This project analyzed the limitation of turbine and new opportunity for power generation at low fluid (air/water) velocity flow places.
‘ This system develops more efficient and less costly method compared to all other power generation techniques. In this project aerofoil are used in place of turbine in which no of aerofoil connected in series and lift obtained from low velocity fluid flow. This lift is sum of all individual lift of an aerofoil. Its capable for appropriate power generation.
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LIST OF FIGURE
Sr. No.
Name of Figure
Page No
1.1
Aircraft
16
1.2
Racecar
17
1.3
Wind farm
17
1.4
Helicopter
18
2.1
General layout of lifting aerofoil mechanism
20
2.2
Lifting aerofoil
21
2.3
Air flow around aerofoil
25
2.4
Pressure difference on both side of aerofoil
25
2.5
Graph of pressure difference
26
2.6
Effect of angle of attack
27
2.7
Mass of air flow around airfoil
29
2.8
Reason for availability of lift
30
2.9
Aerofoil geometry
31
2.10
Graph of AOA vs % of chord
32
6
NOMECLATURE
Cd , Cl = airfoil coefficients of drag and lift
Clmax = maximum lift coefficient
Cp = pressure coefficient
Cpcrt = critical pressure coefficient
c = chord length
D = drag
L = lift
p = static pressure
pd = desired target static pressure
R = governing equations or residual
Re = Reynolds number
S = surface area
t/c = thickness-to-chord ratio
y+ = dimensionless wall distance
?? = angle of attack
??cl max = stall angle of attack
?? = first variation
?? = step size in steepest descent method
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TABLE OF CONTENT
Sr.No. Contents Page No.
1 Introduction 9-18
1.1 Introduction To Energy Sources 10
1.2 Requirement Of Aerofoil Mechanism 11
1.3 History Of Aerofoil Development 11
1.4 Introduction Of Aerofoil 12
1.5 The Potential Of Aerofoil Technology 12
1.6 Advantages Of Aerofoil Mechanism Compare 13
to Other power Generating Technologies
1.7 Application of aerofoil 15
2 Structure Of Lifting Aerofoil Mechanism 19-36
2.1 Layout Of Structure 20
2.2 Component Of Lifting Aerofoil Mechanism 21
2.3 Working Of Lifting Aerofoil Mechanism 23
2.4 Lift 23
2.5 Principle of working 24
2.5.1 Newton’s law lift and deflection of flow 24
2.5.2 Pressure difference 25
2.5.3 Flow on both side of the wing 26
2.5.4 Angle of attack 27
2.5.5 Bernoulli’s principle: lift, pressure and speed 28
2.5.6 Conservation of mass 28
2.5.7 Popular explanation based on equal transit time 29
2.6 Aerofoil Geometry 30
2.7 Aerofoil Pressure Distribution 33
2.8 Stalling 35
2.9 Reynolds Number 35
8
3 Problem Summary 37-40
3.1 Definition Of Problem 38
3.2 Solution Of Problem 38
3.3 Conclusion 40
4 Reference 41-41
9
Chapter:1
Introduction to Aerofoil
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1.1 INTRODUCTION TO ENERGY SOURCES
‘ In today’s modern time people all over the world uses various types of energy. Some of these energy played great or much important role in our life cycle. For example people use various energy like chemical energy of fuel for driving various types of vehicles, electricity for lightning , heat for cocking etc. But from all these energies electrical energy have great requirement and use in today’s life.
‘ Electricity is generate by various method and various sources.
‘ Following types of sources generally used for electricity generation
‘ Solar energy
‘ Chemical energy
‘ Hydraulic energy of water
‘ Wind energy
‘ Geothermal energy
‘ In today’s market because of very high demand of electricity industry is trying to obtain energy from anywhere. Because of limited availability of chemical fuels commonly preferred for power generation.
‘ In various types of renewable sources wind and water is largely used.
‘ For power generation from water dam built on the river and with the help of various types of turbines power generated and in the case of wind by wind mill power generation occurred.
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1.2 REQUIREMENT OF AEROFOIL MECHANISM
‘ Wind energy is big and renewable source of energy so the energy obtained from wind is pollution free energy. So it is very important to somehow find the various method to obtain energy from wind as well as water. Now a day’s turbine is used for that purpose like wind turbine, water turbine etc.
