A fluidized - bed heat transfer correlation
by Ralph Coolidge Huntsinger
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 Ralph Coolidge Huntsinger (1959)
Abstract:
The heat transfer properties of a fluidized bed of coke -particles are investigated in this thesis. A new
correlation that will satisfactorily represent the film heat transfer coefficient in terms of the physical
conditions of fluidization is developed. The correlation is developed for a fluidized bed using two
different gases as the fluidizing mediums, three different coke particle size ranges, and several different
fluidization rates. Air and CO2 were used as the fluidizing mediums. Mean arithmetic average particle
sizes of 0.00768-inch diameter 0.00528-inch diameter, and 0.00333-inch diameter of fluid coke were
used. The approximate mesh sizes were, respectively, 40 to 80 mesh, 50 to 100 mesh, and 100 to 300
mesh. The mass flow rates of the fluidizing gases were varied from 14.8 lb/hr-ft2 to 62.7 lb/hr-ft2. The
fluidized bed was heated from the outside and the heat transferred to water flowing through a loop of
copper tubing in the central portion of the fluidized bed. TheXpesulting correlation for the film heat
transfer coefficients for the film between the central copper loop and the fluidized bed is as follows:
(Formula not captured by OCR) The experimentally determined film heat transfer coefficients range
from 29.4 Btu/hr-ft2-° to 74.2 Btu/hr-ft2-°F. This correlation is applicable for certain fluidization
efficiency ranges as defined by a fluidization efficiency (Gf-Ge)/Gf. In these fluidization efficiency
ranges# the average positive deviation between the experimentally determined film coefficients and the
calculated coefficient at the same conditions from the correlation is 4.2% for 33 runs. The -average
negative deviation is -5.45$ for 31 runs. The correlation is based on the data from 64 experimental
determinations. The exponent on the Prandlt number applies to air or CO2 at l40°C but may not apply
to other gases. . -A FLUIDIZED -* BED HEAT TRANSFER'-. CORRELATION
by
■ RALPH . C. HUNTSINGER
%
. A THESIS
,-Subm itted to th e :■G raduate F a c u lty
In
p a r t i a l f u l f i l l m e n t . o f th e re q u ire m e n ts
f o r . t h e -degree .of
M aster o f S cien ce in Chemical E n g in ee rin g
at
Montana S ta te C ollege
Approved:
Bozeman^ Montana
S e p te m b e r,.1959
IV 31/
/
-2 -
TABLE OF CONTENTS
Page
A b stra c t .....................................................
3
In tr o d u c tio n
........................................
4
.....................................................
12
Theory
D esign and C o n stru c tio n of A pparatus
14
P rocedures
17
..............................................
D isc u ssio n of R e s u lts
.
.
.
.
20
L i t e r a t u r e C ite d
.................................
26
Acknowledgment .
.
27
Appendix
.
.
.
.
.
..............................................
28
137663
ABSTRACT
• The Jaeat t r a n s f e r p r o p e r tie s .of a. f l u i d i z e d bed. o f coke - p a r tic le s a re
i n v e s t i g a t e d .i n t h i s t h e s i s . A .new c o r r e l a t i o n t h a t w i l l - s a t i s f a c t o r i l y
r e p r e s e n t .th e film .h eat t r a n s f e r c o e f f i c i e n t in term s of th e p h y s ic a l
,c o n d itio n s . of f l u i d i z a t i o n is . developed... The c o r r e la tio n i s developed
f o r . a f l u i d i z e d bed u s in g two d i f f e r e n t g ases as th e , f l u i d i z i n g mediums,:
th r e e d i f f e r e n t coke p a r t i c l e s iz e .ranges * and s e v e r a l d i f f e r e n t f l u i d i ­
z a tio n r a t e s . A ir a n d -CO2 were Used a s . the. f l u i d i z i n g mediums. Mean
a r ith m e tic av erag e p a r t i c l e s iz e s .of . 0 . 0076.8-rinc'h .diam eter# 0 . 00528-in c h
d iam eter# and 0.003-33.-^inch d ia m e te r.o f f l u i d , coke were u s e d . • The a p p ro x i. mate mesh s iz e s were# r e s p e c t i v e l y , - 40 to 80 mesh, 50 . to 100 mesh, and 100
to 300 .mesh. - The .mass flow .r a te s of th e f l u i d i z i n g g ases were, v a rie d from
1 4 ,8 I b /h r ^ -ft2 to 6,2.7 l b / h r - f t 2 . • The f Iu id iz e d J b e d was h e a te d from th e
o u ts id e a n d .th e h e a t t r a n s f e r r e d to w a ter flo w in g th ro u g h a loop of copper
tu b in g in th e c e n t r a l p o r tio n of th e f l u i d i z e d b ed . •T h e X p e su ltin g .c o r r e la ­
tio n f o r th e film h e a t tr a n s f e r , c o e f f i c i e n t s f o r th e film lbetw een.- th e
.,.c e n tra l copper loop and .th e f l u i d i z e d b e d . i s . a s fo llo w s :
n Q..53
c ■- I - 6
V ( H el) =■ .1 .4 0 . ( V ^ t )
W
° )
kf
_/* f
kf
The e x p e r im e n ta lly .d e te rm in e d .film h e a t t r a n s f e r .c o e f f i c i e n t s range
from 2 9 .4 .B t u / h r - f t 2- 0-? 'to 7 4 .2 B t u / h r - f I 2- 0F'-. • This, c o r r e l a t i o n is
a p p lic a b le f o r . c e r t a i n - f lu id iz a tio n e f f ic ie n c y .r a n g e s a s .d e f in e d ,b y a,
f lu i d iz a tio n , e ffic ie n c y - (Gf - •Ge )/Gf . - I n t h e s e . f l u i d i z a t i o n e f f ic ie n c y
r a n g e s # .th e average p o s i t i v e d e v ia tio n betw een t h h ..ex p erim en tally d e te r s
.m ined..film c o e f f i c i e n t s and .th e c a lc u la te d c o e f f i c i e n t a t th e same, con•d i t io n s from th e ,c o r r e la tio n i s 4-. 2$ f o r 33 ru n s . The ..'.average n e g a tiv e
d e v ia tio n is. -5 .4 5 ^ f o r -31 ru n s . T h e - c o r r e la tio n is b ased on th e d a ta from
64 e x p e r im e n ta l.d e te rm in a tio n s . • T h e-ex p o n en t. on th e P r a n d lt number a p p lie s
to s i r . o r CQ2 a t l40°C b u t may n o t ap p ly to o th e r g a se s .
4-4
INTRODUCTION
S e v e ra l I n v e s tig a tio n s have been made on th e h e a t t r a n s f e r - p r o p e r t i e s
of beds o f f l u i d i z e d s o l i d s .
The p u rp o se of t h i s th e s i s i s t o . f u r t h e r
i n v e s t ig a te th e .h e at t r a n s f e r p r o p e r tie s of a f l u i d i z e d bed and to o b ta in
a new c o r r e l a t i o n t h a t .w ill s a t i s f a c t o r i l y r e p r e s e n t .th e f il m h e a t trans.~
f e r c o e f f i c i e n t in term s of th e p h y s ic a l c o n d itio n s of f l u i d i z a t i o n .
The re a so n f o r th e i n t e r e s t in th e film h e a t tr a n s f e r . c o e f f ic ie n ts
i s to determ in e th e c a p a b i l i t y o f - a . f l u i d i z e d b e d .to m a in ta in is o th e rm a l
.c o n d itio n s on an exotherm ic h y d ro g e n a tio n r e a c to r in s e r te d , in th e f l u i d i z e d
bed.
E x p erien ce w ith f l u i d i z e d bed te c h n iq u e s.w a s a ls o d e s ir e d .
I
. McAdams ( 6 ) d e s c rib e s a f l u i d i z e d bed in th e ,fo llo w in g .manner:
: "C onsider upward flo w .o f a gas .through a bed o f f in e ly .d iv id e d s o lid
m a te r ia l.
W ith low s u p e r f i c i a l v e lo c ity th e gas flow s th ro u g h th e i n t e r ­
s t i c e s of th e b e d , th e s o l i d rem ain in g f ix e d in p o s i t i o n .
At some h ig h e r
v e lo c ity , th e r e is a s h i f t i n g .of s o l i d w ith a s l i g h t . in c re a s e ..in bed volum e,,
and th e f r i c t i o n a l drag on each s o l i d p a r t i c l e beeoirfes h ig h enough to
su p p o rt i t w ith o u t c o n ta c t w ith o th e r p a r t i c l e s .
-The p r e s s u r e drop a t
t h i s p o in t is e s s e n t i a l l y e q u al to th e w eight of th e bed p e r u n i t cro ss
s e c tio n .
S ince th e p a r t i c l e s form ing th e bed a r e s e p a ra te d by f l u i d ,
-th e bed. is .u n a b le to r e s i s t a s h e a rin g fo r c e and behaves a s . a liq u id .
A b e d .of s o lid s e x h ib itin g t h i s c h a r a c t e r i s t i c i s term ed f l u i d i z e d , and
th e aboye co nditiohl-lis th e p o in t .of minimum f l u i d i z a t i o n .
At th e lo w est f l u i d i z i n g v e l o c i t i e s th e q u ie s c e n t bed h a s . a ..w e lld e fin e d upper -s u r f a c e , -and' th e r e i s l i t t l e m ixing of s o l i d s .
Over a
^5
.ra n g e .o f Q uiescence* s o l i d m ixing in c re a s e s * and. th e r e i s ,pronounced.
C ir c u la tio n - o f .th e f l u i d i z e d m ass.
The bed a t t h i s p o in t i s very, s im ila r
in appearance to a . I iQ u id : o b je c ts l e s s , dense th an th e bed..w i l l .f lo a t
on th e s u rfa c e * and d is tu rb a n c e Of th e s u rfa c e , causes r i p p l e s j th e
f l u i d i z e d .mass p o s s e s s e s h y d r o s ta tic head and w i l l flow betw een c o n ta in e r s .
The c o n fin e d s u rfa c e and smooth flo w .o f gas th ro u g h .the bed is .d e s c r ib e d
a s den se-p h ase f l u i d i z a t i o n .
• H igher gas v e l o c i t i e s r e s u l t . i n an im p o rtan t, change .in the. c h a r a c te r
of f l u i d i z a t i o n .
t h e 'SQ lids o c c u r s .
The bed ,becomes h ig h ly tu r b u le n t ,, and b a p id m ixing of
The s u r f a c e . i s no lo n g e r w e ll d e fin e d b u t .is . d if f u s e
a n d .b o ils v i o l e n t l y , and bubbles of g a s .s im ila r .in , ap p earan ce to th o s e in b o ilin g liq u id s r i s e th ro u g h th e bed.
At s t i l l . h i g h e r gas .v e lo c i tie s th e bubble's become la r g e enough to
fo r c e up m asses of p a r t i c l e s above them,} in sm a ll.b e d s th e s e bubbles may
e x ten d from, w a ll to w a ll.
s lu g g in g .
This c o n d itio ^ , o f ..f lu id iz a tio n i s .c a lle d
A f l u i d i z e d .'sy stem .in which th e s o lid s 'c o n c e n tra tio n is low
..and in w h ich T th eh e-is .no .b o u n d a ry ,d e fin in g th e upper s u rfa c e , of th e bed.
