Heat transfer in the finned fluidized bed tubular heat exchanger
by Joon Taik Kim
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in Chemical Engineering
Montana State University
© Copyright by Joon Taik Kim (1970)
Abstract:
Local and average heat transfer coefficients for bed -to-wall heat transfer from a fluidized bed tubular
heat exchanger with extended surfaces were investigated.
The fluidized bed tubular heat exchanger consisted of a 44-inch long, 5.5-inch inside diameter shell
with 19, 3/4-inch diameter stainless steel tubes arranged in a 1-inch triangular pitch. Air was used as
the fluidizing medium and glass spheres of 0.0185-inch average diameter were used in this study.
Tubes at the four possible tube locations tube were heated electrically. 3/16-inch stainless steel wire
was used as an extended surface. The stainless steel wire was wrapped around the outside of each 19
tubes in a helical sprial. Variables studied include particle concentration, gas mass velocity and twist
ratio.
The Results of This Study Are as Follows 1. Gradual increase in the weighted average heat transfer
coefficients with respect to the number extended surface were observed. Local heat transfer coefficients
decreased with the distance from the entrance of the fluidized bed. Tube locations had only a slight
effect on local heat transfer coefficients.
2. The average sectional coefficients according to the particle mode heat transfer with the extended
surface were higher than the coefficients calculated from the bare tube surface.
3. With local heat transfer coefficients and experimentally determined sectional particle fractions over
the 11 different sections of the fluidized bed, Nusselt numbers were correlated with an equation based
on a particle mode heat transfer mechanism.
4. It is concluded that particle Nusselt numbers are proportional to 0.48 of I-ε. S t a t e m e n t o_f Pevrni ns i on t o Copy
In . p r e s e n t i n g t h i s
requi r ement s
sity,
for
thesis
in p a r t i a l
f u l f i l l m e n t of t h e
f o r an a d v a n c e d d e g r e e a t Mont ana S t a t e U n i v e r ­
I agree t h a t
inspection.
the Li br ar y shal l
make, i t f r e e l y a v a i l a b l e
I f u r t h e r agree t h a t
per mi s s i on f o r e x t e n ­
s i v e copyi ng of t h i s
thesis
f o r s c h o l a r l y p u r p o s e s may be
g r a n t e d by my ma j o r p r o f e s s o r , o r ,
D i r e c t o r of L i b r a r i e s .
p u b l i c a t i o n of t h i s
in his absence,
by t h e
I t i s u n d e r s t o o d t h a y any c o p y i n g o r
thesis
for financial
a l l o we d w i t h o u t my w r i t t e n
permi ssion. .
Date
gain s h a l l
n o t be
FlL 27,; mo
HEAT TRANSFER IN THE FINNED FLUIDIZED BED
TUBULAR'HEAT EXCHANGER
JOON T. KIM
A t h e s i s s u b m i t t e d t o t h e Gr a d u a t e F a c u l t y i n p a r t i a l
f u l f i l l m e n t of t h e r e q u i r e m e n t s f o r t h e d e g r e e
of
MASTER OF SCIENCE
in
Chemi cal
Engineering
Appr oved:
Ch a i r ma n ,
Exa mi ni ng Commi t t e e
MONTANA STATE UNIVERSITY
Boz e ma n, Mont ana
Mar ch,
1970
J o o n Ta l k Ki m, t h e a u t h o r ,
Seoul,
Kor ea.
was bor n March 1 7 , 1 945 , in
He i s t h e son o f Mr.
Young J a Chun.
He r e c e i v e d h i s e l e m e n t a r y and s e c o n d a r y
e d u c a t i o n a t Seoul , Kor e a.
School
i n F e b r u a r y , 1963.
Yons ei
University
He g r a d u a t e d f r om Pai
In Ma r c h,
J a n u a r y , 1 96 7 t o S e p t e mb e r ,
1 968,
he e n r o l l e d a t
conducted vari ous
feasibility
industries
services
e n g i n e e r and
i n gas c o n v e r s i o n .
E n g i n e e r i n g De p a r t me n t a t
Mont ana S t a t e U n i v e r s i t y as a r e s e a r c h a s s i s t a n t
ber
From
s t u d i e s on AID and OECF l oa n
specializing
i n Chemi cal
Engineering.
he wor ked w i t h t h e
Medium I n d u s t r y Bank as a t e c h n i c a l
He e n r o l l e d
1963,
Chai Hi gh
i n Seoul , K o r e a , and g r a d u a t e d F e b r u a r y ,
1967 wi t h a B. S . d e g r e e i n Chemi cal
granted
Chang Hwa Kim and Mrs.
i n Se p t e m­
1 968 wo r k i n g t o wa r d Ma s t e r o f S c i e n c e d e g r e e .
ACKNOWLEDGEMENTS
I would l i k e to t hank Dr. Wi l l i am E. Ge n e t t i o f Montana
S t a t e U n i v e r s i t y f o r h i s a s s i s t a n c e and e ncouragement t hr o ug h o u t t h e d u r a t i o n of t h e
investigation.
I wi s h t o e x p r e s s
my g r a t i t u d e to Mr. Ronald D. Aa f e d t f o r h i s a s s i s t a n c e whi ch
he l pe d me to c o mp l e t e my s t u d y .
So Young Hahn f o r h e r h e a r t f u l
research.
Special
I w o u l d / l i k e to thank Miss
h e l p t o f i n i s h my s t u d y and
t h a n k s go t o my p a r e n t s f o r t h e i r e n ­
c o u r a g e me n t t h r o u g h o u t t h e p e r i o d o f r e s e a r c h .
I wi s h t o a c k n o wl e d g e t h e f i n a n c i a l
support
I received
from t he E n g i n e e r i n g Experi ment S t a t i o n a t Montana S t a t e
University.
I V
TABLE OF CONTENTS
I•
II.
I n t r o d u c t i o n ......................................................
L i t e r a t u r e Su r v e y and Th e o r y
...................................
3
...................................................
28
III.
E x p e r i me n t a l
Ap p a r a t u s
IV.
E x p e r i me n t a l
P r o c e d u r e ................................
V.
Calculations
VI.
Page
-j
45
.................................................................
40
A n a l y s i s o f D a t a .......................53
VI I .
R e s u l t s and C o n c l u s i o n ..................................................
30
VIII' .
L i t e r a t u r e C i t e d .................................................................
33
'
APPENDICES
App e n d i x I
No me n c l a t u r e
Appe ndi x I I
Ev a l u a t i o n of
Appe ndi x I I I
■ Appe ndi x IV
App e n d i x V
86
0 and R-
93
A Typi c al Dat a S h e e t
C a l i b r a t i o n Tabl es f or
T h e r mo c o u p l es
Compl e t e Da t a
( Ta b l e IV)
95
'
97
. 119
V
.LIST OF FIGURES
Page
Fi gure I .
S o l i d movement and gas f l o w as
v i s u a l i z e d by b u b b l i n g bed model .
Figure 2 .
Co r r e l a t i o n for heat t r a n s f e r
c o n t a i n i n g wa l l and f l u i d i z e d
b e t we e n
bed
18
Fi gure 3 .
C o r r e l a t i o n f o r h e a t t r a n s f e r b e t we e n
i n t e r n a l v e r t i c a l t u b e s and f l u i d i z e d
bed.
19
C o r r e c t i o n f a c t o r Cr f o r non a x i a l
l o c a t i o n of i mmer s ed - t ubes .
20
F i g u r e 4.
F i g u r e 5.
7
ICPP m u l t i p l e - t u b e d a t a compar ed wi t h
■V r e e d e n b e r g ' s c o r r e l a t i o n f o r h e a t
t r a n s f e r to a s i n g l e t ube
22
F i g u r e 6.
Fl ow d i a g r a m o f t h e f l u i d i z i n g a p p a r a t u s
29.
Fi gure 7 .
(A)
(B)
31
Fi gure 8 .
Tube l a y o u t :
s howi ng l o c a t i o n s
h e a t i n g el ernen t .
F i g u r e 9.
Di agr am of e l e c t r i c a l
circuit.
36
Fi gu r e 10.
Ex p l o d e d vi ew of t h e t u b e wal l
t e mpe r a t ur e probe.
39
F i g u r e 11 .
Av e r a g e N u s s e l t number s c o r r e l a t i o n
without f l ui di za t i on. .
54
F i g u r e 12.
Vertical
profiles
56
F i g u r e 13.
Local
heat t r a n s f e r c o e f f i c i e n t s .
59
F i g u r e 14.
Local
he a t , t r a n s f e r c o e f f i c i e n t s
61
F i g u r e 15.
Local
heat t r a n s f e r c o e f f i c i e n t s
63
Ge n e r a l Equi pme nt
Gl a s s p a r t i c l e s
fluidized
of
bed t e m p e r a t u r e
34
vi
F i g u r e 16.
Local
heat transfer c o e f f i c i e n t s .
64
F i g u r e 17.
Local
heat t r a n s f e r c o e f f i c i e n t s .
66
F i g u r e 18.
Local
heat t r a n s f e r c o e f f i c i e n t s .
68
F i g u r e 19.
Local
heat t r a n s f e r c o e f f i c i e n t s .
70
F i g u r e 20.
Local
heat t r a n s f e r c o e f f i c i e n t s .
71
F i g u r e 21.
Av e r a g e s e c t i o n a l c o e f f i c i e n t s
batch f l u i d i z a t i o n
for
73
F i g u r e 22.
C o r r e l a t i o n f o r a v e r a g e c o n t a c t t i me .
77
F i g u r e 23.
The p r e s e n t m o d i f i e d c o r r e l a t i o n f o r
s e c t i o n a l p a r t i c l e N u s s e l t n u mb e r s .
7 9'
F i g u r e '24.
The c o r r e l a t i o n f o r n and R.
93
F i g u r e 25.
Nomograph t o c a l c u l a t e Gmf
94
vii
LIST OF TABLES
PageTa b l e I .
E x p e r i me n t a l
Pr ogr am
44
Tabl e II .
D i f f e r e n c e of Local Heat T r a n s f e r
C o e f f i c i e n t Bet ween D i f f e r e n t
Ex t e n d e d S u r f a c e s
65
Tabl e I I I .
The We i g h t e d Av e r a g e Co n t a c t Ti mes
74
Tabl e
Compl e t e Dat a
119-142
IX
V111
ABSTRACT
Local and a v e r a g e h e a t t r a n s f e r c o e f f i c i e n t s f o r bedt o - w a l l h e a t t r a n s f e r f r om a f l u i d i z e d bed t u b u l a r h e a t e x ­
c h a n g e r wi t h e x t e n d e d s u r f a c e s wer e i n v e s t i g a t e d .
"[he f l u i d i z e d bed t u b u l a r h e a t e x c h a n g e r c o n s i s t e d of
a 4 4 - i n c h l o n g , 5 . 5 - i n c h i n s i d e d i a m e t e r s h e l l wi t h 19, 3/ 4 m c h d i a m e t e r s t a i n l e s s s t e e l t u b e s a r r a n g e d i n a 1- i n c h
triangular pitch.
Ai r was us ed as t h e f l u i d i z i n g medium and
g l a s s s p h e r e s o f 0 . 0 1 8 5 - i n c h a v e r a g e d i a m e t e r wer e used in
t hi s study.
Tubes a t t h e f o u r p o s s i b l e t u b e l o c a t i o n s t u b e wer e
heated e l e c t r i c a l l y .
3 / 1 6 - i n c h s t a i n l e s s s t e e l wi r e was
us e d as an e x t e n d e d s u r f a c e .
The s t a i n l e s s s t e e l wi r e was
wr a ppe d a r o u n d t h e o u t s i d e o f eac h 19 t u b e s i n a h e l i c a l
sprial.
Variables studied include p a r t i c l e concentrati on
gas mass v e l o c i t y and t w i s t r a t i o .
The R e s u l t s o f Th i s Study Ar e as Fo l l o ws
1.
Gr a d u a l i n c r e a s e i n t h e w e i g h t e d a v e r a g e h e a t t r a n s f e r
c o e f f i c i e n t s wi t h r e s p e c t t o t h e number e x t e n d e d s u r ­
f a c e wer e o b s e r v e d .
Local h e a t t r a n s f e r c o e f f i c i e n t s
d e c r e a s e d wi t h t h e d i s t a n c e f r om t h e e n t r a n c e of t h e
f l u i d i z e d bed.
Tube l o c a t i o n s had onl y a s l i g h t e f f e c t
on l o c a l h e a t t r a n s f e r c o e f f i c i e n t s .
2.
The a v e r a g e s e c t i o n a l c o e f f i c i e n t s a c c o r d i n g t o t h e p a r t i c l e'-mode h e a t t r a n s f e r wi t h t h e e x t e n d e d s u r f a c e wer e
h i g h e r t h a n t h e c o e f f i c i e n t s c a l c u l a t e d from t h e b a r e •
t ube s u r f a c e .
3.
Wi t h l o c a l h e a t t r a n s f e r c o e f f i c i e n t s and e x p e r i m e n t a l l y
d e t e r m i n e d s e c t i o n a l p a r t i c l e f r a c t i o n s o v e r t h e 11
d i f f e r e n t s e c t i o n s o f t h e f l u i d i z e d be d, N u s s e l t number s
wer e c o r r e l a t e d wi t h an e q u a t i o n ba s e d on a p a r t i c l e
mode h e a t t r a n s f e r me c ha ni s m,
4.
I t is concluded t h a t p a r t i c l e
p r o p o r t i o n a l to 0 . 4 8 o f 1 - e .
N u s s e l t number s a r e
Introduction.
The s t udy o f d e s i g n methods f o r improved f l u i d i z e d bed
h e a t e x c h a n g e r s as i n d u s t r i a l
he a t t r a n s f e r equi pment has
become g r e a t l y i mp o r t a n t , b e c a u s e o f i t s
i s o t h e r ma l
a c t e r i s t i c a l o n g wi t h v a r i o u s a p p l i c a t i o n s
physical
in chemi cal
and
operations.
Fluidization
tional
char­
i s t he phenomenon in which t he g r a v i t a ­
f o r c e a c t i n g on a dens e p a c k e t o f p a r t i c l e s
is
c o u n t e r a c t e d by an upward f l u i d s t r e a m, which c a u s e s t h e s e
particles
t o be ke pt more or l e s s
in a f l o a t i n g s t a t e .
The
uni f orm t e mp e r a t ur e d i s t r i b u t i o n o f the f l u i d i z e d bed i s due
t o t he t u r b u l e n t f l u i d - s o l i d s
continuous,
s us pende d mot i on and the
f r e q u e n t c o n t a c t s between the h e a t i n g s u r f a c e
and a new swarm o f p a r t i c l e s
by t he r a p i d c i r c u l a t i o n o f t he
f l u i d i z e d s t r e am.
Even i f t he f undame nt al s o f f l u i d i z a t i o n were not f u l l y
and c o mp l e t e l y , u n d e r s t o o d , many f l u i d i z e d - s o l i d s
have a c h i e v e d commerci al
success.
Fluid-bed c a t a l y t i c
c r a c k i n g u n i t s wi t h t he c o n v e r s i o n l e v e l
exampl e.
correlations
processes
The need f o r h e a t , mas s ,
of 50-60 percent i s
and momentum t r a n s f e r
in f l u i d i z e d beds was paramount f o r f l u i d i z e d
bed t e c h n i q u e s t o be a s u c c e s s .
•One o f t he n o t i c e a b l e a dv a n t a g e s o f f l u i d i z e d - b e d s to
o n e - p h a s e f l o w i s hi gh r a t e s o f h e a t t r a n s f e r .
It is well-
-2' known t h a t h i g h e r h e a t . t r a n s f e r c o e f f i c i e n t s
wi t h e x t e n d e d s u r f a c e s ,
however, t h i s
effect
can be a c h i e v e d
is
s ome t i mes
d i s m i s s e d as a means t o i mpr ove p e r f o r ma n c e o f a h e a t
e x c h a n g e r b e c a u s e o f t h e c o r r e s p o n d i n g l y h i g h e r power c o n ­
s u mp t i o n .
Numer ous s t u d i e s
of vari ous
have been made t o f i n d out t h e e f f e c t
types of extended s ur f a c e s
t r a n s f e r in t u r b u l e n t
t r a n s f e r e q u i p me n t .
but i t
is
spiral
wi r es
on t h e r a t e
f l ow f o r d i f f e r e n t
Thes e r e s u l t s
of heat
industrial
a r e i n no way g e n e r a l ,
at l e a s t e vi dent t h a t extended s ur f aces
or t w i s t e d s t r i p s
heat
ha ve some e f f e c t s
c r e a s i n g t he r a t e of h e at t r a n s f e r in i n d u s t r i a l
like
on i n ­
heat t r a n s ­
f e r e q u i p me n t f o r s i n g l e p h a s e s y s t e m s .
• A number o f s t u d i e s
coefficients
and a v e r a g e h e a t t r a n s f e r
f o r h e a t t r a n s f e r f r om an i n t e r n a l
bundl e of t u b e s
present
on l o c a l
t o a f l u i d i z e d - b e d have been made.
investigation
transfer rates
t ube in a
is a study of local
The
and a v e r a g e h e a t
i n t h e f l u i d i z e d bed t u b u l a r h e a t e x c h a n g e r
wi t h t h e e x t e n d e d s u r f a c e s .
Local
heat t r a n s f e r
c o e f f i cents
we r e me a s u r e d wi t h a movi ng t h e r mo c o u p l e p r obe i n s i d e an
electrically
me a s u r e l o c a l
heated tube.
Th i s p r o b e made i t
heat t r a n s f e r c o e f f i ci en t s
a tube f or vari ous
gas r a t e s
and p a r t i c l e
p o s s i b l e to
a t any p o i n t a l o n g
concentrations.
The r a t e o f h e a t t r a n s f e r was c o r r e l a t e d wi t h t h e a r e a o f
extended s u r f a c e s .
-3-
■Literature
F l u i d Mechani cal
Su r v e y and Theor y
Appr oach o f FTu i d i zed Beds
By a s s u mi n g a f u l l y
free,
spherical
in the t h r e e - d i me n s i o n a l
in t he t wo - d i me n s i o n a l
approach,
phases
d e v e l o p e d c i r c u l a r b u b b l e and s o l i d -
potential
to p o s t u l a t e
case,
Da vi ds on
useful
cylindrical
(3) a d o p t e d a c o n t i n urn
f l o w f o r bot h t h e f l u i d and p a r t i c u l a t e
t h e mot i on o f r i s i n g b u b b l e .
Da vi ds on model was n o t s u f f i c i e n t l y
first
case,
accurate,
Even i f
i t was t he
a p p r o a c h t o t h e mo t i o n o f a r i s i n g b u b b l e i n
the g a s - s o l i d
f l u i d i z e d bed.
Mur r ay ( 17)
a d o p t e d a c o n t i n u m a p p r o a c h f o r t h e t wo-
p h a s e mo t i o n o f t h e f l u i d and s o l i d s
i n a f l u i d i z e d bed.
Momentum and mass c o n s e r v a t i o n e q u a t i o n s wer e a p p l i e d t o
obtain solutions
the b e d .
f o r t h e mo t i o n c a u s e d by r i s i n g b u b b l e s i n
The s t a b i l i t y
analysis
and t h e e q u a t i o n s
been d e r i v e d t o p r o v i d e a means o f c l a s s i f y i n g
sys t e ms ,
b u t he di d n o t e v a l u a t e
equation,
so t h a t no q u a n t i t a t i v e
Ande r s on and J a c k s o n
purposes
it
the a c t ua l
(I)
the r oot s
had
fluidized
of h i s
secular
r e s u l t s wer e o b t a i n e d .
realized that
for practical
i s n e c e s s a r y t o s e e k some met hod o f s i m p l i f y i n g
p r o b l e m so t h a t i t
system of p a r t i a l
differential
J a c k s o n have us e d a f or mal
mean v a r i a b l e s
to t r a n s l a t e
can be d e s c r i b e d by a s mal l
equations.
m a t h e ma t i c a l
An d e r s o n and
d e f i n i t i o n of l ocal
t h e p o i n t Na v i e r - S t o k e s e q u a t i o n s
—
.4
.
i o r t h e f l u i d and t h e Ne wt oni an e q u a t i o n s o f mo t i o n f o r
t he p a r t i c l e s
somewhat d e v o i d o f number o f t e r ms whose
f or ms a r e y e t u n d e t e r mi n e d .
Ac c o r d i n g , t o t h e r e ne wa l
and F a i r b a n k s
icles
(18),
model
p r o p o s e d by Mi c kl e y
owi ng t o t h e b u b b l e s , p a c k e t s
of p a r t ­
a r e renewed c o n t i n u o u s l y be t we e n t h e b u l k o f t h e bed
and t n e v i c i n i t y
of the wal l .
The r a t e o f , h e a t
b e t we e n a no n - h o mo g e n e o u s f l u i d i z e d
on t he t h e r ma l
r e ne wa l
transfer
bed and a wa l l
c o n d u c t i v i t y of t hese packets
de pe nds
and on t h e i r
frequency.
I t appears
a quantity,
d e t e r m i n e d more s p e c i f i c a l l y
t h e r e n e wa l
a c c o r d i n g t o a more c o mp l e t e
r e p r e s e n u a ci on o f h y d r o d y n a m i c : p r o c e s s .
solid particles
is
f r e q u e n c y to, t o be
I f t h e swarm of
assi mi l a t e d to a q u a s i - f l u i d i t
is
possible
t o w r i t e t h e e q u a t i o n o f mo t i o n f o r t h e t wo - pha s e
s y s t e m.
A vol ume whi c h i s e n c o u n t e r e d h e r e i s s u f f i c i e n t l y
s ma l l
t o be c o n s i d e r e d as i n f i n i t e l y
e nough t o c o n t a i n
Ru c k e n s Le i n
r e ne wa l
a sufficiently
s m a l l , but a l s o large
l a r g e number o f p a r t i c l e s .