‘ Generally turbine will used in both case for power generation but in case of low velocity flow of water like in canal turbine cannot be used and leaving loss is high in case of hydraulic power plant. The power can be generated with the help of lifting aerofoil mechanism from leaving velocity of hydraulic power plant. we can obtained power from canal also.
‘ Wind turbine is used today for obtaining energy from high velocity air flow. There is also some limitation like its use only where high velocity airflow is available but the lifting aerofoil mechanism is capable to obtain energy from low velocity airflow than wind turbine.
1.3 HISTORY OF AEROFOIL DEVELOPMENT
‘ The earliest serious work on the development of airfoil sections began in the late 1800’s. Although it was known that flat plates would produce lift when set at an angle of incidence, some suspected that shapes with curvature ,that more closely resembled bird wings would produce more lift or do so more efficiently. H.F. Phillips patented a series of airfoil shapes in 1884 after testing them in one of the earliest wind tunnels in which "artificial currents of air (were) produced from induction by a steam jet in a wooden trunk or conduit." Octave Chanute writes in 1893, "…it seems very desirable that further scientific experiments be made on concavo-convex surfaces of varying shapes, for it is not impossible that the difference between success and failure of a proposed flying machine will depend upon the sustaining effect between a plane surface and one properly curved to get a maximum of ‘lift’."
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‘ In 1939, Eastman Jacobs at the NACA in Langley, designed and tested the first laminar flow airfoil sections. These shapes had extremely low drag and the section shown here achieved a lift to drag ratio of about 300.
1.4 INTRODUCTION OF AEROFOIL
‘ An aerofoil is a surface designed in order to achieve a desirable reaction from the air in which it moves. The profile (shape) of a conventional wing is a good example of an aerofoil. The top surface of the wing will usually have a much greater curvature than the lower surface.
‘ This difference in curvature between the upper and lower surfaces of the wing builds up what is known as the Lift force. This occurs because the air flowing over the top surface of the wing, must reach the trailing edge of the wing in the same amount of time as the air flowing under the wing. In order for this to happen it requires the air flowing over the top surface to be at a higher velocity than the air flowing on the bottom. According to Bernoulli’s principle, this will in turn create a decrease in pressure on the surface. This will create a pressure differential between the upper and lower surfaces of the wing, thus forcing the wing in an upwards direction.
1.5 THE POTENTIAL OF AEROFOIL TECHNOLOGY
‘ The potential applications for Tethered Airfoil technology are numerous. Some of the applications that should be possible are listed below. The applications that could most easily be developed are listed first followed by those that would require more skill and experience.
‘ Wind power generators that use reciprocating airfoils to produce electricity on the ground.
‘ Water pumps that use reciprocating airfoils to pump water for irrigation.
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‘ Sailing craft that have a Tethered Airfoil to tack into the wind or with the wind — the airfoil being held aloft by aerodynamic lift, or buoyancy (helium or hydrogen), or both.
‘ Recreational airships that fly over water without fuel by tacking in the air while being attached by tether to submerged hydrofoils.
‘ Passive self-regulation of altitude using highly pressurized lighter-than-air structures.
‘ Ship and vessel propulsion assistance with minor retrofitting.
‘ Energy conserving tugs that could deploy Tethered Airfoils to pull unmodified vessels across oceans.
‘ Land Based High altitude wind power generators that use reciprocating Tethered Airfoils to tap winds as high as the jet stream to produce electricity at a generator on the ground.
‘ Sea Based wind power generators (low or high altitude) to produce electricity at a boat or barge.
1.6 ADVANTAGES OF AEROFOIL MECHANISM COMPARED TO OTHER POWER GENERATING TECHNOLOGIES
‘ All of the current and proposed methods of energy generation or fuel synthesis have their advantages and disadvantages. Below the costs of consuming oil are discussed. Afterward, the advantages of Tethered Airfoil Generators are discussed and compared against the current and proposed methods of energy generation. The intent is to lay a foundation that will clearly establish our need for a cleaner, safer, cheaper source of power other than that, which is currently available or proposed.
