Transients in cooling water systems of thermal power plants

TRANSIENTS IN COOLING WATER SYSTEMS

OF THERMAL POWER PLANTS

PART II

«^JOTHEEK V/SG. 5» V/AT£.:>BCUWKUNDE T.H.

Ooi'p.""t;r..-»<;^ 75 OtLFT

iy (P

^ ö o 3

%

TRANSIENTS IN COOLING WATER SYSTEMS

OF THERMAL POWER PLANTS

W T

^ a - ( ^ . -2.

PART II

Bibliotheek TU Delft

«

0640

258

C 3092744 1

^ /feM

H.H. SAFWAT

TABLE OF CONTENTS

3

PART I

Chapter • Page

SYMBOLS . , • 9

LIST OF TABLES • ' . ' " : . . _ 11

LIST OF FIGURES ' , ' 12

LIST OF COMPUTER PROGRAMMES 18

1. INTRODUCTION • 20

1.1. General Aspects of the Problem and Motivation . 20

1.2. Method of Approach to the Investigation 21

1.3. Outline of Dissertation 22

2. WATER-ÏIAMI-IER AND WATER-COLUMN SEPARATION ANALYSIS 25

2.1. Literature Survey 25

2.2. Basic Laws of Fluid Mechanics for Water-Hammer Applications 28

2.3. Characteristics Method 31

2.i+. Finite Difference Solution 33

2.5- Illustrative Description of the Phenomena of Water-Hammer

and Water-Colomn Separation '35

3. EXPERIMENTAL STUDY UO

3.1. Water-Hammer Water-Colomn Separation Experimental Circuit Uo

3.1.1. General description ill

3.1.2. Details and data of main parts of circuit " Ul

3.2. Instrumentation U6

3.3. Experiments i+8

3.3.1. Steady conditions measurements U9

3.3.2. Measurement of transient flow velocities 5I

3.3.3. High speed camera photographic study of water-colomn

separation 56

3.3.i+. Experimental evaluation of the elastic behaviour of .

the pipe wall material 57

3.3.5. Transient conditions 62

4

65

Chapter Page

h.

COMPARISON OF EXPERIMENTAL MEASUREMENTS AND CALCULATED RESULTS

USING CLASSICAL WATER-HAMffiR CALCULATIONS 63

k.^.

Schematization of the Pipe System 63

1+.2. Choice of Input Data for the Programme HOZ

6k

h.3.

Investigated Conditions 65

k.k.

Comparison of Experimental Measurements and Calculated

Re-sults

k.^.

Photographic Study of Water-Column Separation during

Tran-sients in the Horizontal Pipe 67

U.6. Significant Findings 7^

5. NEW MTHEr^ATICAL MODEL _ , 7 6

5.1. Finite Difference Solution 77

6. TRANSIENTS RESULTING FROM CLOSURE OF THE VALVE AT THE UPSTREAM

END OF THE HORIZONTAL PIPE 80

6.1. Typical Experimental Test ' 80

6.2. Schenatization of the Line 80

6.3- Choice of Input Data for the Programme HZD 80 .

6.h.

Comparison of Experimental Measurements and Calculated

Re-sults 85

7. TRANSIENTS RESULTING FROM CLOSURE OF THE VALVE AT THE UPSTREAM

END OF THE SIPHON 89

7.1. Typical Experimental Tests 89

7.2. Schematization of the Line 92

7.3. Choice of Input Data for the Programme WHN 92

7.*+. Comparison of Experimental Measurements and Calculated

Re-sults 9^

8. TRANSIENTS RESULTING FROM CLOSURE OF THE VALVE AT THE UPSTREAM

END OF THE CONDENSER SYSTEM 97

8.1. Typical Experimental Tests 97

8.2. Schematization of the Condenser Configuration 98

8.3. Choice of Input Data for the Programme WCN 98

8.U. Comparison of Experimental ^teasurements and Calculated

Re-sults IQl

9. CONCLUSIONS 108

5

Chapter ^^i®

APPENDIX •

A Digital Calculations of Velocities from Photo-Analyzer Data II9

B On the Pipe Wall Deformation 122

C Numerical Calculations for Transients in a Horizontal Line

Based on Method of Characteristics 125

D Numerical Calculations for Transients in a Horizontal Line

Based on the New Mathematical Model 129

E Numerical Calculations for Transients in the Siphon System

Based on the New Mathematical Model 133

F Numerical Calculations for Transients in the Condenser System

Based on the New Mathematical Model 135

G List of Experimental Measurements Data 130

VITA 139

ABSTRACT 1 Uo

PART II

LIST OF FIGURES 8

9

LIST OF FIGURES (cont'd)

Page_Ul,

View of water filter ^1

Condenser model

^2

View of the condenser model support in a vertical

position ^+3

View of the condenser model support in a horizontal

position

kk

View of the intrumentation ^5

Schematic diagram of instrumentation set ^+6

View of the mounting of a pressure transducer ^7

View of induction flow-meter ^+8

Schematic diagram showing principle of pressure

measure-ments and their recording on the recorders and the scope

^9

Steady conditions points of measurement 50

Steady friction factor in the pipe 51

Measured valve resistance for different opening

posi-tions at steady flow condiposi-tions 52

Photographic system arrangement 53

Typical frames of the film 5^+

Co-ordinates systems used for calculations of ball

dis-placement and time for transient flow velocity

measure-ment using the photographic method 55

Schematic diagram of induction flowmeter 56

Experimental measurements during test used for

compa-rison of the photographic and induction system for

velocity measurements 57

Transient flow velocity changes using the photographic

and induction systems 58

Photographic arrangement 59

Transient pressure changes resulting from linear

clo-sure of the valve in 1 second for a steady flow

10

LIST OF FIGURES (cont'd)

Figure , Page (ll!

U3 View of the tangential and axial strain gauges cemented

on the outside surface of the pipe at location PTp

(Fig. 1+2) 61

1+1+ Strains at the outside surface of the pipe at

lo-cation PT during transients resulting from linear

closure of the valve in 1 second for a steady flow

velocity of 1 m/s 62

1+5 An oscilloscope record (redrawn) showing the

pres-sure P^ and the circumferential strain e ^ at

loca-2

c2

tion PT (Fig. 1+2), during the transient test whose

results are shown in Fig.

kh.

