AERSP 305W
Aerospace Technology Laboratory
Laboratory Section 12
Laboratory Experiment Number 2
Analysis of Flow-field Velocities and Vortex Shedding Using
Hot-Wire Anemometer
Jan. 30, 2012
Performed in Room 8 Hammond Building
Devin O’Connor
Lab Partner’s Names:
Mikhail Abaimov
Rebecca Frey
Shannon Hagarty
Nicholas Svirbely
Lab TA: Kylie Flickinger
Course Instructor: Richard Auhl
1
Abstract
The primary objective of this lab is to calibrate the hot-wire anemometer, and use it to record
and analyze the mean and fluctuating velocity components in order to find turbulence
intensity and to observe the Karman Vortex Street. Calibration of the hot-wire results in a 4th
order polynomial, which accurately provides the velocity of a flow for a given output voltage.
The hot-wire anemometer is capable of sensing instantaneous velocity components in a flowfield; therefore, it is an excellent device for determining turbulence intensity and detecting
vortex shedding. The calibration jet is used to relate the flow velocity to the output voltage in
a 4th order polynomial. Velocity readings are taken in the core and shear region of the jet. A
comparison of these velocity regions shows greater turbulence in the shear region. Small
cylinders of 0.032” and 0.062” diameters are put into the flow one at a time in order to
measure the effects of the Karman Vortex Street using the hot-wire anemometer and the
spectrum analyzer from the LabView program on the computer. The 4th order polynomial
matches accurately with the data collected. The shear region of the jet is found to be more
turbulent than the core region, and the hot-wire is capable of measuring the fluctuations. The
hot-wire is also capable of detecting vortices, which are shed from the cylinders placed in the
flow. The findings in this experiment confirm the velocity measuring capabilities of the hotwire anemometer and show the fluctuation of velocity in shear regions. The experiment also
shows the natural phenomenon known as the Karman Vortex Street, which involves the
formation and cyclic shedding of vortices from the cylinders.
2
Introduction
This experiment is conducted in order to calibrate and confirm the measurement capabilities
of a hot-wire anemometer. A hot-wire anemometer is a type of velocity measuring device that
is capable of sensing instantaneous velocity components in a flow-field. A constant
temperature anemometer is used for this experiment, meaning that the resistance of the wire
is kept constant so that the temperature remains constant. The instrument uses the
convective cooling of the wire to determine the velocity of the air. The actual readings of a
hot-wire are in volts, therefore it is necessary to calibrate the instrument by converting the
voltage readings to velocity. Equation 1 is used to convert the dynamic pressure measured
by the pitot-static tube, to velocity in order to calibrate the hot-wire.
Velocity as a function of Dynamic Pressure
V 
2( q )

(1)
Instantaneous velocity is comprised of two components: mean component ( U ) and
fluctuating component ( u ). A benefit of using a hot-wire anemometer for velocity
measurement is that it can sense both components. The equation relating these components
is shown below and a graphical representation of this equation is included in Figure 1. The
mean component is shown as a red line and the fluctuating component, u , is the difference
between the instantaneous velocity component and the mean.
Instantaneous Velocity Equation
ui  U  ui
(2)
Figure 1. Graphical Representation of Instantaneous Velocity Equation
3
The quality of a flow field is described by the turbulence intensity. The turbulence intensity
relates the fluctuating components of velocity, non-dimensionally, to the mean. Analysis of
the turbulence intensity lends to the determination of laminar versus turbulent flow and the
formation and separation of vortices. The turbulence in the shear region is expected to be
greater than that in the core region due to instantaneous velocity fluctuations from interaction
with other fluid particles along the shear boundary. The non-dimensional turbulence intensity
value is determined by dividing the root mean square velocity by the mean velocity, as shown
in Equation 3.
Turbulence Intensity Equation
Ti 
( u  2  v  2  w 2 )
u  2 u rms
3


U
U
U
(3)
The simplification of Equation 3 above is reasonable because the cross-stream velocity
fluctuations are, in reality, less than the streamwise fluctuations, resulting in a maximum
estimate of the turbulence intensity as opposed to an underestimation. Vortices arise as a
result of turbulence from the viscous forces present in the fluid and pressure gradients as the
fluid flows around a cylinder in steady flow. It is also expected that vortices will be shed by
the cylinders in this experiment. The shedding of these vortices in the wake of the cylinder in
a flow is called the Karman Vortex Street, and it can be seen in Figure 2. Vortices begin to
form when the Reynolds number is greater than 4, but the Karman Vortex Street does not
form until the vortices fully break away when the Reynolds number reaches between 40 and
80. The frequency of this shedding is constant with time and is non-dimensionally
parameterized by the Strouhal Number shown below where D is the diameter of the cylinder
and U is the velocity of the fluid. An empirical formula relating the Strouhal number to
Reynolds number is also provided.
Strouhal Number
St 
f D
 19.7 
or St  0.198 1 

U
Re 

(4a & 4b)
Figure 2. Karman Vortex Street
4
Experimental Procedure
Begin with the calibration of the hot-wire anemometer. Figure 3 shows the layout and
connection of the instruments used for the calibration process. The system of instruments
include: pitot-static probe, hot-wire anemometer, high pass filter, oscilloscope, computer, and
the jet. Ensuring that the pitot-static probe and hot-wire are 1” downstream from the jet,
shown in Figure 4, the power is turned on so that airflow begins to exit the jet. Data is
constantly gathered from the hot-wire and pitot-static probe and recorded in files on the
computer. The motor speed is increased in steady increments and the data is recorded in
computer files as well. To make collected data actually useful, the voltages are converted to
dynamic pressures using the calibration factor provided of 1.497psf/volt. The pressures are
then converted to velocities by first applying the recorded atmospheric pressure and
temperature to Equation 5 to find density.
Ideal Gas Law Equation
 P   Tr 
 
 Pr   T 
  r 
(5)
Then substituting density and pressures into Equation 6 provides the velocity.
Calculate Velocity from Dynamic Pressure
V 
2( P0  Ps )
(6)

Computer
JET
Hot-Wire
Pitot-Static
High Pass
Filter
Oscilloscope
Figure 3. Instrumentation of Experiment
5
Figure 4. Axisymmetric Calibration Jet Facility
The hot-wire calibration graph is formed by plotting the velocities as a function of the output
voltage. The result of this graph is a fourth order polynomial that provides an equation to
determine the velocity of any given flow using the calibrated hot-wire anemometer.
After calibration is complete, the next part of the experiment is observing the core and shear
region flow of the jet. The speed dial of the jet is set to 60% and the hot-wire and probe are
centered in the stream of the jet in order to record the velocity fluctuations of the core region.
The output signal from the hot-wire is viewed with an oscilloscope and 2000 sample voltages
are recorded in data files. The oscilloscope monitor shows the fluctuations of voltages in a
rough version of a sinusoidal wave. The probe is moved toward the jet’s edge until the output
of the oscilloscope displays a messy signal, indicating the turbulent region. Another 2000
sample voltages are recorded from the shear flow region.
The final part of the lab involves measuring the effects of the Karman Vortex Street. Using
the hot-wire, the shedding frequencies of the wakes behind 0.032” and 0.062” diameter
cylinders are measured and recorded. This goal is reached by first inserting the 0.032”
diameter cylinder on the front of the calibration jet and positioning the hot-wire at a specific
location about 5 diameters downstream, as shown in Figure 5.
6
Hot-Wire Anemometer
KSV Cylinder
Pitot-Static Probe
Figure 5. KSV Cylinder Arrangement
The specific location is determined by slowly moving the instrument to the edge of the jet’s
stream and observing the spectrum analyzer on the computer. Shown in Figure 6, the
spectrum analyzer is set up to plot a power spectrum, showing the frequency on the x-axis
and voltage output on the y-axis. A large spike in the data represents a dramatic voltage
fluctuation at that frequency, which indicates the dominant frequency of vortex shedding. The
frequencies are recorded for a full range of flow speeds from 30% to 100% in 10%
increments and 28% to 20% in 1% increments. The process is repeated for the 0.062”
diameter cylinder.
7
Figure 6. Spectrum Analyzer Program on Computer
Results and Discussion
To ensure accurate results, the pressure and temperature were measured and recorded at
the beginning of the experiment. The density of the air was then calculated using Equation 5.
The table below contains the values recorded and used for calculations throughout the
experiment.
Table 1. Atmospheric Conditions
Pressure
29.61 in.Hg= 2094.2psf
Temperature
67.0°F=526.7°R
Density
0.0023164 slug/ft^3
The pitot-static probe was connected to a pressure transducer in order to calculate dynamic
pressure values from the output voltages from the transducer. There is a linear relation
between the voltage and the pressure, which is shown in the Figure 7 transducer calibration.
Notice the slope of 1.497psf/volt. This is the calibration number.
8
Transducer Calibration
16
Pressure (psf)
14
y = 1.497x
12
10
8
6
4
2
0
0
2
4
6
8
10
Voltage (V)
Figure 7. Pressure Transducer Calibration
The output voltages from the transducer were converted to dynamic pressures, and the
pressures were then converted to velocities. Figure 8 shows the graphical relation between
the two and provides a fourth order polynomial equation that can be used to determine the
velocity of any given flow using the hot-wire sensor. Notice the difference in the graph once
the velocity reaches about 20ft/s. This is because in the low velocity range the situation is
governed by free (natural) convection. The room current may be stronger than the jet,
therefore at low velocities the graph is governed by the Grashof number. Velocity above
20ft/s is considered the forced convection region and it shows a more linear relationship
between velocity and the output voltage of the hot-wire. Also, notice that the graph begins at
a voltage of 3.4. The reason for this offset is because the wire has current running through it
to begin with and also has an initial resistance of 5.84ohms.
9
Hot Wire Calibration
Velocity vs Voltage
120
y = -0.78770x4 + 17.96077x3 - 140.85541x2 + 472.49777x - 579.52347
100
Velocity (ft/s)
80
60
Series1
40
Poly. (Series1)
20
0
0
-20
2
4
6
8
Output Voltage (V)
Figure 8. Hot-Wire Calibration
The hot-wire anemometer is capable of measuring instantaneous velocity changes in the
flow. Results of these velocity recordings are shown in Figure 9. Figure 9 displays the velocity
time traces for the shear and core regions of the jet, along with the turbulence intensities.
Obvious differences are visible between the data of the two regions. The shear region has
higher turbulence intensity and also visibly higher amplitude. The frequency of the core
region is greater than that of the shear region.
Shear Region Ti: 0.048568
Core Region Ti: 0.006449
Figure 9. Velocity Time Trace for Shear and Core Regions
As mentioned previously, the Strouhal number is a common non-dimensional parameter that
is used to characterize the frequency of vortex shedding for a given cylinder diameter and
10
free stream velocity. Equation 4b is an empirical formula that relates the Strouhal number and
the Reynolds number, and it theoretically shows that at Reynolds numbers above 200 the
Strouhal number is about 0.2. Figures 10 and 11 are the experimental relationships that were
found between Strouhal number and Reynolds number for the 0.032” and 0.062” diameter
cylinders, respectively. The data points for the experimental graphs are not completely
accurate because at every increment of measurement the velocity was fluctuating; therefore,
it was possible for a lower percentage jet dial reading to record a higher velocity and vice
versa. As a result, the experimental Reynolds number values are not accurate from a jet dial
reading of about 22% to 30%. The experimental data is similar to the theoretical graph in the
aspect that as the Reynolds number increases above 200, the Strouhal number is about 0.2.
.032" Diameter Cylinder Reynolds
Number vs. Strouhal Number
Strouhal Number
0.25
0.2
0.15
0.1
0.05
0
0
500
1000
1500
2000
Reynolds Number
Figure 10. Measured Strouhal Number for 0.032” Diameter Cylinder
11
0.062" Diameter Cylinder Reynolds
Number vs. Strouhal Number
0.25
Strouhal Number
0.2
0.15
0.1
0.05
0
0
500
1000
1500
2000
2500
3000
3500
4000
Reynolds Number
Figure 11. Measured Strouhal Number for 0.062” Diameter Cylinder
The frequency response limitation of 20000Hz exists for the anemometer unit; therefore, the
maximum frequency we can measure is half that value, 10000Hz. This is due to the Nyquist
criteria, which states that in order to see a given frequency, there must be 2 points per wave.
If the frequency of the shedding is above 10000Hz, it would be impossible to measure. The
shedding could exist, but would not be visible to the instrumental measurement. Given a
maximum jet velocity of 109.36ft/s and a maximum measured frequency of 10000Hz the
smallest diameter cylinder that this hot-wire unit is capable of detecting can be found by first
using Equation 4b, by substituting in the Reynolds number value for a velocity of 109.36ft/s to
solve for the Strouhal number and then substitute that into Equation 4a and solve for
diameter. Completing this calculation, the smallest diameter cylinder is found to be 0.0258”.
The wire of the hot-wire probe has a diameter of 8.202e-5 ft. Solving for the Reynolds
number based on diameter, and using the recorded density, viscosity based on temperature,
and maximum velocity the wire has a Reynolds number of 54.2. Since the Reynolds number
is in the range of 40-80, the hot-wire is forming vortices that break away and form the Karman
Vortex Street. The Strouhal number at this point is about 0.126. This value is found using
equation 4b. Substituting this value into equation 4a the frequency of shedding is found to be
168kHz. This means that the hot-wire itself is likely to shed a vortex; however, the frequency
is too high to be measured.
12
Conclusions
The hot-wire calibration matches the 4th order polynomial very well. This shows that reliable
data was collected during the calibration. Therefore, the hot-wire instrument provided
accurate data on the velocity of the flow for the remainder of the experiment. As the velocity
of the flow increased, the graph becomes increasingly linear, but it still matches with the 4 th
order polynomial used to describe it. This region of the graph is considered the forced
convection region and is not affected by various currents created in the experiment room by
people walking around or moving their arms. The hot-wire calibration and resulting
polynomial ensured that velocity reading could be measured for a given voltage. The hot-wire
anemometer is capable of measuring the fluctuating component of velocity, whereas a pitotstatic probe lacks accurate readings of this velocity component. Measurements of the
turbulence intensity and Karman Vortex shedding frequency confirm this capability and
proper working of the anemometer. The hot-wire uses the principles of convective cooling in
order to accurately gather data of the instantaneous velocity fluctuations. The data gathered
shows that both the hot-wire and pitot-static probe are accurate in the core region, but only
the hot-wire is accurate in the shear region. Also, since the hot-wire is capable of measuring
the fluctuations, it can then detect the formation and shedding of vortices since they are
regions of great turbulence and velocity fluctuations. A possible improvement of this
experiment would be to include visualization of the vortices and the vortex shedding by
introducing a larger cylinder and smoke or some other visualization process. This would
make it easier to understand the Karman Vortex Street and the formation of vortices. It would
also confirm the hot-wire’s ability to detect the vortices.
13