(a c o n d itio n more analogous to a gas than, a liq u id ) i s term ed d i s p e r s e . "
Tqomey a n d .Jo h n sto n e (12) in v e s tig a te d , th e ,h e a t t r a n s f e r .between
beds ..of f l u i d i z e d s o lid s and. th e w a l l s . o f th e c o n ta in e r.'
D ata are
p re s e n te d f o r .the .tr a n s f e r of h e a t from a c e n t r a l e l e c t r i c h e a te r - to
a v e r t i c a l f l u i d i z e d , .bed.*., and., th e n ce to th e w a lls of th e b ed .
-The
i n v e s t ig a ti o n w as-concerned o n ly .w ith th e h e a t t r a n s f e r . c o e f f i c i e n t a t
th e boundary, s u rfa c e s , of a f l u i d i z e d .system . . U sing , a i r as a .f lu i d iz in g
medium and B c o tc h lite g la s s beads f o r th e f lu i d iz e d .p a r tic le s ^ ■Toomey
,and.. Johns to n e o b ta in e d th e .fo llo w in g - c o r r e la tio n f o r th e - s u r f a c e h e a t
t r a n s f e r c o e f f i c i e n t y hs
(JLjV)
.lo g
k
where
..w °1 7
Jmf.
.k = h e a t .t r a n s f e r c o e f f ic ie n t
D = D iam eter of p a r t IcvIe s
yur = -V isd o sity o f gas
/O .= D e n sity o f gas
V if “ Gas v e lo c i ty a t minimum -f l u i d i z a t i o n .
U ^ .Gas v e lo c ity
k = Thermal .c o n d u c tiv ity of th e gas
The v a lu es o f h .used in. o b ta in in g th e above - c o r r e l a t i o n ra n g e d .fro m 3 ,2
- B tu /h r ^ f t2 to 118 -B tu Z h rrftV 0F-.
• An improvement in th e c o r r e l a t i o n su g g e ste d by L e v e n sp ie l and-W alton
( 5 ) f o r h e a t t r a n s f e r betw een a f l u i d i z e d bed and a c o n fin in g w a ll was
p ro p o s e d .b y -R u c k e n ste in a n d •S cho rr (1 1 ).
-The fo llo w in g c o r r e l a t i o n was
su g g e s te d :
„
--*0 .5
- ,( h^
).= 0.68 (
k
where
'
Um ^
V
2^
;
V3
0 .5
L jff)
JT~
(Pr)
J z = K in e m a tic .v is c o s ity
P r = P ra n d lt Number
v ■=.R ate of f a l l of p a r t i c l e s n e a r th e w a ll
-Um = .Average v e lo c ity
hw = Film h e a t t r a n s f e r c o e f f i c i e n t
k •=.Thermal c o n d u c tiv ity .o f th e gas
^ = P o r o s ity of th e bed
D = D iam eter of p a r t i c l e s
D
-7 -
A g e n e ra liz e d . .dense.-‘phase .c o r r e la tio n f o r th e film h e a t t r a n s f e r
c o e f f i c i e n t was g iv e n by Men and- Leva (1 5 ).
A f l u i d i z e d bed .heat t r a n s -
.f e r mechanism was proposed, t h a t assumes t h a t th e c h ie f r e s i s t a n c e to h e a t
exchange betw een a -c o n fin in g w a ll and a f l u i d i z e d bed i s in th e lam in ar '
f ilm a t th e v e s s e l .boundary. - Heat flow th ro u g h . th e .film i s by co n d u ctio n .
■The f i n a l c o r r e l a t i o n o f >w a ll- b e d . c o e f f i c i e n t s is as fo llo w s :
0.5
( h Dp) = . 0 .1 6 ( 0S ^ s
—
where
-
-
= Gy
■
p
k
.. s .
0 . 4-
)
*
( j
,0.36
pP ^ )
Ji R
Ge
c
g
CL
Gg
=. .Heat c a p a c ity o f th e p a r t i c l e s
= A c c e le ra tio n -of g r a v ity
= Mass v e lo c i ty ,o f gas
= .Mass v e lo c ity of gas f o r expansion, of bed.,
. but not fo r flu id iz a tio n
R .= Bed ex p an sio n r a t i o
k = Thermal c o n d u c tiv ity of gas
j i = V is c o s ity of gas
D = D iam eter of p a r t i c l e s
.(Og.= D e n sity , of s o lid s
h = F ilm h e a t . t r a n s f e r - c o e f f i c i e n t
The above c o r r e l a t i o n i s compared w ith th e r e s u l t s - o f t h i s t h e s i s on
page 20-.
A ccording ,to Dow.and.Jakob (2) th e f l u i d i z e d bed h e a t t r a n s f e r co­
e f f i c i e n t s vary as th e 0 . 6 5 -power of th e d ia m e te r - h e i g h t.r a tio .
The .hjeat
t r a n s f e r c o e f f i c i e n t s , a c c o rd in g to Dow and .Jak o b , a re a ls o p ro p o rtio n a l,
to th e .0.67 power of th e th e rm a l c o n d u c tiv ity of th e f l u i d i z i n g g as.
■The h e a t t r a n s f e r c o r r e l a t i o n of Wen and Leva has been p u t in to
homograph form by Wen and. Fan (l4 ) . -This f a c i l i t a t e s r a p id com putation
-8 -
.o f th e h e a t t r a n s f e r f ilm c o e f f i c i e n t from p h y s ic a l c o n d itio n s .
A c o r r e l a t i o n of s o lid s tu rn o v e r in f lu id iz e d .s y s te m s a n d .i t s r e l a t i o n
to h e a t t r a n s f e r was p re s e n te d by beya and Grummer (4)„ • The v e lo c i tie s
of f l u i d i z e d p a r t i c l e s and th e r e la tio n s h ip to th e f ilm h e a t tr a n s f e r o o . e f f i c i e n t s were a n a ly z e d .
T he■c o r r e l a t i o n i s as f o llo w s :
s
Ta o
h = 3 .0 x IOb k D (DP
, .
'v
.u R
)
° -6
Symbols a re d e fin e d as in th e c o r r e l a t i o n of Wen an d-L eya.
Leva and
Grummer s t a t e t h a t th e f ilm h e a t t r a n s f e r c o e f f i c i e n t s .a re p r a c t i c a l l y
indep en d en t of th e th e rm a l c o n d u c tiv ity of th e s o l i d s .
.M easurements of c o e f f i c i e n t s of h e a t t r a n s f e r from f l u i d i z e d beds to
h o r iz o n ta l w a te r cooled, tu b e s were perform ed, by Yneedenberg (13)..
The
fo llo w in g q u a n t i t i e s were v a r ie d in th e i n v e s t ig a ti o n : . (I) bed tem pera^
tu n e s * (2 ) mass v e lo c ity , of. th e f l u i d i z i n g a i r , (3 ) mean p a r t i c l e d iam eter,,
.(4 ) p a r t i c l e s h a p e ,•(5) p a r t i c l e d e n s it y , ( 6 ) w a ter tu b e d ia m e te r.
The
c o r r e l a t i o n of c o e f f i c i e n t s of h e a t t r a n s f e r betw een a tu b e -a n d -a gas o r
a liq u id , flo w in g n o rm ally to t h a t tu b e were re p re s e n te d .b y . a s t r a i g h t l i n e
o b ta in e d .b y . p l o t t i n g th e ■NusseTt group d iv id e d by P r0 , 5 .a s a fu n ctio n of
th e Reynolds group. . The fo llo w in g c o r r e l a t i o n was g iv en f o r f in e p a r t i c l e s
.( h P t )
.
.
k
.
(U c0 ; 3
'k
where
.P M
= 0 . 6 6 '1«. Pt Z0 s 1 1 ^ e l )
/0 P
t - '
• D-j,
•G
^
£
;h
jg>
yu
k
c
= D iam eter of tube
.= Mass v e lo c i ty of gas
= D e n sity of p a r t i c l e s
- P o r o s ity of bed
= .F ilm -h eat t r a n s f e r c o e f f ic ie n t
= D e n sity of gas
= V i s c o s i t y . of gas
= Thermal c o n d u c tiv ity of gas
= H e a t.c a p a c ity , o f s o lid s
. The mechanism of h e a t t r a n s f e r to f l u i d i z e d beds was in v e s tig a te d ..b y
- K ik ley an d -F airb an k s- (7 ) . - I n o rd e r to d eterm in e th e n a tu r e .o f th e r e s i s ­
ta n c e c o n tr o llin g h e a t t r a n s f e r betw een f l u i d i z e d
beds and s u rfa c e s in
c o n ta c t w ith them , h e a t t r a n s f e r measurem ents ^ e re made on th e same s o l i d
.c o n s titu e n ts w ith s e v e r a l - d if f e r e n t f l u i d i z i n g ,g ases.
The h e a t t r a n s f e r
C o e f f ic ie n ts o b ta in e d ..with f l u i d i z e d beds a re found to - b e - p r o p o r tio n a l
.to th e . sq u are r o o t of th e th e rm a l c o n d u c tiv ity of th e q u ie s c e n t b e d s ;
This r e s u l t in d ic a te d t h a t th e p ro c e ss c o n tr o llin g f l u i d i z e d .,heat t r a n s f e r
may.be c o n sid e re d to be an u n s te a d y - s ta te d if f u s io n of h e a t in to m obile
elem ents of q u ie s c e n t bed m a t e r i a l s . • This s i t u a t i o n was an aly zed
m a th e m a tic a lly to y i e l d th e fo llo w in g e q u a tio n f o r th e h e a t tr a n s f e r
.c o e f f ic ie n t:
1V= / ' V f n
where
° 'S
Km = Thermal c o n d u c tiv ity , of th e q u ie sc e n t-b e d
/O = D e n sity of q u ie s c e n t s o lid
c = Heat, c a p a c ity of f lu i d i z e d .s o lid
S ,= -Area-mean s t i r r i n g f a c to r
Heat t r a n s f e r c h a r a c t e r i s t i c s . o f f l u i d i z e d beds were in v e s tig a te d
,by M ickley a n d - T r illin g (8 ) .
-The-purpose of t h i s work was to .d e te rm in e
th e e f f e c t ..of th e p re s e n c e -of th e v io le n tly tu r b u le n t s o lid s on h e a t
tr a n s f e r , c o n d itio n s a t s u rfa c e s in c o n ta c t w ith th e gas s o l i d m ix tu re ,
-1 0
G lass sp h eres w ith d ia m e ters ra n g in g from 0.002 in ch es to 0 .0 2 inches were
u se d .
A ir was usfed f o r th e f l u i d i z i n g medium, •Work was done on i n t e r n a l l y
a n d - e x te r n a lly h e a te d b e d s .
The .fo llo w in g c o r r e l a t i o n s . were o b ta in e d , b u t
a re found to be in e r r o r f o r sm all p a r t i c l e s i z e s .
C o r r e la tio n f o r Interj*-...
n a l l y h e a te d b e d s :
h = 0.0433 - ( / f m f j 0 ' 258
D 3
C o r r e la tio n f o r e x te r n a ll y h e a te d b e d s :
0.263
.h = 0.0118 (/^m Go )
DP 3
where
/^m = S o lid c o n c e n tra tio n in f l u i d i z e d m ix tu re
G0 = S u p e r f ic ia l mass r a t e of flow, o f gas
.H eat t r a n s f e r and. f o u lin g of f l u i d i z e d beds was in v e s t ig a te d by OwBn
and Dean (9 ) .
A ccording to them , v a r i a t i o n i n h e a t t r a n s f e r in beds of
p a r t i c l e s f l u i d i z e d w ith a i r app ears to be a. d i r e c t f u n c tio n of p a r t i c l e
m otion and an in v e rs e f u n c tio n of voidage f o r a g iv en s o l i d .
