Scholars' Mine

Masters Theses Student Research & Creative Works

1966

A study of modified plug designs for a globe valveRobert W. Wagner

Follow this and additional works at: http://scholarsmine.mst.edu/masters_thesesDepartment: Mechanical and Aerospace Engineering

This Thesis - Open Access is brought to you for free and open access by the Student Research & Creative Works at Scholars' Mine. It has been acceptedfor inclusion in Masters Theses by an authorized administrator of Scholars' Mine. For more information, please contact weaverjr@mst.edu.

Recommended CitationWagner, Robert W., "A study of modified plug designs for a globe valve" (1966). Masters Theses. Paper 5724.

A STUDY OF MODIFIED

PLUG DESIGNS

FOR

A GLOBE VALVE

BY

ROBERT W. WAGNER

A

THESIS

submitted to the faculty of the

UNIVERSITY OF MISSOURI AT ROLLA

in partial fulfillment of the vork required tor the

Degree ot

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

Rolla Misaouri

1966

Approved by

ii

ABSTRACT

This thesis presents an empirical study of the charac-

teristics of a cylindrical skirted disk valve used as a

flow regulating device. Holes were drilled in two separate

removable cylinders, which, when respectively attached to

the valve plug adapter, provided control of the flow rate.

These cylinders could be moved to permit exposure of more

or less flow area by means of the valve stem and crank

mechanism. At the closed position of the valve no holes

were available for flow within the differential pressure

zone of the valve, while at the full-open position all the

drilled holes were within the flow zone of the valve, per-

mitting maximum water flow rate.

The method used in adding the holes to the cylinders

was "cut and try" because the desired flow rate was already

determined before any holes were drilled. In other words,

holes were drilled until the desired flow rate was achieved.

The flow rate through each cylinder was established

at several cylinder positions by means of the weir trough

measuring device. This relationship was used to determine

the valve characteristic. The valve characteristic is

merely a graphical comparison of the flow rate through the

valve versus the percent valve opening.

A second set of curves was plotted to find the rela-

tionship between the flow rate and the exposed flow area

iii

for each cylinder to establish a possible design criterion.

The cylindrical skirted disk plug exhibits a new and

accurate approach to fluid flow control. The results of

this study indicate that the experimental procedure pur-

sued can be used to obtain desired valve characteristics.

iv

ACKNOWLEDGEMENT

The author wishes to express his appreciation to Pro-

fessor Archie Culp, Associate Professor of Mechanical Engi-

neering, University of Missouri at Rolla, whose suggestions

and guidance made this thesis possible.

Thanks are also extended to the engineering staff of

the Crane Company of Chicago, Illinois, especially Mr. T.

A. Rodda, Engineering Project Supervisor, for sup,gestions and correspondence throughout this investigation.

Finally, appreciation is due my fellow graduate assis-

tants, Mr. Donald Land 1 Mr. Michael Reyburn, Mr. Stephen

Thompson, and Mr. Gary Hinz for their assistance and en-

couragement during the course of this investigation.

v

TABLE OF CONTENTS

Page

ABSTRACT ii

ACKNOWLEDGEMENT iv

LIST OF TABLES vi

LIST OF FIGURES vii

I. INTRODUCTION. 1

II. REVIEW OF LITERATURE. 3

III. DISCUSSION. 5

DESCRIPTION OF APPARATUS. 6

Equipment De sign. 6 Water Supply System 11 Measuring Devices 11

DESIGN ANALYSIS AND PROCEDURE 14

EXPERIMENTAL PROCEDURE. 16

First Test Set-up .. 16 Second Test Set-up. 17 Test Procedure. 17

WEIR AND ORIFICE THEORY . 19

RESULTS 23

IV. CONCLUSIONS 28

v. RECOMMENDATIONS 29

VI. BIBLIOGRAPHY. 31

VII. VITA. 32

VIII. APPENDIX. 33

LIST OF TABLES

Table Page

l

2

3

(Note: these tables are in Appendix)

WEIR CALIBRATION

DATA COLLECTED ON THE LINEAR FLOW PLUG TEST

DATA COLLECTED ON THE LINEAR HEAD PLUG TEST

34

34

35

vi

LIST OF FIGURES

Figure

1

2

3

4

5

6

7

ASSEMBLED VALVE . . . . . . . . . . VALVE TEST SECTION

CYLINDER AND STUD MOUNTED ON THE VALVE CRANK MECHANISM

VALVE SEAL COMPONENTS . .

OVERALL VIEW OF TEST EQUIPMENT.

V-NOTCH WEIR

e

ORIFICE . .

(Note: The remaining figures are in Appendix)

8 VALVE CHARACTERISTIC FOR THE LINEAR FLOW VALVE

vii

Page

5

6

8

10

12

19

22

PLUG. 36

9 HEAD VERSUS PERCENT VALVE OPENING FOR THE LINEAR HEAD VALVE PLUG 37

10 RELATIONSHIP BETWEEN AREA CHANGE AND VALVE PLUG POSITION CHANGE FOR THE LINEAR FLOW PLUG. 38

11 RELATIONSHIP BETWEEN AREA CHANGE AND VALVE PLUG POSITION CHANGE FOR THE LINEAR HEAD PLUG. 39

12 RELATIONSHIP BETWEEN AREA CHANGE AND FLOW RATE

13

14

CHANGE FOR THE LINEAR FLOW VALVE PLUG . . 40

RELATIONSHIP BETWEEN AREA CHANGE AND FLOW RATE CHANGE FOR THE LINEAR HEAD VALVE PLUG

COMPARISON OF YARNALL'S FLOW EQUATION AND THE ORIFICE EQUATION FOR THE LINEAR FLOW PLUG

41

42

15 COMPARISON OF YARNALL'S FLOW EQUATION AND THE

16

ORIFICE EQUATION FOR THB LINEAR HEAD PLUG 42 WEIR FLOW EQUATION FLOw RATE VERSUS ACTUAL FLOW RATE (WEIGHED) 43

1

I. INTRODUCTION

There are two basic functions of a valve in a fluid flow

system. These are; regulation of flow rate or regulation

of pressure. The type of regulation studied in this inves-

tigation was the flow rate through a modified globe valve.

Specifically, the flow rate of water was evaluated both

experimentally and analytically.

There are countless uses of flow control or throttling

valves. Hydraulic systems, oil transmission lines, and city

water supply systems represent a partial list of applications.