Triggering time of the

scope = 1.1+ second. See T-T in Fig. 1+1+ 63

1+6 Strains at the outside surface of the pipe at

loca-tion PT during transients resulting from linear

closure of the valve in 2 seconds for a steady flow

velocity of 1 m/s 61+

1+7 Transient pressure changes at PT (Fig. 1+2)

resul-ting from sudden closure of the auxiliary valve (at

downstream end of the pipe) for steady flow

velo-cities in the pipe of 0.5 and 0.75 m/s 65

1+8 Data sheet

66

1+9 Schematisation of the horizontal line system 67

50 Definition sketch showing space-time grid used for

computer programmes 68

51 Principle of linear interpolation used to obtain

valve resistance during its closure 69

52 Definition sketch showing space-time grid for the

valve boundary condition used for computer programmes 70

53 Definition sketch showing space-time grid for the low

level water reservoir boundary condition used for

com-puter programmes 71

5I+ Comparison of calculated and measured results for test

"\

11

LIST OF FIGURES (cont'd) . . '

Figure - Page (II)

55 Comparison of calculated and measured results for test

number 6155 73

56 Transient pressure changes resulting from closure of

the valve in about 1.7 second for a steady flow

velo-city of 1 m/s 7^

57 Different frames of the high speed film showing water

column separation at the valve 75

58 Finite difference approximation principle 77

59 Space-time grid for finite difference solution using

the new mathematical model • 78

60 Example of a measurement used for determination of

dynamic valve resistances 79

61 Dynamic resistance of valve during closure 80

62 View of arrangement used to visualise small bubbles

in the pipe 81

63 Analytical prediction of celerity in bubble and

stra-tified flow regimes (line l ) , in annular and

dis-persed flow regimes (line II) |2l| . 82

61+ Principle of determination of momentum loss

coeffi-cient "c" using logarithmic decrement procedures 83

65 Comparison of experimental measurements and

calcula-ted results for test number 615I+ 8^+

66 Comparison of experimental measurements and

calcula-ted results for test number 6l55 85

67 Comparison of experimental measurements and

calcula-ted results for test number 6156 86

68 Comparison of experimental measurements and

calcula-ted results for test number 610I+ 87

69 Comparison of experimental measurements and

calcula-ted results for test number 6105 88

70 Comparison of experimental measurements and

12

LIST OF FIGURES (cont'd)

Figure ^^Se_(_Il2

71 Experimental transient pressures and velocity changes

during test number 80OI 90

72 Experimental transient pressure and velocity changes

during test number 8OO5 91

73 View of water column separation at top of the siphon 92

7I+ Comparison of experimental and calculated results for

test number 8008 ' 93

75 Comparison of experimental and calculated results for

test number 8011 9^

76 Comparison of experimental and calculated results for

test number 8016 95

77 Comparison of experimental and calculated results for

test number 8018 . 96

78 Comparison of experimental and calculated results for

test number 2031+ 97

79 Comparison of experimental and calculated results for

test number 20l+3 98

80 Experimental transient pressure and velocity changes

during test number I80 99

81 Experimental transient pressure and velocity changes

during test number 181 100

82 View of water column separation at top of the condenser 101

83 Schematic diagram of the condenser system for numerical

calculations 102

81+ Condenser resistance versus flow velocity in the main

pipe (measured under steady flow conditions) 103

85 Comparison of experimental and calculated results for

test number C3063 IOI+

86 Comparison of experimental and calculated results for

13

LIST OF FIGURES ( c o n t ' d )

P a g e _ U l ]

Comparison of experimental and calculated results for

test number C3065 . " ''0^

Comparison of experimental and calculated results for

test number C2019 . 107

Comparison of experimental and calculated results for

test number CI003 108

Comparison of experimental and calculated results for

test number

C^O'^h

109

Comparison of experimental and calculated results for

test number C6l09 110

Comparison of m-'-asurenents of test numrer C509lt (a

con-denser system) with measurements of test number 80l8

(siphon system) 11 1

Comparison of experimental and calculated results for

test number

CyO')^

(based of a siphon schematization) 112

Experimental transient pressure and velocity changes

during test number C6l09 (based on a siphon

schemati-zation ) 113

Experimental transient pressure and velocity changes

during test numVier C6l07 (based on a siphon

LIST OF COMPUTER PROGRAMMES

Page_[ll]

PDV Digital Calculations of Velocities from Photo-Analyzer

Data 115

HOZ Numerical Computations for Transients in a Horizontal

Line Based on Method of Characteristics 117

HZD Numerical Computations for Transients in a Horizontal

Line Based on the New Mathematical Model 123

WHN Numerical Computations for Transients in the Siphon

System Based on the New Mathematical Model 131

WON Numerical Computations for Transients in the Condenser

System Based on the New Mathematical Model ll+3

Listing of Modifications in Computer Programme WHN 157

CONDENSER

UPSTREAM

\ PUMP ^CHECK VALVE

-^—I

\

-0-DOWNSTREAM

STRAINER

SCHEMATIC DIAGRAM OF A TYPICAL COOLING WATER SYSTEM

OF A THERMAL POWER PLANT

17

HYDRAULIC GR ADELINE

PIPE WALL

("•f^^) 0'lf-)(-f'^)

DATUM

CONTROL VOLUME USED FOR THE CONTINUITY EQUATION

FIG. 2

18

HYDRAULIC GRADELINE

H

T^ nD6x

PIPE WALL

"/ PA5xg /

'V.

PA^if^^x

(^*fH(^*t-)^f^^)f^^lf-)

,dP5x)dA_sx

dx 2/dx

DATUM

CONTROL VOLUME USED FOR THE MOMENTUM EQUATION

FIG. 3

19

t

i

- ^ x

CHARACTERISTIC CURVES ON THE x-t PLANE

FIG. 4

o

t*2/]t i

t*^t <{> o

CHARACTERISTIC LINES ON x-t GRID

FIG. 5

21

ti-^t

t

(x = 0)

i) t*Jt

-X R

(x=L)

CHARACTERISTIC AT LEFT END

CHARACTERISTIC AT RIGHT END

CHARACTERISTIC LINES AT BOUNDARY

CONDITIONS ON x-t GRID

Hs SURGE PRESSURE Hres RESERVOIR Hr RAREFACTION Hv VAPOUR Hs Hre. Hr Hv L 2_L M. 4 4 4

STEREOGRAM SHOWING SEQUENCE OF EVENTS FOR TWO PERIODS AFTER SUDDEN CLOSURE OF A VALVE AT UPSTREAM END OF A PIPE (WATER HAMMER ONLY)

FIG. 7a

At x=0

XrM.

