Hot Wire Lab Report Course: AOE 4254 Ocean Engineering Laboratory

Lab Instructor: Jonathan Murrow

CRN: 90328

Author: Eddie Ball

Date of Experiment: 9/19/11

This experiment uses a hot wire anemometer to determine the wake profiles behind a cylinder in

subcritical and transitioned flow, and how the velocity fluctuates inside the wake.

1

Table of Contents

Table of Contents .......................................................................................................................................... 1

1. Introduction .......................................................................................................................................... 2

2. Description of Experiment .................................................................................................................... 3

2.1. Description of Hot Wire Anemometer (with operating principle) ................................................ 3

2.2. Other Equipment used in Experiment .......................................................................................... 4

2.3. Calibration ..................................................................................................................................... 6

2.4. Finding the Wake Profile ............................................................................................................... 8

2.5. Time History Data Collection ........................................................................................................ 8

2.6. Tunnel Speeds ............................................................................................................................... 9

3. Results of Experiment ......................................................................................................................... 10

3.1. Wake Profiles for Laminar and Predicted Tripped Flow ............................................................. 10

3.2. Time History of Laminar and Predicted Tripped Flow ................................................................ 14

4. Conclusion ........................................................................................................................................... 16

References .................................................................................................................................................. 17

Appendix A .................................................................................................................................................. 18

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1. Introduction

The wake behind a cylinder will be measured using a hot wire anemometer. The anemometer is

traversed through the entire wake and the average of the flow velocity is calculated at each point. This

can help get an idea of the drag on the cylinder. The RMS of the velocity is also calculated to get an idea

of how much the velocity at that point varies. This experiment is done under laminar flow conditions

and also turbulent flow conditions in order to compare the wake profiles. At three points (center of

cylinder, edge of wake, and point of maximum RMS) the time history of the flow will be observed and

compared to one another.

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2. Description of Experiment

2.1. Description of Hot Wire Anemometer (with operating principle)

Hot-wire anemometers are used in fluid mechanics to precisely measure the velocity profiles of

a fluid, especially of turbulent flows, due to their excellent frequency response. Hot-wire anemometers,

as shown in Figure 2.2.1, are composed of a very thin wire, typically made of tungsten, platinum and/or

platinum-iridium alloys.

Figure 2.2.1 Typical hot-wire anemometer

In this experiment a Dantec 56C constant temperature anemometer, made by Thermo-Systems Inc., was

used. The hot-film probe was a TSI type 1212-20, and works based on the fact that the resistance of the

wire changes proportionally with the temperature of the wire. The wire is typically 0.00015 to 0.0002

inches in diameter, and 0.040 to 0.080 inches long, allowing the temperature of the wire to change

quickly as convection heat transfer takes place. A schematic of a bridge circuit shown in Figure 2.2.2,

which is what is used to set up the probe.

4

Figure 2.2.2: Bridge circuit.

This circuit has two constant resistors, and one adjustable resistor. The adjustable resistor is set up with

a resistance which it has for the entire operation. The servo amplifier tried to keep the error voltage

zero to match the resistances of the two lower resistors of the bridge. It does this by adjusting the

bridge voltage so that the current through the probe heats up the wire to give it the required

temperature. Thus the faster the flow, the higher the voltage required to keep the probe at the given

temperature.

2.2. Other Equipment used in Experiment

To acquire the data, a National Instruments USB-6211 DAQ card is hooked up to a computer

running LabVIEW. A Tektronix 2002B oscilloscope is also used as a check to compare the results output

in LabVIEW.

The 0.7 meter open jet wind tunnel test section as seen in Figure 2.3 below has a test section

which is 1.32 meters in length and has an exit nozzle 1.07 meters wide and 0.91 meters high. The open

5

jet wind tunnel is powered by a 30hp BC-SW Size 365 Twin City centrifugal fan, which can pump up to 15

m3/s. The tunnel first consists of a 4 m long diffuser angled at 6 degrees. The flow then proceeds

through a settling chamber 1.47 m-high by 1.78 m-wide. The settling chamber has 0.09m long

honeycomb filters (0.01m cell size), proceeded by three turbulence reduction screens. This is necessary

to help ensure laminar and uniform flow. The flow finally goes through a 5.5 to 1 contraction ratio to

the exit following a fifth degree polynomial.