Heat t r a n s f e r to a l i q u i d f lu i d iz e d .b e d was in v e s tig a te d by- Lemlich
and C aldas (3 ) .
An e x p e rim e n ta l stu d y o f th e r a t e of h e a t t r a n s f e r from
th e r e t a i n i n g w a ll to a f lu i d iz e d .b e d of s o lid s was C a rrie d ou t fo r. l i q u id
w a te r and ..glass s p h e r e s .
Independent v a r ia b le s in c lu d e d mass v e l o c i t i e s ,
p a r t i c l e s i z e , b u lk te m p e ra tu re , and w a ll te m p e ra tu re .
c o r r e la tio n s were g iv e n :
■•hmax
• (Nu)
.P
h
=
34,400 (D 't )
.0.055 (Re)
0..055
k
q
- O.77
P
The fo llo w in g
11-
■where
Iirnfly = Maximum h e a t t r a n s f e r c o e f f i c i e n t
D1-J- = .Diameter of p a r t i c l e in m icrons
N.Up = N u ss e lt number based qn p a r t i c l e s iz e
Re . =. Reynolds number .based .on p a r t i c l e s iz e
G
= Mass .v e lo c ity of l i q u id
^u
= V is c o s ity of l i q u id
k
= Thermal c o n d u c tiv ity of l i q u i d
A h e a t t r a n s f e r c o r r e l a t i o n f o r a f l u i d i z e d b e d .u s in g two d i f f e r e n t
g ases as th e .flu id iz in g .m e d iu m s , th r e e d i f f e r e n t p a r t i c l e s iz e s .a n d s e v e r a l
d i f f e r e n t f l u i d i z a t i o n r a t e s i s developed in t h i s t h e s i s . - The f lu i d i z e d
bed was h e a te d from th e o u ts id e and th e h e a t tr a n s f e r r e d to w a te r . flo w in g
thro u g h a loop o f copper tu b in g in th e c e n t r a l p o r tio n o f th e b ed . - The
h e a t t r a n s f e r c o e f f i c i e n t s in v e s tig a te d in t h i s th e s i s a re th o se f o r th e
f i l m betw een th e c e n t r a l copper loop and th e f lu i d iz e d ,b e d .
THEORY
A d im e n sio n al a n a ly s is was p erfo rm ed .o n th e s e v e r a l v a r ia b le s in
th e f l u i d i z e d system .
Vy a n d S y m b o l s
.The v a r ia b le s c o n sid e re d a re h , k ^ , -D^,
c,gi.
a re defined, a t th e end o f t h i s s e c t i o n y w ith y .a n d
Z3 r e p r e s e n tin g r e s p e c tiv e ly th e gas v e lo c i ty through th e bed and th e
d e n s ity o f th e f l u i d i z i n g g a s.
The fo llo w in g d im e n sio n less groups and
t h e i r R e la tio n s h ip were o b ta in e d by th e "Improved P i Theorem" as d e sc rib e d
i n McAdams. ( 6.) :
(■h D p.)
D,
Q
jif
±0
. ( ° s ^ Dp V
k
)
The t h i r d . l i s t e d group can be f a c to r e d as f o llo w s :
(cS ^ jpP v ) =
f o cS ) (■ Dp y/°)
A
kf
The Q u a n tity V p i s e q u al to Gf .
The r e s u l t i n g r e l a t i o n s h i p can be e x p re s s e d .b y a power s e r i e s of th e
fo llo w in g form :
(. h Pp ) =
■kf
(DP ' Gf ) a ^
' A \'
(A
0S J h l
kf
(A
+ < ( pP &f
A
c S )b2 +
.....
kf
Only th e . f i r s t term of th e s e r i e s ^ i l l be assumed to have s u b s t a n t i a l
v a lu e so th e r e s u l t of th e ■d im en sio n al a n a ly s is i s as f o ll o w s :
( h pP )
Gf )a
A
pS)
A
(5)
The p roposed c o r r e l a t i o n i s o f th e fo llo w in g form:-
V
(rn ) = o C (R e )a (Pr>b
■Ku = .Nussfelt number (h % ,)
Xf
Re = Reynolds number ( Dp Sf )
P r = P r a n d lt .number
cs)
a.yb. = Exponents
oC = C onstant
h
-.E llm h e a t t r a n s f e r .c o e f f ic ie n t
• (B tu /h r - f t Sw°F)
D .= D iam eter of p a r t i c l e s ( f t )
p
Efl •= Thermal c o n d u c tiv ity , of th e f l u i d i z i n g ,gas
(Btu/hr-yf t 2-:°F)
Gf
= .Mass flow r a t e o f .t h e f l u i d i z i n g gas
(Tb/hr-rf t 2 )
Uf
= V is c o s ity of th e f lu i d i z i n g .g a s
(lb /ftr h r )
c
= .H e a t.c a p a c ity of th e s o l i d p a r t i c l e s
’ •
(B tu /lb -^ F )
S
■DESIGN MD CONSTRUCTION OF APPARATUS
The b a s ic purpose o f th e a p p a ra tu s was to p ro v id e a means of
m easuring th e film h e a t t r a n s f e r c o e f f i c i e n t betw een a. f l u i d i z e d bed of
s o lid s and a m e ta l w a ll. . Heat was tr a n s f e r r e d , to th e bed. by two n'ichrome
w ire h e a tin g c o i l s .
C o il "a" was wound around th e upper .h a lf o f th e bed
and C o il "b" was wound around th e low er h a l f of th e bed; (see F ig I),.
The bed s e c tio n of the- a p p a ra tu s was a th re e ^ in c h d ia m e ter s t e e l .pipe*
-27 in c h es in le n g th ; (see F ig l ) . - The top o f th e a p p a ra tu s was an
en larg ed , s e c tio n made o f f iv e - in c h -d iam eter s t e e l p i p e ,.1 2 in ch es in
le n g th .
The e n t i r e a p p a ra tu s was in s u la te d .o n , th e o u ts id e * a n d .th e n
w rapped.w ith aluminum f o i l to m inim ize r a d ia tio n lo s s e s to th e su rro u n d ­
in g s .
-At th e bottom of th e bed was a tw o -in ch d ia m e ter s in te r e d , b ra ss
■porous p l a t e f
This p l a t e s e rv e d .a s th e incom ing gas d is p e r s e r .
At th e
top of th e e n la rg in g s e c tio n th e r e was a sm a ll cyclone to c o l l e c t th e
f in e s a n d .r e tu r n them to th e bed .
A l / l 6rin c h d iam eter s t a i n l e s s . s t e e l
.therm ow ell was lo c a te d in t h e .c e n t e r o f th e b e d ;- (see F ig I ) .
The c e n t r a l .loop was made in two p a r t s .
The s e c tio n th ro u g h th e
■enlarged s e c tio n a t th e top of th e top o f th e .a p p a ra tu s was l / 8-in c h
s ta n d a rd d ia m e te r■s t e e l p ip e . • C onnected to th is * -a n d making a .lo o p th ro u g h
th e c e n t r a l .p o r t i o n of th e f l u i d i z e d b e d , was a s e c tio n of l/4 r in c h
d ia m e ter so ft-d ra w n copper tu b in g w ith i t s lo n g itu d in a l a x is c o in c id in g
w ith th e l o n g itu d in a l a x i s . o f th e f l u i d i z e d bed; (see F ig I),.
The tu b in g
ex ten d ed 25 in c h es down in to th e bed and.was 47 in ch es in le n g th . •The
c e n t r a l loop was I n s u la te d from th e to p of th e bed s e c tio n ,, .up.
The
copper loop was s l i g h t l y ta p e r e d ,.w ith th e d is ta n c e between, c e n te rs a t
th e top o f th e loop .being two in ch es and th e d is ta n c e betw een c e n t e r s .a t
th e b o tto m .o f th e loop b e in g .1-1 /2 in c h e s .
The bend a t th e bottom of th e
■loop was a .s e m i-c irc le w ith a V 1H in c h .r a d iu s . ■The w a ll .th ic k n e ss o f .th e
copper loop was Q.OJ in c h e s .
The bottom of th e loop was 4 -.inches aboye
•th e porous p l a t e a t . t h e bottom e f th e bed.
The bottom of th e loop was
b ra c e d .w ith heayy nichrom e w ire t h a t was wrapped around th e loop and ex­
te n d ed to th e w a lls of th e bed c o n ta in e r .
This was to m inim ize any e f f e c t s
■of v i b r a t i o n . ■Skin therm ocouples were made by imbedding th e therm ocouple
-leads in o p p o s ite s id e s of th e c o p p e r•tu b in g .
Thermocouples made in t h i s
manner were p la c e d one in ch .below th e in s u l a t i o n on th e . i n l e t and o u t l e t
s i d e s .o f th e copper loop and wbre ap p ro x im ately .o n e. in c h below th e top of
th e f l u i d i z e d bed.
The . i n l e t w a ter p r e s s u r e was c o n tr o lle d by a c o n s ta n t p re s s u re
r e g u la to r s e t a t 45 l b / i n 2 . on th e i n l e t w a ter l i n e .
The i n l e t w ater
te m p e ra tu re was m easured w ith a p r e c is io n therm om eter s e t in a therm ow ell
in th e i n l e t w a ter l i n e ; (see F ig 2 ) . - T h e .o u tle t w ater was ru n in to th e
bottom of a q u a rt dewar f l a s k a n d . d r a in e d . o f f th e top of th e f l a s k ; (see
-Pig 2 ) . ■The f l a s k was f i l l e d .w ith aluminum f o i l b a f f le ^ to h elp , m ixing.
■The o u t l e t w a ter te m p e ra tu re was measured, by a. p r e c is io n therm om eter p la c e d
in th e top of th e f l a s k .
■Thermocouples w e re .c o n n e c te d .in o p p o s itio n from
th e i n l e t w a ter therm ow ell and. t h e ■o u t l e t w a ter dewar f l a s k to g iv e th e
m i l l i v o l t s induced by th e i n l e t and o u t l e t w a te r te m p e ra tu re d if f e r e n c e .
- -T -
I 6 -1
The therm ocouples were .connected to a Brown, c o n tin u o u sly re c o rd in g mi111.. v o ltm e te r.
- The . i n l e t w ater f lo w .r a te s were in d ic a te d on a carbon te tr a c h l o r id e
manometer on th e i n l e t w a ter -stream .
The w ater flow .ra te s .w e re c o n tr o lle d
.by. a y a lv e on th e e x i t w a ter stre am so th e w a te r .in th e -c o p p e r loop was
a t a ,c o n s ta n t p r e s s u r e of 45- l b / i n 2 ,
■The i n l e t gas f lo w .r a te s were o b serv ed on a .mercury manometer on th e
i n l e t g a s .s tre a m . - T h e .in le t a i r p r e s s u r e was c o n tr o lle d w ith
p r e s s u r e r e g u la to r s e t a t 3Q l b / i n 2 on th e i n l e t a i r l i n e .
a c o n sta n t
- The CO2 p r e s ­
s u re was c o n tr o lle d w ith a c o n s ta n t p r e s s u r e . r e g u la to r a tta c h e d .to th e CO2
c y lin d e r .
T h e .in le t p r e s s u r e of CO2 was h e ld c o n s ta n t a t 30. l b / i n 2 .