The use of throttling valves is as common as regulating

your shower or controlling the sprinkler for your lawn.

A continuing study of plug designs for globe valves

has been made in order to produce desired valve character-

istics. Again, the characteristic of a valve is a plot of

the flow rate versus percent opening of the valve. A basic

problem encountered in designs using cylindrical plugs is

that of sealing the area between the cylinder and the seat

in order to constrain the flow to the configurations machined

in the wall of the cylinder.

The primary objective of this investigation, therefore, was to design a cylindrical skirt plug for a globe valve

with a positive seal at the valve seat. Two valve plug

configurations were tested in an attempt to achieve the pre-

determined valve characteristics. A secondary objective

of this investigation was to try to establish a more deli-

berate design procedure for programming the valve charac-

teristic.

2

II. REVIEW OF LITERATURE

The study of control valves dates back over one hun-

dred years. Since then butterfly valves, plug valves, gate

valves, globe valves, and others too. numerous to mention

have been investigated and modified to fit almost every

flow requirement. Therefore, to maintain conciseness, this

3

review will be limited to the globe valve and its derivatives.

Before 1900, piston type globe valves were already in

use in the steam engines of railroads and ships. Seely

and Talbot (1) conducted experiments with globe valves in

1918, for the purpose of correlating the head loss within

small globe valves with various valve openings. The prin-

ciple contribution of Seely and Talbot's study was the fact

that the head loss depended primarily upon the shape of

the exit passage of the valve. Their conclusion that head

loss in a valve varied directly with the square of the flow

velocity has proved to be a very useful tool in hydraulic

studies. Lansford (2), in a later study of globe valves, verified these results.

In his treatise on hydraulics, Addison (3) disclosed

that although losses within globe valves ware rather large,

such valves made excellent flow regulators. Rhodes (4), in 19~1, suggested several types of ported plug designs to

achieve desired valve characteristics. One was solid disk

with a symmetrical parabolic cross section designed to

produce a parabolic flow relationship with percent of valve

lift. He also mentioned the V-ported plug valve which pro-

duced a similar parabolic flow characteristic because of

the mathematical relationship between the area and the al-

titude of a triangle. However, Rhodes' most significant

statement in relation to this study was: "Where greater

accuracy is required than will result from the use of the

simple triangular shaped orifice, the plug is made with a

series of small orifices of different shapes so designed

as to give a total flow at any time exactly equivalent to

that needed for perfect control."

Beard (5) completed a thorough investigation of V-port and parabolic plug designs in 1957. His emphasis of valve

rangeability, "the ratio of maximum to minimum flow over

which the usable flow characteristic exists," is something

every valve designer must bear in mind.

4

III. DISCUSSION

The discussion is divided into two primary sections:

the first subdivision is concerned with the equipment re-

quirements and experimental procedure, and the second eub-

division is concerned with analysis of the experimental re-

sults. In addition, a section on experimental apparatus

discusses the purpose and capability of each piece of

equipment.

A section covering design analysis and experimental

procedure dwells on the methods used in designing the flow

PLUG ATTACHMENT

C.RANK AND STEM MECHANISM

DETACHABLE CYLINDER

FIGURE l ASSEMBLED VALVE

5

6

c~ntrolling device. and the procedure used in conducting

the- tests on the complete valve. The remainder of the dis-

cussion tabulates and evaluates the experimental results

w~th known weir and orifice theory in order to establish

a mathematical r .elationship that .can . be used in future de-

sign procedueea~ .

DESCRIPTION OF APPARATUS

EQuipment Design - A-major portion of this research was con-cerned with the diign of a valve with a cylindrical skirt

plug. For convenience. it was decided that the valve plug

J'IGU~l; 2 ~~VE ~E~T ~ECTiON

would be fabricated to fit in an existing 3-inch diameter

Crane globe valve, since this commercial valve was already

installed in a pump test loop in the Mechanical Engineering

Laboratory. The Crane valve stem, plug assembly, and seat

were removed from the body and the plug was modified. The

cylindrical skirt plug illustrated in Figures 1 and 3 was

then installed in place of the plug and seat of the former

valve. The seat of the new valve was machined to the same

thread pitch and pitch diameter of the original Crane seat

since it had to fit the threaded holder within the valve

body.

7

The modified valve seal contained three component parts;

the seat, the plug adapter, and the cylindrical skirt plug.

All three were machined from aluminum round stock. The

purpose of the seat was to provide a machined surface upon

which the valve would seal in the closed position. In or-

der to prevent water flow by the housing, a rubber seal,

which will be described later in the discussion, was in-

stalled. The plug adapter serves as a connection between

the cranking mechanism, the stem, and the actual flow con-

trolling device- the cylindrical skirt plug. The purpose

of using detachable cylinders was to reduce the machining

time in case a cylinder had to be scrapped during the

test period.

The main difficulty associated with modification of

the valve was concerned with finding a method to seal the

8

valve from leaks while under fluid pressure. Close atten-

tion was given to the means of sealing the gap between the

outside diameter of the cylindrical skirt plug and the

inside diameter of the seat. This task was accomplished

by the use of a butyl ORing which was flexible enough to allow relati~e mo~ion between the cylinder and the seat.

In order to keep the diameter of the valve as close to 3 .., : ,. ,, I

inches as possible the outside diameter of the cylinder was ... !

set at 3.000 + .005 inches and a suitable 0-Ring was chosen ..... ... . . ( ~

..

to dynamically seal the cylinder. A # 337 Precision 0-Ring . '

was used. To insure a positive seal on the inside diameter

FlGURE 3 C LillD1!~ AND STUD MOUNTEb ON

THE VALVE CRANK MECHANISM

of the 0-Rinr,, a .025 inch diametral squeeze was recommend-

ed by the manufacturer. Since the inside diameter of the

0-Ring was 2.975 inches, an adequate seal was obtained for

pressure differentials up to 500 psi accordin~ to the

manufacturer's specifications.

q

After the outside diameter of the cylinder was deter-

mined, the inside diameter of the seat was bored to allow

the cylinder to pass through with no interference or scar-

ring. At that time the slot tor containing the O-Rin~ was

bored as close to the leading edge of the seat as possible

to prevent appreciable flow interference by the seat it-

self upon opening the valve. A 45 chamfer was then turned

on the leading edge of the seat to mate with the ~5 bevel

on the plug adapter at the full-closed position of the

valve.

