The Viscosity of Steam

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PU R D U E UNIVERSITY

T H IS IS TO C E R T IF Y TH A T T H E T H E S IS P R E P A R E D U N D E R MY S U P E R V IS IO N

Paul A. Lottes

by

EN T IT L E D

The Viscosity of Steam

C O M P L IE S W ITH T H E U N IV E R S IT Y R E G U L A T IO N S O N G R A D U A T IO N T H E S E S

A N D IS A P P R O V E D B Y M E A S F U L F IL L IN G T H IS P A R T O F T H E R E Q U IR E M E N T S

FO R THE D E G R EE OF

Ph. D. i n .MochojiT n l " n iit

0. ft. M -

P

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r o fesso r

ead

o f

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in

C

ha rge of

cho ol

or

D

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h e s is

epa rtm en t

TO T H E L IB R A R IA N :---T H IS T H E S IS IS N O T TO B E R E G A R D E D A S C O N F ID E N T IA L .

O M

.J t.Q

S s k .

P R O F E S S O R IX

R E G I S T R A R F O R M 1 0 - 7 . 4 7 —1M

CHARGE

THE VISCOSITY OF STEAM A T h e s is S u b m itte d t o t h e F a e u l t y of P u rd u e U n i v e r s i t y by P a u l A lb e rt L o tte s In P a r t i a l F u lf illm e n t o f th e R e q u ir e m e n ts f o r t h e D e g re e of D o c to r o f P h ilo s o p h y J u n e , 1950

ProQ uest Num ber: 27714109

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.

uest ProQuest 27714109 Published by ProQuest LLC (2019). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346

VITA P a u l A# L o t t e s w as b o r n I n P i t t s b u r g h , P e n n s y lv a n ia on A u g u st E , 1 9 8 6 ,

He a t t e n d e d K e l l y Grammar S c h o o l (1 9 3 2 -

3 7 ) , W ilk in s b u r g J u n i o r H ig h S c h o o l ( 1 9 3 7 - 4 0 ) , a n d W il k i n s b u r g H igh s o h o o l (1 9 4 0 -4 3 ) i n P i t t s b u r g h ,

In F e b ru ary 1943,

h e e n t e r e d P u rd u e U n i v e r s i t y an d s t u d i e d to w a rd a B, S , d e ­ g r e e i n M e c h a n ic a l E n g in e e r i n g u n t i l F e b r u a r y 1 9 4 5 ,

At t h i s

tim e h e w as i n d u c t e d i n t o t h e Army A i r F o r c e s a s a P r e - A v i a yt i o n C a d e t , I n Novem ber 1 9 4 5 , h e w as h o n o r a b ly d is c h a r g e d a s & s u r p l u s a i r c re w t r a i n e e .

Upon r e - e n t e r i n g P u rd u e U n i­

v e r s i t y , h e c o m p le te d h i s e n g i n e e r i n g t r a i n i n g a n d r e c e i v e d h i s B ,S .M .E , i n J u n e 1 9 4 6 , I n J u n e 1 9 4 6 , P a u l A# L o t t e s e n t e r e d t h e g r a d u a t e s c h o o l a t Ptardue u n i v e r s i t y . g re e In F e b ru ary 1948,

He r e c e i v e d h i s

de­

He w as t h e n em p lo y ed a s a f u l l tim e

r e s e a r c h a s s i s t a n t b y t h e E n g i n e e r i n g E x p e rim e n t s t a t i o n o f P u rd u e U n i v e r s i t y a n d w orked u n t i l O c to b e r 1949 on h e a t t r a n s f e r t o m a c h in e g u n b a r r e l s , w h i l e t a k i n g c o u r s e s to w a rd a P h , D , i n M e c h a n ic a l E n g i n e e r i n g .

I n O c to b e r 1 9 4 9 , h e b e ­

g a n f u l l tim e w ork to w a rd h i s P h . D . P a u l A« L o t t e s I s a member o f B e ta Sigm a P s l , P i T en S ig m a , an d a n a s s o c i a t e member o f Sigm a % i.

iiâilHÆis ACKNOWLEDGMENTS

T he a u t h o r i s g r e a t l y i n d e b t e d t o B rs* W, L . S i b b l t t , C# B . S t . C l a i r , an d D. C . H a m ilto n f o r t h e i r many s u g g e s ­ t i o n s an d c r i t i c i s m s e x te n d e d th r o u g h o u t t h i s i n v e s t i g a t i o n . The a u t h o r i s a l s o g r a t e f u l t o h i s f e l l o w s t u d e n t s f o r t h e i r a s s i s t a n c e i n some p h a s e s o f t h e w o rk . S p e c i a l t h a n k s a r e due t o t h e W e s tin g h o u s e C o r p o r a t i o n f o r m ak in g t h i s p r o j e c t p o s s i b l e b y s p o n s o r in g a F e llo w s h ip f o r th e a u th o r .

TABLE OF CONTENTS P age L IST OF FIGURES L IST OF TABLES ABSTRACT INTRODUCTION

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I

LITERATURE S U R V E Y ................................................................................

3

DESCRIPTION OF APPARATUS G e n era l C ir c u it

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6

The B o i l e r an d t h e S u p e r h e a t e r ....................................

6

The A n n u lu e

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8

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10

The M an o m eters

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The P r e s s u r e S t a b i l i s e r The C o n d e n se r

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A u x i l i a r y A p p a r a tu s

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11 .

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13

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...... ............................................ .......