The
c o n s ta n t gas p r e s s u re s w ere-needed to a s s u re a c o n s ta n t gas flow , r a t e
th ro u g h th e c o n tro l, v a lv e w ith o u t re p e a te d a d ju stm en t d u rin g a run..
A fte r
p a s s in g through th e m anom eter> th e gases were a t a tm o sp h eric p r e s s u r e . ■
■ The bed., te m p e ra tu re was m easured w ith an iro n * c ons ta n ta n therm o. couple i n s e r t e d . in. th e .c e n tr a l bed th erm o w ell.
. Bed p r e s s u r e drop measurem ents were ,made w ith a g la s s tu b e w ith a
porous p lu g on th e e n d y . in s e r te d , to th e bottom of th e b e d . -The top of
th e tu b e was co n n ected to a carbon t e t r a c h l o r i d e manometer c o n s tru c te d
to m easure a maximum p r e s s u r e d if f e r e n c e of I? in ch es of carbon
te tra c h lo rid e .
-1 7 -
PROCEDURES
■The .heat t r a n s f e r ru n s were s e t up so t h a t th e method of c ro s s p l o t t i n g co u ld be used to o b ta in th e exponents and. c o n s ta n t on th e p ro ­
posed c o r r e l a t i o n from th e r e s u l t i n g d a ta .
Runs were made .in th re e ,blocks
w ith .the p a r t i c l e s iz e b e in g c o n s ta n t f o r each b lo c k .
v a rie d in fo u r s t e p s . f r o m -14.8 l b / h r - f t 2 to
The a i r . r a t e was
6 l b / h r - f t 2 f o r w ater
r a t e s of 125 . l b / h r and IOti- I b / h r . ■CO2 .was th e n used and. i t s flow r a te
was v a rie d from 19. 1 3 .I b /h r - h 't2 to 62. 7 - l b / h r - f t 2 f o r th e same w ater
ra te s .
These w a te r r a t e s w ere b o th .in th e tu r b u le n t flo w ran g e .in. th e
copper lo o p .
Two w a te r .r a t e s were used to p ro v e th e assu m p tio n t h a t
th e w a te r .r a t e on t h e . i n s i d e , o f th e copper loop has v ery l i t t l e e f f e c t
on th e h e a t t r a n s f e r C o e f f ic ie n t betw een th e o u ts id e .of th e tu b e and
th e f l u i d i z e d bed.
D eterm in atio n s o f th e f ilm h e a t t r a n s f e r . c o e f f ic ie n ts a t two con^
d itio n s were re p e a te d s e v e r a l tim es th ro u g h o u t th e e x p erim en t.
This was
done to s e e -w h e th e r a run. co u ld be re p e a te d and g iv e th e same r e s u lts .,
a n d .a ls o to check th e equipm ent f o r m a lfu n ctio n , d u rin g th e c o u rse of th e
e x p erim en t.
This p ro c e d u re th e n gave u s as in d ep en d en t v a r i a b l e s ; type
of f l u i d i z i n g medium, p a r t i c l e s i z e , mass f lo w ,r a te of w ater* and mass
flow r a t e .of g a s . -A ll runs, w ere made w ith th e bed .tem p eratu re a s c lo se
as. p o s s ib le to l40°'C.
The :mean a r ith m e tic average, p a r t i c l e s iz e was d eterm in ed by. a sc re e n
a n a l y s i s ;• (see Table I ) .
The av erag e p a r t i c l e s iz e of any one sample was
d eterm in ed from th e f o llo w in g .e q u a tio n from Brown (I).:
- 18 - '
where
D ( a y e ) -= Average p a r t i c l e s iz e of
^
th e sample
' X1
= W eight f r a c t i o n of p a r t i c l e s
betw een two sc re e n s
D .
= .A rith m etic a v e r a g e ■of th e
p
two s c re e n openings
The average p a r t i c l e s iz e s used in t h i s experim ent were 0 .0 0 7 6 8 -in ch
diam eter-, 0 . 00528*-in ch diam eter., and 0 . 00553-in d h . d ia m e ter of f l u i d
coke. -The approxim ate mesh s iz e s w ere, r e s p e c tiv e ly ,: 4-0 to 80 mesh,
50 to 100 m esh, and 100 to 300 mesh.
The gas manometer was c a li b r a t e d f o r b o th a i r and. CO2 w ith a wet
t e s t m e te r.
The w a ter manometer was c a l i b r a t e d by ,running w a te r .in to
a f l a s k f o r a m easured tim e and w eighing th e f l a s k to d eterm in e th e
w eight of w a ter d e liv e r e d p e r u n i t tim e .
The p re s s u re drop a c ro ss th e bed was m easured by a manometer f i l l e d
w ith carbon t e t r a c h l o r i d e . - The gas flow r a t e f o r e a c h .in c re a s in g ,p re ssu re
drop was m easured w ith a wet t e s t m e te r. ■The v is c o s ity and th e therm al
c o n d u c tiv ity of th e gas f o r each s e t of .c o n d itio n s were d e term in ed ,b y
,.data o b ta in e d from P e rry ( 1 0 ) . . -The o p e ra tio n of th e a p p a ra tu s was
perform ed in th e fo llo w in g m anner: .The a p p a ra tu s was s e t. up as in P ig 2.
W ater was s t a r t e d flo w in g th ro u g h th e copper loop a t th e d e s ir e d flow
r a t e . ■The bed was f l u i d i z e d and th e h e a tin g c o ils were tu rn e d on.
h e a tin g c o ils were c o n tr o lle d by v a r ia b le v o lta g e v a r ia c s .
The
The bed was
-1 9 -
Jie a te d to I 1JrO0C and then, t h e . vari-acs were a d ju s te d to o b ta in s te a d y s t a t e o p e ra tio n a t t h a t te m p e ra tu re . ■Around 5 to 10 m inutes were
allo w ed a t c o n s ta n t c o n d itio n s to a s s u re a good approach to s te a d y s t a t e o p e ra tio n .
The re c o r d e r f o r - t h e te m p e ra tu re d if f e r e n c e , between
i n l e t and o u t l e t w a ter .te m p e ratu res was th e n tu rn e d on. ■I n l e t and
o u t l e t w a ter te m p e ra tu re s were re a d and w r itt e n on th e r e c o r d e r .c h a r t.
When a s t r a i g h t , l i n e appeared ..qn th e r e c o r d e r ,- . th e loop w a ll te m p e ratu res
and th e w a ter te m p e ra tu re s were re c o rd e d f o r th e c o n d itio n s .o f th e ru n .
One or,m ore of th e in d ep en d en t v a r ia b le s were changed .and th e o p e ra tio n
re p e a te d f o r a new ru n .
• This p ro c e d u re was t r i e d f o r a sm all p a r t i c l e s iz e -of s i l i c a alum ina c a t a l y s t .
, The o u t l e t w ater te m p e ra tu re was found to v ary in
c y c le s s e v e ra l, m inutes Io n g y, t h a t k e p t g e ttin g ,lower w ith tim e , even
though th e .c o n d itio n s of th e run re m a in e d ,c o n s ta n t.
-Upon rem oving.and
o b se rv in g th e copper loop a f t e r a, ru n o f t h i s . t y p e , . t h e s u rfa c e of th e
loop was found to be c o a te d w ith a s u b s t a n t i a l l a y e r . of th e p a r t i c l e s
u sed .
I t . i s assumed t h a t th e p a r t i c l e s had b u i l t up a charge of s t a t i c
e l e c t r i c i t y upon f l u i d i z a t i o n and were c lin g in g to th e copper loop by
e le c tro s ta tic a ttra c tio n .
■The p a r t i c l e ty p e was changed to f l u i d coke,
and, th e tro u b le d is a p p e a re d , as carbon is. ,a .very good, co n d u cto r of
■ e le c tr ic ity and th e p a r t i c l e s w i l l n o t r e t a i n a s t a t i c c h a rg e .
-2 0 -
DISCU'SSION OP RESULTS
■Figures 3 and 4 show th e p lo ts o f th e lo g of (Dp h /k p ) p l o t t e d v ersu s
th e lo g of (Dp
f o r CO2 .
The d a ta f a l l s in two lin e s , one f o r a i r and one
D e te rm in a tio n of film ,c o e f f ic ie n ts a t two c o n d itio n s were r e ­
p e a te d s e v e r a l tim es w ith good r e l i a b i l i t y .
These c o n d itio n s were a i r
a t 2 7 .9 T b / h r - f t 2 w ith an av erag e p a r t i c l e s iz e of O.OO768 in c h , and a i r
a t ; 27.9 l b / h r - f t 2 w ith an av erag e p a r t i c l e .s iz e - o f 0.00333 in c h .
A
s t r a i g h t l in e is .d ra w n th ro u g h th e c e n te rs , of th e se two groups o f - p o i n t s .
A second l i n e w ith th e same s lo p e was drawn th ro u g h th e p o i n t s . f o r th e
CO2 ru n s which appeared to b e s t f i t th e d a ta . - The s lo p e of th e two lin e s
i s th e v a lu e of th e exponent " a " .o n th e Reynolds number in th e proposed
.e q u a tio n .
The v alu e of "a" is 0 .5 3 .
■At a c o n s ta n t v a lu e .of (Dp Gfl^juf ) , v a lu es of lo g (h DpA f ) from th e
li n e s a re p l o t t e d v e rsu s lo g . (^if c g/ k f ) > (.see. P ig 5) •
The slo p e of t h i s
l i n e is th e v alu e of th e exponent . "b" on th e P ra n d lt number in th e p ro ­
posed .c o r r e l a t i o n .
(^uf cgA f )
The v a lu e of "b" i s . -I.. 6 .
i s p l o t t e d v e rsu s lo g (h DpA f ) •
On P ig 6 y lo g (Dp
^
A l i n e of s lo p e one,
which appeared to b e s t f i t th e d a t a , was drawn, through th e p o in ts on
th e p l o t .
The i n t e r c e p t , of th e l i n e w ith th e (h DpA f ) ..axis i s th e ■v alu e
o f .t h e c o n s ta n tc < in th e p roposed c o r r e l a t i o n .
-The-.value . . o f i s
-The. fo llo w in g , th e n , i s th e f i n a l c o r r e la tio n :
Dn
kf
1 ,4 0 ( ^ 2 )
/f
- 1 .6
1 .4 0 .
• The p r e s e n ta tio n o f th e e q u a tio n s from which th e f ilm 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 th e o v e r a l l h e a t t r a n s f e r c o e f f ic ie n ts were c a lc u la te d
is found on page 51 in th e append ix .
S a m p le .c a lc u la tio n s f o r ru n No. l 4 l a re as fo llo w s :
■.Data f o r C a lc u la tio n s
■¥.:= 125 (lb ) . (hr)
( I 1^ t 2 ) .= (9 . 9 } (1 .8 ). F°
, Cp-= I (B tu-.)/(lb) ■( 0F)
I k e d - t Skin-l M
r- (W .5 ) u - s i r
. A.= Q.256 ( f t a )
(tbed - tw)M ^ (121-9) (1 . 8 )/9°
V 1 = (25,9)'. (1 . 8 ) 0F
kf
= 0.0198 -B tu /h r-'fI--0F (f o r a i r )
■t2 = (14.0) (1 .8 ) .0F
kf
= .0.0148 B tu /h rM ft-°F (f o r CO2 )
= 0 ..OQO64 f t
P
Gf = 29,7 l b / h r - f t 2
■^uf
,D
=
0.0465 l b / f t - h r (f o r CO2 )'
yif . =
O.O545 I b / f t - h r ( f o r -a ir)
XCg •= 2.675 + 0.002617 T - . I I 690O/T2
Zr = °K from P e rry (10)
,Cg is f o r carbon
. F or a .b e d te m p e ra tu re of '140 0C :
= O'. 256 , BtU
c
b
- 0Fr-Ib
■h ■= WCp V 1 .—. t 2 )
(125) CD- (9 .9 )
-
(0 , 2 5 6 ) (115. 5) (1 .8 )
. A ^ h e d ” t SkirJ M
.-U = -WCp (I1.!- t 2 )
A (tbed
tW^M
(1 , 8 )
-= tl».) 111(9.91(1.8)
(0 . 256) ( 121. 0 ) ( 1 . 8 )
,(Dp
u
J
(Q.0Q964.),(29.7)
(0.0 5 4 5 )
-= 4 2 .0 B t u / h r - f I ^ - 0F
-2 2*.
