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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?