PENN STATE UNIVERSITY
COLLEGE OF ENGINEERING
DEPARTMENT OF AEROSPACE ENGINEERING
HOTWIRE SURVEY REPORT
Date: March 11, 2019
Author: Kartik Kamdar
Section: A04
Teaching Assistant: Kerstyn Auman
Instructor: Dr. Richard Auhl
AERSP 305
1
Abstract
Hotwire Survey Report
Kartik Kamdar
The report determines and compares the velocity and turbulence intensity profiles of flow
in 2 x 3 wind tunnel in Hammond 008 for both downward and upward surveys by using a
hot-wire anemometer probe. Key findings from the experiment include that the velocities
and the turbulent intensities for both the downward and upward surveys are greatest in
the middle of the wake in the test section because of the high number of eddies and
vortices.
This has a huge significance in aircraft design. The tail or any part of the aircraft should not
be placed in the middle of the wake of the wing because this will greatly increase the
velocity and turbulent intensity of the flow on that part, which will increase profile drag
because of an increase in the skin-friction drag. Furthermore, while the velocity in the wind
tunnel is clearly affected by the temperature, there is no clear relationship between
turbulence intensity and temperature.
The conclusions drawn from the experiment are consistent with public knowledge but
there are some discrepancies, which can be attributed to random and human error. These
errors can be eliminated with the use of more sophisticated lab equipment such as a digital
measuring device.
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2
Introduction
Hotwire Survey Report
Kartik Kamdar
The objective of this experiment was to determine and compare the velocity and
turbulence intensity profiles of the 2 x 3 wind tunnel in Hammond 008 for both upward
and downward surveys by using a hot-wire anemometer probe. The hot-wire anemometer
probe used in the experiment is shown in Figure 1.
Figure 1: Hot wire anemometer probe in the 2 x 3 wind tunnel
This experiment required the hot-wire probe to be calibrated to relate the output voltage
to the flow’s instantaneous velocity, which in turn, required the wind tunnel calibration
constant calculated in Lab A1 (to convert the mean voltages from the transducer to
pressure, and then to the velocity in the wind tunnel at the location of the hot-wire probe).
Furthermore, the shedding frequency of the wake behind a thin cylindrical wire was
measured to confirm the frequency response of the hot-wire probe.
This experiment gave the team experience with data acquisition techniques and tools such
as the hot-wire probe, wind tunnel, and LabVIEW. Furthermore, the team also learned
about important aerodynamic concepts such as the Karman Vortex Street. Results obtained
in this experiment could be used in future experiments for estimating velocity profiles and
turbulence intensities at different locations by interpolation.
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Kartik Kamdar
A hot-wire was used to measure instantaneous velocity components in the flow-field. A
platinum hot-film measuring 50.8 microns was used instead of a wire. Using the principle
that as the flow velocity changes near the wire, so do the amount of convective cooling, the
constant temperature anemometer adjusts the voltage to maintain the film at a constant
temperature while convections occurs. The anemometer is calibrated to relate the output
voltage to the flow’s instantaneous velocity. An anemometer probe was used in the
experiment instead of a single hot-wire to allow the determination of multi-component
flow velocities (since it comprises of multiple hot-wire sensors) at the tip of a single probe
as shown in Figure 2.
Figure 2: The Measurement Tip of a Single-Sensor Hot-Wire Probe
Karman Vortex Street is a repeating pattern of swirling vortices caused by vortex shedding,
which is responsible for the unsteady separation of flow of a fluid around blunt bodies
(cylinder in this experiment). Karman Vortex Street only forms at a range of Reynolds
numbers, typically above a minimum of Reynolds number of 90. Table 1 denotes how a
small range of Reynolds number influences the flow behavior in the wake of the cylinder.
