University of Windsor University of Windsor
Scholarship at UWindsor
Scholarship at UWindsor
Electronic Theses and Dissertations Theses, Dissertations, and Major Papers
7-21-1967
Condensation of steam on a vertically rotating cylinder.
Condensation of steam on a vertically rotating cylinder.
Milan Gacesa
University of Windsor
Follow this and additional works at: https://scholar.uwindsor.ca/etd
Recommended Citation Recommended Citation
Gacesa, Milan, "Condensation of steam on a vertically rotating cylinder." (1967). Electronic Theses and Dissertations. 6476.
https://scholar.uwindsor.ca/etd/6476
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UMI’
BY
MILAN GACESA
B. A . S c . , U n i v e r s i t y o f W in d so r, 1965
A T h e s is
S u b m itte d t o t h e F a c u l t y o f G ra d u a te S tu d ie s th r o u g h t h e D ep artm en t o f M e c h a n ic a l E n g in e e r in g i n P a r t i a l
F u l f i l l m e n t o f t h e R e q u ire m e n ts f o r th e D eg ree o f M a s te r o f A p p lie d S c ie n c e
a t t h e U n i v e r s i t y o f W ind sor
W in d so r, O n ta r io , Canada
1967
UMI Number:EC52657
UMI Microform EC52656
Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company 789 East Eisenhower Parkway
P.O. Box 1346 Ann Arbor, Ml 48106-1346
ABSTRACT
I n t h i s e x p e r i m e n t a l i n v e s t i g a t i o n , t h e e f f e c t s o f t h e sp e e d o f
r o t a t i o n o f t h e c o n d e n s e r s u r f a c e and t h e o v e r a l l te m p e r a tu r e d i f f e r e n c e
b e tw e e n t h e c o o l a n t and t h e v a p o u r (AT) on t h e t r a n s f e r o f h e a t fro m t h e
v a p o u r t o t h e c o o le d s u r f a c e , w ere s t u d i e d . I t was fo u n d t h a t t h e h e a t
t r a n s f e r c o e f f i c i e n t (hm) was n o t a f f e c t e d a t low r o t a t i o n a l s p e e d s
( F r < 5 )* F o r F r > t h e h e a t t r a n s f e r c o e f f i c i e n t i n c r e a s e d b y 400$
fro m i t s s t a t i o n a r y v a l u e f o r AT = l8 0 ° F a n d b y 280$ f o r AT = 1 1 0 °F .
A lso a t AT = 1 1 0 °F , t h e h e a t t r a n s f e r c o e f f i c i e n t e x p e r ie n c e d a d e c l i n e
f o r F r > 6 8. Two d i s t i n c t re g im e s w ere o b s e rv e d i n t h e r e l a t i o n s h i p
b e tw e e n N u s s e l t num ber an d W eber n um ber. F o r We < 5 00, i t was fo u n d
t h a t N u s s e l t num ber was a c o n s t a n t w h e re a s f o r We > 5 00, t h e N u s s e l t
num ber i n c r e a s e d .
i i i
The a u t h o r w ould l i k e t o e x p r e s s h i s g r a t i t u d e t o t h e f o ll o w i n g :
D r. A . A . N ic o l f o r g u id a n c e and e n c o u ra g e m e n t, P r o f e s s o r W. G. C o lb o rn e
f o r a d v i c e , M r. R. M yers an d M r. 0 . B rud y f o r t e c h n i c a l a s s i s t a n c e and
t h e N a ti o n a l R e s e a rc h C o u n c il f o r ' f i n a n c i a l a s s i s t a n c e .
i v
TABLE OF CONTENTS
Page
ABSTRACT i i i
ACKNOWLEDGEMENTS i v
TABLE OF CONTENTS • v
LIST OF FIGURES v i
NOMENCLATURE ' v i i i
CHAPTER
1 INTRODUCTION • 1
2 EXISTING THEORY AND EXPERIMENTAL RELATIONS 3
3 APPARATUS AND INSTRUMENTATION 10
Steam S u p p ly 10
C o o lin g W ater S u p p ly and M easurem ent 10
D r iv in g M echanism 11
Steam Chamber 12
C o n d e n sa te C o l l e c t i n g and W eig h in g 13
The C o n d en ser Tube 13
S l i p R in g A ssem b ly l k
T herm ocouple C i r c u i t s an d t h e M e a s u rin g 15
and R e c o rd in g I n s tr u m e n ts
k EXPERIMENTAL PROCEDURE ■ 17
5 DISCUSSION OF RESULTS 20
6 CONCLUSIONS 28
REFERENCES 2 9
APPENDIX A 5 0
APPENDIX B 5 3
APPENDIX C 55
APPENDIX D 6 l
VITA AUCTORIS 63
v
FIGURE
1 SCHEMATIC LAYOUT
2 ■ DETAIL OF STEAM CHAMBER .
3 DETAIL OF THERMOCOUPLE GROOVES
4 ( a ) THERMOCOUPLE CIRCUIT SCHEMATIC LAYOUT
h (t>) ALTERNATIVE THERMOCOUPLE CIRCUIT SCHEMATIC LAYOUT
5 VARIATION OF CONDENSER SURFACE TEMPERATURE WITH
DISTANCE FROM ROOT (TEST SERIES i )
6 VARIATION OF CONDENSER SURFACE TEMPERATURE WITH
DISTANCE FROM ROOT (TEST SERIES I I )
7 VARIATION OF CONDENSER SURFACE TEMPERATURE WITH
DISTANCE FROM ROOT (TEST SERIES I I I )
8 VARIATION OF CONDENSER SURFACE TEMPERATURE WITH
ROTATIONAL SPEED (TEST SERIES i )
9 VARIATION OF CONDENSER SURFACE TEMPERATURE WITH
ROTATIONAL SPEED (TEST SERIES I I )
10 VARIATION OF CONDENSER SURFACE TEMPERATURE WITH
ROTATIONAL SPEED (TEST SERIES I I I )
v i
v i i
11 VARIATION OF CONDENSER SURFACE TEMPERATURE
WITH ROTATIONAL SPEED
12 VARIATION OF HEAT TRANSFER COEFFICIENT WITH
ROTATIONAL SPEED (TEST SERIES I )
13 VARIATION OF HEAT TRANSFER COEFFICIENT WITH
ROTATIONAL SPEED (TEST SERIES I I )
lfc VARIATION OF HEAT TRANSFER COEFFICIENT WITH
ROTATIONAL SPEED (TEST SERIES I I I )
15 VARIATION OF NUSSELT NUMBER (Nu) WITH WEBER NUMBER
16 VARIATION OF NUSSELT NUMBER (Nua ) WITH WEBER NUMBER
17 VARIATION OF NUSSELT NUMBER (Nua ) WITH WEBER NUMBER.
A COMPARISON OF AUTHOR'S RESULTS WITH THOSE OF OTHER
WORKERS IN THE SAME FIELD.
A C o n d en ser s u r f a c e a r e a ( f t ^ )
Cp S p e c i f i c h e a t o f c o n d e n s a te ( B t u / l b . ° F )
D0 j Di E x t e r n a l an d i n t e r n a l d ia m e te r s o f t h e c o n d e n s e r tu b e ( f t . )
d D is ta n c e fro m r o o t o f t e s t s e c t i o n ( i n . )
F D im e n s io n le s s f a c t o r t o a l lo w f o r v a r i a t i o n i n tu b e te m p e r a t u r e
F r F ro u d e num ber (RQw 2/g)
g G r a v i t a t i o n a l c o n s t a n t ( f t / h r ^ )
, 60 mw. . , .
G C o n d e n sa te m ass v e l o c i t y (,= ---) ( l b / h r . f t . ) *D0
hx , L o c a l and m ean h e a t t r a n s f e r c o e f f i c i e n t s ( B t u / h r . f t 2 ° F )
h f g E n th a lp y o f e v a p o r a t i o n ( B t u / l b )
k f T h erm al c o n d u c t i v i t y o f c o n d e n s a te (B tu / h r . f t . °F)
kA T h erm al c o n d u c t i v i t y o f w a te r a t a tm o s p h e r ic c o n d i t i o n s ( B t u / h r . f t . ° F )
mw C o o lin g w a te r f lo w r a t e ( l b / m i n . )
mv Steam flo w r a t e ( o z s / m i n .)