( 24) s u g g e s t e d t h a t a s y n t h e s i s
model
and t h e
linearized instability
b e t we e n t h e
t h e o r y mi ght be
. abl e t o g i v e i n f o r m a t i o n wi t h r e s p e c t t o t h e r e n e wa l
quency.
The e x p e r i me n t a l , r e s u l t s
( 18) show t h a t
fre^.
o f Mi c kl e y and F a i r b a n k s
w i s i n t h e r a n g e I - 10 s e c ^ and t h a t i t
does n o t de pend t o o much on t h e f l u i d i z a t i o n
velocity.
For
-5glass
spheres
c omput ed t h a t
o f 10 ^ me t e r d i a m e t e r R u c k e n s t e i n
t h e r e ne wa l
( 24)
f r e q u e n c y i s a b o u t 4 s e c ~^ and
p r e d i c t e d a weak d e p e n d e n c e of w on v e l o c i t y . ■
-6-
Newly P r o p o s e d Bu b b l e - b e d Model
Several
theoretical
i n ' Heat T r a n s f e r
me c ha ni s ms o f f l u i d i z e d
bed model s
' h a v e been . p r o p o s e d and some of t h o s e have been b r i e f l y
s u mma r i z e d by G e n e t t i
(8 ) for heat t r a n s f e r
in o r d e r to p r o ­
vi de a ba s i s f o r unde r s t a ndi ng c o r r e l a t i o n s
presented
in his
Kuni i
whi ch have been
r e c e n t wor k.
and L e v e n s p i e l
(11,
12)
have p r o p o s e d a model
f o r t h e f l o w of gas t h r o u g h a f l u i d i z e d be d ,
mo d e l ,
o r a t h r e e - r e g i o n model
the bubble-bed
whi ch have vi ewed as uni -
f r o ml y s i z e d b u b b l e s s u r r o u n d e d by c l o u d s and f o l l o w e d by
wa ke s .
A; . s ke t ch o f t h i s model
shown t h a t t h i s model
i s good enough t o f i t
for g a s - s o l i d heat t r a n s f e r ,
conversion
Kuni i
in c a t a l y t i c
I.
They have
the repor t ed data
g a s - s o l i d mass t r a n s f e r and
reactions.
and L e v e n s p i e l
d e n s e b u b b l i n g r egi on. .
i s g i v e n in Fi g .
have o n l y been c o n c e r n e d wi t h t h e
Th i s r e g i o n a p p l i e s whe r e a c o n t i n u o u s
e x c h a n g e o r f l o o wi n g up of s o l i d
particles
t r a n s fe r surface
T h i s c o n c e p t has been
is continuing.
s o me t i me s e x p l a i n e d on t h e b a s i s
■For t h e b u b b l e p h a s e , Kuni i
wi t h s e v e r a l
along the heat
of t h e " p a c k e f ' t h e o r y
and L e v e n s p i e l
( 9).
have s t a r t e d
n e c e s s a r y a s s u m p t i o n s t o s i m p l i f y t h e pr obl e m
f r om t h e Da v i d s o n model
(4).
They have t a k e n t h e b u b b l e s i z e
t o be u n i f o r m t h r o u g h o u t t h e bed o r s e c t i o n o f bed and c a l l e d ,
it
the e f f e c t i v e
cr owd o f b u b b l e s
bubble s i z e .
The v e l o c i t y , o f r i s e of a
has been r e l a t e d
t o t h e v e l o c i t y o f r i s e of
Bubble
phase
Wake
Emulsion
phase
Fjgure I.
S o l i d movement ana gas f l ow as v i s u a l i z e d by
b u b b l i n g bed m o d e l .
- 8a s i n g l e b u b b l e by
umf + u b r " uo
+ 0 . 7 1 1 ( gd^) %
mf
U)
whe r e Ujjr,. = 0. 711 ( d b ) '2.
I g n o r i n g s ma l l
bubbl e
amount s o f s o l i d s
i nsi de the r i s i n g
( me a s u r e d t o be f r om 0 . 2 % t o I % by d i f f e r e n t
igators),
t h e y have t a k e n t h e . b u b b l e voi d f r a c t i o n
The a v e r a g e bed v o i d a g e
\n bubbles
invest­
Ejj = I .
has been r e l a t e d t o t h e v o i d a g e
and e mu l s i o n p h a s e by
e f = Se fa + ( I - S ) E g = S _+■ ( I - S ) E e
whe r e S = t h e vol ume f r a c t i o n
By a s s u mi n g E
of bubbl es
= Emf , v o i d a g e s
( 2)
i n t h e bed.
and bed h e i g h t s
have -
been c o r r e l a t e d by
1- s
and
The b u b b l e p h a s e v a r i a b l e s d b ,
to give u
o
■
1-
mf
U jj
( 3)
and 6 have been c o r r e l a t e d
and u
i .e.
mf
mf 5 1
mf
mf
For t he- e mu l s i o n : p h a.se ,' Kunid; and- Le v e n s p i:eIo ( 1 1 , 1 2 )
have a s s ume d t h e v o i d f r a c t i o n o f t h e wake t o be t h a t o f t h e
e mu l s i o n p h a s e and have c o r r e l a t e d t h e r e l a t i v e v e l o c i t y o f
upwar d p e r c o l a t i n g
gas,
u , and o f downward f l o wi n g s o l i d .
- 9-
us »
the s u p e r f i c i a l
u
gas v e l o c i t y of minimum f l u i d i z a t i o n
“ u
s
( 5a)
5'
The downward v e l o c i t y o f s o l i d i s g i v e n by
aS u^
Us
1- 6 -ctS
whe r e a =
Var i abl es
d ^ , Ufa
vol ume o f wake, d r a g g e d up t o
t h e bed b e h i n d a r i s i n g b u b b l e
( vol ume o f b u b b l e )
$,
ue , and u
have been c o r r e l a t e d - t o g i v e
uo and um f 3 i ' 6 U
b
I
S
(
- a 6 >umf] '
E q u a t i o n 6 has been a p p r o x i m a t e d t o g i v e t he e x p r e s s i o n
t h e whol e r a n g e o f f l o w s ,
and t h e r e s u l t i s
identical
6)
for
to
Equat i on 4
uo " ( 1 “ 6 ) u mf
S
uo
umf
S
( 7)
-10Bed - t o - Wal I Heat T r a n s f e r i n G a s - S o l i d Fl u i d i z e d Beds
Much work has been done on b e d - t o - w a l l
r o r numer ous h e a t i n g s u r f a c e
equations
heat t r a n s f e r
ar r angement s .
Emp i r i c a l
have been d e v e l o p e d t o p r e d i c t h e a t t r a n s f e r
coefficients
Frantz
f o r h e a t t r a n s f e r f r om t h e s e s u r f a c e s .
( 7)
heat t r a n s f e r
has s u mma r i z e d wor k done on s u r f a c e - t o - b e d
in f l u i d i z e d beds.
numer ous propos ed c o r r e l a t i o n s
Genet t i
( 8 ) has d i s c u s s e d
and s e v e r a l
heat t r a n s f e r
me c ha ni s ms f o r f l u i d i z e d bed h e a t t r a n s f e r .
Us u a l l y f l u i d i z e d s y s t e ms have low enough a b s o l u t e
t emperatures
so t h a t
t h e r ma l
c o u n t e d as a s i g n i f i c a n t
i n many m e t a l l u r g i c a l
techniques
contributing
applications
r e c e n t l y have s t u d i e d b e d - t o - w a l l
a r e s u f f i c i e n t l y hi gh
S z e k e l e y and F i s h e r
radiation
of t he st udy of b e d - t o - wa l l
the convect i ve
Ho we v e r ,
r a d i a t i o n may be an i m p o r t a n t p a r t o f t h e
heat t r a n s f e r process.
on t h e b a s i s
factor.
o f t h e f l u i d i z e d bed
the processing t emper at ur es
so t h a t t h e r ma l
over-all
r a d i a t i o n may be s a f e l y d i s ­
( 25)
heat t r a n s f e r
heat t r a n s f e r in
r e g i me done by B o t t e r i 11 and e t
a I (2).
Whi l e none o f t h e propos ed mec hani s ms has been s u f ­
ficient
to p r e d i c t heat t r a n s f e r c o e f f i c i e n t s
different
situations
encountered,
f o r many
v a r i o u s me c ha ni s ms
e x p l a i n i n g t h e hi gh r a t e s o f h e a t t r a n s f e r b e t we e n
■-
..
-11e x c h a n g e r w a l l s and f l u i d i z e d
can be c l a s s i f i e d
(I)
beds have been s u g g e s t e d , and
as f o l l o w s :
van He er de n e t a I ( 10)
and Wi cke and P e t t i n g
t h e f l u i d i z i n g medium ( g a s )
and t h e s o l i d s
fluidized
Therefore,
a c t e d as a s t i r r i n g
t r a n s p o r t e d mos t o f t h e h e a t ,
bed was v i s u a l i z e d
there
(32):
as wel l
stirred
agent
and t he
liquid.
is the s t e a dy s t a t e conduct i on t hrough
t h e e mu l s i o n p h a s e .
(.2)
Leva e t a I ( 1 5 ) ,
Wal t o n
(16):
Dow and J a k o b
(5) and L e v e n s p i e l
and
t h e s c o u r i n g a c t i o n of t h e s o l i d s a l o n g
t h e h e a t e x c h a n g e r wal l
r e duc e s t h e t h i c k n e s s
l a m i n a r gas f i l m and i n c r e a s e s
of t h e
t he r a t e of he a t
transfer.
(3) ,
Mi c kl e y and F a i r b a n k s
(18):
t h e f l u i d i z e d .bed was
as s umed t o be composed o f " p a c k e t s " whi ch renewed i n t e r ­
m i t t e n t l y by t h e v i o l e n t d i s t u r b a n c e
of t he f l u i d i z e d
bed,
in t he core p o r t i o n
and wher e u n s t e a d y - s t a t e d i f f u s i o n
o f h e a t to newl y a r r i v e d mo b i l e e l e me n t s o c c u r r e d .
( 4)
Z i e g l e r e t a I ( 34)
and B o t t e r i l I and Wi l l i a ms
u n s t e a d y - s t a t e c o n d u c t i o n by s i n g l e p a r t i c l e s
c o n t a c t wi t h h e a t e xchange r w a l l s .
been f u r t h e r mo d i f i e d by
Genettf=
Th i s model
(2):
in d i r e c t
has
( 8 ) t o g i v e more
c o mp l e t e p r e d i c t i o n s wi t h r e s p e c t t o e x p e r i m e n t a l
da t a . -
-12Th i s m o d i f i e d model
The r e s u l t s
facts.
i s a d o p t e d i n t h e p r e s e n t wor k.
o f t h i s model
p r e d i c t two e s t a b l i s h e d
The N u s s e l t number i s
c o n d u c t i v i t y of t he s o l i d s
i n d e p e n d e n t o f t he r ma l
(19,34)
and i s p r o p o r t i o n a l
to a bout t he s q u a r e r o o t of t he p a r t i c l e f r a c t i o n ,
I - c (20).
The r e s u l t s
o f t h e model
also predict a
maximum N u s s e l t n u mb e r , whi ch a l s o i s an e s t a b l i s h e d
fact
(15),.''
-13-
1.
A R a t h e r Di f f e r e n t
Bed Model
E x p i a n a t i on A c c o r d i nq t o t h e Bubbl e
Y o s h i d a 1 K u n i i 1 and L e v e n s p i e l
( 33)
have t r i e d
t h e me c ha ni s ms p r o p o s e d by Mi c k l e y and F a i r b a n k s
van h e e r d e n e t a I ( 10) and Wi cke and P e t t i n g
a p p l i e d t h e bubbl e, model
transfer.
However ,
to p o s t u l a t e
They have s t a r t e d
film-penetration
transfer^
this
I
and have
and some of
not we l l - k n o wn .
t h e o r y f o r gas a b s o r p t i o n i n t o l i q u i d s
(26).
The e q u a t i o n whi ch
f i l m - p e n e t r a t i o n model
f o r mass and h e a t
is
3 T
3 T
wher e
(32),
t h e p r e d i c t i o n of t h e b a s i s of t h e
p r o p o s e d by Toor and Ma r c h e l l o
represents
( I S ) 1 and
b e d - t o - w a 11 h e a t
t h e wor k i s n o t c o m p l e t e ,
t he q u a n t i t a t i v e par amet er s are s t i l l
to uni fy
3.2T
________
Pe ^p s
O—
< x —
< Ie
/e
pS^ps ^ ^ - s ITif )
= eff ect ive thickness
o f e mu l s i o n l a y e r .
I ''
A.- t h i n l a y e r o f e mu l s i o n o f t h i c k n e s s I ^ s u d d e n l y c o n ­
t a c t s t h e e x c h a n g e r wa l l and a f t e r a s h o r t t i me i t i s s u d d e n ­
l y moved away t o r e p l a c e a f r e s h e l e me n t o f e mu l s i o n fr om t h e
c o r e p o r t i o n o f t h e b e d . T h e r e f o r e i t wi l l i n c l u d e t h e s t e a d y
s t a t e c o n d u c t i o n o f h e a t t h r o u g h an e mu l s i o n l a y e r a t t h e
wa l l and t h e u n s t e a d y s t a t e a b s o r p t i o n of h e a t by e mu l s i o n
el eme-nts .
-14And b o u n d a r y c o n d i t i o n s
are
T - Tb at
t =
0
Ii
X
CU
T = Tb at
II
X
T = . Tw a t
0
The s o l u t i o n o f t h e above e q u a t i o n
V
V
Tb
sin nrr(l-x/l )
-------— exp ( - n 2Tr2- J - I - )
nf
e
n+ 1
t
2 z t- D
n=I
From t h e above s o l u t i o n ,
fer coefficient
the i n s t a n t a n e o u s
local
( 9)
heat t r a n s ­
i s f ound t o be
1/ 2 r
ke Pe ^ps
ti
is
oo
I + 2
Trt
2 "I 2
z
exp(-n
at
n=I
e "
■n Tr
PO
I + 2
PO
-n
. a t'
I
e
The o b s e r v e d c o e f f i c i e n t o f h e a t t r a n s f e r h
a ve r a ge d v a l ue of t he i n s t a n t a n e o u s
W
(
10)
and t h a t
is
i s t h e t i me
coefficient,
g i v e n by
ht
h t l - I (: t ) d t
( T l )
o
whe r e I ( t )
= t h e age d i s t r i b u t i o n
e l e me n t s on t h e s u r f a c e .
f u n c t i o n o f e mu l s i o n
I
-15Two t y p e s o f age d i s t r i b u t i o n
Case I .
r ene wa l .
r andom s u r f a c e r e n e w a l ,
and Case 2 .
A number o f e x p r e s s i o n s
transfer coefficients,
the d i f f e r e n t
bubbl e f l ow,
uniform s u r f a c e
f o r t he obser ved heat
hw> have been d e r i v e d a c c o r d i n g t o
criterions.
The b u b b l i n g bed model
st r eams.
f u n c t i o n s have been c o n s i d e r e d :
g i v e s a s i mp l e r e p r e s e n t a t i o n o f
t h e e mu l s i o n f l o w and t h e i n t e r a c t i o n of t h e s e
However ,
two e m p i r i c a l
e x p r e s s i o n s whi ch have
been r e p o r t e d by Wen and Leva ( 31) and Wender and Cooper ( 3 0 ) .
are u s u a l l y recommended f o r t he d e s i g n o f t he b e d - t o - w a l l
'
heat t r a n s f e r .
2.
Some ^ n e r a l i z e d De s i gn Equat i ons f o r Wa l l - t o - Be d Heat
Transfer
B e d - t o - e x t e r i o r wa l l
Wen and Leva ( 31)
heat t r a n s f e r :
a t t e mpt e d t o c o r r e l a t e some e a r l i e r
o b s e r v a t i o n s o f s o l i d s mo t i o n i n t h e bed wi t h h e a t t r a n s f e r
phenomena t h r o u g h a b o u n d a r y l a y e r .
the c h i e f r e s i s t a n c e
wa l l
They.considered t hat
t o heat e x c h a n g e bet ween a c o n t a i n i n g
and a f l u i d i z e d bed i s i n t h e l a mi n a r f i l m a t t he
vessel
boundary.
The t h i c k n e s s o f t h e f i l m i s
t he v e l o c i t y of p a r t i c l e s
a l o n g t h e wal l
t he " s c o u r i ng act i on; ' o f t he p a r t i c l e s .
o f p l o t t i n g and c r o s s p l o t t i n g ,
i n f l u e n c e d by
p a r i m a r i l y due t o
By t he usual method
t h e f o l l o w i n g r e l a t i o n was
-16o b t a i ned':
hd
k
P
V R
whe r e n = t h e f l u i d i z a t i o n
efficient
R = t h e bed e x p a n s i o n r a t i o .
Nomogr aphi c s o l u t i o n s
g i v e n i n App e n d i x I I .
‘:Of t h e d i m e n s i o n l e s s
f o r e v a l u a t i o n o f rj and R have been
Wender and Cooper ( 30) made a c u r v e
gr oup Y/F wi t h t h e p a r i Cl e Re ynol ds
number as shown i n F i g u r e 2 wi t h f i v e d a t a s e t s
included.
The t e r m Y and F a r e d e f i n e d a s :
( 13)
F=
I + 7 . Se - 0 . 4 4
Be d - t o - ' i n t e r i o r wa l l
( 14)
heat t r a n s f e r :
I n t e r n a l , v e r t i c a l - t u b e h e a t t r a n s f e r was f o u n d t o be
i ndependent of t ube l e n g t h ,
size di stribution.
particle
s ha pe and p a r t i c l e
Wender and Cooper (30) made a s t r a i g h t
l i n e p l o t o f t h e d i me n s i o n a l
Z/ CR gr oup wi t h t h e p a r t i c l e
Re ynol ds number as shown i n F i g u r e 3 wi t h s i x d a t a s e t s
i nc l ude d f o r the i n t e r n a l
The t e r m Z i s d e f i n e d a s :
vertical
heat t r a n s f e r s u r f a c e .
-17-
Z =
( 15)
( l - e ) ( C s / C g ) 0 - 80
The t e r m
a l l o ws
(p s / p
g ) ° - 66
for non-axial
t u b e l o c a t i o n and may be
e v a l u a t e d f r om F i g u r e 4 whi ch o r i g i n a l l y was g i v e n by
Vr e e d e n b e r g
(
(28).
The e q u a t i o n o f t h i s
0. 43
k[Ir*]
-)(-
0. 33Cp(-
-)
c g pg
Noe and Knudsen ( 2 2 )
f r om a v e r t i c a l
tube
i n a f l u i d i z e d bed.
Th i s
ly d i f f e r e n t
8°(^)(16)
g
have made a s t u d y o f h e a t t r a n s f e r
tubes
T h e i r d a t a was compar ed t o t h e c o r r e l a t i o n
( 30)
t h e i r e xper i ment al
correlation.
\0.23C.
}
( r 1-
is:
l o c a t e d in a bundl e of v e r t i c a l
o f Wender and Cooper
all
V
correlation
u s i n g a v a l u e o f Cr = 2 .
Al most
d a t a was w i t h i n + 50 p e r c e n t o f t h e
i s f a i r a g r e e me n t c o n s i d e r i n g t h e g r e a t ­
geomet r i es.
I mme r s e d ,
horizontal-tube
h e a t t r a n s f e r has been
s t u d i e d by Vreedenberg ( 29) a l o n g wi t h t h e e f f e c t o f t u b e
diameter,
particle
size,
shape,
and d e n s i t y ,
c i t y on t h e h e a t t r a n s f e r c o e f f i c i e n t ,
large-scale
beds.
and gas . v e l o ­
i n c l u d i n g d a t a on
The r ecommended c o r r e l a t i o n s
are:
-18-
0005
°.01
0.1
R
I
10
F i g u r e 2.
C o r r e l a t i o n f o r h e a t t r a n s f e r bet ween c o n t a i n i n g wal l
f l u i d i z e d bed.
and
100
) ------------------------------------ --
SX-?
a
,
X --
(f
* '
T x " :.;. ^
--------------
X
r »
A
>
-
V i
^ -::A
A ‘“
v
^
a
-6 1
r
a
l:x »
-
..............
C
r
%
,
lx^p
F i g u r e 3.
.>
x
-
(Z/CR)X10
s
zX
C o r r e l a t i o n f o r h e a t t r a n s f e r be t wee n i n t e r n a l
*
t u b e s and bed
-20-
Center
of
vessel
DIMENSIONLESS
C o r r e c t i o n f a c t o r Cr
POSITION
Fi gure 4
for nonaxial
l o c a t i o n of i mmer sed t u b e s
V2 I T
V t i
0.66
(-T-M.)0 ' 3
g.
0.44
( dt i ; pq uo ) ( ps
07)
- )( -
f o r Re y n o l d s number l e s s t h a n 2 , 0 0 0 ,
and
hwdt i
420 '( c PSp ) ° - 3
kg
0. 3
( d t i p q llo j j
pg
) ( ■
0 8)
d'P- ' p"s
^ g ■)
f o r Re ynol ds number g r e a t e r t h a n 2 , 5 0 0 .
Petrie,
F r e e b y , and Buckham ( 28)
relation best f i t t i n g
have p r o p o s e d t h e c o r ­
I CPP1. dat a f o r h e a t t r a n s f e r from t h e
v a r i o u s non- . f i nned m u l t i p l e h o r i z o n t a l
f l u i d i z e d bed h e a t e x c h a ng e r .
Nu.
G
14(-
( P r ) 1/ ^
tube bundl es in t he
Th a t i s
Dj
^)2/3
09)
3ITlf
The e x p e r i m e n t a l
d a t a shows a maximum d e v i a t i o n o f 64 p e r ­
c e n t f r om V r e e d e n b e r g 1s c o r r e l a t i o n ,
t h e dat a b e t t e r .