One of the principal machining problems was that of

maintaining the concentricity of the moving parts to in-

sure that the cylinder would not bind or cock as the valve

was opened or reclosed. To prevent this from occurring,

the cylinders were all initially bored to 2.750 inches,

faced and threaded at one end to fit the plug assembly.

The cylinders were then screwed on the plug and turned

down to the specified 3.000 inch outside diameter. This

operation kept the cylinder concentric with the drive

stem. As a final means to prevent binding and cocking,

the drive stem was connected to the plug in such a way as

10

to a.a..low only a "push" or '.'pulil" force to be transferred

to the plug. Hence, the cylinder and plug assembly was

eonfJtrained to move only in,, horizontal translation removing

the possibility that the cylinder would unserew from the

p.).l,ig duri~g st,~ - movement . Figure 3 shows the component par~ of th~ -V8lX' c seal; the _s,a1f, the detachable cylinders,

and the plug . a.dapter.

The .. ctuJ. mechanicf. of the valve is simple. The con-

t ~oll~d va.;c :J:able, v e.ter., _passes t hrough tbe inside of the

cylinder :rrom the hi gh p ressur e side of the valve to the

FIGURE ~ VALVE SEAL COMPONENTS

11

low pressure si de-throus;rh whatever openinr: it "sees" in the

cylinder wall. For water to flow, however, the openinps

must appear beyond the 0-Ring on the low pressure side o~

the seat. It is apparent here that the 0-Ring divides the

high and low pressure sides of the valve. The openin~s

mentioned above are discussed later in this thesis.

Water Supply System - The test set-up shown in Figure 5 was

used in all the tests performed on the valve. The pumn used

was an Aurora centrifugal pump mechanically driven by a

General Electric d-e motor. The pump capacity was 200 ~al

lons per minute and it was already connected in the test

set-up.

The suction side of the pump is connected to a sump

below the lab floor, and the discharge side is connected

to the valve where it empties into the weir trou gh. Upon

leaving the tank, the water flows back into the sump to

complete the circulation process. The piping from the

pump to the valve has a nominal 3-inch inside diameter

which is the same diameter as the pipe at the valve outlet.

The pipe and valve extending above the test valve seen in

the over-all test set-up figure is used for another labora-

tory experiment and was shut off during these tests.

Measuring Devices - Only two pressure gau~es were used in

the experiment and both were used in conjunction with the pump to indicate the pump suction and discharge pressures.

The gauge on the suction side vas a u.s. Gauge with a range

13

weir was actually calibrated for several flow rates by col-

lecting the water for a period of one to two minutes, de-

pending upon the ma~nitude of the head, and weighin~ the

amount collected. A comparison of the calculated flow r~te

obtained from the weir equation and the actual weighed flow

per second is illustrated in Figure 16. The curve indicates

that the weir equation flow rate was nearly equal to the

actual flow rate- the maxirr.um error being about 5%.

The hook gauge mentioned in the previous paragraph was

calibrated in inches. The vernier fixed to the frame of

the gauge allowed the head to be measured to 0.01 inch with

good accuracy. To enhance the accuracy of reading the

head, flow straighteners were placed ahead of the hook

gauge in the flow stream, thereby reducing oscillations

within the measuring tube. Also, to remove the effects of

approach from the head measurement, the ~auge was nlaced

several feet ahead of the weir. The phenomenon of adhesion

of the water to the side of the glass measuring tube was

compensated for by placing the point of the hook one-half

the distance from the center of the cross section to the

wall; i.e., an average reading was taken. During the act-

ual test of the valves, the hook gauge was found to pro-

duce inconsistent results because of a vacuum above the

water level in the hook gauge. The inconsistency was re-

moved by drilling a hole through the top of the instrument

to provide venting.

The actual procedure for locatin~ the water level in

the hook gauge was sicple. The viewer had to merely watch

the mirror image of the hook, while stationed below the

water level, until the actual hook and the mirror image

touched each other. All head readings on the weir had to

be corrected to zero because the actual zero head readin r

was 8.57 inches on the hook gauge. This zero reading was

determined by means of a hydraulic level.

DESIGN ANALYSIS AND PROCEDURE

Valve design is generally concerned with achieving a

desired valve characteristic which is important from the

standpoint of control of fluid flow. This characteristic

is the variation of flow with the change of valve opening.

The valves designed for this study were developed using

two predetermined characteristics, which will be referred

to as control graphs. They were: A linear relationship

between the flow through the valve and the valve opening,

and a linear relationship between head on the weir (flow

measuring means) and the valve opening.

Before the first configuration was machined, the de-

sired graph of flow versus percent valve opening was made

and a straight line relationship was chosen. The chosen

characteristic passed through the origin of the plot to

the known flow at the full flow condition for the previous

3-inch Crane ~lobe valve at maximum opening. This vas done

to obtain maximum flow at the full-open position of the

15

valve. The method emnloyed in achievin~ a desired flow

was to drill holes in the detachable cylinder which allowed

the water to flow from the high pressure inside to the at-

mospheric pressure downstream from the vnlve. The actual

pressure drop across the valve will be discussed in a later

discussion.

A special procedure was used to drill the holes in the

cylinder in order to expedite the experimental procedure.

A random pattern of holes would involve too much experi-

menting time. Therefore. a more expedient way was developed.

Since the thread pitch of the drive screw was found

to be 4 threads per inch. each one-half revolution resulted

in a 1/8 inch cylinder movement. Therefore, the cylinder

was divided in 1/8 inch circular bands. each of which must

contain enough holes to meet the flow requirement for the

corresponding valve position. In this way each successive

one-half revolution would add a new band of holes- no sin-

gle hole of which would be divided by the sealing mechanism

(the 0-Ring). To keep the holes within the respective bands,

a 3/32 inch diameter drill was used together with a ri~id

clamping arrangement that insured that the hole centers

were in the same plane even though the cylinder had to be

removed and rotated each time a hole was drilled.

To determine the number of holes within each band,

reference was made to the two control graphs depicting the

desired flow characteristics. Both cylinders were designed

16

with this procedure. For each 1/8 inch advance of the cy-

linder from the full-closed position to the full-open posi-

tion a corresponding flow rate existed on the respective

control graph. This was the criterion for the design pro-

cedure. Hence, the method was "cut and try" in that a

series of holes was drilled to prevent overrunning the

specified flow rate for the position. When the flow rate

was accomplished, the cylinder was advanced to the next

position and the procedure was repeated.