Figure 2.3: Open jet wind tunnel used in experiment. (image from (0.7m Subsonic Open Jet Wind

Tunnel))

The hot-wire probe is place on a probe support, which is mounted on a traversing system which

raises and lowers the probe into and out of the wake behind the cylinder as seen in Figure 2.4. The

cylinder measures 5.5” in diameter and is placed 14” in front of the probe.

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Figure 2.4: Test setup.

2.3. Calibration

To calibrate the probe, the wind tunnel is run at several speeds and measurements of the

voltage across the probe and dynamic pressure upstream of the probe are taken using a monometer

located inside of the wind tunnel. The voltage and dynamic pressure are sampled at a rate of 1000 Hz,

for 5 seconds. The uncertainty of the dynamic pressure is noted for each point by estimating how much

the dynamic pressure fluctuates, so the uncertainty in the wind speed can be calculated (calculations

shown in Appendix A). The hot-wire responds according to Kings Law as seen in Equation 2.1

�� � � � ��� Equation 2.1

where E is the voltage drop across the wire, u is the velocity of the flow perpendicular to the wire and A,

B, and n are constants. It is assumed in this experiment lab that n is 0.45. A and B can then be

determined using a linear regression of E2 and un. This data can be seen in Appendix A Table 1 and the

linear regression can be seen in Figure 2.5 below. The calibrated values of A and B were calculated to be

Traverse

Nozzle of

open jet wind

tunnel

Circular

Cylinder

14”

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5.9306 and 3.8633 respectively when the experiment was performed. Figure 2.6 shows the estimated

velocity of the flow for a given voltage using these values of A and B, compared to the derived results

using the Pitot-Static pressure.

Figure 2.5: Linear Regression of E2 and u

n.

Figure 2.6: Velocity estimate using Kings Law with error bars.

y = 3.8633x + 5.9306

R² = 0.9986

0.00

5.00

10.00

15.00

20.00

25.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

E^

2

u^n

0.00

5.00

10.00

15.00

20.00

25.00

30.00

2.70 3.20 3.70 4.20 4.70 5.20

u (

m/s

)

E (volts)

Hotwire Prediction

Pitot-Static Velocity

8

2.4. Finding the Wake Profile

Once the probe is calibrated a velocity profile is created by traversing the probe from 9.5 inches

above the center of the cylinder, to 6.0 inches below.

At each point where data is being collected, the mean velocity and RMS of the velocity is

calculated. The mean velocity is calculated using Equation 2.2 below.

� � lim�→�1�� ������

�

� Equation 2.2

The sampling time T is actually finite, so the calculated mean is only an approximation of the true mean

velocity. The RMS of the velocity is calculated using Equation 2.3 and Equation 2.4 below.

�� � lim�→�1�� �������

�

� Equation 2.3

��� ���� −�� Equation 2.4

Once again this is only an approximation because the RMS is calculated over a finite amount of time.

The variance is a measure of how much the velocity of the flow varied over time.

The final important definition is the turbulence intensity, given by Equation 2.5.

TurbulenceIntensity � ���)*

Equation 2.5

2.5. Time History Data Collection

At three separate locations, the probe is set to collect time history data of the velocity. Those three

locations are at:

i. Free Stream : where the turbulence intensity is approximately less than 5%

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ii. Center of the Cylinders Wake: approximately at the center of the cylinder

iii. Location of maximum turbulence intensity

At these locations, 1000 samples are taken at a sample rate of 2000 Hz. This means the total sampling

time is only half a second.

2.6. Tunnel Speeds

The tunnel is run under two conditions. The first condition is a laminar flow condition. This

condition is met by setting the wind speed of the tunnel such that the Reynolds is subcritical (below

500,000). In this experiment, the subcritical flow has a Reynolds number of 176,000. The second

condition is tripped flow, made to represent a supercritical Reynolds number. To make the flow

transition to delay separation as it would with a supercritical Reynolds number, the flow is made

turbulent by placing a trip at about 45 degree on top of the cylinder as seen in Figure 2.7 below.

