\

DEVELOPMENT OF DRAG COEFFICIENTS FOR

OCTAGONAL LUMINARY POLES

by

DAVID C. RITCHIE, B.S.

A THESIS

IN

CIVIL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

CIVIL ENGINEERING

Approved

August, 1990

T3 ACKNOWLEDGMENTS

(f\7^ 2 The author wishes to thank Dr. K.C. Mehta and Dr.

J.W. Gler for their support throughout the conduct of this

project. They encouraged the author to proceed when

things did not work out as planned. The contribution of

Dr. W.K. Wray as a committee member is also greatly

appreciated. In addition, the author is grateful to the

State Department of Highways and Public Transportation

without whose support and patience, this project could not

have succeeded. But most of all, the author is deeply

indebted to his parents and his wonderful wife and family

for making this additional education not only possible,

but more enjoyable than ever could have been imagined.

11

Xir 1- "..J^,

CONTENTS

ACKNOWLEDGMENTS i i

ABSTRACT iv

LIST OF TABLES v

LIST OF FIGURES vi

I. INTRODUCTION 1

Problem Statement 2

Objectives 5

I I . STATE OF KNOWLEDGE 7

Wind Tunnel Studies 7

Tow Tank or Water Tunnel Studies .... 14

Data Corrections 19

III. EXPERIMENTAL PROCEDURE 22

IV. VERIFICATION OF EXPERIMENTAL PROCEDURE ... 42

V. OCTAGONAL CYLINDER RESULTS 56

VI. CONCLUSIONS AND RECOMMENDATIONS 70

REFERENCES 73

APPENDIX 75

1 1 1

ABSTRACT

Highway signs, luminaires, and traffic signal

structures are exposed to wind loads throughout their

lives. The design of the cross-section quite often is

controlled by win^ loads. Improved definition of wind

loads would make luminaires not only more economical but

also more reliable.

The Texas Department of Highways and Public

Transportation sponsored a project at Texas Tech Univer­

sity to determine accurate drag coefficients for octagonal

shaped luminaire supports. The research utilized the tow

tank of the Mechanical Engineering Department for the

experimental work. The tow tank experimental procedure

was verified by obtaining drag coefficients for circular

cylinders and comparing them with previously published

data. One innovation employed in this project was to use

actual industry manufactured luminaire pole shapes. These

specimens matched the geometric parameters of the ones

used in the field, thereby eliminating the test specimen's

surface condition as a possible variable.

Results of this project showed an average drag

coefficient for octagonal cylinders to be in a range of

1.3 to 1.4. This value is about 257. higher than the value

now used to design luminaire supports.

i V

1

LIST OF TABLES

Page

1.1. WIND DRAG COEFFICIENTS (Ce,)

(AASHTO 1975) 5

5.1. TEST SPECIMEN PARAMETERS 58

5.2. TEST RESULTS 65

LIST OF FIGURES

Page

2.1. Drag Coefficient for Circular Cylinder in Wind Tunnel. (Schewe 1983) 9

2.2. Circular Cylinder Drag Coefficients with Variable Surface Roughness to Cylinder Diameter Ratio. (James 1976) 11

2.3. Octagonal Cylinder Drag Coefficients with Corner Normal to Flow Direction and Variable Corner Radius Ratios. (James 1976) 13

2.4. Octagonal Cylinder Drag Coefficients with Different Angles of Attack. (James 1976) 15

2.5. 8-sided, 12-sided, and 16-sided Polygonal Cylinder Drag Coefficients. (James 1976) 16

2.6. Circular Cylinder Drag Coefficients from Water Tunnel Study. (Almosnino and McAlister 1984) 18

2.7. Corrected and Uncorrected Octagonal Cylinder Drag Coefficients. (James 1976) 21

3.1. Texas Tech University Tow Tank 23

3.2. Schematic of Tow Tank, Support

Bridge, and Test Specimen 25

3.3. Schematic of Towing System 26

3.4. Test Specimen Force Diagram 29

3.5. Attachment Plate Diagram 31

VI

Page

3.6. Inscribed Circle Radius and Corner Radius for Octagonal Cylinder Cross-section 37

3.7. Test Specimens with "T" Frame Attachment 39

3.8. Octagonal Cylinder Orientation 41

4.1. Original Attachment Plate Design 44

4.2. 9" and 18" Circular Cylinder Drag Coefficients and Reference Drag Coefficients 46

4.3. 18" Circular Cylinder Drag

Coefficients 48

4.4. New Attachment Frame Design 50

4.5. 9" Circular Cylinder Drag Coefficients 52

4.6. 16" Circular Cylinder Drag Coefficients 53

4.7. 9" and 16" Circular Cylinder Drag Coefficients and Reference Drag Coefficients 55

5.1. 9" Octagonal Cylinder Drag Coefficients 59

5.2. 16" Octagonal Cylinder Drag Coefficients 61

5.3. 24" Octagonal Cylinder Drag Coefficients ^2

5.4. 30" Octagonal Cylinder Drag Coefficients 64

Vll

Page

5.5. Octagonal Cylinder Drag Coefficients with Flat Face Normal to Flow Direction 67

5.6. Octagonal Cylinder Drag Coefficients with Corner Normal to Flow Direction 68

V l l l

CHAPTER I

INTRODUCTION

Single pole supports have been widely used as a

means of supporting signs and lights for many years. In

recent years, significant changes in the shape and size of

support poles have occurred. From early heights of 30

feet and less, support pole heights in excess of 150 feet

are now being used. Most early single pole supports were

made with circular cross-sections. However, supports with

polygonal cross-sections are becoming more common. Most

of this new-found interest in polygonal cross-sections

stems from the fact that it is easier to manufacture a

tapered polygonal cylinder than it is to manufacture a

circular cylinder with taper. Another reason for the use

of polygonal cross-sections is the added structural

stiffness of the pole resulting from the introduction of

multiple "flat sides" that run the full length of the

support pole. With these changes in the height and shape

of modern supports and an increasing desire to manufacture

these support poles as economically as possible, it is

important that the forces acting on the surfaces of these

poles be determined accurately. One such force is caused

by wind blowing against the support pole.

Because support poles are exposed to wind, they

experience a drag force caused by the wind flowing around

the poles. If this drag force can be determined, the

stresses on the support caused by that drag can be

calculated. Prediction of forces and resulting stresses

permit optimum design of poles that can withstand winds

that may be encountered.

Problem Statement

The American Association of State Highway and

Transportation Officials (AASHTO) specifies in its

Standard Specification for Structural Supports for Highway

Signs, Luminaires, and Traffic Signals (AASHTO, 1975), an

equation for the wind induced drag force experienced by

single pole supports. This equation is used by most

designers for predicting the pressure due to wind on these

supports. This equation has the form:

P = (0.00256) (1.3xV) = (Cci) (CH) ( Eq . 1 . 1 )

where: P = average force/unit of projected area (psf)

V = mean design wind speed (mph) C ^ = coefficient reflecting height and

terrain effects (dimension less) C«j = drag coefficient (dimension less)

* 0.00256 converts the kinetic energy of the wind speed to potential energy of velocity pressure.

# 1 . 3 modifies the mean design wind speed to wind gusts.

The only factor in Equation 1.1 that takes into account

the interaction between the wind and the support is the

drag coefficient (Cc.) . It is for this reason that the

drag coefficient is an important parameter for optimum

design of single pole supports.

With such an important role played by the drag

coefficient, it is critical to know what factors influence

the drag coefficient for single pole supports". From

previous studies, the drag coefficient has been shown to

be affected by both the shape of the pole and the Reynolds

number (Rr .) . The Reynolds number is a dimension less

quantity which is a measure of the ratio of inertial

forces to viscous forces acting on the member. Rn is used

as an index of the type of flow characteristics or

phenomena that may be expected to occur. The equation for

Reynolds number has the form:

(V)(D)(e) R„ = (Eq.1.2)

(M)

where: Rr, = Reynolds number (dimension less ) V = velocity (ft/sec) D = member diameter (ft) ^ = fluid density (lb/ft-) H = coefficient of fluid viscosity

(Ib/ft-sec).

