BAerodynamics 1
BAerodynamics 1
BAerodynamics 1
DARSHANA BHUDYE
B00340530
University of the West of Scotland
2
Table of contents
Titles Pages
Introduction
Airfoil …………………………………………………………………. 4
Aircraft Characteristics
1.1 -- Aerodynamic Forces: Lift and drag ………………………. 5
1.2 – Generation of Lift ……………………………………………. 6
1.3 – Coefficient of Lift, Cl ………………………………………… 6
1.3.1 - Variation of Cl vs AOA ………………………… 7
1.4 – Coefficient of Drag, Cd ……………………………………… 7
1.4.1 – Variation of Cd vs AOA ……………………...... 8
1.5 – Lift to Drag Ratio ……………………………………….......... 8
1.5.1 – Variation of Cl/Cd vs AOA ……………………. 9
XFLR5
Features and capabilities …………………………………………. 10 – 13
Conclusion ……………………………………………………………………. 21
References ……………………………………………………………………. 22 - 23
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Introduction
Airfoils
Airfoils are defined as the cross sectional form of a wing which provides
aerodynamic forces such as lift, when moving in air. For different aircrafts, different
airfoils are used.
Wing designs have changed during the past few years. In order to improve the
efficiency of an aircraft aerodynamically, better wing configurations and airfoil
shapes are being generated. The diagram below shows an illustrated airfoil of an
aircraft.
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Aircraft Characteristics
1.1 Aerodynamic Forces: Lift and Drag
Lift is defined as the force opposite to the weight of an aircraft which holds it in
the air and drag is defined as the force which opposes the direction of motion of
an aircraft. The diagrams below show the two forces acting on an aircraft and on
an airfoil.
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1.2 Generation of Lift
According to Bernoulli’s principle, pressure is inversely proportional to velocity.
Thus, pressure decreases with an increasing air velocity, which generates lift on
a wing. The diagram illustrates lift generation on an airfoil.
The coefficient of lift has a maximum value when the aircraft starts to lose airflow
over its wings and has decreased lift (at stalling angle of attack). The difference
in pressure caused by the change in angle of attack in a symmetrical airfoil,
generates lift.
L
Cl =
1 2
ρV A
2
Where,
L is the lift generated
Ρ is the density of air
V is the velocity
A is the area of the wing
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1.3.1 Variation of Cl and Angle of Attack
Since angle of attack is directly proportional to the lift, lift increases with AOA
until a point called stall angle of attack. The graph below shows the variation of
Cl vs AOA.
At point P which is the stalling point, the aircraft has a maximum CL and the
aircraft begins to slow down.
D
Cd =
1 2
ρV A
2
Where,
D is the generated drag
ρ is the density of air
v is the velocity and
A is the area of the wing
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1.4.1 Variation of CD and Angle of Attack
The lift coefficient increases with the angle of attack which causes a change in
the induced drag. The graph below shows the variation of Cd vs AOA
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1.5.1 Variation of CL/CD vs Angle of Attack
The graph below shows that at critical angle of attack, known as the stalling
angle, the aerodynamic efficiency is at its maximum. Thus, the aircraft is unable
to produce lift in order to remain in level flight.
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XFLR5
Xflr5 is a program used to design and analyze 2D airfoils, wings and airplanes
which operates at a given Reynolds and Mach Number. It can also be used to
modify the thickness and camber of an airfoil.
The software uses X and Y coordinates and the required foil name
to perform its task. The figure below shows designing a foil with
Xflr5.
10
This option also allows plotting of graphs of the desired foil at the given
Reynold’s and Mach Number when a range of values of angle of attack
is entered. It therefore plots the graph such as CL/CD against AOA
and Cl vs AOA. The figure below shows the different variation of
graphs.
2. Foil Design
It can modify the thickness, camber, maximum thickness and
maximum camber positions of an airfoil, as shown in the figure
below. The program provides local and global refinements as
well.
.
Figure 2.2 Modification of an airfoil
(Source: xflr5 - Airfoil camber and thickness variation algo – Source Forge)
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3. Analysis/Polar Object
After defining a polar object, the analysis of a foil is performed. A polar
object is determined by the type, the Reynold’s Number and Mach
Number, the change form laminar to turbulent of the airfoil. The graph
below shows the variation of Cl against Cd of a foil polar.
4. Plane Definition
The airfoil is implemented on the program which will allow the defining
of a plane using the chord length of a wing as shown in the figure
below.
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5. Stability Analysis
This is used to position the center of gravity of the aircraft in order to
keep the stability. The figure below shows the stability analysis of a
rectangular airfoil using the software.
The program allows many features in order to facilitate the designing of an airfoil
such as Direct and Inverse Analysis and 3D Designing.
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Generation of Aerodynamic Data
3.1 Airfoil Data
NACA 4-Digit Airfoil Generator
The airfoil is 2% maximum camber at 40% of the chord line and the thickness of
the airfoil is 30% (Based on the two last digits of my banner ID).
Based on 4-digit NACA airfoil provided, the software NACA airfoil generator
created a data-point file, as shown in the Figure 3.1.
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Airfoil Data Points on Excel
The x and y coordinates were plotted on excel as shown in the figure below.
