Heat transfer from a horizontal bundle of continuous, helical finned tubes in an air fluidized bed
by Michael Todd Kratovil
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Chemical Engineering
Montana State University
© Copyright by Michael Todd Kratovil (1976)
Abstract:
Heat transfer coefficients were measured from a horizontal bundle of electrically heated finned tubes to
a rectangular air fluidized glass bead bed. Continuous, helical copper finned tubes were studied.
Experimental parameters included fin height, fin spacing, bed particle diameter and air fluidizing
velocity.
• Results indicated that the coefficient generally increased with increasing fluidizing velocity. A
maximum coefficient was observed in some cases. The coefficient increased with decreasing particle
size. Increases of up to 50 percent were observed between the large and small particles. 'The coefficient
increased with decreasing fin height and increasing fin spacing. The coefficient was very sensistive to
fin spacings as large as 30 particle diameters. At less than 10 particle diameters the coefficient became
less sensitive to fin spacing. The best performing tube as rated on heat delivery was a tube of
intermediate fin spacing and maximum fin height. A particle mode heat transfer mechanism was
successfully used to explain all trends observed.
A correlation independent of fin material was developed relating experimental variables to the particle
Nusselt number. Deviation of the data from the correlation was within the estimated experimental
error. STATEMENT OF PERMISSION TO COPY
In p re s e n tin g t h i s
th e s is -in p a r t i a l f u l f i l l m e n t o f th e re q u ire m e n ts
f o r an advanced degree a t Montana S ta te U n iv e r s it y , I agree t h a t th e
L ib r a r y s h a ll make i t
f r e e l y a v a ila b le f o r in s p e c tio n -. - I f u r t h e r agree
t h a t p e rm is s io n f o r e x te n s iv e co p yin g o f t h i s
th e s is f o r s c h o la r ly
purposes may be g ra n te d by my m a jo r p r o fe s s o r , o r , in h is absence, by
th e D ir e c to r o f L ib r a r ie s .
p u b lic a tio n o f t h i s
I t is
th e s is f o r f in a n c ia l g a in s h a ll n o t be a llo w e d
w ith o u t my w r it t e n p e rm is s io n .
S ig n a tu re
Date
und erstoo d t h a t any co p y in g o r
i? -L V 7 ^
HEAT TRANSFER FROM A HORIZONTAL BUNDLE OF CONTINUOUS, HELICAL
FINNED TUBES IN AN AIR FLUIDIZED BED
-
by
MICHAEL TODD KRATOVIL
A th e s is s u b m itte d in p a r t ia l f u l f i l l m e n t
o f th e re q u ire m e n ts f o r th e degree
of
MASTER OF SCIENCE
in
Chem ical E n g in e e rin g
A pproved:
G raduate Bean
MONTANA STATE UNIVERSITY
Bozeman, Montana
December, 1976
D
D
TT
iii
ACKNOWLEDGMENT
• T h is a u th o r w ishes to th a n k th e D epartm ent o f Chemical E n g in e e rin g
a t Montana S ta te U n iv e r s it y f o r a l l
th e h e lp g iv e n in t h i s
re s e a rc h .
S p e c ia l thanks go to D r . . W. E. G e n e tti who d ir e c te d and a id e d me in a l l
- phases o f t h i s p r o je c t .
My a p p re c ia tio n .g o e s to th e Rome T urney R a d ia to r Company, Rome,
New York and th e Wol v e rin e Tube D iv is io n ,
a s u b s id ia r y o,f U. 0. P.
f o r th e donated fin n e d tubes used, in t h i s
s tu d y .
F i n a ll y , my thanks go to th e N a tio n a l S cience F o u n d a tio n who
p ro v id e d th e fu n d in g f o r t h i s
re s e a rc h (NSF G ra n t No. 6K -39894).
W
7
iv
TABLE OF CONTENTS
Page
VITA....................................; ................ ............................
ACKNOWLEDGEMENT . .
.................. ....
LIS T OF TABLES. . . .
. ........
.
iii
. . .. .
vii
v iii
LIST OF FIGURES .....................................................
ABSTRACT....................................• • \ ..........................
INTRODUCTION. . . .
...................................................
THEORY AND PREVIOUS RELATEDURESEARCH.
ix
I
. . .
7
BED DYNAMICS .....................................................
7
MECHANISMS FOR HEAT TRANSFER ...................
IO
PREVIOUS RELATED RESEARCH...........................
15
EXPERIMENTAL EQUIPMENT. ..
. . . . . : . ..............
20
.
20
FLUIDIZING SYSTEM............................................
24
COLUMN...........................................................
.
ii
ELECTRICAL SYSTEM.............. . . . . . . .
EXPERIMENTAL PROCEDURE.............................................
BEAD S IZE ...............................
MINIMUM FLUIDIZATION VELOCITIES.
. 26
33
33
. . .
33
TUBE THERMOCOUPLE LOCATION ........................
34
HEATER POWER INPUT ........................... . ' . . . .
36
PROCEDURE FOR A TYPICAL RUN........................
37
CORRELATION...........................■ ____ _____________
40
V
TABLE OF CONTENTS ( c o n t)
Page
PARTICLE MODEL FOR HEAT TRANSFER...................... . .
v .■ ■; .
h FROM H n . . . . . . . . . . . . . . . . . . . .
exp
. .
40
..................
46
' CORRELATION DEVELOPMENT............................................................. ....
A DESIGN PROBLEM................ . . . . . . . .
. . . .. . . ■. . . -.
. . .
54
. . .
60
RESULTS AND DISCUSSION
63
h VERSUS G..............................
64
h VERSUS FIN H E IG H T ..................................................... ......................\ ..
.
65
' h VERSUS FIN SPACING........................................................................................
q/AT FOR THE T U B E ................................... ....
. ................................... ..
68
.
73
TUBE DIAMETER................. ............................... ' ........................ ..........................
79
CALCULATIONS . . .- .......... ......................................................
AIR MASS VELO CITY...................
. . . . . . . .
.................................
81
81
BED TEMPERATURE.............................................................
82
TUBE TEMPERATURE. . . . ................ ................................................................
82
HEAT INPUT TO EACH TUBE ..................................................... : .....................
82
AREA OF EACH TUBE . .....................................................
..................
82
hexp: FOR EACH TUBE. . . ...........................................................' ....................
82
h
exp
83
. .
FOR THE BUNDLE. OF TUBES............................................
. . . . . .
AIR VISCOSITY AND THERMAL CONDUCTIVITY...............................
83
PARTICLE REYNOLDS NUMBER.................... .
83
...............................................
PARTICLE NUSSELT NUMBER . . . . . . . . .
. . V ...........................
83
- vi TABLE OF CONTENTS (c o n t)
Page
ERROR ANALYSIS ..........................
. . . . . . . . . . .
84
SUMMARY OF RESULTS AND CONCLUSIONS . . . . . . . . . . . . . . . .
86
RECOMMENDATIONS.
...............................
. . . ....'-V.-. .
.
.V - . . . " . . . .'
.- . .
NOMENCLATURE . '.............................................. ............................ -.................... ....
88
. .
89
BIBLIOGRAPHY..................................................... ' ....................................................... ....
93
LJ
J
-vli
-
LIST OF TABLES
T a b le
. .I
JI
Page
BLAST-O-LITE BEAD SIZE ANALYSIS____
. . . . . . . .
. . . .
TUBE DIMENSIONS. . . . . . . . . . . . . . . . . . . . . . .
I I I AVERAGE PERFORMANCE OF. TUBES . . . ...............................
25
29
78
- v iii
-
LIST OF FIGURES
F i qure
1
IA
Page
MODELS FOR HEAT TRANSFER....................... ....
.
.
.. . .
.
...
. .
. GENERAL MODEL FOR BED-SURFACE HEAT TRANSFER
Tl
15
2
OVERALL VIEW OF EQUIPMENT •................... ‘............................ ......................
21
3
DETAILS OF FLUIDIZING COLUMN.......................
22
4
DETAILS OF A CARTRIDGE HEATER..............................
27
5
TUBE DETAILS AND NOMENCLATURE.................. ■ .............. ....
30
6
PARTICLE MINIMUM FLUIDIZATION VELOCITIES.....................
35
7
HEAT TRANSFER COEFFICIENT VERSUS AIR MASS VELOCOITY
.
VERSUS HEAT F L U X ...............................................................
38
8
PARTICLE MODEL FOR HEAT TRANSFER..................
9
CORRELATION (ALL TUBES INCLUDED)................................................................... 59
10
EFFICIENCY OF CONTINUOUS HELICAL FINS . .
11
h
12
R VERSUS AIR MASS VELOCITY VERSUS FIN HEIGHT ( L ) .
13
R VERSUS AIR MASS VELOCITY VERSUS FIN SPACING ( S ) .............................69
14
R VERSUS Dp/S (CONSTANT FIN H E IG H T ).................................................... 71
15
-R
. . . . . . . . . .
. . .• . .
41
. . .
62
VERSUS G VERSUS PARTICLE DIAMETER ......................................................
66
. . . . .
.
VERSUS Dp/S (ALL T U B E S ).......................................
67
72
16
q/AT VERSUS G VERSUS FIN H E IG H T................................................
17
q/AT VERSUS G VERSUS FIN SPACING.- .
18
q/AT VERSUS G .................................................................. ....
75
............................................................76
. . . . .
. .
77
- ix ABSTRACT
Heat t r a n s f e r c o e f f ic ie n t s were measured from a h o r iz o n t a l bundle
o f e l e c t r i c a l l y heated fin n e d tubes to a r e c ta n g u la r a i r f lu i d iz e d g la s s
bead bed. C o n tin u o u s, h e lic a l copp er fin n e d tubes were s tu d ie d .
E xp e rim e n ta l param eters in c lu d e d f i n h e ig h t , f i n s p a c in g , bed p a r t ic le
d ia m e te r and a i r f l u i d i z i n g v e l o c it y .
• R e s u lts in d ic a te d t h a t th e c o e f f ic ie n t g e n e r a lly in c re a s e d w ith
in c re a s in g f l u i d i z i n g v e l o c it y .
A maximum c o e f f ic ie n t w as.observed in
some cases. The c o e f f ic ie n t in c re a s e d w ith d e c re a s in g p a r t i c l e s iz e .
In cre a se s o f up t o 50 p e rc e n t were observed between th e la rg e and sm all
p a r t ic le s . "The c o e f f ic ie n t in c re a s e d w ith d e c re a s in g f i n h e ig h t and
in c re a s in g f i n s p a c in g . The c o e f f ic ie n t was v e ry s e n s is tiv e to f i n
sp a cin g s as la rg e as 30 p a r t i c l e d ia m e te rs .
A t le s s th a n 10 o a r t ic le
d ia m e te rs th e c o e f f ic ie n t became le s s s e n s it iv e t o . f i n s p a c in g .
The
b e s t p e rfo rm in g tube as ra te d on hea t d e lSvery,.was.-a tu b e o f in te rm e d ia te
f i n sp a cin g and maximum f i n h e ig h t.
A - p a r tic le mode h e a t t r a n s f e r
mechanism was s u c c e s s fu lly used t o e x p la in a l l tre n d s o b se rve d .
A c o r r e la t io n in de p e n d e n t o f f i n m a te ria l was developed r e la t in g
e x p e rim e n ta l v a r ia b le s to th e p a r t i c l e N u s s e lt number.
D e v ia tio n o f
th e d a ta fro m th e c o r r e la t io n was w it h in th e e s tim a te d e x p e rim e n ta l
e rro r.
INTRODUCTION
Use o f f lu i d iz e d beds in c a r r y in g o u t com m ercial u n it o p e ra tio n s
is a gro w in g dynamic f i e l d
to d a y .
A p p lic a tio n s in d r y in g , c a lc in in g ,
m ix in g , c o o lin g to w e rs , and chem ical c a t a l y t i c re a c to rs - have been
d e m on strate d and a m y ria d o f a d d it io n a l. a p p lic a t io n s a re under
deve lop m en t.
.
-
•
A f lu i d iz e d bed c o n s is ts o f a colum n, a porous d i s t r i b u t o r p la te
s u p p o rtin g th e p a r t ic u la t e bed m a te ria l and a f l u i d i z i n g medium,
e it h e r gaseous o r l i q u i d . . The te rm f lu i d iz e d comes abo ut by th e
■
■■
v is u a l appearance and p h y s ic a l c h a r a c t e r is t ic s o f th e f lu i d iz e d bed.
A t low f l u i d i z i n g mass v e l o c it ie s th e p a r t ic u la t e bed a c ts j u s t
l i k e a packed bed.
The f l u i d i z i n g medium flo w s around th e p a r t ic le s
th ro u g h th e in t e r s t ic e s b e tw e e n .th e p a r t ic le s and o u t o f th e bed.
.
P a r t ic le s tend t o rem ain s t a t io n a r y under th e se c o n d itio n s .
As th e f l u i d i z i n g mass v e l o c it y in c re a s e s the p re s s u re drop across
th e bed e v e n tu a lly in c re a s e s so t h a t i t s
o f th e bed o f p a r t ic le s .
minimum f l u i d i z a t i o n
v a lu e is equal to th e w e ig h t
T h is c o n d itio n is c a lle d th e p o in t o f
(M .F .) and th e v a lu e o f th e f l u i d i z a t i o n medium
v e l o c it y i s known as th e minimum f l u i d i z a t i o n v e lo c it y
(M .F .V . ) .
At
M .F. bed p a r t ic le s e x h i b i t . lim it e d m otion and th e bed te n d s to expand.
Each p a r t i c l e
tends to " f l o a t "
in th e f l u i d i z i n g medium and th e e n t ir e
bed ta k e s on th e appearance o f a g ra n u la r l i q u i d .
The a c tu a l p h y s ic a l
p r o p e r tie s o f th e bed are th o s e o f a h ig h ly v is c o u s B in g h a m -p la s tic
f lu id
(I).
- 2 'As th e f l u i d i z i n g medium v e l o c i t y . i s
in c re a s e d beyond th e p o in t o f
M.P. bub ble s o f f l u i d i z i n g medium are seen to .fo r m a t th e porous s u p p o rt
p la te and r is e upward th ro u g h th e bed.
The bubbles expand and
co a le s c e as th e y r is e in th e bed and b u r s t as th e y reach th e upper bed
s u r fa c e .
The bub ble a c tio n te n d s to a g it a t e th e bed in c re a s in g th e
random m o tio n o f th e p a r t ic le s .
p e r c o la tin g bed is
T h is c o n d itio n o f a f r e e ly b u b b lin g o r
known as a g g re g a tiv e f l u i d i z a t i o n .
As th e f l u i d i z i n g medium v e l o c it y is
in c re a s e d s t i l l
f u r t h e r th e
s iz e o f th e bubbles in c re a s e s u n t i l th e b u b b le d ia m e te r approaches th e
s iz e o f th e colum n.
seen r i s i n g
f lu id iz a t io n
Layers o f f l u i d i z i n g medium and p a r t ic le s are
in th e c o lu m n ,in p i s t o n - l ik e a c t io n .
is
known as s lu g g in g .
T h is c o n d itio n o f
Maximum p a r t ic le m o tio n , is achieved
■with s lu g g in g b u t p h y s ic a l. equipm ent damage, e x c e s s iv e p a r t i c l e
d e g ra d a tio n and e n tra in m e n t may r e s u l t .
o p e ra te in th e a g g re g a tiv e re g im e .
Most com m ercial f lu i d iz e d beds
Both a g g re g a tiv e and s lu g g in g regim es
were observed in t h i s s tu d y .
The f l u i d - l i k e
c h a r a c t e r is t ic s
,
p a r t i c l e m o tio n o f th e .b e d produces d e s ir a b le
t h a t can be c o m m e rc ia lly u t i l i z e d .
The f l u i d - l i k e
q u a li t i e s o f th e bed a llo w c o n v e rs io n o f .le s s d e s ira b le , b a tc h processes
t o c o n tin u o u s o p e ra tio n s .
The random p a r t i c l e movement promotes good
p a r t i c l e m ix in g p r o v id in g n e a r ly is o th e r m a l, and u n ifo rm co m p o s itio n
c o n d itio n s th ro u g h o u t th e bed a llo w in g easy c o n tr o l o f p h y s ic a l bed
p a ra m e te rs.
The r a te o f -heat t r a n s f e r between the. bed p a r t ic le s and an
- 3 immersed bed exchanger is h ig h compared t o a f ix e d bed arrangem ent
th u s re d u c in g th e s u rfa c e re q u ire m e n ts and c o s t o f th e h ea t exchanger.
The s c ru b b in g a c tio n o f th e p a r t ic le s on exposed s u rfa c e s v i r t u a l l y
e lim in a te s s u rfa c e f o u lin g . .
Heat and mass t r a n s f e r r a te s between
f l u i d i z i n g gas and bed p a r t ic le s
a re h ig h compared to o th e r c o n ta c tin g
means because o f th e h ig h s u rfa c e area, p ro v id e d .by th e p a r t ic le s .
sm all d ia m e te r p a r t ic le s
The
in a f lu i d iz e d bed a re g e n e r a lly o f a s m a lle r
o rd e r o f m agnitude th a n in a fix e d .b e d thus p r o v id in g a s m a lle r
d i f f u s io n r e s is ta n c e to mass t r a n s f e r .
