Lab 4
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AE 460 Laboratory Note for Experiment 4 Hotwire Anemometer and Cylinder Wake Experiment by Andrew Beusse, Margarita Kuzmanova, Srinu Rayudu TA: Derrick Wiberg Section AB6, Group B, Tuesday, 5:00 - 7:00 pm 10/27/2022
PAGE 1 1. INTRODUCTION This experiment is aimed to measure and analyze the wake behind a cylinder. An isothermal hotwire anemometer system is calibrated through coefficients of fourth-degree polynomial estimation. Then, the performance of the pitot/static probe and hotwire anemometer is compared in degree of accuracy of measuring characteristics of the wake created by the cylinder. Deviation velocity profiles are found with both instruments and the accuracy is compared through the momentum deficit methodology. Frequency content of the turbulent wake over a range of freestream conditions is also analyzed. 2. APPARATUS This lab utilized the Aerolab low-speed wind tunnel to test the measurements of a hotwire anemometer against those of a pitot static testing probe. The pitot static tube utilizes the Dwyer 616-2 differential pressure transducer to record the pressures of the probe which are then processed by LAB View to give data that can be used to compare to the hotwire readings. The probe and hotwire were swept through the test section using the T-SLR 150B linear traversing system to get data readings all throughout the wake from the cylinder. The cylinder was mounted in holes in the side of the tunnel at streamwise positions of 66.7, 104.8, 161.9, and 238.1 mm from the hotwire probe to get data points from different distances to the front of the wake.
PAGE 2 Figure 1. Table. 1. List of Laboratory Equipment and their accuracy as used in the experiment
No. Item Size/Range/Capac
ity Accuracy Use in experiment 1 The Aerolab Low-
Speed Wind Tunnel 9.5:1 contraction ratio / Test section dimensions: 24” x 12” x 12” … Used as the wind tunnel that was being calibrated 2 Pitot/static Probe 0”-6” of water +/- 0.25% measure pressures at various locations in the wake to calculate velocity 3 T-SLR 150B 150 mm +/- 8 μm
Sweep the pitot probe and hotwire across the wake of the cylinder
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PAGE 3 4 Omega PX653 Pressure Transmitter 0”-10” of water ± 0.25% of the measurement measure the difference between atmospheric pressure and static pressure 5 Dantec miniature CTA 54T30 Hotwire controller 10 kHz, wire: 5 μm in diameter and 1.25 mm long. Max rate 150 kHz and max 150 degrees Celsius … Used to find the velocity of the flow 6 Compact Digital Manometer …. ± 0.148 in Hg and ± 1.8
̊
F Used to measure atmospheric pressure and temperature in the lab 7 Plexiglas cylinder 19.05 mm in diameter, 300mm span … used to create a wake to measure in the tunnel 8 Dwyer 616-2 differential pressure transducer 0-6” of water +/- 0.25% of measurement Measure the pressure from the pitot/static probe
PAGE 4 3. RESULTS AND DISCUSSION 3.1. Calibration Coefficients From the data collected, the calibration coefficients were found as follows: a0 = 30.019, a1 = -94.74, a2 =110.925, a3 = -59.735, a4 =12.847 Using the coefficients, the calculated probe velocities were determined by evaluating the fourth-order polynomial below: 𝑈𝑈
(
𝑥𝑥
) =
𝑎𝑎
0 +
𝑎𝑎
1
∗ 𝑥𝑥
+
𝑎𝑎
2
∗ 𝑥𝑥
2
+
𝑎𝑎
3
∗ 𝑥𝑥
3
+
𝑎𝑎
4
∗ 𝑥𝑥
4
Figure 2. Compassion between measured and calculated Probe Velocities As seen from Figure 2, the measured velocities and the calculated velocities are almost identical besides a slight difference near the starting of the data collection. This proves that calibration coefficients were correct, and that the accuracy of the calibration was high. -5
0
5
10
15
20
25
30
1.325
1.701
1.726
1.742
1.763
1.78
1.801
1.819
1.832
1.845
1.858
1.873
1.892
1.912
1.934
1.949
1.965
1.982
2.005
2.035
2.048
2.072
2.087
2.101
2.111
2.132
2.153
2.167
2.183
2.196
2.202
2.209
Probe Velocity (m/s)
Hotwire Ev (V)
Measured vs Calculated Probe Velocities
Velocity Measured
Velocity Calculated
PAGE 5 3.2. Normalized Velocity Profiles Figure 3. Normalized Velocity Profiles for each Nondimensional Lateral Location 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-4
-3
-2
-1
0
1
2
3
4
Velocity (m/s)
Nondimensional Lateral Location (mm)
Normalized Pitot
Static Vel [m/s] @
x=66.7
Normalized Hot
Wire Vel [m/s] @
x=66.7
Normalized
Pitot/Static Vel
[m/s] @ x=104.8
Normalized Hot
Wire Vel [m/s] @
x=104.8
Normalized
Pitot/Static Vel
[m/s] @ x=161.9
Normalized Hot
Wire Vel [m/s] @
x=161.9
Normalized
Pitot/Static Vel
[m/s] @ x=238.1
Normalized Hot
Wire Vel [m/s] @
x=238.1
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PAGE 6 Each velocity profile at every location tested and was normalized using the equation below where the velocity profile was divided by the freestream velocity. 𝑢𝑢
(
𝑦𝑦
)/
𝑈𝑈
∞
(1) The lateral location was normalized with the equation below where y
0
is the location of the minimum velocity location in each profile. 𝑦𝑦−𝑦𝑦
0
𝐷𝐷
(2) As seen from Figure 3, all the normalized velocity curves follow a parabolic pattern. This makes sense because as the position moves from the negative direction to the positive direction, the measuring device passed through the “zero” position where the velocity logically should be the near the normal freestream conditions which will be less than the other position extrema. The greater the position of cylinder was away from the measuring device, the closer the hotwire velocity and the pitot/static velocities were to being the same. When the cylinder position was 66.7 mm, the difference between the Pitot static velocity and the hot wire velocity is very significant as seen from Figure 3. For contrast, when the cylinder position was 238.1 mm, the Pitot static velocity and the hot wire velocity were very similar.