4

2

3L

x = L

p

1 H U - . - . - . . « //

"

. </

-H LLLLLJ

* H rrr

-H

LLL

* ^ 1

1 1 1

J

-^

1

,

1

,

1

,

2L a 4L a 6L a

4 '

V

-Vo * Vo -Vo * Vo -Vo * Vo -Vo * Vo — 1/ ^0 * Vo

1

r"i

J

r - i

lU

IIII 1

1 1

TT T

1

1

m

~i'ir

llllllll

1 1 ,

1

1

rm

11

r-i

Hi

fl-T"!

ILU

TT 1 T

_ _ l 1 L_^

N-x=o

2L a —4 L

T

Vo 2L 4 4L a — 1 — 31 4 SL

a

IL t

_a

H

aVo

PRESSURE AND VELOCITY CHANGES AT DIFFERENT LOCATIONS DURING TWO PERIODS

FOLLOWING SUDDEN CLOSURE OF A VALVE AT THE UPSTREAM END OF A PIPE-LINE

( WATER HAMMER ONLY)

FIG. 7 b

Hs SURGE PRESSURE Hres RESERVOIR PRESSURE Hr RAREFACTION PRESSURE Hy VAPOUR PRESSURE VALVE END x=Q x=L RESERVOIR END _L 2L JL 4 4 4

STEREOGRAM SHOWING SEQUENCE OF EVENTS FOR ONE PERIOD AFTER SUDDEN CLOSURE OF A VALVE AT UPSTREAM END OF A PIPE (WATER HAMMER-WATER COLUMN SEPARATION)

Vo^2.6v X--0

x-.-k

X-.2.L 4 X=L fes^ X--0 4 .2L 4 X= L

TTTT

uJ

Vo=2.8v P

dl

1

mnj

V„^3v

TO

-i 1 r I I I I I > V

1

^

.

^

^ . ^ '

N

_r

L

1^0= 3.P f

•1

J

J

I

uTJin

TTTT

Vo^3.4v

• D ü

IJÏÏÏÏl]

imn"

- ^ K,

PRESSURE AND VELOCITY CHANGES AT DIFFERENT LOCATIONS DURING THE FIRST PERIOD FOLLOWING SUDDEN CLOSURE OF A VALVE AT THE UPSTREAM END OF A PIPE LINE (WATER HAMMER-WATER COLUMN SEPARATION)

FIG 8 b DXh PTl PT2 PT3 PZf PT5 x=0 i

2L

4 4

"v-T

r

10 0\

2 6

-tx-PHASE 1 HORIZONTAL LINE

M

-PHASE 2 SIPHON SYSTEM

H X

-mn

PHASE 3 CONDENSER SYSTEM

THREE PHASES OF THE INVESTIGATION

FIG. 9

2 7

FIG. 10 VIEW OF THE EXPERIMENTAL MODEL

1 PLEXIGLASS PIPE

2 HIGH LEVEL WATER RESERVOIR

3 LOW LEVEL WATER RESERVOIR

5 RETURN PIPE

7 WATER SUMP

9 HIGH LEVEL RESERVOIR OVERFLOW

(NUMBERS ARE THE SAME AS THOSE

- t x i - ^

00

QK

10 01

13

r^xj

^ '"'{Il—

^

lü

_{H ^}

•iXH,-'-

ïf

r. HORIZONTAL PLEXIGLASS PIPE

2. HIGH LEVEL WATERRESERVOIR 3. LOW LEVEL WATERRESERVOIR

4. VALVE AND VALVE STEERING MECHANISM

5. RETURN PIPE

6. V NOTCH WEIR 7. WATER SUMP

8. PUMP

9. HIGH LEVEL RESERVOIR OVERFLOW

10. VALVE ON THE DELIVERY SIDE OF THE PUMP 11. AUXILIARY VALVE

12. WATER FILTER 13 VACUUM PUMP

SCHEMATIC DIAGRAM OF THE EXPERIMENTAL MODEL FLOW CIRCUIT

FIG. 11

X

(1) HORIZONTAL LINE

29

- £

'

M

(2) SIPHON SYSTEM

r^-rr~n

N N

M

r J M CONDENSER SYSTEM (VERTICAL CONDENSER)

Pi AN IN DIRECTION N- N

13)-JI CONDENSER SYSTEM (HORIZONT*! CONDENSER)

EXPERIMENTAL MODEL ARRANOEMENTS FOR DIFFERENT PHASES OF THE INVES' GATION

3 0

FIG.13 VIEW OF THE MEANS OF SUPPORT

OF THE PLEXIGLASS PIPE

1 PLEXIGLASS PIPE

2 BRACKET

PLEXIGLASS PIPE

SUPPORT OF

PLEXIGLASS PIPE

PLEXIGLASS

31

BEND

LOW LEVEL

WATER RESERVOIR

DOWNSTREAM END OF THE PLEXIGLASS PIPE

CONSTRUCTIONAL DETAILS OF SOME

PARTS OF THE MODEL

3 2 FUNNEL TO SUMP

£

FROM PUMP

EX

JL

/«ïni'TiFiTimmTffJii , 'KTi7l'nh"nïïnTi7iii M l . "

-'ll

l , ' l '

S"

,'fiiJjft i|iilT|7i| 'I'llliii' Ml iflil'i ' H l ' l ' i " ' I.Wiil JI'MII noiiiiilC-I noiiiiilC-I •' I I

'SLt~l

-2.0 m -0.0 m TO PLEXI-GLASS ^PIP£

HIGH LEVEL WATER RESERVOIR

3 3

FROM PLEXI

GLASS PIPE

LOW LEVEL WATER RESERVOIR

FIG. 16

34

FIG.17 VIEW OF VALVE AND ITS SERVO-MOTOR

1 PLEXIGLASS PIPE

2 BALL VALVE

3 ANGULAR POSITION TRANSDUCER

4 MOTOR

35

FIG 18 VIEW OF THE SPECIALLY BUILT

ELECTRICAL FUNCTION GENERATOR

1 DIGITAL VOLTMETER

2 VOLTAGE STEPS SELECTORS

3 TIME STEPS SELECTORS

36

ANGULAR POSriON

OF THE VALVE

a

90^

VALVE

CLOSED

VALVE

OPEN

TWO DIFFERENT

EXAMPLES

TO

TC- TIME OF CLOSURE (0.4-5sec)