‘ The Hidden Costs in Oil Consumption
According to the US Geological Survey (the branch of the government that assesses oil reserves) virtually all of the oil that is known to exist or is likely to be discovered in the
14
United States will be consumed within the next twenty five years. Currently, oil is cheap and abundant, yet the purchase of foreign oil is the single biggest contributor to our spiraling trade deficit and global indebtedness. When oil is no longer abundant it will no longer be cheap — in which case our trade deficit and indebtedness will likely soar.
Even in peacetime we spend considerable sums just to secure access to Mideast oil. According to an article in the April 1991 issue of Scientific American, it is estimated that the Pentagon has spent between 15 and 54 billion dollars annually to secure access to Mideast oil ‘ even before the fitrst war in Iraq.
In times of war we spend much more. In the heart of an oil glut we fought the first war in Iraq to secure access to oil. A quarter of a million Iraqis died and over 60 billion dollars was spent by the allied forces alone. Middle Eastern nations such as Iran are arming themselves to exert regional authority and to prepare for such conflicts — this time with nuclear weapons. The point is simple: our need for foreign oil compels us to spend considerable sums to ensure our access to oil in peace time and to fight wars when that access is threatened.
‘ Perhaps most importantly, the consumption of oil or other fossil fuels degrades the environment through smog, acid rain, the green house effect, and inevitable wide spread accidents such as oil tanker spills. According to the article in Scientific American, it is estimated that at the current rate of oil consumption the environmental degradation, increased health care, lost employment, and other factors cost the United States between 100 to 300 billion dollars annually — not to mention the 15 to 54 billion dollars that the pentagon spends in peace time to secure access to Mideast oil — nor the costs of fighting wars to secure access to oil such as in Iraq. These "hidden" costs are in addition to the prices paid at gas pumps. Worldwide these incidental costs may exceed one trillion dollars annually. The world pays an enormous price to consume oil — politically, economically, and environmentally.
‘ Comparing Tethered Airfoil Electricity Generation and the Solar Power
15
Solar power has long been promoted as an energy source that is likely to be used to meet much of the future demand for power. Advocates of solar power point out that it is clean, dependable, and uses a renewable energy source. While true, all of these claims can be made for Tethered Airfoils Wind Power Generators as well.
Compared to solar energy sources, Tethered Airfoil Generators:
‘ Do not require expensive and inefficient energy storage and retrieval systems to convert daytime power into nighttime electricity,
‘ Do not require much sun-favored land since they can share land with agriculture (or go offshore to avoid the use of land altogether),
‘ Can efficiently generate power at far more sites throughout the world (such as anywhere under the jet streams of the northern and southern hemispheres or over the oceans where the installation of solar cell arrays would be impractical, if not impossible),
‘ Can extract energy from a source that is hundreds of times more powerful per unit area (10 kilowatts per square meter is often the average power available in winds in the jet stream versus 100 watts of solar power per square meter), and
‘ Are more efficient at extracting power (even windmills are generally more than four times as efficient as solar cells in extracting power)
‘ Could offer a greater return on investment by generating more power at less cost.
1.7APPLICATION OF AEROFOIL
‘ Aerofoil is used at many places for different purpose. Following are some popular example where aerofoil used.
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AIRCRAFT
‘ An aircraft is a machine that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.
Fig 1.1 Aircraft
‘ In the case of aircraft aerofoil is used for obtaining vertical lift as upward force but in case of racing car it used for obtain downward force.
RACE CAR
‘ In the race care same principle that allows an airplane to rise off the ground by creating lift from its wings is used in reverse to apply force that processes the race car against the surface of the track. This effect is referred to as ‘aerodynamic grip’ and is distinguished from ‘mechanism grip’. The creation of downward force by passive device almost always can only be achieved at the cost of increased aerodynamic drag. The aerodynamic setup for a car can vary considerably between race tracks, depending on the length of the straights and the types of corners; some drivers also make different choices on setup. Because it is a function of the flow of air over and under the car, and because aerodynamic forces increases
17
with the square of velocity, downforce increases with the square of the car’s speed and requires a certain minimum speed in order to produce significant effect. But some cars have had rather unstable aerodynamics, such that a minor change in angle of attack or height of the vehicle can cause large changes in the downforce. In very worst cases this can cause the car to experience lift, not downforce.
