Figure 34.
  • 65. 52 Figure 32: Scaled residuals of calculation of the fluid domain Figure 33: Integral of pressure along the blade of SD7080 airfoil. Then we created a Blade Velocity vector on the blade wall and kept the factor of 50, shown in results. [46]Wall Shear vector on the blade wall was created and kept the factor of 50 as shown in Figure 35.
  • 66. 53 Figure 34: Boundary conditions of the flow domain Figure 35: Wall Shear vector on blade of SD7080
  • 67. 54 7.1 Background The most major downside of many forms of renewable sources, aside from higher capital costs, is that the energy source is widely distributed. This is an inherent issue with producing big amounts of wind energy because it takes a lot of land to generate power adequate for a utility. Having a way to rapidly determine how much space a wind farm will take up is important and beneficial. This presents some challenges because wind farms are frequently placed along ridgelines, making it challenging to determine how much area they actually occupy. The land between turbines can frequently still be used for other purposes, including farming, even if they may need a site with a lot of square meters. 7.2 Methodology Power density of wind (ideal) , Pdensity= 1 2 ⁄ ρAV3 Annual average power output, Pavg = 0.5 ∗ Cp ∗ ρ ∗ v3 *A = Cp*Pdensity*A = Cp*Pdensity* π 4 D2 (7.1) Each turbine will need 64D2 rotor diameters of land area (Larea), with a rotor diameter spacing of around (8D*8D). So, Larea can be assessed as, Larea =64D2 Now equation (1) stands as, Chapter 7 Estimation of Wind Farm
  • 68. 55 Pavg = Cp*Pdensity* π 4 D2 * Larea 64 (7.2) By simplifying equation (2), Pavg Larea = Pdensity 320 Or, Pavg m2 ⁄ = Pdensity 320 (7.3)
  • 69. 56 8.1 Analysis of SD 7080 blade at different Reynolds Number Numerical simulation of SD7080 blade which was carried out at various Re values and variation of the lift coefficient with respect to the different angle of attack are shown in Figure 36. From the results, It was found that the maximum values of Cl = 0.81, 1.15, 1.17, 1.18 and 1.2 were reached for Re = 30000, 60000, 82000, 10000 and 125000 respectively. Figure 36: Lift Coefficient versus tip speed ratio Also, from figure 37, It was found that the maximum values of Cl/Cd = 12.5, 39.7, 46.47, 53.4 and 59.8 were reached for Re = 30000, 60000, 82000, 10000 and 125000 respectively. Finally, It was found that SD 7080 blade starts to produce the maximum power coefficient (Cp) values from lower Re value of 60000 due to the aerodynamic shape of blade which produced maximum Lift to Drag ratio (Cl/Cd) than Re value 30000. A high maximum Cl/Cd value produces a high-power coefficient and a high OTSR. The maximum Cl/Cd values have a significant impact on those values. Chapter 8 Results and Discussion
  • 70. 57 Figure 37: Lift Coefficient versus tip speed ratio 8.2 Power co-efficient analysis of BEMT blade at Re=82000 The performance of a wind turbine is evaluated by determining its power coefficient or coefficient of performance (Cp). The power coefficient as a function of the tip speed ratio depicts the response of BEMT-blades at Re=82000. From MATLAB code generated to perform the BEM simulation through computation process as described previously in Chapter 5.8, Cp of BEMT-blade was found to be 0.3962. Also, Cp from Q-blade simulation as shown was found to be 0.412, close to Cp of BEMT-blade. From figure 38, it can be observed that the Cp values initially increase with the increase in the value of tip speed ratio (λ), reaches the maximum, and then decreases. Furthermore, the blade rotors with a wider range of tip speed ratios offer high power coefficients.
  • 71. 58 Figure 38: Power Coefficient versus tip speed ratio of SD7080 BEMT-blade. Figure 39:Value of Lift Coefficient From the graphical representation, the BEMT-blade SD 7080 generates Cp values of 0.412 at λ = 6 respectively. A high maximum Cl/Cd value produces a high-power coefficient and a high OTSR. The maximum Cl/Cd values have a significant impact on those values.
  • 72. 59 8.2.1 Variation of Lift and Drag Co-efficient the polar curve of the lift coefficient: the horizontal-axis is the value of iteration times and the vertical-axis represents the value of the lift coefficient. Initially, the value of lift coefficient was going down, the lowest value is 0.7 when the simulation was iterated 500 times. Then, it climbs to 1.1. [48] Figure 40: Drag coefficient of SD7080 airfoil According to CFD, the lift and drag forces for airfoil is less than the data provided in airfoil database for wind turbines. This is most likely due to the various Reynolds numbers taken into account in this investigation. [48] 8.2.2 Determination of Tip-Velocity The velocity measurement made by ANSYS in Figure 41, shows how the rotation of the blades causes the local wind turbine blade velocity to rise with radius. The tip's velocity, which is the greatest velocity, is around 85.08 m/s. [46]
  • 73. 60 Figure 41: Blade Velocity vector on blade of SD7080 8.2.3 Calculation of co-efficient of power A torque is a force that spins or twists something. It is the same as the force times the distance for a wind turbine. This implies that longer blades can produce higher torque. Through Function Calculator present in the result section of CFD, Torque in the blade wall was found (T ) = 3665.6 [N m] (one blade ) Applying equation Average Power = 69.094 kW The values of the power coefficient of SD7080 obtained by CFD is smaller than the values of the pressure coefficient obtained by BEM. The results for the power coefficient CP of the HAWT in BEMT, Q-blade simulation and CFD are compared one by one. 8.3 Comparison of co-efficient of power As discussed in Chapter 5.8 and Chapter 8.3, Power Co-efficient of designed blade through BEM Theory was found to be 0.3962 and while simulated the designed blade in Q-blade’s Rotor BEM, Cp was found to be 0.412 previously shown in Figure 38.