Figure 2.7: Circular cylinder with trip. Trip was only along the top of the cylinder.

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3. Results of Experiment

3.1. Wake Profiles for Laminar and Predicted Tripped Flow

The wake profile for the laminar case is shown below in Figure 3.1.

Figure 3.1: Laminar wake profile. Velocity is normalized by the edge velocity Ue and the position of

the probe is normalized by the diameter of the cylinder.

The wake profile for the tripped flow would have shifted the graph to the right, because the velocity

downstream would have been greater on average. From the simplified momentum equation shown

below this can only mean that the drag on the cylinder in subcritical flow is higher.

+ � −∯ -./�0-./ ∗ 234 ��� Equation 3.1

In this equation, D is the drag on the cylinder, -./ is the velocity of the flow, ρ is the density of the air and

23 is a unit vector normal to the surface of the control volume. What this equation tells us is that

because the velocity downstream of the cylinder is lower when the flow condition is subcritical, the drag

on the cylinder will be higher. This makes sense because laminar flow separates easier than turbulent

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1 1.2

Y/D

U/Ue

Approximate Centerline of Cylinder

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flow. Figure 3.2 below shows how the pressure around the cylinder varies based on the flow

characteristics.

Figure 3.2: Theoretical Pressure distribution and experimental pressure distributions for subcritical

and supercritical Reynolds numbers. Here 180 degrees refers to the surface facing the free stream. As

can be seen from the subcritical Reynolds number, the Cp is at a maximum at the leading edge, and a

minimum at the top and bottom of the cylinder. (image (Bertin & Cummings, 2009))

The subcritical line is similar to the cylinder in subcritical flow because the flow in both cases

does not transition to turbulent flow, and separates early over the cylinder. This early separation is

what makes the pressure drag higher for the cylinder in subcritical flow. The supercritical line in Figure

3.2 would have been similar to the tripped cylinder in our experiment because the flow would have

been able to transition from laminar flow to turbulent flow before separating. Separation still occurs,

but it occurs further along the cylinder than for the subcritical flow. The pressure on the cylinder behind

separated flow is much less than if the flow does not separate as is shown though pressure

measurements around the cylinder in previous experiments. This is why supercritical flow or tripped

flow is preferred around a cylinder, in order to decrease pressure drag. It should be noted that

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turbulent flow has increased skin friction drag, however the decrease in pressure drag is much larger

than the increase in friction drag.

The RMS velocity fluctuation through the wake is shown in Figure 3.3 below.

Figure 3.3: Plot of the RMS of velocity though the wake of a cylinder in laminar flow. RMS normalized

by the free stream velocity and traverse position normalized by the diameter of the cylinder.

The RMS is expected to be the least near the edge of the wake, go to a maximum value, and then

decrease to a local minimum at the centerline of the cylinder. This is what is shown in Figure 3.3. A

higher RMS value physically means that the velocity at that point varied more.

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.05 0.1 0.15 0.2 0.25 0.3

Y/D

RMS/Ue

Approxite Centerline of Cylinder

Local Minimum

Local Maximum

Minimum

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Figure 3.4: Above (a) is what separation around a circular cylinder looks like when the flow stays

laminar. Below (b) is what the flow looks like when transition occurs before separation. Figure (a)

shows flow past a subcritical Reynolds number cylinder, and the flow separates much earlier than the

flow past a supercritical Reynolds number as seen in Figure (b). ( (W.J., 2007))

Figure 3.4 shows how for a subcritical Reynolds number, separation occurs much sooner along

the cylinder than a cylinder with a supercritical Reynolds number. This causes the cylinder with a

subcritical Reynolds number to have a much larger turbulent wake as shown in Figure 3.4. Delaying

separation reduces the size of the turbulent wake. From Figure 3.3, a good idea of how large the

turbulent wake is can be seen by looking at where the peak RMS of velocity occurred. Because the

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turbulent wake would be expected to be larger for the laminar flow case, the peak RMS would also be

expected to be further from the center of the cylinder than would be expected if the flow were tripped.

