Aerofoil Experiment Lab Report

Aerofoil Lab Report

Summary

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 leading-edge 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 leading-edge slat. This helped in understanding why stall occurs and the effect of adding a leading-edge slat to an aerofoil. This experiment was compared with an experiment made by NACA in the 20^th century at higher Reynolds number.

Table of Contents

Summary

Introduction

Experimental Procedure

Results

Discussion

Conclusion

References

Appendix 1: Boeing 747 Questions

Appendix 2: Data

Introduction

An Aerofoil is a structure designed with curved edges in a way to give a favorable lift-to-drag 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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The fundamentals of aerofoils such as the wings in an aircraft are similar to the wings of birds. Birds flap their wing downwards which causes a net upward force on the wing while the air is directed downwards. When the National Advisory Committee on Aeronautics (NACA) was developing the aerofoil, a series of tests were conducted to understand the behavior of how birds’ fly. This enabled them to develop the most efficient aerofoils.  Due to the importance of aerofoils in engineering, NACA established a four- or five- digit number which includes the essential characteristics of an aerofoil. Nowadays, this numbering system has been unified, and engineers all over the world can understand the critical characteristic of an aerofoil from the numbers such as the camber, the location of the maximum camber and maximum thickness. Therefore, this has unified the numbering system and made it easier for engineers to understand what aerofoil is needed for a specific function.

The 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 leading-edge slat
• Understand the aerofoil characteristics regarding fundamental fluid dynamics

Experimental Procedure

A NACA 2415 aerofoil is placed in a wind tunnel to calculate the pressure acting on different regions of the aerofoil using pressure tappings placed on the wing. A wind tunnel consists of a fan which is located at the end of the tunnel that enables air to move throughout the tube. The aerofoil is placed in the test section as shown below in Figure 1. Throughout the wind tunnel there is no work done, and therefore Equation 1 is valid. After the test section due to the presence of the fan where work is done, the equation is no longer valid [2].

Figure 1: Schematic Diagram of the Wind Tunnel

The NACA 2415 aerofoil is placed in the working section of a 0.3m wide return circuit wind tunnel as shown in Figure 1. The walls of the test section act as end plate to have a two-dimensional flow over the wing. The wing is also supported by two integrals spigots that pass through the bushes in the Perspex window of the test section. This allows the angle of attack to be changed by a range of  30 using a pointer and protractor.  When the wind tunnel is turned on, the airspeed is measured using a Pitot-Static tube. On the wing, there are 33 pressure tappings in one chordal plane; this allows the computer software to calculate the pressure distribution over the pressure tappings. Since the lift is mainly due to the pressure forces, the shear stress will be disregarded.

According to Bernoulli’s equation assuming fluid is incompressible and inviscid,

${\mathrm{P}}_{\mathrm{}}+\frac{1}{2}\mathrm{}{U}_{\mathrm{}}^2=P+\frac{1}{2}\mathrm{}{U}^2$

        Equation 1

The local static pressure can be represented non-dimensionally in terms of a coefficient pressure C_P:

$C_P=\frac{P–{\mathrm{P}}_{\mathrm{}}}{\frac{1}{2}\mathrm{}{U}_{\mathrm{}}^2}$

          Equation 2

Lift is created when the pressure above the upper surface is higher than the pressure below the surfaces. The total lift is calculated by integrating the pressures around the aerofoil which is dependent upon the angle of attack and geometry.

The lift force (L) can be represented non-dimensionally in terms of a coefficient lift C_L:

$C_L=\frac{L}{\frac{1}{2}\mathrm{}{U}_{\mathrm{}}^{2}S}$

          Equation 3

Where S is the area of the wing in m²

Before the wind tunnel was turned on, all the pressure-tubes were checked to the model and that the Pitot-static tube is connected correctly. The tunnel was then started and set at a speed of 20m/s. The computer programme was then used to calculate the C_P and C_L at each angle of attack. After recording all the values, a leading-edge slat was added to the aerofoil which is based upon a highly cambered NACA 22 aerofoil with a chord of 38.1mm.

Lift is calculated from integrating pressures around aerofoil dependent upon angle and geometry. Using Equation 3, the computer program calculates the non-dimensional coefficient of lift of C_L. Similarly, for the non-dimensional coefficient of pressure, by taking the pressure measured from the tappings, the computer calculates C_P.

Results

After the program was turned on, the coefficient of lift was recorded at various angles of attack. Figure 2 shows the relationship between the angle of attack and the Lift Coefficient at different Reynold Numbers. The Reynolds Number at which the flow in the wind tunnel was operating was found to be $1.72\times {10}^5$

. Figure 2 also shows the relationship between the angle of attack and the lift coefficient of which collected by NACA at different fluid-dynamic 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 4-6 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 Leading-edge 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 leading-edge 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 leading-edge slat. Figure 8 shows the pressure arrows on the aerofoil.

Figure 8: Pressure Arrow Diagram for an aerofoil l with a leading-edge slat at an Angle of Attack of 15

Discussion

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 zero-shear-stress 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 leading-edge 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.

Conclusion

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 leading-edge 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 high-pressure 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.

References

[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 Variable-Density 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/boundary-layer [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 Variable-Density 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 ^oC,  = 1.8  10^-5 kg m^-1 s^-1.

b.  What was the range of Reynolds numbers for the NACA experiments?  Comment.

Question 2

A Boeing 747-400 cruises at Mach 0.86 at an altitude of 35,000 feet. At mid-cruise 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)

1. Determine the Reynolds number of the 747, based on a mean chord of 9.0 m.

2. Determine the lift coefficient and lift-to-drag ratio (L/D) if the wing area is 510 m².

   $\frac{L}{D}=\frac{\frac{W}{\frac{1}{2}\times \rho \times V^2\times S}}{\frac{D}{\frac{1}{2}\times \rho \times V^2\times S}}=\frac{\frac{3.2\times {10}^6}{\frac{1}{2}\times 0.38\times {255.1}^2\times 510}}{\frac{185\times {10}^3}{\frac{1}{2}\times 0.38\times {255.1}^2\times 510}}=\mathit{17}\mathit{.}\mathit{32}$

c.   Compare your calculations with the flight data for the 747-400 shown in Figure A1. With reference to the boundary layer, explain why the lift-to-drag ratio reduces 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 sea-level airspeed of 60 m/s using mechanical high-lift devices. (ρ_SL = 1.2 kg/m³)

     Determine the lift coefficient at landing.

e. A sketch of typical boundary layer velocity profiles for aerofoils employing mechanical high-lift devices is shown in Figure A2. With reference to the boundary layer, discuss how these slats, vanes and flaps increase lift.

Appendix 2: Data

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