T h is is im p o r ta n t in
c a t a l y t i c r e a c to r a p p lic a tio n s .
I t s h o u ld be re a liz e d .h o w e v e r t h a t th e re are a ls o some u n d e s ira b le
p h y s ic a l c h a r a c t e r is t ic s
a p p lic a t io n s .
o f f lu i d iz e d beds t h a t p re v e n t com m ercial
The f lu i d iz e d bed is by no means th e u n iv e r s a l answer
to in d u s t r y 's pro b le m s.
C h a n n e lin g and b y -p a s s in g o f s o lid s by bubbles
p re s e n ts an i n e f f i c i e n t c o n ta c tin g scheme.
The f lu i d iz e d bed is n o t
a p p lic a b le in ca k in g c o n d it io n s . o r processes in v o lv in g - " s t ic k y " re a c ta n ts
o r p ro d u c ts .
when f r a g i l e
P a r t ic le , d e g ra d a tio n and e n tra in m e n t m ay"prove to o c o s t ly
o r e xp e n sive c a t a ly s t p a r t ic le s are used.
The s c ru b b in g
a c tio n o f th e p a r t ic le s prom ote e ro s io n o f v e sse l w a lls and p ip in g .
The f lu i d iz e d bed a c ts l i k e a back-m ixed r e a c t o r re d u c in g th e d r iv in g
fo r c e f o r mass and h e a t..tr a n s fe r and chem ica l r e a c t io n .
F lu id iz e d beds
can however be arra nged and b a f f le d to e x h i b i t lim it e d c o u n te r c u r r e n t
b e h a v io r.
- 4 There have been many im p o rta n t s it u a t io n s t h a t prove fa v o ra b le to
f lu i d iz e d bed p ro c e s s in g .
(1 )
Some a p p lic a tio n s are l i s t e d be lo w .
F r i t z W in k le r 's g a s if ic a t io n o f powdered co a l ( 2 ) .
T h is
was th e f i r s t s i g n i f i c a n t use o f f lu i d iz e d beds, in a
. com m ercial o p e r a tio n . . I t has proved i n e f f i c i e n t and
uneconom ical in to d a y 's p e tro le u m w o rld (1 9 2 2 ).
(2 )
.
U. S. P e tro le u m in d u s t r y 's c o n tin u o u s f lu i d iz e d bed c a t a ly t ic
c ra c k in g u n i t ( I ) .
I t re p la c e d th e f ix e d bed Houdry process
and made p o s s ib le econom ical c o n v e rs io n o f h e a v ie r crude
o il
in t o l i g h t e r more d e s ir a b le p e tro le u m f r a c t io n s
- ( s till
(3 )
(1 9 3 9 ).
in use) .
S tandard O il. Developm ent Company's c o n tin u o u s flu id iz e d - b e d
c a t a l y t i c re fo rm e r ( 2 ) .
Is o m e rizes T ig h t h yd roca rbo n feed
in c o n ta c t w ith a . s u it a b le c a t a ly s t to produce a h ig h e r
o cta n e number g a s o lin e (1 9 5 3 ). ( s t i l l
(4 )
in use)
F lu id iz e d - b e d .d r y in g o f ir o n - o r e c o n c e n tra te (3 ) reduces
m o is tu re c o n t e n t . o f w et c o n c e n tra te ir o n - o r e fro m 4.5% to
1.5% to a llo w h a n d lin g o f th e ore in subzero c o n d itio n s
(1 9 7 4 ).
(5 )
( s till
in use)
C a lc in a tio n o f n u c le a r w astes ( 4 ) .
S o lu tio n o f r a d io a c t iv e
f is s io n p ro d u c ts and s o lv e n t a re sprayed in t o h o t f lu id iz e d
bed.
The s o l v e n t . is v a p o riz e d and r a d io a c t iv e components
s o l i d i f y on bed p a r t ic le s
th u s g r e a t ly re d u c in g th e volume
- 5 and chan gin g th e phase o f n u c le a r w a ste s,
(6 )
( s till
in use)
F l u i d i zed-bed w e t-d ry tow ers in w aste h e a t d is p o s a l
(5 ) are
an a l t e r n a t iv e to c o o lin g ponds and c o o lin g w a te r tow ers
u s in g s h a llo w a i r f lu i d iz e d bed w e t-d ry c o o lin g u n it s ,
(u n d e r
.
- developm ent)
The above l i s t is n o t in te n d e d t o be com plete in any way.
I t is
in te n d e d to show some o f th e s ig n if ic a n c e and d i v e r s i t y o f a p p lic a tio n
t h a t f lu i d iz e d beds have.
. As can be seen fro m th e above l i s t , many a p p lic a tio n s o f f lu i d iz e d
beds r e q u ir e h e a t t r a n s f e r to o r fro m th e bed.
T h is h e a t t r a n s f e r is
a ccom plishe d e i t h e r th ro u g h th e column w a lls o r more commonly th ro u g h .
immersed s u rfa c e s w it h in
th e bed.
The random m o tio n o f th e p a r t ic le s and
th e com plex f l u i d i z i n g medium flo w pa th make a n a ly t ic a l a n a ly s is f o r
d e te rm in in g h e a t t r a n s f e r c o e f f ic ie n t s
im p o s s ib le .
to o r from th e bed v i r t u a l l y
C o n se q u e n tly, e x p e rim e n ta l c o r r e la t io n s a re b e in g developed
r e la t in g th e h e a t t r a n s f e r s u rfa c e geom etry to th e h e a t t r a n s f e r co ­
e f fic ie n t.
W ith th e developm ent o f th e s e c o r r e la t io n s i t
is hoped t h a t
o u r u n d e rs ta n d in g o f what is r e a l l y g o in g on in a f lu i d iz e d bed w i l l
be
enhanced, e n a b lin g s u c c e s s fu l d e sig n and s c a le up o f columns m eeting
re q u ire d s p e c if ic a t io n s .
The purpose o f t h i s
in v e s t ig a t io n w a s .to deve lop a c o r r e la t io n
r e la t in g s u rfa c e geom etry param eters o f h o r iz o n t a l, c o n tin u o u s , h e l i c a l ,
copper fin n e d tubes in an a i r f l u i d i zed-bed to th e c o rre s p o n d in g
- 6 h e a t - t r a n s f e r c o e f f i c i e n t . o f th e tu b e .
g la s s beads o f c o n t r o lle d d ia m e te rs ..
f in
h e ig h t , f i n
v e l o c it y .
The bed m a te ria l c o n s is te d o f
E xp e rim e n ta l v a r ia b le s in c lu d e d
s p a c in g , p a r t i c l e d ia m e te r, and f l u i d i z i n g
gas mass ■
THEORY AND PREVIOUS RELATED RESEARCH
The th e o r y and p re v io u s r e la te d .r e s e a r c h from extended h o r iz o n ta l
s u rfa c e s in dense phase f lu id iz e d : b e d s . is p resen ted in th re e p a r ts .
The f i r s t s e c tio n d e s c rib e s th e in t e r n a l b u b b le , f l u i d i z i n g medium, and
p a r t i c l e b e h a v io r in th e bed; th e .s e c o n d s e c tio n p re s e n ts proposed
mechanisms f o r h e a t t r a n s f e r from immersed s u rfa c e s ; th e t h i r d
s e c tio n
d e s c rib e s p re v io u s r e la te d ,r e s e a r c h .
- Bed Dynamics
As m entioned p r e v io u s ly , i t
is noted t h a t th e r i s i n g bubbles th ro u g h
th e bed induce th e p a r t i c l e m o tio n w it h in th e bed.
V a rio u s re s e a rc h e rs
( 2 , 6 , 7 , 8 ) have in v e s tig a te d bub ble b e h a v io r and th e a s s o c ia te d p a r t ic le
m o tio n in f lu i d iz e d beds and th e f o llo w in g is a summation o f t h e i r
f in d in g s .
.
.
,
As a f i r s t a p p ro x im a tio n a l l o f th e gas in excess o f t h a t needed
t o j u s t f l u i d i z e th e bed passes th ro u g h th e bed as bub ble s w h ile th e
e m u lsio n phase (dense phase bed e x c lu d in g b u b b le s) rem ains a t minimum
f l u i d i z i n g c o n d it io n s .
Sm all bubbles fo rm a t th e d i s t r i b u t o r p la t e ,
c o a le s c e , grow , and speed up as t h e y . r is e th ro u g h th e e m u lsio n phase.
The r i s i n g bubbles are n o t o n ly composed o f gas b u t a ls o c o n ta in fro m
0 .2 p e rc e n t to 1 .0 p e rc e n t s o lid s .
Bubbles are in g e n e ra l s p h e ric a l w ith th e base o f th e bub ble con-;
ca ve .
The reason f o r th e concave base is t h a t th e p re s s u re in th e lo w e r
p a r t o f th e bub ble is
le s s th a n in th e a d ja c e n t e m ulsion phase.
Gas
“ 8 th e r e fo r e flo w s in t o th e base o f th e b ub ble and o u t th e to p r e s u lt in g
in an i n s t a b i l i t y and p a r t i a l bub b le c o lla p s e a t . t h e base w ith t u r b u le n t
m ix in g b eh ind th e b u b b le .
T h is t u r b u le n t m ix in g r e s u lt s in s o lid s
b e in g drawn up beh ind th e b u b b le fo rm in g .a p a r t i c l e wake.
As th e bub ble
r is e s th e p a r t i c l e wake: is drawn upward a t th e b u b b le v e l o c it y and is
c o n t in u a lly exchanged w ith fre s h e m u lsio n s o lid as i t
r is e s .
The
p a r t i c l e exchange in th e b ub ble wake is th e p rim a ry mechanism f o r
p a r t i c l e m ix in g .
The bub ble r o o f s t a b i l i t y is m a in ta in e d by the upward flo w in g gas
in th e b u b b le .
Two t o th re e tim e s as much gas flo w s th ro u g h th e b ub ble
c r o s s - s e c tio n as th ro u g h an e q u iv a le n t s e c tio n o f e m ulsion phase in th e
same tim e i n t e r v a l .
The flo w p a tte r n o f t h i s gas is a c ir c u l a t i n g one.
Gas e n te rs th e bub ble base flo w s o u t th e bub b le r o o f and sweeps around
/
th e o u ts id e p e rip h e ry o f th e r i s i n g b u b b le back to th e base.
c ir c u l a t i n g gas form s a "c lo u d " around th e b u b b le .
The
The th ic k n e s s o f
th e c lo u d and th e amount o f gas r e c ir c u la t e d is a fu n c t io n o f th e bubble
v e l o c it y .
The r e s t o f th e p e r c o la tin g gas in th e bed does n o t m ix
w it h th e c ir c u l a t i n g gas b u t is pushed a s id e w ith th e s o lid e m ulsion as
th e bub b le passes b y .
I t is n o te d t h a t b u b b le s iz e r a t h e r th a n number
in c re a s e s w ith in c re a s e d gas v e l o c it y .
The induced p a r t i c l e m o tio n from th e r i s i n g bub ble s and gas is
as f o llo w s .
is a d e f i n i t e
In d iv id u a l p a r t ic le s wander everywhere in th e bed.
There
up and down movement, th e upward b e in g r a p id , th e downward
b e in g r e l a t i v e l y s lo w .
Thus s o lid s spend most o f t h e i r tim e , moving
downward s lo w ly b u t are o c c a s io n a lly swept upward in th e bed.
Two s tu d ie s fro m /th e -"! it e r a t u r e . d e a lin g w ith 'b u b b le and p a r t ic le
m o tio n around im m e rs e d .h o riz o n ta l tubes are p e r t in e n t .
K e a irn s (9 ) observed f l u i d i z a t i o n
b e h a v io r in a r e c ta n g u la r
f lu i d iz e d bed c o n ta in in g , h o r iz o n ta l bare tu b e s .
in d ic a te d t h a t u n ifo rm f l u i d i z a t i o n
V isu a l- o b s e rv a tio n s
and te m p e ra tu re d i s t r ib u t i o n s around
h o r iz o n ta l tubes are in h ib it e d b y 's ta g n a n t "ca p s" o f , p a r t ic le s on th e
to p o f th e tubes and by d e f lu id iz e d re g io n s between th e tubes and th e
w a lls and in th e c o rn e rs o f a r e c ta n g u la r bed.
In a subsequent paper
he re p o rte d h e a t t r a n s f e r c o e f f ic ie n t s on the to p o f a 2 in c h d ia m e te r
p a ra -d ic h lo ro b e n z e n e c y lin d e r to be 7-12 tim e s s m a lle r th a n c o e f f ic ie n t s
a t th e b o tto m .
Hager and Thomson (1 0 ) d id x - r a y and flo w v is u a liz a t io n s tu d ie s o f
bub b le b e h a v io r around immersed tubes in c lu d in g a h o r iz o n ta l h e lic a l
fin n e d tu b e .
They observed an a i r boundary la y e r below th e c e n tr a l
co re o f th e tu b e w ith no d e f lu id iz e d cap on to p o f th e tu b e .
e n t ir e re g io n w it h in th e f i n s appeared to be d e f lu id iz e d .
The
Most bubbles
were e it h e r d iv e r te d t o one s id e o r d isa p p e a re d w it h in th e f i n s and
•reemerged a t th e to p o f th e f i n .
c o m p le te ly to th e f i n
base.
B ubbles d id .not appear t o p e n e tra te
10 Mechanisms f o r Heat T ra n s fe r
B e d .to s u rfa c e h e a t t r a n s f e r c o e f f ic ie n t s
are many tim e s la r g e r
th a n c o rre s p o n d in g s u rfa c e t o gas o r s u rfa c e t o packed bed c o e f f ic ie n t s .
S e ve ra l models based on v a rio u s c o n t r o ll in g heat t r a n s f e r r e s is ta n c e s
have been p re se n te d t o e x p la in t h i s phenomenon.
R e fe r t o F ig u re I
" f o r a s ch e m a tic r e p re s e n tin g each model d is c u s s e d .
■ ;
-
L e v e n s p ie l and W alton (1 1 ) p re se n te d a . ' f i l m ' m odel.
model a t h in la m in a r f i l m
t r a n s f e r s u r fa c e .
o f f l u i d i z i n g gas is a d ja c e n t t o th e heat
The m a jo r . r e s is ta n c e t o h e a t flo w is
be th ro u g h t h is la m in a r f i l m .
p a r t ic le s a g a in s t th e f i l m
In th e f i l m
The s c o u rin g a c tio n o f th e f lu i d iz e d
decreases i t s
th e r e s is ta n c e t o h e a t f lo w .
c o n sid e re d to
th ic k n e s s , hence d e c re a s in g
Both th e p a r t i c l e v e lo c it y a d ja c e n t to
th e s u rfa c e and th e p a r t i c l e c o n c e n tr a tio n a t th e s u rfa c e a f f e c t th e
film
t h ic k n e s s .
These two f a c t o r s have o p p o s ite e f f e c t s on h ea t
t r a n s f e r ( w it h in c re a s in g p a r t i c l e v e lo c it y , , bed void a g e in c re a s e s and
s u rfa c e p a r t i c l e c o n c e n tr a tio n d e c re a s e s ), th e r e fo r e a maximum heat
t r a n s f e r c o e f f ic ie n t is o b ta in e d when i t
v e l o c it y .
is p lo tt e d a g a in s t gas mass
T h is agrees w ith e x p e rim e n ta l f in d in g s . ,
M ic k le y and F a irb a n ks (1 2 ) viewed th e mode o f h e a t t r a n s f e r as
unsteady h e a tin g o f 'packets' o f e m u lsio n phase, ( 'p a c k e t m o d e l') .
In
t h e i r model a p a cke t o f p a r t ic le s fro m th e co re o f th e em ulsion a t th e
b u lk bed te m p e ra tu re t ^ moves in t o c o n ta c t w ith a f l a t s u rfa c e o f
te m p e ra tu re t ^ .
Unsteady s t a t e c o n d u c tio n begins on c o n ta c t.
Heat
- 11 gro w in g gas f i l m
h e a t t r a n s f e r by
c o n d u c tio n th ro u g h
th e gas f i l m
descending
p a r t ic le s sc o u r
away th e f i l m
s u rfa c e
s u rfa c e @ t,
W
,c
^
!
I
Z
>
Fresh elem ent
t x sweeps away
e m u lsio n a t
th e to p s u r v .y
fa c e
Unsteady s t a te conduc­
t io n in t o em ulsion
elem ent a t s u rfa c e
Heated elem ent
I f - ” .0/ 1e °] le a ve s th e s u rfa c e
Vo.
FILM MODEL
PACKET MODEL
E m ulsion phase
y V
Z
P a r t ic le from
th e b u lk medium
P a r t ic le a t s u rfa c e
r e c e iv in g energy
from f i l m
in te rc h a n g e o f
s o l id s
Moving s o lid s w ith v e lo c it y u
Heated p a r t ic le
r e tu r n in g t o b u lk medium
PARTICLE MODEL
FIGURE I .
MODELS FOR HEAT TRANSFER
THIN-FILM AND EMULSION MODEL
- 12 t r a n s f e r r a te is la r g e s t a t i n i t i a l
l y w ith re s id e n c e .tim e .
c o n ta c tin g and decreases e x p o n e n tia l­
A f t e r a c e r t a in re s id e n c e tim e th e packet
le a ve s the s u rfa c e a n d .b re a ks up d is s ip a t in g i t s
■to th e co re o f th e bed.
excess th e rm a l energy
The p a cke t is re p la c e d by a fre s h p a cke t from
't h e bed core and th e process is re p e a te d .