13

EXPERIMENTAL PROCEDURES G e n e ra l P ro c e d u re s

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C a l i b r a t i o n w ith N i t r o g e n

• • •

15 15

M easu rem en t o f t h e V i s c o s i t y o f S u p e r h e a te d s te a m «

16

E x p e rim e n ta l D i f f i c u l t i e s

17

RESULTS AND SAMPLE CALCULATIONS DISCUSSION OF RESULTS

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20

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30

CONCLUSIONS AND RECOMMENDATIONS

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APPENDIX A D ev elo p m en t o f t h e V i s c o s i t y E q u a t i o n f o r L a m in a r Flow T h ro u g h a n A n n u lu s V is c o m e te r . . . . .

38

P age APPENDIX B C a l i b r a t i o n o f th e A n n u lu s BIBLIOGRAPHY DISPOSITION OF ORIGINAL DATA

V is e o m e te r •

•

•

*

•

41

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54

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56

LIST OF FIGDHES F ig u r e 1.

P age

S c h e m a tic D iag ram o f A n n u lu s a n d A s s o c i a t e d E q u ip m e n t .

£»

A n n u lu s V is c o m e te r .

3.

Two F l u i d M anom eter

4.

V i s c o s i t y o f S u p e r h e a te d S team a t 1000 p a l e

5. 6. 7. 8. 9. 10.

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7

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9

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11

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V i s c o s i t y o f s u p e r h e a t e d s te a m a t 1500 p a i e . . . » ...........................................

27

V i s c o s i t y o f s u p e r h e a t e d s te a m a t 2000 p s i a

............................................ 28

V i s c o s i t y o f s u p e r h e a t e d s te a m a t 1 0 0 0 , 1 5 0 0 , a n d 2000 p s i a

..................................... 29

F o r c e B a la n c e f o r Flow T h ro u g h a n A n n u lu s

..................................... 38

E f f e c t o f T e m p e ra tu re on Y oungf s M o d u lu s C o r r e c t i o n F a c t o r s f o r T e m p e ra tu re a n d P r e s s u r e ............................... .....

.............................................46 53

LIST OF TABLES T a b le

P age

1.

V is c o s ity I n v e s tig a tio n s

2.

E x p e r im e n ta l D a ta a t 1000 p s i a .................................................. 22

3.

E x p e r im e n ta l D a ta a t 1 5 0 0 p s i a

4»

E x p e r im e n ta l D a ta a t 2000 p s i a

5.

E x p e r im e n ta l V a lu e s o f t h e C a l i b r a t i o n C o n s ta n t .

6. 7. 8.

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........................................... 2 3 .

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E f f e c t o f T e m p e r a tu r e on t h e C a lib r a tio n C o n s ta n t . . E f f e c t o f P r e s s u r e cm t h e C a l i b r a t i o n C o n s ta n t .

4

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C om bined E f f e c t o f T e m p e ra tu re a n d P r e s s u r e on t h e C a l i b r a t i o n C o n s ta n t . . . . .

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24 48

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50

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50 .

58

ABSTRACT

The dynam ic v i s c o s i t y o f s u p e r h e a t e d s te a m w as d e t e r ­ m in ed w i t h a n a n n u lu s v i s c o m e t e r .

D a ta w e re r e p o r t e d f o r

p r e s s u r e s o f 1 0 0 0 , 1 5 0 0 , an d 2000 p s i a f o r t e m p e r a t u r e s o f 7 0 0 ° up t o u o o ° r . The a n n u lu s v i s c o m e te r c o n s i s t e d o f two c o n c e n t r i c t u b e s o f 1 8 - 8 s t a i n l e s s s t e e l w i t h a c l e a r a n c e o f 0 .0 0 5 i n c h e s b e ­ tw e e n t h e i n n e r s u r f a c e o f t h e o u t e r t u b e a n d t h e o u t e r s u r ­ fa c e o f th e in n e r tu b e .

The t e s t l e n g t h o f t h e v is c o m e te r

was 4 i n c h e s l o n g . The p r e s s u r e d ro p a lo n g t h e a n n u lu s w as m e a su re d w ith a m e rc u ry a n d w a t e r d i f f e r e n t i a l m a n o m e te r.

The f lo w r a t e

w as d e te r m in e d b y w e ig h in g t h e c o n d e n s a t e on a n a n a l y t i c a l b a la n c e .

T e m p e r a tu r e s w e re m e a su re d w i t h I r o n C o n s ta n ta n

th e rm o c o u p le s . The p r e c i s i o n o f th e I n s t r u m e n t a t i o n w as i : 4#»

The

d a t a o b t a i n e d i n t h i s i n v e s t i g a t i o n a g r e e s w ith t h e d a t a o f T . W. J a c k s o n , b u t d i f f e r s fro m t h e d a ta o f o t h e r I n v e s t i ­ g a to rs . Above t h e c r i t i c a l t e m p e r a t u r e , t h e r a t e o f c h a n g e o f v i s c o s i t y w ith r e s p e c t t o p r e s s u r e a t c o n s t a n t t e m p e r a t u r e w as fo u n d t o b e n e g a t i v e .

