Aerodynamics Lab 1 - Cylinder Lift and Drag

Aerodynamics Lab 1

Cylinder Lift and Drag

David Clark

Group 1

MAE 449 – Aerospace Laboratory

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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

�� = � + 12 �

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.

�) = 12 * ��#'( !"#'(+,

-

�

Equation 8

Finally, the drag coefficient can be expressed as

�. = 12 * ��#'(�/ #'(+,

-

�

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.

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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.

Data Set 1 Data Set 2 Data set 3

Angle (Θ) Pressure (p) Pressure (p) Pressure (p)

0 349 350 346

15 285 286 280

30 90 81 75

45 -175 -176 -176

60 -400 -395 -403

75 -450 -451 -452

90 -400 -403 -402

105 -370 -370 -370

120 -390 -385 -370

135 -400 -400 -395

150 -410 -413 -420

165 -425 -411 -431

180 -440 -420 -439

195 -420 -417 -420

210 -410 -416 -416

225 -400 -409 -395

240 -385 -399 -383

255 -370 -392 -371

270 -400 -396 -387

285 -450 -454 -422

300 -400 -405 -408

315 -175 -172 -172

330 85 85 90

345 288 288 288

360 349 351 348

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

287 6278 296.158

= 1.171 27:;

Equation 10

� = ��.�

1 + ��

=<1.458 × 10>? 27

: A B#296.15 8(�.�C1 + 110.4 8

296.15 8= 1.828 × 10� 27

:

Equation 11

For a Reynolds number of 30,000, the velocity of the airflow must therefore be

= �� =

#30000( <1.828 × 10� 27: A

<1.171 27:;A #1.905 × 10> :(

= 24.59 :

Equation 12

This value is determined using the definition of the Reynolds number where c, the reference diameter, is

the known value of 0.75 inches (converted in the equation to meters.) For reference, the value for q can

be calculated as

E� = 12 � = 1

2 <1.171 27:;A �24.59 :

� = 353.9534

Equation 13

All three data sets can be combined by averaging the three records for each angle.

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Angle (Θ) Pressure (p)

0 348

15 284

30 82

45 -176

60 -399

75 -451

90 -402

105 -370

120 -382

135 -398

150 -414

165 -422

180 -433

195 -419

210 -414

225 -401

240 -389

255 -378

270 -394

285 -442

300 -404

315 -173

330 87

345 288

360 349

Table 2

The value recorded by the DAQ represents the difference in pressure from the pressure port on the

cylinder to the pitot probe in the test section away from the cylinder. Inserting these values into

equation 6 will yield the pressure coefficient on the surface of the cylinder at the specified angle. For

example, the pressure coefficient for 0 degrees can be calculated as

��,�.GH = ∆�E�

= 34834353.9534 = 0.984

Equation 14

The theoretical value for Cp at this angle can be calculated using equation 7.

��,�.GH,JKGLMGJNOP) = 1 − 4 !"#180° − '( = 1 − 4 !"#180° − 0°( = 1.000

Equation 15

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Results

Using equation 6, the pressure coefficient for each 15 degree increment is given in the following

table.

Angle (Θ) Cp Cp (theoretical)

0 0.984 1.000

15 0.802 0.732

30 0.232 0.000

45 -0.496 -1.000

60 -1.129 -2.000

75 -1.275 -2.732

90 -1.135 -3.000

105 -1.046 -2.732

120 -1.079 -2.000

135 -1.126 -1.000

150 -1.171 0.000

165 -1.194 0.732

180 -1.224 1.000

195 -1.184 0.732

210 -1.170 0.000

225 -1.134 -1.000

240 -1.099 -2.000

255 -1.067 -2.732

270 -1.114 -3.000

285 -1.249 -2.732

300 -1.143 -2.000

315 -0.489 -1.000

330 0.245 0.000

345 0.814 0.732

360 0.987 1.000

Table 3

A plot of Cp and the theoretical Cp over versus angle may better visualize the behavior of the

system.

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Figure 1

The theoretical values for Cp match the measured values at low angles on the leading face of the

cylinder. The flow separates at approximately 50 degrees, which correlates to the value of 55 degrees

which is anticipated from empirical charts.

Using a simple numerical integration technique, the integral value for lift as expressed in equation 7

can be determined using the following table.