(h Dp).
kf
^
(4 2 .0 ) (0.Q0064) , = 1>358
(0 . 0198)
( / iI c S )
. (0^0545) ( 0- 25 6 )
-
' (
_ 0 ,7 0 3
0 . 0198)
■Kf
_
1 .4 0 kf
■Dp
.c o r r e la tio n
0 ,5 )
(Pp gf )
/if
»1.6
f f
°s
)
= 1 .4 0
kf
(O.OI98
(0.00064)
(0 .5 5 4 )(1 .7 5 9 1
kC rrela tlo n = ^ ^ 2 B tu /h r r ft^ ° F
* S '= (kc o r r e la tlo n " k )
'
'
'-------- —
^
100 = .0.5#
100
=
4 2 :2
c o rre la tio n
.-E..F D e v ia tio n from c o r r e la tio n
A f lu id iz e d , e f f ic ie n c y ,,.e > .is d e fin e d .a s follow s":
e =
where
Pe --- Gf
(
6)
G = Mass flow r a t e f o r m in im u m -flu id iz a tio n
e
obtained, from F ig s 7 * 8 * 9? 1-0 y U.> & 12.
(.
lk . )
h r-ft2
. Gf = Mass flow r a t e .fo r run, c o n d itio n s
( . - lb
)
h r w f t2
In o rd e r to determ in e th e gas mass flow r a t e s f o r minimum f lu id iz a tio n ,-,
m easurem ents o f th e p r e s s u r e d ro p . a c ro ss th e bed were made a t -various
flo w r a t e s .
These d a ta a re found, on T able IV.
'F ig u res 7 *. 8 y ■9? 10,. 11*
a n d . 12 show, th e p lo t s Qf p r e s s u r e drop v e rsu s gas mass fl'ow. r a t e .
The
.mass flow r a t e at- the.maximum p r e s s u r e drop was ta k en as th e p o i n t of
-
X
minimum f l u i d i z a t i o n in. each ', c a s e .
The m axim um 'pressure d r o p '^as used
\
\
..because i t is th e most s h a r p ly ,d e fin e d p o in t on th e p ilo ts .
‘\
i
'
'
\
•The pro p o sed c o r r e l a t i o n is. p ro v e n good o n ly f o r c e r t a i n ranges'-^of
'
'
-.
- '
f
f l u i d i z a t i o n as d e fin e d by th e .f l u i d i z a t i o n e f f ic ie n c y . A p p licab le I
'
f l u i d i z a t i o n e f f ic ie n c y ranges vary w ith p a r t i b l e s i z e and ty p e of g a s1.
The e f f ic ie n c y range fo r- a i r f o r an av erag e p a r t i c l e s i z e - o f O-.00768
,Inch is. from 0 .6 )2 . to 0 . 79:7 .the range fo r an av erag e p a r t i c l e s iz e o f
O.OO928.in c h i s from 0 . 970. to 0.874-,,.and th e ran g e f o r an av erag e p a r t i c l e
s iz e o f 0 .0 0 )9 9 in ch i s from 0 .7 7 7 -to 0.-994-.. ■ The a p p lic a b le f l u i d i z a t i o n
■e f f ic ie n c y , ran g es f o r CO2 a re .r e s p e c tiv e ly 0.969 to 0 . 991; :0 „497.to 0 , 8 2 8 ,
a n d .0 .6 9 9 .to 0 .9 0 8 . ■Complete .f l u i d i z a t i o n e f f ic ie n c y d a ta a re giv en in
■Table V.
A p o in t a t a s u b s t a n t i a l l y lower, f l u i d i z a t i o n e f f ic ie n c y i s 1
■shown to be in. c o n s id e ra b le e r f o r ; (see Run. No. 120 .bn T able I I I ) .
T able I I .p r e s e n t s ..the .o r ig in a l -ex p erim en tal -data.
The .values ,of
' th e f ilm h e a t t r a n s f e r c o e f f i c i e n t , the, o v e r a l l ,h e a t t r a n s f e r c o e f f i c i e n t ,
th e c o rre sp o n d in g h e a t t r a n s f e r c o e f f i c i e n t computed from th e c o rre la tio n ;,and th e p e r c e n t d e v ia tio n , betw een th e . e x p e r im e n ta l- c o e f f ic ie n t and., th e
,computed .,c o e ffic ie n t, from th e c o r r e l a t i o n a re p re s e n te d , in T able I I I .
■The .-experimentally.determined film heat transfer coefficients used.to
. :
o b ta in th e .c o r r e la tio n ra n g e d from 29 .4 B tu /h r ~ f t^ ° P to 7 ^ -2 -B tu /h r^ ft
and th e .co rresp o n d in g
o v e r a l l h e a t t r a n s f e r c o e f f i e i c i e n t s ranged from
F
■24 -
" 2 7 .9 B t u / h r - f t o
66. 6. B t u / h r - f t ^ - 0? .
■The o v e r a ll h e a t t r a n s f e r c o e f f i c i e n t s were computed to see i f a
s u b s t a n t i a l f ilm r e s i s t a n c e was b u ild in g up on th e in s id e of th e copper
lo o p . -From o b se rv in g th e d a ta on Table I l I f t h i s did. n o t seem to be
•o c c u rrin g .
The o v e r a ll h e a t t r a n s f e r c o e f f i c i e n t s were a ls o used to
check th e c o n s is te n c y of th e r e s u l t s s in c e th e o v e r a ll h e a t . t r a n s f e r
. c o e f f i c i e n t s do n o t in v o lv e th e copper loop w a ll s k in te m p e ra tu re s in
t h e i r com putation.
The te m p e ra tu re .d ro p a c ro s s th e w a ll of th e .copper loop f o r the
maximum q u a n tity of h e a t tr a n s f e r r e d in t h i s experim ent was c a lc u la te d
.to be 0.182 -0F .
ap p en d ix .
d e g re e .
The d e t a i l e d .c a lc u la tio n , i s found, on Fage
in th e
-The w a ll therm ocouples can only be r e a d .to th e n e a r e s t whole
This means t h a t th e w a ll therm ocouples can b e ,i n any p o s itio n
in th e tu b in g w a ll and s t i l l g iv e s a t i s f a c t o r y r e a d in g s .
■The use of th e exponent on th e P r a n d lt num ber,
cs/k p ) , should, be
re g a rd e d w ith c a u tio n , as i t i s good f o r a i r Und-CO2 , b u t may n o t n eces­
s a r i l y ap p ly to o th e r g a s e s .
F u r th e r .in v e s tig a tio n u sin g o th e r gases as
th e f l u i d i z i n g medium i s n e c e s sa ry b e fo re t h i s c o r r e la tio n -can be ex­
te n d ed to in c lu d e a l l g a s e s .
-The a v e ra g e p o s i t i v e - d e v i a t i o n betw een th e e x p e rim e n ta l film co­
e f f i c i e n t s and th e c a lc u la te d c o e f f i c i e n t from, th e c o r r e l a t i o n i s 4 .2 $
f o r 53 r u n s .
The a v erag e n e g a tiv e d e v ia tio n is -.-5.45$ f o r 31 r u n s .
The
maximum p o s i t i v e d e v ia t io n - is 12. 5$ and th e maximum n e g a tiv e d e v ia tio n i s
- 1 6 .9 $ .
From th e s e o b s e rv a tio n s i t can be s a id t h a t f o r th e f l u i d i z a t i o n
e f f ic ie n c y range s p e c ifie d , and u sin g a i r o r CO2 as th e f l u i d i z i n g medium.
•-25
-a v a lu e .o f th e f i l m h e a t t r a n s f e r c o e f f i c i e n t computed from th e g iv en
■ c o rre la tio n sh o u ld be on th e average w ith in h4-.2$ to - 5 .45^ of th e ex­
p e rim e n ta l v alu e t h a t would be o b ta in e d a t th e same c o n d itio n s .
The ,value of th e f ilm h e a t t r a n s f e r c o e f f i c i e n t was c a l c u l a t e d .f o r
ty p c o n d itio n s u s in g th e c o r r e l a t i o n d eveloped by TopMey and .Johnstone '
(12),.
The c o n d itio n s were a i r a t a mass flo w r a t e of 27*9. l b / h r - f t 2 w ith
■average p a r t i c l e s iz e s of 0 . OCfj!-68 in ch and. 0.,00553 in c h .
The c a lc u la te d
v a lu es a re r e s p e c tiv e ly 29.8 B t u / h r - f t 2-° P and 38.1 B t u / h r - f t 2- ° F . ■The
v a lu es of th e f ilm c o e f f ic ie n t- o b ta in e d from, th e c o r r e l a t i o n p re se n te d , in
t h i s th e s i s a re r e s p e c tiv e ly 42.2, B td /h r - f t^ - ° F and 62.31 B t u / h r - f t 2-° F ,
■The p e rc e n t d e v ia t io n s .o f th e film , c o e f f ic ie n t, v alu es o b ta in e d f r o n th e
c o r r e l a t i o n of Toomey. and Johnsto n e fro m th e c o r r e la tio n p re s e n te d in
t h i s th e s e a re .r e s p e c tiv e ly 29.3%..and. 3 9 .8 # .
The v a lu e of .th e film h e a t
t r a n s f e r c o e f f i c i e n t was a ls o c a l c u l a t e d ,f o r th e same two c o n d itio n s u sin g
th e .c o r r e la tio n developed .by Een and-Leva (15) . -For th e - same - seq u e n c e.o f
c o n d itio n s .th e c a lc u la te d ., v a lu es a re r e s p e c t i v e l y 27 .6 -BtuzZ h rifta --0F .and.
31.6 B t u / h r - f t 2-° F .
The p e r .c e n t d e v ia t io n s .o f th e film c o e f f i c i e n t
x
v a lu es from th e c o r r e l a t i o n of Wen and-Leva from th e .v a lu e s o b ta in e d from
th e .c o r r e la tio n p re s e n te d i n t h i s t h e s i s a re 3 7 . 0# .an d 4 9 .3 # * .r e s p e c tiv e ly .
These d e v ia tio n s may p o s s ib ly .b e due to d if f e r e n c e s .in e x p e rim e n ta l te c h ­
n iq u e and. e x p e rim e n ta l a p p a ra tu s .
- 26-
LITERATURE UITED
.1.
B row n,-G. G. . U nit O p e ra tio n s , John W iley and Sons# I n c .# New York#
(195D..
2.
Dow# W. KL. and.. Jakob# M. # ,Heat T ra n s fe r .Between a V e r t i c a l - Tyibe and
a. F lu id iz e d ■M r - S o lid M ixture # Chem. E ngr. P ro g re ss # -4? 637 , (19.51).
