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Table of Contents

Aim	2 Background Theory	2 Apparatus and Setup	3 Calculations and Results	4 Lift Coefficient	5 Drag Coefficient	6 Support Drag Coefficients	6 Moment Coefficient	7 Wind Tunnel Correction Factors	9 Reynolds Number Correction	9 Lift Coefficient Correction	10 Drag Coefficient Correction	10 Moment Coefficient Correction	11 Comparison against literature	12 Variations with Aspect Ratio	15 Lift Coefficient	15 Drag Coefficient	16 Moment Coefficient	17 Conclusion	18 References	19

Aim

To validate collected experimental data by applying wind tunnel correction factors. The effect of 3D experimental results will also be analysed against published 3D experimental literature. The influence of varying aspect ratios will also be determined by analysing 3D experimental results. Background Theory

The NACA 0012 is a symmetrical aerofoil section with a 12% maximum thickness to chord ratio. The generation of lift on a body can be attributed to the theory of surface pressure distribution. Factors which contribute to the distribution of lift include the shape of the body, the angle of attack of the body, the atmospheric conditions and the relative velocity of the body to the medium. I.e. air or water. The coefficient of lift is a function of the above factors and gives a dimensionless quantity to compare differing bodies. It is represented as; C_L=2L/(ρV^2 S) The coefficient of drag is also a function of the above factors and gives a dimensionless quantity to compare differing bodies. It is represented as; C_D=2D/(ρV^2 S) A consequence of pressure distribution is the moment produced by the aerodynamic force applied at the aerodynamic centre of the aerofoil. This typically occurs at a quarter chord from the leading edge. The aerodynamic centre is where the pitching moment does not change with varying angles of attack (AoA). This occurs as pressure (lift) is distributive, and acts at a centre of pressure, with a moment arm being created through the distance between the centre of pressure and aerodynamic centre, which changes with angles of attack. The moment coefficient is a function that gives a dimensionless quantity to compare differing bodies. It is represented as; C_m=2M/(ρV^2 Sc) Apparatus and Setup

The apparatus consists of a 3’ x 4’ low speed wind tunnel and a NACA 0012 aerofoil mounted inside the tunnel. To determine the pressure generated on the aerofoil, the two load sensing supports are placed 45mm from the leading edge. Another support is connected to the rear of the aerofoil in order to vary the angle of attack (AoA).

Different AoA were instigated through in house software control, with different aerodynamic characteristics recorded manually from the software outputs displayed on a computer at differing AoA. Calculations and Results

Wing Chord		= 0.153 m Wing Span		= 0.73 m Wing Area		= 0.11169 m2. Aspect Ratio		= 4.77 Temperature 		= 22.0 °C = 22 K + 273.15 K				= 295.15 K Lab Pressure 		= 766 mmHg = 102125 Pa Therefore, ρ		= 102125/(273.15+22)(287) = 1.206 kg/m3

The in house software calculated airspeed (40.4 m/s) using a density of 1.225 kg/m3 applying the equivalence between indicated and true airspeeds yields a true airspeed; V_TAS= V_IAS √(ρ_IAS/ρ_TAS ) The true airspeed is found to be 40.7 m/s. Because the dynamic viscosity is a function of the temperature, a more specific value can be determined by applying Sutherland’s equation.

This yields a value of μ=1.82x〖10〗^(-5 ) kg/(m/s), as opposed to the reference value of 1.79x〖10〗^(-5 ) kg/(m/s) at 288.15 K. Therefore, the Reynolds number is calculated to be

Re = ρvc/μ

= ((1.206)(40.7)(0.153))/(1.82x〖10〗^(-5) )

Re = 4.118 x〖 10〗^5

This value will provide a reference for further experimental data to be measured against.

Lift Coefficient

The lift coefficient is calculated through the measured lift forces by employing the following formula. C_L=2L/(ρV^2 S)

α (°)	-9.8	-8	-6	-4	-1.9	0	1.9	4	5.9	8	9.8	13 Lift (N)	-84.2	-69.2	-54.3	-33.4	-13.2	0.5	19.8	36.9	54.0	71.9	87.0	81.5 Cl	-0.55	-0.45	-0.36	-0.22	-0.09	0.00	0.13	0.24	0.35	0.47	0.57	0.53

An error in the measurements for lift was introduced by fluctuations outputted by the software of ±0.4N. This error is calculated through the calculations for both maximum and minimum values. This yields an error of less than 1%. There were no fluctuations in the AoA output and hence no error is present.