1

THE VISCOSITY OF STEAM

INTRODUCTION The p u r p o s e o f t h i s i n v e s t i g a t i o n w as t o d e te r m in e t h e d y n am ic v i s c o s i t y o f s u p e r h e a t e d ste a m f o r p r e s s u r e s up t o 2 0 0 0 p s i a a n d t e m p e r a t u r e s up t o 1 1 0 0 ° F , an d i n p a r t i c u l a r t o d e te r m in e v i s c o s i t i e s n e a r t h e c r i t i c a l t e m p e r a t u r e • T* W. J a c k s o n i n a p r e v i o u s I n v e s t i g a t i o n on t h e v i s ­ c o s i t y o f s u p e r h e a t e d ste a m c o n s t r u c t e d a n a n n u lu s v i s c o m e te r a t P u rd u e U n i v e r s i t y *

The a p p a r a t u s c o n s i s t e d o f a s m a ll

c a p a c ity h o l l e r , a s u p e r h e a te r , th e a n n u lu s , a d i f f e r e n t i a l m an o m ete r f o r m e a s u r in g t h e p r e s s u r e d r o p , an d a c o n d e n s e r* J a c k s o n o b t a i n e d d a t a w i t h t h i s a p p a r a t u s f o r p r e s s u r e s up t o 1 5 5 0 p s i a a n d t e m p e r a t u r e s up t o 1100°F *

I t w as i m p o s s i­

b l e f o r him t o o b t a i n d a t a a t p r e s s u r e s much h i g h e r t h a n 1500 p s i a d u e t o t h e d i f f i c u l t y i n m a i n t a i n i n g a c o n s t a n t p r e s s u r e I n t h e sy stem * The w r i t e r u s e d t h e o r i g i n a l a n n u l u s , b o i l e r , s u p e r ­ h e a t e r , an d c o n d e n s e r c o n s t r u c t e d b y J a c k s o n , an d a d d e d a p r e s s u r e s t a b i l i z e r a lo n g w i t h t h e o t h e r n e c e s s a r y c o n t r o l s t o e x te n d t h e r a n g e o f t h e i n s t r u m e n t t o 2000 p s i a * The I n s t r u m e n t w as f i r s t c a l i b r a t e d w i t h n i t r o g e n a t s e v e r a l v a l u e s o f t e m p e r a t u r e an d p r e s s u r e t o d e te r m in e th e c a l i b r a t i o n c o n s t a n t f o r u s e I n t h e v i s c o s i t y e q u a tio n * t a i l s o f th e c a l i b r a t i o n a r e g i v e n i n A p p en d ix B*

De­

B

The h o l l e r w as t h e n f i l l e d w i t h w a t e r a n d t e s t s w e re e o n d u e te d t o d e te r m in e t h e d y n am ic v i s c o s i t y o f s u p e r h e a t e d s te a m fro m t h e c r i t i c a l t e m p e r a t u r e u p t o 1 1 0 0 °F a t p r e s s u r e s o f 1 0 0 0 , 1 5 0 0 , a n d BQQ0 p s i a # A f t e r t h e s e t e s t s w e re p e r f o r m e d , t h e i n s t r u m e n t w as a g a in c a l ib r a t e d w ith n itr o g e n .

V a lu e s o f th e c a l i b r a t i o n

c o n s t a n t s d e te r m in e d b e f o r e a n d a f t e r t h e ste a m t e s t s a r e r e p o r t e d i n A p p e n d ix B*

3

LITERATURE SURVEY A s u r v e y o f t h e l i t e r a t u r e fro m 1949 t o t h e p r e s e n t r e ­ v e a l e d no a d d i t i o n a l i n f o r m a t i o n on t h e v i s e o s i t y o f s u p e r ­ h e a t e d s te a m .

T he f o l l o w i n g t a b l e fro m J a o k s o n 's P h . D .

t h e s i s l i s t s i n v e s t i g a t i o n s up t o 1 9 4 9 , i n c l u d i n g t h e name o f th e i n v e s t i g a t o r , th e ra n g e o f th e e x p e rim e n ts , and th e ty p e o f e q u ip m e n t u s e d b y e a c h i n v e s t i g a t o r .

T h e re I s c o n ­

s i d e r a b l e d is a g r e e m e n t i n t h e l i t e r a t u r e a b o u t t h e v i s c o s i t y o f s u p e r h e a t e d s te a m n e a r t h e c r i t i c a l t e m p e r a t u r e .

For a

c o m p le te t r e a t m e n t o f t h e a v a i l a b l e d a t a on t h e v i s c o s i t y o f w a te r a n d w a t e r v a p o r , t h e r e a d e r i s r e f e r r e d t o a p a p e r by H a a fc in s, S o l b e r g , a n d S i b b l t t . ( 7 ) *

1 N um bers i n p a r e n t h e s e s r e f e r t o t h e B i b l i o g r a p h y , p a g e 5 4 .

4

TABU! 1 V ls o o s ity I n v e s tig a tio n s In v e s tig a to r

T ear

T e m p e ra tu re Range i n F Low H ig h

P r e s s u r e Range i n A tm o sp h e re s Low H ig h

S p e y e re r

1985

818

668

1

10

Schougayew

1933

212

752

1

93

S c h ille r

1934

212

5 3 9 .6

1

30

H a ik in s , S o lb e rg , and P o t t e r

1935

818

1000

1

239

S ig w a r t

1936

529

711

25

870

H a w k in s, S o lb e rg , and P o t t e r

1940

212

1000

1

123

T im ro th

1940

302

1112

1

290

Jackso n

1949

842

1115

1

100

t c o n t i n u e d on f o l l o w i n g p a g e ) N o te :

T h is T a b le w as r e p r o d u c e d fro m T$ W# J a c k s o n • s P h , D .

T h e s i s , P u rd u e U n i v e r s i t y , F e b r u a r y 1 9 4 9 . w as c o m p ile d i n r e f e r e n c e 7 .