5.
L em lich # R. and C aldas #. I . # .- H eat-T ran sf e r to a 'L iq u id F lu id iz e d Bed,
A .I.C h .E . J o u r n a l# ,4
(195^).
4.
L eva# M. a n d ■Grummer# M»# A C o rre la tio n of S o lid s T u rn o v e r.in F lu id iz e d
Systems ,. Chem. -Engr. P r o g r e s s , 48 307 1 (1952).
5. ■Levenspie l# 0. and-W alton# J . S . , Bed-Wall Heat T ra n s fe r i n F lu id iz e d
System s, Chem,. E ngr, - P ro g re ss Symposium# S e r i e s . No. 9# 50' p . 1#
• ( 1 9 5 4 ) .‘
6.
McAdams# W. H .> H eat T ra n sm issio n # T h ird e d itio n # McGpaw-Hill- Book
Co. # , I n c . # New .York# (1994).
7 . . M lck ley #-H. S. and F a irb a n k s# D. F . # Mechanism of H e a t-T r a n s f e r .to
F lu id iz e d Beds # A .I .C h .E .■Jo u rn a l# I ; 574 # (195^7- '
8 . . M ickley#- H. 8, and T r il l i n g # C. A. # -Heat - T ra n s fe r C h a r a c te r is tic s of
F lu id iz e d ,Beds # In c . Eng. Chem., 4 l 1155# (194-9) .
9.
Owen# H. L. and Dean# 0. C.# Heat T ra n s fe r and F o u lin g o f F lu id iz e d
Beds # P etro leu m E n g r ., 25 c25 # (1955)..
10.
P e r r y # J . H .# Chem ical E n g in e e rs ’ Handbook# T h ird edition*,M cG raw H i l l Book C o . , - I n c . , New,York# (1950).
11.
R uckenstein* E. and Schorr* y . > -The L ev en sp iel-W alto n Model f o r Heat
T ra n s fe r Between a F lu id iz e d - Bed and a W all * A c ad .-Rep.- Populare
Romine# ,I n s t . E n e rg e t.# S tu d ii C e r c e ta r i E n ep g et,* 8 7 # (1958).
12
Toomey# R. D. and Jo h n sto n e * -Hv F-., Heat -T ra n s fe r Between Beds of
F lu id iz e d S o lid s and th e W alls of th e .C o n ta in e r* Chem. E ngr. Symposium
■ H F i S T E . ^ M " 7 7 '5 T ;
^
15. -y p e ed e n b e rg * H. A. # Heat T ra n s fe r Between a_ F lu id iz e d ,B e d and £
H o riz o n ta l Tube-# Chem.-E ngr. S c ., 9,# P . 52.
14.
Wen* C. and Fan* L .* C a lc u la te .F lu id iz e d Heat T ra n s fe r b y -Nomograph*
Chem. E n g r ., 64-, No. 7"* 254# (1957)*
15.
Wen* C. and Leva* M ,, F lu id iz e d -B e d Heat -T r a n s f e r , A .I.C h.E. J o u r n a l,
2 482* (1956).
“27"
ACKNOWLEDGMENT
a u th o r-w ish e s to th an k th e .N a tio n al S cience F o u n d atio n f or
sp o n so rin g the' re s e a rc h tinder which t h i s work .was pone;
The a u th o r
a ls o w ishes to thank P r o fe s s o r L. G,.- M dyfielG f o r h i s . a i d , s u g g e stio n s y
.and. c r i t i c i s m s on t h i s . p r o j e c t .
-^2 8 -
APPEArDIX
1 Page
T able I
•Screen A tialysiS . of ■P a r tic le 's • Used
39
TaMe •I I
E x p e rim en ta l-D a ta
31
T able I I I
C a lc u la te d Data, .and iR esu ltd
34
,Bed P re s s u re Drop D ata
37
Table V .
• F lu id iz a tio n E ffic le tid le s
38
F ig u re I .
F lu id iz e d Bed H e a t-T ra n sfe r A pparatus
39
Schematic- Drawing o f E x p e rim en ta l A pparatus
40 -
F ig u re 3
N u ss e lt k o .. ys Reynolds No*..fo r Aip
41
F ig u re 4
N u s s e lt- N o ..vs Reynolds. No* f o r CO2
42
!F igure 5
N u ss e lt N o .,y s P r a n d lt .No, f o r Constant.-'Reynolds. No.
43
■F ig u re 6
N u sse it.: No. ,ys
. T able Iy
■F ig u re 2
.0.53(Dp Gf )
uf
c ' - 1 .6
(uD . s )
kT
-44
'
F ig u re .7
P re s s u re Drop Across Bed vs A ir Mass Flew. R ate
.fo r -a n Average P a r t i c l e S iz e .o f O.OO768 in ch
F ig u re 8
P re s s u re Drop A cross-B ed.vs A ir
f o r an AyePage P a r t i c l e S iz e .o f
■ ■
:
P re s su re ’: Drop Across- BediyS A ir
f o r an Average P a r t i c l e S ize -of
-45
Mass Flow..Rate
0.00528 in ch
,•
Mass, Flow R ate
0.00333 in ch
■ . 4.6
.F igure 10
P re s s u re Dpop Across- Bed ,.Vs-CQ2 ..Mass Flow .R ate
f o r an Average P a r t i c l e S iz e of O..QO768 in ch
■ 48
F ig u r e ■11
-P re ssu re Drop Across .B ed .VS-CO2 Mass-Flow. R ate
for. a n Average P a r t i c l e S iz e -o f 0 .0 0 528 in ch
49
F ig u re 9
47
“2 9 APPENDIX (c o n tin u e d )
Flgtine 12
P re s s u re Drop Across Eed ys CO2 Mass-Flow..R ^ p
f o r an Average P a r t i c l e S ize of 0-.00535 in ch 1
' Page
5P
P r e s e n ta tio n of E q u atio n s From Which th e Film Heat Transfer*
C o e f f ic ie n ts a n d .th e O v e ra ll -H eat-T ran sfer T
C o e f f ic ie n ts Were C a lc u la te d
$1
C a lc u la tio n -of th e Tem perattire Drop Across th e W dll of
th e- Copper Lddp .
53
-3 0 TABLE I .
SCREEN ANALYSIS OF PARTICLES USED.
Sample I
Dl (In ch es)
Xi
Mesh
-40 + 8o
-80 + 120
-120 + 1 6 0
0.831
0.148
0.021
0.0117
0.0059
0.0044
A rith m e tic Mean D iam eter
Dp (a v e ) * " - 00T68 in ch es
Sample 2
Di (in c h e s)
Xi
Mesh
-50 + 80
-80 + 120
-120 + 160
-200 + 300
0.499
0.421
0.0641
0.015
• 0.0093
0.0059
0.0044
0.0024
A rith m etic Mean D iam eter
D ,
. = 0.00528 in ch es
p (av e)
Sample 3
Xi
Mesh
-100
-120
- I 60
-200
-300
+
+
+
+
120
160
200
300
0 .3 #
0 .4 l6
0.107
0.137
0.002
Di ( in c h e s )
0.0054
0.0044
0.0034
0.0024
0.0017
A rith m etic Mean D iam eter
Inches
Dp(ave) =
-5 1 TABLE I I
n No.
105
104
105
106
107
108
109
HO
111
112
115
114
115
ll6
H7
118
119
120
121
122
125
124
125
126
128
150
151
W ater
Flow
R ate
I b /h r
125
125
125
125
125
125
125
125
125
125
125
104
104
125
104
104
125
125
125
125
125
125
125
125
125
125
125
O u tle t
Gas
Skin
. Flow
Temp. 0C
R ate
I b / h p - f t '2
14.8
27.9
56.5
50.6
2 7 .9
19.15
54.7
4 6 .7 5
27.9
62.7
54.7
27-9
50.6
27.9
54.7
62.7
27.9
14.8
27.9
27.9
56.5
50.6
27.9
54.7
4 6 .7 5
62.7
54.7
52
56
58
59
57
27
51
55
56
54
54
40
40
59
56
57
57
27
55
55
57
54
55
29
55
55
28
EXPER!MENTAL DATA
O u tle t
In le t
W ater
Skin
Temp10C Temp10C
22
25
26
27
26
20
22
24
25
24
25
26
26
28
24
26
25
20
24
25
28
25
25
22
22
24
22
2 5 .9
28.5
29-5
29.85
28.45
2 1 .6
25 .0
25.9
2 7 .5
26 .4
24.75
29.0
50.6
50.4
2 6 .5
2 8 .5
27.55
21.55
26.05
2 8.2
29.55
2 7.2
2 5.6
22.75
2 4 .6
2$ .2
22.7
F lu id iz e d
In le t
Water
Bed
Temp10C Temp. °C
15.7
16.0
16.0
16.0
16.2
15.9
15.6
15.65
15.4
15.55
15.55
15.5
15.5
18.5
15.5
15.5
15.5
15.9
15.7
18.7
18.55
15.7
15.5
15.45
15.0
15.2
15.25
140
140
140
140
159
l4 l
159
159
140
140
l4 l
141
140
140
140
140
140
142
140
159
140
140
l4 l
140
140
l4 l
140
Type
of
Gas
A ir
A lr
A lr
A lr
A lr
CO2
CO2
CO2
A lr
CO2
CO2
A lr
A lr
A ir
CO2
CO2
A ir
A ir
A ir
A ir
A ir
A lr
A lr
CO2
CO2
CO2
CO2
Average
P a rtic le
S ize
Inches
0.00528
n
it
11
11
U
11
11
n
n
ti
Tl
Tl
11
11
11
ii
0.00768
ii
11
Tl
Il
11
n
11
11
11
-3 2 -
TABLE I I
Run No.
W ater
Flow
Rate
I b /h r
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
123
104
104
104
123
104
104
123
123
123
123
123
123
123
104
104
104
104
123
123
123
123
123
123
123
123
O u tle t
Gas
Skin
Flow
Temp.
R ate
lb /h r-ft2
27.9
27.9
36.3
50.6
27 .9
34.7
62.7
27 .9
27 .9
27 .9
34.7
4 6 .7 5
34.7
27.9
27.9
36.3
34.7
4 6 .7 5
27.9
27 .9
14.8
36.3
50.6
27.9
19.13
34.7
34
36
38
39
34
28
32
32
34
32
28
30
27
32
35
36
31
32
32
41
34
41
42
40
30
36
EXPERIMENT AL DATA ( c o n t i n u e d )
F lu id iz e d
In le t
O u tle t
In le t
W ater
Bed
W ater
Skin
Temp. 0C Temp. 0C
Temp.0C Temp . 0C
25
24
25
26
25
20
22
23
22
21
20
21
20
22
22
23
21
22
22
29
25
27
27
27
21
24
25.75
27.65
28.7
2 9.2
25.8
21.8
2 4.2
2 3 .4
23.8
23 .9
21 .1
22.75
21 .2
24.15
25.7
26.8
22.75
24.4
2 4 .1
29.8
24.2
29.3
30.5
28.2
22.0
2 5.5
15.45
15.55
15.6
15.7
15.55
13.25
13.25
13.0
1 4.1
14.0
14.0
14.0
14.0
14.0
14.1
14.1
14 .1
14.05
14.0
16.1
14.0
14.0
14.2
14.25
14.45
14.4
141
141
140
140
l4 l
141
140
140
140
140
140
140
140
140
140
140
140
140
140
140
140
140
140
140
140
141
Type
of
Gas
A ir
A ir
A ir
A ir
A ir
CO2
CO2
Air
A ir
A ir
CO2
CO2
CO2
Air
A ir
A ir
CO2
CO2
A ir
A ir
A ir
A ir
A ir
A ir
CO2
CO2
Average
P a rtic le
S ize
Inches
O.OO768
0.00333
-3 3 table
Run No.
