Aerodynamics of Flow Around a Cylinder

Group 2A:

Adya Ali

Andrew Parry

James Sizemore

Dwayne White

Overview

Objective Theory Experimental Procedure Results and Discussion Error Analysis Conclusion

Objective

To find the aerodynamic lift and drag forces on a circular cylinder placed in uniform free-stream velocity.

To find drag, lift and pressure coefficients using different methods:Wake MeasurementsNormal pressure distribution

Theory

Skin friction drag (Df): resultant viscous forces acting on a body

Pressure drag (Dp): due to unbalanced pressure forces caused by flow

separation Total drag = skin friction drag +

pressure dragD = Df + Dp

Method 1- Wake Measurements Determine the velocity profiles in the

wake Select two sections

Section 1 (imaginary)- to account for the pressure difference

Section 2 - to obtain wake measurements

*Courtesy of Dr. Alvi’s Lab Manual (exp 7)

Method 1- Equations

Conservation of Momentum:

W= width of body

u1,u2=velocities

Assume no pressure loss between sections 1 & 2.

112 )( dyuUuWFD

Method 1- Equations (cont’d)

Total Pressure:

Drag Force:

2

2

1upPt

dyppppppWF tttD 2222

Method 1- Equations (cont’d)

Dimensionless Drag coefficient, CD

WdU

FC DD

2

21

d

dy

q

pp

q

ppC ttD

222 12

Method 2-Pressure Distribution

For large Reynolds number (Re>103), skin friction drag is negligible.

Total drag pressure drag

Image reproduced from “Aerodynamics for Engineers”, J. Bertin & M. Smith

Method 2-Pressure Distribution(cont’d)

For a cylinder,

Drag force:

Lift force:

r = radius of cylinder

p = pressure

= angular position

2

0

cos)( drppFD

2

0

sin)( drppFL

Experimental Technique Apparatus

Wind tunnel - airflow driven by a fan

Pitot-static tube - used to measure the velocity of the wind in the wake

Image reproduced from “Fundamentals of Aerodynamics” J. Anderson, Jr.

Experimental Technique

Cylindrical test model - with pressure ports along its circumference

Courtesy Dr. Alvi’s Lab Manual

Experimental Technique

Scanivalve and scanivalve digital interface unit

ADC Card on Pentium-based PC

Computer-controlled vertical drive

Experimental Technique

ProcedureWake Measurement:

Select 2 locations,

Set wind tunnel speed counter at 550; (V=30.68 m/s)

Measure dynamic pressure upstream of the cylinder

Move pitot-static tube to the center of the cylinder

105 D

xand

D

x

Experimental Technique

Measure output at vertical locations (4mm intervals)

Repeat procedure with the cylinder at x/D = 10

Normal Pressure DistributionSet wind tunnel speed counter at 550

(30.68m/s)Record the output gauge pressure at each portRepeat the procedure for counter reading at

350 (17.83m/s)

Results Wake Profile x/D=5

Non-Dimensional Distance vs. Non-Dimensional Velocity (5 units)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1 1.2

Velocity

Vert

icle

Dis

tan

ce

Results Wake Profile x/D=10

Non-Dimensional Distance vs. Non-Dimensional Velocity (10 units)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1 1.2

Velocity

Vert

icle

Dis

tan

ce

Drag Coefficients: V= 30.68 (m/s) X/D=5: Re = 53,649 CD = .76 (+/-) .39 X/D=10: Re = 54,034 CD = .67 (+/-) .013

Theoretical Drag Coefficient: Re = 59,380 CD = 1

V =30.68 (m/s)

Pressure Coefficient

Pressure Coefficient vs Angular Location

-1.5

-1

-0.5

0

0.5

1

1.5

0 15 30 45 60 75 90 105 120 135 150 165 180 195

Angular Location (degrees)

Cp

V = 17.83(m/s)V = 30.68(m/s)theoreticaldistribution

Drag Coefficients V=17.83 (m/s): Re = 35,000 CD = 1.26 (+/-) .54 V=30.68: Re = 60,000 CD = 1.19 (+/-) .079

Theoretical Drag Coefficient: CD = 1; CL = 0 Transition Re: 300,000- 500,000

V =30.68 (m/s)

V =17.83 (m/s)

Lift Coefficients Theoretical Lift Coefficient:

CL = 0

Port number

Velocity (m/s) 4 15 10 14

17.68 -0.0426 -0.053 -0.107 -0.107

30.86 -0.0041 -0.005 -0.0103 -0.101

Error Analysis

Instrument Pitot-static tubeCenter calibration for cylinder wake

Integration Trapezoidal approximation

Wind Tunnel Length of the wind tunnelWidth of wind tunnel

)(max*)(*12

2 xfn

ababError

Conclusion

Method 2 (pressure ports) seems more accurate.

Pressure differential inside the wake is unsteady.

Outside the wake the pressure differential is steady.

The pitot-static tube can measure turbulent fluctuations accurately.

THE END

QUESTIONS?