Design of a high temperature falling bed air preheater for direct coal-fired MHD power generation
using liquid slag droplets
by Raymond Lee Prill
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Mechanical Engineering
Montana State University
© Copyright by Raymond Lee Prill (1977)
Abstract:
A unique design for a falling liquid droplet heat exchanger is presented. The major problem associated
with this type of heat exchanger, that of obtaining uniformly sized liquid droplets, has been solved by
utilizing vibration induced atomization of the liquid. With this method the drops are formed by
disturbing a liquid capillary jet by either vibrating a distributor plate through which the liquid flows or
by holding the plate stationary and producing the disturbance with external sound pressure waves.
Specific use of this type of heat exchanger as a direct coal fired air preheater for MHD power
generation is examined. Digital solution of the governing equations has determined the effect of
particle size and size distribution on the chamber size requirement. Comparisons with other MHD
preheater design concepts, including the cored brick, show the present design has numerous
advantages. STATEMENT OF PERMISSION TO COPY
I n p r e s e n tin g t h i s t h e s i s i n p a r t i a l
f u l f i l l m e n t o f th e re q u ire m e n ts
f o r an advanced, degree a t Montana S ta te U n i v e r s i t y ,
L i b r a r y s h a l l make i t
I agree t h a t th e
f r e e ly a v a ila b le f o r in s p e c tio n .
I f u r t h e r agree
t h a t p e rm is s io n f o r e x t e n s iv e cop yin g o f t h i s t h e s is f o r s c h o l a r l y
purposes may be g ra n te d by my m a jo r p r o f e s s o r , o r , in h is absence, by
th e D i r e c t o r o f L i b r a r i e s .
I t i s und erstoo d t h a t any c o p y in g o r
p u b lic a tio n o f t h is th e s is f o r f in a n c ia l
w i t h o u t my w r i t t e n p e r m is s io n .
S ig n a tu re
g a in s h a l l n o t be a llo w e d
'
. I
DESIGN OF A HIGH-TEMPERATURE FALLING BED AIR PREHEATER FOR DIRECT
' COAL-FIRED MHD POWER GENERATION USING LIQUID SLAG DROPLETS
'
by
RAYMOND LEE PRILL
A t h e s i s s u b m itte d i n 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 the degree
of
•
MASTER OF SCIENCE
in
Mechanical E n g in e e rin g
Approved:
MONTANA STATE UNIVERSITY
Bozeman, Montana
May, 1977
.
iii
acknowledgments '
The a u th o r wishes t o tha n k ,Dr. R. Mussulman f o r h i s guidance
and i n s t r u c t i o n d u r in g th e course o f t h i s p r o j e c t .
S p e c ia l thanks a ls o
goes t o Dr. R. W a rrin g to n f o r h is s u g g e s tio n s and encouragement.
The
w r i t e r a ls o thanks Dr. W. G e n e tti f o r h i s a s s is ta n c e .
T h is s tu d y was s u p p o rte d by ERDA/MHD D i v is i o n and th e Mechanical
E n g in e e rin g Department o f Montana S t a t e U n i v e r s i t y .
■
•
•
.f
TABLE OF CONTENTS
Page
VITA.
................................................. ................................................................... . . .
ii
ACKNOWLEDGMENTS.................................................................. •......................................i i i
LIST OF TABLES.................................................- ................................. .......................... .... v i
LIST OF FIGURES.................................................................................... ' ................... v i i
NOMENCLATURE.
: .......................................
v iii
ABSTRACT..................................................................................................................
CHAPTER I
x ii
...........................* . .............................. .........................................................
INTRODUCTION........................................ ....
. - ................................................
I
I
6
CHAPTER I I .......................................
ANALYTICAL MODEL ....................................................................................................... 6
6
R a d ia tiv e T r a n s f e r .............................................................
D r o p le t Energy Balance ............................................
11
C o n tro l Volume Energy B a la n c e ..........................................................
13
Heat Loss From th e W a l l .......................................................................
13
F a l l i n g D r o p le t Dynamics . ..............................................................
19
D im ensionless R e l a t i o n s .......................................................................
19
Method o f S o lu t io n
24
................................................................................
CHAPTER I I I ........................................................
27
DROPLET FORMATION...................................
27
CHAPTER I V ...................................................................................................................
.
33
RESULTS......................................................................................................' . . .
33
F u l l Load Design . . .
......................
33
I
.
.-/
- V -
TABLE OF CONTENTS ( c e n t )
P a r t i a l Load O p e ra tio n
CHAPTER V.
. ....................................
SUMMARY ....................................
APPENDIX .
' ...................... ' . .
APPENDIX I ...............................