EXPERIMENTAL PROCEDURE

First Test Set-up - The initial set-up was made to test the

feasibility of the valve itself, since the experimental set-

up including the pump, piping, and the flow measuring device

had been tested repeatedly by a Mechanical Engineering Sy-

stems Laboratory class. The first configuration machined

in the cylindrical shell was a triangular shaped hole. The

opening was symmetrical on opposite sides of the cylinder.

The sum of the areas of the two configurations was equated

to the area of the entrance pipe in order to obtain the

maximum flow rate at the full-open position of the valve.

The triangle was isosceles and was positioned so that the

side opposite the apex was parallel and directly under the

periphery of the 0-Ring at the full-open position of the

valve.

Upon testing this cylinder, difficulties were encoun-

tered with severing of the 0-Ring during the valve advance-

ment period. This was caused by the expansion of the r-

Ring in triangular non-seal areas of the cylinder, result-

ing in a pinching action on the 0-Ring by the ed~es sur-

rounding the triangle at the outside surface of the cylin-

17

der. Hence, a different configuration had to be used which

would be compatible with the sealing device or a new seal-

ing device would be required.

Second Test Set-up - With the small 3/32 inch diameter holes

as the new configuration, a new cylinder was tested and

found to perform very smoothly with only a slight vibration

at the initial position of the valve after it was unseated.

A preliminary test indicated that the head level in

the hook gauge was too oscillatory to be measured accurate-

ly, so a short flexible hose was connected to the hook gauge

inlet and extended to the center of the tank- keeping the

opening perpendicular to the flow so as not to add the velo-

city head of the flowing water. This remedied the oscilla-

tion problem in the hook gauge, thus permitting experimen-

tal evaluation of the valve characteristic.

Test Procedure - The actual test procedure was simple and

could be performed by one man. After the holes had been

drilled in the wall of the cylindrical skirt in accordance

with the design procedure, the cylinder was mounted on the

plug adapter and the complete valve was installed in the

housing. The crank mechanism was advanced one-half revolu-

tion from the seated or full-closed position to allow the

18

first l/8 inch band to appear between the high and low pres-

sure zone of the valve. It is in this first band that the

holes were placed to allow just enough flow rate for the initial valve position to correspond to the desired flow

rate from the control curves.

The d-e motor driving the pump was started and the

water in the weir trough was allowed to come to steady-

state for the specific valve position. Since the capaci-

tance of the weir trough was large, time was required to

reach steady-state conditions. For small flow rates the

steady-state condition required approximately one-half

hour.

For each test position (one-half revolution of the crank) the design procedure of "cut and try" was carried out until the desired flow rate corresponding to the re-

spective control curve was realized. The procedure was

repeated until the full-open position was reached. At

this time the overall test of the newly designed cylindri-

cal skirt plug was completed. The procedure for the final

test closely paralleled the previous procedure except that

readings of the pump suction pressure, pump discharge pres-

sure, and the hook gauge were recorded for each valve posi-

tion. This operating procedure was repeated for the second

cylinder and the same readings were recorded for the valve

positions studied.

WEIR AND ORIFICE THEORY

Since the flow rate could not be measured directly

during the ex~ertmental procedure, it had to be calculated

using Yarnall's equation. The following is the derivation

of the weir equation for a 90 V-notch weir. Figure 6 ap-

plies to this derivation, where:

Q =total weir discharge in ft. 3 /sec. H = static head on weir in ft.

h =

e =

cd =

vm =

dh =

static head at any distance below

surface in ft.

included angle of V-notch, 90

coefficient of discharge for the

velocity of approach of upstream

ft./sec.

differential element of head.

FIGURE 6 V-NOTCH WEIR

the water

weir

channe 1 in

19

20

Assumptions:

(1) Torricelli's equation for discharge prevails for

weir discharge or V c (2gh)l.l2. avg

(2) The velocity of approach is negligible, hence the

velocity head at the plate location is negligible.

Therefore,

and,

dQ = C VdA d = Cd[2(H- h)tan l/2e](2gh) 1 /2dh,

where,

dA = 2(H - h)tan l/2edh

V = (2gh)ll2. (Torricelli's equation)

Hence,

II Q = cd(/ [2H tan l/2e(2gh) 1/2- 2h tan l/2e(2gh)l/2]dh),

0

which reduces to

Q = Cd8/15(2g) 1 / 2tan ~ 5 1 2 2

Since for V-notch weirs Cd has been experimentally found

to be 0.58, and e is 90 1 the above equation reduces to

Yarnall's equation which will be referred to as Equation

1 in the following discussion of experimental results,

(1)

21

In the following section. the discussion of experiment-

al results. an analogy using orifice theory will be used

in an attempt to correlate the test results. A brief deri-

vation will be given at this time concerning water flow

through orifices and will serve as a reference for that

article. Figure 7 shows the location of the reference points

1 and 2 with the corresponding nomenclature:

v1 = upstream velocity in ft./sec.

v2 = velocity at the vena-contract a in ft./sec.

pl = pressure at the upstream position in lb!/ft~ P2 = pressure at the downstream position in lb!/ft~ y = specific weight in lb!/ft~ g = acceleration due to gravity in ft./sec~. z 1 = elevation of flow at upstream position in ft.

z2 = elevation of flow at downstream position in ft.

Q = volume flow rate through the orifice in ft~/sec.