The o r i g i n a l d a t a

5

TABLE 1 ( c o n t ♦) In v e s tig a to r

E x p e r im e n ta l M ethod ,

M ethod o f P r e s s u r e D rop M e asu rem en t

R ef *

S p e y e re r

S te a d y flo w th ro u g h a b ra ss c a p illa ry 2 , 4 m e t e r s lo n g

D iffe re n tia l a l c o h o l m anom eter

15

Schougayew

R a n k in P r o c e d u r e (u n s te a d y s t a te )

12 M e rc u ry p e l l e t c r e a te d th e p re s s u re d iffe re n c e

S c h ille r

Flow th r o u g h a n o z z le (L a rg e e x ­ p e r i m e n t a l v a lu e s )

D i f f e r e n t i a l m ano­ m e te r g a v e l a r g e re a d in g s

H a w k in s, S o lb e rg , and P o tte r

L aw aozeck v i s c o ­ m e te r

A m e t a l w e ig h t p ro d u c e d t h e p re ssu re d i f f ,

S ig w a r t

S te a d y flo w th r o u g h M e a su re d b y a r i n g a q u a rtz o r p l a t i ­ b a la n c e num c a p i l l a r y ( a p p r o x , 370mm lo n g )

14

H a w k in s, S o lb e rg , and P o t t e r

S te a d y flo w th r o u g h a lo n g c a p i l l a r y 1 0 3 ,2 f t , lo n g )

D i f f e r e n t i a l Kg m an o m eter (R e ad b y m eans o f a r a d i o ­ g ra p h )

6

T im ro th

S te a d y f lo w th r o u g h a c a p illa ry (384,5m m lo n g )

M e asu red b y a r i n g b a la n c e

Jack so n

S te a d y flo w th r o u g h a n a n n u lu s (4 i n c h e s lo n g )

D i f f e r e n t i a l Hg m an o m eter (R ead b y m eans o f a r a d i o ­ g ra p h )

11

17

8

6

DESCRIPTION OF APPARATUS g e n e ra l C irc u it H ie a p p a r a t u s u se d I n c o n d u c t in g t h i s i n v e s t i g a t i o n c o n s i s t e d o f a s m a ll c a p a c i t y b o i l e r , a s u p e r h e a t e r , t h e a n n u l u s , a d i f f e r e n t i a l m an o m eter f o r m e a s u r in g t h e p r e s s u r e d r o p a lo n g t h e a n n u l u s , a p r e s s u r e s t a b i l i s e r t o m a i n t a i n a c o n s ta n t p r e s s u r e In th e b o i l e r , and a c o n d e n s e r. s h o e s a s c h e m a tic d ia g ra m o f t h e a p p a r a t u s .

F ig . 1

B ach o f t h e s e

c o m p o n e n ts w i l l b e d e s c r i b e d i n d e t a i l . T he B o i l e r a n d S u p e r h e a t e r S team w as g e n e r a t e d I n a b o i l e r c o n s t r u c t e d from, a n 1 8 -8 s t a i n l e s s s t e e l tu b e , Z i

In c h e s o u ts id e d ia m e te r by

1 £ in c h e s I n s id e d ia m e te r by 4 f e e t lo n g .

The b o i l e r w as

s u r r o u n d e d b y a u n i f o r m l y wound h e a t e r w i t h a £ in c h a i r g a p b e tw e e n t h e h e a t e r a n d t h e b o i l e r .

T h re e I r o n C o n s ta n ta n

th e r m o c o u p le s w e re m o u n ted I n w e l l s i n t h e b o i l e r w a l l so t h a t l o n g i t u d i n a l te m p e r a t u r e g r a d i e n t s i n t h e b o i l e r w a l l c o u ld b e o b s e r v e d . The b o i l e r h e a t e r w as wound fro m 165 f e e t o f B . & S . G auge 20 G hrom el nC" w ir e w i t h f o u r t u r n s p e r I n c h o f l e n g t h a lo n g th e b o i l e r .

H ie h e a t e r w as w ir e d I n t h r e e s e p a r a t e

s e c t i o n s so t h a t t h e pow er c o u ld b e v a r i e d t o e a c h s e c t i o n . A s i n g l e th e rm o c o u p le w as Im bedded I n t h e l o w e s t s e c t i o n o f t h e h e a t e r a n d c o n n e c te d t o a I h e e l c o C a p a e i t r o l .

T he

7

dono/ensers of? M a"?omefer Z f y j

F /c f. /.

ySc/rerna^f'c. fJ n n u /u $ ff'S s o c /a fe c /

/ory r a m c tn c/ F q fu ip m e n f

of

8

C a p a e i t r o l h e l d t h e h e a t e r t e m p e r a t u r e c o n s t a n t w i t h i n rb 1 0 °F w i t h a n o n - o f f c y c l e o f a p p r o x i m a t e l y 20 s e c o n d s . S e v e r a l l a y e r s o f i n s u l a t i o n w e re p l a c e d a ro u n d t h e h e a ­ t e r t o r e d u c e t h e h e a t l o s s e s fro m t h e h e a t e r t o t h e ro o m . f h e s u p e r h e a t e r w as c o n s t r u c t e d fro m 4 f e e t o f £ i n c h o u t s i d e d i a m e t e r b y 3 /3 2 i n c h i n s i d e d i a m e t e r 1 8 - 8 s t a i n l e s s s t e e l tu b in g .

The t u b i n g w as b e n t i n t o a s m a ll co m p a ct c o i l

so t h a t t h e a n n u l u s , s u p e r h e a t e r , a n d a b o u t 1 / 3 o f t h e t o t a l l e n g t h o f t h e m an o m eter l e a d s c o u ld a l l b e e n c l o s e d w i t h i n a c o m m e rc ia l h e a t i n g u n i t .