Nux ^ Nu, < Nu > L o c a ls mean an d a v e r a g e v a lu e o f N u s s e l t num ber ( h D o / k f )
Nu^ N u s s e l t num ber (hmD0/2 k ^ )
P r P r a n d t l num ber ( c p P f / k f )
q_w- H eat f l u x b a s e d on c o o l in g w a te r m e a su re m e n ts ( B t u / h r . )
R0 E x t e r n a l tu b e r a d i u s ( f t . )
Re R ey n o ld s num ber ( t e / p f )
Rev R eyn olds num ber (VmD0/ v f )
T f Mean f i l m te m p e r a t u r e (= T0b + Ts ) / 2 (° F )
Ts Steam s a t u r a t i o n te m p e r a t u r e ( °F)
T0i , ^o2-» • * * -*-ol0 C o n d en ser s u r f a c e ' te m p e r a t u r e a t l o c a t i o n s , l /2, 1-1/2, 2- l/ 2 . . . 9-1 /2 in c h e s fro m t h e b o tto m o f t h e t e s t s e c t i o n , r e s p e c t i v e l y (° F )
Toa A verage c o n d e n s e r s u r f a c e te m p e r a t u r e , (T0 l + To2 + . . . To l0) / l 0 (° F )
ATS T em p eratu re d i f f e r e n c e b e tw e e n s te a m te m p e r a tu r e Ts and a v e ra g e c o n d e n s e r s u r f a c e te m p e r a tu r e l o a ( °F)
lo b * ^ o t C o nd en ser s u r f a c e te m p e r a t u r e a t t o p and b o tto m (° F )
ATob T e m p eratu re d i f f e r e n c e a t t h e b o tto m o f t h e c o n d e n s e r (Ts - T0b ) °F
ATob T em p eratu re d i f f e r e n c e a t t h e t o p o f t h e c o n d e n s e r (Ts - To t )
T i , T2 • •• T]_p C o o lin g w a te r te m p e r a tu r e a t l o c a t i o n s , 0 , 1 , 2 , — in c h e s from t h e b o tto m o f t h e t e s t s e c t i o n ,
r e s p e c t i v e l y (° F )
Tw A verag e c o o lin g w a te r t e m p e r a t u r e ,
(Tp + T2 + . . . + T n ) / l l (° F )
AT O v e r a ll te m p e r a tu r e d i f f e r e n c e (Ts - Tw) °F
ATW C o o lin g w a te r o v e r a l l te m p e r a tu r e r i s e (T-q - T-j_) °F
Vm Mean f i l m v e l o c i t y (wR0 ) f t / h r .
W A n g u la r v e l o c i t y (RFM)
w A n g u la r v e l o c i t y ( H r . - 1 )
We Weber number ( 0 )
b o-g
p-f Dynamic c o e f f i c i e n t o f v i s c o s i t y ( l b / f t . h r . )
Vf K in e m a tic c o e f f i c i e n t o f v i s c o s i t y ( f t ^ / h r . )
pp S p e c i f i c w e ig h t o f c o n d e n s a te ( l b / f t 3 )
cr S u rfa c e t e n s i o n ( l b / f t . )
8 . F ilm t h i c k n e s s ( f t . )
n Power in d e x
INTRODUCTION
S in c e t h e o r i g i n a l w ork "by N u s s e lt i n 1 916, c o n d e n s a tio n s t u d i e s
h av e b e e n l a r g e l y c o n f in e d t o t h e p ro b lem o f c o o le d , s t a t i o n a r y s u r f a c e s
im m ersed i n a v a p o u r . R e c e n tly ,' h o w ev er, m ethods o f c o n d e n s a te re m o v a l,
b y m eans o t h e r t h a n g r a v i t y a lo n e h av e b e e n c o n s id e r e d . When a v a p o u r
whose c o n d e n s a te h a s a v e r y h i g h v i s c o s i t y i s t o b e e f f i c i e n t l y c o n d en sed
o r when a c o n d e n s e r h a s t o f u n c t i o n i n s p a c e w here g r a v i t y i s a b s e n t th e n
n o t o n ly t h e p r a c t i c a l i t y b u t t h e n e c e s s i t y o f su c h m etho ds become
a p p a r e n t . S e v e r a l m eth o d s o f re m o v a l h a v e b e e n s u g g e s te d :
1 . R o ta tin g t h e c o n d e n s e r s u r f a c e t o th ro w o f f t h e l i q u i d b y c e n t r i f u g a l f o r c e
2 . I m p a r tin g a l a r g e v e l o c i t y t o t h e v a p o u r t a n g e n t i a l t o t h e s u r f a c e t o b lo w o f f t h e
c o n d e n s a te , an d - •
3 . M e c h a n ic a lly rem o v in g t h e c o n d e n s a te b y s c r a p in g o r o t h e r t e c h n i q u e s .
I n t h i s i n v e s t i g a t i o n , t h e c o n d e n s a te was rem oved b y r o t a t i n g
t h e c o n d e n s e r s u r f a c e , t h e r e b y e f f e c t i v e l y r e p l a c i n g g r a v i t a t i o n a l f o r c e
b y c e n t r i f u g a l f o r c e a s t h e p r im a r y m eans o f re m o v a l.
T h re e d i f f e r e n t h e a t f l u x e s w ere a c h ie v e d b y v a r y in g t h e o v e r a l l
te m p e r a tu r e d i f f e r e n c e b e tw e e n t h e c o o l a n t and t h e v a p o u r, and b y v a r y in g
t h e r a t e o f flo w o f t h e c o o l a n t . C o o lin g w a te r a t 50°F was c i r c u l a t e d
th r o u g h t h e c o n d e n s e r tu b e a t 6 ,6 0 0 l b / h r . f o r one s e t o f t e s t s an d a t
3 ,6 0 0 l b / h r . f o r a n o t h e r . The t h i r d h e a t f l u x c o n d i t i o n was a c h ie v e d
b y c i r c u l a t i n g 120 °F c o o lin g w a te r th r o u g h t h e c o n d e n s e r tu b e a t
k ,8 0 0 l b / h r . F o r a l l t h r e e o f th e t e s t s th e steam c o n d i t i o n s w ere
1
2
c o n s t a n t a t 230 °F an d 21 p s i a . F o r each, o f t h e t h r e e c o m b in a tio n s o f
c o o l i n g w ater, f lo w and t e m p e r a t u r e , t h e r o t a t i o n a l s p e e d o f t h e c o n d e n s e r
t u b e was v a r i e d i n random i n t e r v a l s b e tw e e n 0 an d 2700 REM.
EXISTING THEORY AND EXPERIMENTAL RELATIONS
N u s s e l t i n 1916 made a t h e o r e t i c a l e s t i m a t e o f t h e h e a t t r a n s f e r
f o r t h e c a s e o f f i l m c o n d e n s a tio n o f a p u re s a t u r a t e d v a p o u r on s t a t i o n
a r y s u r f a c e s i n c l u d i n g v e r t i c a l t u b e s . He assum ed t h a t when s t e a d y
s t a t e was r e a c h e d , t h e t h i c k n e s s o f t h e f i l m o f c o n d e n s a te in c r e a s e d
fro m t h e t o p t o t h e b o tto m an d was m a in ta in e d b y a b a l a n c e b e tw e e n t h e
r a t e o f c o n d e n s a tio n an d t h e r a t e o f d r a i n i n g due t o g r a v i t y . He a l s o
assu m ed t h a t t h e f lo w o f t h e c o n d e n s a te l a y e r was la m i n a r and t h a t t h e
t r a n s f e r o f h e a t to o k p l a c e s o l e l y b y c o n d u c tio n a c r o s s i t i n a d i r e c t i o n
p e r p e n d i c u l a r t o t h e s u r f a c e . The te m p e r a tu r e o f t h e s u r f a c e o f t h e
c o n d e n s in g f i l m i n c o n t a c t w ith t h e v a p o u r was assum ed t o b e a t t h e
s a t u r a t i o n te m p e r a t u r e , an d t h e te m p e r a tu r e o f t h e s u r f a c e o f t h e f i l m
i n c o n t a c t w ith t h e w a ll a t w a ll te m p e r a t u r e , w h ich was assum ed u n if o r m .
The f i l m o f c o n d e n s a te was c o n s id e r e d t o b e so t h i n t h a t t h e te m p e r a tu r e
g r a d i e n t th r o u g h i t was a s t r a i g h t l i n e . F o r v e r t i c a l t u b e s he o b ta in e d
t h e f o ll o w i n g e x p r e s s i o n :
Many r e s e a r c h w o rk e rs h av e fo u n d t h a t N u s s e l t 's e x p r e s s i o n a g r e e s f a i r l y
w e l l w ith t h e i r e x p e r i m e n t a l r e s u l t s ; a lth o u g h t h e r e i s a te n d e n c y f o r
1 / 3 - 1 / 3
(1)
t h e m e a su re d r e s u l t s t o be h i g h e r . M c A d a m s ) c o n te n d s t h a t N u s s e l t 's
3
k
a s s u m p tio n o f u n ifo rm c o n d e n s e r w a ll te m p e r a tu r e i s one o f t h e r e a s o n s
f o r t h i s d is c r e p a n c y .- He t h e r e f o r e s u g g e s ts t h e f o ll o w i n g e m p i r i c a l
r e l a t i o n :
(hm)TRUE = F ( hm)NUSSELT ( 2 )
w here F i s o b ta in e d a s shown i n T a b le I .