Al = area of inlet pipe in ft~

A2 = area of cross section of flow at vena-contracta

in ft~

A = area of orifice in ft~ Cv = discharge coefficient of the orifice

Cc = contraction coefficient of the orifice

Bernoulli's equation for steady flow is:

a z t I

t I

CD Al .... !. ? 2

pl vl

.... r -----.--

I

0 _A_~ I 2 I I

P2 v2

FIGURE 7 ORIFICE

I *

r

but because the elevation change for a very small orifice

even for vertical flow is negligible,

According to the continuity equation,

hence,

which, when combined with Bernoulli's equation along with

the discharge and contraction coefficients of the orifice

yields Equation 2,

( 2 )

22

and Equation 3,

C = CvCc//1- C~(A/A 1 )2 RESULTS

( 3)

The resulting curves for the two cylinders tested

proves rather conclusively that nearly any desired valve

characteristic may be produced with the experimental pro-

23

cedure used in this investigation. Figures 8 and 9 are the

basic experimental relationships that were produced from

the two cylinders tested. Figure 8 shows that a linear

relationship between flow rate and percent valve opening

was accomplished. Figure 9 reveals that the second re-

quirement of the investigation - a linear relationship

between weir head and percent valve opening - was also

realized. Although both curves were tested with the same

procedure at one-eighth inch advancements a check was made

at smaller intervals to see if the flow rates at the un-

tabulated positions justified the plotted straight line between the tabulated positions. This investigation re-

vealed that the error in assuming the straight line rela-

tionship between tabulated positions was negligible.

Another important aspect of this investigation was

the relationship between area change and cylinder advance,

depicted by Figures 10 and 11. For the linear head cylin-

drical skirt plug the curve was parabolic in nature, while

the linear flow plug had a very distinct linear curve

24

especially at smaller flow rates. A further and more signi-

ficant analysis produced from these curves is shown, how-

ever, in the flow rate versus percent available area curves,

Figures 12 and 13. These graphs indicate that for both

cylinders the curves did not differ appreciably from a

straight line; hence, the configuration area (the holes) appeared to be directly proportional to , the flow rate. In

orifice theory the flow rate was also found to vary direct-

ly with the area permitting flow, namely,

Q = CA{2g6p/y;

hence, the analogy between the configuration flow through

the cylinders and simple orifice flow may now be support-

ed. First, however, in order to validate the use of this

orifice equation, the following three assumptions were

made:

1. The cylindrical plug is an orifice plate and the

holes in the cylinder wall are considered as in-

dividual orifices.

2. The roundness of the orifice plate is negli g ible

for each orifice because the 3/32 inch diameter

is small compared to the 3-inch diameter of the

cylinder.

3. The high pressure side of the valve will be con-

sidered to be an infinite reservoir with a con~

stant pressure of 20 psig.

25

The first two assumptions are self-explanatory due to

the geometry of the cylinder and the flow configurations.

The third, however, needs some explanation. The pump dis-

charge pressure, recorded for each test position, indicat-

ed a variable pressure, first increasing, then decreasing

with increasing flow rates for both cylinders. Since the

pressure did not change appreciably throughout the tests

and the head losses within the piping system amounted to

approximately 5 psi, the average pump discharge pressure

minus the head losses within the piping system resulted in

the 2 0 psi g pressure at the valve in let. It must be kept

in mind here that a 3 psi pressure drop from the pump to

the valve is immediately accounted for because of the ele-

vation change of the water.

With the assumptions stated, the coefficient C, of

the orifice flow equation may be evaluated. Since by the

second assumpti~, the area of the individual orifices is

small in comparison with the reservoir area, the pipe

cross section, the A/A 1 term of Equation 3 is approximately

zero, hence,

Vennard (6) states that the product of Cc and Cv is 0.61

for a sharp edged orifice and 0.98 for a rounded edge ori-

f i c e An ave rage of t he s e two c o e f f i c i en t s y i e 1 de d 0 8 0

for the discharge coefficient since the sharpness or

roundness of the inside edge of the holes could not be

determined.

tion 4,

Therefore, Equation 2 can be reduced to Equa-

Q = o.8oA/2g6p/y. ( 4 )

This equation evaluates the flow through a single hole

26

in the cylinder, where again, A, is the area of the hole

and p is the pressure drop across the orifice - 20 psi -

since the gauge pressure of the low pressure side of the

valve was atmospheric pressure. To find the total flow

rate for each valve position, Equation 4 was multiplied by

the total number of holes permitting flow. The theoreti-

cal flow rate at each valve position, Equation 4, was then

plotted versus the actual flow rate found Dy the weir equa-

tion. Figures 14 and 15 indicate an equality between the

actual weir flow rate and orifice flow rate for the low

flow rate positions of the valve. The deviation of the

curves from the linear relationship at high flow rates was

expected, however, since the assumption of a constant pres-

sure reservoir was no longer valid due to a finite upstream

velocity in the pipe at the highest flow positions of the

valve. The fact that close spacing of orifices on a plate

reduces the flow capability of each orifice should not con-

tribute a significant error since only the inlet flow stream

is affected by the close spacing of holes. This type of

error would combine directly with the coefficient of dis-

charge, a term that was already approximated. As stated

above, the orifice flow equation was indeed a good

approximation of the flow rate and offers a mathematical

approach to the problem of flow control.

27

28

IV. CONCLUSIONS

The results of this investigation have led to the fol-

lowing conclusions:

l. Almost any flow characteristic can be achieved by

use of the cylindrical skirt plug - depending on-

ly on the cylinder size and stroke length.

2. There exists a linear relationship between configu-

ration area change and percent opening for the

valve plug with a linear characteristic.

3. For small flow rates the orifice flow equation

offers a reliable mathematical approximation of

the flow rate, thus providing a means of predict-~

ing the number of holes required to achieve a giv-"

en flow rate.

4. The flow rate at all but the full-open position

of the valve varied direct+y with the percent

available flow area.

5. The head loss of the cylindrical skirt plug is

greater than the head loss of the ori g inal poppet

plug in the Crane valve.

6. The type of plug designed offers an accurate flow

control capability from the O% to 60% open positions.

V. RECOMMENDATIONS

In order to benefit from what has already been done,

the author suggests that the following minor changes be

made to improve the valve design, as well as system per-

formance. The primary suggestion is that more instrumen-

tation, particularly within the valve test section, be

added because the pressure drop across the cylinder por-

tion of the valve is a critical factor in the valve's de-

29

sign. A pressure tap above the valve, as well as below the

valve is suggested, since at low flow rates a small but

definite suction condition existed due to the vertical

drop in the pipe at the valve exit. This condition could

be heard by obstructing the air flow into the flange with

the hands.

A second centrifugal pump, which is shown in the over-

all test set-up, might be coupled to stabilize and increase

the flow capability of the water supply system. This would

also increase the stability of the upstream pressure in

the valve test section, a very desirable condition.

There are two basic changes within the valve itself

that would improve flow stability through the configuration.

