Aerodynamics Lab 1 - Cylinder Lift and Drag

Aerodynamics Lab 1 Cylinder Lift and Drag

David Clark Group 1 MAE 449 – Aerospace Laboratory

Abstract The lift and drag coefficients are non-dimensional parameters which describe the forces acting on a body in a fluid flow. A cylinder is an excellent specimen to study these forces due to the geometric simplicity, as well as steady continuity across the entire body. Calculating these parameters can be an arduous task, however maintaining steady, incompressible, and irrotational flow with negligible body forces allow the use of the ideal gas law, Bernoulli’s equation, and Sutherland’s viscosity correlation. Using the newly simplified expressions for Cl and Cd, the lift and drag coefficient, the results were calculated using simple pressure measurements along with simple parameters describing the laboratory testing conditions. The lift and drag coefficient of a cylinder with a diameter of 0.75 inches in flow with a Reynolds number of 30,000 was 4.639x10-2 and 69.41 respectively.

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Contents Abstract .................................................................................................................................................. 2 Introduction and Background................................................................................................................. 4 Introduction........................................................................................................................................ 4 Governing Equations .......................................................................................................................... 4 Similarity ............................................................................................................................................. 5 Aerodynamic Coefficients .................................................................................................................. 5 Equipment and Procedure ..................................................................................................................... 6 Equipment .......................................................................................................................................... 6 Experiment Setup ............................................................................................................................... 6 Basic Procedure .................................................................................................................................. 6 Data, Calculations, and Analysis ............................................................................................................. 7 Raw Data ............................................................................................................................................ 7 Preliminary Calculations ..................................................................................................................... 7 Results .................................................................................................................................................. 10 ANSYS CFD ............................................................................................................................................ 14 Conclusions........................................................................................................................................... 16 References ............................................................................................................................................ 16 Raw Data .............................................................................................................................................. 16

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Introduction and Background Introduction The following laboratory procedure explores the aerodynamic lift and drag forces experienced by a cylinder placed in a uniform free-stream velocity. This will be accomplished using a wind tunnel and various pressure probes with a small brass cylinder 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 2  



 

Equation 1

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

Governing Equations To assist in determining the properties of the working fluid, air, several proven governing equations can be used, including the ideal gas law, Sutherland’s viscosity correlation, and Bernoulli’s 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. Sutherland’s 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 K^(0.5))/(m s) and S is 110.4 K. Finally, Bernoulli’s equation defines the total stagnation pressure as 1  =  + 

2 Equation 4

Similarity Using 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.

Aerodynamic Coefficients Three aerodynamic coefficients are used to explore the lift and drag forces on the test cylinder. First, the pressure coefficient expresses the difference in local pressure, the pressure at one discrete point on the cylinder, over the dynamic pressure.
 =

 −  1 2    Equation 6

The theoretical value for Cp can be calculated as
 = 1 − 4 !" #180° − '( Equation 7

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The pressure coefficient can be used in the determination of the 2-D lift coefficient, Cl. 1
) = *
#'( !"#'(+, 2  Equation 8

Finally, the drag coefficient can be expressed as 1
. = *
#'(/ #'(+, 2  Equation 9

Equipment and Procedure Equipment The following experiment used the following equipment: •

A wind tunnel with a 1-ft x 1-ft test section

•

Smooth, ¾ inch diameter brass cylinder with a pressure tap at mid-span

•

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

Experiment Setup Before 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 brass rod to be mounted inside the test section. A degree wheel is rigidly attached to cylinder such that the angle at which the pressure tap is exposed in relation to the fluid flow can easily be adjusted and measured.

Basic Procedure To ensure the working flow is relatively laminar and within a range acceptable for study, the procedure initiated flow with a Reynolds number of 30,000. 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. 6|Page

Using the DAQ hardware, the difference in pressure between the pressure port and the reference pitot tube was recorded for every 15 degrees of cylinder rotation. The raw data from this step is included in the data section.

Data, Calculations, and Analysis Raw Data The following table catalogs the pressure read by the DAQ hardware for every 15 degrees of cylinder rotation. Three data sets were taken to ensure integrity. Angle (Θ) 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360

Data Set 1 Pressure (p) 349 285 90 -175 -400 -450 -400 -370 -390 -400 -410 -425 -440 -420 -410 -400 -385 -370 -400 -450 -400 -175 85 288 349

Data Set 2 Pressure (p) 350 286 81 -176 -395 -451 -403 -370 -385 -400 -413 -411 -420 -417 -416 -409 -399 -392 -396 -454 -405 -172 85 288 351

Data set 3 Pressure (p) 346 280 75 -176 -403 -452 -402 -370 -370 -395 -420 -431 -439 -420 -416 -395 -383 -371 -387 -422 -408 -172 90 288 348

Table 1

Preliminary Calculations First, the density and viscosity of the air at laboratory conditions was calculated. This can easily be accomplished using equation 2 and 3.

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=

99.5234 27  = = 1.171 ; 6 :  287 296.158 278 Equation 10

>? 27 .  .