Fig 1.2 Racecar
WINDTURBINE
‘ A wind turbine is a device that converts kinetic energy from the wind into electrical power.
Fig 1.3 Windfarm
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‘ In the wind turbine aerofoil is used for obtain rotation from the kinetic energy of wind. Which is further used to drive generator an electrical power is produced.
HELICOPTER
‘ A helicopter is a type of rotorcraft in which lift and thrust are supplied by rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward, and laterally. These attributes allows helicopters to be used in congested or isolated areas where fixed wing aircraft and other forms of vertical takeoff and landing air craft cannot perform.
Fig 1.4 Helicopter
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Chapter:2
STRUCTURE OF LIFTING AEROFOIL MECHANISM
20
2.1 LAYOUT OF STRUCTURE
Fig2.1. General Layout of lifting Aerofoil Mechanism
‘ Structure of lifting aerofoil mechanism is shown in the fig.
‘ As shown in fig in the structure of lifting aerofoil mechanism there was many components present. Water flow came from one side from the source like canal, turbine power plant and go through aerofoil mechanism. The water flow exerts lifting force and shaft rotate. The rotation obtain is ultimately produce power. The structure must be strong enough to resist the forces occurred by water flow. One generator coupled with shaft which was connected to aerofoil and generate electricity.
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2.2COMPONENTS OF LIFTING AEROFOIL MECHANISM
‘ As shown in fig system contain
1. Aero foils
2. Generator
3. Controlling system
4. Door
5. Guide vanes
6. Power grid and power transmission unit etc.
1. AEROFOILS
‘ An aerofoil is most important part of this lifting aerofoil mechanism. It is a surface designed in order to achieve a desirable reaction from the air in which it moves. The profile (shape) of a conventional wing is a good example of an aerofoil. The top surface of the wing will usually have a much greater curvature than the lower surface.
‘ Fig 2.2 Lifting aerofoil
22
‘ This difference in curvature between the upper and lower surfaces of the wing builds up what is known as the Lift force. This occurs because the air flowing over the top surface of the wing, must reach the trailing edge of the wing in the same amount of time as the air flowing under the wing. In order for this to happen it requires the air flowing over the top surface to be at a higher velocity than the air flowing on the bottom. According to Bernoulli’s principle, this will in turn create a decrease in pressure on the surface. This will create a pressure differential between the upper and lower surfaces of the wing, thus forcing the wing in an upwards direction.
2. GENERATOR
‘ It is prime mover of this lifting aerofoil mechanism. The mechanical energy produced by the aerofoil is converted into electricity by generator.
3. CONTROLLING SYSTEM
‘ The flow of water passed through the aerofoil is not continuous so rotation obtain at the shaft is also not continuous so we must have to regulate that rotation. For that purpose certain mechanism like governor is used and rotation can be controlled.
4. DOOR
‘ The door is fitted before aerofoil mechanism. It permits flow through the aerofoil. In repairing or maintenance time it should be close. It also provide certain head when flow is slow.
5. GUIDE VANES
23
‘ It is mechanism that provide safety and comfort to aerofoil mechanism. In the time of high velocity flow it avoid loss of money by avoiding accident.
6. POWER GRID AND POWER TRANSMISSION UNIT
‘ The electricity produced by the generator is not stored so we want to supply it where demand is required. That is obtained by power transmission unit.
2.3 WORKING OF LIFTING AEROFOIL MECHANISM
‘ The concrete structure is made in the way of flowing water. With opening of door flow of water passed through the lifting aerofoil mechanism and according to Bernoulli’s principle the energy contained by water is converted into lift of aerofoil. Here number of aerofoils are connected in series so total lift obtained is sum of all individual aerofoil. The aerofoil mechanism further connected to shaft. As shown in fig shaft connected with generator. The generator convert that mechanical energy into electricity. According to the rpm available appropriate generator selected for electricity generation.
‘ As discuss in above section lift is reason on which lifting aerofoil mechanism work.
2.4LIFT
‘ A fluid flowing past the surface of body exerts a force on it. Lift is the component of this force that is perpendicular to the incoming flow direction. It contrasts with the drag force, which is component of the surface force parallel to the flow direction. If the fluid is air, the force is called an aerodynamic force. In water, it is called hydrodynamic force.