One change would be to increase the lift of the valve by

redesigning the stem connection to allow more room for the

stroke. Another possibility would be to remove the volume

on the stud beyond the outside dia~eter of the cylinder since

the valve actually doesn't have to seat at the "off" position.

Thus, the cylinder length could be increased to the con-

strained distance from the 0-Ring to the rear body of the

valve. Both of these suggestions would increase the con-

trol stroke of the valve, the axial distance of the cylin-

der within which all the holes must be located.

30

Aside from the design changes, there are several areas

within the scope of this thesis that merit further investi-

gation. A study of higher flow phenomenon should be under-

taken to see if the control aspects of the valves studied

in this thesis are valid for higher flow rates. A similar

study could be made of the pressure regulation capabilities

of the cylindrical skirt plug at small and large flow rates.

The effect of reducing the hole size should be investigated

to improve control of both pressure and flow rate. An area

that also suggests turther investigation is that of a solid

plug using the percent area available for flow versus flow rate curvea of this thesis as a design criterion.

One of the primary disadvantages of the cylindrical

skirt plug designed in this thesis is the large head loss

incurred by the directional change of the flow stream.

The head loss of the modified plug was larger than the

original poppet plug for all valve openings. A second

disadvantage of the modified plug is concerned with con-

tamination due to solid matter existing in the flow medium.

Because of the size of the holes clogging could become an

acute problem.

31

VI. BIBLIOGRAPHY

l. Seely, F.B. and Talbot, A.N. (1918), University of Illi-nois Experimental Station, Bulletin Number 105.

2. Lansford, W.M. , (1943), University of Illinois Experi-mental Station, Bulletin Number 340.

3. Addison, H. (1934), Applied Hydraulics, John Wiley and Sons, Inc., New York.

4. Rhodes, T.J. (1941), Industrial Instruments for Mea-surement and Control, McGraw-Hill Book Company, Inc., New York and London.

5. Beard, c.s . (1960) 1 Control Valves, Instruments Publish-ing Company, Pittsburgh, Pennsylvania.

6. Vennard, J.K. (1961), Elementary Fluid Mechanics, John Wiley and Sons, Inc., New York and London.

1. Eckman, D.P. (1958), Automatic Process Control, John Wiley and Sons, Inc., New York and London.

8. Caddell, J.R. (1956), Fluid Flow in Practice, Reinhold Publishing Company, Inc.

9. Prandtl, L., and T~etjens, O.G. (1934), Applied Hydro-and Aeromechanics, McGraw-Hill Book Company, Inc., New York and London.

10. Dalby, W.E. (1906), Valves and Valve Gear Mechanisms, Edward Arnold Publishing Co., London.

11. Linford, A. (1949), Flow Measurement and Meters, E. and F.N. Span Limited, London.

12. Schmeer, L. (1909), The Flow of Water, D. Van Nostrand and Company, New York.

13. Rouse, H. (1938), Fluid Mechanics for Hydraulic Engi-neers, McGraw-Hill Book Company, Inc., New York and London.

VII. VITA

The author was born January 20, 1943, in St. Louis,

Missouri. He received his primary and secondary education

in Webster Groves, Missouri, a suburb of St. Louis- In

September, 1960, he entered Colorado University, Boulder,

Colorado, then transferred to the University of Missouri

School of Mines and Metallurgy in February, 1961, where

he received his Bachelor of Science degree in Mechanical

Engineering in May, 1964.

He has been enrolled in the Graduate School of the

University of Missouri at Rolla since September, 1964, and

has held a Graduate Assistantship in Mechanical Engineer-

ing during his enrollment in the Graduate School.

The author is a student member of the American Socie-

ty of Mechanical Engineers and the American Institute of

Aeronautics and Astronautics. He is also a member of Tau

Beta Pi and Pi Tau Sigma engineering honor societies.

32

33

VIII. APPENDIX

The following appendix contains Tables 1 to 3, tabu-

lated data taken during the test period. Table 1 is the

weir calibration curve, while Tables 2 and 3 represent re-

corded and calculated data pertinent to the test of each

cylinder. Figures 8 through 16 are a series of plotted

curves representing the tabulated data in Tables l, 2, and

3.

34

TABLE 1

WEIR CALIBRATION

RUN NUMBER 1 2 3 4

HEAD (in.) .1.360 2. 360 3.080 3. 910 TIME (sec.) 60 120 60 60 WEIGHT ( 1bs. ) 45 330 285 604 DENSITY ( 1 bs. I ft.) 62.4 62.4 62.4 62.4 Qa(ft./sec.) 0.012 o.o44 0.076 0.161 Qth(rt./sec.) 0.011 0.045 0.077 0.151

TABLE 2

DATA COLLECTED ON THE LINEAR FLOW PLUG TEST

% VALVE OPENING PUMP DISCHARGE PRESSURE FLOW RATE (psig) (cfs)

0 0 0

14.3 27 0.035

28.6 30 0.104

42.9 30 0.156

57.2 28 0.196

71.5 27 0.241

85.8 24 0.298

100.0 23 0.348

35

TABLE 3

DATA COLLECTED ON THE LINEAR HEAD PLUG TEST

% VALVE OPENING PUMP DISCHARGE PRESSURE FLOW RATE (psig) (cfs)

0 0 0

16.6 27 0.055

33.2 29 0.027

49.8 30 0.083

66.4 28 0.163

83.3 24 0.280

100.0 23 0.375

rO s:: 0 () Q) til

~ Q) A

:2 l[)

0

l[) ~

I .

'

+=> l[) ) Q) t() ) Q) ~ () t() -rl ;.o 0 ;:j ()

-

[{) N } .

~ P1

.

l N

t

'-

:;>

-

. .

0 ..1~ 0 H fz.t [{)

rl

rl ~ .

0 '

J l() 0 ..

'

'

,.

h~-7( r-i-r

l 'I

..

~ l:-1" -'fl- ,~ 0 0

-

-

-

-- 1-

--

y ~. -L ~L .

;..... ,. t---

I "' i --- H

'

!.,..-'---'-

-+ .A- -h! - - f- -,- -- --,'1l L. lJ H t- --1-- . f- -'- -

. I

12.5 25

-

I

-

~

~ .,..,.,

-

~

.~ '

--

-

io"" , ... ~~ ....

--

- -

--I-

---- -

. - - -

1- - H- T - -- T - i-- ---37.5 50 62.5

PERCENT VALVE OPENING

r' .,.. ..