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Reynolds
Number
0-4
Flow behavior
Hotwire Survey Report
Diagram Representation
Kartik Kamdar
Viscous forces are much larger
than inertial forces and the
flow in this range is much the
same as that of an “ideal fluid”
Attached vortices begin to
form behind the cylinder and
a separated-flow region
develops
Vortices begin to break away
from the cylinder, alternating
from the upper and lower
halves of the cylinder
The Karman Vortex Street
forms at a distance closer to
the cylinder before it breaks
The vortex street becomes
Source:
unstable and irregular, and
https://nptel.ac.in/courses/11210
the flow within the vortices
4159/lecture12/12_2.htm
becomes turbulent.
4-40
40-80
80-100
>200
Table 1: Relation between Reynolds Number and Flow behavior
The frequency of the vortex shedding is constant with time. To characterize this flow, the
frequency (f) can be non-dimensionalized by the diameter (D) of the cylinder and the free
stream velocity (U). This non-dimensional parameter is called the Strouhal number (St)
and is shown in Equation 1. An empirical formula relating St to Reynolds number is given
in Equation 2:
𝑆𝑆𝑆𝑆 =
𝑓𝑓𝑓𝑓
𝑈𝑈
(1)
𝑆𝑆𝑆𝑆 ≈ 0.198 �1 −
19.7
�
𝑅𝑅𝑅𝑅
(2)
As seen in Figure 3, the Strouhal number is approximately 0.2 for a wide range of Reynolds
𝜌𝜌𝜌𝜌𝜌𝜌
numbers (𝑅𝑅𝑅𝑅 =
) of 200 to 200,000.
𝜇𝜇
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Hotwire Survey Report
Kartik Kamdar
Figure 3: Measured Strouhal number for vortex shedding frequency behind a cylinder
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3
Experimental Procedure
Hotwire Survey Report
Kartik Kamdar
a. Hot-Wire Calibration:
The hot-wire probe was mounted in the last window of the test section of the 2 x 3 wind
tunnel at a location x = 176” downstream of the venturi in the test section and y = 18”
above the tunnel floor. The experimental setup is shown in Figure 4.
Figure 4: The experimental set-up
From the previous experiment (A1), the wind tunnel constant K was known to be equal to
0.905. The constant K is given by Equation 3:
𝐾𝐾 =
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
∆𝑃𝑃
=
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑞𝑞
(3)
It was also given that, transducer A, with a gain / “span” setting of 3.75, had a calibration
constant of 3.267 PSF/Volt, t, and was set-up to sense the static pressure drop through the
contraction section using Equation (4):
∆𝑃𝑃 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (3.267) ∗ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
(4)
Using Equation 3, the dynamic pressure was then calculated by making it the subject of the
equation and solving.
Equation 5 was used to calculate the density of air in the tunnel.
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The standard air conditions are:
𝑃𝑃 𝑇𝑇
𝜌𝜌 = 𝜌𝜌𝑟𝑟 ( ) ( )
𝑃𝑃𝑟𝑟 𝑇𝑇𝑟𝑟
𝜌𝜌𝑟𝑟 = 0.002377 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠/𝑓𝑓𝑓𝑓 3
The ambient conditions were:
Kartik Kamdar
(5)
𝑇𝑇𝑟𝑟 = 520.87 °𝑅𝑅
𝑃𝑃 = 30.1 𝑖𝑖𝑖𝑖. 𝑜𝑜𝑜𝑜 𝐻𝐻𝐻𝐻
𝑃𝑃𝑟𝑟 = 14.696 psi
𝑇𝑇 = 61.2 ℉
The calculated density was then used to calculate velocity using Equation 6.
2𝑞𝑞
𝑉𝑉 = �
𝜌𝜌
(6)
The wind tunnel was then powered on and the motor speed was adjusted to 5%. Using
LabVIEW, the mean and time trace of the output voltages from both transducer A and the
hot-wire anemometer were recorded. The speed of the airflow was then increased in
increments of 5% from 5% to 30% and increments of 10% from 30% to 90% by changing
the dial settings. The output voltage time traces at each dial setting were recorded.
The velocities (y-axis) were then plotted as a function of the mean output voltage from the
hotwire (x-axis). This is the hot-wire calibration curve as shown in Figure 5. By fitting a 4th
order polynomial to this data, an equation to determine the velocity of any given flow-field
using this same hot-wire sensor was found.
