MECH 322 Instrumentation
Unsteady Velocity in a Karman
Vortex Street
Performed: 04/12/06
Pablo Araya: I believe, I performed 50% of the work.
N.R.Chalasani: I believe, I performed 50% of the work.
ABSTRACT
• The objective of this lab was to measure the
natural frequency of a Karman vortex street.
• A hot film anemometer was calibrated at steady
speeds using a Pitot probe in a wind tunnel. It
was then used to measure unsteady speeds in
the wake behind a cylinder. The dominant
frequency was determined for a range of wind
speeds using a LabVIEW function.
• The Strouhal number (dimensionless frequency)
was constant (as expected) but consistently 70%
above the predicted value for the investigated
Reynolds number range.
Fig. 1 VI Front Panel
Fig. 2 VI Block Diagram
Formula
Formula: ((v**2-b)/a)**2
Spectral Measurements
This Express VI is configured as follows:
Selected Measurements: Magnitude (Peak)
View Phase: Wrapped and in Radians
Windowing: Hanning
Averaging: None
Table 1 Air Properties and Cylinder Diameter
T
K
300
Patm
mbar
860
D
inch
0.125
m
2
N-s/m
1.82E-05
• Air Viscosity from A.J. Wheeler and A. R. Ganji, Introduction to
Engineering Experimentation, 2nd Edition, Pearson Prentice
Hall, 2004, p. 430.
Table 2 Calibration Data
IG
IP
VCTA
PG
[mA] [mA] [V]
[Pa]
4
4.00 1.490
0
4.06 4.60 2.425 37
4.11 5.07 2.550 69
4.16 5.60 2.633 100
4.3 7.13 2.790 187
4.52 9.32 2.932 324
4.69 11.00 3.017 430
4.89 13.08 3.102 554
4.6 10.00 2.966 374
4.36 7.52 2.821 224
4.1 4.90 2.505 62
4.01 4.00 1.492
6
PP
PABS
[Pa]
0
28
50
75
146
249
327
424
280
164
42
0
[kPa]
86.20
86.24
86.27
86.30
86.39
86.52
86.63
86.75
86.57
86.42
86.26
86.21
r
[kg/m3]
1.01
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.01
SA
[m/s]
0.00
7.43
9.92
12.13
16.96
22.09
25.33
28.82
23.46
17.98
9.10
0.00
• The initial and final no-wind hot film voltage readings
are close but not the same.
Figure 3 Hot Film System Calibration
3.5
10
3.0
VCTA
8
0.5
2.5
2
= 1.3657SA + 2.1951
VCTA [volts]
VCTA0.5 [volts0.5]
12
6
4
2.0
1.5
Extra Credit (not required)
1.0
2
0.5
0
0.0
0
1
2
SA2
3
[m2/s2]
4
5
6
0
5
10
15
20
25
30
SA [m/s]
• The fit equation VCTA2 = aSA0.5+b appears to be appropriate for these data.
• The dimensional parameters are a = 1.366 volts2s1/2/m1/2 and b = 2.195
volts2
35
Fig. 4 Measured Speed vs. Time for Lowest Wind Speed
6
Without Cylinder
Speed, s [m/s]
5
4
3
With Cylinder
2
1
0
0
0.002
0.004
0.006
0.008
0.01
time, t [sec]
•
•
•
The sampling rate appears to be sufficiently fast to capture the shape of the unsteady trace.
Turbulence or instabilities at the tunnel entrance may cause unsteadiness in the speed even
when there is no cylinder in the flow
With the cylinder, there are roughly 6 large peaks in 0.01 seconds, corresponds to a frequency
600 Hz.
SRMS [m/s]
Fig. 5 Spectral Content in Wake for Lowest Wind Speed with and without Cylinder
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
(a) With cylinder
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1400
1600
1800
2000
SRMS [m/s]
Frequency, f [hz]
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
(b) Without cylinder
0
200
400
600
800
1000
1200
Frequency, f [hz]
•
•
The cylinder increases the unsteadiness at all frequencies, but most significantly
near 516 Hz. This frequency is 14% below the observation in Fig. 4.
There is another peak at 268 Hz.
Table 3 Karman Frequency and
Incoming Wind Speed
f [Hz]
3500
3200
2764
2100
1500
516
SA [m/s]
31.49
28.13
23.98
18.89
13.34
4.68
Re [1]
5603
5005
4267
3361
2374
833
St [1]
0.35
0.36
0.37
0.35
0.36
0.35
• The dominant frequency f and centerline speed SA were
determined as several wind speeds.
• The Reynolds number is ReD = SADr/m
• The Strouhal number is StD = fD/SA
Fig. 6 Strouhal versus Reynolds
0.40
0.35
St [1]
0.30
0.25
Reference Value St = 0.2 to 0.21
0.20
0.15
0.10
0.05
0.00
0
1000
2000
3000
4000
5000
6000
Re [1]
• The reference value is from A.J. Wheeler and A.R. Ganji, Introduction to Engineering
Experimentation, 2nd Edition, Pearson Prentice Hall, 2004, p. 337.
• Measured Strouhal number is roughly 70% Above the expected value.
• There may be an error in the anemometer calibration method.
Extra (not part of report)
2006 Summary
1.20
1.00
StD
0.80
0.60
0.40
0.20
0.00
0
2000
4000
6000
ReD
8000
10000
0.
09
0.
11
0.
13
0.
15
0.
17
0.
19
0.
21
0.
23
0.
25
0.
27
0.
29
0.
31
0.
33
0.
35
0.
37
0.
39
0.
41
0.
43
0.
45
0.
47
0.
49
0.
51
0.
53
0.
55
0.
57
0.
59
0.
61
N
Histogram
16
14
12
10
8
6
4
2
0
StD