-
M o d ific a tio n s to th e 'p a c k e t m o d e l1 i . e .
a 'p a r t i c l e m o d e l1 was
p re se n te d by Z ie g le r , K o p p e l, and B ra z e lto n (1 3 ) and l a t e r extended by
G e n e tti and Knudsen ( 1 4 ) .
In th e extended ' p a r t i c l e m odel' a p a r t ic le
fro m th e bed co re a t b u lk medium te m p e ra tu re t ^ comes in t o c o n ta c t w ith
th e s u rfa c e a t te m p e ra tu re t
.
s ta te c o n v e c tio n fro m th e t h in
^b = ^ b + t Wal
The p a r t i c l e re c e iv e s ene rg y by unsteady
la m in a r f i l m
o f gas (te m p e ra tu re
a d ja c e n t t o th e s u r fa c e .
Heat t r a n s f e r by
c o n d u c tio n a t th e p o in t o f c o n ta c t is c o n s id e re d n e g lig ib le .
A fte r
some re s id e n c e tim e th e p a r t ic le r e tu r n s t o th e b u lk o f th e bed where
it
d is s ip a te s i t s
excess e n e rg y.
T h is model is th e one used t o c o r r e la t e d a ta fro m t h i s s tu d y .
The
r e s u lt in g e x p r e s s io n .fo r th e N u s s e lt number fro m th e model and the
m o d ifie d e x p r e s s io n . r e la t in g my e x p e rim e n ta l v a r ia b le s as w e ll as f u r t h e r
e la b o r a tio n on th e model is p re se n te d in th e c o r r e la t io n s e c tio n o f t h is
p a p e r.
One im p o rta n t e xp e rim e n t perform ed by Z ie g le r and B ra z e lto n (15)
s u p p o rts th e
' p a r t ic le m o d e l' h e a t t r a n s f e r mechanism f o r t h e i r e x p e r­
im e n ta l c o n d it io n s .
S im u ltaneo us h e a t and mass t r a n s f e r r a te s were
)
- 13 measured from a 1 -1 /2 in c h . d ia m e te r, c e l i t e sphere s a tu ra te d w ith
w a te r.
T r a n s fe r r a te s were measured in b o th an a i r strea m and in a
f lu i d iz e d bed t h a t c o n ta in e d p a r t ic le s . w it h n e g lig ib le
. a b s o r p t iv it y
f o r w a te r.
C o nsequently th e o n ly mechanism o f im p o rta n ce f o r t r a n s f e r o f
mass is d if f u s io n th ro u g h th e f i l m .
W ith o u t f lu i d iz e d p a r t ic le s mass
and h e a t t r a n s f e r modes- are analogous i . e .
f ilm
d i f f u s io n .
- I f p a r t ic le s
c o n t r ib u te s i g n i f i c a n t l y in hea t t r a n s f e r then th e r a te o f h e a t t r a n s f e r
s h o u ld in c re a s e much more th a n th e mass t r a n s f e r r a te in th e f lu i d iz e d
bed s tu d y .
In c re a s e s in h e a t t r a n s f e r c o e f f ic ie n t s from . 10 to 20 tim e s
were o b se rve d , w hereas, in c re a s e s in mass tra n s fe r, r a te s were o n ly
1 -1 /2 to 2 tim e s th e p re v io u s a i r s tu d y .
They concluded t h a t 80 to
95- p e rc e n t o f th e h e a t is t r a n s fe r r e d b y .th e p a r t ic le mode.
Wicke and P e ttin g
t h in - f ilm
(1 6 ) proposed a model w h ich accou nts f o r b o th
and e m u lsio n r e s is t a n c e s .
Heat is f i r s t conducted from th e
s u rfa c e th ro u g h a la m in a r gas la y e r . o f th ic k n e s s , I - .
T h is h ea t is
absorbed by s o lid s flo w in g p a r a lle l to th e s u r fa c e .in a zone o f th ic k n e s s
I g.
Some o f t h i s
h e a t, q-j. goes i n t o s e n s ib le h ea t o f th e s o lid s , w h ile
th e r e s t , qr , is t r a n s fe r r e d t o . t h e bed core by in te rc h a n g e o f s o lid s .
K u n ii and L e v e n s p ie l. ( 2 ) examined th e p re v io u s m entioned models
f o r h e a t t r a n s f e r and d e cid e d th e models were r e a l l y n o t in c o n f l i c t
b u t r a th e r t h a t each one d e s c rib e d a . d i f f e r e n t . c o n t r o llin g r e s is ta n c e
to heat tr a n s fe r .
They th e r e fo r e p o s tu la te d a g e n e ra l
th e o ry t h a t
- 14 -
. t
a llo w s a l l f o u r mechanisms to be c o n s id e re d .
a t h in f i l m
In t h e i r g e n e ra l model
o f gas o f th ic k n e s s Ig c o a ts th e s u r fa c e , some s o lid s are
in d i r e c t c o n ta c t w ith th e s u r fa c e , and th e em ulsion o f . e q u iv a le n t
th ic k n e s s I
flo w s p a s t th e s u rfa c e and is re p la c e d o c c a s io n a lly by
fr e s h e m u ls io n .
1.
The f o u r mechanisms re p re s e n te d are. th e f o llo w in g :
■ Heat t r a n s f e r th ro u g h a t h in gets f i l m
o f th e o rd e r o f dp
o r le s s .
2.
'
Heat t r a n s f e r by c o n v e c tio n from th e la m in a r f i l m
in c o n ta c t w ith th e s u rfa c e w ith fre q u e n t
3.
by p a r t ic le s
p a r t ic le
re p la c e m e n t.
•
U n s te a d y -s ta te a b s o rp tio n o f hea t by fre s h e m u lsio n w hich is
swept away from th e s u r fa c e .
T h is re p re s e n ts a s u rfa c e
renew al model f o r th e e m u ls io n .
4.
S te a d y -s ta te c o n d u c tio n th ro u g h th e em ulsion la y e r t h a t is
seldom swept away.
They developed c r i t e r i a
to su g g e st w hich mechanism c o n tr o ls and which
ty p e o f model sh o u ld be used to .r e p r e s e n t a p a r t ic u l a r s it u a t io n .
w i l l n o t.b e d is c u s s e d h e re .
f o r f u r t h e r d e t a i ls .
The re a d e r is
T h is
r e fe r r e d to t h e i r book (2 )
- 15 -
%
0 o£s
H eat t r a n s f e r
s u rfa c e
Z
O
N ext packe t o f e m ulsion
to c o n ta c t th e s u rfa c e
0
JI
D ir e c t c o n ta c t o f
p a r t ic le w ith s u r fa c
I
I
T hickness o f gas
f ilm , I g
i
E q u iv a le n t th ic k n e s s o f em ulsion
la y e r , I 0
FIGURE 1A.
GENERAL MODEL FOR BED-SURFACE HEAT TRANSFER
P re vio u s R e la te d Research
Heat t r a n s f e r from th e w a lls o f th e column to th e bed and from th e
bed p a r t ic le s
th e p a s t.
to th e f l u i d i z i n g medium have re c e iv e d much a t t e n t io n
in
Zabrodsky (1 7 ) in c h a p te rs 8 and 10 o f h is book on f l u i d i z a t i o n
su rve ys and summarizes t h is w o rk .
■- p e r t in e n t t o t h i s
S ince these s u b je c ts are n o t d i r e c t l y
in v e s t ig a t io n , th e y w i l l
n o t be d is c u s s e d f u r t h e r .
Many more re c e n t s tu d ie s have d e a lt w ith h ea t t r a n s f e r from immersed
s u rfa c e s .
These s tu d ie s w i l l be summarized h e re .
Vreedenberg (18) perform ed some o f th e i n i t i a l e x p e rim e n ts w ith
immersed tu b e s .
He measured h e a t t r a n s f e r c o e f f ic ie n t s o f h o r iz o n ta l
w a te r-c o o le d bare tu b e s .
V a ria b le s in h is s tu d y were bed te m p e ra tu re .
- 16 mass v e lo c it y o f th e f l u i d i z i n g a i r , p a r t i c l e d ia m e te r, p a r t i c l e shape
p a r t i c l e d e n s it y , and tu b e d ia m e te r.
He c o r r e la te d th e N u s s e lt number
in term s o f th e Reynolds num ber, v o id f r a c t io n , , and f l u i d
p r o p e r t ie s .
and s o lid
D e v ia t io n s .o f e x p e rim e n ta l. va lu e s from h is c o r r e la t io n
were a b o u t 43 p e rc e n t. . V reedenberg, l i k e most f u tu r e in v e s t ig a t o r s ,
observed a maximum in h e a t t r a n s f e r . c o e f f i c i e n t w ith in c re a s in g gas
mass v e lo c it y .
■G e n e tti e t . al (1 9 ) s tu d ie d th e e f f e c t o f bare and s e rra te d f i n
tu b e o r ie n t a t io n
in an a i r f lu i d iz e d b e d ..
V a ria b le s s tu d ie d in c lu d e d
p a r t i c l e s iz e , f l u i d i z i n g mass v e l o c it y and. o r ie n t a t io n a n g le .
s e rra te d carbon s te e l fin n e d tu b e w ith f i n
h e ig h t o f 0 .7 5 i n . ,
th ic k n e s s o f 0 .025 in . and tu b e O.D. o f 0.625 in ..w a s used.
A
f in
A
minimum h e a t t r a n s f e r c o e f f ic ie n t was observed a t o r ie n t a t io n angles o f
45 and 60 degrees (measured fro m th e h o r iz o n t a l) f o r th e bare and fin n e d
t u b e s , r e s p e c t iv e l y .
Maximum va lu e s o f th e c o e f f ic ie n t f o r th e fin n e d
tu b e o c c u rre d a t 30 d e g re e s; th e h o r iz o n t a l. o r ie n t a t io n produced a
c o e f f ic ie n t n ea r th e maximum v a lu e , w hereas, th e v e r t i c a l o r ie n t a t io n
produced a c o e f f ic ie n t o f a b o u t 18 p e rc e n t lo w e r th a n th e h o r iz o n ta l
p o s it io n .
■ P e trie , F reeby, and Buckham (2 0 ) s tu d ie d h o r iz o n ta l bundles o f 19
tu b e s arra nged on 2 .25 in .
a r ra y s .
11 f i n
c e n t e r - t o - c e n t e r t r ia n g u la r and square p itc h
Three tu b e bun dle s were used, p la in tu b e s , 5 f i n
p e r in c h tu b e s .
p e r in c h and
F in s were tra n s v e rs e 0 .4 in c h lo n g h e lic a l
I
)
)
.
-
)
'
A l l tubes were alum inum .
- 17 -
)
f in s .
They found t h a t tubes a c te d in d e p e n d e n t-
;
I y fro m one a n o th e r f o r tu b e . sp a cin g s g re a te r .th a n , 43 p a r t i c l e d ia m e te rs .
The c r i t i c a l d is ta n c e f o r tube independence was n o t d e te rm in e d .
Bare
tu b e d a ta was c o r r e la te d in t o . a s in g le e q u a tio n r e la t in g th e c o e f f ic ie n t
t o th e e x p e rim e n ta l v a r ia b le s . .
E x p e rim e n ta l r e s u lt s fro m t h e i r
• in v e s t ig a t io n a re compared w it h my c o r r e la t io n va lu e s in th e r e s u lt s and
d is c u s s io n s e c tio n o f t h i s t h e s is .
-
A s tu d y by Z ie g le r , K o p p e l, and B ra z e !to n (13) lo o ke d a t th e e f f e c t
o f p a r t i c l e h e a t c a p a c ity and th e rm a l c o n d u c t iv it y on the- h e a t t r a n s f e r
c o e ffic ie n t.
Copper, s o ld e r , and n ic k e l p a r t ic le s were used.
R e s u lts
in d ic a te d t h a t th e s o lid th e rm a l c o n d u c t iv it y had a n e g lig ib le e f f e c t
on th e s u r fa c e -to - b e d h e a t t r a n s f e r c o e f f i c i e n t .
The c o e f f ic ie n t
" d i d in c re a s e w ith , in c re a s in g s o lid h e a t c a p a c ity b u t in a le s s than
lin e a r fa s h io n .
,.
p a r t ic le
U sing t h e i r " p a r t ic le m o d e l1 th e o ry ,fo r r e la t in g th e
N u s s e lt number to, th e v a r ia b le s s tu d ie d , p a r t i c l e re s id e n c e
tim e s a t th e h e a t t r a n s f e r s u rfa c e were b a c k - c a lc u la te d fro m heat
tr a n s fe r , c o e f f i c i e n t s .
T h e s e .c o n ta c t tim e s were in agreem ent w ith
p re v io u s o b s e rv a tio n s and w ith r e s u lts , o f s im p le t h e o r e t ic a l m odels.
Ozkaynak and Chen (2 1 ) measured d i r e c t l y th e re s id e n c e tim e o f
e m u lsio n phase on th e s u rfa c e o f an immersed tu b e in a f lu i d iz e d bed.
A s p e c ia lly designed f a s t response c a p a c ita n c e probe was used.
The
v a l i d i t y o f th e "p a cke t m o d e l1 f o r h e a t t r a n s f e r was in v e s tig a te d .
S a t is f a c t o r y agreement f o r b o th th e s m a ll and la rg e p a r t ic le s
used
- 18 w a s .o b ta in e d when th e
'p a c k e t m o d e l1 was m o d ifie d to a cco u n t f o r
th e change o f v o id f r a c t io n near th e s u rfa c e o f p a c k e ts . .. Gamma and
lo g -n o rm a l, p a cke t s u rfa c e re s id e n c e tim e d i s t r ib u t i o n s were found to
g iv e good r e p r e s e n ta tio n o f th e d a ta .
•' ■ G e n e ra lly th e h e a t t r a n s f e r . c o e f f i c i e n t in c re a s e s w ith d e cre a sin g
p a r t i c l e s iz e s .
Baerns (2 2 ) observed t h a t as th e p a r t i c l e
s iz e was
reduced th e h e a t t r a n s f e r c o e f f ic ie n t in c re a s e d , passed th ro u g h a max­
imum and then decreased.
The d e c re a s in g h ea t t r a n s f e r ra te s corresponded
w ith th e re g io n where th e i n t e r p a r t i c l e a d h e sive fo rc e s
fo rc e s ) a ffe c te d th e q u a li t y o f f l u i d i z a t i o n .
(van d e r Waals
T h e s e .fo rc e s came in t o
p la y when th e p a r t i c l e s iz e is s m a lle r th a n abo ut 50 y (.0 0 2 i n . )
cause a g g lo m e ra tio n and c h a n n e lin g .
were much la r g e r th a n t h i s .
P a r t ic le s
and.
used in t h i s s tu d y
.
B a rte l and G e n e tti (23) measured th e r a t e . o f h e a t t r a n s f e r fro m a
h o r iz o n t a l bundle o f carbon s te e l bare tubes and fin n e d tubes to a bed
o f g la s s spheres f lu i d iz e d w ith a i r .
f in
The e x p e rim e n ta l v a r ia b le s were
h e ig h t, d is ta n c e between, tu b e s , p a r t i c l e d ia m e te r, and f l u i d i z i n g
a i r v e l o c it y .
g a t io n .
The same f l u i d i z i n g column was used a s . in t h i s
A c o r r e la t io n based on th e
in v e s t i ­
‘ p a r t i c l e m o d e l1 was developed
r e la t in g th e p a r t i c l e M u s s e lt number to th e e x p e rim e n ta l v a r ia b le s . ■
The f i n a l c o r r e la t io n was in d e p e n d e n t o f f i n
m a te r ia l.
E xp e rim e n ta l
d a ta agreed w ith th e c o r r e la t io n t o w i t h in + o r - 15 p e rc e n t.
found t h a t th e r a te o f h e a t t r a n s f e r in c re a s e d w ith f i n
They
h e ig h t , b u t th e
)
;
- 19 -
)
r a te le v e le d o f f ne a r a f i n
;
h e ig h t o f abo ut one in c h .
For a bundle
'
o f s h o r t fin n e d tu b e s ( 1 /8 in c h f i n s )
th e r a te o f h e a t t r a n s f e r is
s e n s it iv e t o tube sp a cin g s u n t i l th e re is about 2 in ch e s between tu b e
c e n te rs .
The r a te o f h e a t t r a n s f e r f o r th e 7 /8 in c h f i n
tu b e s was
■ in depe nden t o f tube s p a c in g f o r . . a ll c e n t e r - t o - c e n t e r d is ta n c e s .
P rie b e and G e n e tti (2 4 ) s tu d ie d h e a t t r a n s f e r
c o e f f ic ie n t s o f
h o r iz o n ta l d is c o n tin u o u s fin n e d and sp in e d tubes in an a i r f lu id iz e d
bed.
Heat f l u x , f i n
s p a c in g , p a r t i c l e d ia m e te r, and gas mass v e lo c it y
were th e v a r ia b le s f o r th e d is c o n tin u o u s fin n e d tu b e s .
S pine h e ig h t,
sp in e s per t u r n , s p in e m a t e r ia l, and gas mass v e lo c it y were th e
v a r ia b le s f o r th e s p in e d tu b e s .