APPENDIX I I
BIBLIOGRAPHY
.
- vi ..
T ab le
LIST OF TABLES
'
Page
2 .1
PROPERTIES OF THE INSULATING MATERIALS.
. . . ...........................
15
4 .1
DESIGN SPECIFICATION FOR 3000 MWt MHD PREHEATER . . . . . .
43
4 .2
INSULATION SPECIFICATIONS FOR HEAT EXCHANGER CHAMBERS . . .
44
4 .3
OPERATING SPECIFICATIONS FOR 3000 MWt MHD PREHEATER
AT 3 /4 LOAD.............................................................................................
49
!
■
- v ii LIST OF FIGURES
F i gure
L I
. 2 .1
2 .2
Page
FALLING LIQUID SLAG DROPLET AIR PREHEATER........................................
4
INCREMENTAL SPHERE FOR DERIVATION OF SHADOWING
EFFECT......................................................................................................
8
INCREMENTAL ANNULUS FOR DERIVATION OF RADIATIVE
TRANSFER......................................................................
8
2 .3
DROPLET ENERGY BALANCE ............................................................................
14
2 .4
CONTROL VOLUME FOR'ENERGY BALANCE......................................................
14
2 .5
GEOMETRY FOR THE CASE OF THREE LAYERS OF INSULATION.
20
2 .6
DROPLET FREE BODY DIAGRAM.......................................................................
20
3 .1
EFFECT OF PARTICLE DISPERSION ON LENGTH AND DIAMETER
OF THE UPPER CHAMBER FOR A 3000 WMt MHD FACILITY.
. .
28
EFFECT OF SLAG TEMPERATURE AND CAPILLARY DIAMETER ON THE
PRESSURE DROP THROUGHTHE CAPILLARY ......................................
35
4 .2
EFFECT OF SLAG TEMPERATURE ON SLAG MASSFLOW RATE......................
36
4 .3
EFFECT OF SLAG TEMPERATURE ON CHAMBERLENGTH ..............................
37
4 .4
EFFECT OF CAPILLARY DIAMETER AND DISTURBANCE FREQUENCY
ON THE.UPPER CHAMBER LENGTH .....................................................
39
EFFECT OF CAPILLARY DIAMETER AND DISTURBANCE FREQUENCY
QN THE LOWER CHAMBER LENGTH. ..................................................
40
OPTIMUM DISTURBANCE FREQUENCIES FOR VARIOUS CAPILLARY
' DIAMETERS . ' .......................... ........................ ..........................
41
VARIATION IN PROPERTIES FROM THE TOP OF THE UPPER
CHAMBER.................................... .................................. .... ......................
45
VARIATION IN PROPERTIES FROM THE TOP OF THE LOWER
CHAMBER.........................................................
46
4 .1
4 .5
4 .6
.4.7
4 .8
. . .
■f
- v iii
r-
NOMENCLATURE
SYMBOL
DESCRIPTION
a
a c c e le ra tio n o f g r a v it y
Rosseland a b s o r p tio n c o e f f i c i e n t
ar
C
s p e c i f i c heat
d
d r o p l e t d ia m e te r
f
shadowing f a c t o r o r fre q u e n c y f u n c t io n
h
hea t t r a n s f e r c o e f f i c i e n t
1b
■
b la d k body r a d i a t i v e i n t e n s i t y
k
therm al c o n d u c t i v i t y
Z
le n g t h
ifi
mass f lo w r a t e
n
d r o p l e t number d e n s it y
q .
heat f lu x
r
r a d iu s
sd
( p e r u n i t area and tim e )
s ta n d a rd d e v i a t io n
t
tim e
X
d is ta n c e fro m th e to p o f th e chamber
A
area
CD
drag c o e f f i c i e n t
'D
d ia m e te r
F
fre q u e n c y
Gr
Grashof number
- ix SYMBOL
DESCRIPTION
H
o v e ra ll heat tr a n s fe r c o e f f ic ie n t
L
chamber le n g th
N
t o t a l number o f d e s c re te s iz e s o f d r o p l e t s
Nu
N u s s e lt number
P
chamber p re ssu re
Pr
P r a n d tl number
Qr
r a d i a t i v e h e a t t r a n s f e r r a te
Qcov
c o n v e c tiv e h e a t t r a n s f e r r a te
R
gas c o n s t a n t o r r a d iu s
Re
Reynolds number
T
te m p e ra tu re
T1
te m p e ra tu re a t to p o f upper chamber
T2
te m p e ra tu re a t bottom o f upper chamber
te m p e ra tu re a t to p o f lo w e r chamber
T3
T4
-
te m p e ra tu re a t bottom o f lo w e r chamber
U
d im e n s io n le s s v e l o c i t y param eter
V
v e lo c ity
v e l o c i t y a t to p o f upper chamber
vI
V2
v e l o c i t y a t bottom o f upper chamber
■
v e l o c i t y a t to p o f lo w e r chamber
V3
V4
.