PAGE 7 3.3. Momentum Deficit Method (3) Using the above equation and velocity profiles as measured, the following table shows the drag measured at each streamwise location of the cylinder. Run Type and Distance Force of Drag (Kg) Coefficient of drag RE Pitot/Static at x=66.7mm 4.7972 0.5088 204317 Hotwire at x=66.7mm 4.7932 0.5084 204317 Pitot/Static at x=104.8mm 4.8140 0.5068 205076 Hotwire at x=104.8mm 4.8582 0.5115 205076 Pitot/Static at x=161.9mm 4.8175 0.5061 205302 Hotwire at x=161.9mm 4.8744 0.5120 205302 Pitot/Static at x=238.1mm 4.8046 0.5037 205514 Hotwire at x=238.1mm 4.8114 0.5044 205514 Table. 2 Tabulated Values for Various Runs As can be seen from the table all the values for drag are similar which may indicate that the method is not the most accurate as we would expect to see a greater force of drag at lower x values streamwise. While it is not what was expected in terms of trend in force of drag overall, it is worth noting that the coefficients of drag calculated seem to line up with the graph values from figure 5 in the lab instruction booklet. The lab table seems to indicate for our Reynolds number
PAGE 8 range we would expect a value of around .6 and our values were only .1 away from that estimation. Values calculated using the following: , 3.4. Turbulence Intensity (4) To calculate turbulence intensity, the provided formula from the lab instructions was used which calculated the ratio of the standard deviation of the flow velocity to the freestream velocity.
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PAGE 9 Figure 4. Turbulence Intensity for Pitot/Static Data
PAGE 10 Figure 5. Turbulence Intensity for Hotwire Data It is worth noting that the Pitot tube peaks at or next to zero for all cases whereas the hotwire data does not peak as steeply and in fact dips at zero for cases further away from the cylinder streamwise.
PAGE 11 3.5. FFT Analysis Below is the graph of the FFT amplitudes and their frequencies at three different freestream velocities. Figure 6. FFT Amplitude Spectrum for all Freestream Velocities -2
0
2
4
6
8
10
12
14
16
18
0
200
400
600
800
1000
1200
FFT Amplitude (Vrms)
Frequency (Hz)
Freestream Velocity = 10 m/s
Freestream Velocity = 15 m/s
Freestream Velocity = 20 m/s
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PAGE 12 Table. 3. Wake Characteristics Freestream Velocity (m/s) Reynolds Number Frequency (Hz) Peak Magnitude (Vrms) Strouhal Number 10 12,892.956 93.75 1.411 0.179 15 19,339.434 148.437 2.085 0.189 20 25,785.912 195.312 2.721 0.186 The Reynolds number was calculated with the equation below where U
∞
, 𝜌𝜌
∞
, and µ
∞
are the average freestream velocity, density, and absolute (or dynamic) viscosity, respectively. (5) The Strouhal number was calculated using the equation below where f
s
is the is the vortex shedding frequency.
(6) As the freestream velocity increases, the Reynolds number, frequency and peak magnitude all increases as well. The Strouhal number also increases but not as significantly as the other properties.