In research by James (1976), the drag coefficient for

circular cylinders decreased dramatically in the critical

Reynolds number range of 1x10=* to SxlO'^. James' research

also showed that the drag coefficient for octagonal

cylinders decreased in the critical Reynolds number range

of 1x10= to 3x10=^. For pole sizes of 9 to 30 inches in

diameter and wind speeds between 60 and 100 miles per

hour, the Reynolds number varies between 3.8x10* and

6.5x10=. Thus, the practical design size of poles falls

in the critical Reynolds number range. In the same

research by James (1976), two other factors influenced the

drag coefficient. These factors were the surface rough­

ness of the pole and the corner radius of the joined "flat

sides" (for polygonal shaped poles.)

Cylindrical, dodecagonal (12-sided), and octagonal

(8-sided) shapes are commonly used for support poles.

Table 1.1 shows the drag coefficient values recommended by

AASHTO as a function of Reynolds number. These values

were established from experimental data obtained with

scaled models of the pole sections in wind tunnels.

However, by using scale models of the pole sections, the

effect of the surface roughness and corner radius on the

drag coefficient may not be the same as the manufacturer's

poles. As can also be seen from Table 1.1, drag coeffi­

cient values for octagonal shapes are higher than for the

other shapes over all the ranges of Reynolds numbers

shown. Therefore, an independent experiment using a test

procedure other than the wind tunnel, namely the tow tank,

and using pole sections manufactured by industry could

prove the accuracy of the drag coefficient values for

octagonal shapes.

TABLE 1.1

WIND DRAG COEFFICIENTS (Cc) (AASHTO, 1975)

Type of Member Shape of Member

Structural Supports Cylindrical Dodecagonal Octagonal (Vert. & Horiz. )

Single Member or Truss

Vd < 32 1.10 1.20^ 1.20^

100 9.62^

32 < Vd < 64 1.20^ ( Vd ) • ( Vd ) • -

Vd > 64 0.45 0.79^ 1.20^

Luminaires (with 0.5 rounded surfaces)

Luminaires (with flat 1.20 side shapes)

Nomenclature: V = Wind Velocity (mph) d = Depth (diameter) of member (ft.)

•^Valid for members having a ratio of corner radius to^ distance between parallel faces > 0.125 or 12.57..

Qbiectives

There are two objectives of this research project.

The first is to verify the experimental procedure and the

data acquisition system by performing tests on circular

cylinders. The second objective is to test octagonal

cross-sectioned poles to obtain drag coefficients. These

tests will provide an independent experimental

verification of the coefficients used by AASHTO. Both of

these objectives were accomplished by developing a system

to test sections of actual manufacturer supplied support

pole specimens in the Texas Tech University tow tank. The

system allowed the use of water instead of air as the

fluid for flow simulation. Using water permits lower

velocities to be employed while still obtaining the

desired Reynolds number range for drag coefficient

measurement. Use of pole sections supplied by manufac­

turers provide a more representative testing environment

that closely duplicates the actual conditions in the

field.

CHAPTER I I

STATE OF KNOWLEDGE

Wind Tunnel Studies

The desire to understand the flow of fluid around a

body and the forces caused by that flow on the body has

prompted scientists to conduct experiments that attempt to

simulate those flows and model those bodies. The majority

of aerodynamic experiments conducted today involve the use

of wind tunnel technology. Wind tunnels allow members of

a variety of cross-sections to be tested to determine the

pressures and forces on the members.

Studies on circular cylinders. The flow of fluid

around a circular cylinder remains one of the most

challenging theoretical problems in the scientific world

today. In addition, the effect of forces generated by

flow around circular cylinders has become extremely

important for a wide range of engineering applications.

Experiments conducted in the early 1900's provided a

base of knowledge to expand upon. Von Karman's (1912)

classical works gave insight into the vortex shedding

phenomenon of flow around circular cylinders. Taylor

(1915) provided valuable information on the change in drag

force of a circular cylinder with respect to the smooth­

ness of the cylinder surface. Taylor also showed the

influence of aspect ratio to drag force. Fage and Warsap

8

(1930) investigated the effect of free stream turbulence

and surface roughness on the pressure distribution around

a circular cylinder. Roshko (1961) was first to suggest

at least three identifiable regimes of flow: subcritical

(purely laminar boundary layer separation), supercritical

(laminar separation followed by turbulent reattachment and

eventual turbulent separation), and transcritical (transi­

tion to turbulence in the boundary layer occurring ahead

of separation). In subsequent works, Achenbach (1968) and

Bearman (1968) firmly established that this "laminar—

separation/turbulent-reattachment" was responsible for the

low drag coefficient (C^) which occurs at the beginning of

the supercritical regime. The boundary between the sub-

critical and supercritical regimes is marked by a highly

distinguishable drop in Ce* from approximately 1.15 at

Reynolds number (R„) of 1.5x10= to a C^ of about 0.25 at

Rr of 4x10=. From measurements of 0^ with respect to Rr>

by Schewe (1983) in a pressurized wind tunnel and in

agreement with results of experimentation by

Wieselsberger, the well recognized plot of Cd versus Rr,

for a circular cylinder is shown in Figure 2.1.

In a study by James (1976), drag coefficients

obtained for various diameters of circular cylinders were

plotted versus Reynolds number. The plot demonstrates one

of the main problems encountered when comparing data from

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several different cylinder diameters. Since C^ is depen­

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usually measured as a ratio to cylinder diameter, a shift

in the C<d versus Rr, curve occurs when data is shown on the

same plot. Shown in Figure 2.2, as the surface roughness

to model diameter ratio increases, the C. curve shifts up

and to the left. Therefore, when comparing data of one

circular cylinder to another, the surface condition should

be considered.

Studies on octagonal cylinders. In more recent

yfears, studies of cylinders with configurations other than

circular have been conducted. As application requirements

have changed, especially in the area of support poles for

highway luminaires, the polygonal cylinder shapes have

emerged as a viable and economical design. The need for

experimental data to guide the engineer in the design of

the polygonal cross-sections is great.

Probably the most extensive experimental work done

to this point on polygonal cylinder shapes is the work

done by James at Iowa State University in 1970 and 1976.

James used wind tunnel technology to conduct tests and

obtain drag coefficient results on octagonal, dodecagonal,

and hexdecagonal cross-sections. James verified his

procedure by comparing his circular cylinder results with

previously published data also shown in Figure 2.2.

11

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tured in the lab with the various desired configurations.

During these two-dimensional tests, measurements of the

cross-flow lift and drag forces on the different cross-

sections were recorded. Data was taken on models ranging

from 6 to 24 inches in diameter and at wind tunnel speeds

up to 210 feet per second. With different combinations of

wind speed and cylinder diameter, a Reynolds number value

of up to 2.1x10^ was achieved.

From James experimental results, some conclusions

were drawn about drag coefficients of octagonal cylinders.

One such conclusion described the importance of the corner

radius of the octagonal cylinders. The corner radius is

the radius of the arc where two flat sides of the cylinder

meet; usually expressed as a ratio of the corner radius to

the inscribed circle radius of the cylinder. As the

corner radius ratio increased (the corner became more

rounded), the drag coefficient decreased. Figure 2.3

shows typical data obtained for octagonal cylinders with

various corner radii ratios. The experiment also provided

information on the importance of angle of attack of the

wind on the cylinder. The maximum drag force was general­

ly experienced when the flow was directed toward a corner.

A plot showing this angle of attack variation in drag

coefficient is shown in Figure 2.4.

13

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The data obtained by James that contributed the most

to the need for continuing the study of polygonal cylinder

drag coefficients were the values obtained for the

octagonal cylinder drag coefficients. As can be seen in

Figure 2.5, the drag coefficient for the octagonal

cylinder cross-section is significantly greater than that

for any of the other polygonal test shape.

Tow Tank or Water Tunnel Studies

The use of water as the fluid for simulating flows

around structures (as in tow tanks or water tunnels) is

far less common than the use of air (as in wind tunnels).