Drag Coefficient

The drag coefficient is calculated through the measured drag forces by employing the following formula. C_D=2D/(ρV^2 S)

α (°)	-9.8	-8	-6	-4	-1.9	0	1.9	4	5.9	8	9.8	13 Drag (N)	9.4	7.8	6.6	5.3	4.6	4.5	4.6	5.0	5.8	7.1	8.3	18 CD	0.062	0.051	0.043	0.035	0.030	0.029	0.030	0.033	0.038	0.046	0.054	0.118

Support Drag Coefficients

The support drag variation can be represented as; C_DSupports=(-0.0001× α)+0.0255 The support drag coefficients will be subtracted from the drag coefficient of the aerofoil. Note that alpha is indicated as degrees.

α (°)	-9.8	-8	-6	-4	-1.9	0	1.9	4	5.9	8	9.8	13 C_DSupports	0.0265	0.0263	0.0261	0.0259	0.0257	0.0255	0.0253	0.0251	0.0249	0.0247	0.0245	0.0242 C_DTotal	0.035	0.025	0.017	0.009	0.004	0.004	0.005	0.008	0.013	0.022	0.030	0.094

An error in the measurements for drag was introduced by fluctuations outputted by the software of ±0.3N. This error is calculated through the calculations for both maximum and minimum values, including the subtraction of the support drag. This yields an error of 5%. There were no fluctuations in the AoA output and hence no error is present.

Moment Coefficient

The moment coefficient is calculated through the measured drag forces by employing the following formula. C_M=2M/(ρV^2 Sc) α (°)	-9.8	-8	-6	-4	-1.9	0	1.9	4	5.9	8	9.8	13 Pitch (Nm)	-0.61	-0.52	-0.42	-0.37	-0.22	-0.09	0.10	0.26	0.38	0.51	0.62	-0.2 CM	-0.036	-0.030	-0.025	-0.022	-0.013	-0.053	0.006	0.015	0.022	0.030	0.036	-0.012

Because the pitching moment is measured about the front supports, moments must be translated to the ¼ chord position in order to compare conventional results. C_M (1/4 c)=C_M-C_L d_1/c The moment translation geometry is outlined below.

α (°)	-9.8	-8	-6	-4	-1.9	0	1.9	4	5.9	8	9.8	13 C_MSupports	-0.036	-0.030	-0.025	-0.022	-0.013	-0.053	0.006	0.015	0.022	0.030	0.036	-0.012 C_(M 1/4 Chord)	-0.002	-0.003	-0.003	-0.008	-0.008	-0.053	-0.002	0.001	0.001	0.001	0.002	-0.044

An error in the measurements for pitch was introduced by fluctuations outputted by the software of ±0.02N. This error is calculated through the calculations, including the translation, for both maximum and minimum values. This yields an error of 48%, which can be mostly attributed to the moment translation. However, when viewing moment coefficients holistically, the error becomes less significant. There were no fluctuations in the AoA output and hence no error is present.

Wind Tunnel Correction Factors

Because wind tunnels cannot recreate flowfields identical to the original, corrections are applied to measurements obtained. These correction factors include Buoyancy Solid Blockage Wake Blockage Streamline Curvature These factors will all contribute by adding to a total corrected airspeed, Reynolds number, zero lift drag, and angle of attack. The total correction factors are below V = V_u (1+ε) Re = 〖Re〗_u (1+ε) C_D0 = 〖C_D0〗_u (1-3ε_sb-2ε_wb) A detailed explanation of the specific correction factors and constants used can be found in an Experimental Aerodynamics lecture by Greg Dimitriadis.{1} The aerodynamic coefficients are then recalculated incorporating the corrected velocity and zero lift drag coefficients. For all corrected aerodynamic coefficients, the increase in error was calculated to be negligible and hence they employ the same errors as the uncorrected coefficients. Reynolds Number Correction

At 0 AoA, the corrected Reynolds number becomes Re = 4.118 x 〖10〗^5 (1+0.0126) Re = 4.177 x 〖10〗^5 This value will provide a reference for further experimental data to be measured against. Lift Coefficient Correction

It is evident that the correction factors provide a small change in the lift coefficient throughout the AoA range. The higher the AoA, the greater the decrease (albeit small) in the coefficient of lift and vice versa for negative angles of attack. Drag Coefficient Correction

It is evident that the correction factors provide a small change in the drag coefficient throughout the AoA range. The drag coefficient is decreased by a small factor throughout the entire AoA range.