The same f l u i d i z i n g
/
column was used
as in t h is s tu d y .
■R esults in d ic a te d t h a t th e c o e f f ic ie n t began to f a l l
f in
spa cin g s le s s th a n 10 p a r t ic le 'd ia m e t e r s .
C o e f f ic ie n t s o b ta in e d
f o r copp er s p in e s were g r e a te r th a n f o r s ta in le s s s te e l
. c o n d u c t iv it y th a n c o p p e r).
There was l i t t l e
w ith la r g e r number o f sp in e s
h ig h e r hea t t r a n s f e r r a te s .
r a p id ly f o r
(lo w e r therm al
d iff e r e n c e in c o e f f ic ie n t s
per. t u r n , b u t th e in c re a s e d area y ie ld e d
..
-
Each tube ty p e le d to a c o r r e la t io n r e la t in g th e p a r t i c l e N u s s e lt
number to th e v a r ia b le s s t u d ie d . .. D e v ia tio n fro m th e c o r r e la t io n s was
le s s th a n ± 12.5 p e rc e n t.
By m o d e lin g th e h e a t c o n d u c tio n w it h in th e
s p in e s th e e f f e c t o f s p in e th e rm a l c o n d u c t iv it y on th e c o e f f ic ie n t was
e l im in a te d .
EXPERIMENTAL EQUIPMENT
The equipm ent used in t h i s re se a rch was a lre a d y a v a ila b le h a v in g
been tw ic e p r e v io u s ly used f o r s im il a r h e a t t r a n s f e r in v e s tig a t io n s
o f o th e r geom etry fin n e d tu b e s .
equipm ent w i l l be g iv e n h e re .
Ph.D. th e s is
O nly a b r i e f d e s c r ip tio n o f th e
The re a d e r is r e fe r r e d to B a r t e l's
(4 ) f o r a more d e t a ile d d e s c r ip t io n .
The d is c u s s io n o f th e equipm ent w i l l be d iv id e d in t o th re e
s e c tio n s :
I)
th e colum n, 2) th e f l u i d i z i n g system and 3) th e
e l e c t r i c a l system .
An o v e r a ll sch e m a tic o f the equipm ent -is shown in
F ig u re 2.
,
CoUiim
F ig u re 3 shows a d e t a ile d view o f th e f l u i d i z i n g
colum n.
The
f l u i d i z i n g column is r e c ta n g u la r in shape 94 in ches h ig h , 1 5 -1 /2 in ch e s
w i d e , -8 in ch e s, deep ( o u ts id e d im e n s io n s ).
3 /4 in ch p le x ig la s .
in s ta lla tio n
I t is f a b r ic a t e d o f c le a r
A r e c ta n g u la r column.was chosen to p e rm it easy
and rem oval o f u n ifo rm le n g th e d fin n e d tu b e s .
C le a r
p le x ig la s was used to a llo w o b s e rv a tio n o f th e degree o f f l u i d i z a t i o n
w it h in th e b e d .
The d i s t r i b u t o r p la te c o n s is te d o f two la y e rs o f 140-mesh brass
w ir e c lo t h sandwiched between two 1 / 3 2 - i n . t h ic k s te e l p e rfo ra te d
p la te s ( p e r fo r a t io n s were 1/32 i n . d ia m e te r and 1 /5 i n . c e n t e r - t o c e n te r).
A p a r t i c l e d r a in p ip e , I in . O .D ., was s i l v e r s o ld e re d f lu s h
n ea r one c o rn e r o f th e d i s t r i b u t o r p la t e .
The d r a in p ip e extended
(not drawn to scale)
0
PLEXIG LASS C O L U M N ,0
MICARTA P L A T E ,® AIR BLOWER. @ MAIN AIR LINE VALVE,
®
BYPASS VALVE, ®
®
TUBE AND BED THERMOCOUPLES, ®
ORIFICE, ®
ORIFICE MANOMETER. ®
PRESSURE DROP ACROSS TUBES.
CHART RECORDER, ®
HIGH TEMPERATURE LIMIT
TH E R M O C O U P LE ,® HEATER LEAD W I R E S , ® HIGH TEMPERATURE LIMIT
@
WATTMETER, ( ®
RHEOSTAT, ( ®
FIGURE 2 .
VARIAC, ( ®
OVERALL
POWER SOURCE
VIEW OF
EQUIPMENT
PROTECTOR,
- 22 -
EXIT AIR PORTS
BED THERMOCOUPLES
FINNED
TUBES
MICARTA
PLATE
y/777-/
PRESSURE
TAPS
HEATERS
DISTRIBUTOR PLATE
FLOW STRAIGHTENERS
OOOOOC
OOO
DRAIN
MAIN AIR LINE
FIGURE 3.
DETAILS OF FLUIDIZING COLUMN
)
th ro u g h th e b o ttom o f th e colum n.
A q u ic k opening v a lv e was in s t a l le d
in th e p ip e j u s t below th e colum n.
The d i s t r i b u t o r p la te p ro v id e d
adequate s u p p o rt as w e ll as u n ifo rm f l u i d i z a t i o n
bed.
o f th e g la s s sphere
The d r a in p ip e p e rm itte d easy removal o f th e bed m a te ria l from
th e colum n.
The column extended 18 in . beneath th e d i s t r i b u t o r p la t e .
Nine
3 /4 in . O.D. tubes were in s t a l le d in two rows in t h is s e c tio n o f th e
column to p ro v id e a sm oothing s e c tio n f o r th e f l u i d i z i n g
a ir .
The column extended 74 in . above th e d i s t r i b u t o r p la t e .
a llo w e d ample room f o r th e bed to expand and f l u i d i z e
T his
fr e e ly .
T h is
p a r t o f th e column d id impose l i m i t a t i o n s on th e a i r flo w ra te s
p e r m is s ib le .
A t h ig h e r a i r flo w r a te s th e bed expanded so t h a t pluggage
o f th e e x i t screens o c c u rre d .
Two mi c a r ta p la te s
(la m in a te d canvas) 3 /4 in .
to s u p p o rt th e h e a te r a ssem blies w it h in th e bed.
seven I in .
were d r i l l e d
t h ic k were employed
In one p la te
h o le s in a hexagonal a r ra y (5 in . c e n t e r - t o - c e n t e r sp a c in g )
c o m p le te ly th ro u g h and f i t t e d w ith sw agelock f i t t i n g s
h o ld one end o f th e h e a te rs s e c u re ly in p la c e .
to
In th e o th e r p la te
h o le s 2 /5 i n . deep were d r i l l e d , to s u p p o rt th e o th e r end o f th e h e a te rs .
The m ic a rta p la te s were h e ld in p la c e w ith " t r u n k - l i d " ty p e clam ps.
The column to p was a rem ovable 3 /4 i n . p le x ig la s l i d
r e c ta n g u la r h o le in i t s
c e n te r .
200 mesh s t a in le s s s te e l c lo t h .
w ith a la rg e
The r e c ta n g u la r h o le was covered w ith
A 3 i n . d ia m e te r h o le was c u t near
)
I
)
■
■
■
-
i
'
.
.
!
-2 4
-
)
th e to p on each s id e o f th e column and covered w ith w ire mesh.
)
w as-rem ovable t o a llo w f i l l i n g
:
a llo w d i r e c t o b s e rv a tio n o f th e a lig n m e n ts o f th e tu b e b u n d le .
I
mesh c lo t h p re ve n te d th e bed. m a te r ia l fro m le a v in g th e column w ith th e
f lu id iz in g
The l i d
th e column w ith th e g la s s beads and to
a ir .
The
...
To a id in rem oving th e bed m a te r ia l between runs two p lu g f i t t e d
3 i n . d ia m e te r vacuum p o rts were c u t on o p p o s ite s id e s o f . t h e column
( s h o r t s id e s ) j u s t above th e d i s t r i b u t o r p la te .
.
The column was s u p p o rte d .b y f o u r a n g le iro n s b o lte d to th e f l o o r
w ith wooden b lo c k s wedged between th e column and th e s u p p o r ts .
F lu id iz in g System
A i r was used as th e f l u i d i z i n g medium.
A i r was s u p p lie d by a
p o s it iv e d is p la c e m e n t S u t o r b i lt b lo w e r powered by a 7 t 1 /2 H .P. BrownBrockm eyer e l e c t r i c a l m o to r.
2 - 1 /2 " O.D. sched ule 40 s te e l p ip e was
used bo th f o r an a i r s u p p ly l i n e t o th e column and f o r a column b y­
pass l i n e .
Two ga te v a lv e s were used in th e s u p p ly system , one in th e s u p p ly
l i n e and one in th e by-pass l i n e .
c o n t r o lle d by t h r o t t l i n g
open f o r a l l r u n s .
o r ific e
"
A i r flo w r a te to t h e bed was
th e by-pass v a lv e ; th e s u p p ly v a lv e was l e f t
A i r flo w r a te t o th e bed was measured w ith an
in th e s u p p ly l i n e .
T h e , o r if ic e had a 1 -1 /2 in . d ia m e te r
opening and vena c o n tr a c ta p re s s u re ta p s .
W ater manometers were used
- 25 t o measure th e p re s s u re d ro p a cross th e o r i f i c e .
Back p re s s u re fro m th e column was measured w ith a Duragauge p re s s u re
gauge lo c a te d d o w n s tre a m .o f th e o r i f i c e .
.
Three s iz e s o f B la s t - O - L it e g la s s beads were used as th e bed
m a t e r ia l.
The a v e ra g e ,s p h e re d ia m e te rs were 0.0068 i n . ,
0.0217 in .
0.0103 i n . , and
The s p e c if ic g r a v i t y . o f th e beads was 2 .5 -(1 5 6 # / f t ^ ) .
V ie w in g th e beads under a m icroscope showed t h a t th e y had a sphere co u n t
o f abo ut 80+ p e rc e n t.'
Bead d ia m e te rs were dete rm in e d by m easuring
bead d ia m e te rs o f a random sample o f beads.and d e te rm in in g th e average
v a lu e s .
m e n ts.
A m icroscope w it h a s c a le d o c u la r was used f o r th e se measure.- .
A s ta g n a n t bed h e ig h t o f 23 i n . was used in each ru n ;
Table I
..re p re s e n ts a summary o f th e bead s iz e a n a ly s is .
TABLE I .
( in )
D iam eter
BLAST-O-LITE BEAD SIZE ANALYSIS
( in )
S tandard
D e v ia tio n
Sample
S iz e
Sphere
Count (%)
0.0217
0.0032
300.
80
0.0103
0.00104
300
84
0.0068
0.00105
350
To d e te rm in e th e p a r t i c l e f r a c t io n
'
88
Nominal
Name
Large
.
Medium
Sm all
in th e bed p re s s u re ta p s f o r a
w a te r manometer, were p la ce d on both s id e s o f th e tu b e b u n d le .
The s lu g g in g a c tio n o f . t h e f lu i d iz e d bed made re a d in g th e w a te r
- 26 • manometers d i f f i c u l t .
A t h ig h gas mass v e l o c i t i e s . f lu c t u a t io n s o f
up t o ±30 p e rc e n t in re a d in g s were n o te d f o r th e o r i f i c e manometer and
±50% in re a d in g s were n oted f o r th e bed manometer.
Average va lu e s o f a
number o f h ig h and low re a d in g s were used as th e r e p r e s e n ta tio n o f th e
't r u e '
p re s s u re d ro p s .
R e p r o d u c ib ilit y , o f th e a i r flo w r a te s was
■s u r p is in g ly easy to a t t a in .
E le c t r ic a l System
The e l e c t r i c a l system c o n s is ts o f a power s u p p ly , c a r tr id g e
h e a te rs f o r th e fin n e d tu b e s , and a therm ocouple system .
Power was s u p p lie d to th e h e a te rs from a 240 V o u t l e t , th ro u g h a
p o w e rs ta t, a r h e o s ta t, a bed te m p e ra tu re l i m i t p r o t e c t o r , a w a ttm e te r,
th ro u g h fu se s to th e seven c a r t r id g e h e a te rs w ire d in p a r a l l e l .
The p o w e rs ta t was p ro v id e d to compensate f o r normal b u ild in g power
f lu c t u a t io n s and to m axim ize th e te m p e ra tu re d iff e r e n c e between th e
fin n e d tu b e and th e bed.
The bed ,te m p e ra tu re l i m i t p r o t e c to r was a
s a f e t y c i r c u i t to p re v e n t th e bed from o v e r h e a tin g . ' The se n sin g d e v ic e
f o r t h i s c i r c u i t was a bare the rm o co u p le in s e r te d in th e bed.
The
w a ttm e te r was used to d e te rm in e th e power in p u t to each c a r tr id g e
h e a te r.
Watlow
fir e
\
rod. c a r t r id g e h e a te rs o f a p p ro p ria te d ia m e te rs were
used as th e h e a t source f o r th e fin n e d tu b e s .
each c a r t r id g e h e a te r was 9 ^ 2 /5 in .
As shown in F ig u re 4
lo n g com prised o f a 6 -1 /2 in c h
In s u la te d
S e c tio n
Heated S e c tio n
if
_________________
FIGURE 4.
In s u la te d S e c tio n
_______
DETAILS OF A CARTRIDGE HEATER
1 /8 " L o n g itu d ­
in a l Hole
-/
7
- 28 heated s e c tio n w ith c o ld , in s u la te d ends.
in t o th e p a r t i a l l y d r i l l e d
e le c tr ic a l
The 2 /5 in . c o ld end f i t
mi c a r ta p la te th e lo n g e r c o ld end w ith
leads extended o u t o f th e bed and was h e ld by th e p r e v io u s ly
m entioned swagelock f i t t i n g s .
h o le was d r i l l e d
A 1 /8 i n .
d ia m e te r, 3 in .
lo n g it u d in a l
from th e le a d end in t o th e c a r tr id g e t o a llo w passage
o f th e tu b e th e rm oco uple o u t o f th e bed.
T h is d esign m in im iz e d end h e a t lo s s e s from th e h e a te r .
A 6 -1 /2 in .
fin n e d tu b e was c e n te re d o v e r th e heated s e c tio n o f each c a r t r id g e .
T h e re fo re most o f th e e ne rg y s u p p lie d to th e h e a te r le a ve s by way o f
th e fin n e d tu b e .
In f a c t ,
in t h is s tu d y a l l o f th e h ea t s u p p lie d to
th e h e a te r is assumed to le a v e by way o f th e fin n e d tu b e .
T h is is n o t
a bad assum ption s in c e a t s te a d y s t a t e c o n d itio n s th e te m p e ra tu re o f a
fin n e d tu b e s u rfa c e ranged as h ig h as 280°F whereas th e p r o tr u d in g end
o f th e h e a te r, was o n ly warm t o th e to u c h .
To prom ote good c o n ta c tin g
between th e h e a te r and th e tu b e , th e a n n u la r space was f i l l e d
la y e rs o f copper a n t i- s ie z e compound and aluminum f o i l .
in w ith
The a n n u la r
space was in g e n e ra l le s s than 1/16 in . w id e .
S i x : o f th e tubes s tu d ie d were p ro v id e d by th e Rome-Turney
R a d ia to r Company, Rome, New Y o rk.
h e lic a l copper f i n s .
w a ll .
Rome Turney f i n s were a llo y
bonded t o th e tube
Three o th e r tubes s tu d ie d were s u p p lie d by th e W o lv e rin e T r u f in
Company.
f in s .
A l l tubes s tu d ie d had c o n tin u o u s ,
These tubes had in t e g r a l f in s w ith t h ic k e r tu b e w a lls and
A l I f in s were s l i g h t l y ta p e re d .
Fin. s p a c in g s , f i n s
p e r in c h
- 29 and f i n
lis ts
h e ig h ts were th e g e o m e tric param eters in v e s tig a t e d .
Table
II
th e p h y s ic a l dim ensions o f th e n in e tubes used.
TABLE I I .
Tube F in
No. O.D ( i n )
Tube
O .D .( in )
TUBE DIMENSIONS
A v e .F in
F in
W idth
H e ig h t( in )
( in )
Fins
Per
Inch
F in
Spacing
( in )
A vg.
T o ta l
Tube
A re a (ft/)
I
1.453
0.625
0 .414
.016
9
0.0951
1.1449
2
1.375
0.625
0 .375
.024
9
0.0871
1.0608
3
1.328
0.625
0.352
.016
9
0.0951
0.9314
4
1.094
0.625
0.234
.016
5
0.1840
0.3540
5
1.094
0.625
0 .234
.016
9
0.0951
0.6004
6
1.094
0.625
0 .234
.016
14
0.0554
0.8893
7
1.094
0.625
0.234
.016
18
0.0396
1.0463
8
1.000
0.453
0 .274
.025
5
0.1750
0.3541
9
1.500
0.750
0.375
.020
7
0.1229
0.9372
Tubes 2 , 8 and 9 were p ro v id e d by W o lv e rin e Tube D iv.
A ll
o th e r tubes
were p ro v id e d by Rome-Turney R a d ia to r Company
As shown in F ig u re 5 each fin n e d s e c tio n used was 6 - 1 /2 in lo n g .