However , t h e a g r e e me n t o f t h e p r o p o s e d
d a t a wi t h V r e e d e n b e r g ' s c o r r e l a t i o n
a single
wh i l e E q u a t i o n 19 f i t s
tube is good.
f or heat t r a n s f e r to
T h e i r d a t a i s shown i n F i g u r e 5 .
The At omi c Ener gy Co mmi s s i o n ' s
cessing plant.
I daho Chemi cal
Pr o-
1000
800
600
(GDtyL y V f s / l )
0.03
F i g u r e 5.
0.10
ICPP m u l t i p l e - t u b e d a t a compar ed wi t h V r e e d e n b e r g 1s c o r r e l a t i o n .
-23-
3.
C o r r e l a t i o n Model , Used i n Th i s Wor k, For Wal I - t o - Be d
Heat T r a n s f e r
The model
initially
s u g g e s t e d by Z i e g l e r e t a I (34)
and B o t t e r i 11 and Wi I Ltams ( 2) f u r t h e r e x t e n d e d by Ge n e t t i
( 8 ) i s mo d i f i e d in t h i s
and Br aze I t on
( 34)
fer coefficients
present study.
Ziegler,
Koppel ,
showed t h a t t h e w a l I - t o - b e d h e a t t r a n s ­
v a r i e d wi t h s o l i d h e a t c a p a c i t y ,
was i n d e p e n d e n t o f s o l i d t h e r ma l
conductivity,
C , but
Ps
k .
A p a r t i c l e whi c h has been i n t h e b u l k medi um i s vi ewed
t o move a d j a c e n t t o t h e wa l l
s u r f a c e wher e t h e p a r t i c l e
s u d d e n l y b a t h e d by t h e f l u i d
a d j a c e n t t o t h e wa l l
wa l l
t emperature.
In t h e mean t i me t h e p a r t i c l e
h e a t by c o n v e c t i o n f r om t h e f l u i d
a t t he
receives
adj a ce nt to the w a l l .
A f t e r s ome t i me t h e p a r t i c l e
leaves
t h e b u l k f l u i d i z e d medi um.
The ma j o r p o r t i o n o f h e a t
t r a n s f e r is
several
is
t h e wal l
a s s ume d t o o c c u r by t h i s
and r e t u r n s
mec hani s m.
to
With
a s s umpt i ons t he boundary probl em d e s c r i b i n g t he
t emper a t ur e p r o f i l e , T ( r , 8 ),
j a c e n t t o t h e wa l l
i n a p a r t i c l e wh i l e i t
is solved.
is ad­
The t i me a v e r a g e d h e a t f l u x
i s o b t a i n e d as:
(20)
(H
* |_ ) 2
where
8=
the
average
contact
time
In o r d e r t o g e t t h e e x p r e s s i o n f o r t h e h e a t t r a n s f e r f l u x
b a s e d on t h e wa l l
surface
surface,
per u n i t area wi l l
of p a r t i c l e s
particle
fraction,
to
have t o be d e r i v e d .
p e r u n i t a r e a , Yp » w i l l
(I - e )0' 48.
at the
The number
be r e l a t e d t o t h e
I - e , and t h e p a r t i c l e d i a me t e r .
heat t r a n s f e r c o e f f i c i e n t
portional
t h e number o f p a r t i c l e s
The
has been c a l c u l a t e d t o be p r o ­
A relation
o f t h e f o l l o w i n g f or m
is proposed:
(21
For a c o m p l e t e l y c o v e r e d s u r f a c e wi t h h e x a g o n a l
Yp , and I - e
packing.
are
(
e = 1 4/ 27
22)
( 23)
Therefore
K1 = I . 59
( 24)
and
(25)
)
By s u b s t i t u t i n g
E q u a t i o n 24 and Equat i on 25 i n t o
E q u a t i o n 2 1 , . we can g e t t h e f o l l o w i n g e x p r e s s i o n f o r
T . 59 ( I - e ) 0. 48
Y,
:
( 26)
By m u l t i p l y i n g q p by Ypj we can w r i t e an e q u a t i o n f o r
1P ^ ' P
t h e h e a t f l u x f r om t h e wa l l s u r f a c e :
S 1Q O - O 0 - ^ k n (Tw- T h )
-(27]
9 = YpSp
6k
vi
The p a r t i c l e
+
8
^
p
)2
N u s s e l t number i s
5 ( l - e ) 0.48
Nu
( 28)
6k 8
r.)
( 1 +-
p Sc Sd P1
Wi t h t h e a i d o f d i me n s i o n a l
a n a l y s i s Ge n e t t i
duced t h e f o l l o w i n g . e q u a t i o n f o r
1/ 2
97
By s u b s t i t u t i n g
E q u a t i o n 28,
d,
g"
( 8 ) has i n t r o ­
■
(-V ) 4 / 3
as e x p r e s s e d i n Eq u a t i o n 29,
the f ol l owi ng c o r r e l a t i o n
number s can be o b t a i n e d :
( 29)
into
f or aver age Nus sel t
■“ 2 6 -
5 ( ^ n - f e ) 0 - 48
'Nu.
P
I +
580
Re
(-
)(-
Most o f t h e d a t a c a l c u l a t e d
wi t h t h e c o a r s e g l a s s
( 30)
-J1 - P A f ) 4 / 3 ' 2
by G e n e t t i
for f l u i di za t i on
s p h e r e s and t h e al umi num p a r t i c l e s
are
w i t h i n +20 p e r c e n t of E q u a t i o n 30.
Ki dd ( 14)
has s t u d i e d h e a t t r a n s f e r and p r e s s u r e dr op
f o r n i t r o g e n f l o wi n g
i n t u b e s c o n t a i n i n g t w i s t e d t a p e s and
has i n t r o d u c e d t w i s t r a t i o Y.
T wi s t r a t i o Y has been d e f i n e d
as t h e number o f t u b e d i a m e t e r p e r 180° t w i s t .
About t h e c o n s t a n t of E q u a t i o n 28 as a r e s u l t of
several
a s s umpt i ons Ge n e t t i
generalization
( 8 ) has r e p o r t e d 5.
For
E q u a t i o n 28 can be r e w r i t t e n :
Ci(l-e)0'
1Nu „ =
( 31)
—
( 1+ - 9 - ^
P^C^dp'
-)■
6k e
The d i m e n s i o n l e s s gr oup ----- g d 2
ps s p
r e l a t e d to the fol l owi ng v a r i a b l e s :
'I.
v
mass v e l o c i t y G
2.
p a r t i c l e d i a m e t e r d^
3.
twist ratio Y
4.
gas v i s c o s i t y u
i n E q u a t i o n 31 can be
.
-
21
Wi t h t h e a i d of d i me n s i o n a l
less
-
analysis
t he f o l l o wi n g d i me n s i o n ­
g r oup can be o b t a i n e d :
(-Izl-).
Y.
H
Wi t h t h e s e g r o u p s an e q u a t i o n o f t h e f o l l o w i n g f or m f o r t h e
6 k_6"
di mensi onl es s
-i s o b t a i ned :
gr oup
- S c Sd P
6f
% =
P5 = Sd P2
1
( 32)
— M= C ( ■
2
Substituting
2
'
E q u a t i o n 32 i n t o E q u a t i o n 31,
the f ol l owi ng
is obtained:
C1 ( V e )
%
0.48
Co ( Y-I
I
+
( 33)
\bl2
E x p e r i me n t a l
The e x p e r i m e n t a l
Ap p a r a t u s
e q u i p me n t o f t h e p r e s e n t
investigation
was d e s i g n e d and a s s e mb l e d i n o r d e r t h a t : t h e s t u d y o f l o c a l
and a v e r a g e h e a t t r a n s f e r c o e f f i c i e n t s
fluidized
c o u l d be made i n a
bed t u b u l a r h e a t e x c h a n g e r wher e an e l e c t r i c a l l y
h e a t e d bundl e of v e r t i c l e
t u b e s wer e s y m m e t r i c a l l y p l a c e d .
Some o f t h e e q u i p me n t c omp o n e n t s us e d i n t h i s
wer e us e d i n a p r e v i o u s
p r e s e n t study
s t u d y u n d e r t a k e n by G e n e t t i
The ma j o r i t e ms o f e q u i p me n t a r e a model
e x c h a n g e r , an a i r b l o w e r ,
an e l e c t r i c a l
s o u r c e , a n d . . me a s u r i n g d e v i c e s .
fluidized
( 8 ).
bed h e a t
s y s t e m and power
The me a s u r i n g d e v i c e s
include
m a n o m e t e r s , t h e r m o c o u p l e s and a p r e c i s i o n p o t e n t i o m e t e r .
general
A
f l o w d i a g r a m o f t h e e q u i p me n t i s shown i n F i g u r e 6
and a p h o t o g r a p h of t h e e q u i p me n t
i s shown i n F i g u r e 7 ( A) .
1. S i l e n c e r
2.
Compressor
3. D r a i n
4 . S h u t off v a lv e
5.O rific e m e te r
6.
Experimental t u b e
7. D i s e n g a g i n g s e c t i o n
8. D ist ri b u t i o n s e c t i o n
Tem p e r a t u re
probe
handle
T : T e m p e r a t u re p r o b e
R: P r e s s u r e t a p
H e a t i ng
element
© .
r
Ex h a u s t
P° rf
©
Tubes
inside
t t
Fi gure 6 .
Flow d i a g r a m of t h e f l u i d i z i n g a p p a r a t u s .
-30-
T jre' E x p e r i me n t a l
The e x p e r i m e n t a l
vertical
h e a t e x c h a n g e r col umn c o n s i s t e d o f a
t ube bundl e c o n t a i n i n g
The E x p e r i me n t a l
shell
Heat Ex c h a n g e r Column
was c o n s t r u c t e d
distributing
section,
Shel l :
h e a t i n g e l e me n t s and a s h e l l .
The o u t s i d e o f t h e e x p e r i m e n t a l
in t h r e e s e c t i o n s ,
t he e xpe r i me nt a l
t he c o n i c a l
section,
air
the d i s e n ­
gaging s e c t i o n .
The c o n i c a l
air distributing
section
is a t t a c h e d at the
l o we r p a r t o f t h e col umn t o e xpand t h e a i r f l o w f r om t h e
p i p e d i a m e t e r t o t h e col umn d i a m e t e r .
A i ron-constantan
t h e r m o c o u p l e was i n s e r t e d t h r o u g h t h e wal l
t o me a s u r e t h e a i r
inlet
The e x p e r i m e n t a l
of t h i s
section
temperature.
s e c t i o n was c o n s t r u c t e d f r om t h e
6 - i n c h OD and 4 4 - i n c h l ong c a s t a c r y l i c t u b e wi t h t h e 1/ 4
i nch t h i c k wa l l .
El e v e n i r o n - c o n s t a n t a n t h e r mo c o u p l e s wer e
i n s e r t e d t h r o u g h t h e wa l l
shown i n F i g u r e 6 .
screen shields
a i r only:
wa l l
of t h i s
e xpe r i me nt a l
The t h e r m o c o u p l e s a r e p r o t e c t e d by
i n o r d e r t o g i v e c o n t a c t wi t h t h e f l u i d i z i n g
El e v e n p r e s s u r e t a p s a r e a l s o p l a c e d
of t h i s
col umn as
e xpe r i me nt a l
i n t he
col umn as shown i n F i g u r e 6 .
Th e s e
pr essure taps
have f i n e s c r e e n c o v e r s s o l d e r e d on t o p r e v e n t
the f l u i d i z e d
particles
f r om r u n n i n g i n t o t h e t a p s .
The d i s e n g a g i n g s e c t i o n was c o n s t r u c t e d f r om t h e 9 - i n c h
-31 -
(A)
F i g u r e 7.
(A) Ge n e r a l e q u i p me n t
(B) Gl a s s p a r t i c l e s
-32-
OD and 1 2 - i n c h l ong c a s t a c r y l i c
thick wall.
t u b e wi t h t h e 1 / 4 - i nch
Four h o l e s , I 1 / 2 - i n c h i n d i a m e t e r , wer e d r i l l ­
ed i n t h e wa l l
o f t h e d i s e n g a g i n g s e c t i o n I 1/ 2 - i n c h e s f r om
t he top to l e t
the f l u i d i z i n g
air
escape.
The s e h o l e s wer e
c o v e r e d wi t h f i n e mesh s c r e e n t o p r e v e n t t h e h i g h l y f l u i d ­
ized p a r t i c l e s
f r om b e i n g bl own o u t o f t h e c ol umn.
One h o l e ,
i n c h i n d i a me t e r , , was made i n t h e t o p p l a t e whi c h i s c o v e r i n g
the di sengagi ng s e c t i o n ,
to put t he p a r t i c l e s
and t h a t h o l e was o c c a s i o n a l l y us ed
i n t o t h e bed and t o bl ow o u t t h e u n ­
necessary p a r t i c l e s
f r om t h e b e d .
An a l u m e l - c hr ome !
c o u p l e was i n s e r t e d
t h r o u g h t h e wa l l
t h e r mo ­
of t he d i s e n g a g i n g
s e c t i o n .to me a s u r e t h e a i r o u t l e t t e m p e r a t u r e .
The Tube Bundl e wi t h t h e He a t i n g E l e m e n t s :
b u n d l e i s 6 0 - i n c h l ong and c o n s i s t s
less
steel
The t ube
o f n i n e t e e n 321 s t a i n ­
t u b e s 3 / 4 - i n c h OD wi t h 0 . 0 1 2 - i nc h t h i c k a r r a n g e d
in I -inch t r i a n g u l a r
shown i n F i g u r e 7.
pitch.
The c o mp l e t e t u b e l a y o u t i s
The 3 / 1 6 - i n c h s t a i n l e s s
steel
wi r e has
been wr a ppe d a r o u n d t h e o u t s i d e o f eac h t u b e i n a h e l i c a l
spiral.
A f t e r e x a mi n i n g t h e e f f e c t of t h e f i r s t wi r e as an
ext ended s u r f a c e , the second,
the t h i r d ,
and t h e f o u r t h wi r e
was wr a p p e d a r o u n d eac h t u b e t o s e e t h e g r a d u a l
wal I - vt o - b e d h e a t t r a n s f e r .
E x p e r i me n t a l
Pr ogr a m.
The d e t a i l s wi l l
i n c r e a s e in
be e x p l a i n e d i n
One end of e a c h - t ube' , e x c e p t t h e
>-33he a t i n g t u b e s , was f i t t e d wi t h a p l a s t i c
fitting
i n t o t h e l o we r t u b e s h e e t .
The h e a t i n g t u b e s
•
(4 t u b e s as shown i n F i g u r e 8 ) a r e
f i t t e d wi t h c o p p e r e l e c t r o d e s
top e l e c t r o d e
pl ug t o f a c i l i a t e
on t h e t op and t h e b o t t o m.
has a p o r c e l a i n t u b e i n s e r t e d i n i t
The
to prevent
c o n t a c t b e t we e n t h e e l e c t r o d e and t h e al umi num t u b e h o u s i n g
the l eads
faciliated
i n s i d e the h e a t i ng t u b e .
to f i t
The bot t om e l e c t r o d e
is
i n t o t h e l o we r t u b e s h e e t and has a 1/ 4 -
i n c h h o l e t o . a c c e p t a No.
10 c o p p e r wi r e us ed as a power
lead.
The b o t t o m t u b e s h e e t i s made o f a p e r f o r a t e d s t e e l
s h e e t wi t h a 200 mesh wi r e s c r e e n we l de d t o i t
t h e movi ng p a r t i c l e s
section.
to prevent
f r om r u n n i n g o u t f r om t h e e x p e r i me n t a l
The h e a t i n g t u b e s a r e i n s u l a t e d f r om t h i s
sheet
wi t h r u b b e r r i n g s .
The A i r BI o w e r :
air
Ai r was s u p p l i e d by a S u t o r b i l t 57-TP
b l o we r d r i v e n by a 1 750 RPM, 7 1 / 2 HP AC i n d u c t i o n mo t o r .
Two and one h a l f
inch s t e e l
a i r to t he e xpe r i me nt a l
p i p e was used t o t r a n s p o r t t h e
heat exchanger.
The 2 1 / 2 - i n c h p i p e
was r e d u c e d t o two i n c h e s b e f o r e e n t e r i n g t h e a i r
section.
intake
The a i r f l o w r a t e was c o n t r o l l e d by two g a t e v a l v e s .
On e , a t w o - i n c h - b y - p a s s
valve,
c o n t r o l l e d t h e a i r f l o wi n g
t hr ough a by- pas s t o t he a t mo s p h e r e .
The. ot her control
-34-
.
Fi gure 8 .
Tube l a y o u t :
e l e me n t .
:
' • :
s howi ng l o c a t i o n s
of h e a t i n g
v a l v e was i n t h e 2 1 / 2 - i n c h a i r s u p p l y l i n e .
was me t e r e d by a s h a r p - e d g e d o r i f i c e
The a i r f l ow
located
i n t h e mi d d l e
o f t he a i r s uppl y l i n e .
The ETec t'r i c Sys t em and Power S o u r c e :
A voltage t r a n s ­
f o r me r was us e d t o s u pp l y e n e r g y t o t h e wi r e wr a ppe d s t a i n ­
less
steel
circuit
heating tubes.
A di agr am of t he e l e c t r i c a l
i s shown i n F i g u r e 9.
The r e s i s t a n c e
in the c i r c u i t
was a d j u s t e d so t h a t t h e c u r r e n t was a b o u t 48 amps.
The
emf and c u r r e n t wer e me a s u r e d by an AC v o l t m e t e r wi t h a
r a n g e o f z e r o t o 15 v o l t s
z e r o t o 50 amps .
and an AC ammet er wi t h a r a n g e of
H e a t in g
tubes
Constant
vo l t a g e
tranform er
-36-
A : Ammeter
V Volmeter
No. 10
Copper w ire
No.10 /
Copper wire
F i g u r e 9.
Di agr am of e l e c t r i c a l
circuit.
-37-
Me a s u r i n q De v i c e s
s u r e : The U- t u b e ma nome t e r s have been us ed t o
me a s u r e t h e p r e s s u r e drop a c r o s s t h e bed and an i n c l i n e d
( an a n g l e o f 30° )
U- t u b e ma nome t e r has been us e d t o me a s u r e
t he p r e s s u r e dr op a c r o s s t h e s h a r p - e d g e d o r i f i c e me t e r .
A
c o l o r e d manometer f l u i d wi t h a d e n s i t y o f 1 . 0 0 gm/ cm3 was
used .
T e mp e r a t u r e :
tubes
The wal l
t e mp e r a t u r e of t h e h e a t i n g
(4 t u b e s as shown i n F i g u r e 8 ) wer e measured u s i n g
c h r o me ! - a l u me l
t her mocoupl e s .
The t h e r mo c o u p l e . p r o b e was
d e s i g n e d t o move up and. down t h e h e a t i n g t u b e .
manner wa l l
t u b e wal l
temperatures at various posi t i ons
wer e m e a s u r e d .
In t h i s
i n s i d e t he
Two i n s u l a t e d t he r mo c o up l e s wer e
r un t h r o u g h t h e p r o b e c a s i n g whi ch r ounde d t o t h e s ha pe of
t he t u b e w a l l ,
and b o t h wer e embedded i n two c oppe r c o n t a c t .
Each copper c o n t a c t was h e l d a g a i n s t t h e i n s i d e t u b e wal l
wi t h a s p r i n g .
The p r o b e a s s e mb l y i s shown i n F i g u r e 10.
ly ment i oned,
e l e v e n i r o n - c o n s t a n t a n t he r mo c o upl e s were
i n s e r t e d t h r o u g h t h e wa l l
of t he e x p e r i me n t a l
me a s ur e t h e bed t e m p e r a t u r e s .
a c h r o me l - a l u me l
:
col umn t o
An i r o n - c o n s t a n t a n t h e r mo ­
c o u p l e was p l a c e d i n s i d e the a i r d i s t r i b u t i n g
■■ ■ .i :
As p r e v i o u s ­
s e c t i o n and
t h e r mo c o u p l e was p u t i n t o t h e mi d d l e of
v. I .. . - I .
.•
v 11
..'e r r .
o
. u y■ .
■
• -i r-
■■ . . .
-38-
the di sengagi n s e c t i o n .
let
and o u t l e t
Bot h wer e t o me a s u r e t h e gas
temperature.
k e p t i n an i c e b a t h a t 3 2 ° F .
Al I r e f e r e n c e j u n c t i o n s wer e
The t h e r mo c o u p l e emf was
r e a d u s i n g a Leeds and No r t h r o p Co.
0381600.
A switching
t he r moc oupl e c i r c u i t s .
in­
p o t e n t i o m e t e r model
s y s t e m was u s e d t o c o mp l e t e t h e
-39-
TOP
VIEW
Micarta
— i Ti. d i a .X "77" i n.
Spring
-— in.d ia.X -r- in-
16
^
— in.dia.X -y in -
Copper contact
0 . 7 3 8 in.
FRONT
F i g u r e 10.
VIEW
Ex pl ode d vi ew of t h e t u b e wal l
probe.
t emper at ur e
-4 .0 -
Exper i mental
Exper i me nt al
Program and Procedure
Program:
The o b j e c t i v e o f t h i s
to de t e r mi ne heat t r a n s f e r c o e f f i c i e n t s
study is
in a v e r t i c a l l y
arranged U n ite d t u b e b u n d l e f o r a i r f l o wi n g t h r o u g h a
fluidized
steel
bed a t v a r i o u s o p e r a t i n g c o n d i t i o n s .
The s t a i n l e s s
wi r e s wr a ppe d a r o u n d t h e o u t s i d e of each t u b e i n a
helical
spiral
'
have been us ed t o i n c r e a s e t h e r a t e of h e a t
transfer.
