### Introduction

This report aims to investigate the effect the angle of attack of an aerofoil has on the air flow around it. This was done by recording the lift and drag forces the aerofoil experienced when positioned at different angles of attack. The experimental lift force the aerofoil experienced when positioned at different angles of attack was then compared with theoretical values. An attempt was made to explain any discrepancies between experimental and theoretical values.

## Theory

When air is blown over an aerofoil, it separates into two distinct sets of streamlines above and below it separated by a dividing streamline.

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The shape of the aerofoil results in a particular air circulation pattern around it. This air circulation pattern results in the air above the aerofoil to have higher velocities than that below it. This generates higher pressures below the aerofoil and results in a net lift force that varies with the its angle of attack vis a vis airflow. As the angle of incidence increases, the point of flow separation moves forward towards the trailing edge of the aerofoil thus increasing the lift force.

However, as the angle of attack increases, the rate of increase of lift force decreases. This pattern continues until the aerofoil reaches a point where the increase in angle of incidence no longer produces increase in lift force, this position is called the Stall. The theory also predicts that up to stall angle, the air circulation around the aerofoil is normal, it travels above and below the aerofoil from front to back. After stall angle however, a wake is formed above the aerofoil causing air above the aerofoil to recirculate to the front. Apparatus

The apparatus used for this lab experiment consists of two NACA0015 aerofoils placed one in front of the other in a wind tunnel. One of the aerofoils was lined with nylon tufts and had force balance amplifiers connected to voltmeters enabling measurements for lift and drag to be taken. The other one had pressure tappings above and below it connected to the series of manometers. Both aerofoils were mounted on protractors that rendered it possible to change their angle of attack.

Manometers connected to pressure tappings on the second aerofoil. The manometers on the left represent the pressure sensors on the bottom while the ones on the right represent those on the top. The pictures represent the pressure distributions above and below the air foil when the angle of attack is 0°, at stall, and after stall.

## Methodology

First, the protractor on which the aerofoil with tappings attached manometers was used to vary the aerofoil’s angle of attack. The effect this had on the manometers was observed.

To determine the velocity of airflow in the tunnel, both aerofoils (assumed to be sufficiently apart to not be affected by any disturbances) were set at an angle of attack of 0°. The difference in the fluid level of two manometers was then used to determine the stagnation deflection, which was found to be 14mm was then plugged in equation (1) to calculate the difference between atmospheric and stagnation pressure. (1) was calculated to be 137,34 kPa was the plugged into equation (2) to determine the velocity of the airflow in the wind tunnel. (2) Airflow velocity calculated was 14.68 m/s.

The protractor of the aerofoil connected to the lift and drag voltmeters was then used to vary the aerofoil’s angle of attack from 0° to 20°. Lift and Drag voltage values measured for each angle were recorded and calibration coefficients of 6.7 and 6.4 were used to obtain force Newton values for lift and drag. The lift and drag forces obtained for each angle were then plugged into equations (3) and (4) to obtain lift and drag coefficients. Equation (5) was used to calculate a theoretical value for the lift coefficient. (3) A represents the area of the aerofoil

The values obtained were then tabulated, graphed and compared. -The Reynolds number of this experiment was then calculated using equation (4) where c is the length of the aerofoil chord and is the dynamic viscosity of air. (6)

## Results

Equation (6) was used to calculate the Reynolds Number which equated to 119366.

## Discussion

The graph in Figure 3 confirms the theory stating that as the angle of attack of an aerofoil increases, the lift force it experiences also increases until it reaches stall position. The graph clearly shows the lift coefficient steadily increasing with angle of attack. This is due to the fact that as that as angle of attack increases, the point at which the airflow separates into streamlines going above and below the aerofoil moves forward thus providing more lift force.

Lift force continues to increase until the angle of attack reaches 13° marking the angle at which the aerofoil at stall. The graph shows that as the angle of attack increases from 0° to 13°, the rate at which lift increases slowly decreases. This is dues to the fact that the point of airflow separation is starting to reach the trailing edge of the aerofoil. The geometry of the trailing edge causes lift to be transmitted less efficiently. The line representing the theoretical value of the lift coefficient does not show any change in the rate of increase of lift because it assumes the object experiencing lift force is an infinite flat plate. Thus, it assumes that there is no change in geometry. After 13° the lift force experienced by the aerofoil decreases while the drag force increases dramatically. This is due to the fact that at stall, the point of separation of the airflow streamlines travels beyond the part of the trailing edge that allows it to produce lift. Thus the lift force exerted on the aerofoil decreases. The more the angle of attack increases, the bigger the perpendicular area of the aerofoil to the airflow and the larger the drag force .The total resultant force applied on the aerofoil is composed of lift and drag. Therefore, if the resultant force on the aerofoil stays relatively constant, drag force will increase as lift decreases.

The way by which the data from which the lift and drag coefficient lines are plotted has certain sources of inaccuracy. Errors could come from the inaccuracy of measurements taken to calculate the pressure head and the angles. Furthermore, major sources of inaccuracy are the voltmeters used as the values displayed were in constant fluctuation. Moreover, the airflow in the wind tunnel could experience fluctuations that affect readings. The theory was confirmed by the observation of the effect pf changing the angle of attack of the aerofoil on the pressure distribution above and below it. As the angle of attack was changed, the manometers measuring the pressure above and below the aerofoil (above- on the left side, below- on the right side respectively) behaved differently.

As the angle of attack increased to stall, the slow airflow created a high pressure below the aerofoil that pushed the fluid on the left side manometers down. Meanwhile, the fast airflow above the aerofoil created a relatively small pressure that lets the fluid on the right side manometers go up. This pressure difference creates a net lift force. However, as the angle of attack is increased above the angle of stall, the difference in pressure decreases and so does the lift force. The observation of the nylon tufts lining the top of the aerofoil demonstrates the theory that at stall the streamline separation at the edge of the aerofoil create a wake above the aerofoil. The nylon tufts are brushed by the airflow thus showing its direction. Up to the stall angle, the nylon tufts were all brushed backwards by the airflow. After the stall angle, the tufts were less homogenous and started to be brushed towards the front of the aerofoil. This indicates that a wake has formed above the aerofoil and is recirculating air towards the front.

### Conclusion

Though there were some sources of inaccuracy, the experiment successfully supported theory. Through this experiment, it was determined the Reynolds number was 119366 and that for the aerofoil investigated, the stall angle was 13°.

### Bibliography

- Greated, C. (2013) Fluid Mechanics 3 Lecture Notes, University of Edinburgh
- Kinnas, Dynamic Viscosity of Air as a Function of Time, http://www.ce.utexas.edu/prof/kinnas/319lab/Book/CH1/PROPS/GIFS/dynair.gif Accessed on 15/04/2013