Aerofoil Experiment Lab Report
✅ Paper Type: Free Essay  ✅ Subject: Sciences 
✅ Wordcount: 6642 words  ✅ Published: 23rd Sep 2019 
In this experiment, a NACA 2415 was placed in a wind tunnel and was tested by changing the angle of attack to examine how this will vary the coefficient of lift and hence how much lift is generated at a certain angle. It was found that the lift coefficient increased linearly up to a maximum and suddenly dropped at a certain angle called the critical angle of attack. The aerofoil was then altered by adding a leadingedge slat which was found to increase the angle of attack at which stall occurs. Throughout the experiment, pressure arrow diagrams were drawn on aerofoils at different angles of attack and on an aerofoil with a leadingedge slat. This helped in understanding why stall occurs and the effect of adding a leadingedge slat to an aerofoil. This experiment was compared with an experiment made by NACA in the 20^{th} century at higher Reynolds number.
Appendix 1: Boeing 747 Questions




An Aerofoil is a structure designed with curved edges in a way to give a favorable lifttodrag ratio [1]. When an aerofoil moves in a fluid, such as air, an aerodynamic force is created. This force is due to the pressure and stress acting on the surface. The perpendicular force to the flow is called the lift, and the parallel force is called drag. Aerofoils are being widely used in the aviation industry such as the fixed wings of an aircraft or mechanical devices such as compressors and propellers.
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Essay Writing ServiceThe main objectives of this experiment
 To measure the pressure distribution for a range of angles of attack on the NACA 2415
 Calculate the Lift coefficient and compare it with the published data
 Determine the effects created by a leadingedge slat
 Understand the aerofoil characteristics regarding fundamental fluid dynamics
Figure 1: Schematic Diagram of the Wind Tunnel
According to Bernoulli’s equation assuming fluid is incompressible and inviscid,
The lift force (L) can be represented nondimensionally in terms of a coefficient lift C_{L}:
Where S is the area of the wing in m^{2}
Lift is calculated from integrating pressures around aerofoil dependent upon angle and geometry. Using Equation 3, the computer program calculates the nondimensional coefficient of lift of C_{L}. Similarly, for the nondimensional coefficient of pressure, by taking the pressure measured from the tappings, the computer calculates C_{P}.
. Figure 2 also shows the relationship between the angle of attack and the lift coefficient of which collected by NACA at different fluiddynamic conditions.
Figure 2: Relationship between Angle of Attack and the Coefficient of Lift for different Reynolds Numbers.
The Linear Region of the relationship between the angle of attack and the Lift Coefficient at a Reynolds Number of $1.72\times {10}^{5}$
was plotted in Figure 3. The slope of the linear region was found to be 0.102. Whereas, the theoretical slope of the $2\pi $
increase in C_{L} per radian of was found to be 0.109. Therefore, there is a discrepancy of 6.9%.
Figure 3: Line of Best Fit for the Linear Region
The values for C_{P} were computed for a range of angles of attack. Hence, the pressure arrows were drawn on the aerofoil for angles of attack 2,8 and 15. Figures 46 shows the pressure arrows for the listed range of angles.
Figure 4: Pressure Arrow Diagram for an Angle of Attack of 2
Figure 5: Pressure Arrow Diagram for an Angle of Attack of 8
The Leadingedge slat was added to the aerofoil and placed in the wind tunnel. Figure 7 shows the relationship between the angle of attack and the lift coefficient of the aerofoil with a leadingedge slat at a Reynolds number of $1.72\times {10}^{5}$
along with the data shown in Figure 2.
Figure 7: Relationship between the angle of attack and the coefficient of lift
The values for C_{P} for each pressure tapping were computed for a 15 angle of attack on an aerofoil with a leadingedge slat. Figure 8 shows the pressure arrows on the aerofoil.
Figure 8: Pressure Arrow Diagram for an aerofoil l with a leadingedge slat at an Angle of Attack of 15
Figure 3 shows there is a linear relationship between the angle of attack and the lift coefficient. Beyond that range, the relationship is no longer linear. An increase in the angle of attack will lead to airflow passing an obstacle leading to a narrower path and an increase in speed; hence C_{L} increases linearly with the angle of attack. After a particular angle of atatck, there is a sudden drop in the lift which is shown in Figure 2, this angle is called the critical angle of attack. As the angle of attack increases, the stagnation point, point at which the coefficient of pressure is 1, moves further along the lower surface. Moreover, on the upper surface the coefficient of negative pressure which is referred to as an adverse pressure gradient will increase leading to a higher lift.
Lift of an aerofoil occurs when there is a difference in pressure between the upper and lower region. This is due to the relative speeds of the fluid and the aerofoil. The aerofoil splits the fluid in two directions. Due to this asymmetric split, the fluid travels faster above the aerofoil. From Equation 2, having a higher velocity in the upper region will lead to a lower pressure. This is the primary reason for having lift at a zero angle of attack. This phenomenon is referred to a Positive Camber.