The v a r i a b l e s
transier
gas;
t o be c o n s i d e r e d
in g a s - s o l i d f l u i d i z e d
d e n s i t y , pg ; v i s c o s i t y ,
conductivity,
density,
kg ( 2)
properties
ps ; s p h e r i t y ,
city,
uq
( 4)
static
specific
heat,
of t he s o l i d s :
fl ow c o n d i t i o n s :
and ( 5)
bed h e i g h t ,
f e r s u r f a c e , type of f i n ,
Cp s ;
properties o f '
C
; t h e r ma l
di amet er ,
velocity,
superficial
velo-
g e o me t r i c p r o p e r t i e s :
and h e a t i n g t u b e l o c a t i o n .
in t h i s
gas v e l o c i t y ,
study are s t a t i c
h e a t i n g t ube l o c a t i o n ,
and t h e e x t e n d e d s u r f a c e a r e a .
He a t f l u x ,
t u b e wa l l
t emperat ure p r o f i l e ,
b u l k gas t e m p e r a t u r e p r o f i l e
d ;
( 3) c o n d i t i o n s
t he l engt h of he at t r a n s ­
V a r i a b l e s under c o n s i d e r a t i o n
bed h e i g h t s u p e r f i c i a l
(I)
mi ni mum f l u i d i z a t i o n
; voi d f r a c t i o n ,
bed d i a m e t e r ,
beds a r e :
specific heat,
a t mini mum f l u i d i z a t i o n :
um f ; v o i d a Se ’ emf
y;
in b e d - t o - w a l I heat
and v e r t i c a l
have been me a s u r e d i n o r d e r t o
•r 41 calculate
t h e r a t e o f h e a t t r a n s f e r and t o f i n d o u t t h e
e f f e c t of t he i n c r e a s i n g s u r f a c e a r e a .
Ai r has been us e d as t h e f l u i d i z i n g medi um and o n l y
one t u b e b u n d l e c o n f i g u r a t i o n
i nch s t a i n l e s s
steel
has been c o n s i d e r e d .
The 3/ 16-
wi r e has been us ed as an e x t e n d e d s u r ­
face.
Properties
solid particle
of S o l i d s :
Onl y one t y p e and one s i z e of
has been us ed i n t h i s
study.
Co a r s e g l a s s
s p h e r e s , m a n u f a c t u r e d by 3M Company, o f 0 . 0 1 8 5 - i n c h a v e r a g e
d i a m e t e r wer e u s e d . The d e n s i t y o f g l a s s p a r t i c l e s i s
3
156 I b / f t . A m i c r o p h o t o g r a p h o f t h e p a r t i c l e s ( F i g u r e ; SB)
shows t h a t t h e g l a s s
particles
S t a t i c Bed H e i g h t s :
and n i n e i n c h e s
are spherical.
Static
bed h e i g h t s o f f i v e ,
have been i n v e s t i g a t e d .
taken wi t hout p a r t i c l e s
■
seven
Dat a wer e a l s o
i n o r d e r t o compar e wi t h d a t a
r e p o r t e d by Donohue ( 6) and G e n e t t i
(8).
Static
bed h e i g h t s
wer e me a s u r e d wi t h a s c a l e whi ch was on t h e e x p e r i m e n t a l
h e a t e x c h a n g e r c ol umn.
F l u i d Mass V e l o c i t y :
was us e d i n t h i s
A wi de r a n g e o f gas v e l o c i t i e s
s t u d y t o d e t e r m i n e t h e most e f f e c t i v e
v e l o c i t y and t o f i n d t h e e f f e c t i v e n e s s o f e x t e n d e d s u r f a c e s
as a f u n c t i o n o f gas f l o w r a t e s .
He a t i n g Tube L o c a t i o n :
Since v e r t i c a l l y ar r anged
•,/ .'“ 4 2 f i n n e d t ube l a y o u t
i s s y mme t r i c a l
as i t
i s shown i n F i g u r e 8
o n l y f o u r h e a t i n g t u b e l o c a t i o n s wer e needed t o i n v e s t i g a t e
all
p o s s i b l e h e a t i n g t ube l o c a t i o n s .
t r a n s f e r has been s t u d i e d a t a l l
for various
static
The r a t e o f h e a t
f our d i f f e r e n t
bed h e i g h t s , g a s
velocities
locations
and t he
i n c r e a s i n g ammount o f e x t e n d e d s u r f a c e ( wr a ppe d s t a i n l e s s
steel
wires).
The h e a t i n g t u b e l o c a t i o n s
F i g u r e 8, and w i l l
tion
be r e f e r r e d b y - n u mb e r .
i s number ed o n e ;
the l o c a t i o n
a r e shown in
The c e n t e r l o c a ­
h a l f t h e d i s t a n c e from
t h e c e n t e r i s number ed two and t h e two o u t e r l o c a t i o n s
are
number ed t h r e e and f o u r .
The h e a t i n g t u b e wa l l
eleven p o s i t i o n s
were I 1 / 2 .
27 1 / 2 ,
a l o n g t h e t ub e .
3 1/2,
31 1 / 2 ,
t u b e t e m p e r a t u r e was me a s u r e d a t
7 1/2,
11 1 / 2 ,
For a l l
f uns t h e l o c a t i o n s
15 1 / 2 ,
19 1 / 2 ,
23 1 / 2 ,
35 1/ 2 and 39 1 / 2 i n c h e s f r om t h e bot t om
wer e us e d t o g e t t h e n e c e s s a r y d a t a t o o b t a i n t h e t e m p e r ­
a t u r e p r o f i l e along the t u b e .
The s e e l e v e n p o s i t i o n s a r e
c o r r e s p o n d i n g p o s i t i o n s o f t h e t h e r mo c o u p l e s whi ch wer e
i n s e r t e d t h r o u g h t h e wal l
of t he e x p e r i me n t a l
col umn t o
me a s u r e . t h e . t e m p e r a t u r e s of t h e bed.
lir e Type o f FJ_n:
The 3 / 1 6 - i n c h s t a i n l e s s , s t e e l
■has been us e d as an e x t e n d e d s u r f a c e .
The s t a i n l e s s
wi r e
steel
wi r e has been wr a ppe d a r o u n d t h e o u t s i d e o f e a c h 19 t u b e s
r 43r
in a h e l i c a l
spiral .
A f t e r e x a mi n i n g t h e f i r s t
the second,
the t h i r d ,
wi r e as an e x t e n d e d s u r f a c e ,
and t h e f o u r t h wi r e was wr apped
around each t ube to see t he gr adual
transfer
wal I - to-bed heat
i n c r e a s e wi t h t h e i n c r e a s i n g amount o f e x t e n d e d
surface.
For t h e f i r s t w i r e ,
t he rate of he a t t r a n s f e r
wer e me a s u r e d f o r d i f f e r e n t s t a t i c
velocities
at all
different
bed h e i g h t s and gas
h e a t i n g t ube l o c a t i o n s .
same pr oc e dur e was us e d f o r t h e s e c o n d , t h e t h i r d ,
f o u r t h wi r e.
and t h e
The f o l l o w i n g c h a r t shows t h e c o mp l e t e
pr ogr a m o f t h i s
various s t a t i c
The
study at d i f f e r e n t
bed h e i g h t s ,
heating l ocati ons
gas v e l o c i t i e s
i ng amount o f e x t e n d e d s u r f a c e .
for
and t h e i n c r e a s ­
-44-
Ta b l e I
No . o f
FBH
No. of
Wi re
SBH
5"
SBH
7"
SBH
9"
Wl
w2
I
w3
w4
wl
w2
w3
w4
2
i
Wl
w2
w3
3
w4
wl
w2
w3
4
w4
wI = one e x t e n d e d s u r f a c e
w3 = t h r e e e x t e n d e d s u r f a c e s
w2 - two e x t e n d e d s u r f a c e s
w4 = f o u r e x t e n d e d s u r f a c e s
SBH = s t a t i c
bed h e i g h t
FBH = f l u i d i z e d
1 = slightly
2 = fairly
3 . = we l l
bed h e i g h t
fluidized
fluidized
fluidized
4 = highly f l u i d i z e d
( a b o v e minimum f l u i d i z a t i o n )
••-41Ex p e r i m e n t a l
The f o l l o w i n g
r o u t i n e pr ocedur e is f ol l owed bef or e
maki ng eac h e x p e r i m e n t a l
1.
Procedure
run:
The d e s i r e d amount o f g l a s s
in t he e xpe r i me nt a l
and t h e c o n t r o l
f l ow r a t e .
c o l u mn ’.
gate valves
particles
is placed
The a i r b l o we r i s t u r n e d o n 3
i s a d j u s t e d t o g i v e t he d e s i r e d
The d e s i r e d f l u i d i z e d
bed h e i g h t
is obtained
by a d j u s t i n g t h e c o r r e c t o p e n i n g s f o r t h e s e two c o n t r o l
valves.
The v a l v e s a r e t i g h t e n e d t o m a i n t a i n t h e c o n s t a n t
fl ow r a t e d u r i n g t he e x p e r i me n t a l
2.
The power s u p p l y i s
in the e l e c t r i c
wi l l
circuit
period.
t u r n e d on.
The r e s i s t a n c e
i s a d j u s t e d so t h a t t h e c u r r e n t
be a b o u t - 4 6 - 5 0 a mpe r es and t h e v o l t a g e a b o u t 7 . 8 -
8 .6 v o l t s .
3.
A t hermos f l a s k i s f i l l e d wi t h c r u s h e d i c e and
wat er .
The t h e r mo c o u p l e r e f e r e n c e j u n c t i o n s
is pl aced in
t h e f l a s k t o g i v e a r e f e r e n c e t e m p e r a t u r e o f 32° F.
4.
ternal
The p o t e n t i o m e t e r i s b a l a n c e d a g a i n s t an i n standard c e l l .
5.
to t h e i r
6.
t u b e wa l l
The t u b e wa l l
initial
p r o b e t h e r mo c o u p l e s
have been s e t
positions.
When s t e a d y s t a t e
has been o b s e r v e d i n regard to
t e m p e r a t u r e e mf s , t h e r e c o r d i n g o f d a t a i s begun
-46The i o i l owi ng p r o c e d u r e has been used i n r e c o r d i n g t h e
necessary data:
1.
The v o l t a g e and c u r r e n t f r om t h e power s u p p l y a r e
me a s u r e d wi t h an AC v o l t m e t e r and an AC a mme t e r .
s u r e dr op a c r o s s t h e m e t e r i n g o r i f i c e
The p r e s ­
i s me a s u r e d wi t h a
w a t e r ma n o me t e r .
2.
The t u b e wa l l
wi t h a p o t e n t i o m e t e r .
p r o b e t h e r mo c o u p l e emf i s me a s u r e d
The probe i s t h e n p l a c e d i n t h e
s e c o n d p o s i t i o n and t h e p r o b e i s a l l o we d t o a t t a i n
state.
The same pr oc e dur e i s c o n t i n u e d u n t i l
positions
3.
Whi l e, t h e p r o b e i s comi ng t o s t e a d y s t a t e
gas t e m p e r a t u r e s ,
bet ween
t h e r e ma i n i n g dat a are m e a s u r e d .
The gas i n l e t t e mp e r a t u r e ,
gas o u t l e t t e mp e r a t u r e ,
11 b u l k
and bed p r e s s u r e drops a r e r e c o r d e d a t 11
t i me i n t e r v a l s
4.
11 p r obe
have been m e a s u r e d .
p r o b e emf me as ur e me nt s ,
e qua l
all
steady
d u r i n g t he course of t he r un.
The power s u p p l y v o l t a g e and c u r r e n t a r e c he c ke d
a g a i n and a v e r a g e d . ■ The o r i f i c e
p r e s s u r e dr op i s a l s o
c h e c k e d a t t h e end o f t h e r u n .
After all
t h e data a r e r e c or de d f o r one r u n , t h e e q u i p ­
ment i s t u r n e d o f f ,
a not he r fun.
or t he p r o c e d u r e i s r e p e a t e d a gai n f o r
In t h i s m a n n e r , d a t a a r e t a k e n f o r t h e
different static
bed h e i g h t s ,
gas f l o w r a t e s ,
and an i n -
... ■ in ­
c r e a s i n g . amount o f e x t e n d e d s u r f a c e a r e a a t d i f f e r e n t h e a t ­
i ng t u b e l o c a t i o n s .
App e n d i x I I I .
A typical
d a t a s h e e t can be f ound in
C a l c u l a t i ons
Ihe basi c c a l c u l a t i o n s
calculations
f r om t h e r mo c o u p l e e m f ' s ,
d i f f e r e n c e s-s h e a t f l u x ,
we i ght e d l oc a l
transfer
a r e gas f l ow r a t e , t e m p e r a t u r e
local
local
heat t r a n s f e r c o e f f i c i e n t s ,
heat t r a n s f e r c o e f f i c i e n t s ,
coefficient,
above c a l c u l a t e d
t emper at ur e
and s e c t i o n
aver age heat
pressure dr ops .
d a t a bed s e c t i o n v o i d f r a c t i o n s
s e c t i o n average heat t r a n s f e r c o e f f i c i e n t s
From t h e
and bed
have been c a l c u l ­
ated .
Al I c a l c u l a t i o n s
have been p e r f o r me d wi t h t h e a i d of
SDS SIGMA 5/ 7 and HEWLETT-PACKARD 2116B d i g i t a l
Sof t war es
are l i s t e d
us e d a r e B a s i c ,
Fortran
IV and APL.
c o mp u t e r s .
Al I of t h e s e
i n Appe ndi x IV.
Co mp u t a t i o n s Us i ng Re a d i n g s :
The key emf v a l u e s whi ch b r a c k e t t h e t e m p e r a t u r e range
me a s u r e d f o r t h e l o c a l
t emperat ure are 1. 52,
i ng a f i f t h - o r d e r
t h e good f i t
results
t u b e wa l l
1.98,
p o l y n o mi a l
2.45,
t e m p e r a t u r e and gas o u t l e t
2.89, 3.36,
Pa s s
through t hese si x poi nt s gives
over t he t e mpe r a t ur e r a n g e .
The c a l c u l a t e d
have been c ompa r e d with' c a l i b r a t i o n
t h e r mo c o u p l e c h r o m e ! - a Iumel
and 3 . 8 1 .
tables
for
t h e r m o c o u p l e s i n Appe ndi x V.
The key v a l u e s whi c h b r a c k e t t h e t e m p e r a t u r e r a n g e me a s u r e d
.•-49-
f o r the l ocal
bul k f l u i d i z e d
bed t e m p e r a t u r e and gas i n l e t
t e mp e r a t u r e .ar e 1. 65 , 1. 79 , I . 94,
2.52.
2.23,
2.38,
and
The f or m o f t h e La g r a n g i an f o r mu l a g i v e n by a s i x t h -
o r d e r p o l y n o mi a l
t h r o u g h t h e s e 7 p o i n t s g i v e s t h e good f i t
over t he t e mpe r a t ur e range.
The c a l c u l a t e d r e s u l t s
been c ompa r ed wi t h c a l i b r a t i o n
t he r moc oupl e s
i n App e n d i x V.
p o l a t i o n f o r mu l a
intervals,
tables
have
for iron-constantan
Si nce t he L a g r a n g e ' s
i s a p p l i c a b l e f o r e i t h e r e qual
the i n t e r p o l a t e d
t o any g i v e n E( x)
functional
inter­
or unequal
value corr espondi ng
i s g i v e n by T.
The b u l k f l u i d i z e d
f o r t h e 11 t u b e wa l l
ical
2.08,
bed t e m p e r a t u r e s a r e c a l c u l a t e d
probe p o s i t i o n s
met hod d e s c r i b e d a b o v e ,
a c c o r d i n g t o t h e nume r ­
and t h e n t h e l o c a l
t emper at ur e
d i f f e r e n c e . i s c a l c u l a t e d f r om t h e f o l l o w i n g e q u a t i o n :
AT I oc
V
( 34)
Tb
The h e a t f l u x was c a l c u l a t e d
dissipated
in t he h e a t i n g e l e me n t .
by d e t e r m i n i n g t h e power
The p r o d u c t o f t h e
me a s u r e d c u r r e n t and v o l t a g e d r o p g i v e s t h e power d i s s i p a t e d
i n t h e h e a t i n g e l e me n t and t h e c o n n e c t i n g l e a d s .
p r e s s i o n us e d f o r t h e h e a t f l u x t h e e l e c t r i c a l
the l eads
under c o n s i d e r a t i o n
0.87(1
V -
The e x ­
r e s i s t a n c e of
is:
0.03122
r
)
(35).
.-50-
The l o c a l
heat t r a n s f e r c o e f f i c i e n t
i s c a l c u l a t e d f r om
the f ol l owi ng e q u at i on:
( 36)
h I oc = 9 / ATl o c
The e q u a t i o n us e d t o c a l c u l a t e
f er c o e f f i c i e n t
the aver age heat t r a n s -
i s as f o l l o w s :
hOV
( 37)
- V A T av
whe r e
AT.
Th i s i n t e g r a l
ATl o c dZ
has been n u m e r i c a l l y e v a l u a t e d u s i n g a l e a s t -
s q u a r e p o l y n o mi a l
fit
o f d e g r e e n.
The p r e s s u r e dr op a c r o s s
the sharp-edged o r i f i c e
me a s u r e d wi t h a ma n o me t e r i n c l i n e d a t 30° .
b a l a n c e o f t h e two col umns
is
The p r e s s u r e
i n t h e i n c l i n e d U- t u b e manomet e r
gives
ipOHfice =
i h ( PL- P g ) s i n
(38)
whe r e Ah = t h e r e a d i n g o f manomet e r i n f e e t .
The a c t u a l
gas f l o w r a t e G i s c a l c u l a t e d f r om t h e s h a r p -
edged o r i f i c e c a l i b r a t i o n .
The g e n e r a l i z e d e q u a t i o n t o
calculate
t h e mass f l o w r a t e
t hr ough; a c o n s t a n t - a r e a d i f ­
ferential
t y p e o f f l u i d me t e r i s
r
5.1 -
A = KAmY[2%gT( P ^ - P g ) ] ! / 2
w + actual
mass f l ow
Am = t h e c r o s s
Pgl
( 39)
sectional
a r e a o f a f l ow m e t e r , f t
3
= gas d e n s i t y u p s t r e a m l o c a t i o n , I b fflZ f t
and f o r a c o m p r e s s i b l e f l u i d t h e e x p a n s i o n f a c t o r ,
2
Y, is'
us ed and i s g i v e n by
I - ( 0. 41
4
P-i - P?
+ 0 . 3 5 3 )YP I
( 40)
whe r e 3 = t h e r a t i o o f t h e d i a m e t e r s
T = Cp/ Cv
Kr e t z s c h me r ( 26) has shown t h a t
K _
"
C
c i - eV
(41 )
Z2
whe r e C = c o e f f i c i e n t o f d i s c h a r g e ,
However ,
di mensi onl ess.
t h e e q u a t i o n whi ch has been used t o ' c a l c u l a t e
t he
gas f l o w r a t e f r om t h e p r e s s u r e d r o p a c r o s s a c o n c e n t r i c ,
sharp-edged o r i f i c e
is
( 42)
1/ 2
3600K YA.
[ZScAPorificePST]
N
whe r e G
mass f l o w r a t e ,
I b fflZhr f t
2
Ao : c r o s s s e c t i o n a l a r e a of o r i f i c e o p e n i n g , f t '
2
Ah : c r o s s s e c t i o n a l a r e a of h e a t e x c h a n g e r , f t
9 c : 3 2 . 1 7 4 l b f f t / l b ffls e c 2
The - p r e s s u r e dr op a c r o s s
ferent positions
me t e r f l u i d
bed o v e r 11 d i f ­
a r e me a s u r e d wi t h ma nome t e r s u s i n g a mano­
having a s p e c i f i c
i ng e q u a t i o n g i v e s t h i s
APfa = -*j—
the f l u i d i z e d
g r a v i t y of 1. 00.
The f o l l o w ­
p r e s s u r e drop:
Ah ( p b - p g )
( 43)
whe r e Ah = t h e ma nome t e r r e a d i n g i n f t .
C o m p u t a t i ons From t h e C a l c u l a t e d D a t a :
The v o i d f r a c t i o n s ,
positions,
e , a r e c a l c u l a t e d f o r eac h of 11
wher e p r e s s u r e
taps are l o c a t e d ,
of t h e h e a t e x ­
c h a n g e r f r om t h e me a s u r e d v a l u e s o f bed s e c t i o n p r e s s u r e
drops.
The f o l l o w i n g e q u a t i o n i s a good a p p r o x i m a t i o n f o r
batch f l u i d i z a t i o n :
1-e
APb
g C
( 44)
Lg Ap
The mini mum f l u i d i z a t i o n mass v e l o c i t y i s c a l c u l a t e d
using the f ol l owi ng equat i on
(21):
0 . 0 0 1 2 5 Dp2 ( p s - p q) ° - 9 pq 1 - 1 g
• mf =
U
( 45)
•? 5"3 A n a l y s i s : o f Dat a
Av e r a g e N u s s e l t Numbers C o r r e l a t i o n Wi t h o u t F l u i d i z a t i o n
Dat a wer e t a k e n w i t h o u t f l u i d i z a t i o n
resulting
t o compar e t h e
a v e r a g e N u s s e l t number s wi t h the. f o l l o w i n g c o r ­
relation:
—
kg
= Cn D °* 6 ( de-G- ) 0 , 6 P r 1
Oe
v P z
( 46)
whe r e Dg = t h e e q u i v a l e n t d i a m e t e r i n i n c h e s ba s ed on
f o u r t i me s t h e h y d r a u l i c r a d i u s .
The t e r m (— ^
^
3 ) was c a l c u l a t e d f r om t h e
9
d a t a wi t h P '= 7 . 0 5 i n a l l c a s e s .
Thi s d i m e n s i o n l e s s p r o r
' dt G
d u c t i s p l o t t e d v e r s u s t h e d i me n s i o n a l t er m Dg— p— i n F i g ­
u r e Tl .
The c o r r e l a t i o n of G e n e t t i
i n F i g u r e Tl .
