Transcript Aerodynamics of Flow Around a Cylider

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 Measurements
Normal 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 drag

D = 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:
FD  W  u2 (U   u1 )dy1
W= width of body
u1,u2=velocities

Assume no pressure loss between
sections 1 & 2.
Method 1- Equations (cont’d)

Total Pressure:

Drag Force:
FD  2W  pt 2  p2
1 2
Pt  p  u
2


pt  p  pt 2  p dy
Method 1- Equations (cont’d)
Dimensionless Drag coefficient, CD
CD 
CD  2
FD
1
2
U Wd
2
pt 2  p2
q

1 

pt 2  p
q
 dy

 d
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:

2
FD   ( p  p )r cosd
0
Lift force:
2
FL   ( p  p )r sin d
0
r = radius of cylinder
p = pressure
 = angular position
Experimental Technique

Apparatus
Wind tunnel - airflow driven by a fan
Image reproduced from “Fundamentals of Aerodynamics” J. Anderson, Jr.
Pitot-static tube - used to measure the
velocity of the wind in the wake
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

Procedure
Wake Measurement:
Select 2 locations,
x
 5 and
D
x
 10
D
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
Experimental Technique
Measure output at vertical locations (4mm
intervals)
Repeat procedure with the cylinder at x/D = 10
Normal Pressure Distribution
Set wind tunnel speed counter at 550
(30.68m/s)
Record the output gauge pressure at each port
Repeat 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)
3.5
Verticle Distance
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
Velocity
0.8
1
1.2
Results
Wake Profile x/D=10
Non-Dimensional Distance vs. Non-Dimensional Velocity
(10 units)
3.5
3
Verticle Distance

2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
Velocity
0.8
1
1.2
Drag Coefficients: V= 30.68 (m/s)

X/D=5: Re = 53,649




CD = .76 (+/-) .39
X/D=10: Re = 54,034
Theoretical Drag Coefficient:
Re = 59,380

CD = 1

CD = .67 (+/-) .013
V =30.68 (m/s)
Pressure Coefficient
Pressure Coefficient vs Angular Location
1.5
1
Cp
0.5
0
0
15
30
45
60
75
90
105
120
-0.5
-1
-1.5
Angular Location (degrees)
135
150
165
180
195
V = 17.83
(m/s)
V = 30.68
(m/s)
theoretical
distribution
Drag Coefficients

V=17.83 (m/s): Re = 35,000

Theoretical Drag Coefficient:



CD = 1.26 (+/-) .54
V=30.68: Re = 60,000
CD = 1; CL = 0
Transition Re: 300,000- 500,000

CD = 1.19 (+/-) .079

V =17.83 (m/s)
V =30.68 (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 tube
 Center calibration for cylinder wake

Integration
 Trapezoidal approximation
ba ba 2
Error 
*(
) * max f ( x )
12
n

Wind Tunnel
 Length of the wind tunnel
 Width of wind tunnel
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?