Figure 7 shows that after a particular angle of attack the C_{L} increase, but there is a sudden drop in lift. This is mainly due to the Boundary Layer Separation [3]. As air passes over the aerofoil in the wind tunnel, a boundary layer is created due to viscous forces between the fluid and the surface in contact. As the angle of attack is increased, the speed of the boundary layers increases until reaching a point where the relative velocity is zero, and a zeroshearstress is acting on it [4]. Hence, a boundary layer separation occurs. The boundary layer thickens suddenly and is then forced off by the reversed flow of the lower surface. This leads to an increase in drag and a decrease in lift causing an Aerodynamic Stall.
From Figure 7, it can be concluded that an aerofoil with a leadingedge slat has a higher angle of attack at which stall occurs. This is due to the presence of a secondary airflow. The secondary airflow which passes between the slat and the aerofoil injects a high momentum fluid onto the upper surface. This fluid energizes the boundary layer and decreases the drag and increases lift. This leads to increasing the angle of attack at which stall occurs. Moreover, a different Reynolds number, i.e. a different fluid or different speed conditions will lead to different angles of attack at which stall occurs. A fluid with a higher Reynolds number will have more energy and this forced boundary layer to stick on the surface for a longer distance. This shifts the point of separation more towards the trailing edge where drag will decrease causing a higher lift [5].
There was a discrepancy between the experimental and theoretical data due to Experimental Uncertainties that arose during the experiment. Firstly, when aligning the angle of attack of the aerofoil using the spigots at the desired angles, it was difficult to align it due to the parallax effect. Secondly, there were multiple interpretations and different people interpreting data. Since different people have different accuracy, this led to high uncertainty. Thirdly, the programme uses the trapezium rule rather than integrating to find the pressure around the aerofoil. Finally, the compression tube was long which may have influenced the speed of the air.
The experiment compared the characteristics of an aerofoil at different angle of attacks. The values interpreted from the experiment was also compared to the NACA 2415 at different Reynolds Numbers. It also showed the difference in crucial characteristics upon adding a leadingedge slat such as the increase of the angle of attack at which stall occurs. The maximum lift coefficient of the aerofoil without slats was found to be 1.246 and with slats was found to be 1.456. From the pressure diagrams, it was concluded that there was a highpressure gradient at the leading edge and decreased through the aerofoil. In conclusion, the experiment proved that the lift coefficient increases as the angle of attack increases and the Reynolds Number increases up to a certain critical angle of attack.
[1] Wikipedia, “ Airfoil,” [Online]. Available: https://en.wikipedia.org/wiki/airfoil. [Accessed 12 October 2018].
[2] Jacobs, Eastman N.; and Pinkerton, Robert M.: Tests in the VariableDensity Wind Tunnel of Related Airfoils Having the Maximum Camber Unusually Far Forward. NACA Rep. 537, 1935.
[3] Encyclopedia Britannica. (2018). Boundary layer  fluid mechanics. [online] Available at: https://www.britannica.com/science/boundarylayer [Accessed 13 Oct. 2018].
[4] Lock G., “ME20022 Fluid Dynamics Aerofoil Experiment,” University of Bath,2018.
[5]Jacobs, Eastman N.; and Pinkerton, Robert M.: Tests in the VariableDensity Wind Tunnel of Related Airfoils Having the Maximum Camber Unusually Far Forward. NACA Rep. 537, 1935.
Appendix 1: Boeing 747 Questions
Question 1
a. Calculate the Reynolds number (based on chord) for this experiment. Note the airfoil chord, c = 127 mm and the viscosity of air at 15 ^{o}C, = 1.8 10^{5} kg m^{1} s^{1}.
Ans. Reynolds Number, $\mathit{Re}=\frac{\mathit{\rho VC}}{\mu}=\frac{1.225\times 20\times {127\times 10}^{\u20133}}{{1.8\times 10}^{\u20135}}={1.73\times 10}^{5}$
b. What was the range of Reynolds numbers for the NACA experiments? Comment.
Ans. Reynolds Number Range: $3\times {10}^{6}\u20139\times {10}^{6}$
Our Reynolds Number is much smaller, by an order of magnitude ( ${10}^{1}$
) however results are nearly the same. This is shown in Figure 7
Question 2
A Boeing 747400 cruises at Mach 0.86 at an altitude of 35,000 feet. At midcruise the aircraft weight is 3.20 MN and the total thrust from four engines is 185 kN.
Data at 35,000 feet: static temperature and pressure are 219 K and 23.8 kPa, respectively.
(γ = 1.4, R = 287 J/kgK; at 219 K, = 1.7 10^{5} kg m^{1} s^{1})
 Determine the Reynolds number of the 747, based on a mean chord of 9.0 m.
Ans. $\mathit{Re}=\frac{\rho \times V\times C}{\mu}=\frac{0.38\times 255.1\times 9}{{1\times 10}^{\u20135}}=\mathit{5}\mathit{.}\mathit{11}\mathit{}\mathit{\times}{\mathit{10}}^{\mathit{7}}$
$\rho =\frac{P}{\mathit{RT}}=\frac{23.8\times {10}^{3}}{287\times 219}=0.38$
kg/m^{3} $V=M\times a=M\times \sqrt{\gamma \times R\times T}=0.86\times \surd (1.4\times 287\times 219)=255.1\mathit{m}/s$