Wind tunnel studies and the use of wind tunnel technology

are ahead of tow tank or water tunnel technology because

of the experience gained from wind tunnel usage over a

much longer period. It is for this reason that there are

few published reports and data from tow tank or water

tunnel studies.

Studies on circular cylinders. One such report was

a study of transition flow around circular cylinders in a

water tunnel. The study was performed at the Ames

Research Center and Aeromechanics Laboratory, U.S. Army

Research and Technology Laboratories by Almosnino and

McAlister (1984). The purpose of this study was to

confirm the phenomenon of asymmetric flow separation from

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a circular cylinder in the critical Reynolds number range.

In addition, an attempt was made to visualize this flow

separation and correlate the visualizations with measured

lift and drag coefficients.

The study examined the flow around circular cylind­

ers for Reynolds numbers of up to 5x10=. As can be seen

in Figure 2.6, the average drag coefficient measured for

the circular cylinder tested remained in a somewhat

constant range between C^ of 1.3 to 1.5 up to a Reynolds

number of 3.1x10=. At this point, the average drag

coefficient for the cylinder abruptly decreased to 0.8.

The decrease continued up to a Reynolds number of 3.45x10=

where the drag coefficient reached a minimum value of

0.44. Continuing to increase the Reynolds number brought

a slight increase in the drag coefficient. No surface

roughness parameters were available in this published

study, but the data obtained exhibited the same trend as

the classical drag coefficient versus Reynolds number

plots for circular cylinders in previous wind tunnel

studies.

Studies on octagonal cylinders. A thorough search

of the technical literature did not reveal any studies

performed with either tow tank or water tunnel technology

to measure and document drag forces on octagonal

18

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cylinders. It is hoped that this study will fill that gap

and provide the stimulus for continuing research in this

area.

Data Corrections

Models tested in wind and water tunnels differ from

actual structures on location in one important aspect.

Winds that flow around structures in nature have no

boundaries (except the ground) that restrict their flow

patterns. Test fluids used in wind or water tunnels are

constrained by the walls of the tunnel within which the

tests are conducted. When a model is placed inside the

test section of the tunnel, it takes up space in the test

section. To compensate for this decrease in space in the

test section for the fluid to flow, the fluid velocity

must increase to allow the same volume of fluid to pass.

This results in what is called blockage effect. The net

effect of this blockage is an effective increase in the

dynamic pressure from which drag forces are calculated.

Several methods have been developed to overcome this

blockage effect problem. Equations developed by Glauert

(1933), Allen and Vincenti (1944) and Maskell (1963) have

provided a means to correct for blockage effects in wind

tunnel experiments. James (1976) used Maskell s correc­

tion equations for models with diameters up to 12 inches.

For the larger models, Maskell's method failed and the

method of Allen and Vincenti was used. Figure 2.7 shows

the drag coefficient values obtained by James for an

octagonal cylinder. The figure shows a comparison between

uncorrected and corrected drag coefficient values.

By using the tow tank to simulate wind forces on

poles, the blockage effect is minimized. The cross-

sectional area of the tow tank is large enough compared to

the cross-sectional area of the test specimen, to make the

increase in the dynamic pressure caused by the fluid

velocity increase around the test specimen negligible.

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CHAPTER I I I

EXPERIMENTAL PROCEDURE

The main objective of this study is to obtain drag

coefficients for octagonal cross-section cylinders. The

experimental apparatus used to obtain these values of drag

coefficients was the Texas Tech University Tow tank.

Tow Tank. The tow tank shown in Figure 3.1 is

located in the Mechanical Engineering Aerodynamics

Laboratory on the Texas Tech University campus. The tank

is an above ground fiber reinforced structure 32 feet

long, 16 feet wide, and 4 feet deep. The tank is designed

to hold a water depth of 42 inches. A towing system

accompanies the tow tank. This towing system includes a

structural bridge spanning the length of the tank. This

bridge supports a carriage plate for the attachment of

specimens to be tested. A Zenith Data Systems personal

computer with a Metrabyte Dash 16 A/D converter is used to

control the input parameters of each test run. Receiving

output from the computer, a Westinghouse Accutrol 110

adjustable frequency controller controls the frequency

signal sent to a Reliance 5-HP, 1730 RPM, AC motor. The

frequency sent to the motor determines the speed at which

the test specimen is towed through the water. A 22:1

reduction V-belt drive system, connected to the motor,

22

23

Figure 3.1 Texas Tech University Tow Tank

24

and tow cable attached to the carriage plate permit the

specimen to be tested at a variable speed of up to 4 feet

per second. The computer control also allows the control

of the acceleration, deceleration, or variable velocity

profile of the specimen during the tow test. The control

system has a switch panel that allows the operator to

manually control the towing direction and speed and also

provides a safety "dead man" switch for emergency stop of

the towing system. Figures 3.2 and 3.3 show schematic

representations of the tow tank and towing system.

A few modifications to the towing system were per­

formed in order to perform drag coefficient experiments on

octagonal shape poles. One such modification was the

addition of guy wire stabilizers to the structural bridge

spanning the length of the tank. Initially, concern was

expressed as to the ability of the bridge to resist

lateral movement induced by the towing of large specimens.

This concern was confirmed with preliminary test runs with

24-inch and 30-inch diameter cylindrical specimens. The

bridge exhibited lateral movement during these test runs.

Four sets of guy wire lateral stabilizers were used to

stabilize the bridge. Two sets of the guy wires were

placed on each side of the bridge with each set having one

guy wire to the top of the bridge and one guy wire to the

bottom of the bridge. The opposite ends of the guy wires

25

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27

are attached to structural joists of the building's roof.

The wires are approximately at a 30" angle with the

horizontal thus providing both vertical and lateral

support to the bridge.

Another modification was the replacement of a 25:1

toothed gear reducer with a V-belt drive system for the

towing motor. During preliminary test runs, high

frequency "noise" was evident in the recorded data. After

several investigations, the toothed gear reducer was

determined to be the source of the high frequency "noise".

By changing to the V-belt drive system, the high frequency

noise, though not completely eliminated, was reduced to a

point where it was no longer significant.

Drag force measurements. Measurements of the drag

force on the specimens are accomplished by the use of a

Lebow 3132-500 load cell rated at 500 pounds capacity in

both tension and compression. The test specimens are

suspended vertically from an attachment plate into the tow

tank. The attachment plate, shown in Figure 3.3, attaches

to the carriage plate by a three point support system.

Two attachment plate designs were developed during the

course of the study. The original attachment plate

design did not perform as expected. The drag coefficient

va lues obtained during the experimental procedure verific-

tion were biased due to the location of the attachment

28

struts on the original design. A more detailed discussion

of the problem encountered with the use of the original

attachment plate is provided in Chapter 4.

Figure 3.4 shows the couple formed by vertical

reactions that counteracts the moment produced by the

horizontal drag force acting on the specimen. The horizon­

tal drag force is the resultant force of an assumed

uniformly distributed force acting on the test specimen.

This resultant force acts at mid-depth of the water height

on the test specimen. The location of the resultant force

application point is known because of the method used to

tow test cylinders. The location was also confirmed with

preliminary tests of circular cylinders in the tow tank.

The test specimens were kept open on bottom allowing the

water level on the inside and outside of the specimen to

be equal. The hydrostatic water pressure acting on the

outside of the test specimen varies because the change in

depth of the water. However, the pressure variation is

cancelled due to an equal and opposite hydrostatic water

pressure acting on the inside of the test specimen. By

cancelling the effect of the depth of the water on the

force acting on the test specimen, the hydrostatic

pressure does not have an effect on the resultant force.

29

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In designing the three-point attachment system, care

is exercised to make sure that no horizontal force is

transferred to the single load cell attachment joint. To

accomplish this, rod end bearings are placed on either

side of the load cell to isolate the load cell and make

that attachment incapable of resisting any horizontal

force. Provisions for handling the total horizontal force

on the test specimen are provided by the remaining two

attachment struts. These two struts are horizontally

rigid and are able to resist the total horizontal force

imparted on the test specimen during a test run.