TABLE I
F ^ o b /A T 0t
O.9 6 0 .5
1.0 1.0
1 .0 6 2 .0
1 .1 5 5 -0
P e rh a p s t h e more im p o r ta n t r e a s o n f o r t h e d is c r e p a n c y b e tw e e n t h e
r e s u l t s o b ta in e d u s in g N u s s e l t 's e x p r e s s io n and t h e e x p e r i m e n t a l r e s u l t s
i s N u s s e l t 's a s s u m p tio n t h a t f lo w i s la m in a r . Many w o r k e r s ^
h av e o b s e rv e d t h a t t h e r e a r e i n f a c t waves form ed a t t h e c o n d e n s a te f i l m
s u r f a c e . The o m is s io n o f t h e e f f e c t o f t h e s e waves i n N u s s e l t 's i n v e s t i
g a t i o n w ould t h e r e f o r e c a u s e h i s e s t i m a t e s t o b e lo w .
Colburn^-'-) d e r iv e d a t h e o r e t i c a l r e l a t i o n i n th e t u r b u l e n t r a n g e ,
w hich was o f t h e fo rm :
2 l / 3 l / 3 0 . 2
hm ( — -) = 0 .0 5 6 ( P r ) (R e) (3 )
kf3 pf^g
I t i s g e n e r a l l y a g r e e d t h a t e q u a t io n (3 ) s h o u ld b e u s e d f o r v a l u e s
o f R eynolds number h i g h e r t h a n 2 10 0.
S in c e t h e o r i g i n a l w ork b y N u s s e l t , c o n d e n s a tio n s t u d i e s h av e b e e n
l a r g e l y c o n fin e d t o t h e p ro b le m o f c o o le d s t a t i o n a r y s u r f a c e s im m ersed
i n a v a p o u r . R e c e n tly , h o w ev er, m ethods o f c o n d e n s a te re m o v a l from th e
c o n d e n s in g s u r f a c e "by m eans o t h e r t h a n g r a v i t y a lo n e h a v e b e e n c o n s i d e r e d .
One o f t h e s e i s r o t a t i o n o f t h e c o n d e n s e r s u r f a c e c a u s in g re m o v a l o f t h e
l i q u i d c o n d e n s a te h y c e n t r i f u g a l f o r c e a n d t h i s i s t h e m e th o d p ro p o s e d
f o r t h e p r e s e n t i n v e s t i g a t i o n .
A lth o u g h no w ork h a s b e e n done on v e r t i c a l l y r o t a t i n g c y l i n d e r s ,
t h r e e s t u d i e s h a v e b e e n r e p o r t e d on h o r i z o n t a l l y r o t a t i n g c y l i n d e r s .
E ac h o f t h e s e w i l l b e d is c u s s e d s e p a r a t e l y an d t h e a s p e c t s w h ich a r e
deemed a p p l i c a b l e t o t h e p r e s e n t i n v e s t i g a t i o n w i l l b e s t r e s s e d .
Y eh(lO ) i n 1953 d i d t h e p i o n e e r i n g w o rk . H is te c h n i q u e h a s b e e n
c r i t i c i z e d b y s u b s e q u e n t w o r k e r s ^ ) an d h i s r e s u l t s a r e c o n s id e r e d
q u e s t i o n a b l e . H is w ork was c a r r i e d o u t on a h o r i z o n t a l l y r o t a t i n g
c y l i n d e r c o o le d o n t h e i n s i d e b y w a te r a n d e n c l o s e d i n a s te a m ch am b er.
The s te a m c o n d e n s e d on t h e o u t s i d e o f t h e c o o le d c y l i n d e r an d t h e c o n
d e n s a te was d r a i n e d a n d c o l l e c t e d . D u rin g t h e c o u r s e o f h i s w o rk , Yeh
d i s c o v e r e d t h a t t h e f lo w an d h e a t t r a n s f e r c h a r a c t e r i s t i c s o f t h e s y ste m
w ent th r o u g h t h r e e d i f f e r e n t p h a s e s . A t lo w r o t a t i o n a l s p e e d s ( F r < 2 . 6 ) ,
t h e c e n t r i f u g a l f o r c e and t h e f r i c t i o n f o r c e b e tw e e n t h e s h a f t an d t h e
c o n d e n s a te f i l m te n d e d t o c o u n t e r a c t t h e f o r c e o f g r a v i t y an d t h e c o n
d e n s a te l a y e r t h i c k e n e d c a u s in g a r e d u c t i o n i n h e a t t r a n s f e r . The se c o n d
p h a se o c c u r r e d a t h i g h e r r o t a t i o n a l s p e e d s (2 8 > F r > 2 . 6 ) a t w h ich tim e
t h e l i q u i d was s p r a y e d o f f t h e c y l i n d e r i n a l l d i r e c t i o n s c a u s in g t h e
l i q u i d f i l m t o becom e t h i n n e r and t h u s a l l o w t h e h e a t t r a n s f e r r a t e t o
i n c r e a s e . A t h i g h r o t a t i o n a l sp e e d s ( F r > 28 ) t h e f i l m becam e v e r y
t h i n an d d r o p l e t s o f t h e c o n d e n s a te a p p e a r e d . F i n a l l y i t becam e d i f f i c u l t
t o f i n d a n y e v id e n c e o f a c o n tin u o u s f i l m w h ile t h e d r o p l e t s e lo n g a te d
and u l t i m a t e l y becam e s t r e a k s . D u rin g t h i s l a s t p h a s e t h e h e a t t r a n s f e r
r a t e becam e p r o g r e s s i v e l y s m a l l e r .
Yeh p ro p o s e d a m odel f o r t h e seco n d p h a s e o n ly a n d d e r i v e d . t h e
f o ll o w i n g t h e o r e t i c a l r e l a t i o n :
. hm = ^ P f V^ 2 ( 4 )
og
E x p e r i m e n t a l l y he d is c o v e r e d t h a t t h e d a t a c o u ld b e c o r r e l a t e d i n th e
t h r e e re g im e s t h u s :
I = C o n s t. (R e)n (5 )
w here I = hm /kf pf Vm2/<rg, Re = — - f e
vf
I n t h e f i r s t re g im e n = - 1 . 4 , 7 3 -7 6 .1 0 ^ < C < 1 0 2 .7 - 1 0 ^ .
I n t h e se c o n d re g im e n = 2 .3 4 , 3 6 .42 .10 ® < C < 8 7.1 6 .1 0 ® .
I n t h e t h i r d re g im e n = 3 - 3 4 , C = 0.1956.10-*-®.
T h is i s a r a t h e r p o o r c o r r e l a t i o n s i n c e t h e v a l u e s o f t h e c o n s t a n t
C v a r y n o t o n ly f o r d i f f e r e n t R ey n o ld s num bers b u t a l s o f o r d i f f e r e n t
p r e s s u r e s a t t h e same R ey n o ld s num ber. M o reo v er, t h e v a l u e o f n a l s o
v a r i e s w ith R ey n o ld s num ber a s shown a b o v e .
S in g e r an d P r e c k s h o t^ 9 ) c a r r i e d o u t h e a t t r a n s f e r m e asu re m en ts on
a p p a r a tu s s i m i l a r t o Y e h 's w ith some m o d i f i c a t i o n s w h ich p r o b a b ly made
t h e i r r e s u l t s m ore r e l i a b l e . An i n t e r e s t i n g p o i n t i n t h e i r e x p e r im e n ta l
te c h n iq u e was t h e f a c t t h a t t h e y d i d n o t m e asu re t h e te m p e r a t u r e on t h e
r o t a t i n g s h a f t , t h e r e b y o b v i a t i n g a n y p ro b lem s w hich m ig h t h av e b e e n
e n c o u n te r e d i n u s in g s l i p r i n g s . They w ere a b l e t o m e a su re t h e o v e r a l l
te m p e r a tu r e d ro p b e tw e e n t h e c o o l in g w a te r and t h e ste a m atm o sp h e re b y
means o f s t a t i o n a r y p r o b e s . Knowing t h e h e a t f l u x , fro m w a te r flo w and
te m p e r a tu r e r i s e m e a su re m e n ts, t h e y w ere a b l e t o c a l c u l a t e t h e o v e r a l l
h e a t t r a n s f e r c o e f f i c i e n t - T hey d e te rm in e d t h e w a te r s i d e h e a t t r a n s f e r
c o e f f i c i e n t from t h e r e s u l t s o f Kuo e t a l ( D 2 ) . Knowing t h e o v e r a l l
and t h e w a te r s id e c o e f f i c i e n t s , t h e y w ere a b le t o c a l c u l a t e t h e steam
s i d e c o e f f i c i e n t .
T hey a l s o r e p o r t e d t h e p re s e n c e o f t h e t h r e e re g im e s d e s c r i b e d b y
Y eh. T hey, ho w ever, a l s o p r e s e n t e d p h y s i c a l m o d e ls and t h e o r e t i c a l
e s t i m a t e s o f t h e h e a t t r a n s f e r f o r tw o o f t h e r e g im e s . I n t h e f i r s t
re g im e , t h e y w ere a b le t o show t h a t t h e c o n d e n s a te f i l m t h i c k n e s s
i n c r e a s e d w ith r o t a t i o n a l s p e e d an d h en ce t h a t t h e h e a t f l u x d e c r e a s e d .