( 8)
is also represented
The c o r r e l a t i o n o f Ge n e t t i
p e r c e n t o f Do n o h u e ' s c o r r e l a t i o n
( 8)
i s w i t h i n +25
(6).
C a l c u l a t e d N u s s e l t number s u s i n g e q u a t i o n 46 a r e a l l
h i g h e r t h a n t h o s e c a l c u l a t e d f r om Ge n e t t i
Th i s
( 8)
and Donohue ( 6)
i s wha t woul d be e x p e c t e d s i n c e e x t e n d e d s u r f a c e a r e a
for heat t r a n s f e r
is a v a i l a b l e .
Genetti' s results
f o r a b a r e b u n d l e wi t h 3 / 4 - i n c h t u b e s .
Vertical
The s o l i d l i n e shows
F l u i d i z e d Bed T e mp e r a t u r e P r o f i l e s
Wi t h t h e a i d o f 11 t h e r m o c o u p l e s p r o t r u d i n g f r om t h e
Genett i ( 6"shel l , 3 / 4 " t u b e s )
( Nu
)( Pr)
-54-
IOOO
Fi gure 1 1 .
1500
2 000
4000
5000
6000
Ave r a ge N u s s e l t number s c o r r e l a t i o n wi t h f l u i d i z a t i o n .
7000 8000 9000
.r.55-
o u t e r wa l l
of v e r t i c a l
wer e d e t e r m i n e d .
Static
i n c h e s wer e e x a mi n e d .
f o r we l l
c o l u mn ,
fluidized
f l u i d i z e d bed t e m p e r a t u r e s
bed h e i g h t o f s e v e n i n c h e s and n i n e
Vertical
b u l k gas t e m p e r a t u r e p r o f i l e s
beds a r e shown i n F i g u r e 12.
shown mass v e l o c i t i e s
a r e a p p r o x i m a t e l y same.
For t h e u s e s
Two d i f f e r e n t
amount of e x t e n d e d s u r f a c e s wer e c o mp a r e d .
F i g u r e 12 (A) and (B) a r e s t a t i c
i n c h e s and n i n e
tended s u r f a c e .
bed h e i g h t s
o f s e v e n and n i n e i n c h e s ,
Al I p r o f i l e s
t emperat ure p r o f i l e ;
effect
was a p p r o x i m a t e l y 31 i n c h e s ,
Local
but wi t h f o u r t i me s
show a u n i f o r ml y
h o we v e r , f o r g r e a t e r e x ­
i s more n o t i c e a b l e .
bed h e i g h t o f s e v e n i n c h e s t h e f l u i d i z a t i o n
ization
ex­
F i g u r e 12 (C) and (D) a r e a l s o f o r s t a t i c
t ended s u r f a c e area t h i s
static
of s e ven
i n c h e s r e s p e c t i v e l y and f o r t h e f i r s t
the ext ended s u r f a c e a r e a .
distributed
bed h e i g h t s
For
height
and f o r ni n e i n c h e s t h e f l u i d ­
h e i g h t s wer e a r o u n d 3 8 - 4 2 i n c h e s .
He a t Tr a n s f e r C o e f f i c i e n t s , f o r Bat ch F l u i d i z a t i o n
Local
heat t r a n s f e r c o e f f i c i e n t s
t h e p r o b e number f r om t h e e x p e r i e mnt al
c o n s t a n t gas mass v e l o c i t y .
heat t r a n s f e r c o e f f i c i e n t s
t u b e e n t r a n c e of a
The we i g h t e d a v e r a g e l o c a l
of f o u r d i f f e r e n t t ube l o c a t i o n s
have been c a l c u l a t e d f o r each r u n .
Tocalheat transfer
are p l o t t e d versus
coefficients
Thi s w e i g h t e d a v e r a g e
o f one e x t e n d e d s u r f a c e
■
-56-
88
RUN 7WIK3
Ui
si
87
=
g
86
t-
85
~
....^
G - 1, 320
E
4
8
12
16 20
DI STANCE FROM ENTRANCE, INCHES
(B)
106
,o
16
20
24
28
32
36
40
DI STANCE FROM ENTRANCE, KiCHES
"I
103
UJ
io m
C 3
cj f- 102
^ O
d
UrLJ
°
Ti- i m
tfl S
I- ui
100
I
•o— V'
a
----- 1------- 1------Z -----" ^ 4
28
2?.
°
DISTANCE ' f r om ENTRANCE, INCHES
•c
O
L u .
I
DISTANCE
Figure
12.
1
° •• ©
G =1,230
RUN 7W4H3
3o
40
T
102 —
r
r~- i
Ui
t/) D
O-----*s
—
<5 S i o i
os
Ul
o- 100 - RUN 9W4H3
TEI
I
-O---- o-
-45-
G = l , 254
I
FROM
Vertical
28 32
ENTRANCE, INCHES
fluidized
36
bed t emperat ure p r o f i l e s
457-
are c ompa r ed t o t h e a v e r a g e l o c a l
heat t r a n s f e r c o e f f i c i e n t s
o f two s t h r e e and f o u r e x t e n d e d s u r f a c e s t o o b s e r v e t he
e f f e c t o f t h e i n c r e a s i n g amount o f t h e e x t e n d e d s u r f a c e .
Wi r e .1 i n d i c a t e s one e x t e n d e d s u r f a c e .
one more a d d e d , t h e r e f o r e ,
two e x t e n d e d s u r f a c e s
A p p r o x i m a t e l y t h e same s t a t i c
bed h e i g h t s ,
Wi r e 2 i n d i c a t e s
bed h e i g h t ,
and so on.
fluidized
and gas mass v e l o c i t i e s wer e us ed t o a s s u r e
t h e same c o n d i t i o n s
f or four d i f f e r e n t extended sur f ace
areas considered.
F i g u r e 13 shows l o c a l
the s l i g h t l y
ization)
of f i v e
heat t r a n s f e r c o e f f i c i e n t s for
(just a l i t t l e
fluidized
bed.
b i t above t h e mini mum f l u i d ­
The d a t a a r e f o r s t a t i c
i n c h e s and mass v e l o c i t i e s
For t h e s e mass v e l o c i t i e s
o f 526 and 481 l b ^ / h r f t 2 .
p a r t i c l e s wer e f l u i d i z e d t o t he
h e i g h t s o f a p p r o x i m a t e l y e i g h t and n i n e i n c h e s .
these heights
heat t r a n s f e r c o e f f i c i e n t s .
Since the f l u i d i z e d
one,
bed h e i g h t s wer e a r o u n d e i g h t and
t h e we i g h t e d a v e r a g e c o e f f i c i e n t s
probe. t wo,
Profiles
Above
t h e amount o f e x t e n d e d s u r f a c e had no s i g n i ­
f i c a n t e f f e c t on l o c a l
ni ne i n c h e s ,
bed h e i g h t
pr obe, t h r e e ,
f o r pr obe
and p r o b e f o u r have been compar ed
o f Wi r e I and Wi r e 2 show t h a t t h e c o e f f i c i e n t s
Wi r e 2 a r e s l i g h t l y
h i g h e r t h a n Wi r e I .
Profiles
of
of Wi r e 3
and Wi r e 4 a l s o show t h a t t h e c o e f f i c i e n t s . o f Wi r e 4 a r e
slightly
h i g h e r t h a n Wi r e 3 and bot h a r e r e l a t i v e l y
higher .
than t he c o e f f i c i e n t s
of Wi r e I and Wi r e 2.
a r e l o we r i n t h e s e c a s e s
velocities,
Coefficients
t h a n f o r r u n s a t h i g h e r mass
and a r a p i d dr op i n h e a t t r a n s f e r c o e f f i c i e n t s
i s o b s e r v e d a t t h e p o s i t i o n above p r o b e 4.
The h i g h l y f l u i d i z e d
i s shown i n F i g u r e 14.
1442,
all
bed o f f i v e
1 4 58, 1 410, and 1360 l b ^ h r f t 2 r e s p e c t i v e l y .
The o v e r ­
s e c t i o n was 44 i n c h e s , and i n t h i s
of r u n s p a r t i c l e s wer e f l u i d i z e d
a p p r o x i m a t e l y 33 and 38 i n c h e s .
f luidized condition for s t a t i c
investigation.
i nches
The d a t a a r e f o r mass v e l o c i t i e s o f
l e n g t h of t he t e s t
series
bed f o r s t a t i c
Gr a dua l
to.the
h e i g h t s of
The s e a r e t h e mos t h i g h l y
bed o f f i v e
increase
inches
in t h i s
i n t h e we i g h t e d a v e r a g e
c o e f f i c i e n t s wi t h r e s p e c t t o t h e number of. e x t e n d e d s u r f a c e
is observed.
Compar i ng t h e h e a t t r a n s f e r c o e f f i c i e n t s , l o c a l
heat t r a n s f e r c o e f f i c i e n t s
t han the o t h e r .
fficients
o f Wi r e 4 a r e r e ma r k a b l y h i g h e r
For Wi r e I , Wi r e 2, and Wi r e o t h e c o e ­
are s l i g h t l y
i n c r e a s i n g wi t h t h e number of w i r e s .
In t h e l o we r p a r t o f t h e f l u i d i z e d
in l ocal
heat t r a n s f e r c o e f f i c i e n t s
Wi r e 2 , and Wi r e 3.
bed s i g n i f i c a n t
i s o b s e r v e d f o r Wi re I ,
In t h e h i g h e r s e c t i o n of t h e F i g u r e
t h e amount o f i n c r e a s e on l o c a l
heat transfer c o e f f i c i e n t s
o f Wi r e 4 compar e t o Wi r e 3 was 29- 38 B t u / h r f t
decr ease in l ocal
increase
0F.
Gr a dual
h e a t t r a n s f e r c o e f f i c i e n t s wi t h d i s t a n c e
-59-
TRANSFER
COEFFICIENT,
SBH 5 INS.
VV 3
LOCAL
HEAT
@
Probe N um ber
F i g u r e 73.
Local
From
Entrance
heat t r a n s f e r
coefficients.
is observed.
particle
and i t
In t h e l o we r p a r t o f t h e f l u i d i z e d
concentration
profiles
(27).
i s g r e a t e r than the hi ghe r s e c t i o n .
causes the hi gher heat t r a n s f e r r a t e .
bed h e i g h t o f f i v e
inches
a r e o f Type I ,
For r e l a t i v e l y
served t h a t local
local
For s t a t i c
heat t r a n s f e r c o e f f i c i e n t
as d e s c r i b e d by Toomy and J o h n s t o n e
l ow s t a t i c
bed h e i g h t
heat t r a n s f e r p r o f i l e s
Th i s a g r e e s wi t h G e n e t t i
that
bed t h e
( 8 ).
heat t r a n s f e r c o e f f i c i e n t
Genet t i
it
has been o b ­
a r e o f Type I .
has a l s o
profiles
investigated
f o r s t a t i c , bed
h e i g h t o f f o u r i n c h e s wer e of Type I e x c e p t f o r t h e c o e ­
fficient
profile
The we l l
inches
fluidized
2.
bed f o r s t a t i c
i s shown i n F i g u r e 15.
o f 1 335,
cities
at tube l o c a t i o n
bed h e i g h t o f s e v e n
The d a t a a r e f o r mass v e l o c i t i e s
1 238 , and 1 235 l b ^ / h r f t ^ .
For t h e s e mass v e l o ­
p a r t i c l e s wer e f l u i d i z e d t o t h e h e i g h t s o f a r o u n d 30
inches.
Gr a dua l
increase
i n t h e we i g h t e d a v e r a g e c o e f f i c i e n t s
wi t h r e s p e c t t o t h e number o f i n c r e a s e d e x t e n d e d s u r f a c e
observed.
In t h e l o we r p a r t o f t h e f l u i d i z e d
particle
concentrations
a r e hi gh
of l o c a l
h e a t t r a n s f e r c o e f f i c i e n t s wi t h t h e
probe 3 l ocal
heat t r a n s f e r c o e f f i c i e n t s
t he i n c r e a s e
increasing
For i n s t a n c e ,
in
f o r Wi r e I , Wi r e 2,
Wi r e 3 and Wi r e 4 wer e 3 6. 43 , 3 9 . 2 2 , - 4 0 . 4 3 ,
respectively.
bed wher e
( I - e = 0 . 1^ 0 . 3)
amount o f e x t e n d e d s u r f a c e was o b s e r v a b l e .
is
and 4 5 . 2 3
The same t e n d e n c y was o b s e r v e d up t i l l
p r obe 8,.
-61 -
LOCAL
HEAT
TRANSFER
C O EFFCI ENT,
BTU/Hr. F t^ 0F
SBH 5 INS.
W4
Probe
F i g u r e 14.
Number
Local
From
Entrance
heat t r a n s f e r c o e f f i c i e n t s .
-
162-
For Wi r e I and Wi r e 2 p r o f i l e s
Johnstone
( 27) c o n c l u d e d t h a t
prevailed
in al l
runs
a r e o f Type I .
Toomey and
i n t h e s t u d y c u r v e s of Type I
i n whi ch t h e d i m e n s i o n l e s s gr oup
dpLf / Ay was g r e a t e r t h a n 0 . 0 0 8 .
Ho we v e r , t h e p r o f i l e s
of
Wi r e 3 and Wi r e 4 a r e of Type 11 wh i l e t h e v a l u e o f t he
di mensi onl ess
g r oup d pLf / Ay i s 0 . 0 0 9 1 .
The g e n e r a l
f l ow
p a t t e r n w i t h i n t h e s y s t e m a p p a r e n t l y d e t e r m i n e s t h e s ha pe
of t he c u r v e .
dpl ^/ Aj
Wi t h t h i s
i n mi nd t h e d i m e n s i o n l e s s gr oup
i s t oo s i mp l e r e p r e s e n t a t i o n t o d e t e r m i n e t h e
shape of c u r v e .
For G = 1490,
fluidized
the e n t i r e
for s t a t i c
shows t h e s e r u n s .
e xpe r i me nt a l
col umn was
bed h e i g h t o f s e v e n i n c h e s .
Particularly,
local, he at t r a n s f e r c o e f f i c i e n t s
p a r t o f t h e bed was o b s e r v e d .
significant
F i g u r e 16
increase
in
f o r Wi re 4 i n t h e de ns e
At p r obe 4 h e a t t r a n s f e r
c o e f f i c i e n t s , seem somewhat i n c o n s i s t e n t s i n c e t h e ma g n i t u d e
of i n c r e a s e
in the c o e f f i c i e n t s
f o r Wi re 2 and Wi r e 3
i s s u p p o s e d t o be l a r g e r t h a n Wi r e I ,
c e n t s o f t h o s e a r e l o we r t h a n Wi r e I .
and y e t t h e c o e f f i *
Heat t r a n s f e r p r o f i l e s
f o r t h e s e r u n s a r e o f Type I .
F i g u r e 17,
F i g u r e 18 and F i g u r e 19 a r e o f s t a t i c
h e i g h t of ni ne i nc h e s .
Ob s e r v a b l e i n c r e a s e
in l ocal
bed
heat
t r a n s f e r c o e f f i c i e n t wi t h r e s p e c t t o t h e e x t e n d e d s u r f a c e
- 63 -
LOCAL HEAT TRANSFER COEFFICIENT, BTU/ Hr. Ft
SBH 7 INS.
A
W2
Probe
Figure
15,
Local
Number
heat t r a n s f e r
From E n t r a n c e
coefficients.
"6 4-
1,490
LOCAL
HEAT
transfer
COEFFICIENT, B T U / H r . F t 2 C r
S B H 7 I MS .
w 3
Probe
Figure
16
Local
heat
Number
From E n t r a n c e
transfer coefficients.
■- 6 5 -
a r e a was o b s e r v e d .
For s t a t i c
bed h e i g h t o f n i n e i n c h e s
t h e d i f f e r e n c e o f t h e c o e f f i c i e n t bet ween Wi r e I ,
Wi re 2 ,
Wi r e 3 and Wi r e 4 wer e r e ma r k a b l y l a r g e c ompar ed t o s t a t i c
bed h e i g h t o f f i v e and s e v e n i n c h e s .
Tabl e II
D i f f e r e n c e o f Local Hea.t T r a n s f e r
C o e f f i c i e n t Bet ween D i f f e r e n t
Ex t e n d e d S u r f a c e
Ext e n d e d
Surface
Local
Wi r e I
Wi r e 2
Wi r e 3
Wi r e 4
He at T r a n s f e r C o e f f i c i e n t
Bt u / h r f t 2 °F
Pr obe 2
Pr obe 3
Pr obe 4
Pr obe 5
37.69
40. 16
36.34
40. 03
2 9. 33
36.87
1 8 . 54
21. 14
62.45
66. 91
67. 45
6 2 . 34
59. 81
81.13
77.58.
76.98
T a b l e 11 shows t h e d i f f e r e n c e of h e a t t r a n s f e r c o e f f i ­
c i e n t b e t we e n d i f f e r e n t
e x t e n d e d s u r f a c e f o r mass v e l o c i t i e s
o f 745 and 886 I b ^ / h r f t ^ .
are.fluidized
Local
particular
r un p a r t i c l e s
t o h e i g h t s of a p p r o x i m a t e l y 18 t o 21 i n c h e s .
heat t r a n s f e r
c o e f f i c i e n t s we r e hi gh w h i l e i n t h e
d e n s e p a r t o f ..the f l u i d i z e d
profiles
For t h i s
bed I - e was a r o u n d 0 / 3 .
o f Wi r e I and Wi r e 2 a r e o f . T y p e I .
The
-66-
SBH 9 INS
Q
W3
PROBE NUMBER FROM ENTRANCE
F i g u r e 17.
Local
heat t r a n s f e r
coefficients.
-:r:;&7T
In F i g u r e 18 p a r t i c l e s wer e f l u i d i z e d
t o 29 i n c h e s .
the p r o f i l e s
I f we c o n s i d e r up t o probe 8 i n t h e s e r uns
all
di me ns i onl es s
a r e o f Type 1 1 wh i l e t h e v a l u e o f t h e
g r oup d p Lf / AT i s we l l
ma t e l y 0 . 1 0 8 ) .
The p r o f i l e s
17 a r e a l s o o f Type I I .
increases
t o h e i g h t s o f 24
over 0. 008
(approxi­
o f Wi r e 3 and Wi r e 4 i n F i g u r e
Genet t i
( 8 ) has i n d i c a t e d t h a t
i n t h e ma g n i t u d e o f t h e g r o u p , Dt 2/ L f Sfa, a p p e a r
to i n c r e a s e t he t e n de nc y toward Type II p r o f i l e s .
For s t a t i c
bed h e i g h t o f n i n e i n c h e s and i n F i g u r e 19 t h e gr oup
2
Dt /' Lf Sb 15 ^ b o u t 0 . 0 0 2 5 .
T h i s a g r e e s wi t h G e n e t t i ( 8 ) s i n c e
t he p e r c e n t a g e o f Type I p r o f i l e s was 20 p e r c e n t , when t he
v a l u e o f t h e goup Dt 2/ L f Sb i s 0 . 0 3 0 6 .
In F i g u r e 19 t h e d i f f e r e n c e o f l o c a l
coefficients
between W i r e . I ,
Wi r e 2 , Wi re 3 , and Wi re 4 are
e v i d e n t l y c o mp a r a b l e a t each p r o b e .
local
heat t r a n s f e r c o e f f i c i e n t s
R e l a t i v e l y l ow c o e f f i c i e n t s
The h i g h l y f l u i d i z e d
inches
1665,
1693,
Wi r e 4 l o c a l
Wi r e 3.
Gr adual
d e c r e a s e in
wi t h d i s t a n c e
i s o bs e r v e d .
f o r Wi r e I a r e o b s e r v e d .
bed f o r s t a t i c
i s shown i n F i g u r e 20.
e xpe r i me nt a l
heat transfer
bed h e i g h t o f n i ne
The e n t i r e s e c t i o n o f t he
col umn was f l u i d i z e d .
Mass v e l o c i t i e s
1637 and 1506 I b ^ / h r f t 2 wer e e x a mi n e d .
heat t r a n s f e r c o e f f i c i e n t s
of
For
a r e l o we r t h a n
Ho we v e r , t h e u n i f o r m t e m p e r a t u r e d i f f e r e n c e from
-68-
HEAT TRANSFER COEFFICIENT, BTU/Hr. Ft .
SBH 9 INS.
W2
LOCAL
A
Probe N um ber
F i g u r e 18.
Local
From
Entrance
heat t r a n s f e r c o e f f i c i e n t s .
r.6?probe I
t o probe 6 ( l o c a l
heat t r a n s f e r c o e f f i c i e n t s
a r o u n d 35 B t u / h r f t 2 °F) wer e o b s e r v e d .
local
Gr adual
h e a t t r a n s f e r c o e f f i c i e n t s wi t h d i s t a n c e
are
decr eas e in
is also
observed.
F i g u r e 20 and F i g u r e 21 a r e t y p i c a l
w e l l - f l u i d i z e d bed.
Vertical
i n t h e c a s e of t h e
f l u i d i z e d gas t e mp e r a t ur e s
a r e u n i f o r m and t he t e mpe r a t ur e d i f f e r e n c e bet weeh t he' ,
fluidized
bed and t h e h e a t i n g wa l l
t h r o u g h o u t t h e bed a r e
g r a d u a l l y i n c r e a s i n g w i t h t h e s ma l l
magni t ude.
With t h e
i n c r e a s e d amount o f e x t e nd e d s u r f a c e s t h i s e f f e c t was pa r t icularly
fficients
noticeable.
T h e r e f o r e , local
heat t r a n s f e r c o e ­
wer e i n c r e a s i n g g r a d u a l l y wi t h t h e i n c r e a s e d a-
amount o f e x t e n d e d s u r f a c e s .
The Dependency, on Tube L o c a t i o n s
No s i g n i f i c a n t d e p e n d e n c y on t u b e l o c a t i o n has been
observed.