- i ^ ^ time

VALVE CLOSING CHARACTERISTICS

(ANGULAR POSITION - TIME)

37

Ag EFFECTIVE OPENING AREA

av. ANGLE AT WHICH VALVE IS CLOSED

. 'S

I

?

zzzzzz

i

_^//////

rcos Or

777777

AgJ(Ucosa) r2sin-1(]/l-(yl-1)tan^ - | - ; 1 - [ s / n a r ^ l / f ^ .i),]/^!^-1) tan^ SL "I

% -- 2 tan-''

v^r:72'

Ae/Ao 10

I

O.S 0.0

\

r= 50mm R = 76,5 mm

JO

50

90

I ot

EFFECTIVE AREA RELATION WITH ANGLE OF

CLOSURE FOR THE BALL VALVE

Electronic

function

generator.

ext. stajt

Direct-cur-rent voltage

Bource.

Direct

cur-rent voltage

source.

Direct-cur-rent voltage

source.

X

, buffer-ampl. i

' gain var.0-1 [

:~n

Icombined operational

lerror-ampljgain v a r . l - I )

I power amplifier i

I with adjustable ' *,

tachogenerator '

'Lfeedback. ^

00

X

10

pree

turn.

p^t.m»

I buffer-ampl. {

[gain var.0-1 i

A9>-S.E.N, type

AS 1415

max. power 3 IcW.

servo

Tacho-generat oj^

TV/lOOO rpm

perm, magnet d.c. j

printed motor; CE.KL

type MF I9/5602O ,

"max = ^500 rpm. |

nom.torque 0,32 kgm. 1

i_ma2._tQrgue. 2 , ^ JtgniAJ

•©-0*^-pree, pot.m.ltum.

Gear box

36:1

Speetrol mod.400 5k

Balli valve

Ball detector

(on pipe lin^

Actuator,

actuates

etart/etop switch

(see above)

manual start.

PRINCIPLE OF ELECTRIC CIRCUIT OF THE FUNCTION GENERATOR

FIG. 20

39

a

VALVE

CLOSED 90

VALVE OPEN

I lOV

-l\JY

-i

^v,

\

\

1

« r

1

V~7

1 /

1 /

^ ^ ^

r~

/

1 —

1 /

/

1 —

1 /

y

r 1

/

^Z^^^^^^'^

t

CHOICE OF VOLTAGE AND TIME STEPS

FOR THE FUNCTION GENERATOR TO

OBTAIN A REQUIRED VALVE

CLOSING CHARACTERISTIC

FIG. 21

4 0

FIG.22 VIEW OF VACUUM PUMP IN OPERATION

1 VACUUM POMP

2 MOTOR

4 1

FIG.23 VIEW OF WATER FILTER

1 WATER FILTER

2 CIRCULATING PUMP

3 MOTOR

xsPOSS/BLE PRESSURE MEASUREMENT POINTS

CONDENSER MODEL

FIG. 24

4 3

FIG. 25 VIEW OF THE CONDENSER MODEL SUPPORT IN A VERTICAL POSITION

1 UPPERSTREAM WATER-BOX

2 DOWNSTREAM WATER-BOX

3 CONDENSER TUBES

4 4

IN

GUI

FIG. 26 VIEW OF THE CONDENSER MODEL SUPPORT IN A HORIZONTAL POSITION

1 UPPERSTREAM WATER-BOX

2 DOWNSTREAM WATER-BOX

3 CONDENSER TUBES

45

FIG.27 VIEW OF THE INSTRUMENTATION

1 OSCILLOSCOPE

2 RECORDERS

3 CHARGE AMPLIFIERS

w

PT, VA

PT.

PT.

A,B,C,T)

see Fig. 2^

•PT

4 PT,

_PT^

time

signal

n

PT

5

PT

PT

PT

pot.m.

D

J$L lp.

J^

Jp.

5v5

25 mm,

5vS

25 mm.

5v=

25 ram.

5v=

25 mm.

5v=

15 mm.

4) > 4^ 4^ 4^ 4^

RECORDER 1.

PT

PT

PT

PT

PT

induction

flowmeter

8

m m [^ [^

5vS

25 mm.

5

^v

v=

25 mm.

5v5

25 mm,

5vS

25 mm.

time

signal

D

1.38V

• 2 0 rni*

4) 4 4^ 4 4^

RECORDER 2.

JSi

KISTLER PIÈZO PRESSURETRANSDÜCER type 4IOB ( l - 6 ) j 6O3I (7 and 8 )

KISTLER CHARGE AI^IPLIFIER t y p e 5001j 5O4M5, 5O4.

p o t . m . » p o t e n t i o m e t e r

SCHEMATIC DIAGRAM OF INSTRUMENTATION SET

SIMENS AMPLIFIER A 298-A2

SIEMENS GALVO type M 290-A2

4 7

FIG. 29 VIEW OF THE MOUNTING OF A PRESSURE TRANSDUCER

(FLUSH WITH THE INNER FACE OF THE PIPE)

1 PIEZOELECTRIC PRESSURE TRANSDUCER

2 CONNECTING CABLE ( TO CHARGE AMPLIFIER )

3 MOISTURE PROTECTOR

48

FIG.30 VIEW OF INDUCTION FLOWMETER

1 MAGNETIC COIL

2 ELECTRODES ( IN-SIDE THE PIPE )

3 PREAMPLIFIER

4 PHASE DEMODULATOR

5 OSCILLATOR

« •

IH ti -p ca •

SS"

r-\ u a <D - P f H

. "^

o m co ca 0) (U 0} ft ft ft +^ ca • o •

f2

I

Uj

«o

Lu

O.

