The effects of angle of attack on the coefficient of lift of an aerofoil are important in the design of helicopters as they are limited by rotor blades stalling. A NACA 2415 aerofoil was placed in an open-loop wind tunnel to test aerofoil characteristics, namely lift coefficient at different angles of attack. A leading-edge slat was then added to identify its effects on the system. Increasing the angle of attack increased the coefficient of lift in a linear fashion until the aerofoil reached a critical angle of attack. At that angle of attack, flow separation over the wing occurred reducing the lift coefficient considerably, known as stall. Adding the slat increased the maximum coefficient of lift by 0.3 and increased the critical angle of attack by a few degrees. Implementing aerodynamic devices, such as the leading-edge slat tested, to helicopter rotor blades could increase helicopter speeds in the future.
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Appendix – Boeing 747 Questions 9
Figure 1 - Retreating Blade Side (Blue) and Advancing Blade Side (Red) of a Helicopter\'s Rotor 3
Figure 2 - Retreating Blade Side (Blue) and Advancing Blade Side (Red) of a Chinook\'s Rotors 4
Figure 3 - Coefficient of Lift versus Angle of Attack 6
Figure 4 - Coefficient of Lift Versus Angle of Attack Plot With NACA Data 6
Figure 5 - Coefficient of Lift Versus Angle of Attack with and without Leading Edge Slat 7
Table 1 - Experimental Results: Coefficient of Lift at Different Angles of Attack 5
Aerofoils are integral to aerodynamic design as they create a force normal to the direction of a fluid’s velocity over it. This is caused by the aerofoil curving the streamlines along the aerofoil surface resulting in lower pressure on one side and higher pressure on the other “sucking” the aerofoil upwards.
The local static pressure at different points on the aerofoil can be represented non-dimensionally with the coefficient of pressure (Sangan & Lock, 2016).
█'(C_P=(P-P_∞)/(1/2 ρU_∞^2 )#(1) )
where P is the static pressure measured at surface, P∞ is the freestream static pressure and the denominator is the dynamic pressure of the freestream. Integrating the pressure over the area of the aerofoil gives the lift force. The lift force can also be represented non-dimensionally with the coefficient of lift
█'(C_L=L/(1/2 ρU_∞^2 S)#(2) )
where S is the wing area as the aerofoil spans the wind tunnel, S=c×1, where c is the aerofoil chord.
Reynold’s number is calculated with the chord length c, free stream flow velocity V∞ free stream density ρ.
█'(Re=(ρV_∞ c)/μ#(3) )
Studying the characteristics of aerofoils is imperative as modelling fluid dynamics is still poorly understood. An example of aerofoils’ use in engineering is in helicopters. Helicopter rotor blades are long thing aerofoils. When the rotor spins, air flows over the rotor blade producing lift. Helicopters are generally limited to 320 km/h due to a phenomenon called retreating blade stall. A retreating blade (in blue on Figure 1) has slower air speed over it and thus produces less lift (Equation 2). This difference in lift between both sides of the helicopter would cause it to roll.
Figure 1 - Retreating Blade Side (Blue) and Advancing Blade Side (Red) of a Helicopter\'s Rotor
To compensate for the lower relative air speed, most helicopters are designed to increase the angle of attack of retreating rotor blades to increase their lift coefficient. Some helicopters have semi-rigid blades which can ‘flap’ vertically to achieve this. Other helicopters have fully articulated rotor systems which will slow down advancing blades slightly and increase the speed of retreating blades to try equalise their relative speeds and produce the same amount of lift.
However, with increasing speeds the angle of attack must be increased. At a certain speed the rotor blade will reach a critical angle of attack and it will stall, no longer producing lift. This is the primary factor limiting helicopter speeds and is the reason why the Boeing CH-47 Chinook is one of the fastest helicopters in production (315km/h) despite being a heavy-lift cargo helicopter. This is because the two rotors spin in opposite directions allowing the dissymmetry of lift to be cancelled out (Dobson, 2016) as shown in the figure below.
Figure 2 - Retreating Blade Side (Blue) and Advancing Blade Side (Red) of a Chinook\'s Rotors
Although helicopter blades are generally passively controlled, trailing edge flaps for active blade control are currently being researched (Kessler, 2011).