Moment Coefficient Correction

Again, it is evident that the correction factors provide a small change in the moment coefficients throughout the AoA range. The moment coefficient is decreased towards 0 by a negligible factor throughout the entire AoA range.

Although these correction factors provide a seemingly small change in aerodynamic coefficients, they can have a major influence in high end applications that require precise, accurate knowledge of aerodynamic performance. Comparison against literature

The results are compared against published experimental data. NACA report 460 [2] was published in 1933 and provides an extensive library of 3D experiments. It also incorporates a correction the for tunnel wall effect. Experimental data for low Reynolds numbers (as calculated) was not found so the lowest value found (3.2x10^6) was used. Large negative AoA were omitted as the data was not supplied in NACA 460. It is evident that the published experimental data aligns with the experimental data. It is also apparent that the correction factors provide a convergence closer to the published experimental data. At high angles of attack however, a difference occurs. This could be due to the difference in the tested Reynolds number, which dictates the stall AoA. Through linear regression, a lift curve slope gradient of 0.0734 is found, or 1.33π if radians is used. This verifies the accuracy of the experiment against the published data which, through linear regression, has a lift curve slope of 1.32π. The low lift curve slope (against a value of 2π) is elucidated by the fact that the experiments are undertaken in 3D, where vortices and other factors reduce the lift and increase the drag when compared to 2D experiments. It is evident that the experiment data does not align with the published data. This could be due to the omission of the influence of the support drag in the published experimental data. When considering the calculated drag coefficients with the support drag, the data aligns closer to the published experimental data. A further consideration in regards to the size of the supports in NACA 460 due to the tunnel size being 5’x 30’ aligns the published drag coefficients with the experimental data. Because of the large discrepancy in drag coefficients, the correction factors cannot be analysed against the published data.

It is evident that the published experimental data aligns with the experimental data. At high angles of attack however, a difference occurs. This could be due to the difference in the tested Reynolds number, which dictates the stall AoA. Because of the negligible impact of the correction factors, and the inaccuracies in extracting the experimental data, the correction factors cannot be analysed against the published data.

Variations with Aspect Ratio

The effect on aspect ratio against aerodynamic coefficients are analysed through experimental procedure. Data from various 3D experiments was supplied by ‘Aerodynamics for Students’. [3] Observed error was omitted from the experiment and will therefore be absent from the results. Lift Coefficient

It is clear that as the aspect ratio is increased, the greater the magnitude of the lift coefficient for a given angle of attack. The same is true for negative angles of attack. This is mainly due to the 3D effects of the experiment. Vortices generated during the experiment have less of an effect on higher aspect ratio wings, hence the reduction in lift for short aspect ratio wings. Drag Coefficient

It is clear that as the aspect ratio is increased, the lower the drag coefficient for a given angle of attack. Again, this is mainly due to the 3D effects of the experiment allowing lower aspect ratio wings to produce more induced drag. Vortices generated during the experiment are reduced along the span of the wing towards the root, hence the reduction in drag for high aspect ratio wings. Moment Coefficient

Although smaller in scale, it is clear that the moment coefficient is lowered throughout the angle of attack range as the aspect ratio is increased. Conclusion

By testing a NACA 0012 aerofoil in a wind tunnel in 3D, its aerodynamic coefficients were found. Wind tunnel correction factors were then calculated and compared to published 3D experimental results. Experimental data agreed with the published data, except for the drag coefficient comparison, where the possible non omission of support drag in the published data may have had an effect on the results. The effect of aspect ratio against aerodynamic coefficients in 3D was also analysed. The advantages of using a high aspect ratio aerofoil were made clear due to the reduction of drag and increase in lift over the AoA range. By analysing the effect of 3D experimental results in the aerodynamic coefficients, an understanding of its impact can be realised. This is pivotal in the understanding and design of aerofoils due to its real world implication when compared to two dimensional flows.

References

[1] Dimitriadis, G. (n.d.). Experimental Aerodynamics. Retrieved October 21, 2012, from UNIVERSITE de Liege: http://www.ltas-aea.ulg.ac.be/cms/uploads/Expaero03.pdf [2] NACA report No. 460, The Characteristics of 75 related airfoil sections from tests in the variable density wind tunnel, 1933, National Advisory Committee for Aeronautics. [3] Srinivas, A. &. (n.d.). Wind Tunnel Experiment Data Files. Retrieved October 21, 2012, from Aerodynamics for Students: http://web.aeromech.usyd.edu.au/aero/labs/index.html