Each s e c tio n had a 1 /8 i n . d ia m e te r h o le d r i l l e d
f in s
fro m one end to th e tu b e c e n te r .
a t th e base o f th e
A s in g le ir o n c o n s ta n ta n therm o­
co u p le was w ire d and s o ld e re d in t o a f i l e d
groove in th e tu b e w a ll a t
J,
D iam eter
1}]T
F in
H e ig h t
T
W
O
8 f in s p e r in ch
F in
T hickness
SIDE VIEW
FIGURE 5.
TUBE DETAILS AND NOMENCLATURE
31
-
-
the tube cen ter and threaded through the base o f th e .fin s out o f the
.
'
J
*
bed through the d r ille d c a rtrid g e heater.
............................... .................
.
-
The o th e r end o f the finn ed
tube had a 3/8 in . sectio n o f fin s removed w ith 'a set screw attached
to hold the tube in place on the he ate r. '
.
-
Ten iro n constantan thermocouples were used. . Seven thermocouples,
one fo r each tube o f the tube bundle, were used to measure the tube
w a ll tem peratures.
Three thermocouples placed above, below and w ith in
the tube bundle were used to measure the bed tem perature.
The in bed thermocouples were threaded in to .1/8 in diameter copper
tubing w ith w ire mesh over the tube end to p ro te c t the thermocouple
from the bed a c tio n .
Consequently th e bed f l u i d temperature was
measured ra th e r than the p a r tic le tem perature.
An unprotected thermo­
couple in d ic a te d th a t the p a r t ic le - f lu id temperature was less than 3°F
hig her than the protected thermocouples.
Al I thermocouples were connected through a sw itching, box to a
- Honeywel I -Brown c h a rt recorder... A c h a rt recorder was used so th a t an
average tube w a ll temperature could be obtained.
' showed some tendency f o r c y c lin g .
This is expected as p a rtic le s and
f l u i d a r riv e and leave the tube su rface.
as ± 3°F.
A ll tube temperatures
Some flu c tu a tio n s were as high
S a tis fa c to ry average values were obtainable in most cases
to w ith in ±1.5°F.
-
The physical s o ld e rin g o f the thermocouples to the tube w a lls
was c r i t i c a l to th is stud y.
Small e rro rs in temperature measurement
- 32 r e s u lt in. la rg e e rro rs .in the e x p e rim e n ta lIy determined heat tr a n s fe r
c o e f f ic ie n t .
In an e f f o r t to m inim ize th is e r r o r seven tubes o f the
same kind are used in each tube bundle.
The average o f a l l seven tube
re s u lts is used as re p re s e n ta tiv e o f the tube ty p e .
hoped
In
th is way i t was
th a t e rro rs in reading the charts and e rro rs caused by v a ria tio n s
in thermocouple to w a ll c o n tac tin g would tend to average o u t.
Indeed
d e v ia tio n s o f ± 20 percent in in d iv id u a l tube h e a t/tr a n s fe r c o e ffic ie n ts
were observed.
EXPERIMENTAL PROCEDURE
Bead S ize
I
I n i t i a l l y 0 .0 5 inch average diam eter p a r tic le s were used as one
kind o f bed m a t e r ia l.
These 0 .0 5 inch p a r t ic le s were approaching the
s iz e o f th e f i n spacings on the 9 o r more f i n per inch ( F . P . I . ) tubes.
Problems re s u lte d in p a r t ic le s • lodging between th e f in s , preventing
fr e e p a r t ic le movement in and out o f th e f i n spaces, thus s h ie ld in g
much o f th e tube surface from p a r t ic le mode heat t r a n s f e r .
and u n p re d ic tab le heat tr a n s f e r c o e ffic ie n ts re s u lte d .
E r r a t ic
The tubes
a c tu a lly proved to be a good p a r t ic le .s ie v e since in a bed o f very
d ilu t e co n cen tratio n o f th e la r g e r 0 .0 5 inch beads the tubes would
s e le c t iv e ly tra p these la r g e r beads.
'
Bead s iz e is an im p ortan t param eter to be considered f o r any
a p p lic a tio n o f finn ed tu b es.
Fin spacing should be o f the o rd er o f 2
or more tim es the la r g e s t p a r t ic le diam eter o f the bed to prevent
loss o f heat tr a n s fe r su rface from p a r tic le s lodging between the fin s
p reve n tin g p e n e tra tio n o f th e p a r tic le s to the depths o f the f i n spaces.
Minimum F lu id iz a tio n V e lo c itie s
Minimum f lu i d i z a t i o n v e lo c itie s
were determ ined.
( M .F .V .'s ) o f the 3 p a r t ic le sizes
The f i r s t tube bundle was assembled in the column.
The column was f i l l e d to a f l u f f e d 23 i n . h e ig h t o f s ize d beads.
The
a i r and heaters were turned on and the column was allow ed to heat up
f o r several hours.
This was to d riv e o f f any m oisture from the bed
I
I
■
I -
'
.
'
- 34 )
■
th a t would cause the beads to s t ic k to g e th e r.
)
The M .F.V . was determ ined by t h r o t t l i n g the a i r flo w r a te u n t il
in itia l
f lu i d i z a t i o n or d e f lu id iz a t io n o f th e bed was v is u a lly v e r i f i e d .
A micro water-manometer was used.to in c re a s e .p re c is io n in measuring
these M .F .V .’ s.
bundles.
This procedure was repeated w ith d if f e r e n t tube
Average values o f . a l l
readings were used as the M .F .V . v a lu e .
-D eviatio n s o f less than 10 percent were observed fo r a l l
cases.
■‘
M .F .V .1s
I
f o r the th re e bead sizes are shown in Figure 6 .
Tube Thermocouple Location
B a rte l
(4 ) in v e s tig a te d tube su rface tem perature v a r ia tio n w ith
s e r r a t e d - f in carbon s te e l .tu b es.
A t a tube tem perature o f 200°F, he
found the g re a te s t tem perature d iffe re n c e between any 2 po in ts on a .
tube was only about 2 °F .
-•
He concluded th a t th e re was. e s s e n tia lly no
tem perature g ra d ie n t on the tube su rface in e ith e r the lo n g itu d in a l
o r angular d ir e c tio n .
In t h is in v e s tig a tio n ang ular tem perature g rad ien ts were looked
a t.
This was done by a llo w in g th e column to come to steady s ta te and
- ta k in g tube surface tem perature readings as the tubes were ro ta te d 360°
in 15° increm ents.
The la r g e s t observed tem perature d iffe r e n c e w ith a
tube tem perature o f 270°F was ±3°F.
No d e f in it e p a tte rn o f tem perature
v a r ia tio n w ith an g u la r p o s itio n could be determ ined.
Since no angular
dependency was observed, the lo n g itu d in a l dependency was not examined.
- 35 -
£
cr
CZ)
S-C
CO
-Q
+->
U
O
fQJ
>
CO
CZ)
<0
S-
C
.005
.010
.015
.020
P a r t ic le Diam eter ( i n . )
FIGURE 6.
PARTICLE MINIMUM FLUIDIZATION VELOCITIES
.025
- 36 As mentioned p re v io u s ly ( 9 , 10) stagnant caps (areas o f l i t t l e
p a r t ic le movement) may be present a t the top and bottom, o f h o rizo n ta l
tubes in a f lu id iz e d bed.
No corresponding tem perature g ra d ie n t was
observed w ith these tu bes. . I f the caps were present th e high thermal
c o n d u c tiv ity o f the copper ap p aren tly 1conducted away 1 any observable
tem perature g rad ien ts on or w ith in the tubes.
I t was decided f o r t h is work to place a s in g le thermocouple
centered on th e tube w all and fa c in g upward.
This is b e lie v e d to give
heat t r a n s fe r c o e ffic ie n ts th a t may be c o n s e rv a tiv e .
The possible
stagnant cap on the top o f the tube would mean less p a r t ic le movement,
a h o tte r lo c a l surface tem p eratu re, a la r g e r tube-bed AT, and a s m a lle r
c o e f f ic ie n t .
H eater Power In p u t
P riebe (2 3 ) looked a t the e f f e c t o f heat f lu x v a r ia tio n on the
h ea t tr a n s f e r c o e f f ic ie n t in s e rra te d f i n , carbon s te e l tubes.
He
observed th a t the c o e ff ic ie n t
increased less than 10 percent w ith a
2 - f o ld increase in h eat f lu x .
To account f o r th is increase he
p o s tu lated th a t w ith increased h ea t f lu x the thermal boundary la y e r
ad ja c e n t to the tube w a ll increased in th ic kn ess .
Hence, more p a r tic le s
a d jace n t to the w a ll were immersed in th is hot f ilm thus- in creasing
the r a te o f heat t r a n s f e r .
As was mentioned p re v io u s ly small e rro rs in tem perature measurement
- 37 r e s u lt in la rg e e rro rs in experim ental c o e f f ic ie n t s .
With increased
p a r t ic le s iz e (g r e a te r M .F .V .) la r g e r a i r mass v e lo c it ie s were used,
s i g n if ic a n t ly decreasing th e tube w all tem perature.
In an e f f o r t to
maximize the tube w a ll-b e d AT the tubes were run a t higher voltages
when the la r g e r beads were used.
• H eater Voltage
• Bead Diam eter
Heater
Wattage
0.0068 in .
115v
230
0.0 1 0 3 in .
120v
255
0.0217 in .
125v
270
With a 17 percent in crease in heat f lu x between the 0 .0 0 6 8 -in .
and 0.0217 in .p a r t ic le s
the e f f e c t on the heat tr a n s fe r c o e f f ic ie n t
1
due to t h is increased heat f lu x was less than 5. percent (see Figure 7 ) ,
whereas tube w a ll-b e d AT increased by 16 p e rce n t.
Thus some increased
accuracy o f experim ental r e s u lts was obtained by th is method.
Procedure fo r a Typ ical Run
The same procedure was used f o r a l l runs.
A s e t o f tubes 6 -1 /2 in .
long was s e le c te d ; thermocouples and s e t screws were attached to the
tubes; tubes were mounted.on c a rtr id g e h e a te rs .
Layers o f copper-
a n ti -s ie z e compound and aluminum f o i l were used to promote contacting
between the heaters and the tubes.
The tube bundle was assembled in the column w ith a l l
tube thermo-
— 38 50
I
I
I
40
O
O
O
Heat T ra n s fe r C o e ffic ie n t (B T U /h r-ft-s q °F )
O
V o lts
O
Q
O
Heat Flux ( B t u /h r - s q .f t )
O
125
980
e
ns
840
Fin H eig h t = 0.375 i n
Fin Spacing = 0.1229 i n
F .P .I. = 7
I
i
0
250
350
i
(Large P a r tic le s )
l
i
t
450
l
550
A ir Mass V e lo c ity ( I b s / h r - s q . f t )
FIGURE 7.
HEAT TRANSFER COEFFICIENT VERSUS AIR MASS VELOCITY
VERSUS HEAT FLUX
650
- 39 couples facin g upward.
th e tubes in p la c e .
The column mi c a rta p la te s p o s itio n ed and held
The in te r fa c e between the mi c a rta p la te s and the
p le x ig la s s column was sealed w ith s ilic o n e la te x s e a la n t to prevent a i r
and p a r t ic le leakage.
P a r tic le s o f the d es ired s iz e were poured in from the top o f the
column to a f lu f f e d s t a t ic bed h e ig h t o f 23 in ch es.
The column I id
was secured in place and. the blower and heaters were turned on and s e t.
The column was allow ed to reach steady s t a t e .
Steady s ta te was
determined by observing the c en ter bed thermocouple h is to r y on the
re c o rd e r.
Data included tube w all and bed tem peratures; power in p u t to the
h e a te rs ; and supply a i r and bed manometer re a d in g s .
Steady s ta te
readings were repeated f o r d i f f e r e n t supply a i r flow r a te s .
s ta te fo r the i n i t i a l
Steady
h eat up o f th e bed req u ired about 4 hours and
f o r successive readings about 2 hours each.
To change p a r t ic le s , the p a r t ic le d ra in pipe was used along w ith
th e vacuum p o rts .
To change the tube bundle, p a r tic le s were drained
and the o u te r mi c a rta p la te w ith the tube bundle was removed.
A new
tube bundle was assembled as before and the procedure was repeated.
)
CORRELATION
A s in g le e q u a tio n .r e la tin g the experim ental parameters to the heat
tr a n s f e r c o e f f ic ie n t was developed.
Recall th a t the experim ental
parameters were f i n h e ig h t, f in .s p a c in g , p a r t ic le diam eter and gas mass
v e lo c it y .
The form o f the equation used.to c o r r e la te the experim ental
r e s u lts was based on th e
'p a r t i c l e ' mode heat tr a n s fe r model presented
by Z ie g le r , Koppel, and Braze!ton. (1 3 ) and extended by G en etti and
Knudsen ( 1 4 ) .
This s e c tio n is presented in th re e p a rts .
F i r s t , the
' p a r t i c l e ' mode heat t r a n s fe r th eo ry and r e s u ltin g mathematical model
is discussed.
Second, the f in therm al c o n d u c tiv ity param eter is
e lim in a te d from the d a ta .
F i n a l ly , the procedure used, in c o r r e la tin g
the data is presented.
. .
P a r t ic le Model fo r Heat T ra n s fe r
.
.
Figure 8 is a schematic showing the d e ta ils o f the proposed
p a r t ic le heat tr a n s f e r mechanism.
A p a r t ic le from th e bulk o f the bed
a t tem perature t^ moves ad jace n t to th e heat tra n s fe r s u rfa c e .
While
a t the surface the p a r t ic le receives therm al energy by unsteady s ta te
convection w ith the lam in ar f l u i d la y e r ad jacen t to th e w a ll.
Temperature o f :t h is f lu i d t^ is the a rith m e tic average o f t w and t ^ .
A f t e r some residence tim e t h e ,p a r t ic le re tu rn s to th e bulk o f the bed
w h e re .its excess therm al energy is d is s ip a te d .
In developing a m athem atical expression d escrib in g th is model the
fo llo w in g assumptions were made:
W W W W W W W W W W W X W
- 41 -
P a r t ic le a t bulk
tem perature
t
f
t(r ,e )
t
P a r t ic le resides a t w all re c e iv in g
heat by unsteady s ta te convection
from surrounding f l u i d .
f
t
> t,
Hot p a r t ic le re tu rn s
to bulk bed
FIGURE 8 .
PARTICLE MODEL FOR HEAT TRANSFER
- 42 1.
The f lu id iz e d p a r tic le s are spheres o f uniform d iam eter.
2.
The physical and thermal p ro p e rtie s o f the s o lid and gas
are co n sta n t.
3.
The f l u i d tem perature adjacent to the su rface is a t the
••
4.
a r ith m e tic mean o f th e w all and bulk bed tem perature.
The m ajor p o rtio n o f h eat tr a n s fe r occurs by the mechanism
o u tlin e d above.
5.
Radiant heat tr a n s fe r from th e surface to the p a r t ic le is
n eg lec ted .
Baddour and Yoon (2 5 ) have shown t h is e f f e c t to
be n e g lig ib le in packed beds a t tem peratures below 600°C.
6.
Conduction a t the p o in t .o f co n tact o f the p a r t ic le s and the
su rface is n e g lig ib le .
The boundary value problem d e s crib in g the tem perature p r o f ile in
the p a r t ic le w h ile i t
.Knudsen ( 1 4 ) .
is near the su rface is presented by G enetti and
Assuming a gamma d is t r ib u t io n fo r p a r tic le -s u r fa c e
residence times and a hexagonal packing o f spheres next to the surface
- th e fo llo w in g equation.was developed d e s c rib in g the ra te o f heat tr a n s fe r
from a su rface in a f lu id iz e d bed:
Nu.
7 .2
p s S Dpr
Note:
G en etti and Knudsen (1 4 ) suggest re p la c in g the 7 .2 in. (a) w ith
- 43 the q u a n tity I O ( I r e )
0 .5
where.
NUp = p a r t ic le NusseTt number, dim ensionless, hOp/k^
h
= heat tr a n s f e r c o e f f ic ie n t , B TLI/hrft^0F
Dp
= average p a r t ic le d ia m e te r, inches
Ps
•=• d e n s ity o f bed p a r t ic le s , I b s / f t
kg
= thermal c o n d u c tiv ity o f f lu i d i z in g medium, B T U /h rft °F
Cs
= heat c a p a c ity o f bed p a r t ic le s , BTU/lbs°F
0
= p a r tic le -s u r fa c e co n tac t tim e , hr
3
2
1- e = p a r t ic le f r a c t i o n , dimensionless
In th is study a i r was the only f l u i d i z in g medium and the various
sized glass beads were o f the same d e n s ity and heat c a p a c ity .
Consequently, the denominator o f ( I )
fl
[ I + C1 :------- 5— ]
1 . Dp^
can be w r itte n as:
6k
where C1 is a constant = — --S-----1
%rs
(b )
P a r t ic le residence tim e a t the s u rfa c e , 0 , was not measured
d i r e c t l y , however, i t is a fu n c tio n o f f i n geometry, p a r t ic le d iam eter,
and p a r t ic le Reynolds number. Rep.
.Using dimensional a n a ly s is to
re p res en t 0 w ith parameters th a t a f f e c t i t , equation ( I )
in the fo llo w in g form:
can be w ritte n
- 44 -
7 .2
Nup =
(c)
t I * C2 (Rep) a(_ V - , b(
where.