PAGE 13 Since the wake characteristics are governed by viscous effects such as boundary layer and flow separation, the Reynolds number is the main parameter utilized to characterize the wake created in subsonic flows in this experiment. Observing the Reynolds numbers, all three freestream velocity cases have a Reynolds number between 300 and 300,000. As the Reynold number enters this region, the flow becomes periodic and unstable with vortices forming and alternating from one downstream side of the cylinder to the other. This resembles the Karman vortex street. In the figure below it shows the alternating vortex pattern behind the cylinder. Figure 7. Characteristics of the wake behind a cylinder Here, the Karman vortex street becomes turbulent and the laminar boundary layer separates from the cylinder. The turbulent vortices shed at the frequencies above in Figure 7 respectively. Typically, for Reynolds numbers above 1000, the Strouhal number is approximately constant at around 0.2. The Strouhal numbers that were determined from the experiment was also very close to 0.2 for all freestream velocities with very minor discrepancies.
PAGE 14 3.6. Other Wake Characteristics Figure 8. The schematic of the wake of cylinder in a control volume The thickness, L
0
of the wake behind the cylinder is a parameter that characterizes the spreading of the wake as shown in Figure 8. The wake thickness is the half wake thickness for the flow around the cylinder. The location of minimum velocity is given by the equation below where U
∞
is the freestream velocity and U
m
is the minimum velocity of the profile. (7) From the Reynolds numbers that were determined in this experiment, the wake thickness can be determined from the equation below where D is the cylinder diameter, x is the streamwise distance from the cylinder, K is an experimentally determined constant, and x
0
is termed the origin.
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PAGE 15 (8) The location of minimum velocity should decrease as the wake thickness increases. This makes sense not just from the calculations but also because as the streamwise distance from the cylinder increases, the wake length also increases. When there is a larger wake, there is more disturbed flow that becomes turbulent and the laminar boundary layer separates from the cylinder. This results in a lower velocity in the downstream locations of the flow. 4. CONCLUSIONS In this experiment, the students successfully found a fourth-degree polynomial fit for the calibration coefficients, which resulted in a trend almost identical to the velocity attained in lab. The Velocity Profiles for each Nondimensional Lateral Location were then normalized, resulting in a parabolic pattern with a dip near the freestream velocity conditions. As the freestream velocity increases, it was observed that the Reynolds number, frequency, and peak magnitude all increases as well. The Strouhal number also increases but not as significantly as the other properties. Karman vortex street was observed, as all the wake turbulences were in the range for it to occur. The Strouhal number stayed nearly constant around 0.2 after Re=1000. Further analysis might improve the results and trend observations if the velocity is measured at more locations, especially closer to the first one, as it had the most discrepancy with the calculated result. More data would give an insight into where that discrepancy starts occurring and, potentially might answer the question of why there. Additionally, more testing
PAGE 16 may be performed at a higher Reynold number (above 300000) to observe the turbulent wake behind the bodies and how much it differs visually and upon a more detailed inspection. 5. REFERENCES [1] “Experiment #4: Hotwire Anemometer and Cylinder Wake Experiment,” Laboratory Writeup for AE 460, University of Illinois at Urbana-Champaign, 2022. [2] “Hotwire Anemometry”, Dantec PowerPoint presentation, from Dantec website http://www.dantecdynamics.com/CTA/Princip/Download/Index.html, downloaded, September 2004. [3] Doebelin, E.O. Measurement Systems Application and Design, McGraw-Hill Book Company, New York, 1976. 6. APPENDIX APPENDIX A: SAMPLE CALCULATIONS 𝑢𝑢
(
𝑦𝑦
)/
𝑈𝑈
∞
(1) u(y): velocity profile U∞: freestream velocity 𝑦𝑦−𝑦𝑦
0
𝐷𝐷
(2) y: tested location y0: location of the minimum velocity D: diameter/length
PAGE 17 (3) L: the half height of the control volume U1: the freestream velocity ρ
∞: freestream de
nsity w: width (4) u(y): the average velocity at the y location u’(y): the instantaneous velocity N: the total number of measurements used to compute the statistics
(5) Re: Reynolds number
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PAGE 18 ρ
∞: freestream density
D: diameter/length U∞: freestream veloci
ty 𝜇𝜇
∞: freestream density
(6) St: Strouhal number Fs: vortex shedding frequency U∞: freestream velocity
(7) U
∞
: the freestream velocity U
m
: the minimum velocity of the profile (8)
PAGE 19 D: the cylinder diameter X: the streamwise distance from the cylinder K: an experimentally determined constant x
0
: the virtual origin
PAGE 20 “Derive the drag force on the cylinder from the momentum deficit method”
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PAGE 21 APPENDIX B: RAW DATA
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PAGE 22 APPENDIX C: GROUP MEMBER CONTRIBUTIONS Laboratory Note #4 Group Member Contribution to Technical Note Andrew Beusse Did apparatus section and 3.3 and 3.4 of analysis. Srinu Rayudu Worked on the results and analysis section. Finished sections 3.1, 3.2, 3.5, 3.6, and 3.7. Margarita Kuzmanova Wrote the introduction and the conclusion.
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Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY