aerodynamics report

8/2/2019 Aerodynamics Report

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AERSP 305W

Aerospace Technology Laboratory

Laboratory Section 05

Laboratory Experiment Number 2Hot-Wire Calibration and Validation

March 28, 2012Performed in Room 8 Hammond Building

Eric Kachel

Lab Partners Names:Marcia CastilloToby FabisiakHsiaoting Ko

Kimberly Norvina

Lab TA: Kylie Flickinger

Course Instructor: Richard Auhl


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Abstract

The objective of this lab was to calibrate and confirm the measurement capabilities of a hot

wire anemometer. A secondary objective was to compare the hot-wires performance to readings from

the Pitot-static probe. This information is needed for future experiments so it is known whether it is

more appropriate to use a hot-wire anemometer or the Pitot-static probe. After a fourth order

polynomial was used to calibrate the hot-wire it was used to try and detect turbulence in expected

regions, and detect shedding vortices. Through this experiment it was found that the hot-wire

anemometer performed well in detecting rapid fluctuations in the flow velocity. Although the Pitot-

static probe works well for constant velocities it was unable to detect the rapid changes in the shear

flow regime.


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Introduction

The objective of this lab was to calibrate and confirm the measurement capabilities of a hot

wire anemometer. It is important to understand the capabilities of the hot-wire so that it can be used in

later experiments.

In order to calibrate the hot-wire the velocity of the flow needed to be determined. In this

experiment this measurement was performed using the Pitot-static probe. The Pitot-static tube

measured dynamic pressure (q), using this pressure, and the density of the air in the lab ( ), the

velocity of the flow could be determined using Equation 1 below.

)(2 qV (1)

Using this velocity a fourth order polynomial can be used to calibrate the hot-wire. Once the

hot-wire is calibrated its capabilities can be further examined. The first measure of hot-wire

performance was through the measurement of turbulence intensity. In order to do this we look at the

instantaneous velocity equation, Equation 2 below. Here this equation states that the instantaneous

deviation of the velocity is equal to the total velocity minus the average velocity.

ii uUu or Uuu ii (2)

Figure 1, in the Appendix, is an example of the type of data seen later in the experiment. The

components of the instantaneous velocity equation have been labeled on the figure to help enhance

clarity of what each of these terms mean. By taking how much the velocity is fluctuating from the

mean (u ) and taking the root mean square of that value the amount of fluctuation in the system can be

quantified. If the root mean square velocity is then divided by the average velocity turbulence intensity

is found. Notice how the v and w terms were neglected. This is because flow from the get is in only

one direction and the instruments can generally only accurately measure velocity in one direction. This

allows the unidirectional assumption to be made. Equation 3 below is for the turbulence intensity

calculation.

U

u

U

u

U

wvu

Ti rms

2

222

3

)(

(3)

Another way to validate the use of the hot-wire is through measuring the Karman vortex street.

The Karman vortex street is when flow passes by a cylinder at a particular Reynolds number (80-200)

it sheds off periodic vortices at a set frequency. By using the hot-wire to try and measure the frequency


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of these vortices we can gain a better understanding of its capabilities. Figure 2 shows a flow past a

cylinder at varying Reynolds numbers. The Karman vortex street occurs between eighty and two-

hundred.

The non-dimensional parameter that describes vortex shedding is the Strouhald number. The

Strouhal number relates the frequency of the vortex shedding to the diameter of the cylinder, and to the

flow velocity. The Strouhal number can also be approximated using the Reynolds number. Both the

equation for exact and approximate Strouhal number can be seen below in Equation Set 4.

U

DfSt

and

Re

St7.19

1198.0 (4)

Figure 2: Flow Past a Cylinder for Varying Reynolds Numbers


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Experimental Procedure

The experimental configuration for consisted of mainly the jet and the probes (Pitot-static and

hot-wire). These probes were located apart from one another by 0.2 to avoid interference between the

probes themselves. The instrumentation was also placed on a multi-axis track so that its position could

be managed precisely. Figure 3 shows the experimental jet, and how the instruments are oriented.

For the data processing the Pitot-static tube voltage was sent to Channel 0 in the data

acquisition system (DAQ), and then sent straight to LabView where it could be processed. The hot-

wire voltage took a more complicated path. The voltage was first sent to the digital readout so it could

be viewed real time to help locate the shear region of the flow. Then the unfiltered portion of the

hotwire data entered Channel 1 of the DAQ. The hot-wire data was also sent through an oscilloscope,

and high pass filter (sampling at 20,000 Hz) before returning to the DAQ through Channel 2. The hot-

wire data was also then accessible through LabView. Figure 4 shows a diagram of this process.

HOT-WIREANEMOMETER

HIGH PASSFILTER

DATA ACQUISITIONSYSTEM

LABVIEW

DIGITALREADOUT

OSCILLOSCOPE

PITOT-STATICPROBE

CH 1

CH 0 CH 2

Figure 4: Block Diagram of Data Processing

Hot-WirePitot-StaticProbeFlow

Direction

0.2 Offset

Figure 3: Jet Calibration Facility


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Hot-Wire Calibration

In order to use the hot-wire anemometer in later portions of the experiment it first needed to be

calibrated. While both the Pitot-static and hot-wire probes were 1 away from the jets exit nozzle the

jet was turned to multiple dial settings. Using the known calibration factor of 5.27 volts/psf for the

Pitot-static probes transducer the dynamic pressure was found at each dial setting. Using the dynamicpressure from the Pitot-static probe and the atmospheric data collected in the lab the velocity data was

able to be determined. This velocity was then used to calibrate the hot-wire anemometer.

Turbulence Intensity

Once the turbulence hot-wire is calibrated the next part of the experiment was measuring the

turbulence intensity of different regions in the flow. For this portion of the experiment the dial setting

for jet velocity was set at a constant 77%. First the hot-wire was placed in the core (center) of the jets

flow field. Here 2000 samples of velocity were taken. Then the probe was moved toward the edge of

the jets flow field in the shear region. The location of this region was found by observing the hot-wire

voltage displayed on the oscilloscope and adjusting the position of the probe accordingly. These same

steps were also performed with the Pitot-static tube.

Karman Vortex Street

In order to examine the frequency of shedding vortices this experiment studied a 0.032 and a

0.062 cylinder. Only the hot-wire was used for this portion of the experiment. As with the hot-wire

calibration a variety of jet velocity settings were used in order to capture the shedding characteristics.

In order to have the best chance of finding the vortices the hot-wire was originally placed five diameter

lengths of the cylinder downstream, and two diameters below the cylinders center line. A diagram

showing this set-up can be seen below in Figure 5.

D

5 D

2 D

Hot-Wire

Flow

Figure 5: Hot-Wire Location for Measuring Vortex Shedding


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A spectrum analyzer was then used to examine the shedding frequency. If there was not a

strong response where the hot-wire was located the position was altered until the spectrum showed a

distinct peak, which was then recorded.


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Results and Discussion

In order to perform the necessary calculations atmospheric data in the lab was measured before

the experiment. The temperature and pressure of the air were measured directly. From these values the

air density and dynamic viscosity were also calculated. Since the jet is an open system, unlike the

closed wind tunnel, there was no temperature variation through this experiment. The atmospheric

values are shown below in Table 1.

Pressure (lb/ft2) Temperature (R) Density (slug/ft3) Dynamic Viscosity slug/(ft*s)

2059.55 459.67 0.002262 3.8457E-07

Once the atmospheric conditions in the lab were known the hot-wire anemometer could be

calibrated. In order to do this the velocity of the jet must first be determined. The Pitot-static probe was

used to determine the velocity of the flow. The conversion factor for the volts to dynamic pressure in

psf was given to be 5.27 (volts/psf). This factor was applied at the various dial settings of the jet to

convert the voltage reading to useful dynamic pressure data. Figure 6 shows the pressure transducer

calibration.

Once the voltage from the Pitot-static probe was converted in to dynamic pressure the velocity of

the flow could be determined. This was done by also using the air density calculated from the

atmospheric conditions in the lab. The velocity and voltage from the hot-wire anemometer were

plotted together in Figure 7. A fourth order polynomial was then fitted to the plot and served as the

conversion factor from volts to psf for the experiments hot-wire readings. This polynomial can also be

found in Figure 7.

Table 1: Laboratory Atmospheric Conditions

Figure 6: Transducer Calibration Data


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The limiting factor for the hot-wire calibration was the fact that the jet could not operate at

lower velocities. The lowest data collected was at the 24 percent dial setting. The offset point at zero

velocity could also be recorded to be 3.4 volts when there was no flow over the wire. By examining the

fourth order trend line it can be seen that it matches the collected data points very closely. The R

2

valuefor the equation is 0.9999. If the trend line were to match the data exactly the R 2 value would equal

one. This shows that using this equation for converting the hot-wires voltages to pressure will be

accurate.

The next part of the experiment was using the calibrated Pitot-static probe, and hot wire to examine

the turbulence intensity of the flow. Measurements were taken in the core, and shear regions of the

flow with both instruments as discussed in greater detail in the experimental procedure. During this

section of the experiment the velocity was recorded over a time sample. From this time sample the

mean velocity, and turbulence intensity were calculated. The time trace along with mean velocity and

turbulence intensity can be seen in Figure 8 for the hot-wire anemometer.

Figure 7: Hot-wire Calibration Data


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By examine a smaller time slice of this data it may be easier to examine some of the features. A

smaller time slice of the data represented in Figure 9 can be found in the Appendix in Figure 1. Figure

1 shows how the velocity for both the core and shear values fluctuates about the average. In the shear

region this fluctuation appears to be much greater. This can be represented quantitatively by

calculating the turbulence intensity also provided for both regions in Figure 9. As expected the

turbulence intensity is greater in the shear region where turbulent features such as eddies cause the

large fluctuations in instantaneous velocity.

The turbulence intensity in both the core and the shear region was also examined by using the

Pitot-static probe. Similarly to the hot-wire method the data recorded from the Pitot-static tube can be

seen below in Figure 10.

Figure 8: Hot-wire Turbulence Analysis


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From Figure 10 it can be seen that the turbulence intensity is very low for the Pitot-static probe.

From the hot-wire analysis we know there is turbulence in the shear region that the Pitot-static probe is

unable to record. The sampling mechanism is too low for this device to pick up the rapid fluctuations

in velocity associated with turbulent flow characteristics. Using this information we know that in

future experiments a Pitot-static tube will not be a good instrument to measure turbulence. Figure 11 in

the Appendix shows a time slice of Figure 10. When viewed alongside Figure 1 showing the

turbulence intensity from the hot-wire, the lack of fluctuation can be observed in the Pitot-static data.

After the turbulence intensity was determined the Karman vortex street was also observed. The

procedure for this was discussed earlier. For a 25 micron wire at maximum velocity the Reynolds

number will be 87. The vortex street occurs when the Reynolds number is between 80 and 200, so it is

likely that there will be vortex shedding. Since the sample rate of the hot-wire anemometer was 20,000

Hz using the Nyquist sampling criteria we can only detect frequencies up to 10,000 Hz. Using the

theoretical formula presented earlier, and the maximum Reynolds number for the experiment it was

found that the smallest diameter cylinder that shedding could be detected from had a

Figure 10: Pitot-static Probe Turbulence Analysis


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0.000365diameter. This corresponds with a 9.271 micron cylinder. Therefore if the 25 micron hot-

wire probe does produce a vortex it is likely to be detected.

For the 0.0032 and 0.0062 diameter cylinders the Reynolds number and Strouhal number were

calculated at each dial setting. This plot was again limited by the minimum velocity of the jet. The

theoretical equation discussed earlier is shown along with the experimental data for both cylinders inFigure 12.

The achievable Reynolds number was limited to be approximately 200 for this experiment. Figure

12 helps to show that the experimental data followed the theoretical calculation closely.

Figure 12: Vortex Shedding Analysis


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Conclusions

Overall this experiment yielded very useful results. The first portion of the experiment was

calibrating the hot-wire anemometer. This was done by adding a fourth order trend line to the plot of

velocity vs. hot-wire voltage. This fourth order polynomial was then used throughout the rest of the

experiments in order to convert the voltage readings to velocity. Because of this it is important that the

equation used closely represents the data. Calculating the R2 value of the trend line to the data gives a

quantitative number of how well the trend line fits that data. If R 2 equals one the equation matches

exactly. For the fourth order conversion equation the value was 0.9999. Since this value is extremely

close to 1 the calibration used was a very accurate one.

Ultimately the goal of calibrating the hot-wire was that we could confirm that it was working so

that it could be used in further experiments. To do this the hot-wire was tested under several well

documented flow conditions. By placing the anemometer in the core of the jet flow the instrumentsability to measure a constant velocity was examined. Another place the hot wire tested was in the shear

region of the jets flow field. Here there will be turbulent eddies and the velocity at a particular set

point would be expected to fluctuate. The hot-wire detected these turbulent properties. Lastly the hot-

wire was used in order to measure the Karman vortex street. By using the Reynolds number to

theoretically estimate the Strouhal number the frequency of the vortex shedding can be determined. By

examining the data from this test it was seen that the hot-wire detected flow properties similar to the

theoretical data. The fact that the hot-wire detected all of the expected flow characteristics shows that it

can be accurately used to determine flow properties other than just pure constant velocity.

Data was also collected using the Pitot-static probe for the core and shear regions. Although the

Pitot-static tube performed was at the constant velocity setting at the core, it was unable to detect much

turbulence intensity in the shear region. This is because the velocity was changing so rapidly that the

transducer didnt have time to record the difference in pressures. So when designing an experiment if

the turbulence of the flow is of interest the hot-wire should be used. However, if turbulence is not a

parameter in the experiment a Pitot-tube can be used in order to reduce noise.

One of the improvements that could be made to this experiment is with the jet itself. The

current jet can only operate above twenty four percent power. It may be useful to try and make the

flow through the jet slower. This way more data points could be taken to better characterize the results.

Also a lower velocity may allow for the use of smoke to visualize the Karman vortex street. If the

frequency shedding was visible the frequency could be observed visually and then compared to the

spectrum frequency data to better enhance confidence in the results.


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The Appendix

iu

iu

U

Figure 1: Hot-wire Turbulence Analysis Time Slice

Figure 11: Pitot-Static Turbulence Analysis Time Slice

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