3.2. Time History of Laminar and Predicted Tripped Flow

Unsteady velocity measurements are also made at three separate locations for the subcritical

flow about a cylinder. The three locations are the free stream, the center of the cylinder wake, and the

location of maximum turbulence intensity. The graphs below show how the velocity at those points

change with time. The velocity measurements are taken at a sample rate of 2000 Hz for half a second.

Figure 3.5: Time history of wake edge velocity for subcritical flow.

Figure 3.6: Time history of velocity at point of maximum RMS for subcritical flow.

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

U (

m/s

)

Time (s)

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

U (

m/s

)

Time (s)

15

Figure 3.7: Time history of velocity at centerline of cylinder for subcritical flow.

As is expected, the velocity fluctuates at the edge of the wake are much lower than at the other

two points as shown in Figure 3.5. This is because the air is not heavily influenced by the cylinders wake

this far from the cylinders centerline. Figure 3.6 shows how the velocity fluctuations are greatest at the

point of maximum RMS. This is no surprise because the point of maximum RMS by definition is the

point with the most variance. The velocity fluctuations at the centerline of the cylinder as shown in

Figure 3.7 are not as great as in the point of maximum RMS, but are still more than at the wakes edge.

This is because this is the local minimum of the RMS as shown in Figure 3.3.

Similar plots would have been seen for the time history at the 3 points for the supercritical flow.

The velocity fluctuations at the wakes edge would have been small, and the velocity fluctuation at the

center of the cylinders wake and point of maximum RMS would have been relatively larger.

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

U (

m/s

)

Time (s)

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4. Conclusion

In order to reduce pressure drag, separation around the cylinder needs to be delayed. This can

be done with turbulent flow induced by supercritical Reynolds numbers or by tripping the flow to force

transition. The sooner separation occurs, the larger the turbulent wake behind the cylinder will be. The

manner in which the turbulent wake propagates from the center of the cylinder outward would have

been similar for both subcritical and supercritical flows, even though the size of the wakes would differ.

For each case, the flow will have the most fluctuations in velocity somewhere in between the centerline

of the cylinder and the edge of the wake.

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References

0.7m Subsonic Open Jet Wind Tunnel. (n.d.). Retrieved March 15, 2010, from Virginia Tech:

http://www.aoe.vt.edu/research/facilities/openjet.php

Bertin, J. J., & Cummings, R. M. (2009). Aerodynamics for Engineers. Upper Saddle River: Pearson

Prentice-Hall.

W.J., B. a. (2007, January 24). Experiment 3- Flow Past A Circular Cylinder. Retrieved September 19,

2011, from AOE 3054 Experimental Methods Course Manual.:

http://www.dept.aoe.vt.edu/~devenpor/aoe3054/manual/expt3/index.html

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Appendix A

Table 1: Kings Law Coefficients Calculation

Δ P (in H2O) Δ P (Pa) u (m/s) δ(u) (m/s) δ(u)/u (m/s) E (volts) E2 u

n u pred

0.19 47.01 9.15 1.78 0.19 4.04 16.35 2.71 9.06

0.30 74.49 11.52 1.46 0.13 4.19 17.54 3.00 11.52

0.41 102.04 13.49 1.26 0.09 4.30 18.52 3.22 13.81

0.60 149.54 16.33 1.06 0.06 4.41 19.43 3.51 16.13

0.76 189.48 18.38 0.95 0.05 4.50 20.25 3.71 18.39

1.00 248.61 21.05 0.83 0.04 4.59 21.08 3.94 20.84

1.20 300.05 23.13 0.76 0.03 4.68 21.86 4.11 23.29

Uncertainties were calculated using this equation:

where δ(R) is the derived uncertainty in R, and a, b, and c are the primary measurements, each with

uncertainties of δ(a), δ(b), δ(c), etc.