For the load cell to sense the vertical force reac­

tion, the two rigid attachment struts must have the

ability to allow the attachment plate, to which the

specimen is attached, to rotate. As shown in Figure 3.5,

the rotation of the attachment plate transfers the

vertical reaction force to the load cell. This vertical

reaction force counteracts the moment caused by the

horizontal drag force. The required rotation of the

attachment plate is accomplished by placing a rod end

bearing at the point where each of the remaining two

attachment struts attach to the attachment plate.

The force that the load cell senses is transmitted

by an electrical cable to a Measurements Group Model 2310

signal conditioner/amplifier/filter. The filtering

[XraotVsn

4 * 1 1 i C i .

/ 1 ' ?q, Ti blnB

A • > V •'

^\.--r i >- ^y' \ I \ I \ v ^ <

' 1/2" Alum. Plots

,-— Attoohment Pkit» 4" CtiOTin*!

"— 1*9\ Sp*clrriM (24- Oot. ahowr.)

- — Spedmeri Frame 1 4 ' Q^arin«l

Comer Normol to Row

31

PLAN VIEW

AttooHment StruU

S ft--_ Rod End

»'T9W A - A

'-— SpAi2(tnan From*

.— T*at Sp«cim

Rc-d Erid

5p«ofm«i Fj'flrw*

SpMlman

—^^r

L-:jM"

Att'Mhrnant Stnjla

• Aliaehmwii

VTew B-B

ELEVATION VIEW

Figure 3.5. Attachment Plate Diagram,

32

ability of the instrument is not used; however, the

amplifier was needed to amplify the load cell signal. The

load cell's output signal has a rated magnitude of 3

millivolts per excitation voltage for a maximum load of

500 pounds. For example, typical loads recorded by the

load cell during this study had an upper range of ap­

proximately 100 pounds with an excitation voltage of 15

volts. The load cell under this condition produces an

output signal of 9 millivolts. This signal requires

amplification for use with the ±5.0 volts A/D converter.

The output signal from the load cell is amplified by a

factor of 100 to give a signal that can be accurately

resolved by the A/D converter.

The signal conditioning ability of the 2310 instru­

ment is also used. A zero balance circuit makes it

possible to null the zero offset caused by the static

hanging weight of the test specimen. This "new" zero

reading allows calculation of the drag coefficient

directly without having to compensate for the weight of

the test specimen. The amplified and conditioned load

cell output signal is sent to the Metrabyte Dash 16 analog

to digital converter which converts the analog load cell

signal to a signed 12-bit integer that can be processed by

the computer.

33

Data acquisition. The procedure for obtaining the

desired data follows a straight-forward sequence. Each

test specimen is mounted to the attachment plate which in

turn is attached, via the three-point support system, to

the carriage plate (see Figure 3.5). A computer program

called "cyldrag," developed and refined throughout the

study, is used to collect data during the tests.

The program asks for operator input of such variables as:

number of data samples per second, speed of test specimen

in feet per second, the magnitude of amplification used to

enhance the load cell output signal, and the inscribed

cylinder diameter of the specimen in inches.

To test a particular specimen and obtain all the

data desired, several steps are required. After the

specimen to be tested is mounted to the attachment plate,

the signal conditioner is reset to give a zero reading

while the specimen is stationary. Once this has been

accomplished, the computer program is started and the

desired test variables asked for by the program are input

into the computer. With the test specimen at the starting

position in the tow tank (at one end of the tow tank), the

program is engaged and the test begins. Using the input

variables, the program internally calculates the distance

the specimen will travel and sends an output signal to the

motor controller which controls the distance the motor

34

tows the specimen. The test specimen is accelerated up to

the desired speed by the computer and that speed is held

constant. The program collects data samples at the

specified number of samples per second while the test

specimen is being towed at the constant speed. As the

specimen reaches the end of the calculated distance to be

traveled, the computer stops collecting data, decelerates

the specimen and brings the specimen to a stop. The

program takes the data collected during the constant speed

section of the test run and calculates the drag coeffi­

cient for each data sample by using the following equa­

tion :

(F) Cc =

(0.5)(€)(V=)(A) (Eq.3.1)

where: F = drag force (lbs) Ccd = drag coefficient (dimension less) € = fluid density (slugs/ft^) V = velocity of specimen (ft/sec) A = projected area of specimen (ft=)

The calculation of the drag force (F) is also performed

within the program by taking the load cell output data in

voltages, converting it to load in pounds, and using

statics and the location of the forces to find the

horizontal drag force. The procedure described above is

referred to as a test run. The test run is repeated ten

times with the same test specimen at the same speed. The

program then performs one final calculation by determining

an average drag coefficient.

For this study, Reynolds number values covering a

range from 5x10^ to ^xJ^O^ are desired. By knowing the

Reynolds numbers at which drag coefficients are wanted,

the required velocities, to be input into the computer

program, are calculated using the following equation:

V = (Rr,) (M)

(D) ( ) (Eq.3.2)

where: Ro = Reynolds number (dimension less) M = coefficient of fluid viscosity

(Ib/ft-sec) D = specimen diameter (ft) e = fluid density (Ib/ff).

As mentioned earlier, the tow tank has a maximum velocity

of 4 feet per second. By varying the size and towing

speed of the test specimens, the desired Reynolds number

range from 5x10*^ to 7x10° is obtained.

Each drag coefficient data point is an average of

approximately 150 data samples recorded by the computer.

The large number of samples helps decrease the possibility

of error in the data due to small variations in experi­

ments. More than 15 data points with varying Reynolds

number are obtained for each of the test specimens.

Test specimens. One of the significant aspects of

this study is the use of actual manufacturer supplied

sections of support poles. The sections were supplied by

Falcon Steel in Fort Worth, Texas, and by Valmont

Industries in Valley, Nebraska. By using these sections,

drag coefficient values obtained in this study are as

close as possible to the drag coefficient values ex­

perienced in the field.

The test specimens received from support pole

manufacturers included both circular and octagonal shaped

sections. The circular cross-sections have diameters of

12 and 16 inches. The octagonal cross-sections are con­

structed of 3/16-ipch thick steel plates with diameters

(measured by the inscribed circle of the cylinder) of 9,

16, 24, and 30 inches. Figure 3.6 shows a cross-sectional

view of the octagonal cylinders and identifies the

inscribed circle of the cylinder along with corner radius

of the cylinder. Although most support poles are manufac­

tured with a slight taper along their lengths, the

specimens received for this project are not tapered. The

exterior surfaces of the octagonal cylinders had a gal­

vanized coating. The coating on the test specimens

provides the same surface roughness as that of the support

po les used in the field. Additional circular cylinders

were obtained from a pipe supplier. These circular

cylinders have diameters of 9, 18, and 36 inches. The

0)

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38

36-inch diameter cylinder was actually constructed of flat

plate rolled to a 36-inch diameter. All circular test

specimens are constructed of 1/8-inch thick steel with a

single coat of paint on the exterior surface.

All the test specimens obtained from the manufac­

turers were initially 5 feet long. Each specimen was cut

to 48.625 inches long for placement into the tow tank.

When the test specimens were attached to the attachment

plate, the gap between the bottom of the tank and the

bottom of the test specimen was less than 0.5 inch. The

clearance to the bottom of the tow tank is intentionally

held as small as possible to simulate two-dimensional flow

around the specimen.

The attachment of the test specimen to the attach­

ment plate is accomplished by mounting a 4-inch channel

"T" frame on the test specimen. Figure 3.7 shows the test

specimen standing vertically, with the "T" frame welded

into the top of the cross-section. Three holes drilled in

the "T" frame line up with holes drilled into the attach­

ment plate allowing the specimen to be bolted rigidly to

the attachment plate. This rigid attachment allows

transfer of the forces acting on the test specimen to the

attachment plate and subsequently to the load cell.