O.

co

i

00 ki

o.

o

Co to

tÖ Lu

Lu

Cfc O . lO Ci Co

Lu

ci:

S

co

I

co

§

f*)

cd

L L

u

o

••»

$

+= o o <! +=

a

o FH CH

.1

_-\k-^

PTi

I

CLOSED

a:

90°

a

• J OfrO

OPEN

'l-4 '2-3

\Ph

\Ph

_i

Ph

STEADY CONDITIONS POINTS OF MEASUREMENTS

•ix\-

:H.

o

51

ij

co

co

0.034

O 033

0.032

0.031

0.030

0.029

0.028

0.027

0.026

0.025

0.024

0.023

0.022

0.021

0.020

0.019

0.018

0.017

0.016

\ \

• +

^

\

\

+

%

\ \

\

V

.N

• • •

\

\

k

N

•,

• V

'•

KAr-tr'i ini-n i #»/t. . . . -. o » . i /Al 1 ir •c /lowiTci/ ryii.ut^o

nn-rn aiarr /OCCCaChinO Tceil

omuuin rirc i n t . r t r » t » » o t / i ^ » . ^

+

S,^

^

's,^ ' • • • • . .

f>"k^

^ *>

> ^

' -^

+

'..._

•.'*r

• - - +

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1. 1.2 1.3 1.4 1.5

^ STEADY VELOCITY IN PIPE (m/s)

STEADY FRICTION FACTOR IN THE PIPE

o

co

o

3.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

/ /

f

1

/

/

/ /

/

/

/ / ( t

l

= .

1

I

1

( 1 (^

J^l

>-^ ^ ^

2

i

ï;

5

4.0

o

co

3.5

3.0

2.5

15

30

45

60 75

-*- VALVE ANGULAR POSITION

2.0

90°

MEASURED VALVE RESISTANCE FOR DIFFERENT OPENING

POSITIONS AT STEADY FLOW CONDITIONS

34.3m

- ELECTRICAL SIGNAL

1. VALVE AND VALVE STEERING MECHAHISH 2. RECORDER

3. AMPLIFIER-RELAY COMBINATION 4. BALL INJECTOR

5. PHOTOCELLS DETECTOR RING 6. ILLUMINATION LAMPS

7. GLASS PLATE 8. TIME BASE MOTOR 9. HIGH SPEED CAMERA 10. INDUCTION FLOWMETER

11. PRESSURE TRANSDUCER

•i^

POINT OF PRESSURE MEASUREMENT POINT OF VELOCITY MEASUREMENT (USING INDUCTION FLOWMETER) V4P POINT OF VELOCITY MEASUREMENT

(USING PHOTOGRAPHIC SYSTEM)

PHOTOGRAPHIC SYSTEM ARRANGEMENT

FIG, 35

FIG. 36 TYPICAL FRAMES OF THE FILM. (NUMBERS SHOWN ON

THE FIGURE GIVE THE SEQUENTIAL FRAME NUMBER, Rj AND R^

ARE REFERENCE POINTS).

PHOTO'ANALYZER SCREEN

CO-ORDINATES SYSTEMS USED FOR CALCULATIONS OF

BALL DISPLACEMENT AND TIME FOR TRANSIENT FLOW

VELOCITY MEASUREMENT USING THE PHOTOGRAPHIC METHOD

FIG. 37

*tS y Q o TQ RECORDEU

24VÜ

1. MAGNETIC COIL 2. ELECTRODES 3. PREAMPLIFIER 4. PHASE DEMODULATOR 5. OSCILLATOR

SCHEMATIC DIAGRAM OF INDUCTION FLOWMETER

FIG. 38

VALVE OPEN 0.0 1.22.

1

m/s

^STA 1 1 PI P2 P3 1 1 P4 1 1 1 V4 RTING

^^

- ^

OF VAL\

^

' ^

" " • - - i — 'E CLO

^ ,

\

SURE

^

X

'

VALVE CLOSED •

/

\ /

/

/

/

r

1

1

1

J

' j

(1

1

4

/

i O ^ v\

r

/

A

\c

I V .

s,

V

/

JK

^

-A

/

^

/

— fl

J

AJ

1

J

- ^

i./l

/I

V

V

\

1

s

I

k/

V /

^

hi

^'^

r

r-

^

. , „,

^7^ N / PTg PTj

\]0J,

's.n

rt O'? * AH 34.3 m

_

I

4 0 m 1 1 1 1 LJ - T — • • • J

A

?\

\

^

L

V ^

_{^ \}

-^

^

pu

v^p ^i

- ' • 1

— ^

0.0 TIME SCALE

ANGULAR POSITION OF THE VALVE.SCALE PRESSURE SCALE VELOCITY SCALE 1cm - 0,193 second 1cm .- 30 degrees 1cm = lOm(WATER) 1cm ' 0,45m/s TIME

EXPERIMENTAL MEASUREMENTS DURING TEST USED FOR COMPARISON OF THE

PHOTOGRAPHIC AND INDUCTION SYSTEMS FOR VELOCITY MEASUREMENTS.

-2.2S -1.8 -1.3S -0.9 -4.5 0.0 *a45 *0.9 *1.35 *1.8 VELOCITY *2.2S (m/s) oQ

.-

^^ ^

4

y.

y y

/

/ /

/ /

f ^

y

1

/

/ /

//

//

\/

/

A

1

1

\

i

!

ƒ

V y

V

_V

/

//

7 0 /

/ \

'A,

)

i

1

\ /

r^

e "" N ^ ,

" ^ ^

• -- • UI 00 0.965

INDUCTION FLOWMETER RESULTS PHOTOGRAPHIC SYSTEM RESULTS

1.930 2.895 3.660

-^ TIME(s)

TRANSIENT FLOW VELOCITY CHANGES USING THE

PHOTOGRAPHIC AND INDUCTION SYSTEMS.

59

r

t

ELECTRICAL SIGNAL

1. VALVE AND STEERING MECHANISM 2. 3. 4. 5 6. 7. 8

a

RECORDER ACTUATOR ILLUMINATION LAMPS GLASS PLATE TIME BASE-MOTOR HIGH SPEED CAMERA PRESSURE TRANSDUCER PLEXIGLASS PIPE

PHOTOGRAPHIC ARRANGEMENT

10C.PS. TIME SIGNAL

VALVE

OPEN

FIG. 42

-^TIME(s)

Transient pressure changes resulting from closure of the valve ' in 1 second for a steady flow velocity of 1 m/s.

Results are redrawn from the recorder records.

P,» P2 5 Pg are pressure changes at locations PT , FT , PT .

The time axis is based on the recorder speed anè the 10 c?p.s. time signal should be used for accurate values of

time.