W ater
Plow
R ate
I b /h r
158
159
160
161
162
163
164
165
166
167
168
169
123
123
123
123
104
104
104
123
104
104
104
123
II.
EXPERIMENTAL DATA ( c o n t i n u e d )
In le t
O u tle t
Gas
Skin
Skin
Plow
Temp0C
Temp.0C
R ate
Ib /h r-ft 2
u tle t
W ater
Temp. °C
36
39
40
37
43
43
44
39
39
40
42
39
26.75
28 .2
27.65
25.4
30.6
31.5
33.0
28.3
27.9
29 .4
31.7
28 .9
4 6 .7 5
27.9
62.7
34.7
27.9
36.3
50.6
27 .9
34.7
4 6 .7 5
62.7
27.9
25
27
25
24
29
28
28
26
26
27
28
27
F lu id iz e d
In le t
Bed
W ater
Temp. 0C Temp. °C
14.4
14.4
14.35
14.4
14.5
14.4
14.7
14.5
15.1
15.1
15.1
15.15
140
140
140
140
140
140
140
140
140
140
l4 l
140
Type
of
Gas
CO2
A ir
CO2
CO2
A ir
A ir
A ir
A ir
CO2
CO2
CO2
A ir
Average
P a rtic le
S ize
Inches
0.00333
II
It
II
II
Il
II
II
Il
Il
II
II
-
TABLE I I I .
Run
No.
120
121
122
125
132
153
156
159
140
141
145
146
150
125
154
147
124
155
126
151
157
142
144
148
128
143
Type
of Gas
A ir
It
I!
It
It
It
It
It
It
It
It
U
It
It
Il
Il
It
It
CO2
II
Il
Il
It
Il
It
It
Gas
Flow
Rate
lb /h r-ft2
14.8
27.9
Il
Il
Il
II
It
It
Il
Il
Il
Il
Il
56.3
It
11
50.6
11
34.7
11
11
It
tl
Il
46.75
It
W ater
Flow
R ate
I b /h r
Average
P a rtic le
Size
Inches
(t BED- t SKIN
.123
123
123
123
123
104
123
123
123
123
123
104
123
123
104
104
123
104
123
123
104
123
123
104
123
123
O.OO768
Il
II
11
Il
11
Il
11
Il
Il
Il
Il
It
tl
Il
It
tl
Il
Il
It
11
It
Il
Il
Il
It
118.5
111.5
109.0
113.0
111.5
111.0
111.5
112.5
112.0
115.5
115.0
111.5
115.0
107.5
108.5
110.5
I I O .5
107.5
114.5
115.0
117.0
116.0
116.5
114.0
112.5
114.5
C0
54'
CALCULATED DATA AND RESULTS
^t BED- t W^M
C°
125.2
119.1
115.5
120.5
120.4
119.4
120.3
121.8
121.0
121.0
120.9
120.1
120.9
116.0
117.8
119.5
118.5
117.5
120.9
121.0
123.4
122.4
122.4
121.5
120.2
121.6
( I 1- I 2 )
C0
5.45
10.35
9 .5
10.3
10.3
12.1
10.25
10.4
9 .7
9 .9
10.15
11.6
10.1
10.8
15.1
12.7
n .5
15.5
7 .5
7 .4 5
8 .5 5
7 .1
7 .2
8 .6 5
9 .6
8 .7 5
u
IfDp Gf \
B tu /h r
f t 2-°F '
J
21 .2
41 .8
59.6
4 1 .2
4 1 .1
4 1 .2
4 0 .9
4 1 .1
58.5
39-4
4 0 .4
59.2
4 0 .2
4 4 .7
4 5 .1
4 3 .2
4 6 .6
4 6 .7
29 .0
29 .5
28 .1
27.9
2 8 .2
28.9
38.4
34.6
0.174
0.328
Il
Il
II
Il
It
Il
It
Il
Il
Il
Il
0.426
11
Il
0.594
Il
0.478
II
It
It
It
Il
0.643
It
h
0.7143
1.445
1.554
1 .4 l6
1.435
1.430
1.425
1.435
1.345
1.558
1.596
1.567
1.587
1.558
1.582
1.509
1.615
1.648
1.525
1.545
1.284
1.271
1.284
1.551
1 .7 7 5
1.587
22 .1
4 4 .7
4 1 .9
4 3 .8
4 4 .4
4 4 .2 5
4 4 .1
4 4 .4
4 1 .6
4 2 .0
4 3 .2
4 2 .3
4 2 .9
4 8 .2
4 8 .9 5
4 6 .7
4 9 .9
51.0
30 .6
51.1
29.7
29 .4
29.7
30.8
4 1 .0
56.7
h Cor­
re la tio n
50.17
4 2 .2
It
It
Il
II
Il
It
It
Il
Il
Il
11
4 8 .4 5
11
Il
57.82
11
51.12
Il
11
It
11
tl
56.46
It
%E
-2 6 .7
+ 5-9
- 0 .7
+ 5.8
+ 5 .2
+ 4 .9
+ 4 .5
+ 5 .2
- 1 .4
- 0 .5
+ 2 .4
+ 0 .2
+ 1.7
- 0 .5
+ 1.0
- 5 .6
- 15.7
- 11.8
- 1.7
- 0 .1
- 4 .6
- 5 .5
- 4 .6
- 1 .0
+12.5
+ 0 .7
-3 5 '
TABLE I I I .
Run
No.
149
130
138
103
104
107
111
114
116
119
105
106
115
108
109
113
117
HO
112
118
152
151
155
159
162
165
169
153
Type
of Gas
CO2
I!
Il
A ir
Il
Il
II
Il
It
11
Il
Il
Il
CO2
11
Il
Tl
II
11
It
A ir
Il
11
Il
Il
11
Il
11
Gas
Flow
R ate
lb /h r-ft2
W ater
Flow
R ate
I b /h r
46.75
62.7
Il
14.8
27.9
Il
Il
Il
Il
11
104
123
104
123
123
123
123
104
123
123
123
123
104
123
123
123
104
123
123
104
123
123
123
123
104
123
123
123
36.3
50.6
Il
19.13
34.7
Il
Il
46.75
62.7
II
14.8
27.9
It
Il
11
Il
II
36.3
Average
P a rtic le
Size
Inches
O.OO768
Il
Il
0.00528
II
It
Il
Il
Il
11
II
Il
Il
11
11
Il
Il
Il
Il
Il
0.00333
Il
Il
Il
II
11
Il
11
CALCULATED DATA
^t BEDwtSK IN ^
C°
113.0
112.5
113.0
113.0
109.5
107.5
108.5
108.0
106.5
109.0
108.0
107.0
107.0
117.5
112.5
112.5
110.0
110.5
110.0
108.5
110.5
105.0
106.5
107.0
104.0
107.5
107.0
106.0
RESULTS ( c o n t i n u e d )
(t BED- t W ^
h Cor­
relation
%E
35.46
42.98
II
+ 2.0
- 0.7
-8.6
- 3.4
+ 7-1
+ 8.9
+ 8.3
+ 1.0
+ 7-5
+ 5.9
+ 4.1
— 9*8
-16.9
-13.9
+ 8.1
+ 8.4
+ 9.5
+ 2.6
- 4.8
- 4.1
- 1.7
+ 0.5
+ 0.9
- 0.7
+ 0.9
- 1.0
- 1.0
- 3.4
C°
120.7
120.8
121.2
125.2
117.8
116.6
118.5
118.7
115.5
118.6
118.2
117.0
117.0
112.3
H 8 .7
121.0
119.0
118.2
119.1
118.0
120.9
117.0
118.8
H 8 .7
117.4
118.6
117.9
118.3
10.35
10.0
10.95
8 .2
12.3
12.25
12.1
13.5
11.9
12.05
13 .5
13.85
15 .1
5.7
9 .4
9 .4
11.0
10.25
11.05
13.0
10.2
13.7
13.95
13.8
16.1
13.8
13.75
15.3
34.8
39.8
36.7
31.4
50.2
50.6
4 8 .0
4 6 .3
4 9 .9
4 8 .9
54.9
56.8
52.4
2 2 .4
38 .1
37 .3
37 .5
4 1 .6
4 4 .6
4 4 .8
4 0 .5
56 .2
56.4
55.8
55.75
55.9
56.0
62.0
0.645
0.877
11
1.609
1.846
1.699
0.119 0.773
0.225 1.198
Il
1.218
Il
1.211
Il
1.129
It
1.202
11
1.184
0.293 1.338
0.409 1.382
Il
1.272
0 . l 8 l 0.693
0.328 1.192
Il
1.195
11
1.207
0.442 1.323
0.593 1.436
Il
1.448
0.0752 0.6198
0.142 O.8758
11
0.8800
Il
0.8660
Il
0.8800
II
0.8632
II
0.8632
0.184 0.9709
37 .2
4 2 .7
39.3
34.8
53.9
54.8
5 4.5
50.8
54 .1
53.3
60.2
62.2
57-25
23 .3
4 0 .1
4 0 .2
4 0 .6
4 4 .5
4 8 .3
4 8 .7
4 4 .3
62.6
62.9
61.9
62.9
61.7
61.7
69.4
36.02
50.31
Il
Il
Il
Il
11
57.84
68.92
Il
27.05
37.09
Il
11
43.39
50.76
Il
45.05
62.31
II
Il
Il
Il
Il
71.82
-3 6 TABLE I I I .
Run
No.
163
154
164
156
157
161
166
158
167
160
168
Gas
Plow
Rate
lb /h r-ft2
W ater
Plow
R ate
I b /h r
Average
P a rtic le
S ize
Inches
Air
Il
11
3 6 .)
50.6
Il
0.00333
Il
Il
CO2
11
Il
Il
11
Il
Il
II
19.13
34.7.
It
II
104
123
104
123
123
123
104
123
104
123
104
Type
of Gas
46.75
Il
62.7
n
0.003)3
Il
Il
11
Il
II
II
Il
CALCULATED DATA AND RESULTS ( c o n t i n u e d )
( t BED- t SKIN^M
C°
104.$
105.5
104.0
114.5
111.0
109.5
107.5
109.5
106.5
107.5
106.0
( t BED- V w
C°
117i.O
117.6
116.1
121.8
121.0
120.1
118.5
119.4
117.7
119.0
117.6
( t i - t 2)
C0
17.1
16. )
18.3
7 .5 5
ll.l
11.0
12.8
12.35
14.3
13.3
16.6
U
B tu /h r
T t2- 0F
59.25
66.6
63.9
29.8
4 4 .0
4 4 .0
4 3 .9
4 9 .7
4 9 .4
53.6
57.4
hA
I0p0f
V f /
0.184
0.257
Il
0.114
0.207
0.207
0.207
0.278
0.278
0.374
0.374
\
h
h Cor­
re la tio n
%E
r /
0.9275
1.0381
0.9989
0.5933
0.8984
0.9031
0.9059
1.0144
1.0200
1.1136
1.1904
66.3
7 4 .2
7 1 .4
31.7
4 8 .0
4 8 .2 5
4 8 .4
54.2
54.5
59.4
63.6
71.82
8 5.71
M
33.61
4 6 .16
4 6 .16
4 6 .1 6
54.03
54.03
63.07
63.07
- 7- 7
-1 3 . 4
- 16. 7
- 5. 7
+ 4. 0
+ 4. 5
+ 4. 9
+ 0.3
+ 0. 9
- 5.,8
+ 0 .,8
-3 7 -
TABLE IV.