24
‘ Lift is the force generated by propellers and wing to propel the aircraft and keep them in air. Birds, bats, insects, fish, flying reptiles, and even falling plant seeds have usefully exploited lift for millions of years.
‘ Lift is most commonly associated with the wing of fixed wing aircraft, although lift is also generated by propeller, kites, helicopter rotor, rudders, sails and keels on sailboats, hydrofoils, wings on auto racing cars, wind turbines and other stream line objects. Lift is also exploited in animal world, and even in the plant world by the seeds of certain trees. While the common meaning of word ‘lift’ assumes that the lift oppose weight, lift in its technical sense can be in any direction since it is defined with respect to direction of flow rather than the direction of the gravity. When an aircraft is flying straight and level most of the lift opposes gravity. However, when an aircraft is climbing, descending, or banking in a turn lift is tilted with respect to vertical. Lift may also be entirely downwards in some cases like the wing on the racing car. In this last case the term downforce is used. Lift may also be largely horizontal, for instance on sail on sailboat.
2.5 PRINCIPLE OF WORKING OF LIFTING AEROFOIL
‘ There are several ways to explain how aerofoil generates lift. Some are more complicated or mathematically rigorous than others. For example, there are explanation based on Newton’s law of motion and explanation based on Bernoulli’s principle.
2.5.1Newton’s law: lift and the deflection of flow
‘ Lift is a reaction force an aerofoil deflects the air as it passes the airfoil. Since the foil must exert the force on the to change the direction, the air must exert the force of equal magnitude but opposite direction on the foil. In the case of an airplane wing exerts downward force on the air and the air exerts the equal force on the wing.
‘ This follows from the second and third of Newton’s laws of motion: The net force on an object is equal to its rate of momentum change, and: To every action there is an equal and opposite reaction.
25
Fig 2.3 Air flow around the aerofoil
‘ The air changes direction as it passes the airfoil and follows a path that is curved. Whenever airflow changes direction, a reaction force is generated opposite to the directional change.
2.5.2 Pressure difference
‘ Lift may also be described in terms of air pressure: pressure is the normal force per unit area. Whenever there is net force there is also a pressure difference, thus deflection/flow turning indicates the presence of a net force and therefore a pressure difference. The direction of the net force implies that the average pressure on the upper surface of the wing is lower than the average pressure on the underside.
Fig 2.4 Pressure difference on both side of aerofoil
26
‘ Whenever a fluid follows a curved path, there is a pressure gradient perpendicular to the direction. This direct relationship between curved streamlines and pressure differences was derived from Newton’s second law by Leonhard Euler in 1754
‘ Where R is the radius of curvature, p is the pressure, ?? is the density, and v is the velocity. This formula shows that higher velocities and tighter curvatures create large pressure differentials and that for straight flow the pressure difference is zero.
2.5.3 Flow on both sides of the wing
Fig 2.5 Graph of pressure difference on both side of aerofoil
‘ In the picture above, observe that the air in turned both above and below the wing so both the upper and lower surface contribute to the flow turning and therefore the lift. In fact, at subsonic speeds the top surface contributes more flow turning than the bottom surface, and the pressure deviation along the top is significantly larger than along the bottom. A common explanation describes lift as merely the result of the air molecules bouncing off the lower surface of the wing, but since this ignores the airflow around the top of the wing it usually leads to incorrect result. However, at hypersonic speeds, this model becomes applicable.
27
2.5.4Angle of attack
‘ The angle of attack is the angle between an airfoil and the incoming air. A symmetrical airfoil will generate zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream velocity increases, resulting in more lift. For small angles a symmetrical airfoil will generate a lift force roughly proportional to the angle of attack.
‘ As the angle of attack grows larger, the lift reaches a maximum at some angle; increasing the angle of attack beyond this critical angle of attack causes the air to become turbulent and separate from the wing; there is less deflection downward so that airfoil generates less lift. The airfoil said to be stalled.
Fig 2.6 Effect of angle on attack
‘ Cambered airfoil will generate lift at zero angle of attack. When the chord line is horizontal, the trailing edge has a downward. When a cambered airfoil is upside down, the angle of attack can be adjusted so that the lift force is upwards. This explains how a plane can fly upside down.