The h e a t i n g u n i t f o r t h i s s y s te m

w as 6 i n c h e s i n s i d e d i a m e t e r b y 1 2 i n c h e s l o n g .

The h e a t e r

w as s u r ro u n d e d w i t h i n s u l a t i o n t o r e d u c e h e a t l o s s e s . C a l c u l a t i o n s on h e a t t r a n s f e r t o t h e f l u i d a s i t p a s s e d t h r o u g h th e s u p e r h e a t e r i n d i c a t e d t h a t t h e t e m p e r a t u r e d i f ­ f e r e n c e b e tw e e n t h e v a p o r a n d t h e s t e e l tu b e w a l l a t t h e I n ­ l e t t o t h e a n n u lu s w as to o s m a ll t o b e m e a s u r e d .

For th is

r e a s o n t h e a n n u lu s tu b e w a l l t e m p e r a t u r e s w e re r e c o r d e d a s th e vap o r te m p e ra tu re s . T he A n n u lu s The a n n u lu s v i s c o m e te r a s o r i g i n a l l y d e s ig n e d an d b u i l t b y T . W. J a c k s o n i s

shown i n F i g . 2 .

I t c o n s i s t e d o f tw o

c o n c e n tr ic tu b e s o f 1 8 -8 s t a i n l e s s s t e e l w ith a c le a r a n c e o f 0 .0 0 5 i n c h e s b e tw e e n t h e i n n e r s u r f a c e o f t h e o u t e r tu b e an d th e o u te r s u r f a c e o f th e in n e r t u b e .

The o u t e r a n d i n n e r d i ­

a m e te r s o f t h e a n n u l a r s p a c e w e re 0 .3 1 2 5 i n c h e s an d 0 .3 0 2 5

9

î %

ï

10

In c h e s re s p e c tiv e ly *

f h e t e s t l e n g t h o f t h e a n n n lu s v i s ­

c o m e te r i a s 4 i n c h e s ,

f h e p r e s s u r e t a p s w e re l o c a t e d s u f ­

f i c i e n t l y f a r fro m t h e e n d s so t h a t no c o r r e c t i o n s w e re n e c ­ e s s a r y f o r k i n e t i c e n e rg y c h an g e s a t th e i n l e t and o u t l e t o f th e a n n u lu s .

f h e i n n e r tu h e o f t h e a n n u lu s w as t u r n e d down

t o 0.30215 i n c h e s w i t h a s m a ll l e n g t h a t e a c h e n d tu r n e d down t o o n ly 0 .3 1 B 5 i n c h e s so t h a t t h e tw o t u b e s w e re a s s e m b le d w ith a f o r c e f i t .

f h e e n d s o f t h e a n n u lu s w e re t h e n a r e w e ld ­

e d s h u t w i t h s t a i n l e s s s t e e l w e ld in g r o d . f h e M a n o m eters f h e m an o m eter l e a d s w ere made fro m 9 /1 6 i n c h o u t s i d e d i a m e t e r b y 5 /1 6 i n c h i n s i d e d i a m e t e r 1 8 - 8 s t a i n l e s s s t e e l tu b in g .

T h e s e l e a d s w e re i n s t a l l e d

so t h a t t h e y s lo p e d down

to w a rd t h e a n n u lu s t o k e e p c o n d e n s a t e fro m f i l l i n g t h e l e a d s . A t t h e end o f e a c h s l o p i n g m anom eter l e a d a v e r t i c a l t u b e o f t h e same d im e n s io n s w as a t t a c h e d w ith a s m a ll c o n d e n s e r on e a c h v e r t i c a l l e g t o k e e p t h e m a n o m e te rs a t room t e m p e r a t u r e . A t t h e t o p o f e a c h v e r t i c a l m a n o m ete r l e g , w h ere t h e l e g w as a t t a c h e d t o t h e s l o p i n g m an o m eter l e a d , t h e r e w as a s m a ll b u i l t - i n w e i r t o k e e p t h e w a t e r l e v e l c o n s t a n t i n e a c h le g .

R e f e r r i n g to F i g . 3 , we may w r i t e a p r e s s u r e b a l a n c e

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30

DISCUSSION OF RESULTS The c a l i b r a t i o n c o n s t a n t I n t h e e q u a t i o n (

( s e e A pp en d ix A)

IV

changed d u rin g th e i n v e s t i g a t i o n •

The v a lu e b e f o r e t h e t e s t s

« e r e c o n d u c te d « a s 0 ,0 0 1 1 8 ± 0 .0 0 0 0 8 a n d t h e v a lu e a f t e r t h e t e s t s m ere c o n d u c te d w as 0 .0 0 1 0 9 ±

0

.00002.

As t h e l a t t e r c o n s t a n t w as n o t d e te r m in e d u n t i l a f t e r t h e t e s t r u n s I t w as n e c e s s a r y t o r e c a l c u l a t e t h e v i s c o s i t y v a l u e s , a s su m in g t h a t t h e c a l i b r a t i o n c o n s t a n t c h a n g e d l i n ­ e a r l y w i t h t h e t o t a l m ass o f w a t e r v a p o r p a s s e d t h r o u g h t h e a n n u lu s . F ig # ? .

The r e s u l t s o f t h e s e c a l c u l a t i o n s a r e shown i n The r e c a l c u l a t e d v a l u e s show t h a t ab o v e t h e c r i t i ­

c a l te m p e r a t u r e t h e v i s c o s i t y d e c r e a s e d w i t h a n i n c r e a s e i n p r e s s u r e a t c o n s ta n t te m p e ra tu re .