However,
mass v e l o c i t i e s ,
i n l ow s t a t i c
wa l l
bed h e i g h t and i n low
t e mp e r a t u r e s vary s l i g h t l y
t o t u b e . , wi t h no c o n s i s t e n t t r e n d .
h e i g h t s and a t hi gh mass v e l o c i t i e s
i n wa l l
f r om t u b e
At hi gh s t a t i c
bed
negligible difference
t e mp e r a t ur e s bet ween d i f f e r e n t t u b e l o c a t i o n s , has
been n o t i c e d . ■
-70-
LOCAL
HEAT
TRANSFER
COEFFICIENT, BT U / H r . F t ? 0 F
SBH 9 INS.
$
W3
10
Probe
Figure
19.
Number
Local
From
neat
it
Entrance
transfer
coefficients.
-71 -
SBH 9 INS.
O
I
2
3
4
5
Probe N u m b e r
Figure
20.
Local
heat
. i**
6
From
7
8
9
10
11
Entrance
transfer
coefficients.
r72.
Av e r a g e S e c t i o n a l C o e f f i c i e n t s
Genet t i ' s C o r r e l a t i o n
f o r Bat ch F l u i d i z a t i o n
E q u a t i o n 30, t h e c o r r e l a t i o n f o r a v e r a g e N u s s e l t
n u mb e r s ,
static
i s shown i n F i g u r e 21.
The c a l c u l a t e d d a t a f o r
bed h e i g h t o f n i n e i n c h e s u s i n g Eq u a t i o n 30 a r e
a l s o shown i n F i g u r e 2 1 .
Wi t h e x p e r i m e n t a l I y d e t e r m i n e d s e c t i o n a l
fractions
and l o c a l
ferent sections
coefficients
heat t r a n s f e r c o e f f i c i e n t s
of t he f l u i d i z e d
f o r .Wire I ,
particle
o v e r 11 d i f ­
bed a v e r a g e s e c t i o n a l
Wi r e 2, Wi r e 3, and Wi r e 4 a r e
c o mp a r e d .
None o f t h e d a t a c a l c u l a t e d u s i n g E q u a t i o n 30 i s
bel ow G e n e t t i ' s d a t a .
sectional
area
Not i ceabl e
increase
in average
c o e f f i c i e n t s wi t h r e s p e c t to e xt e nde d s u r f a c e
is not iced.
The l e a s t
s quare f i t s
of t h e d a t a f o r
e a c h e x t e n d e d s u r f a c e show t h a t t h e e x p o n e n t f o r I - e
r a n g e f r om 0 . 4 6 t o 0 . 5 2 .
One o f t h e v a r i a b l e s
heat t r a n s f e r
i s ge o me t r i c p r o p e r t i e s
on a v e r a g e s e c t i o n a l
Th i s v a r i a b l e
t o be c o n s i d e r e d i n b e d - t o - w a l I
coefficients
of e x t e n d e d s u r f a c e
s h o u l d be d e t e r m i n e d .
s h o u l d a l s o c o r r e l a t e wi t h t h e e x p r e s s i o n of
average sect i onal
coefficients .
040
<X>t-40 (0<3) GD.
coefficie
4€Z3Za
Ave r a ge s e c t i o n a l
GO
F i g u r e 21.
-7 3-
5 2 2 5
0 0 4 - 0
%
.0£74-._
The Mo d i f i e d C o r r e l a t i on Ac c o r d i n g t o The S e c t i o n a l
Coefficients
E q u a t i o n 31 has been us e d t o c a l c u l a t e
t imes,
0:
average contact
' '
0
Wi t h l o c a l
sectional
( 47)
N u s s e l t number s and e x p e r i m e n t a l I y d e t e r mi n e d
particle fractions
of t he f l u i d i z e d
bed,
o v e r t h e 11 d i f f e r e n t s e c t i o n s
average p a r t i c l e c o n t a c t
times, 6,
wer e c omput e d and t h e we i g h t e d a v e r a g e s o f e a c h r un have
been c a l c u l a t e d wi t h C^ = 1 0 .
Tabl e I I I
The We i ght e d Av e r a g e C o n t a c t Ti mes
Amount of
Ex t e n d e d S u r f a c e s
UD
Ii
>-
wI ,
CXl
Il '
> -
w2 . Y= I 2
w3 , Y= I 8
. w4 ,
• Y-I
Y
0 , sec
0.83333
0. 9 1 6 6 7
0.587
0.483
'0.94444
0.95833
0.395
0.376
75
■
C a l c u l a t e d we i g h t e d a v e r a g e c o n t a c t t i me s of s t a t i c
heights
bed
s e v e n i n c h e s and n i n e i n c h e s a r e shown i n Ta b l e I I I .
As e x p e c t e d wi t h t h e i n c r e a s i n g amount o f e x t e n d e d s u r f a c e s
t h e a v e r a g e c o n t a c t t i me s wer e d e c r e a s e d .
of b e d - o f - wa 11 h e a t t r a n s f e r
If the process
i s v i s ua-l-i zed as t h e p e n e t r a t i o n
o f t h e b o u n d a r y l a y e r by q u a s i - f l u i d
(particles
g a s ) eddies
f r om t h e b u l k o f t h e s t r e a m and t h e s c o u r i n g a c t i o n of t h e
fluidized
particles,
Woul d be e x p e c t e d
to
a v e r a g e c o n t a c t t i me .
of h e a t t r a n s f e r .
then obviously
the
exert
influence
the most
turbulence
intensity
on t h e
Th a t woul d be a l s o t r u e on t h e r a t e
The amount o f e x t e n d e d s u r f a c e s ,
in
o t h e r wor ds t u r b u l e n c e p r o m o t e r s , have been i n c r e a s e d f r om
Y-I
t h e v a l u e ----- y— o f 0. 8 3 3 3 t o 0. 91 667 , 0 . 9 4 4 4 4 and t o 0 . 9 5 8 3 3 .
Particularly
t h e s i z e o f e d d i e s whi ch woul d be e x p e c t e d
.
t o have some e f f e c t on t h e N u s s e l t number woul d e x e r t some
influence
i n t h e a v e r a g e c o n t a c t t i me .
Be c a u s e t h e amount
o f b o u n d a r y l a y e r d i s r u p t i o n and e n e r g y d i s s i p a t i o n wi t h
t h e i n c r e a s e amount o f e x t e n d e d s u r f a c e s
pr omot e r s )
are proport ional
(or t u r b u l e n t
t o t h e eddy s i z e .
C a l c u l a t e d c o n t a c t t i me s a v e r a g e d 0 . 5 5 5 s e c o n d s
for s t a t i c
bed h e i g h t of 5 i n c h e s .
i n t h e r a n g e r e p o r t e d by G e n e t t i
Thes e v a l u e s a r e a l l
( 8 ) and Z i e g l e r e t a I ( 3 4 ) .
■To o b t a i n a c o r r e l a t i o n f o r t h e c o n t a c t t i m e s ,
-76-
Q
.
■
' 6k 0
t h e d i m e n s i o n l e s s - q u a n t i t i e s ——9---
wer e c a l c u l a t e d .
scales
The s e q u a n t i t i e s
i n F i g u r e 22.
Y-I
Y
and
a r e p l o t t e d on l o g a r i t h m
The f o l l o w i n g c o r r e l a t i o n
represents
the d a t a :
P s c S dP1
Y-I
Y
6 . 8 5 6 Re.
-R
•By s u b s t i t u t i n g 6 3 as e x p r e s s e d
x- 0 .8
-)
( 48)
i n E q u a t i o n 48 i n t o
E q u a t i o n 31 ,' t h e f o l l o w i n g c o r r e l a t i o n f o r p a r t i c l e
N u s s e l t number s can be o b t a i n e d wi t h
= 10:
NUp =_______ IO cH I - e ) 0 - 48
( 49)
6.856 ( I z l - ) - 0 .8
whe r e <f> = s p h e r i t y ,
2
t h e r a t i o o f t h e s u r f a c e a r e a of
the p a r t i c l e
^
to t he s u r f a c e a r e a of a s phe r e
o f same a v e r a g e d i a m e t e r .
'
Y = number o f t u b e d i a m e t e r p e r 180° t w i s t .
Mi c r o s c o p i c e n l a r g e m e n t s o f p a r t i c l e s
[ F i g u r e 7 ( B) ] shows
t h a t the gl ass
study are s p h e r i c a l ,
particles
and 9 - I was u s e d .
data,
us ed i n t h i s
E q u a t i o n 49 as wel l
a r e shown i n F i g u r e 23.
Static
as t h e e x p e r i me n t a l
bed h e i g h t s o f f i v e .
-77 -
O
©
+
X
= 6 . 8 5 6 Re
S S
P
Fi g ur e 22.
0.8333
0.9167
0.9444
0.9583
O ©
C o r r e l a t i o n f o r a ve r age c o n t a c t t i me.
s e v e n , and n i n e i n c h e s are r e p r e s e n t e d
i n t h e d a t a shown i n
F i g u r e 23.
The v a l u e s Y o f 6 , 1 2 , - 1 8 ,
and 24 have been
represented
i n t h e d a t a shown i n F i g u r e 23.
c o r r e l a t i o n accor di ng to the s e c t i o n a l
The mo d i f i e d
coefficients
has
been s t u d i e d o v e r 11 d i f f e r e n t p o i n t s a l o n g t h e f l u i d i z e d
bed wi t h d i f f e r e n t mass v e l o c i t i e s .
( a b o u t 95 p e r c e n t )
in t h i s
Most o f t h e d a t a
a r e w i t h i n +25 p e r c e n t o f E q u a t i o n 49
study.
The e x p o n e n t 0 . 4 8 f o r I - e c i t e d by G e n e t t i
r ef e r enc e to ot her
present
investigators
investigation.
( 8 ) wi t h
( 18,. 2 0 )' a g r e e s wi t h t h e
B a c k - c a l c u l a t e d we i g h t e d a v e r a g e
c o n t a c t t i me s c o r r e l a t e wi t h t h e p r e s e n t m o d i f i e d d i m e n s i o n ­
less
g r o u p s and a r e i n a g r e e me n t wi t h t h e p r e v i o u s c a l c u l a ­
tions.
9
8
9 S 8 ’9
8
1.25
F i g u r e 23.
2
3
4
5
6
7
8
9
10 1
Humb^r6 s e n t m° d i f 1 e d c o r r e l a t i o n f o r s e c t i o n a l
2
3
p a r t i c l e Nus s e l t
-80-
R e s u l t s and Co n c l u s i o n
Local
and a v e r a g e he-at t r a n s f e r c o e f f i c i e n t s
b e d - t o - w a 11 h e a t t r a n s f e r f r om a f l u i d i z e d
for
bed t u b u l a r h e a t
e x c h a n g e r wi t h e x t e n d e d s u r f a c e s wer e i n v e s t i g a t e d .
was us e d as t h e f l u i d i z i n g medi um and c o a r s e g l a s s
wer e f l u i d i z e d
in t he e x p e r i me n t a l
He a t t r a n s f e r c o e f f i c i e n t s
Ai r
particles
h e a t e x c h a n g e r col umn.
f o r a i r f l o wi n g t hrough t h e h e a t
e x c h a n g e r w i t h o u t f l u i d i z a t i o n wer e a l s o i n v e s t i g a t e d .
Av e r a g e N u s s e l t Numbers w i t h o u t F l u i d i z a t i o n
The a v e r a g e h e a t t r a n s f e r c o e f f i c i e n t s
f o r a i r alone
have been c ompar ed wi t h t h o s e c a l c u l a t e d f r om an a c c e p t e d
correlation
f or m ( 6 , 8 ) :
it
is concluded t h a t
c o e f f i c i e n t s wer e o b t a i n e d i n t h i s
s u r f a c e area f or heat t r a n s f e r
F l u i d i z e d Bed Ther mal
fluidized
very s ma l l .
tributed
Local
st udy s i nc e extended
is avai l a bl e.
Gr adi ent s
From me a s u r e me n t s of v e r t i c a l
profiles,
higher
bed t h e r ma l
fluidized
bed t e m p e r a t u r e
g r a d i e n t s a r e shown t o be
Al I p r o f i l e s wer e s howi ng u n i f o r m l y d i s ­
t emperat ure p r o f i l e s .
He a t T r a n s f e r C o e f f i c i e n t s
Gr a dua l
coefficients
increase
i n t h e we i g h t e d a v e r a g e h e a t t r a n s f e r
wi t h r e s p e c t t o t h e number of e x t e n d e d s u r f a c e
“
'
"
'8
-1
-
is observed t hr oughout the runs.
coefficients
heat t r a n s f e r
a r e o b s e r v e d t o d e c r e a s e wi t h t h e d i s t a n c e f r om
t he e n t r a n c e of t he f l u i d i z e d
coefficients
Local
bed.
Local
heat t r a n s f e r
v a r i e d s l i g h t l y wi t h d i f f e r e n t t ube l o c a t i o n s .
Av e r a g e S e c t i o n a l
Coefficients
The a v e r a g e . s e c t i o n a l
coefficients
have been compar ed
wi t h t h e d a t a c a l c u l a t e d
f r om an e s t a b l i s h e d c o r r e l a t i o n
None o f t h e d a t a of t h i s
s t u d y i s bel ow G e n e t t i ' s d a t a f o r
bare t u b e s .
As e x p e c t e d ,
( 8 ).
an i n c r e a s e i n a v e r a g e s e c t i o n a l
c o e f f i c i e n t s . wi t h r e s p e c t t o e x t e n d e d s u r f a c e a r e a i s o b ­
tained.
I t i s f ound t h a t t h e e x p o n e n t f o r 1 - e r a n g e f r om
.0.46 t o 0 . 5 2 .
The Mo d i f i e d C o r r e l a t i on Ac c o r d i n g t o t h e S e c t i onal
Coefficients
Wi t h l o c a l
heat t r a n s f e r c o e f f i c i e n t s
d e t e r mi n e d s e c t i o n a l
ferent sections
particle
f r a c t i o n s o v e r t h e 11 d i f ­
of t he f l u i d i z e d
c o r r e l a t e d wi t h E q u a t i o n
b e d , N u s s e l t number s a r e
49.
10 tj) ( I - e )
Nu
0.48
( 49)
6.856
1+
i :i
I
and e x p e r i m e n t a l Iy
ReP
-82-
Several
conclusions
1.
ratio,
Particle
Y,
can be drawn f r om t h i s
correlation;
N u s s e l t number s a r e d e p e n d e n t on t w i s t
Th i s a l s o
i mp l i e s
t h a t p a r t i c l e N u s s e l t number
i s d e p e n d e n t upon e x t e n d e d s u r f a c e a r e a .
2.
P a r t i c l e N u s s e l t number s a r e p r o p o r t i o n a l
t o ( I - c ) 0 *48
3.
P a r t i c l e N u s s e l t number s have weak d e p e n d e n c y on
gas mass v e l o c i t i e s .
Most o f t h e d a t a a c c o r d i n g t o t h e mo d i f i e d c o r r e l a t i o n
this
in
i n v e s t i g a t i o n a r e w i t h i n +25 p e r c e n t o f E q u a t i o n 49.
-83-
L i t e r a t u r e Ci t ed
I.
An d e r s o n , T . B. and J a c k s o n ,
6 , 527 ( 1 9 6 9 ) .
2.
B o t t e r i l I , J.. S . M. and W i l l i a m s ,
Chem. E n g r s . , 41, 21 7 ( 1 963 ) .
3.
Da v i d s o n ,
(1961 ) .
4.
Da v i d s o n , J . F . , H a r r i s o n , D. , " F l u i d i z e d P a r t i c l e s , "
Ca mbr i dge U n i v e r s i t y P r e s s , New York ( 1 9 6 3 ) .
5.
Dow, W. M. and J a k o b , M. , Chem. Eng . P r o g . ,
(1951).
6.
Donohue , D. A. , I n d . Eng . Chem. , ± 1 > 2499 ( 1 9 4 9 ) .
'I.
J.F.,
Trans.
Roy,
Inst.
I n d . Eng.
Chem. Fund
J . R. , T r a n s .
Inst.
Chem. E n g r s . , 1 9 ,
F r a n t z F . J . , I . Chem. Eng. . , 6_9, 1 61 ( S e p t ,
I I . I b i d . , page 89 ( Oc t . I , I 962)
I I I . I b i d . , page 103 ( Oc t . 29 , 1 96 2 ) .
P h . D. T h e s i s ,
230
47., 537
1 7, 1 962)
8.
G e n e t t i , W. E. ,
University.
1 968 , Or egon S t a t e
9.
G e l ' p e r i n, N. I . , A i n s h t e i n , V. G. and K o r o t y a n s k a y a ,
L . A. , I n t . Chem. E n g . , I , I 37 ( 1 96 9 ) .
11.
Ku n i i , D. and L e v e n s p i e l , O. ,
7, 446 ( 1 9 6 8 ) . .
12.
Ku n i i , D. and L e v e n s p i e l , O. , I n d . Eng. Chem. P r o c e s s
De s i gn and De v e l o p me n t , _7 , 481 ( 1 9 6 8 ) . .
13.
Kret zschmer , F., Forshung. ,
pa g e s 9 3 - 9 5 .
14.
Ki d.d, G. J . , J r . ,
15.
Leva , M. , We i n s t r a u b , M. and Gr ummer , M. , Chem. Eng
P r o g . , 45, 563 ( 1 9 4 9 ) .
I n d . En g . Chem. F u n d . ,
V o l . 4, Ma r c h - Ap r i I ,
OO
OY
van H e e r d e n , C . , Nobel , P . and van K r e v e l en , D. W. ,
Chem. En g . S c i . , I , 51 ( 1 9 5 1 ) .
CO
10.
A. I . Ch.
E. J ; , 4,
581 (1 9 6 9 ) .
-84-
16.
L e v e n s p i e l , 0. and Wa l t o n , J . S . , Chem. Eng. Pr og.
Symp. S e r . , No. 9, V o l . 50, " He at T r a n s f e r - R e s e a r c h
S t u d i e s f o r 1 9 5 4 , " A. L. Ch-. E . , pgs . 1 - 1 3 .
17.
Mu r r a y ,
18.
Mi c k l e y , H. S. and F a i r b a n k s ,
I , 374 ( 1 9 5 5 ) .
19.
McAdams, W. H. , " He a t T r a n s m i s s i o n , "
Y o r k , M c G r a w - H i l l , 1954, page 299.
20.
Mi c k l e y , H. S. and T r i l l i n g ,
41, 1135 ( 1 9 4 9 ) .
21 .
M i l l e r , C. 0.
I 220 ( 1 951 ).
22.
Noe, A. R. and Kn u d s e n , J . G. , Chem. Eng . Pr og. ■ Symp.
S e r . , V o l . 64, No. 82, " He a t T r a n s f e r , " A. I ., Ch'. E . ,
1968, 2 0 2 - 2 1 1 .
23.
P e t r i e , J . C. , F r e e b y , W. A. and J . A. , Chem.. Eng.
Pr og . , Erl, 45 ( 1 9 6 8 ) .
24.
R u c k e n s t e i n , E . , P r o c e e d i n g s o f t h e T h i r d I n t e r n a t i onal
He a t T r a n s f e r C o n f e r e n c e , P a p e r s 113 -151 , Vol . IV, page
298- 301 ( 1 9 6 6 ) .
25.
S z e k e l y , J . and F i s h e r ,
833 ( 1 9 6 9 ) .
Chem.
Eng . Sci . , 24,
26.
Toor , H. L. and Mar chel I o , J . M. , A.
4, 97, ( 1 9 5 8 ) .
I . Ch . E . J • S
27.
Toome y, R. D. and J o h n s t o n e , H. F . , Chem; Eng. Pr og.
Symp. S e r . , V o l . 49, No. 5, " He a t T r a n s f e r , " A. I .
E. , 1953, pa ge s 5 1 - 6 3 .
J.D.,
J.
F l u i d Me c h . ,
2J_, 465 ( 1 9 6 5 ) .
D . F . , A.
C. A. ,
3rd,
Ch . E . J . ,
ed.,
I n d . Eng.
New
Chem. ,
K . , I n d . En g . Chem. , 43^
and Logwi nuk, A.
R. J . ,
28.
V r e e d e n b e r t , H. A. , J . Appl . Chem. ,
29.
V r e e d e n b e r g , H. A. , Chem.
30.
We n d e r , L . and C o o p e r , G. T . , A.
15 ( 1 9 5 8 ) .
Eng.
I.
Sci.,
2_, 526 ( 1 95 2 ) .
1J_, 274 (I 960) .
I . Ch. E . J . ,
£,
Ch .
-85-
■31.
Wen5 C. Y. and Leva, M. , A.
(1956).
F. ,
I . Ch. E. J . , 2, 482
32.
Wi c ke 5 E. and p e t t i n g ,
301 (1.954.
Chemi e- I ngr .
Tech. , 26
—
33.
Y o s h i d a 5 K. , K u n i i 5 D. and Levenspi e l , 0 . ,
Heat Mass T r a n s f e r , 1_2 , 529 ( 1 9 6 9 ) .
34.
Z i e g l e r , E. N. , Ko pp e l 5 L. B. and B r a z e ! t o n , W. T
I n d . Eng. Chem. Fund. , 3_, 224 (1 96 4 ) .