61

FIG 43 VIEW OF THE TANGENTIAL AND AXIAL STRAIN GAGES CEMENTED ON THE

OUT-SIDE SURFACE OF THE PIPE AT LOCATION PT2 (FIG.42). THE PIEZO ELECTRIC

PRES-SURE TRANSDUCER APPEARS IN THE PICTURE

10m

(WATER)

\ ^

\

\

\

200^

MICRO-STRAIN

\s,:

90°

VALVE

OPEN-DE

1

-^

1

Pi

P2

^C2 ^X2

/

,/f

.10 C.P.S. TIME SIGNAL

1

1 1

»v,^^

»^

^

1

^

1 1

1 1 1

" 1

1 1

/

/

1

/

'' '

T

-If

/

J,

^l

jf

\

MLVE CLC

1 1

1

iL

\

L

t

f

tSED

1 1

^J

Jrr,

L

^ 1

1

/

J

\->

J

i l

_u

s ^

V

r\

,

A

/

\

\

A

\

\

/

y

1

LA

A

M^.

1

r

1

/ "

/

.

/ ^

/

A

'-'^^V

•

1 1

I

\ _

\

\

V

\

V.

• ^

-/

1 1

/

7

/\

J

I

^

11

A

\

\

\

\

^

\

^

1 1

T-T

1

J

é

J

/

^

1 1

SEE FIG.

\

\

A.

\

^ ,

\

^ " ^

/

1/

J

U\

j ^

^

45

\

\

^ \ ,

N ^ s ^

^

1 1

y

y

'vr

<-*•

1 1

N,

\

j ^ ^^v.

=^

1 1

y'

^

,^

^^

to

0.0

Strain

valve

Result

^ ' ^2

P+ (F

values

1.0

2.0

_{FIG. 44}

3.0

4.0

_TIME(s)

s at the outside surface of the pipe at location FT during transients resulting from linear closure of the

in 1 second for a steady flow velocity of 1 m/s.

s are redrawn from recorder records.

are pressure changes at locations PT

1'

FT and

^c2' ^x2

^^^ ^^^

circumferential and the axial strains at

location-ig. 42). The time axis is based on the recorder speed and the 10 c.p.s. time signal should be used for accurate

10 m

(WATER)

200 \

MICRO-STRAIN^

I

^

. ^

/

/

/

/

/

/

^

§—

« «

-"

• - ' - —

^

~ ^

s.

\

\

,

\

/"

STEADY-FLOW PRESSURE

' AT PT2

{^STEADY-FLOW

CIRCUMFERENTIAL STRAIN

AT PT2

1.4 1.42 1.44 1.46 1.48 1.5 1,52 1.54 1.56 1.58 1.6

'^TIME (s)

An oscilloscope record (redrawn) showing the pressure P„ and the circumferential

strain_e^2

^^

location PTj (Fig. 42), during the transient test whose results are

shown in Fig. 44. Triggering time of the scope =1.4 second. T-T in Fig. 44

10m

(WATER)

H

\

1

200

MICRO-

^STRAIN-\a2\

90°

VALVE

OPEN

u

1

-: ^ ^

1 /

Pi

P2

^C2 ^X2 ^ ^ / /

1

10C.PS. TIMESIGNAL

1 1 1 1 1 1

^ ^

1 1

• ^

-1 -1

1

₁

/ /

J

1

1

\ ^ ^

1

f\

\

\

f\

A,

>

1

/

J

J

\J

"'"^-^^ \

\

\

A

/N

1

/

k/1

V

v ^

1

A

\

r\

^ ^

^yALVE CLOSE 1

.

1 1

J *

N/

^ - ^

1 1

r ^ .

^ ^ ^ ^ v

1 1

- ^

^ ~ ^

1 1 1 1

^ '

1 1

1

- ^

1 1

» = ^ •

GO

/.O

2.0

3.0

_4.0

_-^TIME(s)

strains at the outside surface of the pipe at location PT2 during transients resulting from closure of the valve in

? seconds for a steady flow velocity of 1 m/s. Results are redrawn from recorder records.

Fi , Po are pressure changes at locations PT;^, PT2 and

e^2-> ^x2

^r^^ the circumferential and the axial strains at

lo-(Fig. 4 2 ) .

cation PT2 (Fig. 42),

The time axis is based on the recorder speed and the 10 c.p.s. time signal should be used for accurate values of time,

FIG. 46

10m

(WATER)

-i

1

\

\

\

\

]

1 1

1 1

1

1-Ps

Ps

1 \

^

X

^l

1

J

'

r-P

1

T

T

JP

J

^

1

10C.PS. TIMESIGNAL

1

r

J

^

I

'/OC.i

1

1

\

\

1

11

PS. r/

1 1

1-i

/

J

iji

MESt

1

/

/

\

\

I6NAL

1

1

^

\

IL

/

1

1 1

jL

/I

\

\

I 1

/I

J\

f

'

/ ^

r

1 1

I

V

\

\

1 1

1 1

J

1 ^

A/

/

/

1 1

1 r

j

\

\

V

^

1 1

/

/

/ ^

/

J 1

0.2second

1 1

, /

K

_\

/

/

v^

1 1

1 1

1 1 1 1

1 1

Vo=015m/s

/ "

f

S^

Xy

,^^

1 1 •

VQ=0.5m/s

/ ^

1 1

1 1

,-^

1 1

.1 1

/^\

1 1

^

1 1

11

^ >

1 1

1 1

1

—

1 1

—.,^_

1

1

TIME

Transient pressure changes at PT^ (Fig. 42) resulting from sudden closure of the auxiliary valve (at downstream

end ot the pipe) for steady velocities in the pipe, of 0.5 and 0.75 m/s.

DATA SHEET

X h

₊

_N

DATE: AIR TEMPERATURE: "C BAROMETER READING: mmHG WATER TEMPERATURE: "C STEADY CONDITIONS:

HIGH LEVEL RESERVOIR: LOW LEVEL RESERVOIR :

LEVEL DIFFERENCE BETWEEN TWO RESERVOIRS: V NOTCH READING :

STEADY VELOCITY IN THE PLEXIGLASS PIPE : VALVE CLOSURE : TIME OF CLOSURE : TYPE OF CLOSURE : RECORDERS DATA :. PRESSURE SCALE VELOCITY SCALE PAPER SPEED OSCILLOSCOPE DATA :

UPPER CHANNEL SCALE LOWER CHANNEL SCALE TRIGGERING TIME

SWEEP TIME : REMARKS:

H,

-o<^

'o'

'o o 2g

T:

• * - V

H,

SCHEMATISATION OF THE HORIZONTAL LINE SYSTEM

t=0

,

i

^<

1

R

JX

f

p

H

a

s

i

MF

M=1

NR.