E ven I f th e d a t a a s shown

in T a b le s 2 -4 a r e ta k e n a s th e t r u e v a lu e s o f v i s c o s i t y w ith ­ o u t a p p l y i n g t h e c o r r e c t i o n f o r t h e c h an g e i n t h e c a l i b r a t i o n c o n s t a n t , i t m ay b e n o t i c e d t h a t t h e v i s c o s i t y s t i l l d e ­ c r e a s e d w ith a n I n c r e a s e i n p r e s s u r e .

The e r r o r s in v o lv e d

i n o b t a i n i n g th e d a t a w e re n o t m ore t h a n ± 4$ d u e t o i n s t r u ­ m e n ta tio n .

A rfc 4 # e r r o r c o u ld n o t a c c o u n t f o r t h e s e p a r a ­

t i o n o f th e th r e e p r e s s u r e - v i s c o s i t y c u rv e s n e a r th e c r i t i ­ c a l te m p e ra tu re . T . W. J a c k s o n , i n a P h . D . T h e s i s a t P u rd u e u n i v e r s i t y , s ta te d a te n ta tiv e o u tlin e f o r a th e o ry o f v is c o s ity .

Ac­

c o r d i n g t o D o rs e y ( 2 ) , t h e r e i s a n a p p a r e n t d i f f e r e n c e I n

31

d e n s i t y o f s e c t i o n s o f w a t e r v a p o r a t t h e c r i t i c a l te m p e r a ­ t u r e t h a t d e f i e s a l l s t i r r i n g o r m ix in g *

I f t h is d iffe re n c e

i s a t t r i b u t e d t o th e f a c t t h a t t h e e f f e c t i v e d i a m e t e r o f some o f t h e m o le c u le s c h a n g e s a t t h e c r i t i c a l t e m p e r a t u r e , th e n th e r e i s re a s o n to s u s p e c t p e c u l ia r b e h a v io r o f th e v i s ­ c o s i t y n e a r th e c r i t i c a l p o i n t , s i n c e v i s c o s i t y I s a phenom ­ en o n a s s o c i a t e d w ith t h e t r a n s f e r o f momentum o f m o le c u le s * fh e d a ta o b ta in e d in t h i s i n v e s ti g a t i o n s u p p o rts t h i s t e n t a ­ t i v e t h e o r y , i n t h a t a d e c r e a s e i n v i s c o s i t y w as o b s e rv e d f o r an in c re a s e in p r e s s u r e a t te m p e ra tu re s above th e c r i t i ­ c a l te m p e ra tu re *

52

CONCLUSIONS AND RECOMMENDATIONS One o f t h e d i f f i c u l t i e s i n o b t a i n i n g v i s c o s i t y d a t e a t h i g h p r e s s u r e s i s t h e m e a su re m e n t o f t h e p r e s s u r e d ro p a lo n g a g i v e n l e n g t h o f c a p i l l a r y o r a n n u lu s »

The maximum p r e s ­

s u r e d ro p t h a t may be a t t a i n e d w i t h o u t b r e a k i n g down t h e flo w p a t t e r n d e p e n d s on R e y n o ld s m o d u lu s» . T he c r i t i c a l R e y n o ld s m o d u lu s f o r t h e a n n u lu s v i s c o m e te r u s e d i n t h i s I n v e s t i g a ­ t i o n w as a b o u t 500»

T h is v a lu e w as o b t a i n e d b y I n c r e a s i n g

t h e flo w r a t e a t a g i v e n p r e s s u r e a n d t e m p e r a t u r e u n t i l t h e c a l c u l a t e d v i s c o s i t y d a t a s u d d e n ly i n c r e a s e d •

T h is i n c r e a s e

w as d u e t o t u r b u l e n t flo w an d t h e r e s u l t i n g i n c r e a s e i n p r e s s u r e d ro p »

When t h e s e h ig h v a l u e s o f p r e s s u r e d ro p w e re

s u b s ti t u t e d i n to e q u a tio n ( 5 " ) , th e v i s c o s i t y a p p a r e n tly I n ­ c r e a s e d s h a r p ly »

I t w as n e c e s s a r y t o s t a y b e lo w a R e y n o ld s

m o d u lu s o f 500 t h r o u g h o u t t h e I n v e s t i g a t i o n . W ith I n c r e a s i n g p r e s s u r e s a t c o n s t a n t t e m p e r a t u r e , t h e d e n s i t y o f ste a m i n c r e a s e s »

F o r t h i s re a s o n th e f l u i d v e lo c ­

i t y m u st b e d e c r e a s e d a t h i g h e r p r e s s u r e s I f t h e R e y n o ld s m o d u lu s i s t o re m a in b e lo w t h e c r i t i c a l v a lu e »

A d e c re a se

i n v e l o c i t y m eans a d e c r e a s e i n p r e s s u r e d ro p s i n c e t h e p r e s ­ s u r e d ro p i s d i r e c t l y p r o p o r t i o n a l t o t h e f l u i d v e l o c i t y i n l a m i n a r flo w » The u se o f a two f l u i d d i f f e r e n t i a l m an o m eter w i t h tw o f l u i d s o f a p p r o x i m a t e ly t h e same d e n s i t y d i d n o t w ork s a t i s ­ fa c to rily » m an o m e te rs»

C a rb o n t e t r a c h l o r i d e w as t r i e d w ith w a t e r i n t h e T h e o r e t i c a l l y t h i s c o m b in a tio n s h o u ld b e i d e a l

33

f o r m e a s u r in g s m a ll p r e s s u r e d i f f e r e n c e s , s i n c e th e d e n s i t y d i f f e r e n c e o f t h e tw o f l u i d s i s a b o u t o f w a te r.