Although not important with the circular cylinder

tests, the ability to rotate the octagonal cylinders is

39

Figure 3.7. Test Specimen with "T" Frame Attachment

40

required to determine what effect the orientation of the

cylinder with respect to the fluid flow has on the drag

coefficient values. As would be expected, and verified by

James (1976), the orientation of the cylinder to the fluid

flow has a significant effect on the drag coefficient

values of octagonal cylinders. For this reason, and to

accommodate different size test specimens, the attachment

plate was provided with a series of holes designed to

allow different sizes of octagonal test specimens to be

rotated. Two orientations of the cylinders to the towing

direction, shown in Figure 3.8, were studied in this

project. The first orientation studied was where a flat

face of the octagonal cylinder was normal or perpendicular

to the towing direction of the cylinder. The second

orientation studied was where a corner of the octagonal

cylinder was normal to the towing direction of the cyl­

inder. These two orientations were selected because they

represented the extreme cases which produced the highest

drag coefficient values.

Flow Direction

Flow Direction

4 1

/

\ / \ _

Flat Face Normal to Flow Direotion

I

!

\

Corner Normal to Flow Direction

Figure 3.8. Octagonal Cylinder Orientation

CHAPTER IV

VERIFICATION OF EXPERIMENTAL PROCEDURE

As with most research projects, one of the critical

parts of this project was the verification of the experi­

mental procedure. At the beginning of the study, verifica­

tion of the procedure was not considered to be a difficult

task to accomplish. However, as the research progressed,

verification proved to be a "thorn in the side."

Circular cylinder results. The verification process

followed the same technique that has been used in previous

studies for verifying an experimental procedure for

obtaining drag coefficients of various cross-sectional

shapes. The process uses the drag coefficients obtained

for circular cylinders in previous experimental projects

as a reference for comparison with drag coefficient values

obtained using this study's experimental procedure. The

study of circular cylinder drag coefficients dates back to

the early 1900's and has available the most amount of data

documenting 2-D flow. It is for this reason that circular

cylinder drag coefficients are used as the reference of

comparison to verify new experimental drag measurement

procedures.

Several circular cylinders of different diameters

were tested and the drag coefficients measured. To

42

43

encompass the range of Reynolds numbers desired, cylinder

diameters of 9, 16, 18, and 36 inches were used. Initial­

ly, the project plan was to test the circular specimens by

towing them in the direction which would cause a tension

force in the load cell. Tension was preferred due to

concern about the possibility of slack in the joint

attachments. Any slack in the attachments on either side

of the load cell would be taken up by the weight of the

specimen before the test run would begin. If the direc­

tion of towing produced a compression force on the load

cell, slack in the joint attachments could have a detri­

mental effect on the force registered by the load cell.

As the study progressed, there proved to be a problem

which had not and could not have been foreseen.

The original attachment plate design, shown in

Figure 4.1, called for the two rigid attachment struts to

be separated from the single load cell attachment by 28

inches with the centerline of the test specimen at mid-

distance between the rigid and load cell joints. The

separation allowed an easy connection of the test specimen

to the attachment plate. Another reason for the 28 inch

separation between the rigid struts and the load cell

joi nt was that the distance from the attachment plate to

the line of action of the drag force was also 28 inches.

This meant that the load cell would be reading the actual

4 4

PLAN VIEW

C a r r i a g e Plate L (1 /2 ' Alum. Plaie)

Rigid Attachment Struts (2x2x1/4 Alum. Angle)

Attachment Plate ( 3 / 8 ' Alum. Plate)

Rod End Bearings^:- _» Load Cel l

9'

16'

24'

30'

ELEVATION VIEW

Figure 4.1. Original Attachment Plate Design.

45

drag force directly thereby eliminating a calculation of

the drag force from the load cell reading.

The tests on the circular cylinders began and drag

coefficients were recorded. Tests on all the different

cylinder diameters were made at the Reynolds number range

where a marked decrease in the drag coefficient had been

documented in previous studies. Figure 4.2 shows refer­

ence drag coefficients and the drag coefficients recorded

with the 9-inch and 18-inch diameter circular cylinders in

this experiment. The drag coefficients measured in this

experiment do not compare favorably with the reference

drag coefficients. Where the reference drag coefficients

would have values of 1.0 to 1.2 at Reynolds numbers less

than 1x10*, tests made during this experiment would

produce drag coefficients of 1.4 to 1.5. Where the

reference C^'s would have values of 0.3 to 0.4 at a

Reynolds number of approximately 3.5x10=^, this experi­

ment's tests would produce Cc's of 0.9 to 1.0. In other

words, drag coefficients in this experiment are consis­

tently higher than the drag coefficients reported in

previous studies.

Several theories were presented to try to explain

the discrepancies between the reference C^ values and the

Cej values of this experiment. With each theory, steps

were taken to try to correct the problem. For example, a

4 6

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nd

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ficie

nts

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CN •

QJ L 3 Oi

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D o a

Q M O O O O • • • • • — U — • d*- OtJ

47

theory of wave action inside the hollow cylinder due to

the cylinder's open bottom was considered. To eliminate

this problem, one of the test specimens had the bottom

opening sealed. To overcome the buoyancy of the specimen

when placed in the water, sand was added to give the

cylinder just enough weight to achieve neutral buoyancy.

However, when new tests were run on the modified cylinder,

there was no appreciable change in the drag coefficient

values of the cylinder.

After several theories were investigated and modifi­

cations made to the towing system and test specimens which

produced no change in the data recorded, the decision was

made to test the specimens with the load cell reading a

compressive force. Since the circular cylinder's drag

coefficient is not dependant on the orientation of the

cylinder to the fluid flow, the Cc* values for the tension

and compression tests should be equal. The tests were

conducted with the 18-inch diameter circular cylinder.

Figure 4.3 shows the drag coefficients for the 18-inch

circular cylinder plotted for the tests with the load cell

in tension and compression. The difference between the

drag coefficients obtained with the load cell reading in

tension and the values with the load cell reading in

compression are easily discernable and not within the

tolerance of experimental error. Drag coefficient values

4 8

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§ 2

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d o M

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d o »4

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QJ T3 C

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u •<-= QJ QD 0

V)

QJ L 3 CP

Q M O Q I O O •*•*««« U * « « d*- OX)

49

with the load cell in tension are consistently higher than

those values with the load cell in compression. This

could only mean that a vertical force was acting upon the

test specimen during the test runs. A downward force

acting on the specimen during the tension test run would

increase the load cell reading in tension thereby increas­

ing the registered drag coefficient for the cylinder. The

same downward force acting on the specimen during the

compression test run would decrease the load cell reading

in compression thereby decreasing the registered drag

coefficient for the cylinder. Figure 4.3 verifies this

theory.

Since the source of the vertical force acting on the

test specimen was not understood and could not be removed,

an effort was begun to eliminate the effect of a vertical

force acting on the test specimen during the test run. To

accomplish this task, a new attachment plate design was

developed as shown in Figure 4.4. The main difference

between the original attachment plate and the new attach­

ment plate design was the location of the rigid attachment

struts. The rigid struts were now located in line with

the centerline of the test specimens. By locating the

rigid struts in line with the centerline of the test

specimens, the vertical force did not have an effect on

50

Carr iage Plate

Rigid Allachmenl Struts

Attach men t Frame

(4' channel)

9'

Rod E Bean

•nd/F_

V 16'

\

V 24'

30'

12'

Load Cell

Figure 4.4. New Attachment Frame Design,

51

the load cell, if the action of that force was along the

specimen centerline.

Another difference between the two attachment plates

was the material used in their fabrication. The original

attachment plate had been fabricated out of 3/8-inch flat

aluminum plate. As the early tests of the project were

performed, the weakness of the aluminum plate to support

the larger specimens was noticeable. When the need for a

new design of the attachment plate arose, the new "plate"

was fabricated, not out of plate, but out of 4-inch

channel sections. The new attachment "plate" was now a

frame. The new attachment frame was constructed in a

square pattern with crossmembers, one spanning the length

and one the width, from one corner to the opposite corner

(see Figure 4.4).