In t . J
Appendix
I
Nomenclature
Symbol
Definition
A v e r y s ma l l c o n s t a n t f o r
E q u a t i o n 18
A1
Di me ns i ons
Di me n s i o n l e s s
A
To t a l s u r f a c e a r e a o f p a r t i c l e s
i n t h e bed
ft2
Ah
Crossectional
changer
ft2
Am
C r o s s - s e c t i o n a r e a o f a f l o w me t e r
ft2
Ao
Cross-sectional
opening
ft2 ;
a
• b
B1
C.
cO
cI
C2
Cg
Sg
Cps
CR
Cs
D1
a r e a of o r i f i c e
■Sur f ace a r e a o f p a r t i c l e / u n i t
l e n g t h o f bed
- AP
AT
a r e a of he a t e x ­
'
S u r f a c e a r e a of e n t i r e
bed
coefficient
solid
ft2 /ft
ft2
f o r E q u a t i o n 32
Di me n s i o n ! e s s
C o e f f i c i e n t f o r E q u a t i o n 32
Di me n s i o n l e s s
Di me n s i o n l e s s
A c o n s t a n t whi ch i n c r e a s e s wi t h
p a r t i c l e s i z e f o r E q u a t i o n 18
C o e f f i c i e n t of d i s c h a r g e
Const ant
Di me n s i o n l e s s
Const ant
Di me n s i o n l e s s
Di me n s i o n l e s s
Const ant
S p e c i f i c h e a t o f gas
Specific
constant
Specific
constant
h e a t o f gas a t
pressure
h e a t of s o l i d a t
pressure
C o r r e c t i o n f o r n o n - a x i al tube
l o c a t i o n , f o r case of i n t e r n a l
heat t r a n s f e r surface
S p e c i f i c h e a t of s o l i d
Ou t e r d i a m e t e r of a x i a l
cylinder
Di me n s i o n l e s s
Bt u Z l b m0 F
B t u / 1 b m°F
B t u / l b m°F
D i me n s i o n l e s s
Bu t Z l b m0F
' ft
- .8 7 -
a Z-
Da i me t e r o f f l u i d i z e d
d b
E f f e c t i v e d i a me t e r of bubbl e
P a r t i c l e di amet er
ft .
Tube d i a m e t e r
ft
d P- d P
bed
ft
ft
dt i '
Ou t e r d i a m e t e r o f h o r i z o n t a l
tube
i mmer s ed
emf
E l e c t r o m o t i v e f o r c e p r o d u c e d by
t h e t h e r mo c o u p l e
F
Term d e f i n e d
g
A c c e l e r a t i o n due t o g r a v i t y
Di me n s i o n l e s s
ft/hr2
9C
Gravitational
l b Hf t
i n E q u a t i o n 14
Const ant
ft
mi I i vol t s
I b .cs e c 2
G
S
.
Gas mass v e l o c i t y
I bm/ h r f t 2
Mass v e l o c i t y o f f l u i d i z a t i o n
o f a bed
Ib^/hr f t 2
•
^nif
C a l c u l a t e d mi nimum f l u i d i z i n g gas /■ ' I bm/ hr f t 2
mass v e l o c i t y
h
Heat t r a n s f e r c o e f f i c i e n t
Btu/hr ft°F
hav
Av e r a g e h e a t t r a n s f e r c o e f f i c i e n t
Btu/hr ft °F
^loc
Local
B t u / f t 2oF
ht
T i me - a v e r a g e d h e a t t r a n s f e r
coefficient
B t u Z f t 2oF
ht i
Local i n s t a n t a n e o u s h e a t
transfer coefficient
B t u Z f t 2oF
hW
He a t t r a n s f e r c o e f f i c i e n t
b e t we e n bed and s u r f a c e
B t u Z f t 2oF
Ah
Manomet er , r e a d i n g s
’
I(t)
I
heat t r a n s f e r c o e f f i c i e n t
■
I
•!
ft
I
•
. Age d i s t r i b u t i o n f u n c t i o n of
e mu l s i o n e l e me n t s on t h e
surface
C u r r e n t f l o wi n g t h r o u g h t h e
h e a t i n g e l e me n t
g
Di me n s i o n l e s s
.
'
■
Amperes
•
‘
■
I
I
I
'!
■T
-88
K
Kr e t z c h me r c o e f f i c i e n t
k
Ther mal
k.
E f f e c t i v e t h e r ma l c o n d u c t ­
i v i t y of e mu l s i o n l a y e r
Ther mal c o n d u c t i v i t y o f gas
B t u / f t h r 0F
Ther mal
B u t / f t h r 0F
L
L
conductivity
c o n d u c t i v i t y of s o l i d
Effective thickness
I ayer
Bed h e i g h t
o f e mu l s i o n
Mean h e i g h t o f f l u i d i z e d
Le ngt h o f h e a t t r a n s f e r
' mf
bed
Btu/hr f t °F
Bt u/ f t ° f
ft
ft
ft
surface
ft
He i g h t o f bed a t mini mum f l u i d ­
izing conditions
Bed s e t t l e d h e i g h t
ft
Term d e f i n e d
i n E q u a t i o n 20
up
Particle
N u s s l e t number
ua v
Av e r a g e p a r t i c l e
h a v V kg
'
Di me n s i o n l e s s
D i me n s i o n l e s s
hW
N u s s l e t n u mb e r ,
Di me n s i o n l e s s
Pressure
I b^/ f x
I
Ups t r e a m p r e s s u r e
Ib^/ft2
2
Downs t r eam p r e s s u r e
Ib^/ft2
O r i f i c e p r e s s u r e dr op
lbf / f t 2
Prandtl
Di me n s i o n l e s s
AP
number C ^ p / kg
Heat f l u x f r om h e a t t r a n s f e r
surface •
Btu/hr f t 2
*1
Ra t e o f h e a t l o s s f r om
f l u i d i z e d bed
Bt u/ hr
R-
Bed e x p a n s i o n r a t i o
D i me n s i o n l e s s
.89-
qP
: Re
Cd
But/hr f t 2
Re y n o l d s number
Di mens i on!
Particle
Di mens i on!
T e mp e r a t u r e
l
CD
T .
C
'r
Re y n o l d s n u mb e r , D G/y
P
Ra d i a l d i s t a n c e f r om t h e c e n t e r
o f t h e bed
TV
I n l e t and o u t l e t t e m p e r a t u r e
respectively
T2
ft
°F
°F
Bed t e m p e r a t u r e
0F
Av e r a g e t e m p e r a t u r e o f gas a t any
l e v e l i n bed
0F
e mp e r a t u r e o f b u b b l e g a s , and of
Tg b 5 Tge T
e mu l s i o n gas
0F
Tb
"
He at t r a n s f e r t o a p a r t i c l e
near the heat t r a n s f e r sur f a ce
Tg
Tgi
•
Tgo
T S
TW
I n l e t gas t e m p e r a t u r e
0F
Initial
0F
gas t e m p e r a t u r e .
Solid t emperat ure
0F
Wal l
°F
t emperat ure
"b'"br
Ri s i n g v e l o c i t y of a bubbl e in a
b u b b l i n g bed and v e l o c i t y o f bubbl ewi t h r e s p e c t t o e mu l s i o n a head o f i t
ft/hr
ue
Upward gas v e l o c i t y w i t h i n e mu l s i o n
phase
f t / hr
■ uf
uITlf
%
us
V
-
umf / e mf '
S u p e r f i c i a l gas v e l o c i t y a t
mi ni mum f l u i d i z a t i o n c o n d i t i o n s
S u p e r f i c i a l gas v e l o c i t y . ( ba s e d on
empt y t u b e )
Downward v e l o c i t y o f s o l i d s i n .
e mu l s i o n p h a s e
Vo l t a g e dr op a c r o s s t h e h e a t i n g
e l e me n t
ft/hr
f t / hr
ft/hr
ft/hr
volts
- -9 0-
V
Vf
W
wg
'
Vg
Vo l u me t r i c f l o w r a t e
f t J/hr
V e l o c i t y o f gas
ft/hr
Ac t u a l mass f l ow r a t e
Gas f l o w r a t e
1V
ws
Superficial
v e l o c i t y o f gas
X
Fi l m t h i c k n e s s o r d i s t a n c e from
t he heat exchange s u r f a c e
t i me s s p e c i f i c
ft/hr
wC
Gas f l o w r a t e
o f gas
Y
Ex p a n s i o n f a c t o r
Y
Y
Term d e f i n e d i n E q u a t i o n 13
T wi s t r a t i o ; t h e number of t u b e
d i a m e t e r p e r 180° t w i s t
Z
Term d e f i n e d
i n E q u a t i o n 15
hr
heat
ft
BTU
°F hr
D i me n s i o n l e s s
Di me n s i o n l e s s
D i me n s i o n l e s s
Di me n s i o n l e s s
;--91 -
Vol ui net r i c F r a c t i o n o f S o l i d s
Definition
Symbol
' Volume o f e mu l s i o n t r a n s p o r t e d
upwar ds b e h i n g a b u b b l e pe r
v o l ume o f a b u b b l e
’ Ra t i o of t he o r i f i c e d i a me t e r ■
to t he pi pe di amet e r
Vo l u m e t r i c f r a c t i o n of s o l i d s
'a
Y
Number of p a r t i c l e s
surface area
. YP
per uni t
- Di mens i ons
Di me n s i o n l e s s
D i me n s i o n l e s s
Di me ns i onl ess
0
parti c l e s / f t
Voi d f r a c t i o n
Voi d f r a c t i o n of e mu l s i o n pha s e
Di me n s i o n ! e s s
Av e r a g e Voi d f r a c t i o n i n t h e
f l u i d i z e d bed
Voi d f r a c t i o n of s t a t i c bed
Di me n s i o n l e s s
Voi d f r a c t i o n o f bed a t minimum
f l u i d i z a t i o n conditions-
Di me n s i o n l e s s
£mf
V
n
F l u i d i z a t i o n e f f i c i e n c y , or
D i me n s i o n l e s s
0
0
■ V TS
tV t S
C o n t a c t t i me
Av e r a g e c o n t a c t t i me
hr
hr
8
E0
e
ef
£m
Bed d e n s i t y
Pb
■ pe
-
' Ap p a r e n t d e n s i t y o f e mu l s i o n
D i me n s i o n l e s s
D i me n s i o n l e s s
p
I b mZf t 3
Gas d e n s i t y
1V f t S
I b mZ f t 3
Gas d e n s i t y o f u p s t r e a m l o c a t i o n
I b mZ f t 3
p gi
. pS
V
- Particle
density
Viscosity
Gas v i s c o s i t y
yg
I b mZ f t 3
I b raZ f t hr
. l b m/ f t
hr
-9v 2’'
Ki n e ma t i c v i s c o s i t y
f . t 2/ hr
Sphericity.
D i me n s i o n l e s s
Rat i o of t he p a r t i c l e s ur f ace,
a r e a t o t he a r e a of a s p h e r i c a l
p a r t i c l e of t h e same d i a m e t e r
Di me n s i o n l e s s
Vol ume f r a c t i o n o f b u b b l e s
f l u i d i z e d bed
D i me n s i o n l e s s
in
Appe ndi x 11
E v a l u a t i o n o f p and R
-E6-
Paruiclo Diameter, inch
0.012
£
Fi gure 24.
t-
The c o r r e l a t i o n f or g and R.
-94-
NOTIl -
L i f t fcrricht] s c o l t
of
CC rrtsponJs to
G„<
(Ib/ftfhr)
0 f (inch)
Ia ft (or right) scaio of Grnf
3 0 0 0 - o IOOOOO
U r (C-P)
0 .0 3 5 :
0 .0 3
(Ps-PfrIPFtIi/0*
O.C5
0.03
20— 800
•500
■:
0.02
|
0.02
j o o
5 J-200
0 01
-too
0005
0.01
0 003
L 0.002
.O O flj
F i g u r e 25.
Nomograph t o c a l c u l a t e
.
Appe ndi x I I I
A typical
data sheet
-95Sampl e Raw Dat a S h e e t
Run:
9H3W3
J u n e 2,
Time S t a r t e d :
Ti me F i n i s h e d :
1 969
1 0 : 2 5 A. M.
2. 45
P.M.
Number of Exended S u r f a c e s :
3
S t a t i c Bed H e i g h t :
9 inches
F l u i d i z e d Bed H e i g h t :
38 i n c h e s
Vo l t me t e r Readi ngs :
7.5 v o l t s ,
7. 7 v o l t s
Ammet er R e a d i n g s :
50 amps
51 amps
Manomet er ( I ) r e a d i n g : (22 3 / 8 rV 22 1/ 4 i n c h )
(21 3 / 8 % 21 1 / 4 i n c h ) ( f o r a i r f l o w r a t e )
Tube Wal l
Pr obe I
Pr obe 2
Pr obe 3
Pr obe 4
Pr ove 5
Pr obe Th e r mo c o u p l e s
emf by mv
Locati on I Location 2 Location 3 Locati on 4
2.380
2.458
2. 549
2. 319
2. 197
2. 273
2. 332
2. 077
1. 975
2 . 01.8
2. 018
. 853
1. 791
1. 815
I .7 97
. 740
1. 671
1. 695
1. 637
. 587
1. 570 •
I . 587
1.588
I . 549
1. 559
I . 575
Pr obe 8 . I . 543
Pr obe 9 . I . 551
I . 541
1. 5 5 7
I . 568
I . 569
I . 559
I . 575
1. 557
Pr obe 10 I . 571
Pr obe 11 I . 598
I . 566
1. 574
I . 563
I . 542
I . 542
Pr obe 6
Pr obe 7
. 552
I . 557
•
■
I
'96r.
Bul k Bed Th e r mo c o u p l e s
emf by mv
Section
I
Section 2
Section 3
Section 4
Section 5
Section 6
I . 815
I . 838
I . 837
I . 834
I . 825
Section■ 7
■r.. 825
8
9
I . 804
I . 809
I . 807
I . 815
Section
Section
S e c t i o n 10
S e c t i on I I
I . 825
Manomet er (2)
'
Readi ng,
Inches
Manomet er
I
Ah
Manomet er
2
Ah
3. 25
3. 00
Manomet er
Manomet er
3
4
Ah
Ah
2 . 25
2 . 00
Manomet er
5
Manomet er
6
Ah
Ah
I . 25
•o. 75 •
Manomet er
Manomet er
7
Ah
8 .
Ah
0 . 50
0 . 125
Manomet er
9
Ah
Manomet er 10
Manomet er I I
'
Ah ■
Ah
0 . 00
0 . 00
4. 00
Ii
Appe ndi x
IV
C a l i b r a t i o n T a b l e s f o r Ther mocoupl
I
2
3^
Th e r mo c o u p l es
4
5
6
7
8
9
0F
0
60
0 . 618
0 . 640
0 . 662
0 . 684
0 . 706
0 . 729
0. 751
0. 774
0. 096
0. 818
70
0 . 840
I . 064
0 . 862
I . 086
I . 311
0 . 884
I . I 09
I . 334
0 . 906
I . 131
I . 357
0 . 929
0 . 951
I . 176
I . 403
0. 974
I . I 99
0. 996
0. 221
I . 01 9
I . 041
I . 426
I . 448
I . 244
I . 471
I . 266
I ., I 93
I . 538
I ., 561
I . 607
I .,653
I ., 882
I ., 676
I .,699
I ., 837
I . 630
I . 859
I .,905
I ., 928
I . 722
I ., 951
80
90
I . I 54
I . 380
100
I . 289
I . 516
I 10
I . 745
I . 768
I ..791
I . 583
I . 814
120
I . 974
I .. 997
2 . 020
2 . 043
2 ., 066
2 . 088
2..111
2.,134
2., I 57
2.J 80
I 30
140
I 50
2 . 203
2 ,. 433
2 . 663
2 .. 225
2 . 455
2 ,. 685
2 . 248
2 ,. 478
2 ,. 708
2 . 270
2 ,. 500
2 ,. 730
2 . 293
2 ,. 523
2 . 753
2 . 316
2..340
2..363
2.,409
I 60
2 . 892
3 . I 22
2 ,. 91 5
2 . 937
2 . 960
2 . 982
2 . 546
2 . 776
3. 006
2..569
2 .799
3,. 029
2,.593
2 . 822
3,. 052
2.. 386
2,. 61 6
2,. 846
3 . 076
3 . 145
3 . I 69
3 . 262
3 . 285
3 . 309
3 . 378
3. 469
3 . 492
3 . 515
3 . 538
3 .562
3 . 585
3 . 818
3 . 608
3 . 841
3 . 402
3 . 632
3 .21 5
3 . 447
3. 239
3 . 355
3 . 192
3 . 424
2,.869
3,. 099
3,. 332
3 . 655
3 . 883
3 . 678
3 .91 I
3. 701
3 . 934
3 . 725
3 . 958
3 . 748
3 .981
3 .771
4 . 004
3 . 795
170
I 80
I 90
200
3 . 865
2..639
4 . 028
“Z6“
Chr omel - Al ume l
I r o n C o n s t a n t a n T h e r mo c o u p l es
I
2^
3
0F
O
60
0 ,. 785
0 ,. 813
O. 842
0 ,. 871
0 . 900
0 ,. 929
O. 957
0 . 986
I ,. 01 5
I . 044
70
I ,. 073
I . 361
I ,. 101
I ,. I 59
I ,. 447
I ,. 188
I . 476
I . 736
2 ,. 026
I . 765
2 . 055
I . 217
I . 505
I ,. 794
I ,. 246
I ,. 533
I ,. 823
I . 274
I . 389
I . 678
I ,. 968
I . 30
I . 418
I . 797
1997
I ,. 332
I ,. 620
I ,. 910
2 ,. 084
2 ,. 113
I . 562
I . 852
2 . 143
I ,. 303
I .591
I ,. 881
2 . 259
2 . 289
2 . 318
2 . 347
2 . 376
2 . 405
2 . 435
80
90
100
I ,. 939
2 . 230
5
6
7
8
9
2 . 1722 2 ,. 201
2 . 464 2 ,. 493
-98-
no
I . 649
4
Appendix V'
Compl e t e Dat a
(Table
IV)
-99-
FBH
RUN NOBWl Hl
G= =527
IN 9
lbm / h r f t ? .
18.228
1— 6
h |yc, Btu/ hr ft2 °F
I
0.0
0.79
2
0.0
1.12
3
4
0.0
I .29
0.0
I .87
0.0
2.27
0.0
2.69
7
8
0.0
3.90
0.0
6.65
9
0.0
21.49
10
0. 1
34.23
11
0.375
34.10
Probe no.
5
6
Btu / hr ft2 ,
“ =267
RUN MO.
hOV " 9 . 0
FBH
llW H r f t - ,
5 WI H2
G - - 1 009
B t u / hr f r °F
IN 16
Rep —24 g
i —e
h |oc , B t u / Hr f t 2 o F
I
0.0
3.05
2
0.0
3.29
3
4
0.0
3.49
0.0
3.78
5
0.0
4.51
6
0.0
6.20
7
0.0
11.09
8
0.00625
22.34
0. 1
38.37
10
0.225
39.24
11
0.325
45.65
Pr obe no.
9
Q = 333
Dt u/ hr f t 2 ,
Hq v -
1 6 . 4 B t u / Hr ft 2 °F
RUN NO- 5W1H3
G — 1 2 54
Probe no.
IN 5
Rep - 4 3 . 3 7 5
h |0(_, Bfu/ hr ff2
I— E
I
0.0
2.89
2
0.0
3.24
3
4
0.0
3.46
0.0
4.44
3
6
0.0
6.18
0.0625
8.71
7
0.0125
18.11
8
0.05
23.13
9
0.15
28.74
10
0.25
30.35
11
0.225
33.70
Q = 301
btu/hrft2 ,
RUN NO. 5W1H4
1 443
G ==
Pr obe no.
14.3
Hqv =
FDH
lbm/ | i r ft2.
I—E
B t u / hr ft2 °n
IN 3 8
Rep = 4 9 . 9 1 2
h |oc,
BtuZhrft2 o F
0.0
4.33
2
0.0
5.14
3
4
0.0
6.18
0.0
7.42
3
0.0125
1 0 . 1 2
6
0.025
14.87
7
0.0375
18.96
8
0.075
25.21
9
0.15
0.275
Q = 316
B t u / hr f t 2 ,
OJ
OD
11
29.59
OO
0 . 2
'd-
10
rx>
I
rx>
'
rtit^
lbm / hr f t ,
h a v — 1 6 . 3 g t u / hr f t 2 o F
-101 -
FBH
RUN N0. 5W2
G — 527
Probe no.
'
I b m / h r f t 2 ,
0.0
2
0.0
5
0.0
4
0.0
5
6
0.0
7
8
0.0
0.0
9
0.0
neP ^ 18 . 2 2 8
I'i |o , Btu/ hr ft2 °F
I—E
I
IN 8
0.69
0.86
1. 11
I . 58
2.29
0.0
2.77
3.86
5.76
10
0.075
ii
0.375
Q = 280
RUN NO.
G=
Btu/ hr
5W2H2
I 009
2.125
,
FBH
Ibm/ hr
I—6
Pr obe no.
39.28
___ 3 9 , 7 8 _
BvuZhrf f2 o F
hov — 9*5
IN
Rep =
14
34.9
h Ioc , Bt u/ hr ft* 0F
0.0
2.60
2
0.0
2.83
3
4
0.0
3.12
0.0
3.48
5
0.0
5.86
6
0.0
7.63
7
0.0
11.28
8
0.0
25.01
9
0. 1
38.85
10
0.225
41 . 2 3
11
0.325
Q =
294
Bt u / hr ft^ ,
C\
LT
I
h Qv =
I 6 • I B t u / hr f t ^ °F
-102-
RUN
I—€
IN 25
Rcp = 4 3 . 9 9 7
Btu/ hr
h
I
0.0
3.45
2
0.0
3.77
3
4
0.0
4.84
0.0
6.22
3
0.0
9.53
6
0.025
14.78
7
8
0.05
20.62
0.0875
26.48
9
0.125
38.38
H
O
Probe no.
'
FBH
i b m / h r f t 2.
2 H3 9 7 o
ij — \ c I 6
0.2
38.67
11
0.275
45.16
Q—
285
Btu/hrft2 ,
I—e
P robe no.
I
0.0
2
0.0
3
4
0.0
5
0.125
6
0.025
7
0.0375
8
0.0875
9
0.125
10
0.175
11
0.275
Q=
1 8 • 6 B t u / hr fI2 c T-
hc v "
F BH
lbm / h r ( t 2
RUN NO. 5W2H4
G = 1455 I
IN
Rep =
,
B t u / h r ft ' ,
33
50.43
h Iqc z Bt u/ hr ft2 °F
4.66
5.55
7.33
0.0
281
°F
9.73
12.25
17.47
19.51
22.83
27.61
30.05
J 4.33
=
1 7 . i B t u / h r f t 2 °F
run
NO. 5W3H1
G — 481
Probe no.