0 .6

t im e s t h e d e n s i t y

P r a c t i c a l l y , t h e c o m b in a tio n w as v e r y d i f f i c u l t

to u se f o r s e v e r a l r e a s o n s .

F i r s t o f a l l , t h e tw o f l u i d ma­

n o m e te r w as s l u g g i s h an d th e i n d i c a t e d p r e s s u r e d ro p w as n e v e r th e tr u e p re s s u re d ro p .

V a lu e s o f v i s c o s i t y c a l c u l a t e d

fro m d a t a u s i n g CCl^ I n t h e m a n o m e te rs w e re a b o u t 70% to o lo w an d f u r t h e r t e s t s show ed a d e c r e a s e i n v i s c o s i t y w ith a n in c r e a s e in te m p e ra tu re .

T h e se r e s u l t s w e re i n e r r o r .

In

f a c t , s t e a d y flo w c o n d i t i o n s w e re n e v e r a t t a i n e d f o r a s u f ­ f i c i e n t l e n g t h o f tim e t o g e t t r u e p r e s s u r e d ro p d a t a w ith C C l^ i n t h e m a n o m e te rs . The se c o n d d i f f i c u l t y i n u s i n g t h i s p a r t i c u l a r f l u i d c o m b in a tio n l a y i n t h e f a c t t h a t t h e m e n is c u s b e tw e e n t h e tw o f l u i d s w as n e v e r c l e a r l y d e f i n e d .

Any s m a ll a m o u n ts o f

g r e a s e , d i r t , o r r u s t on th e m an o m eter g l a s s c a u s e d a d i s ­ t o r t e d m e n is c u s , s i n c e t h e GGI4 w o u ld w e t t h e g l a s s a t t h e s e p la c e s .

I n some i n s t a n c e s , a m e n is c u s w as o b s e r v e d t h a t

s l a n t e d 4 5 ° fro m t h e h o r i z o n t a l p o s i t i o n . I n a two p h a s e s y s te m su c h a s a p p a r a t u s f o r m e a s u r in g s te a m v i s c o s i t i e s , i t i s p r a c t i c a l l y i m p o s s i b l e t o p r e v e n t c o n d e n s a te fro m c o l l e c t i n g i n t h e m an o m eter l e g s .

At b e s t,

t h i s e f f e c t c a n o n ly be c o n t r o l l e d a s e x p la in e d on p a g e

10

,

b y t r y i n g t o m a i n t a i n a c o n s t a n t c o n d e n s a te l e v e l i n e a c h m an o m e te r l e g .

I f t h e c o n d e n s a te i s t o b e a v o id e d e n t i r e l y ,

t h e m anom eter m u st b e k e p t a t some e l e v a t e d t e m p e r a t u r e a b o v e

34

th e s a t u r a t i o n te m p e ra tu re o f th e f l u i d in th e b o ile r *

In

a l l p r o b a b i l i t y , t h i s t e m p e r a t u r e w ould b e h ig h enough t o e v a p o r a t e t h e m anom eter f l u i d , u n l e s s g a l l i u m o r some o t h e r h i g h b o i l i n g p o i n t m a t e r i a l w ere u s e d a s t h e m an o m eter f l u i d * I n a d d i t i o n t o t h i s p r o b le m , t h e d i f f i c u l t i e s i n s e a l i n g s u c h a h i g h p r e s s u r e - h i g h t e m p e r a t u r e m an o m eter w ould b e c o n s i d ­ e ra b le • % e w r i t e r b e l i e v e s t h a t a m e r c u r y m an o m ete r i s s t i l l t h e m o st s a t i s f a c t o r y m eth o d o f o b t a i n i n g s m a ll p r e s s u r e d i f ­ fe re n c e s*

From t h e s t a n d p o i n t o f s e a l i n g t h e s y s te m s a t i s ­

f a c t o r i l y an d e x te n d in g t h e p r e s s u r e r a n g e o f t h e s y s te m , i t w o u ld b e p o s s i b l e t o u s e chrom ium p l a t e d c a s t i r o n f l o a t s on t o p o f m e r c u ry I n a s t a i n l e s s s t e e l TJ t u b e m anom eter* p o s i t i o n o f t h e f l o a t c o u ld b e l o c a t e d w i t h i n

0*0001

The in c h e s

u s i n g a l i n e a r d i f f e r e n t i a l t r a n s f o r m e r o f t h e t y p e m a n u fa c ­ t u r e d b y t h e S h & e v itz E n g in e e r i n g C o r p o r a tio n *

By e m p lo y in g

tw o o f t h e s e t r a n s f o r m e r s , o n e f o r e a c h m anom eter l e g , i t w o u ld be p o s s i b l e t o s e t up a n u l l b a la n c e ty p e o f e l e c t r i ­ c a l c i r c u i t t o l o c a t e th e p o s i t i o n o f th e c a s t i r o n f l o a t * T h is m eth o d w as f i r s t s u g g e s te d t o t h e w r i t e r b y W* L* S i b b i t t who h ad a l r e a d y u s e d t h i s ty p e o f p r e s s u r e d ro p m e a s u re m e n t. The S h a e v i t z E n g in e e r i n g C o r p o r a t i o n h a s p u b l i s h e d in fo r m a ­ t i o n a b o u t t h e i r t r a n s f o r m e r s , one o f w h ic h h a s a l i n e a r r a n g e o f a p p r o x i m a t e ly 0 ,0 5 i n c h e s a n d w i l l l o c a t e a c a s t i r o n c o r e w ith in