T h e i r t h e o r e t i c a l e s t i m a t e o f h e a t t r a n s f e r i n t h i s reg im e was o f th e
fo rm :
bX D0 o ^ 8 Do3 h f g (P f-P v 0 , • 3 Cp AT l A - l / 2
Nux = — --- =
(f)---
--- =T T-(1 +
}
<5 >
(6)
kf 3 vf k f (Ts - T0 ) 8h f g
w here 8+ = f (8) an d c a n b e e v a l u a t e d .
The a v e ra g e v a lu e o f N u s s e l t number i s t h e n :
2*
< Nu > = h I h ^ D° / k f ) d ^ ( 7 a )
o
and t h e mean v a lu e i s :
L
Nu =
^J<
Nu > dL (7 b ) oV a lu e s o f N u s s e lt number a s o b ta in e d fro m e q u a t io n (7 b ) w ere fo u n d t o b e
1 3 .9 $ b e lo w t h e e x p e r im e n ta l v a l u e s i n t h e same r e g im e . F o r m o d e ra te
r o t a t i o n a l sn eed s t h e t h e o r e t i c a l e s ti m a t e o f h e a t t r a n s f e r was o f t h e fo rm :
hx D0
- 2 ["(I ♦ W h )1 /3 I
(8)
NUx = = 2 : (1 + 2We / ,
* f u. J
8
F o r v e r y h i g h r o t a t i o n a l s p e e d s t h e a u t h o r s s u g g e s t t h a t N u s s e l t number
i s a f u n c t i o n o f (We r a t h e r t h a n ¥ e ^ a s i s t h e c a s e f o r lo w e r
s p e e d s , i n d i c a t i n g a l e v e l l i n g o f f o f t h e h e a t t r a n s f e r .
P r e s e n t i n g t h e e x p e r i m e n t a l d a t a i n t h e fo rm s u g g e s te d b y
e q u a t i o n (8) ( i . e . , p l o t t i n g N u s s e l t num ber v e r s u s ¥ e b e r num ber) p ro v e d
t o b e u n s a t i s f a c t o r y s i n c e t h e e x p e r i m e n t a l d a t a n o t o n l y d i s a g r e e d w ith
t h e t h e o r e t i c a l e s t i m a t e b u t a l s o t h e r e a p p e a re d t o b e a d e f i n i t e
f a m i l y o f c u r v e s f o r v a r y in g v a l u e s o f o v e r a l l te m p e r a t u r e d i f f e r e n c e
(£ d l). F o r t h i s r e a s o n t h e a u t h o r s p ro p o s e d a n e m p i r i c a l c o r r e l a t i o n
o f t h e fo rm :
Nu (g D0 ^ p f h f g / v f k f AT) = C o n s ta n t . We n (9)
As j u s t i f i c a t i o n f o r t h e u s e o f t h e m o d if ie d N u s s e l t n um ber, t h e y c i t e t h e
f a c t t h a t f o r a s t a t i o n a r y c o n d e n s e r t h e f o l l o w i n g r e l a t i o n h o ld s t r u e :
. Nu = C (g Dq3 P f h f g / v f kf AT)+1//4 , (1 0 )
w here C i s a c o n s t a n t . T h e i r d a t a when p l o t t e d a c c o r d in g t o e q u a t io n (9)
y i e l d e d :
C = 0 .0 1 3 7 0 , n = 0 .7 3 5 f o r 250 < ¥ e < 9 0 0
and C = 2 7 .2 0 6 , n = 0 .3 8 5 f o r 900 < ¥ e < 1 7 , 0 0 0
H oyle and M a t t h e w s ( 5 ) i n v e s t i g a t e d t h e e f f e c t o f d ia m e te r s i z e a s
w e ll a s t h e sp e e d o f r o t a t i o n on t h e t r a n s f e r o f h e a t fro m s te a m t o
h o r i z o n t a l l y m o u n ted , w a te r c o o le d c y l i n d e r s . T h e i r a p p a r a tu s was
s i m i l a r t o t h a t u s e d b y S in g e r and P r e c h s h o t e x c e p t t h a t p r o v i s i o n s had
t o b e made f o r u s in g c y l i n d e r s o f d i f f e r e n t d i a m e t e r s . They a l s o h ad
t o make p r o v i s i o n s f o r m e a s u rin g t h e s u r f a c e te m p e r a t u r e o n a r o t a t i n g
c y l i n d e r . The c y l i n d e r s u s e d i n t h e i r ' s t u d y w ere o f 4 , 8 and 10" o u t
s i d e d i a m e t e r s . B ased on p h o to g r a p h ic s t u d i e s , t h e y c o n te n d e d t h a t t h e
c o n d e n s a te l a y e r was i n lam i n a r f lo w th r o u g h o u t a l l t h e t e s t s . B ased
on t h e s e o b s e r v a t i o n s , t h e y made a t h e o r e t i c a l e s t i m a t e o f t h e h e a t t r a n s
f e r and o b ta in e d t h e f o ll o w i n g r e l a t i o n s h i p :
The e x p e r im e n ta l r e s u l t s f o r t h e 4 , 8 and 10" c y l i n d e r s v a r i e d
fro m e q u a t io n ( l l ) b y 1 5-5.? 1 2 .9 an d l6 .8 p e r c e n t , r e s p e c t i v e l y .
H oyle and M atthew s 1 r e s u l t s form ed s e r i e s o f c u r v e s c o r r e s p o n d in g t o
d i f f e r e n t c y l i n d e r s s u c h t h a t H u s s e lt num ber v a r i e d d i r e c t l y w ith Weber
number f o r a l l v a l u e s o f Weber num ber. T h is o f c o u rs e i s u n li k e t h e
r e s u l t s o f Yeh w here t h e H u s s e lt num ber e x p e r ie n c e d a d e c l i n e f o r Weber
num ber g r e a t e r th a n 1700 o r S in g e r and P r e c k s h o t who r e p o r t e d a d e c l i n e
i n H u s s e lt number f o r v a l u e s o f W eber num ber g r e a t e r th a n 9 0 0 . 2 kA
I n o r d e r t o com pare t h e i r r e s u l t s w ith th o s e o f Y e h (io ) and S in g e r
an d P re -c k sh o t( 9 ) t h e y e x p r e s s e d th em i n te rm s o f t h e v a r i a t i o n o f
N u s s e l t number (h D0 / 2 kA) w ith t h e Weber num ber (D0 p f/c r)^ (D qW ^/29)/2.
CHAPTER
3
APPARATUS AND INSTRUMENTATION _
Tlie a p p a r a tu s an d in s tr u m e n ts r e q u i r e d t o c o n d u c t t h e e x p e r im e n ts
w i l l h e d e s c r i b e d u n d e r e i g h t s e p a r a t e h e a d i n g s : S team S u p p ly ; C o o lin g
W ater S u p p ly and M easu rem en t; D r iv in g M echanism ; S team Cham ber;
C o n d e n sa te C o l l e c t i n g an d W e ig h in g ; The C o n d en ser T u b e; S l i p - r i n g
A ssem b ly ; T herm ocouple C i r c u i t a n d T herm ocouple O u tp u t M e a su rin g a n d
R e c o rd in g I n s t r u m e n t s . L e t t e r r e f e r e n c e i s t o ite m s i n F ig u r e 1 u n l e s s
o th e r w is e s t a t e d .
k
S team S u p p ly
The steam r e q u i r e d f o r t h e e x p e r im e n t was g e n e r a te d b y a 25 H .P .
N apanee A u to m a tic B o i l e r (A) w h ich d e l i v e r e d 99$ d r y ste a m a t a n y
p r e s s u r e b e tw e e n 0 and 125 p s i g . The s te a m fro m t h e b o i l e r was c o n
v ey ed b y means o f
1 - l/V
la g g e d s t e e l p i p e s t o t h e s te a m cham ber ( e ) .B e fo re e n t e r i n g t h e s te a m cham ber i t h ad t o p a s s th r o u g h a f lo w c o n t r o l
v a lv e an d a p r e s s u r e r e g u l a t i n g v a lv e ( c ) and (D), r e s p e c t i v e l y . A t
t h e low p o i n t o f t h e p i p i n g a S a rc o BMS-4 Steam T ra p was i n s t a l l e d (B)
i n o r d e r t o d r a i n o f f a n y c o n d e n s a te t h a t may h av e form ed i n t h e p ip e s
up t o t h a t p o i n t and a llo w c o n d e n s a t e - f r e e steam t o e n t e r t h e steam
ch a m b e r.