Average
P a rtic le
Size
Inches
P re ssu re
Drop
Inches of
C C l4
A ir Plow
R ate
lb /h r-ft2
O.OO768
II
I!
Il
11
Il
Il
Il
0.00528
Il
11
11
11
U
Il
0 . 00)53
Il
Il
11
II
IT
8 .0
10.0
12.0
13.8
14.2
13.6
13.8
13.8
8 .0
10.0
12.0
12.6
14.0
I) .6
I) .8
8 .0
10.0
12.0
12.4
12.6
12.6
5.74
6.97
8 .5 1
9.77
10.25
11.5
15.8
15.8
3.66
4 .4 5
5.38
5.74
6.35
7.57
9.90
2.08
2 .56
) .0 5
).7 8
5 .1 )
9.0 5
BED PRESSURE DROP DATA
Approx.
Mesh S ize
of
P a rtic le s
40-80
50-100
100-300
Average
P a rtic le
S ize
Inches
0.00768
Il
Il
Il
Il
Il
II
0.00528
Il
It
Il
11
11
11
Il
0.00333
It
11
Il
11
11
11
P re s su re
Drop
Inches of
C C l4
8 .0 .
10.0
12.0
14.0
14.6
14.2
14.2
8 .0
10.0
12.0
14.0
14 .6
1 3 .6
13.8
13.8
8 .0
10.0
12.0
14.0
16.0
13.8
13.8
CO2 Plow
R ate
lb /h r-ft2
Aprox.
Mesh S ize
of
P a rtic le s
12.05
15 .6
18.0
21.0
21.9
26 .2
30.8
6.12
7 .4 1
8 .9 0
10.4
10.95
13.0
18.2
2 7 .1
2.78
3.52
4.0 8
4 .8 2
5.75
8 .3 5
19 .1
40-80
50-100
100-300
-3 8 TABLE V
FLUIDIZATION EFFICIENCIES
Gas
P a r t i c l e S ize
(mesh)
F lu i d iz a tio n E f fic ie n c y
_________ Range__________
CO2
40-8 O
0.369 - 0.531
CO2
50-100
0.437 - 0.828
CO2
100-300
O.699 - O.908
A ir
40-80
0.632 - 0.797
A ir
50-100
0.570 - 0.874
A ir
100-300
0.777 - 0.934
-3 9 -
F ig u re I .
I.
2.
3.
4.
5.
6.
78.
F lu id iz e d Bed Heat T ra n s fe r A pparatus
W ater I n l e t
W ater O u tle t
l / l 6" S ta in le s s S te e l Thermowell
1/8" S td . D ia . S te e l Pipe
I n s u la tio n
5" S td . D ia . S te e l Pipe
Skin Thermocouple L o c a tio n
F lu id iz e d Bed
910.
11.
12.
13.
14.
15.
1/4" O.D. Copper Loop
H eatin g C o il Leads
3" S td . D ia . S te e l Pipe
Porous P la te
Gas I n l e t
Cyclone
Gas O u tle t
-4 0 -
<-
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
F igure 2.
Schem atic Drawing of
E xp erim en tal A pparatus.
W ater O u tle t
P r e c is io n Thermometers
W ater C o n tro l Valve
Gas O u tle t
Thermowell
W ater C onstant P re s s u re R e g u la to r
I n l e t W ater Valve
W ater I n l e t
Manometer f o r W ater Flow R ates
F lu id iz e d Bed
Manometer f o r Gas Flow R ates
Gas C o n tro l Valve
Gas I n l e t
I n l e t Gas Valve
Gas C onstant P re s su re R e g u la to r
Q uart Dewar F la sk
-4 1 -
Symbol
Gas
O
A
Mr
Mr
A ir
P a r t i c l e S ize
(Approx, Mesh)
4 0 - 80
50-100
1 00-500
-4 2 -
F ig u re 4 .
Symbol
X
~h
W
N u ss e lt No. v s. Reynolds No. f o r CO2 .
Gas
____
P a r t i c l e S ize
(Approx. Mesh)
CO2
CO2
CO2
40- 80
50-100
100-500
-4 ?-
h D /k
D G
G1
0 .6
F ig u re 5 .
0 .7
0 .8
0 .9
1 .0
N u sse lt No. v s . P r a n d lt No.
f o r C o n stan t Reynolds No.
-4 4 -
F ig u re 6 .
N u sse lt No. v s . (D
Symbol
Gas
O
A ir
A ir
A ir
CO2
CO2
CO2
❖
X
+
Gf Zuf.) 0.5 3
(uf CgZkf )
P a r t i c l e S ize
(Approx. Mesh)
4 0 - 80
50-100
1 0 0 -5 0 0
4 0 - 80
50-100
1 0 0 -5 0 0
-I.
P Inches of C C l4
-4 5 -
Mass Plow Rare
F ig u re 7 •
Ib /h r-ft
P r e s s u r e D ro p A c r o s s B e d v s . Air Mass Plow Rate
f o r a n A v e r a g e P a r t i c l e S i z e o f 0 . 0 0 7 68 i n c h .
P Inches of C Cl
-4 6 -
Mass Plow R ate I b / h r - f t
F ig u re 8 .
P r e s s u r e D ro p A c r o s s B e d v s . A i r M ass P lo w R a t e
f o r a n A v e r a g e P a r t i c l e S i z e o f 0 .0 0 5 2 8 i n c h .
P Inches o f C Cl
-4 7 -
Mass Plow R ate I b / h r - f t
F ig u re 9-
P re s su re Drop Across Bed v s. A ir Mass Flow R ate
f o r an Average P a r t i c l e S ize of 0 .0 0 528 in c h .
Z
Inches of C Cl
-4 8 -
PL,
Mass Flow R ate I b / h r - f
F ig u re 10.
P r e s s u r e D ro p A c r o s s B e d v s . CO2 M ass F lo w R a t e
f o r a n A v e r a g e P a r t i c l e S i z e o f O.OO 768 i n c h .
Inches o f C C l4
-4 9 -
Mass Flow R ate I b / h r - f t
F ig u re
CO
**>j
Ce
GD
CO
11.
P r e s s u r e D ro p A c r o s s B e d v s . CO2 M ass F lo w R a t e
f o r a n A v e r a g e P a r t i c l e S i z e o f 0 .0 0 5 2 8 i n c h .
A P-In ch es of C Cl
-5 0 -
Mass Plow R ate I b / h r - f t
F ig u re 12.
P re s su re Drop Across Bed v s. CO2 Mass Flow R ate
f o r an Average P a r t i c l e S iz e o f 0.00533 in c h .
presentation op equations
.. FROM WHICH
THE :FILM HEAT TRANSFER .COEFFICIENTS
AND THE.OVERALL .HEAT TRANSFER ,COEFFICIENTS WERE ,CALCULATED
The h e a t t r a n s f e r r e d from th e w a ll o f th e hopper loop to th e w a ter
. in s id e is .fo .u h d from th e fo llo w in g ,e q u a tio n :
q .= W C p f t 1 - t 2 )
q .=. Heat t r a n s f e r r e d
W.= W ater h a te
ti=
(
lb
hr
(I)
( , B tu )
hr
)
O u tle t w a ter te m p e ra tu re
t 2 = I n l e t w a te r-te m p e ra tu re
The h e a t t r a n s f e r r e d from th e f l u i d i z e d b e d .to th e w a ll of th e
copper loop i s g iv e n by th e ,f o llo w in g .e q u a tio n ;
^ ^ h ^^bed
^skin) , m
A = O u tside a re a of. tk e copper loop ( f t 2 ) = 0.256 f t 2
h = E ilm h e a t t r a n s f e r c o e f f i c i e n t
(
, B tu
. )
h r - f t s r-... uF •
'^bed - .Bed- te m p e ra tu re
tSkin = Skin te m p e ratu re
M = . I n d ic a tio n t h a t a mean s k in to bed te m p e ratu re d if f e r e n c e
must be used
At s t e a d y - s t a t e .o p e r a t i o n th e h e a t e n te r in g th e w a ll a n d .th e h e a t
- le a v in g th e w a ll .must be th e same so th e two p re v io u s e q u a tio n s can
be e q u a te d .
- '
¥
52-
'
( t x - . t 2 ) = h A (tbed ^ t s k l n ) M
-R earranging th e e q u a tio n g iv e s th e .fo llo w in g r e s u l t :
'h - W cD Ct1 - t a )
•A ( t bed ^ t S k in ^ M,
From th e above e q u a tio n th e e x p e rim e n ta l f ilm h e a t t r a n s f e r co­
e f f i c i e n t s can be c a lc u la te d .
The h e a t t r a n s f e r r e d from th e f l u i d i z e d bed to th e w a te r.c a n be
re p re s e n te d by th e fo llo w in g e q u a tio n :
•q .= U A ( t bed
t w) M
U = O v e ra ll 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 - f t 2
°F
t w = W ater te m p e ra tu re
(o th e r symbols as p r e v io u s ly . defined)At s t e a d y - s t a t e o p e ra tio n t h i s h e a t i s alg o e q u al to th e h e a t
g a in ed by th e w a te r so th e two e x p re ss io n s may be' e q u a te d :
V A (tbed
M = * Cp ( t l ' t s )
R earran g in g th e above e q u a tio n g iv e s th e fo llo w in g e x p re s s io n f o r th e
o v e r a ll h e a t t r a n s f e r c o e f f i c i e n t :
.U =
cp (t]_ "" t g )
' A ( ^ b e d ' " t w) M
From th e above e q u a tio n th e e x p e rim e n ta l .o v e r a ll h e a t t r a n s f e r co­
e f f i c i e n t s can be c a lc u la te d .
-5 3 calculation OF TEMPERATURE .DROP
ACROSS' THE .WALL OF THE, COPPER■LOOP
D ata f o r Run Hoi 154
^ t w = 16.5', $ 1 .8 ) . °E
(te m p e ra tu re in c re a s e •of w ater)
Cp.= (h e a t c a p a c ity o f w a t e r ) . = I (BtuZ0F -Ih )
W. = (w eight of w ater) = 123 I b /h r
X.= (w a ll th ic k n e s s of tu b e) =
0 . D. o f tu b e = 0. 25
'
0 -°3 f t .
.12
ft.
12
1 . D. o f tube = 0 . 1 9
12
ft..
'
D,, (mean d ia m e ter) = 0.22;
12
ft.
L ( le n g th .o f tu b e ) =
ft.
47
12
kjyj ( th e r m a l.c o n d u c tiv ity of copper) = 2$£) B tu /h r - f t 2- ° ^ _
A^ •(mean a r e a ) = T T " - L ( f t 2 )
q_ ,= R eat t r a n s f e r r e d a c ro ss w a ll (B tu /h r)
A t=
Tem perature drop a c ro ss th e copper w a ll ( 0F)
A t
A x"
A. t
% Cp
■w C p A t w A x
kM AM
A t=
■ ( 123) (I.) (16..3) ( 1 . 8 ) (.0.03) (12) (12)
. (220)
(0 : 2 2 ) ( 4 ? ) ( 1 2 )
A t'-.= 0.182 °F. ■This was th e maximum v alu e ,of A t e n co u n tered in
th e e x p e rim e n ta l work.
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