I :-,-, l I

'

-t -'

75

'

....

~ ... ;;;; ;ii' '

.,..

,.(.,.;;;; !-'

""'

I

FIGURE 8 -

VALVE CHAR-ACTERISTIC FOR THE LINEAR FlOW VALVE PLUG

--

87.5 100

-

""'

-

l

l 1 1

w 0\

"

= ~ !.. ; ~ . '(

, .....

- ( rJl

..Q 0 a -n -

~ H ..

~ r z 0 A ~

..

..

...

k

-

:vl

I GJ

I I I I I I I I I Ill II I I H+H I I I I I+H+I ,-, I I rTH=+I I I I I l=t I I I l=t-1 I llitJttttrLtJltFIII I IIII I IIII I IIII 1111111111111111 1111 11111 11 1 LLH+tllllll l llll l llll l llll l ll ll l llil ,1!1fH I I I I I I I I ITI I I I I I I I I I !*1 1111 11111 11111 11 111 1 111'1 1

+-++-

I I I I I llll I I I I u_ttltlittLUJl LIIIIIIIIIIIIIIIIJJliJ II ttlliJIITIIIIIIII IIIII IIIII I f 11 t r Ffl r I 1 111~ 1 111111!1 +--1-~-~t=ttH=I I IIII I IIII ~~lE 11111111-1 atHEtf! I 1 1111 1 1111 1 111 I I I 111 1 1111 1 1111 1 -1--+-1--J......l-1--J--l - -

1 I ! ! ! I ! ! ! ! 1-++++H-t+-H I I I I I I I I I I I I I I I I I I I I ! l 1 n I I I I I U~ Wflllllllllllllllllllllllllllllllllllll J I I I I I ' 11 \ I \ H-t+H~tltm-till lll l llll l llll l ~-~l~I=OOl+P=FU+TI I IIII I IIII I IIII I IIII I IIll l ll ! I I _ttllmmtfffllf-H II II IT}llfffflir~J_> illiEIII I-EEfEH+t+ff11111 11111 1111flfffR i II II H-t-H+I-H+IIIII H*+tl lit~l l +t~~tttJU=U-U=UtltHI IIll l flln 1111 1 1111 1 1111 1 111 111111 1 Y'

~ :r;; ; ;;;; ; ;;;:fJJtiJIIIIlllilfff1ffi1 1 1111 1 1111 1 1111 1 1111 1 1111 1 1111 1 1111 1 1111 1 1111 1

0

V' t-H I I I I I I I I I ++++++bJfll llll l llll llll t-HtH llll l llll l llll l l-lll l llll l llll l llii i iiii i iJII I

',1'

I - J - J.--J-l-I.....J.-1--+-t-t-t-t

1--+-1- H -H-LI-If-..1.-.t--t-1-l-'-+--t- l--_...j__j._~-+--t-!-;-W-1-1-+-H -+-t-H-- f- -f- 1-- f-H - -

-t- . f+-'-1 __ ~ 1--,: r -T - l- -r-~-- - 17 -

12.5 25 37.5 50 62.5 75

PERCENT VALVE OPENING

FIGURE 9 - HEAD VERSUS PERCENT VALVE OPENING FOR THE . LINEAR HEAD VALVE PLUG

87.5 100 w

~

-. .

,

. '

1-- 1-

- ,.

Ell: s

~ - --r-

iod fz:t ~ 90 I 0 fz:t

~ ~ SITION CHANGE FUR THE LINEAR FIDW PLUG

.. -~

87.5 100

'

: ;

w ())

a: 0 ~ ~ 0 J%.1

~ j H . ~ E-1 ~ 0 p:::

~ ~;;.

I 11 I I. I I I I I 1-

100

90

80

70

60

50

40

;:3.0 .

20

10

0

T7

J)

I I I I I I I I I H-1-1-+++-+-H - H I I I I I I I I I 1--1-++++++++++-1-++-1 I I I I 1--1--l-+++- ~~- v D

!/ I I I I I I I 1--1-+-1-

H- H-++H I I . I I I I I I I 1-+-+-J-..l- lttl--l-l.L'l

-f-+-f-H---+-1--+-1

1 111111 111 1--+-+-H I I I I I 1 I I I I I I f-H-H-+++H-1+1 I I I I I I I I I H-+71 I I I I I I I I I I I I I I I I I I I I I 1--l-t-l-1 I I I I I

~I I I I I I I ~H+H++Htlm 111111 11 attmlrr--= 11m lllll lllll lllll llltu 1111 1 I I I I I I I I I- ffE- 11 1 I f-+- _J__j H" t -'-l l.....j__I--1--1--1--1--H+ + -H-t-1- --1- + I l 1 FF

I I I I I I I I I I 1 --1--l=l=t=-l~l=t--tt J--i- -l--1-...J.-I--1-+- ~-\)/" -H- t-j ' I -W-U-W-++-J-+-H-/-t+t-H-t~-:~'! 1_t- _ _-I--- j_ ~

I -l--1-t-+ 1-H-+-H- ..... ~- --f.-- --1- - I Jt-t--' 1 1 1 1 1 1 1 1 1 + -1- +--+-H-1-l- t=trf-_-1-f--1-t-_: !;;;. ~ !;- H- = ---1-=r=- ~- -=-= - ---lT8-, I I I I I H++i~1=r::t:J=1~1Jr.-t-+ ,- ,- ~:E,~~, :: -1__ -1- t , _____ :1n 1-- , , ' I _ ! ! 1 L -- - -- - .. __ , I, I I T I . '

I _(:) j- ; : / I I : I I I . I I l I I I I I j- i 0 12.5 25 37.5 50 62.5 75

PERCENT VALVE OPENING

FIGURE 11- RELATIONSHIP BETWEEN AREA CHANGE AND VALVE PLUG R>SITION CHANGE FOR THE LINEAR HEAD PLUG

f37.5 100 w \0

-~-

I I I I I 111 I I I I I I I I I I I I I I 11 I I I I I I I i ' I I I I I I I I I I I I I I I I I I I 1' 1 I I I I I I I I I I I I I 1.1 I I I-I il I I I IA-H-1 I I I I I I I I I I I; 11 m ir.rRTFll n 1 r lllllllll l lllTJ IT IIIIII I ITil iii iiTFFr ITITffH+-11 J' 111 -11! 111 Y1 1 1 1 1 , 1 1 1 1 ' 1 1 1 1 , 1li iiiiiiiiiii - 111111111111 1111 1 11111SitJitflN$~+lll UJ 111 11 H l I r IIII I U1tii-III IIITLIII III