C o o lin g W ater S u p p ly and M easurem ent
C o o lin g w a te r was o b ta in e d fro m t h e b u i l d i n g m a in s . C o ld w a te r
an d h o t w a te r w ere p ip e d t o a 3-w ay m ix in g v a lv e (F ) w h ich c o u ld s u p p ly
10
50 g a l / m i n . o f w a te r a t a n y te m p e r a t u r e b e tw e e n 1 3 0“i1 an d 5 0°F w hich w ere
t h e h o t an d c o l d w a te r te m p e r a t u r e s , r e s p e c t i v e l y . From t h e m ix in g
v a l v e w a te r e n t e r e d a r e c e i v i n g t a n k ( g ) w here i t was m ix ed f u r t h e r b y
m eans o f b a f f l e s . The r e c e i v i n g t a n k a l s o s e r v e d a s t h e a n c h o r in g
b a s e f o r t h e p a c k in g h o u s in g ( k ) , a b e a r i n g ( l ) and t h e h o u s in g f o r
t h e c o ld w a te r te m p e r a t u r e p ro b e ( h ) . From t h e r e c e i v i n g t a n k w a te r
e n t e r e d t h e c o n d e n s e r t u b e (M) fro m w h ich i t was e j e c t e d th r o u g h t h r e e
r a d i a l h o l e s i n t o t h e e m p ty in g ta n k ( n ) . T h is ta n k a l s o s e r v e d a s
a r e c e p t i c l e f o r t h e p a c k in g h o u s in g ( p ) . By m eans o f t h e p ro b e (H)
w h ich h o u s e d a c o p p e r - c o n s t a n ta n th e rm o c o u p le w ir e , t h e te m p e r a t u r e o f
t h e c o o l in g w a te r a t an y p o s i t i o n i n s i d e t h e c o n d e n s e r tu b e (m) c o u ld
b e m e a s u re d . The c o n d e n s e r tu b e an d t h e p ro b e a r e a l s o shown i n more
d e t a i l i n F ig u r e 3- From t h e em p ty in g t a n k ( n ) w a te r was p ip e d t o
t h e w e ig h in g m echanism (Q,). As c a n b e s e e n fro m t h e f i g u r e i t was
p o s s i b l e t o d is c h a r g e t h e w a te r d i r e c t l y i n t o t h e d r a i n o r t o c o l l e c t
an d w eig h i t and t h e n d i s c h a r g e i t . The w e ig h t a n k h a d a c a p a c i t y
o f k-5 g a l l o n s an d t h e T o led o S c a le u s e d , M odel 2 l 8 l , h a d a c a p a c i t y o f
725 l b s . and was a c c u r a t e t o w i t h i n 0 .1 0 l b s .
D r iv in g M echanism
The c o n d e n s e r tu b e was r o t a t e d b y m eans o f a n l / k H . P . , D. C.
M o to r . The pow er fro m t h e m o to r t o t h e tu b e was t r a n s m i t t e d b y m eans
o f p u l l e y s an d a b e l t . The m o to r t o r q u e an d s p e e d w ere c o n t r o l l e d b y
a n S . C. R. Dodge C o n tr o l U n i t . The pow er f o r t h e c o n t r o l u n i t was
o b ta in e d fro m a n o r d i n a r y 110 v o l t , 15 amp. w a ll o u t l e t . The r a t e d
maximum s p e e d o f t h e m o to r was 1725 R .P .M . b u t a sp e e d v a r i a t i o n on
12
t h e c o n d e n s e r tu b e fro m 0 - 2 7OO R .P .M . was a c h ie v e d h y r e d u c in g t h e
p u l l e y s i z e fro m t h e m o to r t o t h e t u b e .
S team Chamber
The p o s i t i o n o f t h e s te a m cham ber w ith r e s p e c t t o t h e o t h e r e q u i p
m ent i s shown i n F ig u r e 1 , Ite m ( D ) . I n F ig u r e 2, t h e cham ber i s shown
i n m ore d e t a i l . A l l t h e im p o r ta n t d im e n s io n s a r e g iv e n i n F ig u r e 2 an d
w i l l n o t b e r e p e a t e d h e r e . . .
As can b e s e e n fro m F ig u r e 2 , t h e cham ber c o n s i s t e d o f tw o c o n c e n t r i c
b o x e s . E ach box was made i n tw o h a l v e s and p u t t o g e t h e r b y means o f
v e r t i c a l f l a n g e s w ith t h e i n n e r b o x s e c u r e d t o t h e o u t e r . Steam
e n t e r e d t h e o u t e r b o x th r o u g h t h e o p e n in g i n t h e b a c k an d was d e f l e c t e d
b y a b a f f l e so t h a t i t d i f f u s e d e v e n l y th r o u g h a l l f o u r s i d e s o f t h e
i n n e r b o x . S l o t s i n t h e s id e w a l l s o f t h e i n n e r box h av e a com bined
a r e a m ore th a n tw ic e t h e s u r f a c e a r e a o f t h e c o n d e n s e r tu b e t o e n s u r e
minimum steam v e l o c i t y a s i t d i f f u s e d to w a rd s t h e c o n d e n s e r . L o u v res
c o v e r in g th e s l o t s w ere i n s t a l l e d t o p r e v e n t d r o p l e t s o f c o n d e n s a te fro m
b e in g th ro w n fro m t h e tu b e an d o u t th r o u g h t h e s l o t s . S team t h a t c o n
d e n s e d on t h e w a ll s o f t h e o u t e r bo x was d r a in e d o f f th r o u g h th e
s e c o n d a r y c o n d e n s a te o u t l e t (S ee F ig u r e l ) and d is c a r d e d , and t h e c o n
d e n s a te w h ich fo rm ed on t h e c o n d e n s e r tu b e was c o l l e c t e d and w eighed
a t t h e p r im a r y c o n d e n s a te o u t l e t .
Where t h e c o n d e n s e r tu b e em erged fro m t h e o u t e r b o x , t o p and b o tto m ,
t h e r e was a s e a le d b e a r i n g f i t t e d o v e r t h e tu b e and a t t a c h e d t o t h e b o x ,
w hich s e r v e d b o th a s a b e a r i n g and a s e a l . The o u t e r b o x was a l s o
e q u ip p e d w ith a p r e s s u r e gauge an d a ste a m te m p e r a tu r e p ro b e ( s e e V,
and T i n F ig u r e 1 ) .
C o n d e n sa te C o l l e c t i n g a n d W eighing
A h ig h p r e s s u r e b o i l e r g l a s s tu b e was i n s t a l l e d i n t h e p r im a r y
c o n d e n s a te o u t l e t l i n e a n d by m eans o f t h e tw o v a l v e s (S ee F ig u r e l ) ,
t h e c o n d e n s a te l e v e l i n s i d e t h e g l a s s tu b e was h e l d c o n s t a n t when i t
was b e i n g c o l l e c t e d f o r w e ig h in g . The c o n d e n s a te was c o l l e c t e d i n a
c o v e re d b e a k e r an d w e ig h e d -o n a s m a ll C e n t r a l S c i e n t i f i c Company
s c a l e w h ich was a c c u r a t e t o w i t h i n 0 .0 1 o z .
C o n d e n se r Tube
The c o n d e n s e r tu b e c a n b e s e e n i n F ig u r e 2 and a l s o i n more
d e t a i l , i n some r e s p e c t s , i n F ig u r e 5 ( s e e a l s o A ppendix C ). The tu b e
was made fro m ASE60-61 alum inum tu b e 1" O.D. x 1 /k " w a l l x 4 ' lo n g .
T h ree g ro o v e s ^ /8 " x V 8 " w ere m i l l e d on t h e o u t s i d e o f t h e tu b e a t 120°
i n t e r v a l s , r u n n in g t h e w hole l e n g t h o f th e tu b e e x c e p t f o r 5 " a t one
e n d . S t a r t i n g a t t h e b o tto m o f th e g ro o v e an d m oving up ( l " a t a t i m e ) /
10 c i r c u m f e r e n t i a l s l o t s w ere g ro u n d , p e r p e n d i c u l a r t o e a c h g r o o v e ,
a p p r o x im a te ly l / l 6 " w ide an d s u c h t h a t th e b o tto m o f t h e s l o t was l / 8 "
b elow th e s u r f a c e ( i . e . , same d e p t h a s t h e g r o o v e s ) a t t h e end w h ich
i n t e r s e c t e d t h e g ro o v e an d th e n t h e b o tto m s l a n t e d up so t h a t i t was
a t th e o u t e r s u r f a c e o f t h e t u b e when th e s l o t was
l / V
lo n g , a s showni n F ig u r e 3-1*
F IG . 3 - 1 : GROOVE AND SLOT DETAIL
C i r c u m f e r e n t i a l H ole
S l o t
Groove
H o le s -0 ^ 0 " i n d ia m e te r w ere d r i l l e d a t t h e en d s o f t h e s l o t s s t a r t i n g
i n t h e s l a n t e d b o tto m o f t h e s l o t s , f a r enou gh fro m t h e s h a llo w end so
t h a t t h e d r i l l c o u ld h e s t a r t e d w ith o u t s p l i t t i n g t h e s u r f a c e . H o le s
w ere d r i l l e d i n t h e same c i r c u m f e r e n t i a l d i r e c t i o n a s t h e s l o t s an d w ere
t e r m i n a t e d when t h e d r i l l j u s t em erged fro m t h e s u r f a c e 3 /3 2" b eyo nd t h e
en d o f t h e s l o t . The w eld ed j u n c t i o n o f e a c h c o p p e r - c o n s t a n ta n th e r m o
c o u p le was i n s e r t e d i n s i d e a c i r c u m f e r e n t i a l h o le ( a t t h e en d o f e a c h
s l o t ) . The w ir e s w ere th e n p r e s s e d i n s i d e t h e s l o t s an d l a i d a lo n g t h e
b o tto m o f t h e g ro o v e s u n t i l t h e y em erged a t t h e end o f t h e t u b e . The
w ir e s w ere p a c k e d (10 i n e a c h g ro o v e ) so t h a t t h e y f i l l e d a p p r o x im a te ly
2 /3 o f t h e g ro o v e d e p t h . The r e m a in d e r o f t h e g ro o v e was f i l l e d w ith
D evcon Aluminum P a s t e w h ich c o n s i s t s o f 80$ alum inum pow der an d 20$
p l a s t i c f i l l e r . When t h e alum inum f i l l e r d r i e d , p o r t i o n s o f i t t h a t
p r o tr u d e d above t h e s u r f a c e o f t h e t u b e w ere m ach in ed o f f so t h a t t h e
g ro o v e s a g a i n assum ed a t e x t u r e v e r y n e a r l y t h e same a s t h e re m a in d e r
o f t h e tu b e . Two d i s c s (S ee F ig u r e 2 ) made o f alum inum w ere n e x t
f i t t e d t o t h e tu b e 1 0" a p a r t a t t h e s e c t i o n o f th e t u b e w here t h e
th e rm o c o u p le j u n c t i o n s w e r e . T h ese d i s c s e f f e c t i v e l y d e f i n e d t h e t e s t
s e c t i o n an d a l s o p r e v e n te d le a k a g e o f u n w anted c o n d e n s a te i n t o o r o u t
o f th e i n n e r b o x . The d i s c s w ere i n s u l a t e d fro m t h e tu b e b y means o f
T e f l o n s l e e v e s . The tu b e was t h e n i n s t a l l e d i n t o t h e s te a m cham ber a s
shown i n F ig u r e 2 .