:
'
FBH
IN 9
Bep= 16. 637
,bm / hrfl ,
h | o , Btu/ hr f f2 °F
1— 6
I
0.0
2
0.0
3
4-
0.0
2.08
0.0
2.76
5
0.0
3.55
6
0.0
4.25
7
8
0.0
5.70
0.0
9.77
9
0.0125
I . 02
I . 93
32.60
io
0.125
41 . 71
ii
0.35
32.11
Q = 261
Bt u/ hr ft2 ,
RUN N O . 5W3H2
G == 1 009
P robe no.
h QV = = 1 1 - 6
FBH
Ibm/ h r ft7- ,
I—G
B t u / hr ft2 °F
IN 16
Bep — 3 4 . 9
h | o c , B t u / hr ft 2 °F
I
0.0
3.56
2
0.0
3.98
3
4
0.0
4.20
0.0
4.69
5
0.0
5.80
6
0.0
8.54
7
0.0
18.08
8
0.025
26.98
9
0.075
41.21
10
0.325
40.71
11
0.30
35.68
Q —
= 276
Q
B t u / hr f t 2 ,
hav =
17
B tu Z h r tt2oF
-104-
RUN
NO.
G —
5W3H3
1273
FEH
lbm / h r f t /
I—6
Rep=
I
0.0
4.35
2
0.0
4.86
2
0.0
5.70
l.\.
0.0
7.42
5
0.00625
10.61
6
0.01875
16.38
7
0.025
20.44
8
0.075
24.93
9
0.125
31.16
0.175
34.27
11
0.25
34.55
Q=
276
RUN
NO.
B t u / hr ft2 .
IN 38
Rep = 4 8 . 7 7
lbm, / h r f t 2 ,
I —G
P r o b e no.
h
Ioc
,
Btu/hr U2 o F
I
0.0
9.18
2
0.00625
9.62
5
4
0.0125
10.18
0.025
I 2.2 7
5
0.025
15.26
6
0.0125
19.19
7
0.0375
22.48
8
0.0875
24.37
9
0. 1
29.16
10
0.175
31 . 8 4
ii
0.25
20.95
Q =
269
G tu/hrft2 ,
9 7
1 7 . 3 B t u / h r ft2 °F
hav =
FBH
5W3H4
G= 1 4 1 0
_9
Io ^z B t u / h r f t 2 °F
O
h
43
H
P r o b e no.
25
|M
ha v =
I 9 . 2 B t u / h r ft2oF
-105-
RUN NO-
5W4H1
G — 481
h |o ( ,
I—€
P r o b e no.
IN 9 •
Rep= 1 6 . 6 3 7
FBH
lbm / h r f t 2,
B t u / h r f t 2 °F
I
0.0
I .78
2
0.0
2.10
5
4-
0.0
2.46
0.0
3.04
5
0.0
3.38
G
0.0
4.04
7
0.0
5.51
8
0.0
9.42
9
0.00625
33.43
10
0. 1
41.17
■ 11
0 .4
37.49
Q = 236
B tu/ Urft2 ,
= I2
FEH
bm/ h r i i 2,
RUN NO.
5W4H2
G = 1 032
P r o b e no.
hav
I—G
h
B t u / hr
IN
Rep =
I oc
,
16
35.661
B t u / hr f t2 ° r
I
0.0
3.58
2
0.0
4.02
5
0.0
4.40
4-
0.0
5.27
5
6
0.0
6.20
0.0
8.82
7
0.0625
17.16
8
0.0375
25.63
9
0. 1
33.47
10
0.2
30.99
11
0.3
24.91
Q = 232
B t u / hr f t 2 ,
ha v =
ft2 cT
1 4 . 7 B t u / h r ftZoF
-106-
RUN NO.
G=
Probe no.
:
•
5W4H3
1217
_ FBH
Ibm Z l l r f l '
IN 24
Rep =
42.06
h |o c , Btu/ hr ft2 0F
1— €
I
0.0
4.31
2
0.0
4.86
3
4
0.0
5.63
0.0
7.36
5
6
0.0
10.19
0.0125
15.40
7
0.025
21 .91
8
0.0625
35.65
9
0. 1
46.00
io
0.3
48.63
ii
0.25
38.47
Q=T 240
Btu/ h r (t2 ,
RUN NO. 5W4H4
G =- 1 3 6 0
21,3
t
h
B t u / hr ft2 °F
I N38
Rep- ^y
FBH
l l ' m/ br f
i— e
Pr obe no.
Ha v =
Ioc
, Bt u/ hr f (2 °F
I
0.0
7.16
2
0.0
8.42
3
4
0.00625
10.37
0.0125
12.72
5
0.0125
16.25
6
0.025
20.12
7
0.05
23.79
8
0.0625
30.43
9
0. 1
37.04
10
0.15
38.99
11
0.25
39.00
Q=
2 54
Bt u / hr f t 2 ,
ha v =
041
21 . 9 Bt u/ hr f t 2 °F
-107-
RUN
Probe no.
:
'
FDH
IN I 2
lbInZhrft , Rup = 2 3 . 5 2 1
NO;
h | o , B t u / hr ft2 °F
I— €
I
0.0
I .67
2
0.0
I .49
3
4
0.0
I . 52
0.0
2. 11
5
6
0.0
2.79
0.0
3.70
7
0.0
6.34
8
0.0
17.67
9
0.5
33.89
io
0.35
42.01
ii
0.375
47.74
Q = 276
Btu/ hr ft2 ,
BtuZhrft2 o F
CxJ
CsJ CO
Il
2 ZK
7W1H2
RUN NO.
G = 1 097
hav = = 1 3 . 4
FBH
IbmZ h r f t 7-
I—G
h|oc , Btu/ hr ft2 °F
I
0.0
2.94
2
0.0
3.21
3
4
0.0
3.53
0.0
4.91
5
0.0
7.56
6
0.0
14.96
7
0.025
30.94
8
0.125
40.16
9
0.25
41.12
10
0.25
40.46
11
0.275
46.91
Probe no.
Q =
292
B t u / hr f t 2 ,
Hq v =
21 . I B t u / h r H 2 o F
-1087WI HS
G = 1325
RUN
FBH
NO.
R ep= 4 5 .855
h | o c , B t u / h r f t 2 °F
1— 6
P r o b e no.
31
in
Ibm / h r f t 2 ,
I
0.0
3.84
2
0.0
4.77
5
0.0
6.12
lV
0.0
7 . 57
2
6
0.025
13.34
0.05
21 . 7 2
7
8
0.125
33.27
0.175
32.29
9
0.2
36.43
10
0.2
37.10
11
0.275
44.49
Q=
run
310
B l u / hr ft2 ,
7W1H4
G - — 1490
NO.
21.6
FBH
ltW h r ft7-,
I—6
P r o b e no.
hav =
B t u / hr ft'-
IN 40
R e p = s i . 538
h |oc ,
B t u / hr f t 2 °F
I
0.0
6.54
2
0.00635
8.25
3
4
0.00635
9.85
0.0125
11.30
5
0.0375
14.55
6
0.05
21 . 63
7
0.05
32.54
8
0.125
37.72
0.125
43.52
10
0.175
43.91
11
0.225
58.40
9
Q =
# @)
Btu/hrft2 ,
°F
h Qv = 2 5 . 6
B tuZ hrft2oF
-109-
FBH
RUM NO. 7W2H1
G = 68 0
—€
h
Io f , B i u / h r f t 2 °F
I
0.0
2.43
2
0.0
2.63
3
0.0
2.99
4
0.0
3.52
5
6
0.0
4.47
0.0
6.04
7
0.0
10.42
8
0.0
28.94
9
0.0875
58.58
O
I—I
'
lbm A ' ft ,
I
P r o b e no.
12
S fp = 23.521
in
0.3
60.50
11
0.375
70.98
Q = 352
RUN NO.
G=
P r o b e no.
B t u / hr f t 2 ,
7 W2 H2
I 097
21.1
Iia v -
FBH
IbmZ h r f t 2-,
B i V h r ft2 °F
IN 19
R = P = 37.91
HIoc / B t u / h r f t - ° F
i —e
I
0.0
2.90
2
0.0
3.25
3
4
0.0
3.60
0.0
4.35
3
0.0 .
5.63
6
0.0
8.49
0.0625
20.81
0.075
30.99
0.25
33.62
10
0.25
34.03
11
0.325
36.07
7
8
9
Q — 294
B tu /h r ft2
,
h Qv = 1 g
2 B t u / h r ftZoF
RUN NO.
G=
7 W2 H3
1325
FDH
Ib m / h ’ fl ,
1— 6
Probe no.
IN
Rep h
| o c
27
45.865
, B t u / h r f t 2 °F
I
0.0
3.59
2
0.0
4.17
3
4
0.0
5.36
0.0
7.65
5
6
0.0
13.20
0.025
21.28
7
8
0.075
30.29
0.125
34.19
9
10
0.175
39.22
0.225
36.57
ii
0.275
42.28
Q=
run
285
B t u / h r f t 7-
7 VJ2 H4
.
G -= 1 49 0
I
2I. 4
Iio v =
FBH
IbmZ h r f t 2 ,
n o
P r o b e no.
,
— 6
B t u / hr ft2 c F
IN 38
Rep = J 1 5 3 8
^loc7
*ir f
I
0.0
4.58
2
0.0
5.54
0.00625
8.56
3
4
0.025
12. 01
0.0375
16.56
6
0.05
26.12
7
0.0625
32.52
8
0.175
33.06
0.2
35.64
10
0.245
36.15
ii
0.275
39.53
5
9
q =
Q
=
281
Bt u / hr f t 2 ,
H q v :=r 2 2 . 7
Btu/hrft^°F
-111-
FBH
' km Z hr f t '
RUN NO. 7W3H1
G = 680
Probu no.
in
I5
R- p —2 3 . 5 2 1
h | oc , Btu/ hr ft2 0F
i—e
I
0.0
2.75
2
0.0
3.15
5
4
0.0
3.52
0.0
4.17
5
0.0
4.98
6
0.0
7.23
7
8
0.0
13.83
0.0
44.11
9
0.0625
47.65
0.175
45.55
0.3
37.11
10
■ 11
Q =255
Bt u/ hr ft7',
7W3H2
RUN NO.
G- =
I 009
Ha v =
18,9
FBH
IbmZhr ft2,
Bt u Zh r f l 2 o F
IN
22
R e p = 24 g
i —e
h |o£ , Bt u/ hr ft2 °F
I
0.0
3.85
2
0.0
4.34
5
0.0
5. 11
4
0.0
6.65
5
0.0
10.76
6
0.0
20.72
7
0.025
36.53
8
0. 1
45.33
9
0.225
43.75
10
0.225
43.66
11
0.35
34.09
Pr obe no.
Q — 259
B v u / hr f t 2 ,
ha v — 2 3 . 2 G t u / h r f t Z F
RUN NO.
G=
P r o b e no.
'
7 W3 H3
1 238
I—
| f\j
FBH
! b m / h r f l 2,
€
31
42.821
Rep =
h
|oc ,
B t u / h r f t 2 °F
I
0.0
4.88
2
0.0
5.88
3
4
5
0.0
7.83
0.00625
11.05
0.025
15.65
6
0.0375
23.76
7
0.075
35.12
8
0.15
37.61
9
0.2
40.43
0.25
36.77
0.35
36.99
10
11
O = 268
B t u / hr ft2 ,
7W3H4
RUN NO.
G = - 1 49 0
P r o b e no.
23 3
hc v —
"
IN 41
Rcp= 51 _ 533
FBH
lbm Zhr ftz ,
1— 6
h
B f u / h r ft2 °F
Ioc
,
Bt u/ Itr
f t 2 °F
0.0
10.38
0.125
12.62
5
4
5
0.025
14.35
0.05
17.38
0.05
20.61
6
0.075
26.15
0.1
32.05
0.1
34.01
0.15
37.62
1
2
7
8
9
10
11
Q =27 I
0.15
'
0.225
Bt u / hr f t 2 ,
36.37
40.16
ba v =
2 5 . 5 B t u / h r ft Z°F
-113RUN
7W4H1
G=745
Probe no.
'
F BH
NO.
in
lbm' Z hr f t '
I5
fieP ^ s . 769
i—e
h
|o ( , Btu/ h r ft^ °F
I
0.0
2.96
2
0.0
3.31
5
4
0.0
3.85
0.0
4.54
5
0.0
5.94
6
0.0
8.96
7
8
0.0
20.31
0.025
54.88
9
0.2
62.02.
10
0.3
52.86
11
0.4
58.34
Q = 234
RUN
Bfo/ hr ft' ,
7W4H2
1054
FBH
NO.
G r=
lbm/ h r f t 2-,
I—e
P ro b e no.
Hciv — 2 4 . 5
Biu/ hr r l ? ° F
8N 22
Rep =
hIoc'
36.422
B f u Z h r f t 2- 0 F
I
0.0
3.95
2
0.0
4.66
3
4
0.0
5.53
0.0
6.88
5
0.0
10.70
6
0.0125
21 . 41
7
0.0375
37.30
8
0.15
50.53
9
0.25
55.22
10
0.3
46.47
11
0.3
38.57
Q=
230 ,
B t u / h r ft
^,
Hq v =
. R ' u / h r f t ?-°F
25.16
RUN NO- 7W4H3
G = i^3b
Re
'
IN 31
P
42.717
h | oc, R f u / h r f t 2 o F
I— 6
Probe no.
'
FKH
Ibmz / h r ft '
I
0.0
5.03
2
0.0
6 .3 7
3
0.0
8 .33
L\-
0.00625
13.52
5
0.0125
17.10
6
0.05
26.33
7
0. 1
39.20
8
0.125
40.37
9
0.2
45.23
IO
0.2
38.92
11
0.3
36.75
Q=
249
Bt u/ hr ft2 ,
RUN NO. 7 W4 H4
G := ' 4 9 0
25.4
—
FBH
IbmZ h r f R S
I—G
Pr obe no.
hav
B t u / hr ft2 °F
IN 44
Rep =S i . 538
h
Ioc
, Bf u / hr f
2
0.0
14.90
3
4-
0.0
15.96
0.00625
18.96
5
0.0125
21 . 57
6
0.05
7
0.1
32.89
8
0.125
36.31
9
0.2
47.12
10
0.2
60.56
11
0.3
61.19
q
—
246
B t u / hr f t ^ ,
OJ
12.80
OJ
0.0
r^.
I
°F
hQ v— 3 0 . 9Btu/lir
F
RUN NO.
G
=
■
9W1H1
745
h I o c , Bt u/ hr ft2 °F
I— €
Probe no.
•
FDH
IN 21
Ibm A r f t 2z R e p = 2 5 . 7 6 9
I
0.0
2.41
2
0.0
2.70
3
4
0.0
3.02
0.0
3.61
5
0.0
4.61
6
0.0
6.99
7
0.00625
18.54
8
0.15
29.33
9
0.3
36.34
10
0.3
37.69
11
0.375
4 7 . 20
Efu/ Urfi1 ,
Q = 271
9W1H2
G = = 745
IN 29
FEH
RUN NO.
Ibm/ hr ft2-,
I —6
Pr obe no.
1 6 . 7 Bt u / h r f r ° F
hav —
Rep = 3 4 . 9
hI
q c
,
Bt u/ hr ft2 °F
I
0.0
3.48
2
0.0
4.35
3
4
0.0
5.52
0.0
8.53
5
0.025
14.406
6
0.05
2 4 . 094
7
0.125
36.119
8
0.175
31
9
0.2
37.21
10
0.3
36.91
Ii
0.325
47.58
Q =
292
Bt u / hr ft ^
,
hav
—
.
99
22.5 Btu/hr
f t 2' ° F
RUN
NCk _9W1H3
G — 745
Probe no.
:
PB"
»M
! b m/ h r f t , Rep-
42
50.431
h |oe , Btu/ hr ft2 °F
1— 6
I
0.0
8.98
2
0.025
9.87
3
4
0.025
11.53
0.05
12.79
3
0.05
15.23
6
0. 1
17.54
7
0. 1
18.89
8
0.15
21 . 92
9
0.2
23.95
0.25
26.96
0.35
34.43
io
ii
hav = 1 8 . 1
Bl u/ hr ft2 ,
Q =279
9W1H4
RUN NO.
G — 887
FBH
IbrnZ h r t f S
IN
48
Rep = 5 7 . 6 2 5
h
I—6
Pr obe no.
B t u / hr ft2 c F
Ioc
, Bt u/ hr ft2 °F
I
0.0
11.09
2
0.025
13.34
3
4
0.025
13.29
0.0375
14.58
3
0.05
16.28
6
0. 1
19-85
7
0.125
21 . 4 9
8
0.15
21 . 8 0
9
0.175
28.23
10
0.175
35.57
ii
0.25
47.16
Q =
297
B t u / hr ft
,
h (JV=
2 I . 5 Bt u / h r f t 2 °F
RUN NOG=
9 W2 HI
1009
FBH
|N I 7
A r f t 7z Rep = 2 5 . 7 6 9
h I o c , B t u / hr f t 2 °F
I— 6
Probe no.
I
0.0
3.50
2
0.0
4.37
5
0.0
4.82
4
0.0
5.88
5
0.0
7.23
6
0.0
12.39
7
0.0
21.14
8
0.0625
36.67
9
0.225
40.03
10
■ ii
0.325
40.16
0.375
43.91
289
hr f t 2 .
B tu/
9W2H2
RUN NO.
G — 1 054
hov = 1 9 . 5
FBfi
IbmZ h r f t 2,
IN 24
Rep -
36.42
, Btu/ hr ft2 °F
I—€
Pr obe no.
B t u / hr ft2 0 F
I
0.0
4.95
2
0.0
6.03
5
0.0
6.90
4
0.0
10.57
5
0.0
14.74
6
0.0125
24.68
7
42.73
8
0.1
0 .2
9
0.325
39.53
10
0.325
40.66
11
0.45
34.33
Q=
294
Bt u / h r ft2 ,
45.37
hQV=
24 . 7Btu/ hr ft2 °F
-USRUN
N O-
G
Probe no.
'
9W2H3
1 0 09
38
ifsj
pbh
lbm / h r f t 2 ,
Rep =
50.43
h |o(Z B t u / hr ft2 °F
I— €
I
0.0
6.11
2
0.0
8.71
5
0.0125
12.35
4
0.0375
17.43
5
0.0625
21 . 59
6
0.1
31 . 95
7
0.15
32.49
8
0.15
31 . 47
9
0.225
32.03
1 0
0.225
33.18
i i
0.35
36.67
Q = 291
Bt u/ Iirft2 ,
9W2H4
G — 1054
RUN NO.
Huv — 2 4 . 2
FDH,
Ibm, / hr fU,
B t u / hr
ft7
cF
IN 47
Rep = 5 7 . 6 2
i — e
h ^ , Bt u/ hr ft 7- °F
I
0.0
15.75
2
0.0375
18.34
0.05
20.43
0.075
21 . 0 6
0.07 5
23.54
0.075
27.96
0.075
28.07
I .0
29.87
0.125
34.94
0.175
38.67
0.25
48.32
P robe no.
3
4
5
6
7
8
9
1 0
1 1
Q =355
B t u / hr f t 2 ,
h OV "
2 7 . 6 BtuA r f t 2 0F
RUN
NO
9W4H1
I 666
FBH
,m 2 I
lbH1A rft ,
Rep =
30.68
i—e
h B t u / hr ft- °F
I
0.0
3.77
2
0.0
4.50
3
4
0.0
5.36
0.0
7.07
3
6
0.0
13.06
0.0125
28.97
Probe no.
7
8
0.05
76.98
0.225
77.58
9
0.25
81.13
10
0.25
66.91
11
0.35
66.19
Q — 244
RU N
Bt u/ hr A >
9W4H2
G — I 694
MO.
P robe no.
btiV— 3 9 . 2
FBH
IbmZhr ft2 ,
I — e
h
Bt u / h r
IN 27
Rep = 3 6 . 4 2 2
Ioc
,
B t u / hr f t 2 °F
1
0.0
4.78
2
0.0
5.31
0.0
7.90
3
4-
5
6
7
8
9
10
11
Q =
246
0.00625
12.73
0.0125
21 . 66
0.05
36.15
0.125
46.49
0.225
43.45
0.25
45.07
0.35
38.82
0.35
34.95
B t u / hr ft^ ,
°F
ha v =
2 7 . 5 B t u / h r f t ? °F
RU N
NO.
G
9W4H3
1638
Probe no.
•
'
IN 38
FBH
lbm / hrft2.
i—e
43.375
llIoc' BfU//*,r ff2 0 f
I
0 .0
2
0.00625
3
4
0.0125
5
6
0.05
7
0.075
8
0.175
9
0.25
10
0.25
11
0.3
0.025
0.075
Q — 246
Bt u/ hr ft “ ,
RUN NO.
G = I 506
IbmZlir ft2-,
I—6
Pr obe n o .
hav — 3 1 . 6 DiuZhr ft7 °t.
IN 47
Rep - 5 2 . 0 5 6
H
, B t u / hr ft7-°F
Ioc
I
0 .0
15.19
2
0.0375
17.97
3
4-
0.05
20.42
0.0625
24.61
5
0.1
27.23
6
0.1
34.97
7
0.1
36.15
8
0.175
35.65
9
0.2
36.17
10
0.3
36.62
11
0.25
35.75
q
_
249
Btu/hrft2 ,
^q v — 3 0 . 4 Ct u/ hr ft2 F
MONTANA STATE UNIVERSITY LIBRARIES
N378
K562
cop. 2
Kim, Joon Taik
Heat tr a n s fe r in the
fin n ed f lu id iz e d bed
tubular h a t exchanger
NAMK AN O A O D w K Sg