The objectives of the experiment were to study the effects of angle of attack on an aerofoil’s coefficient of lift as well as the effects of aerodynamic devices such as leading-edge slats.
A NACA 2415 aerofoil with a chord of 127mm was placed in an open-return circuit wind tunnel. The angle of attack of the 0.3m wide aerofoil could be changed manually within the range of ±30°. The airspeed inside the wind tunnel was measured upstream of the model with a static pitot tube. Pressure tappings at fixed points in one chordal plane along the aerofoil measured the pressure distribution on the aerofoil at a fixed angle of attack and air speed. These measurements were taken using probes on the aerofoil connected to a computer controlled Scanivalve unit and transducer. This gave the coefficient of pressure for each point on the aerofoil (Equation 1). Integrating the pressure over the surface of the aerofoil gave the total lift force. The coefficient of lift could then be calculated from that using Equation 2.
A leading-slat based upon the highly cambered NACA 22 aerofoil with a chord of 38.1mm was added to study its effects on flow separately.
The numerical results are tabulated below (Table 1).
Table 1 - Experimental Results: Coefficient of Lift at Different Angles of Attack
Angle of Attack (degrees) Coefficient of Lift (w/o Slat) Coefficient of Lift (w/ Slat)
10 1.098 1.226
11 1.119 1.228
12 1.234 1.316
13 1.187 1.4
14 1.225 1.492
15 1.222 1.422
16 1.215 1.413
17 0.758 1.401
18 0.732 1.336
19 0.76 1.254
20 0.786 1.177
The lift coefficients were plotted against different angles of attack (Figure 3).
Figure 3 - Coefficient of Lift versus Angle of Attack
The curve shows a distinct linear region which then reaches a maximum before dropping again, this is the aerofoil stalling. A linear fit of this region is very close to a theoretical slope of 2 increase in CL per radian of .
The flow in the wind tunnel was calculated as having a Reynolds number of 172.9E+03. Although this is orders of magnitude smaller than the Reynold numbers in the NACA data, the curves are still comparable.
Figure 4 - Coefficient of Lift Versus Angle of Attack Plot With NACA Data
All the linear regions follow the theoretical slope of 2 even with very different Reynold’s numbers. Higher Reynold’s numbers indicate either higher airspeed, higher density or lower viscosity which would lead to higher lift coefficients. Higher Reynold’s numbers led to slightly higher critical angles of attack.
When the air speed is too low or the angle of attack was too high, separation of flow occurs. This is when the air flowing over the aerofoil separates from the aerofoil leaving a pocket of almost static air and therefore higher pressure (per Bernoulli’s principle). This pressure differential will even cause air to retreat along the aerofoil towards the leading edge. As seen in the figure below.
If the angle of attack is too high, the separation of the boundary layer may take place not far downstream of the maximum suction point. This will cause such a redistribution of the flow over the aerofoil that the large area of low pressure near the upper surface leading edge is seriously reduced with the result that the lift force is also greatly reduced. This condition is known as aerodynamic stall.
The leading-edge slat increases the speed of the air that flows between it and the aerofoil, increasing the momentum of the flow and pushing the separation point further towards the trailing edge of the aerofoil. Thus, increasing the lift coefficient at higher angles of attack and increasing the critical angle of attack. This can be seen in Figure 5.
Figure 5 - Coefficient of Lift Versus Angle of Attack with and without Leading Edge Slat
The leading-edge slat increased the maximum lift coefficient by almost 0.3 and increased the critical angle of attack by a few degrees.
A major cause of uncertainty in the procedure was the manual setting of the angle of attack. The aerofoil was set with a precision of about ±0.5° accuracy. The leading-edge slat was also a major contributor to error in the results as its angle was set visually without a strictly consistent angle setting.
Increasing the angle of attack, increased the coefficient of lift until boundary layer separation causes stall at too high an angle of attack (typically around 16°). Adding a leading-edge slat increases the critical angle of attack as it pushes back the point of boundary layer separation. It also increases the coefficient of lift. Successfully implementing aerodynamic devices such as the leading-edge slat tested could lead to increases in the speed of helicopters as it could alleviate retreating blade stall.
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