28
Limitations of deflection/turning
‘ While the theory correctly reasons that deflection implies that there must be a force on the wing, it does not explain why the air is deflected. Intuitively, one can say that the air follows the curve of the foil, but this is not very rigorous or precise.
‘ The theory, while correct in as far as it goes, is not sufficiently detailed to support the precise calculation required for engineering.
2.5.5 Bernoulli’s principle: lift, pressure, and speed
‘ Bernoulli’s principle states that within an airflow of constant energy, when the air flows through a region of lower pressure it speeds up and vice versa. Thus, there is a direct mathematical relationship between the pressure and the speed, so if one knows the speed at all points within the airflow one can calculate the pressure, and vice versa. For any airfoil generating lift, there must be a pressure imbalance, i.e. lower average air pressure on the top than on the bottom. Bernoulli’s principle states that this pressure difference must be accompanied by a speed difference.
‘ Bernoulli’s principle does not explain why the air flows faster over the top of the wing; to explain that requires some other physical reasoning.
2.5.6 Conservation of mass
‘ If one takes experimentally observed flow around an airfoil as a starting point, then lift can be explained in terms of pressure using Bernoulli’s Principle and Conservation of mass.
‘ Returning to principle from the previous section, the flow approaching an airfoil can be divided into stream tubes, which are defined based on the area between two streamlines. By definition, fluid never crosses a streamline in a steady flow.
‘ Assuming that the air is incompressible, the rate of flow must be constant within each stream tubes since matter is not created or destroyed. If a stream tube becomes narrower, the flow speed must increase in the narrower region to maintain the constant flow
29
rate. This idea is called ‘conservation of mass’, and for incompressible flow mass is conserved within each stream tube.
Fig 2.7 Mass of airflow around airfoil
‘ The picture shows that the upper stream tubes constrict as they flow up and around the airfoil. Conservation of mass says that the flow speed must increase as the stream tube area decreases. Similarly, the lower stream tubes expand and the flow slows down.
‘ From Bernoulli’s principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower. The pressure difference thus creates a net aerodynamic force, pointing upward and downward to the flow direction. The component of the force perpendicular to the stream is lift; the component parallel to the free stream is drag. In conjunction with this force by the air on airfoil, the airfoil imparts the equal and opposite force on the surrounding air that creates the downwash, in accordance with Newton’s law. Measuring the momentum transferred to the downwash is another way to determine the amount of lift on the airfoil.
2.5.7 ‘Popular’ explanation based on equal transit time ‘ An explanation of lift frequently encountered in basic or popular sources is the equal transit-time theory. Equal transit-time states that because of the longer path of the upper surface of an airfoil, the air going over the top must go faster in order to catch up with the air flowing around the bottom, i.e. the parcels of air that are divided at the leading edge and travel above and below an airfoil must rejoin when they reach the trailing edge.
30
Bernoulli’s Principle is then cited to conclude that since the air moves faster on the top of the wing the air pressure must be lower. This pressure difference pushes the wing up. Fig 2.8 Reason for availability of lift ‘ However, the hypothesis of equal transit time has no basis in theory and is universally contradicted by experiment. Although it is true that the air moving over the top of a wing generating lift does move faster, there is no requirement for equal transit time. In fact the air moving over the top of an airfoil generating lift moves much faster than the equal transit theory would imply. ‘ The assertion that the air must arrive simultaneously at the trailing edge is sometimes referred to as the "Equal Transit-Time Fallacy’.
2.6 AEROFOIL GEOMETRY
‘ Airfoil geometry can be characterized by the coordinates of the upper and lower surface. It is often summarized by a few parameters such as: maximum thickness, maximum camber, position of max thickness, position of max camber, and nose radius. One can generate a reasonable airfoil section given these parameters. This was done by Eastman Jacobs in the early 1930’s to create a family of airfoils known as the NACA Sections.
31
Fig 2.9. Aerofoil geometry
‘ Leading Edge:
It is usually a circular arc are blended into the main profile and specified by its radius as a percentage of the maximum thickness.
‘ Trailing Edge:
It is ideally sharp i.e. of zero radius, but this is impossible from strength consideration. It is also a circular arc specified as percentage of the maximum thickness.