S l i p R in g A ssem b ly
I n o r d e r t o co n v ey t h e th e rm o c o u p le em f. s i g n a l fro m th e s h a f t when
t h e l a t t e r was r o t a t i n g t o t h e s t a t i o n a r y m e a s u rin g an d r e c o r d i n g
i n s t r u m e n t s , i t was n e c e s s a r y t o em ploy s l i p r i n g s . B ased on r e p o r t e d
d i f f i c u l t i e s o f o t h e r r e s e a r c h e r ^ ^ 3 .)• who a tte m p te d t o make t h e i r
own s l i p - r i n g a s s e m b l i e s , i t was d e c id e d t o buy a read y -m ad e s l i p - r i n g
u n i t f o r t h e p r e s e n t i n v e s t i g a t i o n . A 10 r i n g u n i t , m a n u fa c tu re d b y
M ic h ig a n S c i e n t i f i c Company, was p u r c h a s e d . T h is u n i t i s shown
i n s t a l l e d i n F ig u r e 1 .
T herm ocouple C i r c u i t s and th e
M e a su rin g & R e c o rd in g I n s tr u m e n ts
The th e rm o c o u p le c i r c u i t f o r t h e w ir e s a t t a c h e d t o t h e c o n d e n s e r
t u b e was o r i g i n a l l y made up a s shown i n F ig u r e 1 ( a ) . O r i g i n a l l y , i t
h a d b e e n p la n n e d t h a t a l l o f t h e th e rm o c o u p le s a t t a c h e d t o th e c o n d e n s e r
tu b e (30 o f th e m ) w ould be c o n n e c te d t o t h e m e a s u rin g in s tr u m e n ts .
H ow ever, t h e c o s t o f a s l i p - r i n g u n i t h a v in g t h i r t y - o n e (3 1) r i n g s was
p r o h i b i t i v e an d h e n c e a t e n r i n g u n i t was p u rc h a s e d w hich made i t
p o s s i b l e t o m o n ito r t h e s i g n a l s from o n ly n in e o f t h e t h i r t y th e rm o
c o u p l e s . A l l t h e c o p p e r le a d s (9 o f th e m ) w ere s o l d e r e d t o g e t h e r and
t h e n a t t a c h e d t o a s i n g l e l e a d on t h e r i n g s id e o f t h e s l i p - r i n g u n i t .
The n in e c o n s t a n t a n le a d s w ere a t t a c h e d s i n g l y t o t h e r e m a in in g le a d s
on t h e r i n g s i d e o f t h e s l i p - r i n g u n i t . On t h e b r u s h s id e o f th e s l i p -
r i n g u n i t , a c o p p e r l e a d was a t t a c h e d t o t h e b r u s h c o r r e s p o n d in g t o t h e
r i n g t o w h ich a l l t h e c o p p e r le a d s w ere a t t a c h e d ; and a c o n s ta n t a n le a d
was a t t a c h e d , one t o e a c h b r u s h , s u c h t h a t th e b r u s h e s m ated w ith th e
r i n g s w hich had c o n s ta n t a n w ir e s a t t a c h e d t o them . The c o p p e r le a d and
t h e c o n s ta n t a n le a d s w ere t h e n a t t a c h e d t o a T h e rm o v o lt I n s tr u m e n t
Company m u l t i p l e s w i tc h . From th e o u tp u t t e r m i n a l s o f th e s w itc h , a
c o p p e r le a d was a t t a c h e d t o t h e common c o p p e r s i d e , an d a c o n s ta n ta n
l e a d was a t t a c h e d t o th e o t h e r t e r m i n a l . The o t h e r end o f th e c o n s ta n t a n
16
l e a d was jo i n e d t o a c o p p e r l e a d t o co m p rise t h e r e f e r e n c e j u n c t i o n (See
F ig u r e 4 ( a ) ) . The tw o f r e e c o p p e r le a d s w ere t h e n c o n n e c te d a c r o s s a
p o t e n t i o m e t e r and a l s o a c r o s s a r e c o r d e r . The p o t e n t i o m e t e r u s e d was a
H o neyw ell P o t e n t io m e te r M odel No. 27^-5* The c o n tin u o u s p e n r e c o r d e r
M odel 7100B was m a n u fa c tu r e d hy H e w e le tt P a c k a r d .
I t was s u g g e s te d t h a t a d i f f e r e n t c i r c u i t s h o u ld h e u s e d t o o b v ia te
t h e p o s s i b i l i t y o f a n e r r o r a r i s i n g fro m , e]_ an d -e-^ a n d , a n ^- -e 2
(S ee F ig u r e Ha) n o t c a n c e l l i n g . S e v e r a l o f t h e th e rm o c o u p le c i r c u i t s
w ere t h e n ch anged t o t h e c o n f i g u r a t i o n shown i n F ig u r e H ( b ) . The
m a jo r change was t h e e l i m i n a t i o n o f t h e Emf l s a^ an(^ _e2 . H ow ever, i t
was s t i l l n e c e s s a r y t o co m p en sate f o r Emf. e-j_ and t h e r e f o r e t h e compen
s a t i n g c i r c u i t shown i n F ig u r e h (b ) was i n c l u d e d . T h e re was no
s i g n i f i c a n t d i f f e r e n c e i n t h e p o t e n t i o m e t e r ( a n d /o r r e c o r d e r ) r e a d i n g
when t h e tw o c i r c u i t s w ere in t e r c h a n g e d f o r a n y one th e rm o c o u p le . I t
was f e l t , n e v e r t h e l e s s , t h a t t h e c i r c u i t shown i n F ig u r e H-(b) was more
r e l i a b l e and t h i s one was u s e d .
A l l o t h e r th e rm o c o u p le s w h ich m easu red te m p e r a tu r e s on s t a t i o n a r y
members w ere c o n n e c te d t o t h e m e a s u rin g in s tr u m e n ts u s in g a c i r c u i t
i d e n t i c a l t o t h a t i n F ig u r e H- ( a ) , when t h e l a t t e r h a s th e s l i p - r i n g
p o r t i o n o f th e c i r c u i t rem oved.
EXPERIMENTAL PROCEDURE
The p r i n c i p a l o b j e c t i v e o f t h i s i n v e s t i g a t i o n was t o s tu d y t h e e f f e c t
o f t h e r o t a t i o n o f a c o n d e n s e r tu b e on t h e o u t s i d e o r s te a m s i d e h e a t
t r a n s f e r c o e f f i c i e n t . The e f f e c t o f t h e o v e r a l l t e m p e r a t u r e d i f f e r e n c e
(Ts - Tw) was a l s o i n v e s t i g a t e d .
B e fo re t h e a p p a r a tu s was a s s e m b le d , t h e o u t s i d e s u r f a c e o f t h e t e s t
s e c t i o n was th o r o u g h l y c le a n e d u s in g s t e e l w o o l; i t was t h e n p o l i s h e d
u s in g a b r a s i v e pow der an d f i n a l l y w ashed w i t h a l c o h o l . T h is was done
i n o r d e r t o e n s u r e c o m p le te w e t t i n g o f t h e c o n d e n s in g s u r f a c e . Then t h e
ste a m cham ber was c l o s e d . A t t h e b e g in n in g o f e a c h e x p e rim e n t t h e e q u i p
m ent was a llo w e d t o o p e r a t e w ith t h e ste a m an d c o o l i n g w a te r t u r n e d on
f o r a t l e a s t 30 m in u te s b e f o r e t h e f i r s t r e a d i n g s w ere r e c o r d e d . A ls o ,
when t h e ste a m f i r s t e n t e r e d t h e cham ber, a v a l v e a t t h e h ig h p o i n t o f
t h e cham ber was o p en ed t o a llo w t h e re m o v a l o f a i r fro m t h e ch am b er.