To verify the elimination of the effect of the

vertical force on the drag coefficients by the use of the

new attachment plate design, tests were again performed

subjecting the load cell to both tension and compression

forces using the 9-inch and 16-inch diameter circular

cy linders. Figure 4.5 for the 9-inch and Figure 4.6 for

the 16-inch show the drag coefficients produced during

these tests. The differences between the drag coefficient

V alues produced during the tension test and the

52

0, B o o

o o d o

on 05 L

Q

L QJ

TD C

-I- "

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in

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53

o o o o o o

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+ d o

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cn 05 L

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= QJ >0 O -H U

QJ L 3

cn •H IL

o»«at> ooo*< on

54

compression test are well within the tolerance of the

experimental procedure and are therefore considered

acceptable.

In comparing the drag coefficient values obtained

for the 9-inch and 16-inch diameters circular cylinders to

the reference drag coefficient values for circular

cylinders from previous studies, a favorable agreement is

seen in Figure 4.7. Allowing for the differences in

surface roughness values between the cylinders and

freestream turbulence in the tests, the C^ values obtained

in this study not only fit the trend of the reference

data, but also matched, within experimental tolerances,

the C«3 values at the various Reynolds numbers tested. The

fit of the experimental data to the reference data,

considered to be good, provides the verification of this

study's experimental procedure.

5 5

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9"

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Coe

O »• d t» O o •«-i«<o« u*« • d * ' OtJ

CHAPTER V

OCTAGONAL CYLINDER RESULTS

The main objective of this study was to obtain drag

coefficients for octagonal cross-section cylinders used

for luminaire supports. To accomplish this objective,

several prerequisites had to be satisfied. As described

in Chapter 3, the first prerequisite completed was the

design of the test system used to tow the specimens. With

that being accomplished, effort could be turned toward the

verification of the experimental procedure as described in

Chapter 4. Finally, with the experimental procedure

verified, the main objective, obtaining drag coefficients

for octagonal cylinders, could be completed. This chapter

presents the results which were obtained along with an

explanation of some problems and their solutions as the

study progressed.

The octagonal cylinder tests were conducted follow­

ing the same procedures as used during the circular cylin­

der tests. There were, however, different concerns that

influenced the number of tests made with each cylinder.

Unlike the circular cylinder drag coefficient values, the

octagonal cylinder drag coefficient values depend upon the

orientation of the cylinder to the fluid flow. Another

56

57

influence on the drag coefficient values for the octagonal

cylinders is the corner radius ratio, as pointed out in

the study by James (1976). With these two concerns in

mind, the drag coefficient results of the octagonal

cylinders were obtained. They were compared to published

drag coefficient data for octagonal cylinders that most

closely matched the specimens used in this study.

The test specimens used for the octagonal tests were

actual manufacturer supplied sections of octagonal support

poles as used in the field. The four specimens each had

different diameters, as measured by the inscribed circle

of the cross-section, of 9, 16, 24, and 30 inches.

Different diameters were used to allow the tests to span a

Reynolds number range from 5x10^* to 7x10=*. Each cylinder

was tested in both towing directions where the load cell

registered in tension and compression. This procedure

allowed drag coefficients to be obtained during tests when

the load cell was in tension and compression. The tests

were conducted starting with the smallest cylinder and

ending with the largest cylinder.

Table 5.1 shows test parameters of the specimens.

The table shows the diameter, the test velocities cor—

re spending to the Reynolds number range, and the surface

roughness of that particular specimen

>*• «i \.>i.-...>.

58

TABLE 5.1

TEST SPECIMEN PARAMETERS

Parameters Specimen Diameter (inches)

16 24 30

Max. Test Velocity (ft/sec) 3.63

Min. Test Velocity (ft/sec) 0.83

Surface Roughness^ (inches) .006

3.26

0.57

.006

.72

0.54

.006

3.04

0.43

.006

^Values for galvanized surface ( Ingersol-Rand 1984)

Figure 5.1 shows the drag coefficient values

rec orded for the 9-inch octagonal cylinder. The drag

coefficient values for the flat face normal to the flow

range from a low of .97 to a high of 1.38 with a calcu­

lated average Cc over the complete range of Reynolds

numbers of 1.2. There also seems to be some dependence of

the C<d values upon Reynolds numbers starting at a Reynolds

number of 1.4x10®.

The drag coefficient values of the 9-inch cylinder

for the corner normal to the flow range from a low of 1.23

to a high of 1.58 with a calculated average Cc value over

the complete range of Reynolds numbers of 1.35 (see Figure

5.1). The drag coefficient values are more independent of

Reynolds number as demonstrated by a more constant drag

^f^.

5 9

o mm

a. o B

X

o

o mi,

M

d O

o 4-

cn 05 L

Q

L QJ TD C

u ^ in 15 -M

c c 0 QJ O* •'^ 05 U

U H-O 4-

QJ : 0 C> U

in

QJ L 3 cn •H li_

O »« o t> o o e^**-* u<^ • d** U-d

60

coefficient value throughout the Reynolds number range

tested. Also of interest is the increase in the drag

coefficient values for the corner orientation as compared

to the flat face orientation. This agrees with the

findings in the study by James (1976).

Drag coefficient values for the 16-inch octagonal

cylinders are shown in Figure 5.2. The drag coefficient

values range from a low of 1.06 to a high of 1.44 for the

flat face normal to the flow. The average drag coeffi­

cient value over the total range of Reynolds numbers is

1.30. There is evidence, similar to the 9-inch cylinder,

of a dependency of drag coefficient on the Reynolds

number.

The drag coefficients of the 16-inch specimen with a

corner normal to the flow direction range from a high of

1.59 to a low of 1.20 (see Figure 5.2). The average Cd

value over the Reynolds number test range is approximately

1.35. The drag coefficient values show less dependency on

the Reynolds number values.

The test of the 24-inch octagonal cylinder was

conducted with the drag coefficient results shown in

Figure 5.3. The Ccj values for the flat face normal to the

flow range from a high of 1.45 to a low of 1.10. The

average C^ value over the total range of Reynolds numbers

is 1.25. There seems to be less drag coefficient

6 1

O

fiu

O

B

X

I o

o o

+

CP 05

Q

V. QJ

13 C

u

15 in c -M 0 c • > Qj 15 H •M U U H

o •<-: QJ sQ O

CN

m

QJ

3

•H U .

Q t a Q Q l U O • « • * • * « U«« • d * - OXJ

6 2

o o 8 O o

d

o B

o d i PC

o

o

B p<

X

I O

d

o o

15 L

o L QJ

TD C

u

05 C 0 CP 15 4J U O

: <t CN

in • ^

c QJ •H

u •H 4 -<•-QJ 0 U

in

QJ i -3 CD» •H

O o o

Q * * d t > O O •«•«<•« u<-« A d * - OtJ

0 ^

63

dependency on Reynolds number than exhibited in the

smaller octagonal cylinders in the flat face orientation.

Drag coefficient results for the 24-inch specimen

with a corner normal to the flow direction range from a

high of 1.74 to a low of 1.28 (see Figure 5.3) with a

calculated average Ca value over the complete range of

Reynolds numbers of 1.50. The data collected has more

scatter with no definite trend or pattern visible. The

drag coefficient values show no dependency of C^ on

Reynolds number.

The 30-inch octagonal cylinder drag coefficient

results are shown in Figure 5.4. The Cd values for a flat

face normal to the flow range from a low of 1.02 to a high

of 1.61. The average C^ value over the complete Reynolds

number range is 1.30. The data shows more scatter than

previous tests with no trend or pattern visible. Drag

coefficient dependency on Reynolds number is not apparent

with these tests.

The drag coefficients obtained for the 30-inch

specimen with an orientation of a corner normal to the

flow range from a low of 1.40 to a high of 2.25. The

average Ca value over the total Reynolds number range of

the test is 1.77. The drag coefficient data obtained in

this test also exhibits more dependence upon the Reynolds

number.

6 4

o o 8 o o

d

*m

o d

o a. o

B

X

g BU

o

d u O U

+

cn 15 L

Q L QJ

TD C

•H

05 in c +J 0 c CP QJ 05 - H

•M U U - H

O f -

: QJ O O K) U

in

Qj L 3

o o o o

Q * « d t > O o •<»««-i<« u«« • d * - OTJ

65

Table 5.2 gives a summary of the drag coefficients

obtained for the octagonal cylinders tested in this study.

