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This lab was a b#tch to write. It probably isn't 100% correct, but it's good enough for partial credit.

Aerodynamics Lab 3Direct Measurement of Airfoil Lift and Drag

David Clark Group 1 MAE 449 Aerospace Laboratory

AbstractThe characterization of lift an airfoil can generate is an important process in the field of aerodynamics. The following exercise studies a NACA 0012 airfoil with a chord of 4 inches. By varying the angle of attack at a known Reynolds number, the lift coefficient, Cl, can be determined by using a two-component dynamometer. Normalizing the lift and drag forces against the reference area, as well as correcting for some disturbances due to the experiment setup. The lift and drag coefficient calculated using this setup is less accurate than previous methods.

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ContentsAbstract .................................................................................................................................................. 2 Introduction and Background................................................................................................................. 4 Introduction........................................................................................................................................ 4 Governing Equations .......................................................................................................................... 4 Similarity ............................................................................................................................................. 5 Boundary Corrections ......................................................................................................................... 5 Equipment and Procedure ..................................................................................................................... 7 Equipment .......................................................................................................................................... 7 Experiment Setup ............................................................................................................................... 7 Basic Procedure .................................................................................................................................. 8 Data, Calculations, and Analysis ............................................................................................................. 8 Raw Data ............................................................................................................................................ 8 Preliminary Calculations ..................................................................................................................... 9 Results .................................................................................................................................................. 13 Discussion and Conclusions .................................................................................................................. 16 References ............................................................................................................................................ 17 Raw Data .............................................................................................................................................. 17

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Introduction and Background IntroductionThe following laboratory procedure explores the aerodynamic lift and drag forces experienced by a NACA 0012 cylinder placed in a uniform free-stream velocity. This will be accomplished using a wind tunnel and various pressure probes along an airfoil as the subject of study. When viscous shear stresses act along a body, as they would during all fluid flow, the resultant force can be expressed as a lift and drag component. The lift component is normal to the airflow, whereas the drag component is parallel. To further characterize and communicate these effects, non-dimensional coefficients are utilized. For example, a simple non-dimensional coefficient can be expressed as = 1 2Equation 1

where F is either the lift or drag forces, AREF is a specified reference area, is the density of the fluid, and V is the net velocity experienced by the object.

Governing EquationsTo assist in determining the properties of the working fluid, air, several proven governing equations can be used, including the ideal gas law, Sutherlands viscosity correlation, and Bernoullis equation. These relationships are valid for steady, incompressible, irrotational flow at nominal temperatures with negligible body forces. The ideal gas law can be used to relate the following =Equation 2

where p is the pressure of the fluid, R is the universal gas constant (287 J/(kg K)), and T is the temperature of the gas. This expression establishes the relationship between the three properties of air that are of interest for use in this experiment.

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Another parameter needed is the viscosity of the working fluid. Sutherlands viscosity correlation is readily available for the testing conditions and can be expressed as =.

1+

Equation 3

where b is equal to 1.458 x 10-6 (kg)/(m s K^(0.5)) and S is 110.4 K. Finally, Bernoullis equation defines the total stagnation pressure as = + 1 2

Equation 4

SimilarityUsing the previous governing equations, we can use the Reynolds number. The Reynolds number is important because it allows the results obtained in this laboratory procedure to be scaled to larger scenarios. The Reynolds number can be expressed as =Equation 5

where c is a characteristic dimension of the body. For a cylinder, this dimension will be the diameter. As a result, the Reynolds number based on diameter is referenced as ReD.

Boundary CorrectionsThe following experiment must consider three different corrections due to the setup of the tunnel section. First, the squeezing of the inviscid flow causes the streamlines to flatten and push toward the center of the test section. This effect is referred to as horizontal buoyancy. To correct for this effect, the following expressions can be defined. = 6

Equation 6

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=

48

Equation 7

The parameters used in these expressions include h, the height of the wind tunnel section , the body shape factor (estimated from empirical charts) dp/dx, the static pressure gradient c, the chord of the foil The second consideration corrects for blockage due to equipment within the wind tunnel itself. Like the previous correction, simple expressions have been derived to adjust the parameters. =Equation 8

=

0.96

Equation 9

=

+Equation 10

=

/ 4

Equation 11

Though some parameters have already been defined, the corrections for blockage introduce the following parameters. Volstrut, the volume of the strut Atunnel, the cross-sectional area of the tunnel Cdu, the uncorrected drag coefficient

Finally, the last set of expressions corrects for the presence of the floor and ceiling within the wind tunnel. = 57.3 2 +3

Equation 12

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,

=Equation 13

,

1 = 4Equation 14

,

where Clu, the uncorrected lift coefficient Cmc/4u, the uncorrected c/4 moment coefficient The use of each correction equation is further explained in the calculation section.

Equipment and Procedure EquipmentThe following experiment used the following equipment: A wind tunnel with a 1-ft x 1-ft test section NACA 0012 airfoil section A transversing mechanism to move the pitot tube to various sections of the test section A Pitot-static probe Digital pressure transducer Data Acquisition (DAQ) Hardware Two-component dynamometer (to measure lift and drag forces)

Experiment SetupBefore beginning, the pressure and temperature of laboratory testing conditions was measured and recorded. Using equations 2 and 3, the density and viscosity of the air was calculated. The UAH wind tunnel contains cutouts to allow the NACA airfoil to be mounted inside the test section. The two-component dynamometer can measure the force exerted perpendicular and parallel to the airflow, which represent the lift and drag respectively.

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Basic ProcedureTo ensure the working flow is relatively laminar and within a range acceptable for study, the procedure initiated flow with a Reynolds number of 250,000. The velocity at which the laboratory air must be accelerated was determined by solving equation 5 for velocity. First, the density and viscosity of the air must be calculated using equations 2 and 3 respectively. Using the DAQ hardware, the lift and drag at each angle of attack and specified dynamic pressure was recorded.

Data, Calculations, and Analysis Raw DataThe following table catalogs the pressure read by the DAQ hardware for the specified rotations. Three data sets were taken to ensure integrity.

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Data Set 1Angle -4 -2 -0.25 2 4 6 8 10 12 Angle -4 -2 0 2 4 6 8 10 12 Angle -4 -2 0 2 4 6 8 10 12 Dynamic Pressure 868 868 867 865 866 867 864 868 867 Lift -2.50 -0.65 1.32 2.41 5.77 8.58 9.92 10.90 8.10 Lift 1.35 1.50 3.48 5.83 7.18 8.49 9.23 10.97 8.17 Lift 1.35 1.43 3.03 4.25 5.95 8.43 10.05 10.75 9.30 Drag -0.51 -0.43 -0.28 -0.35 -0.42 -0.54 -0.63 -0.75 -2.95 Drag -0.40 -0.38 -0.41 -0.44 -0.50 -0.57 -0.58 -0.77 -2.99 Drag -0.38 -0.40 -0.40 -0.42 -0.45 -0.56 -0.67 -0.75 -2.35

Data Set 2Dynamic Pressure 869 868 868 867 868 868 869 867 868

Data Set 3Dynamic Pressure 867 868 866 867 867 868 867 867 868Table 1

Preliminary CalculationsFirst, the density and viscosity of the air at laboratory conditions was calculated. This can easily be accomplished using equation 2 and 3. = = 287 99.1 296.15 = 1.1660

Equation 15

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=

.

1+

=

1.827 10 1+

110.4 296.15

.

296.15