-3.500

-3.000

-2.500

-2.000

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

0 30 60 90 120 150 180 210 240 270 300 330 360

Cp

Angle (Degrees)

Cp Versus Angle

Cp

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Angle (Θ) Cp Cp * sin(Θ) trap

0 0.984 0.000 1.556

15 0.802 0.207 2.425

30 0.232 0.116 -1.764

45 -0.496 -0.351 -9.963

60 -1.129 -0.977 -16.564

75 -1.275 -1.231 -17.747

90 -1.135 -1.135 -16.089

105 -1.046 -1.010 -14.581

120 -1.079 -0.934 -12.976

135 -1.126 -0.796 -10.361

150 -1.171 -0.585 -6.708

165 -1.194 -0.309 -2.317

180 -1.224 0.000 2.299

195 -1.184 0.306 6.686

210 -1.170 0.585 10.402

225 -1.134 0.802 13.155

240 -1.099 0.952 14.873

255 -1.067 1.031 16.090

270 -1.114 1.114 17.407

285 -1.249 1.207 16.471

300 -1.143 0.990 10.015

315 -0.489 0.346 1.674

330 0.245 -0.122 -2.498

345 0.814 -0.211 -1.580

360 0.987 0.000 0.000

Table 4

The Cp is repeated from the previous calculations. As sample calculation is given in equation 13. The

third column is the product the Cp for the corresponding angle and the sine of the angle. The fourth

column, labeled as the trap, is expressed as

QR4�N =��#'( ∙ !"#'(�N + ��#'( ∙ !"#'(�NTU

2 × |'N + 'NTU| Equation 16

To numerically integrates the integral of equation 7, Cl can be calculated as.

�) = − 12 W QR4�N

X

N= 4.639 × 10>

Equation 17

The lift coefficient lends some insight into the accuracy of the experiment. Since no lift is anticipated

for a stationary cylinder in steady flow, and deviation from a lift coefficient can be attributed to error.

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A similar procedure can be used to determine the drag coefficient. The table below is used to

numerically integrate equation 7.

Angle (Θ) Cp Cp * cos(Θ) trap

0 0.984 0.984 13.191

15 0.802 0.774 7.313

30 0.232 0.201 -1.128

45 -0.496 -0.351 -6.865

60 -1.129 -0.564 -6.706

75 -1.275 -0.330 -2.474

90 -1.135 0.000 2.030

105 -1.046 0.271 6.075

120 -1.079 0.539 10.015

135 -1.126 0.796 13.576

150 -1.171 1.014 16.252

165 -1.194 1.153 17.824

180 -1.224 1.224 17.756

195 -1.184 1.144 16.178

210 -1.170 1.013 13.614

225 -1.134 0.802 10.138

240 -1.099 0.550 6.194

255 -1.067 0.276 2.072

270 -1.114 0.000 -2.425

285 -1.249 -0.323 -6.710

300 -1.143 -0.571 -6.878

315 -0.489 -0.346 -1.002

330 0.245 0.212 7.487

345 0.814 0.786 13.301

360 0.987 0.987

Table 5

An expression to numerically integrate the integral of equation 8 can be created using numerical

integration techniques. Cd can be calculated as

�. = 12 W QR4�N

X

N= 69.41

Equation 18

where the trap can be calculated as

QR4�N =��#'( ∙ �/ #'(�N + ��#'( ∙ �/ #'(�NTU

2 × |'N + 'NTU| Equation 19

ANSYS CFD

Below are screenshots taken from inputting the geometric and laboratory conditions into ANSYS

CFD 11. The explanation into the setup and validity of these results is beyond the scope of this lab,

however the results visually describe the phenomenon that results from the flow around the cylinder.

The first image is the vector field of the flow perpendicular to the length of the cyl

separation, as well as the disturbance behind the cylinder is clearly visible.

The second image rotates the view to display an isometric view of the body

the body represents the pressure on the surface of the cylinder.


setup and validity of these results is beyond the scope of this lab,


The first image is the vector field of the flow perpendicular to the length of the cylinder. The

separation, as well as the disturbance behind the cylinder is clearly visible.

Figure 2

The second image rotates the view to display an isometric view of the body. The color gradient on

on the surface of the cylinder.

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setup and validity of these results is beyond the scope of this lab,


inder. The

. The color gradient on

The final image displays the pressure gradient across the aft side of the body.

Figure 3

The final image displays the pressure gradient across the aft side of the body.

Figure 4

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Conclusions

The lift and drag coefficient of a cylinder with a diameter of 0.75 inches in flow with a Reynolds

number of 30,000 is 4.639x10-2

and 69.41 respectively.

References

“Aerodynamics Lab 1 – Cylinder Lift and Drag”. Handout

Raw Data

Aero Lab 1

Group 1

Fall 07

R= 287

p 99500 b= 0.000001458

t 23 S= 110.4

rho 1.171

u 1.828E-05

q 354

V 24.59

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Data Set 1 Data Set 2 Data set 3

Angle (Θ) Pressure (p) Pressure (p) Pressure (p)

0 349 350 346

15 285 286 280

30 90 81 75

45 -175 -176 -176

60 -400 -395 -403

75 -450 -451 -452

90 -400 -403 -402

105 -370 -370 -370

120 -390 -385 -370

135 -400 -400 -395

150 -410 -413 -420

165 -425 -411 -431

180 -440 -420 -439

195 -420 -417 -420

210 -410 -416 -416

225 -400 -409 -395

240 -385 -399 -383

255 -370 -392 -371

270 -400 -396 -387

285 -450 -454 -422

300 -400 -405 -408

315 -175 -172 -172

330 85 85 90

345 288 288 288

360 349 351 348

Documents

Aerodynamics Lab 1 - Cylinder Lift and Drag