Determine the lift coefficient and lifttodrag ratio (L/D) if the wing area is 510 m^{2}.
$\frac{L}{D}=\frac{\frac{W}{\frac{1}{2}\times \rho \times {V}^{2}\times S}}{\frac{D}{\frac{1}{2}\times \rho \times {V}^{2}\times S}}=\frac{\frac{3.2\times {10}^{6}}{\frac{1}{2}\times 0.38\times {255.1}^{2}\times 510}}{\frac{185\times {10}^{3}}{\frac{1}{2}\times 0.38\times {255.1}^{2}\times 510}}=\mathit{17}\mathit{.}\mathit{32}$
c. Compare your calculations with the flight data for the 747400 shown in Figure A1. With reference to the boundary layer, explain why the lifttodrag ratio reduces significantly as the Mach number increases from 0.86 to 0.88.
Ans. The speed of the air over the upper surface of the wing increases with in Mach 1 when the actual speed is Mach 0.86. But when the actual speed raises to Mach 0.88 the speed of the air over the upper surface of the wing increases over Mach 1 and hence results in the formation of shock waves. The boundary layer formed separates the shock waves from the flow. Hence the lifttodrag ratio is reduced significantly as the Mach number increases from 0.86 to 0.88.
d. Due to fuel burn, the weight of the 747 reduces to 2.4 MN when it lands with a sealevel airspeed of 60 m/s using mechanical highlift devices. (ρ_{SL} = 1.2 kg/m^{3})
Determine the lift coefficient at landing.
Ans.
${C}_{L}=\frac{W}{\frac{1}{2}\times \rho \times {V}^{2}\times S}=\frac{2.4\times {10}^{6}}{\frac{1}{2}\times 1.2\times {60}^{2}\times 510}=2.18$
e. A sketch of typical boundary layer velocity profiles for aerofoils employing mechanical highlift devices is shown in Figure A2. With reference to the boundary layer, discuss how these slats, vanes and flaps increase lift.
Ans. Slats alter a small amount of high energy air from just below the loading edge to be redirected along the upper surface of the wing. The highly energized air moves through the slat gap which energizes the boundary layer and increase lift by preventing the stall at a higher angle of attack.
Angle 
CL Without Slat 
CL with Slat 
10 
0.855 

9 
0.802 

8 
0.731 

7 
0.712 

6 
0.593 

5 
0.511 

4 
0.327 

3 
0.114 

2 
0.003 

1 
0.08 

0 
0.153 

1 
0.275 

2 
0.482 

3 
0.59 

4 
0.655 

5 
0.733 

6 
0.824 

7 
0.856 

8 
0.947 

9 
1.061 

10 
1.145 
0.954 
11 
1.154 
1.091 
12 
1.164 
1.086 
13 
1.226 
1.276 
14 
1.161 
1.348 
15 
1.112 
1.43 
16 
0.916 
1.459 
17 
0.969 
1.229 
18 
0.741 
1.254 
19 
0.743 
1.029 
20 
0.789 
1.207 
Angle (α) 
NACA CL (Re:3 x10^{6}) 
NACA CL (Re:6 x10^{6}) 
NACA CL (Re:9 x10^{6}) 
18 
0.900 

17 
1.150 

16 
1.350 

14 
1.250 

12 
1.050 

10 
0.825 
0.825 
0.875 
8 
0.625 
0.625 
0.675 
6 
0.400 
0.400 
0.450 
4 
0.225 
0.225 
0.225 
2 
0.000 
0.000 
0.000 
0 
0.200 
0.200 
0.225 
2 
0.400 
0.400 
0.425 
4 
0.625 
0.625 
0.625 
6 
0.800 
0.800 
0.850 
8 
1.000 
1.025 
1.075 
10 
1.200 
1.200 
1.275 
12 
1.300 
1.400 
1.425 
14 
1.425 
1.500 
1.570 
16 
1.300 
1.600 
1.650 
18 
1.175 
1.300 
1.575 
20 
1.075 
1.125 
1.350 
22 
1.025 
1.075 
1.250 
24 
1.050 
1.000 
1.325 
Table 2: NACA data – lift coefficients for different Reynolds numbers at various angles of attack
Table 1: Experimental C_{L} data for the NACA 2415
Aerofoil with and without slat
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