0 ,0 0 0 1

in c h e s *

I f m e rc u ry an d w a t e r w ere u s e d i n t h e m a n o m e te rs and

35

v e r y s m a ll p r e s s u r e d i f f e r e n c e s m ere m e a s u r e d , t h e r e w ould s t i l l be a so u rc e o f e r r o r i f th e w a te r l e v e l s d id n o t r e ­ m a in c o n s t a n t a s p r e d i c t e d w i t h t h e i n s t a l l a t i o n o f w e i r s a s e x p l a i n e d o n p a g e 10*

R e f e r r i n g t o F ig * 3 p a g e 1 1 , we c a n

n o tic e th e fo llo w in g ite m s : S u p p o se t h e r e i s no f l u i d flo w a lo n g t h e a n n u lu s i n i ­ tia lly *

The w a t e r l e v e l s w ould b e a t some g i v e n l e v e l an d

t h e m e r c u ry l e v e l s w ould be a t some g iv e n v a lu e *

As so o n a s

some flo w b e g i n s t h r o u g h t h e a n n u l u s , t h e m e rc u ry l e v e l w ould f a l l i n one m an o m eter l e g an d r i s e i n t h e o t h e r m an o m eter le g *

T h e o r e t i c a l l y some w a te r s h o u ld c o n d e n s e i n t h e h i g h e r

p r e s s u r e l e g an d some w a t e r s h o u ld b e e j e c t e d fro m t h e lo w e r p r e s s u r e m an o m eter l e g u n t i l t h e w a t e r l e v e l s a r e a g a i n a t t h e i r i n i t i a l v a lu e .

H o w ev er, i f t h i s a c t i o n d o e s n o t o c c u r

a n d t h e t o t a l am ount o f w a te r i n e a c h l e g r e m a in s u n c h a n g e d , th e n e q u a tio n ( 3 ) p ag e A P

-

10

b eco m es

(fyy- fao

The l a s t t e r m on t h e r i g h t h an d s i d e o f th e e q u a t i o n i s due t o t h e f a c t t h a t t h e w a t e r l e v e l s a r e n o t t h e same a s t h e y w e re i n i t i a l l y .

T h is w ould m ean a maximum e r r o r i n r e a d i n g

t h e p r e s s u r e d ro p o f a b o u t 7*5%,

36

I f t h i s e r r o r d o e s e x i s t , i t e o u ld h e f o m d a p p r o x i ­ m a t e l y b y o b t a i n i n g d a t a f o r s lo w ly I n c r e a s i n g f lo w r a t e s a n d f o r s lo w ly d e c r e a s i n g flo w r a t e s *

I n t h i s w ay t h e i n ­

d i c a t e d p r e s s u r e d ro p w ould f i r s t be l o w e r t h a n t h e t r u e v a lu e a s i n t h e c a s e o f s lo w ly i n c r e a s i n g f lo w r a t e s , an d t h e n b e h i g h e r t h a n t h e t r u e p r e s s u r e d ro p a s i n t h e e a s e o f s lo w ly d e c r e a s i n g flo w r a t e s *

I t w as fo u n d i n t h i s i n v e s t i ­

g a tio n t h a t a s in g le f ix e d s e t t i n g o f th e c o n tr o l li n g th r o t» t i e v a lv e a t t h e c o n d e n s e r c a u s e d a s lo w ly d e c r e a s i n g f lo w ra te ,

E v id e n c e o f t h i s c o n d i t i o n i s

shown I n T a b l e s 2 -4 *

O r d in a r y h i g h p r e s s u r e t h r o t t l e v a l v e s w ould n o t b e s a t i s ­ f a c t o r y f o r v e r y s e n s i t i v e c o n t r o l a t low f lo w r a t e s * I t i s t h e w r i t e r f s b e l i e f t h a t t h e a n n u lu s v i s c o m e te r i s v e r y u s e f u l i n d e te r m i n i n g t h e v i s c o s i t y o f l i q u i d s o r gases*

As lo n g a s t h e a n n u lu s v i s c o m e te r i s u s e d a s a s e c ­

o n d a r y I n s t r u m e n t b y c a l i b r a t i n g t h e I n s t r u m e n t w ith a g a s b f known v i s c o s i t y , t h e e x a c t sh a p e o f t h e a n n u lu s I s n o t im p o rta n t.

W arps o r I r r e g u l a r c r o s s - s e c t i o n s s h o u ld n o t a f ­

f e c t t h e e x p e r i m e n t a l d a t a , when s m a ll c o r r e c t i o n f a c t o r s a r e I n v o lv e d * B e f o re f u r t h e r w ork i s d o n e w i t h t h i s i n s t r u m e n t , t h e f o l l o w i n g ite m s s h o u ld be i n v e s t i g a t e d * (1 ) M ethod o f c l o s e r t e m p e r a t u r e c o n t r o l f o r t h e a n ­ n u lu s * ( 8 ) M ethod o f m ore s e n s i t i v e c o n t r o l o v e r t h e f lo w ra te *

37

(3 ) Use o f a s t a i n l e s s s t e e l m an o m eter e m p lo y in g m er­ c u ry w ith o a s t ir o n f l o a t s and l i n e a r d i f f e r e n ­ t i a l t r a n s f o r m e r s f o r a c c u r a t e l y o b t a i n i n g s m a ll p re s s u re d iffe re n c e s *

38

APPENDIX A D e v elo p m en t o f t h e V i s c o s i t y E q u a t io n f o r L a m in a r F lo # T h ro u g h a n A n n u lu s

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