160
y = - 0.0272x4 + 1.617x3 - 13.176x2 + 38.708x - 39.327
140
R² = 0.9999
Velocity (ft/s)
120
100
80
60
40
20
0
2.5
3.5
4.5
5.5
6.5
7.5
8.5
Mean hotwire output voltage (V)
Figure 5: Hot-wire Calibration Curve (Adjusted)
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Kartik Kamdar
The graph is non-linear simply because the output voltage from the constant temperature
anemometry is non-linearly related to the flow’s instantaneous velocity. A 4th order
polynomial trendline best fits the curve.
The zero-velocity offset voltage of the hot-wire anemometer calibration graph can be
attributed to the presence of free convection, which when detected by the hot-wire probe,
resulted in a convective cooling effect that caused an output of a non-zero voltage.
It should also be noted here that there are problems associated with using the hot-wire at
very low velocities because, at low velocities, the “free convection” and the “forced
convection” cooling are comparable and contribute to a very high turbulent intensity. On
the other hand, the “free convection” cooling does not factor in at high velocities since it is
dominated by the “forced convection” cooling and thus turbulent intensity is low.
Once the 4th order polynomial was determined, it was used to calibrate each point of the
hot-wire time trace to generate a time trace table of velocities for each dial setting. The
time trace graph of velocities for the wind tunnel operating at 30% power is given in Figure
6.
46.2
46
45.9
45.8
45.7
45.6
0
77
154
231
308
385
462
539
616
693
770
847
924
1001
1078
1155
1232
1309
1386
1463
1540
1617
1694
1771
1848
1925
Instantaneous velocity (ft/s)
46.1
Time (seconds)
Figure 6: Time trace graph of velocities for the wind tunnel at 30% power
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Kartik Kamdar
�) and fluctuating
The instantaneous velocity (u) can be separated into a mean velocity (𝑈𝑈
component (u′) as given in Equation 7:
�) were calculated using Equation 8:
The arithmetic mean velocities (𝑈𝑈
(7)
(8)
The root-mean-square (𝑢𝑢𝑟𝑟𝑟𝑟𝑟𝑟 ) of the streamwise velocity fluctuations were calculated by
using Equation 9:
(9)
These values were used to determine the approximate turbulence intensity at each dial
setting.
Turbulence intensity relates the fluctuating components of velocity non-dimensionally to
the mean and is widely used by experimentalists to describe the quality of a flow field. It is
mathematically defined as the sum of the root mean squares of the orthogonal streamwise
and cross-stream velocity fluctuations (u′,v′,w′) normalized by the mean freestream
�). Often an assumption is made that the cross-stream velocity fluctuations are
velocity (𝑈𝑈
equal to the streamwise velocity fluctuations (u′ = v′ = w′).
This relationship for turbulence intensity is given in Equation 10. In many practical
applications, the cross-stream velocity fluctuations are less than the streamwise
fluctuations, so that this simplification results in a maximum turbulence intensity for a
given flow field.
(10)
The turbulence intensity as a function of free-stream velocity in the wind tunnel is shown
in Figure 7:
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Kartik Kamdar
0.016
0.014
Turblulence intensity
0.012
0.01
0.008
0.006
0.004
0.002
0
0
20
40
60
80
100
120
140
160
Free-stream velocity in the wind tunnel (ft/s)
Figure 7: Calculated Turbulence Intensity vs. Free-stream velocity
The turbulence intensity decreases as the tunnel speed increases. This is because, at low
velocities, the “free” and “forced” convection is comparable and contribute to the turbulent
intensity, while at high velocity the “forced” convection dominates, and the “free”
convection is negligible, resulting in low turbulent intensity.
b. Measuring the Karman Vortex Street Frequencies:
For this, the spectrum analyzer was set-up to time-average the instantaneous output from
the hot-wire anemometer and 20 averages were used to plot a power spectrum with
frequency on the x-axis and voltage output on the y-axis. Since the y-axis is logarithmic in
nature, each spike in the data represents a dramatic voltage fluctuation at that frequency.