‘ The Chord Line:
The straight line joining the centers of curvatures of the leading and trailing edges.
‘ The Chord:
The chord defined as the distance from the leading edge to the trailing edge of the section measured along the Chord Line.
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‘ The Mean Camber Line
The line drawn halfway between the upper camber and lower camber.
‘ The Thickness/Chord Ratio:
The ratio of maximum thickness to the length of the chord is comparable to the fineness ratio of a streamlined body.
‘ The Angle of Attack:
The angle between the Chord Line of the section and the direction of the relative airflow.
Fig2.10. Graph of AOA vs. % of Chord from leading edge
‘ The Angle of Incidence:
The angle between the Chord Line and the longitudinal axis of the aircraft.
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2.7 AEROFOIL PRESSURE DISTRIBUTION
‘ The aerodynamic performance of airfoil sections can be studied most easily by reference to the distribution of pressure over the airfoil. This distribution is usually expressed in terms of the pressure coefficient:
‘ Cp is the difference between local static pressure and free stream static pressure, non-dimensionalized by the free stream dynamic pressure.
‘ What does an airfoil pressure distribution look like? We generally plot Cp vs. x/c.
x/c varies from 0 at the leading edge to 1.0 at the trailing edge. Cp is plotted "upside-down" with negative values (suction), higher on the plot. (This is done so that the upper surface of a conventional lifting airfoil corresponds to the upper curve.)
‘ The Cp starts from about 1.0 at the stagnation point near the leading edge…
‘ It rises rapidly (pressure decreases) on both the upper and lower surfaces…
‘ …and finally recovers to a small positive value of Cp near the trailing edge.
‘ Various parts of the pressure distribution are depicted in the figure below and are described in the following sections.
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Fig2.11. Graph of Pressure Distribution
‘ Upper Surface:
The upper surface pressure is lower (plotted higher on the usual scale) than the lower
surface Cp in this case. But it doesn’t have to be.
‘ Lower Surface :
The lower surface sometimes carries a positive pressure, but at many design conditions is
actually pulling the wing downward. In this case, some suction (negative Cp ->
downward force on lower surface) is present near the mid-chord.
‘ Pressure Recovery:
This region of the pressure distribution is called the pressure recovery region. The
pressure increases from its minimum value to the value at the trailing edge. This area is
also known as the region of adverse pressure gradient. As discussed in other sections, the
adverse pressure gradient is associated with boundary layer transition and possibly
separation, if the gradient is too severe.
‘ Trailing Edge Pressure:
The pressure at the trailing edge is related to the airfoil thickness and shape near the
trailing edge. For thick airfoils the pressure here is slightly positive (the velocity is a bit
35
less than the free stream velocity). For infinitely thin sections Cp = 0 at the trailing edge. Large positive values of Cp at the trailing edge imply more severe adverse pressure gradients.
‘ CL and Cp :
The section lift coefficient is related to the Cp by: Cl = int (Cpl – Cpu) dx/c (It is the area between the curves.) with Cpu = upper surface Cp and recall Cl = section lift / (q c).
‘ Stagnation point:
The stagnation point occurs near leading edge. It is point at which V=0. Note that in incompressible flow Cp=1.0 at this point. In compressible flow it may be somewhat larger.
2.8 Stalling
‘ When the angle of attack is increased gradually up to a positive angle of attack (front of aerofoil lifting upwards) the lift component will increase rapidly. This will happen up to a certain point that we call the angle of maximum lift or the Stall Point. This angle is called the critical angle of attack which once reached will cause the air to stop flowing smoothly over the top surface of the aerofoil. This causes air to break away from the upper camber line of the wing producing turbulent air over the aerofoil. Once this has occurred the amount of lift being produced will drop tremendously and drag will become much more excessive. This point can be seen by the dropping of the nose of the aircraft
2.9 Reynolds Number
‘ Early investigations into the theory of fluid dynamics have predicted a certain number of constants to which similar disturbances (and an airfoil in the air is a disturbance) produce similar effects – in hydrodynamics, these are referred to as ‘Froude Numbers" (hulls of boats); in high speed aerodynamics the "Mach Number’ are other examples. For our
36
smaller and slower aircraft, the only "number" which really needs to be considered is the "Reynolds Number" and it is defined as:
Re = V x I / v
Where: V = Relative speed (m/sec) I = typical "length" of a solid body (M) v = cinematic viscosity of the air (sec/m2)
37
Chapter:3
PROBLEM SUMMARY
38
3.1 DEFINATION OF PROBLEM
‘ The energy of the water in the cannel is wasted and cannot be use for any purpose that energy might be used by converted in to some form like electricity. Lifting foil mechanism can be used at that place to obtain electricity.