MR

N M

/

\

NQ MQ

NS.

MS

• 00

x=0

x=L

Nzl

2 3 4 5 6 7 8 9 10 NF=11 x

x-t PLANE

GRID TERMINOLOGY FOR COMPUTER PROGRAMS

DEFINITION SKETCH SHOWING SPACE-TIME

GRID USED FOR COMPUTER PROGRAMS.

PRINCIPLE OF LINEAR INTERPOLATION USED TO

OBTAIN VALVE RESTISTANCES DURING ITS CLOSURE

p

\

\

\

\

s

x=0

H,

Up

^P

l(t)

H

_u

W.

I

m

t

N.M

,

\

\

N

\

\

\ NS.MS

O

' •• :-'{~v.'' _ — '

X N:1 N=2

• H(N.M)

HUVO i

-I V(N.M)

ZZ(M)

CASE OF NO VOID AT THE VALVE

' ^ H(N,M)-PV

VBL.^ VBR

• IPl

ZZ(M)

CASE OF A VAPOUR VOID AT THE VALVE

DEFINITION SKETCH SHOWING SPACE-TIME

GRID FOR THE VALVE BOUNDARY CONDITION

USED FOR COMPUTER PROGRAMS.

R

c\''

/

/

/

p

x=i

NR.MR

~7

N.M

NzNF

V(N,M)

H(N.M)

DEFINITION SKETCH SHOWING SPACE-TIME

GRID FOR THE LOW LEVEL WATER RESERVOIR

CONDITION USED FOR COMPUTER PROGRAMS.

72

_{PRESSURE ^ V E L O C I T Y HLONG L I N E}

EXPMES-- G1Ü4

C A L C U L H T E D

VÜ--1.ÜG

M / S E C

. MEASURED

TC--2..00 SEC

PG p ( N - i c ; V (N-^J ^ . M ^ ' - ' ^ l i j - J l ^ j ' ^ ^ n .ij-b"! i ^ T > , ^ « - l , r ^ * ^ ' < ^ " VELeC.'TT 1CM-- C i M/3EC .

-w-

V6 C.C'LI C.4C1 C.^C i , 2 0 I , ' ] : '

_{r.. cu}

2 . 4 C 3 . JÜ l . G C

T!Mf" IN SF.CCNDS

F/6. 54 COMPARISON OF CALCULATED AND

PRESSURE ^ VELOCITY flL

EXPMES- 6155

V0=Ü.75 M/SEC

TC=1.G0 SEC

Pi

ONG LINE 73

CRLCULflTED

MEASURED

P2

P4

Ps

0 U 8 12 16 20 24 28 32 36 ^0 METERS N= 1 2 4 6 8 9 10 1 . I I I I I I I I I I SCRLES; PRESSURES 1CM=10 M.W.C. VELOCITY ICM^ 0.5 M/SEC

Vfl

-^

V8

0.00

0.40

0.80

1.20

1.60

2.00

2.40 2.50 3.20

TIME IN S E C O N D S

3.GO

FIG. 55 COMPARISON OF CALCULATED AND

10CPS. TIMESIGNAL

VALVE

OPEN

4.0

0.0 1.0 2.0

Transient pressure changes resulting from the closure of the valve in about 1.7 s. for a steady flow velocity of

1 m/s. Results are redrawn from recorder records.

' ^1» ^ 2 ' ^3 ^"'^ P4 s^s pressure changes at locations PT^, PT2, PT3, PT4.

The time axis is based on the recorder speed and the 10 c.p.s. time signal should be used for accurate values of time,

I I

12

13

[^fl

f

17

j 1

_{^ ^ H}

^^1

LÉMI^MHI

r"

•

•

i

18

I 9

113

l U

115

119

120

121

w 00

110

111

112

116

117

118

1 2 2

123

I2Z»

TC=^1.2s

Ha = 1.12m

•^Vo=1m/s

-L = 46m

A

Hb=0.5m

DIFFERENT FRAMES OF THE HIGH SPEED FILM SHOWING

WATER COLUMN SEPARATION AT THE VALVE

7 7

(X.-JX.ti)

4

•

1

(x,.t,)

'

(Xi.tf*Jt)

'3

2

'5

(Xj.ti-Jt)

(Xi*^X.ti)

FINITE DIFFERENCE APPROXIMATION PRINCIPLE

t *Jt

o

00

t -^t O

SPACE-TIME GRID SCHEME FOR FINITE DIFFERENCE

SOLUTION USING THE NEW MATHEMATICAL MODEL

79

O VELOCITY Vi

O 0.49 0.98 147 1.96 2.45 2.94 3.43 3.92 '^TIME(s)

EXAMPLE OF A MEASUREMENT USED FOR

DETERMINATION OF DYNAMIC VALVE RESISTANCES

8 0

Uj 10

5

to

p'

UJ Cfc UJ :^ - j

S 10

a

6

ld

8

6

4

1

0.8

0.6

0.4

0.2

0.1

— STEADY FLOW * 5102 VO'ljO m/sec ; TC = 4.0 t 5052 .. :12 .. ; .. =4.0 A 5176 .. .-0.75 .. : .. =1.0 O 5178 „ zO.75 ., : .. =0.5 a 5071 „ =1.2 .. : .. =1.0

f

/

8

to t2>

to

S

z

10"

8

6

10'

8

6

10"

8

6

10'

8

6

10 20 30 40 50 60 70 80 90

^VALVE ANGLE (degree)

10

UI

5

to

5

DYNAMIC RESISTANCE OF VALVE DURING CLOSURE

8 1

FIG. 62 VIEW OF ARRANGEMENT USED TO VISUALISE SMALL BUBLES IN THE PIPE

1 PLEXIGLASS PIPE

2 PLEXIGLASS WATER BOX

3 SEAL

82

o

1.0

\

AIR-WATER .P= 25 psia

E

J

1 1 1 1

0.2

0.4 0.6 0.8 1.0

^ VOID FRACTION, et

a CELERITY IN

TWO PHASE

a„ CELERITY IN

GAS

ANALYTICAL PREDICTION OF CELERITY IN BUBBLE

AND STRATIFIED FLOW REGIMES f LINE I) ,IN

ANNULAR AND DROPLET DISPERSED FLOW

REGIMES (LINE 11) [2lJ

/ n y ^ ' - T - ' '