The ste a m p r e s s u r e a t t h e b o i l e r was a d j u s t e d so t h a t when t h i s s o u rc e
steam was t h r o t t l e d t o t e s t c o n d i t i o n s o f 6 .3 p s i g i t was a l s o s u p e r
h e a te d b y 2 F ° . A t t h e s t a r t o f e a c h e x p e r im e n t t h e b a r o m e tr ic p r e s s u r e
was r e c o r d e d .
The f i r s t r u n was r e p e a t e d a f t e r 30 m in u te s t o e n s u r e t h a t s t e a d y
s t a t e was a c h ie v e d , and t h e n t h e s p e e d o f r o t a t i o n was ch an g e d ( i n e v e r y
i n s t a n c e t h e s p e e d o f r o t a t i o n was i n c r e a s e d , i n random i n t e r v a l s from
z e ro RPM t o 2700 RPM). A f t e r e a c h s p e e d ch an g e t h e e q u ip m en t was a llo w e d
t o o p e r a t e f o r 30 m in u te s b e f o r e t h e n e x t s e t o f r e a d i n g s was r e c o r d e d .
17
18
F o r e a c h r u n tw o s e t s o f r e a d in g s w ere r e c o r d e d and a v e r a g e d . The
p a r a m e te r s m e te r e d w e r e :
1 . C o o lin g w a te r te m p e r a tu r e a t 11 p o i n t s a lo n g t h e l e n g t h o f t h e - t e s t s e c t i o n one in c h a p a r t , s t a r t i n g a t t h e t o p .
2 . S team s i d e c o n d e n s e r s u r f a c e te m p e r a tu r e a t 10 p o i n t s one in c h a p a r t , s t a r t i n g l / 2 i n c h fro m t h e t o p .
3 • C o o lin g w a te r flo w r a t e .
4 . C o n d en sate flo w r a t e .
5 . Steam t e m p e r a t u r e .
6 . S team p r e s s u r e .
7 - S peed o f r o t a t i o n o f t h e c o n d e n s e r t u b e .
A l l t h e te m p e r a tu r e s w ere m easu red u s in g c o p p e r - c o n s t a n ta n th e rm o
c o u p l e s . The th e rm o c o u p le s i g n a l s from t h e w ir e s a t t a c h e d t o t h e r o t a t
in g s h a f t w ere c o n d u c te d t o t h e s t a t i o n a r y i n s tr u m e n ts b y means o f s l i p
r i n g s . T hese an d a l l o t h e r th e rm o c o u p le s i g n a l s w ere e i t h e r r e c o r d e d b y
a s t r i p c h a r t r e c o r d e r o r m e a su re d m a n u a lly on a p o t e n t i o m e t e r .
C o o lin g w a te r te m p e r a tu r e was m e asu re d b y m eans o f a th e rm o c o u p le
i n s e r t e d i n t o a l / l 6 n O.D. x 0 .0 4 8 " I .D . s t a i n l e s s s t e e l t u b e , (H) i n
F ig u r e 1 , w hich was i t s e l f i n s e r t e d i n s i d e t h e c o n d e n s e r tu b e from th e
b o tto m an d s e c u r e d t o t h e s t a t i o n a r y t a n k , (g) i n F ig u r e 1 . One in c h
from t h e th e rm o c o u p le j u n c t i o n , a s m a ll p r o p e l l e r was a t t a c h e d t o th e
s t a i n l e s s s t e e l tu b e t o e n s u r e th o ro u g h m ix in g o f t h e c o o l in g w a te r .
The th e rm o c o u p le t h e n m e asu re d t h e b u lk te m p e r a tu r e o f t h e w a te r .
D u rin g t h e w a it in g p e r io d r e q u i r e d f o r s t e a d y s t a t e t o o c c u r , t h e p ro b e
was p u sh ed i n so t h a t t h e p r o p e l l e r was w e l l d o w nstream o f t h e t e s t
s e c t i o n . I n o r d e r t o le a v e t h e flo w , u p s tre a m o f t h e p o i n t w here m e a s u re
m en ts w ere b e in g r e c o r d e d , u n a f f e c t e d , t h e f i r s t r e a d i n g ta k e n was a t a
t e s t s e c t i o n l o c a t i o n f a r t h e s t d ow n stream . -The p ro b e was t h e n moved
u p s tr e a m one in c h a t a tim e u n t i l t h e w hole l e n g t h o f t h e t e s t s e c t i o n
was c o v e r e d .
The te m p e r a t u r e o f th e c o o l i n g w a te r was m e a su re d t o w i t h i n + 0 .1 0 F°.
E le v e n te m p e r a t u r e r e a d in g s w ere p l o t t e d a g a i n s t t h e i r a p p r o p r i a t e
l o c a t i o n on t h e s h a f t an d a l i n e draw n th r o u g h th e m i n o r d e r t o e s t a b l i s h
a c o n tin u o u s c u r v e . A v erag e te m p e r a tu r e r i s e o f t h e c o o l i n g w a te r
b etw ee n s t a t i o n s 1 and 11 was 1 .5 F ° . S in c e t h e te m p e r a t u r e i s m easu red
t o w i t h i n + 0 .1 0 F ° , t h e r e s u l t i n g e r r o r i n Tw i s 2 . 0 $ .
C o o lin g w a te r and c o n d e n s a te flo w r a t e s w ere m e a su re d b y c o l l e c t i n g
and w e ig h in g t h e q u a n t i t i e s in v o l v e d .
The w e ig h s c a l e u s e d f o r c o o l i n g w a te r m e asu re m en ts was a c c u r a t e t o
w i t h i n + _ 0 .1 0 l b . The l e a s t w e ig h t o f w a te r c o l l e c t e d was 60 lb /m in .
H ence, t h e maximum e r r o r r e s u l t i n g fro m t h i s m easu rem en t was 0 . 2 $ . T hen,
t h e maximum e r r o r w hich c o u ld a r i s e i n e v a l u a t i n g h e a t f l u x , an d h en ce
t h e h e a t t r a n s f e r c o e f f i c i e n t , by m u l t i p l y i n g t h e c o o l i n g w a te r mass
f lo w r a t e and te m p e r a tu r e r i s e w ould be 2 .2 $ .
The h e a t t r a n s f e r r e d t o t h e c o o l in g w a te r was com pared t o t h e h e a t
r e q u i r e d t o co n d en se th e c o n d e n s a te c o l l e c t e d , an d i t was fo u n d t h a t
t h e d i f f e r e n c e b etw een t h e tw o was n e v e r g r e a t e r t h a n 5$*
Steam p r e s s u r e was m e a su re d b y means o f a p r e s s u r e gauge w hich
was a c c u r a t e t o w ith i n 1 o z / i n , b etw ee n z e r o an d 10 p s i g .
The r o t a t i o n a l sp e e d o f t h e c o n d e n s e r tu b e was m e a su re d u s in g a
ta c h o m e te r an d a s tr o b o s c o p e .
S e v e n t y - s i x (7 6) e x p e r im e n ts w ere p e rfo rm e d , v a r y in g t h e r o t a t i o n a l
s p eed from z e r o t o 2700 RPM a n d t h e c o o l in g w a te r te m p e r a t u r e an d flo w
fro m ^5°F t o 120°F and 36OO l b / h r . t o 7200 l b / h r . r e s p e c t i v e l y .
CHAPTER 5
DISCUSSION OF RESULTS
Some o f t h e e x p e r i m e n t a l d a t a f o r t h e t e s t s e r i e s , I , I I and I I I ,
i s shown i n i t s e l e m e n t a l fo rm i n F i g u r e s 5 } 6 an d J , r e s p e c t i v e l y . No
te m p e r a t u r e r e a d i n g s w ere r e c o r d e d f o r l o c a t i o n d = 6 .5 b e c a u s e th e
th e rm o c o u p le a t t h a t l o c a t i o n c o u ld n o t be accom m odated on t h e s l i p -
r i n g . The r e a d i n g s from t h e th e rm o c o u p le l o c a t e d a t d = 7 * 5 w ere n o t
r e c o r d e d b e c a u s e t h e y w ere o b v io u s ly i n ' e r r o r . A l l t h r e e o f t h e f i g u r e s
( 5 , 6 , 7 ) e x h i b i t th e same t r e n d . As t h e s p e e d o f r o t a t i o n was
i n c r e a s e d , t h e s u r f a c e te m p e r a tu r e o f t h e c o n d e n s e r tu b e a l s o i n c r e a s e d .