The table also shows the Reynolds number range over which

each specimen was tested along with corner radius ratio

and calculated average C^ value.

TABLE 5.2

TEST RESULTS

Data Specimen Diameter (inches)

16 24 30

Max . R,., 2.4x10=^ 4.0x10' 5.0x10' 7.0xl0»

Min. Rr, 5.0x10* 7.0x10* 1.0x10' 1.0x10=

Corner Radius Ratio C/.)^ 44 25 13 11

Specimen A Orientation

B A B B B

Max . C< 1.38 1.58 1.44 1.59 1.45 1.74 1.61 2.25

Min. C< 0.97 1.23 1.06 1.20 1.10 1.28 1.02 1.40

Avg . C< 1.20 1.35 1.30 1.35 1.25 1.50 1.30 1.77

A. Flow Directed at Flat Face of Specimen B. Flow Directed at Corner of Specimen ^Ratio of corner radius to inscribed circle radius of

specimen.

The overall drag coefficient value for the octagonal

shape specimen was higher than the C^ values for circular

shape. For each size of octagonal test specimen, the drag

coefficient values were consistently higher for the

specimen orientation of a corner normal to the flow

66

direction than for the flat face normal to flow direction.

As the size of the test specimen increased, the scatter of

the data also increased. The increased scatter was caused

by not being able to completely achieve a steady state of

fluid flow around the larger diameter cylinders. With the

smaller diameter cylinders, the size of the tow tank

allowed a constant speed test distance between 25 and 30

diameters. These distances allowed the fluid flow around

the cylinder to reach a steady state flow. However, with

the larger cylinders, the test distance translated to

between 10 to 12 diameters. The fluid flow around the

cylinder did not reach a steady state flow during every

test run. The lack of a steady state flow resulted in the

increased scatter of the data collected.

Comparison of Results. To try to better understand

the results obtained in this study. Figures 5.5 and 5.6

show results of this study, results from a previous study

by James (1976), and the values recommended by AASHTO.

Figures 5.5 and 5.6 show the drag coefficient values for

octagonal cylinders with a flat face normal to the flow

and a corner normal to the flow, respectively. As can be

seen in the graphs, the majority of drag coefficient

values obtained in this study lie above the AASHTO

recommended value of 1.20. Average of the experimentally

measured values of C^ is approximately 25*/. higher than the

6 7

O o o o o o

0000

o

^^ d « ^^

*m • A B p

M t ) o d • •

m^ K

N • tJ d

m0 mm

•

u • ^ c«

D

•4

• t l d

0 • «

+

>•

Stn

d

•

a d ^

0

in 4J

c QJ • H

u •H -•- 2 «H 0

0 L. U

0 CP -P 15 i_ ^ 0 15

E

QJ 0 T3 Z c

Cy

li

Fa

ce

r^ 4J 05 15 C ^ 0 Li. CP 05 r

U -H 0 2

•

c 0

4J

u QJ

Dir

- • >•

« o

in •

in

QJ L 3 cn •H LL

O

o

Q »« d t» U O •*«*<'-« u«« • d * - OtJ

6 8

O o o o o o

000

o o

o o o o

d « x.^

•

B p 2 M

tJ 0 d

i «

• 00%

>i o ^

u O k

•^ Ct

D

mm

>•

o

o •

+

•^ >•

o • • u o « <h

m

>* n p

M • a d

<3

r ^

>•

o *m

u o % O «

X

in c -M 0 C H Qt -P H U U QJ •H L

"H Q QJ 0 2 U 0

cnu. 05 u 0 Q -P

L ^ Qj 05 TD E C i .

Cy

li

er

No

— C 05 L C 0 0 U CP 05 IZ -P -P

ure

5

.6.

Oc w

i

O' • H

l i .

Q M Q O O O •<>««•«« U « « 9 0 « . O t J

69

value recommended by AASHTO. The cumulative results in

Figures 5.3 and 5.4 also show that there is little

dependence of Cd values on the Reynolds number.

CHAPTER VI

CONCLUSIONS AND RECOMMENDATIONS

The results of this research project have provided

additional information that can be useful for the design

of octagonal luminaire supports. The research has also

demonstrated the ability of tow tank experimental proce­

dures to produce drag coefficient values for circular

cylinders that agree with drag coefficient values produced

using wind tunnel procedures. This agreement between the

Cd values for the tow tank procedure and the Cd values for

the wind tunnel procedure open new doors for the testing

of structural shapes that previously might have been

limited to the wind tunnel.

Information, both of interest and importance,

gathered during this project have been used to develop the

following conclusions:

1. The tow tank experimental procedure can be

a viable and effective procedure for

determining drag coefficients for luminaire

poles.

2. Flow normal to a corner of the octagonal

cylinder produced drag coefficient values

of 107. to 207. higher than that for flow

normal to a flat face.

70

71

3. Drag coefficient values for octagonal

shapes did not exhibit dependency on the

Reynolds number as shown in previous

studies. The drag coefficients remained in

the range of 1.2 to 1.7 over the range of

Reynolds numbers of from 5x10* to 7x10=^.

4. The corner radius ratio in the range of 11

to 44 percent did not have an effect on the

drag coefficient values obtained.

5. For the octagonal cylinders tested with the

corner normal to flow direction orienta­

tion, the drag coefficient had an average

value of 1.5. This value is 25"/. higher

than the one recommended in the current

AASHTO standard.

During the course of this project, several recommen­

dations were formulated which would have a beneficial

effect on the future research. These recommendations are

based on many hours of work on this project by the author.

The recommendations are as follows:

1. The use of pressure measurements along and

around the cylinder would provide addition­

al data to be used to calculate drag

coefficients to compare to existing values.

72

The tow tank enhances the ability for flow

visualization. Flow visualization could be

accomplished with injection of dye into the

flow and would greatly increase the under­

standing of flow around various structural

support shapes.

With several of the towing speeds used

during this project, the tow tank length

limited the length of the test run. With a

new, longer tow tank in the final stages at

Texas Tech, the effect of the limited test

run on the data collected could be elimi­

nated .

Provisions should be made for a system to

dampen the wave action of the water surface

of the tow tank. Having to wait for the

water surface to calm between test runs

added considerable time to the total

research project.

^^xw-

REFERENCES

!• AASHTO Subcommittee on Bridges and Structures, "Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals," Washington, D.C., 1975.

2. Achenbach, E., "Distribution of Local Pressure and Skin Friction around a Circular Cylinder in Cross-flow up to Re = 5x10-^," J. Fluid Mech. . Vol. 34, pp. 625-640, 1968.

3. Achenbach, E., "Influence of Surface Roughness on the Cross-flow around a Circular Cylinder," J. Fluid Mech.. Vol. 46, part 2, pp. 321-335, 1971.

4. Allen, H.J. and Vincenti, W.G., "Wall Interference in a Two-dimensional-flow Wind Tunnel, with Consideration of the Effect of Compressibility," National Aeronautics and Space Administration, Washington, D.C., Tech. Report, NACA TR 782, 1944.

5. Almosnino, D. and McAlister, K.W., "Water Tunnel Study of Transition Flow around Circular Cylinders," Ames Research Center, National Aeronautics and Space Administration, Moffett Field, California, 1984.

6. Bearman, P.W., "The Flow around a Circular Cylinder in the Critical Reynolds Number Regime," NPL Aero Report 1257, 1968.

7. Page, A. and Warsap, J.H., "The Effects of Turbulence and Surface Roughness on the Drag of a Circular Cylinder," Aeronautic Research Committee, London, England, Report and Memo., ARC R&M 1283, 1930.

8. Fox, R.W. and McDonald, A.T., Introduction to Fluid Mechanics. John Wiley and Sons, pg. 463, 1985.

9. Glauert, H., "Wind Tunnel Interference on Wings, Bodies, and Airscrews," Aeronautic Research Committee, London, England, Report and Memo., ARC R&M 1566, 1933.