Calipers were used to measure and record the diameter (in inches) of the wire protruding
from the tunnel wall. The height of the hot-wire probe was adjusted to be about 2 cylinder
diameters below the center, and 5 diameters down-stream, of this wire. The dominant
frequency present in the wake of that cylinder for a range of flow speeds were recorded,
starting at 5%, then increasing to 6%, 7%, 8%, 9%, 10% and then up to 90%, in the same
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Kartik Kamdar
increments used in the previous procedure. For each dial setting, the voltage from
“transducer A” was recorded to calculate the velocity of the wind tunnel.
Then the Karman Vortex Street frequencies were measured by using Equation 1 (reprinted
below)
𝑆𝑆𝑆𝑆 =
𝑓𝑓𝑓𝑓
𝑈𝑈
(1)
Where 𝑓𝑓 was the dominant frequency recorded, 𝐷𝐷 was the diameter of the wire measured,
and 𝑈𝑈 was the free-stream velocity in the wind tunnel, which was calculated using
Equations 6 and 8, as described above.
The dynamic viscosity µ was then calculated using Equation 11
𝜇𝜇 = 2.27 × 10−8 �
𝑇𝑇 1.5
�
𝑇𝑇 + 198.6
(11)
Where 𝑇𝑇 was the ambient temperature in the Rankine scale (=520.87 °𝑅𝑅)
This was then used to calculate the Reynolds number using Equation 12
𝑅𝑅𝑅𝑅 =
𝜌𝜌𝜌𝜌𝜌𝜌
𝜇𝜇
(12)
The theoretical Strouhal number was then calculated using Equation 2 (reprinted below)
𝑆𝑆𝑆𝑆 ≈ 0.198 �1 −
19.7
�
𝑅𝑅𝑅𝑅
(2)
The theoretical Strouhal number and the measured Strouhal number were then graphed on
the same plot against the Reynolds number to confirm the frequency response of the hotwire probe as shown in Figure 8. Series 1 shows the measured Strouhal Number vs.
Reynolds number graph, while Series 2 shows the theoretical Strouhal Number vs.
Reynolds number graph.
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0.24
0.22
Strouhal Number
0.2
0.18
Series1
Series2
0.16
0.14
0.12
0.00
200.00
400.00
600.00
Reynolds Number
800.00
1000.00
Figure 8: Strouhal Number as a function of Reynolds Number
The hot-wire Reynold number ranges from 10.09 for wind tunnel operating at 7.2% power
to 115.06 for wind tunnel operating at 70% power. As such, it is quite possible that at high
velocities, the hot-wire sheds vortices of its own. The shedding can be detected by placing
another hot-wire anemometer probe in the wake of this hot-wire.
c. Recording and Comparing the Two Velocity Profiles:
For this, the venturi calibration from Lab A1 and the calibration constant for transducer A =
3.267 PSF/Volt were used to calculate the voltage needed on Transducer A (measuring ∆P
directly), to obtain a velocity of approximately 100 ft/sec at the hot-wire location. The wind
tunnel was then turned on and the dial setting adjusted to the desired voltage for
Transducer A. A velocity survey of the empty test section was then performed using and
using the stepper motor controller buttons, the hot-wire probe was moved to an elevation
in the wind tunnel that was approximately even with the 2nd slot down from the top of the
traverse mechanism (about 24” above the floor).
Using LabVIEW, velocity readings were recorded every 0.2” as the probe moved downward
from its starting position of y = 24” and data was acquired from the hot-wire anemometer,
pressure transducers, and the thermocouple at each measurement location. The results
obtained from the thermocouple are shown in Figure 9:
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Vertical position (inches)
30
25
20
15
10
5
0
65.4
65.6
65.8
66
66.2
66.4
66.6
66.8
67
67.2
Temperature (deg. F)
Downward survey
Upward Survey
Figure 9: Vertical position vs. Temperature at each y location for Downward and Upward Survey
The LabVIEW code recorded a time trace at each location and determined the mean
velocity and turbulence level at each measurement location during the experiment. Once
the downward survey was completed, the survey was repeated in the upward direction.