The following equation is used to calculate the thickness distribution of the airfoil
using the x and y coordinates which is generated by the NACA software:
𝑡
𝑦𝑡 = (0.2969√𝑥 − 0.126𝑥 − 0.3516𝑥 2 + 0.2843𝑥 3 − 0.1015𝑥 4 )
0.2
where x is a position along the chord line and t is the value of maximum thickness.
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3.2 XFLR-5 Platform
The airfoil was generated based on the foil coordinates uploaded on the platform,
shown in the figure below.
A range of angle of attack 0º to 25º and a range of Reynold’s number were used
for the graphs of Cl vs AOA at a given Mach Number, as shown in Figure 3.3 and
3.5.
Figure 3.3 Aerodynamic Calculations for given AOA and Reynold’s Number within the
range 100,000 and 500,000.
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After analysing the aerodynamic calculations for the range of Reynold’s Number,
the following graphs were obtained.
Figure 3.5 Aerodynamic Calculations for given AOA and Reynold’s Number within the
range 500,000 and 900,000.
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After analysing the aerodynamic calculations for the range of Reynold’s Number,
the following graphs were obtained.
Figure 3.7 Cl vs AOA for Re Number 100 000 – 500 000 Figure 3.8 Cl vs AOA for Re Number 500 000 – 900 000
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The graphs show the variation of Cl against AOA for different range of Re
Number. Since lift is directly proportional to AOA, thus it increases with the angle
of attack and so does the Cl, until a certain point called the stall angle.
For Reynold’s Number lower than 500 000, the flow is laminar as shown in figure
3.7 whereas for higher Reynold’s Number, the flow is turbulent as shown in figure
3.8.
In Figure 3.7, the maximum value of Cl is at 1.1 at a stall angle of attack of 20º as
compared to in Figure 3.8, it reaches its peak value at 1.22 at an angle of 20º.
The curve starts to incline slightly which shows loss of lift effectiveness. At the
maximum Cl, the lift decreases rapidly causing loss in lift and stalling of aircraft.
The table below shows the different Reynold’s Number relating to the stall angle
of attack and the Cl.
The maximum glide ratio occurs at the most efficient angle that is at an angle of
7º.
As AOA increases, drag also increases, so does the drag coefficient, thus the
aircraft loses balance in flight.
If Re 500000, the flow is turbulent and if Re 500000, the flow is laminar.
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From the chosen airfoil, a rectangular wing was designed. The wing span and
chord length was inspired from the airfoil of Piper PA-38.
- From the formula, Length x Width (Wing span x Chord length, for a
rectangular wing), the wing area is obtained.
- From the formula, AR = b2/A, where AR is the aspect ratio, b is the wing span
and A is the area, the value of the airfoil’s aspect ratio is obtained.
Area 11.60 m2
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Conclusion
Airfoils are very essential components for an aircraft since they are used for its flight.
Thus, change in their designs may cause a great impact on the aircraft. The factors to
be considered for designing a wing are its planform area, cross sectional area,
thickness, aspect ratio and taper ratio.
Moreover, the generation of lift is the most essential part during the flight since it
balances the aircraft during the flight condition. The main factors affecting the
generation of lift on an airfoil of an aircraft is the Reynold’s number, the Mach number
and the range of angle of attack. At high Reynold’s Number, the Cl is higher than at low
Reynold’s Number.
The Principle of Bernoulli states that pressure acting on the airfoil is inversely
proportional to the velocity of the aircraft. The slower the pressure, the higher the
velocity. Thus at higher Reynold’s Number, the velocity of the aircraft increases. High
velocity of aircraft causes turbulent flow which leads to imbalance in the flight condition
which is between 15º – 20º of stall angle of attack at maximum lift coefficient.
The software XFLR5 has used its features such as direct analysis and batch analysis
and plane definition to design the airfoil at low Reynold’s Number. The range of
Reynold’s Number was taken from 100 000 to 900 000 since exceeding this range will
cause instability in the flight condition due to high unsteady flow. The value of Mach
Number is considered 0.2 so as the speed of the aircraft will be less than the speed of
sound which is known as the subsonic speed. The graphs indicate that the aircraft
moves in a steady flow till it reaches the maximum lift coefficient at a stall angle of
attack where separation of flow begins.
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References
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http://avstop.com/ac/apgeneral/bernoulli%27sprinciple.html.
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https://physics.stackexchange.com/questions/83432/difference-resultant-
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[3] Coanda Effect. Formula 1 Dictionary, 2017. http://www.formula1-
dictionary.net/coanda_effect.html.
[4] rotorhead8900 (DRAG – The Drag Formula). WordPress, 2011.
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https://www.recreationalflying.com/tutorials/groundschool/umodule4.html.
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https://sourceforge.net/p/xflr5/discussion/679396/thread/dc794cfd/.
[8] Aero World. aeroworldjay.blogspot, 2014.
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https://www.google.mu/search?q=full+inverse+analysis+xflr5&rlz=1C1CHBF_enMU
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:.
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[14] Rutkowski, T., Yowell, J., Zarske, M., Hill, G. and Conner, A. Lesson: May the
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