L = f i n h e ig h t, inches
S = f i n spacin g, inches
Dp = p a r t ic le d ia m e te r, inches
Q u a n titie s Cg, a , b, and c a re .e v a lu a te d from the data from th is
study.
Raw data from th is .s tu d y included th e tube w all tem p eratu re, t
,
the bulk bed tem p eratu re, t ^ , and th e energy in p u t to each fin n ed tu b e ,
q.
From t h is in fo ra m tio n an experim ental h e a t.tr a n s fe r c o e ff ic ie n t fo r
convection from a s u rfa c e , K0
, was determined w ith th e fo llo w in g
expressions:
(d)
hexp = 9 / 4 ( t w - 4 )
where
A1- = t o ta l fin n ed tube a re a , f t
2
I f a t t h is p o in t values o f heXp and o th e r p e rtin e n t in fo rm atio n
were s u b s titu te d in to (c ) to o b tain
'b e s t f i t '
values f o r C2 , a , b , and
c the c o r r e la tio n would be good only f o r copper tubes since only copper
tubes were used.
The hexp d efined in (d ) is a co n servative value and is
a fu n c tio n o f the f i n m a te r ia l..
The actu al d riv in g fo rc e f o r the
45 t r a n s fe r o f heat from th e fin n ed area o f th e tube is le s s than ( t - t )
w b
because o f the tem perature drop along the length o f the f i n .
Consequent­
l y the 't r u e ' value o f the c o e f f ic ie n t over the e n t ir e tube surface
is somewhat higher than heXp and.would.be d if f e r e n t f o r d if f e r e n t f i n .
m a te r ia ls .
The h ig h e r the. thermal c o n d u c tiv ity o f the f i n m a te ria l the
s m a lle r the tem perature g ra d ie n t along th e f i n and the la r g e r the value
fo r ( V V I f the tem perature g ra d ie n t in th e f i n is accounted fo r when
determ ining the heat t r a n s fe r c o e f f ic ie n t then t h a t c o e ff ic ie n t is
independent o f th e f i n thermal c o n d u c tiv ity .
in t h is manner is defined as fi.
The c o e f f ic ie n t determined
I f h . values and o th e r p e r tin e n t
in fo rm a tio n are s u b s titu te d in to (c ) to o b ta in
‘ best f i t '
values fo r
Cg, a , b , and c the r e s u ltin g c o r r e la tio n would describe th e e ffe c ts
o f th e experim ental parameters on Fi and would be v a lid f o r any tube
.m a te r ia l.
The next sec tio n discusses how the tem perature g ra d ie n t in the f i n
is accounted fo r when determ in ing h.-
The above discussion and fo llo w in g
discussion assumes h to be constant over the e n t ir e su rface o f the fin n ed
tu b e.
This is probably not s t r i c t l y t r u e , e s p e c ia lly near the depths o f
the f i n spaces, however the a n a ly s is is too com plicated w ith o u t th is
assumption.
- 46 fi from h
exp
To o b tain h from Mgxp the fo llo w in g procedure
1)
is fo llo w ed :
develop an expression fo r the tem perature d is t r ib u t io n in
a fin .
2)
determ ine the mean f i n tem perature.
3)
use an area weighted tem perature d iffe re n c e fo r ( t w- t ^ ) in
the convection equation to ob tain R.
The h e lic a l fin s were s l ig h t l y tap ered ; th is ta p e r was taken
in to account in determ ining the f i n tem perature d is t r ib u t io n .
I t was
l a t e r found th a t th e ta p e r was so s lig h t as to not s ig n if ic a n t ly
a f f e c t th e f in a l values fo r h.
To o b ta in the tem perature d is t r ib u t io n in the f i n a steady s ta te
energy balance is taken around a d i f f e r e n t i a l f i n elem ent.
Assuming
angular symmetry, the problem becomes 1-dim ensional in the r - d i r e c t i on
(see s k e tc h ).
Heat flows by conduction in to the l e f t face o f the
elem ent, w h ile heat flow s out o f the element by conduction through
the r ig h t face and by convection from t ' i s u rfa c e .
r
o
EDGE VIEW
END VIEW
- 47 To account f o r the change in surface area o f the f i n due to the
f i n ta p e r the Pythagorean theorem was used to express I (s u rfa ce
le n g th ) in terms o f r (d is ta n c e from f i n base) and a ( 1/2 t o ta l change
in f i n th ic k n e s s ).
Al
(w - w )
where Aa = A r ----- ------------- » w0 = base f in
+ Aa
thickness
Wg = end f i n
thickness
s u b s titu tin g f o r da:
4L 2 + (w0 - Wg ) 2
= A1 Ar
Al = Ar
where
(W 0
'I
-
We ) '
I +
Under steady s ta te con ditio ns the energy balance becomes:
-k 2irr w
+ k 2iTr w -g
|
Rate o f h eat flow
by conduction in to
element a t r
2 R2rrrA1A r ( t - t [ J) = 0
I
r+Ar
r
-
r a te o f heat flow
r a te o f heat flow
out o f element
by convection from
a t (r+ A r)
surfaces between
r and (r+ A r)
accum ulation o f energy
w ith in the element
- 48 where:
w ■=■ lo c a l f i n w idth (fu n c tio n o f r ) , f t
t = lo c a l f i n tem p eratu re, 0Fk = thermal c o n d u c tiv ity o f..th e f i n , B T U /h rft°F
D iv id in g through by Ar and ta k in g th e l i m i t as Ar goes to zero and
s im p lify in g ,th e fo llo w in g d i f f e r e n t i a l equation f o r the tem perature
d is t r ib u t io n in th e f i n is obtained:
jC r w -f-)
Zlifli r
dr
( t - t b)
(I)
k
To get th e above expression in to dim ensionless form the fo llo w in g
dim ensionless v a ria b le s are defin ed :
t-t
T =
b
R
w
w
W=
V tb
0
s u b s titu tin g the dim ensionless v a ria b le s in to th e d i f f e r e n t i a l e q u a tio n ,
th e fo llo w in g expression is obtained:
2fiA1r 0R ( t - t b)
I
-gjT ( r oR woM ' W
r odR
-)
-
S im p lify in g ,
d
, nt, dT
2RA,r dR
Io
W K
0
T = O
- 49 -
2hV o
Let Ar
( la )
w Ok
s u b s titu tin g in Ag
(RW
-) - A9 RT = 0
Expanding out the d e r iv a tiv e term .
W dT
. R dT
dW
“ dR" +
"dR------- dT"
, RW d‘ T
+
n n-r _ n
' A2 RT " 0
Rearranging,
d2I
_
r
----- 0 ~ -
-L
I
.
I
- 6 ---- + - Q
W----
dW ,
dT
- AdR
D - ]J
,
dR
+
dW
Now determ ine a s u b s titu tio n fo r 1/W
A2T
( 2)
W
in terms o f R.
Looking
a t the sketch,
Wzx -
(r0
dW
D efine
Wzx
I - 5, - e)dR)
=
- A3 = - I 2-
(
W = - g — = I - (— ^ ---- — )
lo _
I
W
dW
dR
We
W0 -We
dW
so:
, V
I
(R -I) = I - A3 (R -I)
, wQ-wO'
V
W-
/
I - (-% ^ - ) - X
( R - I)
,)
- 50 S u b s titu tin g Ag fo r -dW/dR,
I
dW
= ________ S __________
W
dR
Ag ( R - I ) - I
Now s u b s titu tin g fo r
d2 T
=
I _______
R - I -
l/A g
in to ( 2 ) ,
_ t_ J _
dR2
=
+
R
I
]
dl
R -I - l/A g
+
dR
A2T
I-A 3(R -I)
F in a lly , upon re a rra n g in g , the fo llo w in g expression d e s crib in g the
tem perature d is t r ib u t io n in the f i n in terms o f the dim ensionless
v a ria b le s is obtained:
r 2R - I - ! / * 3
L R (R -1-1/A g)
,
J
dT
dR
,
*2?
I - A 3 ( R - I)
(3 )
Two boundary con d itio n s are needed to solve th is second o rd er d i f f e r n t i a l
eq u atio n .
t - t.
The f i r s t one is th a t T = —r— z-----t W ^b
= I when R = — — = I
ro
The second one is obtained by making an o v e ra ll energy balance on the
fin n ed tu b e.
In words th is balance s ta te s th a t the heat supplied to
the fin n ed tube is equal to the heat le a v in g the bare tube surface plus
the heat e n te rin g the f in s .
obtained:
In symbols, the fo llo w in g expression is
- 51 -
A = fi Ab< V ' b )
" NT k 2 lrrOwO T
-
I r= r
0
where,
N_ = number o f fin s on the tube.
I
In dim ensionless form th is equation becomes,
t W - t Of - NT k 2rrrOwO
A = frV
(
!?0 b 1
l R=1
s im p lify in g ,
RAj3 - Ny k Zttw0
N0W R “ hexp = T
V
dl
dR
(4 )
R = I
W
Using hex - as a f i r s t approxim ation f o r h equation (4 ) is w r itte n in
th e fo llo w in g form:
R At = R Ab
S o lving f o r
dl
dR
dl
dR
-
dl
Nt k Zmv
T
o
dR
R
I
R = I
RAt - RAb
R = I
-N Tk Z ™
I
o
S u b s titu tin g Ay = Ay-A^, the f in a l
c o n d itio n becomes.
form fo r the second boundary
- 52 -
-NTk2mw
o
The 1t r u e 1 fi value is d efined as fo llo w s :
h =
At ( t " t b ) i
( t - t b ) m is an area weighted AT d is t r ib u t io n equal to the fr a c tio n o f
tube surface area th a t is bare times the w a ll-b e d tem perature d iffe re n c e
plus the f r a c tio n o f the tube surface th a t is fin n e d times the average
fin -b e d tem perature d iffe r e n c e .
Ab
( t - t h)
b'm
A^
Aj,
( VW b
t I))
v
' + - i nAt—
( t - Vb'm
, f
v
where ( t - t b)^ t is the mean fin -b e d tem perature d iffe re n c e defined
as fo llo w s :
/
( t - t h)
b'm f
2*27r r ( t - t b)dr
_^ g ______________
2tt
( r e2 - r Q2 )
To get in to dim ensionless form both sides are d ivid ed by ( t w~ tb ) and
a new dim ensionless v a r ia b le is d e fin e d ,
/ re
r 2 r T dr
( t ~t b) mf
( V t b)
53 Now s u b s titu tin g r^R fo r r and changing th e lim it s on the in t e g r a l,
th e f in a l form f o r
'
in terms o f dim ensionless v a ria b le s is o b ta in e d ,
V 'o
/
V
=
- l ^
2RT dR
---------------
:
<7 >
(------- O----- I )
Equation ( 6 ) can now be w r it te n as fo llo w s :
.
h
(W + _ C f _
or
( 8)
(V V W
V m f
A computer program in v o lv in g f i n i t e d iffe re n c e d expressions and
num erical in te g ra tio n subroutines was used to determ ine th e tem perature
R value by t r i a l and e r r o r . ( 2 7 ) .
The procedure fo llo w ed in the program
is l is t e d below.
. I)
Using hexp as th e f i r s t guess f o r h an A2 and
— |
value using equations ( l a a n d .5) r e s p e c tiv e ly were determined
and the tem perature d is t r ib u t io n in th e f i n was solved fo r
using equation ( 3 ) .
2)
From the f i n tem perature d is t r ib u t io n a
using equation ( 7 ) .
value is obtained
- 54 3)
N e x t, a new fi value is obtained using equation ( 8 ) .
4)
I f th is new F is not w ith in ±.0 1 u n its o f the o ld R value
steps
I through 3 are repeated w ith the newly determined h.
5)
Steps
I through 4 are repeated u n t il h converges.
cv
c r i t e r i a is Rfiew = Rq ^
Convergence
+.01 u n its .
Al I h
values were co rrected to R values by th is method.
exp
These
h values are th e ones used to c o r r e la te the data from th is in v e s tig a tio n .
The c o r r e la tio n procedure is o u tlin e d in the next s e c tio n .
C o rre la tio n Development
As an i n i t i a l
attem p t in c o r r e la tin g the d a ta , the fo llo w in g form
o f an equation was used.
T h is , as mentioned p re v io u s ly , is based on
the 'p a r t i c l e ' mode mechanism fo r h eat t r a n s fe r .
Nu„
______________ I J l _________________
[ I + C2 (Re p) 3 ( Y — ) b ( - § — ) C]
I)
To o b tain a value fo r a ,
rearrang e and take the log o f both sides:
[ J " ¥ i r ~ ■ 1 J = a l o Q Rep + l o Q t C2
From the experim ental data 26 s t r a ig h t lin e s o f log [
7 .2
Nu
- I I
- 55 versus log Re^ were constructed using method o f le a s t squares.
The slopes o f these lin e s are the 'a' values.
these lin e s are the log [C2
— ) b(-g —
The in te rc e p ts o f
) c ] v alu es .
The dependence o f 'a ' w ith Re^ and Nu^ was u n clear;
'a ' was
• assumed to be some fu n c tio n o f ( -~<P- —) and (— g— ) i . e .
a = f (
P
-) or
M d(V)6
" C3 ( S
The n eg ative signs are introduced above because 'a ' values were
n e g a tiv e , which p rese n t d i f f i c u l t i e s when ta k in g th e log o f both sides
Taking th e log o f both sides:
D
log ( - a ) = d log ( - ^ — ) + log (-C 3 (-g —
)e)
Three p a r t ic le diam eters were used w ith each tube.
Consequently
9 le a s t square lin e s (3 points per l in e ) are obtained when log ( - a ) is
p lo tte d a g a in s t log (Dp/S) f o r constant values o f ( L /S ) .
The slopes o f these lin e s are th e 'd ' values,
be a s t r a ig h t l in e fu n c tio n o f (L /S ) i . e .
'd ' was found to
d = -.6 8 5 (L /S ) + 1 .9 6 .
The in te rc e p ts o f these lin e s are the log (-C g f-g —
) e ) values.
Expanding th is term o u t gives:
in te rc e p ts = e log (-^ — ) + log (-C 3)
P lo ttin g th e log (L /S ) versus the in te rc e p ts gives a s t r a ig h t lin e f i t
- 56 to the 9 p o in ts .
The 'e '
value is - 3 .4 and the a n tilo g o f the in te rc e p t
is the Cg value which is - 8 .5 7 .
So the 'a '
value turns out to be the fo llo w in g :
D - -.6 8 5 (L /S ) + 1.96
a = -8 .5 7 ( - g £ - )
2.
To ob tain values f o r Cg, b, and c ,
the in te rc e p ts from the 26 curves o f log
Rep equals log [C2 ( - ^ —
) D( — g— ) c ] .
)~3 ' 4
b
I
Nu
■y—2—
I ] versus log
Expanding th is term out
gives:
D
in te rc e p ts = b log
—
) + log (C2 (— — ) c )
9 le a s t square lin e s are obtained by p lo ttin g in te r c e p t versus
log (Dp/S ) fo r constant values o f ( L / S ) .
The slopes o f these lin e s are values o f 1b 1.
The values f o r 1b 1
turns out to be r e l a t i v e l y con stant; the average value is - .7 7 .
The in te rc e p ts o f these lin e s are values o f log (C 2 ( L /S ) c ) .
Expanding th is term out g iv e s ,
in te rc e p ts = c log (L /S ) + log C2
A s t r a ig h t lin e is obtained when the in te rc e p ts are p lo tte d ag a in s t
log ( L / S ) .
The slope o f th is lin e is the ' c ' value which is .7 5 .
The a n tilo g o f the in te r c e p t o f th is l in e is the C2 value which
is .0 7 4 .
- 57 The c o r r e la tio n is now determ ined.
I t is :
7 .2
Nu,
,
- 3 .4 Dn -.6 8 5 (L /S )+ 1 .9 6
[-8 .5 7 (4 -)
(4 -)
. ]
[ I + .074 Re
The data from th is in v e s tig a tio n was p lo tte d on a lo g -lo g p lo t o f
(N U p /7.2) versus th e denominator on th e r ig h t hand sid e o f th e equation
([
] ).
The p lo t took on a fan shape w ith a d e f in it e (L /S ) dependency.
A f u r th e r refinem ent in the c o r r e la tio n is necessary.
Leaving the
r e s u lts w ith in th e brackets in th e denominator on.the r ig h t hand side
alone ( [
]),
the fo llo w in g form o f the c o r r e la tio n is assumed:
%
----------t T —
t
]
where A and B ar&som e fu n ctio n s o f ( L / S ) .
Taking the log o f both
sid es:
log NUp = -B log [ ] + log A
P lo ttin g log NUp versus log [ ] f o r con stant (L /S ) v a lu e s , 9 le a s t square
lin e s were o b tain ed .
The slopes of. these lin e s are 1B 1 v alu es .
The in te rc e p ts o f these lin e s are v a lu e s .fo r log A.
Least square
s t r a ig h t lin e s were then obtained from p lo ts o f (L /S ) versus
and (L /S ) versus 1A 1 v a lu e s .
The r e s u lts :
1B 1 values
- 58 A = - .2 6 (L /S ) + 7.1
B =
.24 (L /S ) + 1 .0
The f in a l form o f the equation is then.