  • 74. 61 Figure 42: Power Curve of Enercon E-30 And from Chapter 8.3.1, Cp of designed blade through CFD was found to be 0.3878. From above shown figure 42, Maximum Power Coefficient for Enercon E-30 Turbine provided in is seen to be 0.4. Figure 43, shows the comparison of Cp among designed blade through 3 different procedure and Enercon E-30. From figure, it can be observed that the Cp of the blade simulated in Q-blade V2 has highest while CFD result shows lowest Cp. The reason for the difference in power coefficient with CFD and BEM may be due to the differences between the 2D case (BEM) and the 3D case (CFD). The lift/drag ratio in the 2D airfoil aerodynamics data was taken at a low Reynolds number, thus resulting in a lower power coefficient in BEM. To identify the cause of the previously mentioned difference, it could be assumed that there was negligible interference between the neighboring blade elements and that only lift and drag forces were acting on the blade elements. And finally, through the graph, it is observed that the selected turbine Enercon E-30 while working at full efficiency have similar power coefficient as the power coefficient of designed blade but has less power generation than the designed blade.
  • 75. 62 Figure 43: Comparison of Cp for designed blade and Enercon E-30. 8.4 Annual Power Output For the purpose of evaluating wind turbine performance and determining the amount of energy that could be gathered from wind turbines in the Hatiya area, Enercon E-30 has been chosen. The wind turbines chosen are considered for operation at standard hub heights of 50m. We calculate average power output, annual energy power output and capacity factor. 8.5 Cost estimation The cost of the electricity produced by wind turbines is usually relevant to the economic viability of wind turbine projects. The project should be adjusted in this way to produce energy at the lowest cost per kWh possible. The price of electricity generated by wind turbines depends on a variety of elements, including wind speed, taxes, installation, operation, and maintenance. 0.375 0.38 0.385 0.39 0.395 0.4 0.405 0.41 0.415 Q-Blade BEM CFD Enercon E-30 Cp Turbine
  • 76. 63 The cost of wind turbines is the only one that varies by location. Wind turbine prices can differ depending on the manufacturer. Table 8.1: Calculation of power output and capacity factor Present value of cost can be assessed as follows: PVC=I +𝐶𝑜𝑚𝑟 ( 1+𝑖 𝑟−𝑖 ) ∗ {1 − ( 1+𝑖 1+𝑟 ) 𝑛 } − 𝑠 ( 1+𝑖 1+𝑟 ) 𝑛 (8.1) The Cost estimation (kWh) of energy produced by the nominated three turbines at Hatiya region has been done under the following assumptions [n] Investment (I) includes the turbine price and its 20% for the civil work and other belongings. Operation maintenance and repair cost (Comr) is considered to be 25% of the annual cost of the turbine (machine price/lifetime). The lifetime of the machine (n) is assumed to be 20 years. The interest rate (r) and inflation rate (i) are taken to be 15 and 12%, respectively. Scrap value S was taken to be 10% of the turbine price and civil work. Serial Terms Values 1. Cut-in speed, 𝑉 𝑐 2.5 (𝑚𝑠−1 ) 2. Cut-off speed, 𝑉𝑓 13.5 (𝑚𝑠−1 ) 3. Rated speed, 𝑉 𝑟 25 (𝑚𝑠−1 ) 4. Scale factor, c 6.39 5. Shape parameter, k 2 6. Average power output,𝑃 𝑎𝑣𝑔 59.22 KW 7. Annual energy power output (𝐸𝑜𝑢𝑡) 174.3 MWh 8. Capacity factor, Cf 19.74%
  • 77. 64 The cost of each kWh produced by the turbine in $/kWh, within the pay-off period, t, is calculated from the following equation 8.2, Costkwh= PVC Eout (8.2) Table 8.2 : Calculation of PVC and and unit cost Serial Terms SD7080 Enercon E-30 1. Investment, I 317400 USD 414000 USD 2. Pay back period, n 10 years 10 years 3. Lifetime,T 20 years 20 Years 4. Comr 3306.3 USD 4312.5USD 5. Inflation rate,i 0.12 0.12 6. Interest rate,r 0.15 0.15 7. Scrap value,s 31740 USD 41400 USD 8. PVC 101389.6 USD 132246.7 USD 9. Eout 198.5 MWh 174.3 MWh 10. Unit cost($/KWh) 0.051 USD 0.076 USD
  • 78. 65 8.6 Required land area for wind farm Table 8.3: Calculation of Required land area for two turbines Serial Terms SD7080 Enercon E-30 1. Wind speed 5.41 ms-1 5.41 ms-1 2. Power density 96.984 Watt/m2 96.984 Watt/m2 3. Power available per square meter 2.63 Kwh/year/m2 2.63 Kwh/year/m2 4. Annual power output 198.5MWh 174.3MWh 5. Land area 75475.29 m2 66282.89 m2