17

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I l+t+H I I I I I I I I I H-:-1 I I I I I t+Vfti+l I I I I I' I I I I I I I I I I I I I I I II

: :::: :=~~:~i iiii i i i iiiil-lllllllll l llll l llll l IIIII mm Jill t#Y4illlllll Mm~tP-,-~ - : -~-1 I I I I I I I I I 1- H-++-H -H-H I I I I I I I I I 1++-t- 1 1 J , _j. ~ - -

- r '- -

+-+ ---- r-r- __..~j-1- ,-

- + -~ -I. I I I I I I I I I I I I I I I-I I I I I I ! I I I 1 1 1 1 1 1 - !~W-t-- 1-t-L --1-

- ~~;i-" - 1-+--,--t-lll llllttffFH--! ! ~ ~ . - t- - 1~ ~ - - - - -+-+- - - . --L 1--

-rR ~ - ~~ 1--1-- - I- 1- t--- - -t--- - 1-f- . H - rt-~- -- -:-7 . 1--- r- t- - - --t-+- . r- t --

.-1: I I I I I I I ! 1-i ~f 1 ~7"'-1- r - l-+1 . ' . - ~ -I- - -- -I- - _j it- -1 1--!-H-+--1--t.J -),--" - j-1-1- - -t L .L - -f

I I . --, - - -- - - - - - - f - 1- - 1- - - - -- 1 _l l - -r _ tH -f+__::- j- - - - - - --r+ --- - - -- -- + - -- -+ i i - --- j , -J-,.l- --=-- r-- 4 -4= , , r- LLU_

I I L L lr::l

0.05 0.1 0.15 0.2 0.25 0.3

FLOW RATE (cubic feet per second)

FIGURE 12 - RELATIONSHIP BETWEEN AREA. CHANGE AND FIDW RATE CHANGE FOR THE LINEAR FlOW VALVE PLUG

0.35 0.4 ... .

.... ..

~ 0

.. ~

-~~---: . : .": . ~: ~ . ~ .+-.~r~(ll f . . r r ..

F--.. .

rO s:= G () Q) 10

J.t G) P4 ~ G) G) \-i ()

..... .

.g ()

-

~ ~

~ 0 H ~ -

1%1 0 H

~ ~ 0

. - ~ .

10 ;,

0 I

tt -.. f-

' . f-- H

) f-- . -l -

~

0 lr

..

~'I--

.. 1/ ~--~ I -* ~I

I t-- I

'

f- - t-r- I ~

'

I

J 0 ''-,.,

-f- ~ ~

-if .. 1 II' :t~ '

-- j-j ;< -t-I . r w . -- p --

~' - ,f++~ clr. " =t t ; I 1- tt= f--y >=- . t-- _( ~~-T )~ I -t r!~T ~+ ..... -

I ' .

> J.

_L 1 __ 1 J .

.

\ t ll ~-+ --. FIGURE 14- COMPARISON 1 ' J.l OF YARNALL'S FLOW EQUATION

1- 7. 2 ~~1!-1-t ~-: AND THE ORIFICE EQUATION

r. + -=:.: -~ 1 .: FOR THE LINEAR F'I.OW PLUG

N .

0

..-4 .

0

o 0.1 0.2 0.3 0.4

YARNALL'S EQUATION FLOW RATE (cubic feet per second)

'd s:: 0 C) Q) 0)

tO

0

I h ~ Q) . P. 0 '

,.-

- .

.

"1. ........

.

.f.) Q) Q) IH

+-

.

C) ~ t

-z 0 H 8

~p'd as= f::z:10

0 C/)Q)

~ D) H

H~

G-4

~0 ~~

~ ~0 o-

~

~ -~ -r-t I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I . I I I I I I I ., I I I I I I I I ' l i) I I I I I I I I I I I I I I I I j I I I I I I I I I I i -

v o II-I f I I 11 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 11 II I I I I I I L1 1-1 I I I I I I I I I I I I I I I I I I I I II I I I I I I I

~1111111111 11111 flllllllllllllll fll M-Il~ ll~ 1 1~11111111 11 H ----H +--+A-----+++-1 I I I I I I I I I I I I I I I I I I I I I I I I 11 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I -I I I I I I I I I I I I H -- 1-------H ----1--l-l+!:k-1-+1- I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

, 1 1111111 -111111 1 1111111111111111111 t~t~-I:= I:~Utffl lll f1t---+H---+H I I I I I I 11 I I I I I J I I II I I I I I I I I I I I I I I ~ I

0 1-HIII~II--H-11++11 ++---IIIH--tll++ll-t+ll ++II t-HIII++II++II +---+----IIIH--tll-++-11 t l=tat:tttti i iiii i iUJJJJJJ __ +---M I I I I I I I I I I ------ --1----+-- - ___ 1--J-::_ = ~ t---H------ -I f-- - --1------1 - 1------l 1 1 ;' i;'r ~- H--~ . ~ 1------ ---

0 ,_ - . ' 1--t- ~ f- + -0

- . .. ....... I 10 1-t---+---l C\l -0

+------1---++-~+H-H-H I I I I H+-1------f-----1- H --+--+---+ ---+------!-----1-. +++-+---

-1------1--- ---l------1 I I I I I I ! I I I I I I I I I I I I I I

1-------1-++1 I I I I I I l l I I Ill I I II I I I I I I I I I I I I I I I

-.. ":EE 1------l-----4 I I I I I I I I I I I I I I I I' I 1+1 I I I I FIGURE 16 - WEIR FIDW: EQUATION FIDW RATE VERSUS

ACTUAL FIDW RATE (WEIGHED ) riffll l !j i . .. - ~ . . 0 0.025 0.05

~~.w:-:~~~~~LLIIIIIIII:J:l::!:t!llli::!:J.._-------- ._. ~--0.0'75 0.1 0.125 0.15 0.1?5 0.2 -~ .

-.

ACTUAL FLOW RATE (cubic feet per second)

.r:-w

-.

Scholars' Mine1966

A study of modified plug designs for a globe valveRobert W. WagnerRecommended Citation

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