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4
Results and Discussion
Hotwire Survey Report
Kartik Kamdar
Figure 10 shows a plot of velocity (x-axis) at each y location (y-axis) for both surveys on the
same graph.
30
Vertical position (in)
25
20
15
Upward Survey
Downward Survey
10
5
0
92.5
93
93.5
94
94.5
Velocity (ft/s)
Figure 10: Vertical position vs. Velocity for Downward and Upward Surveys
Though the data is very scattered, it is clear that the velocity is highest around the middle
vertical positions for both the downward and upward surveys, and as the distance from the
middle increases, the velocity decreases. Therefore, the top and bottom of the test section
have least velocities. A temperature increase in the tunnel increases the velocity profile
measurements. The positive difference of temperature between the two direction surveys
proves that the air inside the wind tunnel heated up and as the power of the wind tunnel
was not changed, it lost energy as heat to the air. Then, less work needed to be done to
accelerate the air inside the wind tunnel.
The eddies in the wake contribute to turbulent flow, which is characterized by high
velocities. The velocities are way more evenly spread out than the turbulent intensities.
Figure 11 shows a plot of turbulence intensity (x-axis) at each y location (y-axis) for both
surveys on the same graph.
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30
Vertical position (in)
25
20
15
Upward Survey
Downward Survey
10
5
0
0
0.0005
0.001
0.0015
0.002
0.0025
Turbulence intensity
Figure 11: Vertical position vs. Turbulent Intensity for Downward and Upward Surveys
The plot shows that the turbulent intensities are concentrated in between the values 0.001
and 0.0005. The reason for this is because, at high velocities, the turbulent intensities are
low because of the dominance of the “forced” convection. The turbulent intensities are
greatest in the middle and decrease as the distance from the middle increases. This is also
because of the eddies in the wake, which contribute to turbulent flow.
There is not a clear connection between the temperature and turbulence intensity because
data points from both the upward and downward surveys are concentrated in similar
positions in the graph.
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AERSP 305
5
Conclusions
Hotwire Survey Report
Kartik Kamdar
The hot-wire anemometer probe calibration curve had a 4th order equation of slope and the
measured Strouhal number vs. Reynolds number graph had a similar shape to the
theoretical graph for Reynold number values ranging from 200 to 700. However, the
measured values increase rapidly for Reynolds number>700, but the theoretical values
continue to increase slowly. These discrepancies can be attributed to two major sources of
discrepancies in this experiment:
Human error: Several parts of the procedure were performed directly by humans such as setting the pressure transducer to the desired voltage, setting the wind tunnel to the
desired power was done, measuring the diameter, and setting the position of the hot-wire
anemometer. All these tasks may have lacked precision and accuracy because of the human
error involved in readings numbers from measuring devices, and more.
Random Error and systematic error: The power displayed by the wind tunnel power meter
never reached 100% and kept fluctuating because of the varying heat loss in the wind
tunnel and it was, therefore, difficult to get the corresponding reading using the DAQ
system. Furthermore, the voltage collected by the DAQ system may not have been accurate
due to internal resistance and heat loss in the devices used.
For future experiments, multiple runs of the experiment should be carried out to minimize
random error and ensure consistent data. For repeatability purposes, the ambient
conditions mentioned in the report should be maintained while conducting the re-runs.
Furthermore, more advanced sensors with such as digital measuring devices should be
used to minimize human error. Automating data processing by using computer algorithms
(MATLAB code or similar) was another way to both speed up processing and avoid
calculation errors.
The plots for velocity and turbulent intensity profiles with vertical position have a huge
significance in aircraft design. The tail or any part of the aircraft should not be placed in the
middle of the wake of the wing because this will greatly increase the velocity and turbulent
intensity of the flow on that part, which will increase profile drag because of an increase in
the skin-friction drag.
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