A ls o e v i d e n t i n a l l t h r e e o f t h e f i g u r e s 5 s t h e te m p e r a t u r e d ro p from
t h e c e n t r e t o t h e en d s o f t h e t e s t s e c t i o n . T h is was c a u s e d b y end h e a t
l o s s e s . From F ig u r e 5 i t can be s e e n t h a t t h e te m p e r a t u r e d i f f e r e n c e /NT
v a r i e s fro m 70 F° a t z e r o RPM t o 30 F° a t 2610 RPM. T h is o f c o u rs e
i m p lie s t h a t , o v e r t h e same s p e e d r a n g e , t h e h e a t t r a n s f e r c o e f f i c i e n t
s h o u ld i n c r e a s e b y more th a n 100$, i f t h e h e a t f l u x i s h e l d c o n s t a n t . I n
f a c t , t h e h e a t t r a n s f e r c o e f f i c i e n t i n c r e a s e d b y m ore t h a n 200$ (See
F ig u r e 12) s in c e t h e h e a t f l u x was a l s o i n c r e a s i n g w ith r o t a t i o n a l s p e e d .
S in c e t h e h e a t f l u x was n o t c o n s t a n t , t h e n t h e c o n d e n s e r s u r f a c e te m p
e r a t u r e , b e in g a d e p e n d e n t p a r a m e te r , i s n o t a t r u e i n d i c a t i o n o f t h e
ch ang e i n h e a t t r a n s f e r c o e f f i c i e n t . N e v e r t h e l e s s , i t i s o b v io u s ly a
good q u a l i t a t i v e i n d i c a t i o n . o f t h e phenom enon an d j u s t i f i e s f u r t h e r
d i s c u s s i o n . F o r t e s t s e r i e s I I , F ig u r e 6 , AT d ro p p e d fro m 90 F° t o 25 F °
a s t h e r o t a t i o n a l sp e e d was i n c r e a s e d fro m z e r o RPM t o 2L60 RPM, im p ly in g
a n a lm o s t 300$ i n c r e a s e i n h ^ w h e re , i n f a c t , i n c r e a s e d b y a lm o s t lf-00$ .
F o r t e s t s e r i e s I I I , F ig u r e "J, ^ d ro p s fro m 110 F° t o 1+0 F° im p ly in g a n
a lm o s t tw o f o l d i n c r e a s e i n hm, w h ere, i n f a c t , h^, i n c r e a s e d b y a lm o s t kOO$ .
- 20
I n b o th t h e l a t t e r c a s e s t h e r e a s o n f o r t h e d i s c r e p a n c y i s th e same a s
c i t e d f o r t e s t s e r i e s I ; t h e f a c t t h a t TQ i s a d e p e n d e n t p a r a m e te r makes
i t r e l a t i v e l y i n s e n s i t i v e t o a change i n h e a t f l u x , s i n c e t h i s l a t t e r
ch an g e c a u s e s a com bined ch ange i n b o th hm. an d AT.
A ls o e v i d e n t i n F ig u r e s 5 , 6 an d 7 i s a c o n s i s t e n t t r e n d f o r th e
s u r f a c e te m p e r a t u r e a t t h e t o p o f t h e t e s t s e c t i o n t o change fro m a
v a l u e l e s s t h a n t h e a v e ra g e a t z e ro RPM t o a v a l u e v e i l above o r t h e
same a s t h e a v e r a g e a t t h e same r o t a t i o n a l s p e e d above 1000 RPM. T h is
i n d i c a t e s t h a t t h e f i l m o f c o n d e n s a te i s t h i n n e r a t t h e u p p e r en d o f th e
c o n d e n s e r t u b e . As t h e s p e e d i s i n c r e a s e d , t h e te m p e r a tu r e o f t h e
r e m a in d e r o f t h e tu b e r i s e s t o e q u a l t h a t a t t h e to p m o st th e rm o c o u p le
p o s i t i o n . The te m p e r a tu r e a t th e b o tto m o f t h e t e s t s e c t i o n n e v e r
r e a c h e s t h e same v a lu e a s t h a t a t t h e t o p , e x c e p t a t z e ro RPM when b o th
p o s i t i o n s h av e a te m p e r a tu r e f a r b e l o v t h e a v e r a g e . A ls o e v i d e n t from
t h e t h r e e f i g u r e s (5 , 6 and 7 ) i s t h e f a c t t h a t th e u p p e rm o st te m p e r a tu r e
r e a d i n g ch an g e s v e r y l i t t l e a t h ig h s p e e d s , i n d i c a t i n g a l e v e l l i n g - o f f
o f t h e s u r f a c e te m p e r a t u r e . T h is i s more e v i d e n t i n t h e t h r e e f i g u r e s
8, 9 and 10*
F ig u r e s 8 , 9 and 10 w ere draw n assu m in g a c o n s t a n t c o n d e n s e r s u r f a c e
te m p e r a tu r e a t a n y one r o t a t i o n a l s p e e d an d p l o t t i n g t h e a c t u a l te m p e r a
t u r e s a g a i n s t t h e c o r r e s p o n d in g s p e e d . By d o in g t h i s and b y d ra w in g a
l i n e th r o u g h t h e m ost f r e q u e n t l y o c c u r r i n g te m p e r a tu r e p o i n t s , i t i s
im p lie d t h a t t h e a v e ra g e te m p e r a tu r e i s t h e m o st f r e q u e n t l y o c c u r r i n g
te m p e r a tu r e r a t h e r th a n th e c o n v e n t i o n a l l y a c c e p te d a v e r a g e . I t was
f e l t t h a t t h i s was a n a c c e p t a b l e mode o f d ra w in g t h e c u rv e s s in c e i n f a c t ,
t h e m a j o r i t y o f th e te m p e r a tu r e s w ere a lm o s t t h e same an d t h e o n es t h a t
22
w ere n o t ( n o r m a l ly t h e en d t e m p e r a t u r e s ) when a v e ra g e d i n w ith t h e r e s t
i n t h e c o n v e n t i o n a l m anner r e s u l t e d i n a n e r r o r i n hm. o f l e s s t h a n 5$
i n t h e w o r s t c a s e .
F i g u r e s 8 , 9 an d 10 show t h e d a t a i n a much m ore m e a n in g f u l fo rm ,
i n some r e s p e c t s , t h a n F ig u r e s 5 , 6 an d 7 s i n c e now a l l t h e d a t a a r e
p r e s e n t e d and t h e o v e r a l l t r e n d c a n be f o l l o w e d . Now, h o w ev er,
( i n F i g u r e s 8 , 9 an d 1 0 ) t h e te m p e r a t u r e c h an g e a lo n g t h e l e n g t h o f
t h e c o n d e n s e r tu b e i s somewhat c a m o u fla g e d . F ig u r e s 8 , 9 and 10
a l l show b a s i c a l l y t h e same t r e n d i n t h e d a t a : t h e c o n d e n s e r s u r f a c e
te m p e r a t u r e i n i t i a l l y d ro p s a s t h e r o t a t i o n a l sp e e d i s i n c r e a s e d up t o
a c e r t a i n r o t a t i o n a l sp eed and t h e n t h e t e m p e r a t u r e s u d d e n ly r i s e s .
The o n l y d i f f e r e n c e b e tw e e n t h e f i g u r e s l i e s i n t h e am ount o f t h e te m p e r a
t u r e d r o p an d t h e sp e e d l o c a t i o n a t w h ich t h e t e m p e r a t u r e b e g i n s t o r i s e .
The f a c t t h a t t h e te m p e r a tu r e i n i t i a l l y d r o p s i n d i c a t e s t h a t a f i l m
o f c o n d e n s a te fo rm s on t h e c o n d e n s e r s u r f a c e a n d becom es t h i c k e r a s t h e
sp e e d o f r o t a t i o n i n c r e a s e s . When t h e c o n d e n s e r i s r o t a t e d , t h e r e s u l t
in g c e n t r i f u g a l f o r c e te n d s t o th ro w t h e c o n d e n s a te o f f t a n g e n t i a l l y .
H ow ever, t h e s u r f a c e t e n s i o n f o r c e b e tw e e n t h e a d j o i n i n g l i q u i d m o le c u le s
te n d s t o k eep t h e c o n d e n s a te l a y e r a t t a c h e d t o t h e t u b e . When t h i s
l a y e r g e t s l a r g e en o u g h , t h e s u r f a c e b r e a k s down and t h e l i q u i d i s
th ro w n o f f i n a l l d i r e c t i o n s . A lth o u g h i n f a c t t h e s u r f a c e t e n s i o n
f o r c e v a r i e s i n v e r s e l y w ith t h e f l u i d te m p e r a t u r e , t h i s i s n o t b o r n e
o u t v e r y c l e a r l y b y t h e e x p e r i m e n t s . A t a s u r f a c e t e m p e r a t u r e o f
a p p r o x im a te ly 1 7 0 °F , th e s u r f a c e t e m p e r a t u r e d e c l i n e d u n t i l a r o t a t i o n a l
sp e e d o f 850 REM ( F r = 1 0 .0 5 ) was r e a c h e d , a t w h ich tim e t h e te m p e r a t u r e