‘ Mostly energy obtain from hydraulic dam and water by turbine that is passed out in cannel or river has also much energy but because of turbine limitation we can’t convert that energy into electricity but with the help of that lifting foil electricity is generated.
‘ Currently wind turbines offer the most practical and cost effective means of generating electricity from a renewable energy source, but Tethered Airfoil Wind Power Generators promise to offer a much more cost effective solution. Wind Turbines will probably always be more efficient, but Tethered Airfoil Generators should be much less expensive to install and maintain when generating equal power.
3.2 SOLUTION OF PROBLEM
‘ The aerofoil is suitable for solve that limitation of wind and hydro power generation problem. In lifting aerofoil mechanism is system by which we produced power from low velocity flow and it has several advantages over wind and hydro power generation.
‘ Unlike standard wind turbines, Tethered Airfoil Generators would not require:
1. Towers,
2. Stationary platforms,
3. Rigid, fragile blades,
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4. Airfoil sizes to be limited to the strengths of the towers,
5. Expensive custom low speed generators,
6. Operation in the slow and variable winds close to the earth, or
7. Land.
‘ Tethered Airfoil Generators could use standard generators. Since they would have no rotating blades they would not be subject to the strong vibrations and torsional forces that have caused many wind turbines to fail. They would be constructed of inflatable fabrics rather than rigid materials so they would bend and deform in excessive winds rather than fracture and break. Most importantly, they could fly at higher altitudes where the winds are stronger and more constant.
‘ Generally over level terrain the velocity of the wind varies in relation to the elevation above ground by the "one seventh power law":
velocity_high / velocity_low = (elevation_high / elevation_low) ^ (1 / 7)
‘ The power available in the wind is proportional to the cube of the velocity, so over level terrain the power in the wind varies in relation to the elevation above ground by the "three sevenths power law":
power_high / power_low = (elevation_high / elevation_low) ^ (3 / 7)
‘ From this equation comes the simple relationship that winds that are 5 times higher are very nearly twice as powerful. Similarly, winds that are 25 times higher are 4 times more powerful. Thus, if Tethered Airfoils were to fly just a half mile in the air above standard level terrain they should encounter winds that would be over 4 times more powerful than the winds encountered by turbines that were 30 meters (nearly 100 feet) above ground — and over 6.5 times more powerful than turbines at 10 meters (nearly 33 feet). These comparisons are for winds above level terrain — the general case. Near mountain ridges, and other places where the terrain funnels the air, the power available can increase far more with
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changes in height. Likewise, at sea, when strong breezes blow, the power available in the winds varies more markedly with changes in altitude. This is because strong breezes make waves that effectively slow the winds closer to the earth even more — which causes a greater change in velocity with height.
3.3 CONCLUSION
‘ The conclusion of these discussions is to show that Tethered Airfoils could tap into winds that are much stronger than those accessible by commercial wind turbines — even if the Tethered Airfoils were to fly relatively low. But as the technology progresses, and as it becomes practical to fly as high as the jet stream, then Tethered Airfoils could tap into winds that can be hundreds of times more powerful.
‘ Besides being able to tap into much stronger winds, Tethered Airfoils could also be more practically constructed and deployed in larger sizes. This would allow them to extract power from a greater area.
‘ Compared to wind turbines, Tethered Airfoils would be more practical to scale up to larger sizes for two reasons:
1) Within reasonable limits, key materials are more economically manufactured, more readily available, and easier to manipulate in larger sizes, and
2) Tethered Airfoils would not have to be limited to the sizes that towers can accommodate.
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4. References
1. www.google.com
2. www.wikipedia.com
3. Fluid Power Engineering 4th Edition By Prof. V.L.Patel, Dr. R.N.Patel.
4. Fluid Mechanics by R.K.Bansal
5. Books of safari