- .2 6 (L /S ) + 7 .1
Nu„
,
- 3 .4
[ - 8 .5 7 ( 4 — )
[ I + .074 Rep L
D
- .7 7
( - / - )
S
,
( - f )
D
-.6 8 5 (L /S )+ 1 .9 6
(-4 -)
.75
]
.2 4 (L /S )+ 1
i
A ll o f the experim ental data is p lo tte d in Figure 9 w ith the
c o r r e la tio n l i n e .
Most o f the data lie s w ith in ±20% o f the c o r r e la tio n
This ±20% is the e r r o r determined in the e r r o r an a ly s is on page 84. .
The range o f c o r r e la tio n a p p li c a b i li t y is given below.
RANGE
VARIABLE*I
P a r t ic le diam eter
0 .0 0 6 8 , 0 .0 1 0 3 , 0.0217 inches
Fin h e ig h t
0 .2 3 4 , 0 .2 7 4 , 0 .3 5 2 , 0 .3 7 5 , 0.414 in
Fin spacing
0.0396 to 0.1840 inches
Tube diam eter
-0 .4 5 3 , 0 .6 2 5 , 0 .7 5 0 inches
Fin thickness
0 .0 1 6 to 0.025 inches
Fins per inch
5 to 18
F lu id iz in g v e lo c ity
100 - 700 l b / h r f t 2
G/Gmf
I to 7
Bed tem perature
160 to 260°F
Tube w a ll tem perature
185 to 275°F
- 5 9 -
S(In)
F .P .I
K in )
O
.0951
.414
9
□
.0871
.375
9
O
.0951
.352
9
>
.1840
.234
5
O
.0951
.234
9
O
V
.0554
.234
14
.0396
.234
18
►
.1750
.274
5
©
.1229
.375
7
20%
(-0 .2 6
+
7.0
^ Dp ^-.685(L/S)+1.96
( I + .074 Re,
FIGURE 9 .
[-8.57(4—)'3"4
CORRELATION (A L L TUBES INCLUDED)
(^ )
L
(> )
8.0
9.0 10.0
.75 . 2 4 ( 5 —)+!
I
)
- 60 VARIABLE
RANGE
Heat f lu x
700 to 2600 B T U /hrft'
Bed m a te ria l
glass (s p .g . = 2 .5 )
A Design Problem
The c o r r e la tio n developed accounts fo r the e f f e c t o f f i n geometry
on h , independent o f f i n thermal c o n d u c tiv ity .
A ty p ic a l design problem
would be to determ ine th e number o f continuous, h e lic a l fin n ed tubes o f
a c e r ta in m a te ria l re q u ire d to d e liv e r a given h eat load a t a s p e c ifie d
"
A d d itio n a l s p e c ific a tio n s would in clude f i n h e ig h t, f i n .
spacing, tube a re a , p a r t ic le d ia m e te r, and gas mass v e lo c it y .
From the
c o r r e la tio n a value f o r Nu^ is obtained and subsequently a value fo r R.
The standard equation is used to o b ta in the heat d e liv e r y c a p a b ility
per tube.
q - h At Tit
( V t b)
where
nt is the t o ta l e f fic ie n c y o f th e s u rfa c e , accounting fo r the
therm al c o n d u c tiv ity o f the f i n m a te ria l
Vt =Ab+Vf
n
f
. _
~
ac tu a l heat tra n s fe rre d by the f in
h eat tra n s fe rre d i f the e n t ir e f i n
were a t t
- 61 Values o f
versus a param eter accounting f o r f i n thermal
c o n d u c tiv ity and f i n geometry are presented g r a p h ic a lly in Figure 10 ( 2 6 ) .
Once the h eat d e liv e r y o f a s in g le tube is determined the number o f
tubes req u ire d f o r the job is e a s ily determ ined.
1.8
(ro + 2
FIGURE 10.
" r i^
2 R /k t (T q- T 1-)
EFFICIENCY OF CONTINUOUS HELICAL FINS
2.0
- . RESULTS AND DISCUSSION
Note:
A ll average heat tr a n s f e r c o e f f ic ie n t s , F , rep o rted in th is
s e c tio n a llo w f o r th e tem perature g ra d ie n t from the base to
the top o f the f i n .
In some e a r ly p io n ee rin g work P e t r ie , Freeby, and Buckham (20)
rep o rted heat tra n s fe r c o e ffic ie n ts obtained using continuous, h e l i c a l ,
aluminum fin n ed tubes in an a i r f lu id iz e d bed.
1 1 - F . P . I. tubes were used.
in ch es.
Bare, 5 - F . P . I . , and
Fin h e ig h t fo r both fin n ed tubes was 0.406
The bed m a te ria l was sand w ith an average diam eter o f 0.02
in c h e s .
A maximum d e v ia tio n o f 64 percent from Vreedenberg1s c o rre la tio n
(1 8 ) was observed w ith th e bare tubes.
Vreedenberg's maximum reported
d e v ia tio n from h is own c o r r e la tio n was 29 p e rc e n t.
P e t r ie , Freeby
and Buckham observed a 43 percent d e v ia tio n from the bare tube
c o r r e la tio n developed from t h e ir d ata.
T h e ir rep o rted c o e ffic ie n ts fo r th e finn ed tubes were compared w ith
values obtained using t h e i r f i n dimensions and th e c o r r e la tio n determined
from my experim ental re s u lts
(see page 5 8 ) .
The h values from my
c o r r e la tio n were adjusted fo r the aluminum f i n m a te ria l by using f i n
e f f ic ie n c y values from F ig u re . 1 0 , page
62.
-
.
My c a lc u la te d R values d iff e r e d from 15 to 69 percen t from t h e ir
rep o rted experim ental c o e f f ic ie n t s .
a higher c o e ffic ie n t-
In a l l cases my c o r r e la tio n reported
B a r t e l . (4 ) rep o rted lower c o e ffic ie n ts o f the
- 64 order o f 10 percent when i r r e g u l a r sand p a r t i c l e s were used instead o f
sp h erica l glass beads in his studies w ith s e rra te d fin n ed tubes.
T h e re fo re , i t seems reasonable t h a t my r e s u lt s should be higher than
t h e i r reported values in a l l cases.
Using t h e i r reported d ev iatio n s from Vreedenberg1s c o r r e la t io n
and t h e i r own c o r r e la t io n as a yard s t i c k i t is suggested t h a t the R •
values obtained in my in v e s t ig a t io n are 'reasonable' g ivin g some
confidence to my l a t e r reported r e s u l t s .
h versus G
I t has g e n e r a lly been observed t h a t R increases, reaches a
maximum value and then decreases w ith in creasing f l u i d i z i n g gas mass
v e l o c i t i e s , G.
This maximum is a r e s u l t o f two opposing f a c t o r s .
F i r s t , p a r t i c l e movement increases as G increases r e s u lt in g in sh o rter
p a r t ic le - s u r f a c e residence times and a r e s u l t in g higher c o e f f i c i e n t .
Second, the void f r a c t i o n o f the bed increases as G increases r e s u lt in g
in a lower p a r t i c l e concentration a d jace n t to the surface and
consequently lower heat t r a n s f e r c o e f f i c i e n t s .
In t h i s study the small p a r t i c l e s (0 .0 0 6 8 inch diam eter) e x h ib ite d
steeper p o s it iv e slopes follow ed by the medium p a r t ic le s
(0 .0 1 0 3 -in c h
d ia m e t e r ) , follow ed by the la rg e p a r t i c l e s (0.0217 inch diameter) on
the R versus G p l o t s .
O ccasionally a maximum value o f R was obtained
w ith the small and medium beads.
A ,n e g a tiv e slope was observed w ith two
- 65 d i f f e r e n t fin n ed tubes w ith the la rg e beads in d ic a t in g t h a t the values
of R
obtained were on the downward side o f the maximum.
The c o e f f i c i e n t , h increased w ith decreasing p a r t i c l e s iz e s .
The
increase was l a r g e r between the l a r g e , and medium beads than between the
medium and small beads.
Increases in R o f up to 50 percent were noted
in the c o e f f i c i e n t between the la rg e and small beads.
The s e n s i t i v i t y
o f th e c o e f f i c i e n t on p a r t i c l e s iz e diminished as the f i n spacing
decreased and as the f i n h e ig h t increased.
A r e p r e s e n ta tiv e p l o t o f
sizes is shown in Figure 11.
R
versus G w ith th e 3 d i f f e r e n t bead
This shows the performance o f tubes with
f i n height (L) o f 0.375 inches, f i n spacing (S) o f 0 . 0 8 7 1 -inches, f in s
per inch ( F . P . I . ) o f 9.
R
versus Fin Height
Four tubes w ith F . P . I . values o f 9 were used to determine the
dependency o f R w ith f i n h e ig h t.
Fin heights v a rie d from 0.234 inches
to 0 .4 1 4 inches.
Figure 12 is a re p r e s e n ta tiv e p l o t showing the e f f e c t on
R
w ith
in creasing f i n h e ig h t as the f l u i d i z i n g gas mass v e l o c i t y is increased.
Large beads were used in t h is case.
Note t h a t the c o e f f i c ie n t . in c r e a s e d .w it h decreasing f i n h e ig h t.
L i t t l e increase in
R
occurred as the f i n h e ig h t was reduced from
0 .4 1 4 inches to 0.352 inches.
A l a r g e r increase in
R
is noted as the
- 66 -
►
.0068
O
.0217
F .P .I.
.0871 in
375 i n .
200
300
400
500
A i r Mass V e lo c it y ( I b s / h r s q f t )
FIGURE 11.
h VERSUS G VERSUS PARTICLE DIAMETER
67 _
s(in)
L( I n)
■0951
.0871
■0951
■0951
(La
"9* P a r tf c e s ,
O
9
250
350
f Lgure
F-P-I .
- 68 f i n h eig h t is reduced from 0.352 inches to 0.234 in ch es.
This in creasin g c o e f f i c i e n t w ith decreasing f i n height is what is
p re d ic te d from ' p a r t i c l e ' mode heat t r a n s f e r t h e o r y . , P a r t i c l e motion
i n t o and out o f the depths o f the f i n space i s more hindered w ith longer
fin s .
Hindering p a r t i c l e motion increases p a r t i c l e to surface contact
times reducing the r a t e o f heat t r a n s f e r per u n it o f surface area.
h versus Fin Spacing .
Four tubes w ith f i n heights o f 0.234 inches were used to determine
the dependence o f h w ith f in .s p a c in g .
0.0396 inches to 0.1840 inches.
Fin spacings v a rie d from
Nominal F . P . I . values were 5 , 9 , 14
and 18.
Figure 13, is a re p r e s e n ta tiv e p l o t showing the e f f e c t s of f i n
spacing on R as G is v a r ie d .
d a ta .
Medium beads were used f o r t h i s set o f
I t is noted t h a t as the f i n spacing increases the c o e f f i c i e n t
increases ac c o rd in g ly .
I t is also apparent t h a t the magnitude o f the
increase o f th e c o e f f i c i e n t is: p ro p o rtio n a l to the magnitude o f the
f i n spacing change.
These trends are c o n s is te n t w ith ' p a r t i c l e ' mode h ea t t r a n s f e r
th e o ry .
As the distance between f i n s increases p a r t i c l e motion in to
and out o f th e f i n space depths becomes e a s ie r thus reducing p a r t i c l e surfaee contact residence tim e, in creasin g the r a te o f heat t r a n s f e r
per u n i t surface area.
- 69 -
S (in )
L (In )
F .P .I.
.1840
.234
5
.0951
.234
9
.0554
.234
14
.0396
.234
18
(Medium P a r t i c le s )
200
300
4
A i r Mass V e lo c it y ( I b s / h r . s q . f t )
FIGURE 13.
R VERSUS AIR MASS VELOCITY VERSUS FIN SPACING (S)
- 70
Figure 14- shows the e f f e c t o f the dimensionless r a t i o Dp/S
( p a r t i c l e diameter t o f i n spacing r a t i o ) on fi.
This data was obtained
w ith tubes w ith 0.234 inch f i n height a t a reduced gas mass v e l o c i t y
r a t i o (GZGfnin) equal to 4 . 0 .
A constant GZGfffin value was used to
obtain dynamic s i m i l a r i t y o f the 3 p a r t i c l e s i z e s , thus e lim in a tin g
the p a r t i c l e diam eter parameter from the f ig u r e .
The curve is steep f o r f i n spacings g r e a te r than 10 p a r t i c l e
diameters and begins to f l a t t e n out f o r f i n spacings less than 10
p a r t i c l e diam eters.
This in d ic a te s t h a t R is q u ite s e n s it iv e to f i n
spacings g r e a te r than 10 p a r t i c l e diameters but becomes less s e n s itiv e
as the f i n spacing is reduced f u r t h e r .
As the f i n spacing is reduced
p a r t i c l e movement in to and out o f the depths o f the f i n gaps becomes
more and more hindered c re a tin g s u b s ta n tia l d e f l u i d i z a t i o n in the inner
regions o f the f i n gaps.
This region o f the finned tube begins to
a s s im ila t e a packed bed w ith i t s corresponding lower c o e f f i c i e n t s .
F i n a l l y as the f i n spacing is reduced f u r t h e r p a r t ic le s become lodged
in the f i n spaces' reducing p a r t i c l e packing adjacent to the surface
and p a r t i c l e movement w it h in the f i n space thus reducing the c o e f f i c i e n t
fu rth e r.
Figure 15, is also a p l o t o f Dp/S versus h a t GZGfffin equal to 4 .0
only now a l l 9 tubes are included in the p l o t .
The various tube f i n
heights have added some s c a t t e r to the curve but the same general
trends as p re v io u s ly discussed are s t i l l
apparent.
In the range o f f i n
- 71 -
Fin Height = 0 . 2 3 4 - i n .
Note:
0
Fi f o r a bare tube (0 /S=0)=120 B t u /h r f t s q ° F ( 4 )
.1
.2
.3
V s
FIGURE 14.
Fi VERSUS Dp/S (CONSTANT FIN HEIGHT)
.4
- 72 -
Note: h f o r a bare tube (D /S=0)=120 B t u / h r f t °F(4)
FIGURE 15.
h VERSUS Dp/S (ALL TUBES)
- 73 heights and f i n spacings looked a t in t h i s t h e s i s , f i n spacing seems
t o have a more dominant in flu e n c e on h than does f i n h e ig h t.
Priebe (24) looked a t the e f f e c t o f f i n spacing on the c o e f f i c i e n t
w ith s e rra te d finn ed tu b e s .
He observed l i t t l e
spacing was g r e a te r than 10 p a r t i c l e diam eters.
diameters the c o e f f i c i e n t f e l l
e f f e c t when the f i n
At less than 10 p a r t i c l e
r a p i d l y up to a p o in t where the spacing
is less than 2 p a r t i c l e diam eters.
From t h a t point on the curve f e l l
very slo w ly .
The observations from my study are not in c o n f l i c t w ith P r ie b e 's
re s u lts .
A continuous f i n presents much more in te r fe r e n c e to p a r t i c l e
motion much e a r l i e r than does a s e rra te d f i n .
P a r t i c l e motion is mostly
r e s t r i c t e d to an in and out motion in the f i n space w ith a continuous
f i n whereas, p a r t ic le s can move in to and around the s e rra te d f i n s .
Consequently f o r a f i n spacing as high as 30 p a r t i c l e diameters marked
p a r t i c l e motion in te r f e r e n c e is noted w ith a continuous finned tube.
The f i n spacing o f a continuous finned tube is e s s e n t i a l l y d e f lu id iz e d
a t a f i n spacing o f 10 or less p a r t i c l e diameters hence f i n spacings
in t h is range have l i t t l e
e f f e c t on h.
q/AT f o r the Tubes
A convenient way o f r a t in g the performance o f a l l
the tubes
i r r e s p e c t iv e o f f i n geometry. is by determining q/AT v a lu e s .
q/AT values
are in d ic a t iv e o f how much heat a given tube can tra n s m it to the bed
- 74 per u n i t degree o f temperature d r iv in g f o r c e .
An e q u iv a le n t expression
f o r q /A l is the product o f ^ xp £and the tube area.
determine the q /A l valu e .
Two opposing fa c to rs
Increasing the tube area e i t h e r by decreasing
the f i n spacing or in creasin g the f i n height r e s u lts in a lower heat
tra n s fe r c o e ffic ie n t.
Designing a tube to obtain a maximum q/AT value
involves ju g g lin g the f i n h eig h t and f i n spacing parameters.
Figure 16 is a p lo t o f q/AT versus G with fo u r tubes w ith equal
f i n spacing but d i f f e r e n t f i n h eig h ts .
da ta .
Large beads were used f o r t h is
As can be seen q /A l increased w ith increasing f i n h e ig h t.
The
magnitude o f the q/AT change decreased w ith increasing f i n h e ig h t.
It
is c le a r t h a t a maximum q/AT value would be obtained a t a higher f i n
h e ig h t.
Figure 17 is a p l o t o f q/AT versus G w ith fo u r tubes o f equal f i n
h eig h t but d i f f e r e n t f i n spacings.
d a ta .
Medium p a r t ic le s were used f o r t h is
q/AT increased w ith decreasing f i n spacing.
Again i t is c le a r
t h a t a maximum q/AT value would be reached a t some s m alle r f i n spacing.
Figure 18 is a re p r e s e n ta tiv e p l o t o f q/AT versus G f o r a l l tubes
stu d ie d .