PRINCIPLE OF DETERMINATION OF MOMENTUM LOSS COEFFICIEHT c

USING LOGARITHMIC DECREMENT PROCEDURES

FIG. 64

84 PRESSURE

Sr

VELOCITY RLONG LINE

EXPMES= 6 1 5 ^ CflLCULflTED

VÜ-0.75 M/SEC

MEASURED

TC=:2.00 SEC

Ps

P5

Pe

p (N^n

P IN=4) p (N=9; P (N^IO) V (N=2) 0 4 9 12 16 20 24 29 32 3S 40 METERS N= 1 2 4 6 3 9 10 J 1 1 L. _l I l_ SCRLES- PRESSURES 1CM=10 M.W.C. VELBCITT 1CH= 0.5 M/SEC-Vfl V8

^ ^

0.00

0.40

0.3Q

1.20

1

.50

2.00

FIG. 65 COMPARISON OF EXPERIMENTAL AND

CALCULATED RESULTS FOR TEST NUMBER 6154

2.40 2.30 3.20

TIME IN SECONDS

PRESSURE ^ VELOCITY RLONG LINE 85

EXPMES= 6 1 5 5 CRLCULRTED

VÜ = 0 . 7 5 M/SEC MEASURED

T C = 1 . 0 0 SEC

V(N

V (N

\/^^^^H^^^

0 4 a 12 16 20 24 29 32 36 40 METERS N» 1 2 4 6 9 9 10 I ' I I I I I I I I I SCALES: PRESSURES 1CM=10 M.W.C. VELOCITY ICM- 0.5 M / S E C

frt

M

•tü VB

•n—N

0 . 0 0 0 . 4 0 0 . 3 0

_1.20

_1.60

2 . 0 0 2 . 4 0 2 . 3 0 3 . 2 0

TIME IN SECONDS

FIG 66 COMPARISON OF EXPERIMENTAL MEASUREMENTS

AND CALCULATED RESULTS FOR TEST NUMBER 6155

86 PRESSURE ^ VELOCITY RLONG LINE

EXPMES= 6156 CRLCULRTED

V0 = 0.75 M/SEC^

MEASURED

TC=0.50 SEC

Vlf^'lr iw 'p' fiii/'VVi/^^^^^^""" —^'

0 4 8 12 16 20 24 29 32 38 40 METERS N= 1 2 4 6 9 9 10 i I I I 1 1 I I I I I SCALES- PRESSURES 1CM=10 M.W.C. VELOCITY ICM» 0.5 M/SEC.

Vfl

M

M

-N ^

VB

Ü.00 0 . 4 0 0 . 3 0 1 . 2 0 1 . 6 0 2 . 0 0 2 . 4 0 2 . 3 0 3 . 2 0

TIME I N SECONDS

FIG 67 COMPARISON OF EXPERIMENTAL MEASUREMENTS

AND CALCULATED RESULTS FOR TEST NUMBER 6156

PRESSURE ^ VELOCITY RLONG LINE 87

EXPMES= 610^ CRLCULRTED

V0=1.00 M/SEC

MEASURED

T C = 2 , 0 0 SEC

[ 5 F tN=3i

P

Je ptN=ioi

V^^'^^^^^lw-^s

-,. V l ^ — h ^ M^-^^j^>^ f^^^--p .m r^ - 0

V (N=2)

''r^

fi^

^ t wf> ' VA V (N=.9)

A^-^v^^^-^'

0 4 3 12 16 20 24 29 32 35 40 METERS N= 1 2 4 6 8 9 10 I I • I I I I I I I I SCALES: PRESSURES lCM-10 M.W.C. VELOCITY ICM» 0.5 M/SEC.

Vfl

•tr

VB

0.00 0.40 0.90 1,20 1.60 2.00 2.40 2.30 3.20

TIME IN SECONDS

FIG 68 COMPARISON OF EXPERIMENTAL MEASUREMENTS

AND CALCULATED RESULTS FOR TEST NUMBER 6104

88 PRESSURE ^ VELOCITY RLONG LINE

EXPMES= 6105 CRLCULRTED

V0=1.00 M/SEC

TC^l.OO SEC

MEASURED

\ '^\i\J^yr^/^^^^f^-^,

S C A L E S : P R E S S U R E S l C M = i O M . W . C . V E L O C I T Y I C M ^ 0.5 M / S E C . Vfl

-h

•ti: VB

•n

^

0.00

0.40

0.30

1.20

1.60

2.00

2.40 2.80 3.20

TIME IN SECONDS

FIG 69 COMPARISON OF EXPERIMENTAL MEASUREMENTS

AND CALCULATED RESULTS FOR TEST NUMBER 6105

PRESSURE &. V E L O C I T Y RLONG L I N E

EXPMES- 6 1 0 6

V 0 = 1 . 0 0 M/SEC

T C = 0 . 5 0 SEC

89

CRLCULRTED

MEASURED

0 4 N= 1 2 I I 12 16 20 24 23 32 38 40 METERS 4 6 9 9 10 _ i I I _i [_

SCALES: PRESSURES lCH=iO M.W.C. VELOCITY lCM-= 0.5 M/SEC Vfl

-N

-k

- ^

VB

•n

0 . 0 0 0 . 4 0 0 . 3 0 1 . 2 0 1 . 6 0 2 , 0 0 2 . 4 0 2 . 3 0 3 . 2 0

TIME IN SECONDS

FIG. 70 COMPARISON OF EXPERIMENTAL MEASUREMENTS

AND CALCULATED RESULTS FOR TEST NUMBER 6106

>o

i 3

O 10 20 3.0

AT t-0 Pf !=-1.66mi % '^ -7.5m ; Pj'^0.35m EXPERIMENTAL TRANSIENT PRESSURES AND VELOCITY CHANGES DURING TEST NUMBER 8001

AT t-O P,=. 1.66m. P^^-7.5mi Pj~0.3Sm EXPERIMENTAL TRANSIENT PRESSURES AND VELOCITY CHANGES DURING TEST NUMBER BOOS

9 2

FIG 73 VIEW OF WATER COLUMN SEPARATION AT TOP OF THE SIPHON

(SEE LOCATION C ON THE SIPHON SCHEME IN FIG. 72)