/i.*.:

74

10. Ingersol1-Rand Company, Cameron Hydraulic Hand­book . Sixteenth Edition, Third Printing, Wood-cliff Lake, N.J., pg. 3-5, 1984.11.

11. James, W.D., "Effects of Reynolds number and Corner Radius on Two-dimensional Flow around Octagonal, Dodecagonal, and Hexdecagonal Cylinders," Engineering Research Institute, Iowa State University, 1976.

12. Jorgensen, L.H., "Prediction of Static Aerodyna­mic Characteristics for Slender Bodies alone and with Lifting Surfaces to very high Angles of Attack," National Aeronautics and Space Adminis­tration, Washington, D.C., Tech. Memo., NASA TMX-73, 123, June 1976.

13. Maskell, E.C., "A Theory of the Blockage Effects on Bluff Bodies and Stalled Wings in a Closed Wind Tunnel," Aeronautical Research Council, Ministry of Aviation, London, England, Report and Memo., ARC R&M 3400, 1963.

14. Roshko, A., "Experiments on the Flow past a Circular Cylinder at a very high Reynolds Number," J . Fluid Mech., Vol. 10, pp. 345-356, 1961.

15. Schewe, G., "On the Force Fluctuations Acting on a Circular Cylinder in Cross-flow from Sub-critical up to Transcritical Reynolds Numbers," J. Fluid Mech.. Vol. 133, pp. 265-285, 1983.

16. Taylor, G.J., "Pressure Distribution around a Cylinder," Tech. Report, Advisor Committee for Aeronamities, 1915.

17. Von Karman, Th. and Rubach, H., "Uber den Mechanismus des Flussigkeits- und Luftwider-standes," Phys. Zeitschrift XIII, 1912.

APPENDIX

Note: All graphs show tension values only.

Figure 4.7 Raw Data

9" Dia. 9" Dia. 16" Dia. 16" Dia Reynolds Cir.Cyl. Cir.Cyl. Cir.Cyl. Cir.Cyl Number Tension Compress. Tension Compres<

5.0x10=^ 0.88 6.0x10=^ 1_^ 1 .04 7.0x10=^ 0.95 1.02 0.80 0.89 8.0x10=^ 0.96 0.98 9 . 0 x 1 0 = 1 .0x10 '^ 1 . 2 x 1 0 * 1 . 6 x 1 0 * 2 . 0 x 1 0 * 2 . 2 x 1 0 * 2 . 4 x 1 0 * 2 . 6 x 1 0 * 2 . 8 x 1 0 * 3 . 0 x 1 0 * 3 . 2 x 1 0 * 3 . 4 x 1 0 *

0 . 9 6 0 . 9 2 0 . 8 9 0 . 6 8 0 . 5 1

0 . 5 6

0 . 9 5 1 .00 0 . 9 5 0 . 7 7 0 . 4 9

0 . 5 9

0 . 7 3

0 . 7 8 0 . 7 2 0 . 6 3 0 . 5 9 0 . 5 8 0 . 6 0 0 . 6 0 0 . 6 4 0 . 6 4

0 . 7 8

0 . 7 2 0 . 5 8 0 . 5 6 0 . 5 6 0 . 5 4 0 . 5 4 0 . 5 9 0 . 6 2 0 . 6 3

3.8x10* 0.67 0.66 4.2x10* 0.68 0.71

Figure 5.1 Raw Data

Corner to Flow Flat to Flow 9" Dia. 9" Dia. 9" Dia. 9" Dia.

Reynolds Oct.Cyl. Oct.Cyl. Oct.Cyl. Oct.Cyl. Number Tension Compress. Tension Compress

5.0x10= 1.58 1.57 1.13 Q.s_97 6.0x10= 1.35 1.40 1.20 1-20 7.0x10= 1.54 1.48 1.21 1-20 9.0x10= 1.32 1.49 1.37 LLII 9.0x10= 1.54 1.41 1.30 LJAI l.OxlO*^ 1.47 1.44 1.26 1-16 1.2x10* 1.33 1.44 1.27 1-24 1^.4x10* 1.27 1.34 1-33 1.33 1.6x10* 1.26 1.27 1.39 1-36 1_.8xl0< 1.23 1.47 1.34 1-28 g.OxlO* 1.22 1.24 1.24 1-22 2.2x10* 1.20 1.27 1.17 1.16 2.4x10* 1.23 1.30 1.08 1.06

75

Figure 5.2 Raw Data

76

Reynold' Number

Corner to Flow 16" Dia. 16" Dia. Oct.Cyl. Oct.Cyl. Tension Compress

Flat to Flow 16" Dia. Oct.Cyl. Tension

16" Dia. Oct.Cyl. Compress

7.0x10= 8.0x10= 9.0x10= 1.0x10' 1.2x10*

1.50 1 .45 1.59 1.34 1 .45

Figure 5.3 Raw Data

1 .56 1.45 1.48 1.57 1.47

1.23 1.14 1.31 1.36 1.31

1.26 1.36 1.24 1.18 1.21

1 .4x10* 1 .6x10* 1.8x10* 2.0x10* 2.2x10* 2.4x10* 2.6x10* 2.8x10* 3.0x10* 3.2x10* 3.6x10* 4.0x10*

1.40 1.30 1.32 1.26 1.24 1.31 1.42 1.22 1.29 1.32 1.29 1.20

1.42 1.28 1.25 1.22 1.35 1.34 1.30 1.26 1 .24 1.25 1 .29 1 .23

1.29 1.37 1.36 1.44 1.40 1.33 1.34 1.32 1.24 1.21 1. 16 1.06

1.30 1.36 1.41 1.40 1.42 1.43 1.39 1.34 1.27 1.27 1.22 1.14

Reynolds Number

Corner to Flow 24" Dia. 24" Dia. Oct.Cyl. Oct.Cyl. Tension Compress

Flat to Flow 24" Dia. Oct.Cyl. Tension

24" Dia Oct.Cyl Compres'

1.0x10* 1.2x10* 1.4x10* 1.6x10* 1.8x10* 2.0x10* 2.2x10^ 2.4x10* 2.6x10* 2.8x10* 3.0x10* ^.4x10* 4.0x10* 4.4x10^ f5.0xlO*

1.49 1.57 1.51 1.42 1.67 1.46 1.45 1.34 1.45 1 .56 1.74 1 .44 1 .38 1.33

1.50 1.29 1.52 1.45 1.52 1.68 1.81 1.57 1.43 1.65 1.49 1.36 1.49 1.38

1.37 1.43 1.21 1.39 1.45 1.22 1.40 1.36 1.39 1.28 1.37 1.30 1.17 1.27 1.15

1.28

1.24 1.31 1.43 1.28 1.27 1.34 1.26 1.24 1.28 1.23 1.23 1.23 1.10

Figure 5.4 Raw Data

77

Reynolds Number

Corner to Flow 30" Dia. 30" Dia. Oct.Cyl. Oct.Cyl. Tension Compress

Flat to Flow 30" Dia. 30" Dia. Oct.Cyl. Oct.Cyl. Tension Compress

1.0x10* 1 .2x10* 1.4x10* 1.6x10* 1.8x10* 2.0x10* 2.2x10* 2.4x10* 2.6x10* 2.8x10* 3.0x10* 3.4x10* 4.0x10* 4.4x10* 5.0x10^' 6.0x10* 7.0x10*

1 .66 1.73 1.41 1 .95 1.92 1.92 1.99 2.04 1.96 1 .84 1.74 1.57 1.57 1.57 1.49 1 .53 1 .49

1.88 1.73 2.26 1 .97 1 .98 1 .81 1.87 2.14 1.88 2.04 1.71 1.73 1.93 1.50 1.56 1 .54 1 .60

1.20 1.33 1.12 1.27 1.61 1.52 1.41 1.38 1.39 1.45 1.55 1.37 1.28 1.33 1.40 1.39 1 .31

1.44 1.34 1.03 1.26 1.27 1.20 1.21 1.34 1.13 1.15 1.34 1.18 1.27 1.36 1.28 1.20 1.20

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