Large p a r t ic le s were used f o r t h i s d ata.
3 tubes shown, span the range o f data f o r a l l
The r e s u lt s o f the
9 tu b es.
Only 3 o f the
nine tubes are shown.to give c l a r i t y to the f ig u r e .
In Table I I I a l l nine tubes are l i s t e d in order o f decreasing
average q/AT values f o r a l l 3 p a r t i c l e s iz e s .
I t was found t h a t the
order o f ranking is independent o f p a r t i c l e diam eter.
The best
- 75 -
F. P. I .
.0951
.414
.0871
.375
.0951
.352
.234
(Large P a r t i c le s )
150
450
550
A i r Mass V e lo c it y ( I b s / h r . sq. f t )
FIGURE 16.
q/AT VERSUS G VERSUS FIN HEIGHT
- 76 -
F. P. I .
■
.1840
O
.0951
•
.0554
D
.0396
(Medium P a r t i c le s )
A i r Mass V e lo c ity ( I b s / h r . s q . f t )
FIGURE 17.
q/AT VERSUS G VERSUS FIN SPACING
- 77 -
F. P. I .
O
.0951
.414
□
.0554
.234
.274
(Large P a r t i c le s )
!00
300
400
500
600
A i r Mass V e lo c it y ( I b s / h r . s q . f t )
FIGURE 18.
q/AT VERSUS G
TABLE I I I .
q/AT
Rank
F .P .I.
Fin
Spacing ( i n )
Fin
Height ( i n )
AVERAGE PERFORMANCE OF TUBES
q / /T
q/AT
Ranking
q/AT
BTU/hr F
BTU/hr F
BTU/hr F
Based
(small beads) (Med. Beads)(Large Beads) on R
I
9
0.0951
0.414
56.16
47.55
38.77
8
2
9
0.0871
0.375
54.85
49.00
38.33
5
3
7
0.1229
0.375
51.02
42.35
33.28
4
4
18
0.0396
0.234
45.83
42.24
-
9
5
9
0.0951
0.352
44.77
40.96
32.23
6
6
14
0.0554
0.234
43.67
39.57
30.77
7
7
9
0.0951
0.234
39.27
33.54
26.17
9
8
5
0.1840
0.234
31.69
26.95
20.78
I
9
5
0.1750
0.274
24.98
20.42
15.65
2
- 79 performer.was a tube o f in te rm e d ia te f i n spacing w ith maximum f i n
h e ig h t.
Tube Diameter 9
*
Two tubes studied had id e n t ic a l f i n heights w ith d i f f e r e n t f i n
spacings and tube diam eters.
Tube
F. P. I .
The s p e c i f i c dimensions are:
L (in )
S ( in ) _____ Tube Diameter ( i n )
2
9
0.375
0.0871
0.625
9
7
0.375
0.1229
0.750
The la r g e r diameter tube (tube 9) had the same f i n h eig h t but
l a r g e r f i n spacing.
From previous noted tre n d s , fi would be expected
t o be l a r g e r f o r tube 9 than tube 2 because o f the g r e a te r degree o f
freedom o f p a r t i c l e motion w ith in the l a r g e r f i n spacing.
This was not
observed; w it h in experimental e r r o r both tubes had th e same heat t r a n s f e r
c o e ffic ie n ts fo r a ll
three p a r t i c l e diam eters.
One q u a l i t a t i v e conclusion can be.drawn from these r e s u l t s .
The
heat t r a n s f e r c o e f f i c i e n t tends to decrease w ith in creasing tube
diam eter.
This phenomenon can be explained w ith the p a r t i c l e thqery
f o r heat t r a n s f e r .
Fin surface area increases w ith in creasin g tube
diam eter f o r a constant f i n h e ig h t.
The more f i n surface t h a t the
random moving p a r t ic le s have t o i n t e r a c t w ith the more hindered they
become.
Again, the more hindered p a r t i c l e motion becomes the sm aller
- 80 —
the c o e f f i c i e n t .
I t should be noted t h a t the tube diameter e f f e c t on the c o e f f i c i e n t
was not s i g n i f i c a n t enough t h a t tube diam eter had to be included as a
parameter in the c o r r e l a t i o n .
■.
CALCULATIONS
A i r Mass V e lo c ity
As mentioned p revio u s ly a vena co n tracts o r i f i c e w ith a water
manometer were used to determine the a i r mass v e l o c i t y to the column.
A standard equation f o r an o r i f i c e is used.
where.
G = a i r mass v e l o c i t y , I b m / h r - f t
2
C = o r ific e c o e ffic ie n t
o
Y = expansion f a c t o r , dimensionless
Sc = cross sec tio n a l area o f the o r i f i c e , f t
Ac = cross sec tio n a l area o f the column, f t
2
.
2
2
• gc = g r a v i t a t i o n a l con stant, f t - l b m / h r - Ib ^
P^-Pg
= pressure drop a c ro s s .th e o r i f i c e , l b ^ / f t
2
Pj = d en sity o f a i r a t the upstream pressure, I b m / f t
3
B = r a t i o o f o r i f i c e diameter to in s id e pipe diam eter, dimensionless
For a square edged o r i f i c e , the expansion f a c t o r is given as:
(.41 -
I -
35 B )
V r
where
V
cV
The o r i f i c e c o e f f ic ie n t is a fu n c tio n o f the Reynolds number, and
- 82 was found by t r i a l and e r r o r .
and equal to 0 .6 ( 4 ) .
I t was found to be very n e a rly constant
This value was used in a l l
c a lc u la t io n s .
Bed Temperature
Bed temperature was determined by averaging the 3 in bed thermocouple
readings.
A ll
■
3 in bed thermocouples read w it h in I or 2
degrees o f each o th e r.
Tube Temperature
. Each tube temperature was read d i r e c t l y o f f the c h a rt reco rd e r.
Heat Input to Each Tube
E l e c t r i c a l power in p u t to each tube was measured w ith a Simpson
Wattmeter.
A conversion f a c t o r o f 3.413 BTU/watt-hr was used to convert
the measured watts to BTU/hr.
Area o f Each Tube
The surface area o f each tube was determined by c a lc u la t in g the
bare tube area and adding on the finned a re a .
Finned area was determined
by m u ltip ly in g the area o f a f i n by the number o f f i n s on the tube.
heXp f o r Each Tube
The experimental heat t r a n s f e r c o e f f i c i e n t f o r each tube was
- 83 c a lc u la te d from the standard equation f o r convection from a surface,
BTU
exP
h
A1- ( t w - t b)
h r - f t 2oF
f o r the Bundle o f Tubes
^exp ^or
bundle o f tubes was determined by averaging the 7
in d iv id u a l ^ exp values.
A i r V is c o s ity and Thermal C o n d u c tiv ity
A i r v is c o s it y was determined by using an equation f i t to
experimental data.
Pf = [ 2 . 4 5 ( t b-3 2 ) + 1538.1] ( 2 .6 8 8 . x I ( T 5 ) 9 I b / f t - h r
t b is in 6F.
A i r thermal c o n d u c tiv ity was determined by l i n e a r in t e r p o la t io n
between selected l i s t e d values in K re ith ( 2 6 ) .
was ( t w + t b) / 2 .
P a r t i c l e Reynolds Number
dimensionless
Re_ =
P a r t i c l e Nusslet Number
RD
Nu
,
dimensionless
Evaluation temperature
ERROR ANALYSIS
Assuming Iiexp is only a ffe c te d by the experimental determ inations
o f q and ( t ^ - t ^ ) , the e r r o r analysis is performed on the fo llo w in g
equation:
'
h
exp
________ g__________
X U lil - t j
' t v vw
b;
N -
The w attm eter is assumed to be accurate to w it h in ± 5 percent.
No e r r o r is assumed in determining the area o f the f i n .
The bed
temperature is assumed to be measured to w ith in ± 0 .5 ° F .
The tube w all
temperature could be measured to w it h in ± 1 .5 ° F .
A minimum U w- ^ )
value o f 15°F was e x p e rim e n ta lly observed.
Using the above assumed experimental accuracies maximum and
minimum e rro rs f o r hQ ■ are determined.
exp
This analysis is based on an
hexp ’ t r Ue ' value o f 1 . 0 .
Maximum h
.exp
exp
1.05
1 -2 /1 5
1.21
E rro r = (1 .2 1 - 1 .0 ) x 100 = + 21 percent
Minimum h
________ exp
exp
.95
I + 2/15
84
E rro r = ( . 8 4 - 1 .0 ) x 100 = -16 percent
Therefore the experimental e r r o r range bracketing a l l
p e rc e n t, -16 percent.
r e s u lt s is +21
T h e re fo re , maximum d ev iatio n s from 1t r u e 1 values
should be about ±20 percent.
SUMMARY OF RESULTS AND CONCLUSIONS
The fo llo w in g are based on r e s u l t s a n d 'conclusions, from t h is study.
I t was g e n e ra lly observed t h a t the heat t r a n s f e r c o e f f i c i e n t
increased w ith increasing a i r mass v e l o c i t y .
A maximum was
observed in some cases with, small and medium beads.
The heat t r a n s f e r c o e f f i c i e n t increased w ith decreasing p a r t i c l e
s iz e .
The increase was l a r g e r between the la rg e and medium beads
than between the medium .and small beads.
Increases in the
c o e f f i c i e n t o f up to 50 percent were observed when going from
la rg e to small beads.
Some increased experimental accuracy re s u lte d by using higher heat
flu x e s w ith the tubes when l a r g e r beads were used.
No r a d i a l . t u b e w all temperature g ra d ie n t was observed.
The heat t r a n s f e r c o e f f i c i e n t increased w ith decreasing f i n
h e ig h t.
L ittle
increase is observed in the c o e f f i c i e n t as the f i n
h eig h t was reduced from 0.414 to 0.352 inches.
A l a r g e r increase
is noted as the f i n h eig h t is reduced from 0.352 to 0.234 inches.
The heat t r a n s f e r c o e f f i c i e n t increased p r o p o r t io n a lly w ith
increased f i n spacing.
The heat t r a n s f e r c o e f f i c i e n t was very s e n s it iv e to f i n spacings
as la rg e as 30 p a r t i c l e diam eters.
The c o e f f i c i e n t was less
s e n s it iv e to f i n spacings o f less than 10 p a r t i c l e diameters.
I t is believed t h a t d e f l u i d i z a t i o n in the f i n spaces was
s i g n i f i c a n t f o r f i n spacings less than 10 p a r t i c l e diameters.
- 87 -
8)
The h ea t t r a n s f e r c o e f f i c i e n t decreased w ith in creasin g tube
diam eter.
9)
•
The best performer as f a r as heat d e l i v e r y c a p a b i l i t i e s was a
tube o f in te rm e d ia te f i n spacing and maximum f i n h e ig h t.
10)
A c o r r e l a t io n r e l a t i n g experimental parameters to the heat t r a n s f e r
c o e f f i c i e n t was developed.
percent o f the c o r r e l a t i o n .
. from an e r r o r a n a ly s is .
Most o f the data f e l l w it h in ±20
This was the maximum e r r o r determined
RECOMMENDATIONS
Three studies ( 2 3 ,2 4 ) in clu d in g t h is one have now been completed.
S e rr a te d , spined, and continuous finn ed tubes have been examined.
Parameters have included tube spacings, f i n geometries, f i n m a t e r ia ls ,
bed m a t e r i a l , sizes and shapes.
The ' p a r t i c l e ' heat t r a n s f e r theory
has s a t i s f a c t o r i l y accounted f o r a l l
trends observed.
This is
s i g n i f i c a n t in t h a t what is a c t u a l l y going on in f l u i d i z e d beds is
being r e a l i z e d .
The c o r r e la tio n s developed are based on narrow ranges of
operating co n d itio n s .
Furthermore extension of the c o r r e la tio n s t o .
o th er conditions would probably give u n s a tis fa c to r y r e s u l t s .
Research
o f t h i s kind is in te r e s tin g .a n d somewhat pioneering but not d i r e c t l y
u s e fu l.
Studies o f t h i s nature are performed in the hopes t h a t
e v e n tu a lly f l u i d i z e d bed dynamics w i l l be f u l l y r e a l iz e d .
Then,
perhaps, more general and more useful c o r r e la tio n s with wide design
a p p l i c a b i l i t y w i l l be developed.
We have a long way to go.
One s p e c if i c recommendation f o r f u r t h e r study is to extend the
ranges o f a p p l i c a b i l i t y o f the e x is t in g c o r r e l a t io n s .
us c lo s e r to a 1g e n e r a l' c o r r e l a t i o n .
This would bring
Areas f o r f u r t h e r in v e s tig a tio n
include using d i f f e r e n t f in . d i m e n s i o n s , d i s t r i b u t o r p l a t e s , column
dimensions, tube lo c a t io n s , bed m a t e r ia ls , shapes, and s iz e s .
Determin
ing means to su c ces s fu lly s c a le up r e s u lt s from previous studies would
be a real break through f o r the design er.
NOMENCLATURE
. 1/2 t o t a l change in f i n thickness from
base to t i p
a
CO
&5b jC 5d $
>
Dimension
D e fin itio n
Symbol
Ab
Ac
Af
At
cO
cP
cV
cS
0P
G
9c
.
ft
Functions o f experimental parameters in
c o r r e la t io n 'e q u a t io n
" dimensionless
Functions o f (L /S ) in c o r r e l a t io n equation
dimensionless
Bare tube area
ft2
In s id e c ro s s -s e c tio n a l area o f column
n 2
Finned area o f tube
ft2
Total tube area ( f i n + bare areas)
ft2
O rific e c o e ffic ie n t
dimensionless
Heat c a p a c ity a t constant pressure
B T U /h r - f t 2- ° F
. B T U /h r -f t 2- ° F
Heat c a p a c ity a t constant volume
B T U /h r - f t 2- ° F
S o lid p a r t i c l e heat cap acity
P a r t i c l e diameter
. inches
A i r mass v e l o c i t y
lb s /h r-ft2
Constant
.,lbs- - f t / l b f o r c e - h r 2
Gmin
A i r mass v e lo c ity , a t minimum f l u i d i z i n g
conditio ns
h
Heat t r a n s f e r c o e f f i c i e n t , average
B T U /h r - f t 2- ° F
^exp
Experimental heat t r a n s f e r c o e f f i c i e n t ,
average
B T U /h r - f t 2- ° F
lb s /h r-ft2
- 90
D e fin itio n
Symbol
R
Heat t r a n s f e r c o e f f i c i e n t independent o f
f i n m a t e r i a l , average
k
Thermal c o n d u c tiv ity o f f i n
kg
kr
v B T U /h r-ft-°F
B T U /h r-ft-°F
Ratio o f C /C
dimensionless
P
V
Fin surface length
L
Fin height
'g.
B T U /h r - f t 2 - ° F
Thermal c o n d u c tiv ity o f f l u i d i n g medium
I
1B
Dimension
ft
inches
E q uiv ale nt thickness o f emulsion la y e r
ft
Thickness o f gas f i l m
ft
Number o f f i n s on tube
dimensionless
Nup
P a r t i c l e Nusselt number=hDp/k/
dimensionless
(P 1-P 2 )
Pressure drop across the o r i f i c e
q
Rate o f heat t r a n s f e r
BTU/hr
9l
Rate o f sen sib le heating o f moving s o lid s
BTU/hr
%
Rate o f heat t r a n s f e r to bulk bed by
p a r t i c l e exchange
BTU/hr
r
Distance from base o f f i n
R
r lr 0
nt
re
ReP
Radius o f tube a t f i n t i p
P a r t i c l e Reynolds number, GDpZpf
lb /ft2
ft
dimensionless
ft
dimensionless
- 91 Symbol
D e fin itio n
Radius o f tube a t . f i n base
S
Fin spacing
Sc
Cross-sectio nal a r e a . o f the o r i f i c e
t
Local tube temperature
T
( M 5) Z ( V t b)
. .
Dimension .
ft
inches
°F
dimensionless
Bulk bed temperature
°F
F lu id temperature adjacent to heat t r a n s f e r
s u rfa c e . A rith m e tic average o f t^ and t
°F
( t - t b) mf/ ( t w- t b)
dimensionless
P a r t i c l e temperature
0F
Heat t r a n s f e r surface temperature
°F
t(e)
Unsteady s t a t e p a r t i c l e temperature
°F
AT
Temperature d iff e r e n c e
0F
Mean finn ed tube-bed AT
0F
Mean f in - b e d
°F
(t-tb'm
(t-tb'm f
AT
V e lo c it y o f s o lid s
W
Fin thickness
W
W/wo
W
O
Y
ft/s e c
ft
dimensionless
Fin t i p thickness
ft
Fin base thickness
ft
Expansion f a c t o r
dimensionless
- 92 Symbol
D e fin itio n
Dimension
3
Ratio o f o r i f i c e diameter to in sid e
pipe, diameter
dimensionless
(1-e)
P a rtic le fra c tio n
dimensionless
E f f ic i e n c y o f f i n surface
dimensionless
E f f ic i e n c y o f e n t i r e finn ed tube surface
dimensionless
nf
6
Average p a r t ic le - s u r f a c e contact time
V is c o s ity o f f l u i d i z i n g gas a t t^
hr
Ib s /h r-ft
Density o f s o lid p a r t ic le s
lb /ft3
Density o f a i r a t upstream pressure
lb /ft3
/
/
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