v e l o c i t y a t bottom o f lo w e r chamber
,
X
SYMBOL
DESCRIPTION ' '.
a
a b s o r p tio n c o e f f i c i e n t
B
volume c o e f f i c i e n t o f expansion
Tl
d im e n sio n !e ss d is ta n c e
<t>
.
d im e n s io n le s s te m p e ra tu re param eter
y
dynamic v i s c o s i t y
p
d e n s it y
a
S te fa n -B o ltzm a n n c o n s ta n t
as
fi!
s u r fa c e t e n s io n
sol i d a n g le
d im e n s io n le s s q u a n t i t y c h a r a c t e r i z i n g h e a t t r a n s f e r
chamber re q u ire m e n ts
SUBSCRIPTS
a
a ir
C
c a p illa r y
g
gas
in
in n e r ;
J
je t
m
mean
max
maximum
mi n
minimum
O
o u te r
'
,^
- xi DESCRIPTION-
SYMBOL
opt
optimum
r
r e la t iv e o r ra d ia tiv e
S
s la g
term
t e r m in a l
W
' wal I
SUPERSCRIPTS
I
*
d e r iv a tiv e
d im e n s io n le s s q u a n t i t y
ABSTRACT
A unique design f o r a f a l l i n g l i q u i d d r o p l e t hea t exchanger i s
p re s e n te d .
The m a jo r problem a s s o c ia te d w i t h t h i s ty p e o f hea t
e x ch a n g e r, t h a t o f o b t a i n i n g u n i f o r m ly s iz e d l i q u i d d r o p l e t s , has
been s o lv e d by u t i l i z i n g v i b r a t i o n induced a t o m iz a t io n o f th e l i q u i d .
W ith t h i s method th e drops a re formed by d i s t u r b i n g a l i q u i d c a p i l l a r y
j e t by e i t h e r v i b r a t i n g a d i s t r i b u t o r p l a t e thro ugh w hich th e l i q u i d
f lo w s o r by h o ld in g th e p l a t e s t a t i o n a r y and p ro d u c in g th e d is tu r b a n c e
w i t h e x t e r n a l sound p re s s u re waves.
S p e c i f i c use o f t h i s ty p e o f
h e a t exchanger as a d i r e c t coal f i r e d a i r p r e h e a te r f o r MHD power
g e n e r a tio n i s examined.
D i g i t a l s o l u t i o n o f th e g o v e rn in g e q u a tio n s
has determ ined the e f f e c t o f p a r t i c l e s iz e and s iz e d i s t r i b u t i o n on
th e chamber s iz e r e q u ire m e n t.
Comparisons w i t h o t h e r MHD p r e h e a te r
d e sign c o n c e p ts , i n c l u d i n g th e cored b r i c k , show th e p r e s e n t design
has numerous advantages.
CHAPTER I
INTRODUCTION
The e f f i c i e n c y o f a f o s s i l
f u e le d open c y c le magnetohydrodynamic
power g e n e r a tin g p l a n t depends s t r o n g l y on th e te m p e ra tu re o f the
w o rk in g g a s .
The r e q u i r e d com bustion te m p e ra tu re s , on th e o r d e r o f
SOOOKj can be a chieved by e i t h e r , p r e h e a tin g th e com bustion a i r to
a high te m p e ra tu r e , around 2000K, o r by use o f oxygen e n r ic h e d a i r .
Because o f th e amount o f oxygen t h a t would be needed i n a l a r g e s c a le
MHD power p l a n t , th e l a t t e r o f these methods was n o t c o n s id e re d in
t h i s s tu d y .
There are two b a s ic types o f a i r p re h e a te rs f o r open c y c le MHD
a p p l i c a t i o n s - th e d i r e c t l y f i r e d and i n d i r e c t l y f i r e d .
f i r e d p r e h e a te r u t i l i z e s
The d i r e c t l y
th e therm al energy o f th e e xh a u s t gas from
th e MHD channel t o p re h e a t th e a i r w h il e th e i n d i r e c t l y f i r e d f a c i l i t y
uses th e e xha ust gas fro m a s e p a r a t e ly f i r e d , cle a n f u e l
combuster.
The i n d i r e c t l y f i r e d p r e h e a t e r , though n o t having t o w it h s t a n d the
d e l e t e r io u s p r o p e r t ie s o f th e f l y ash s l a g , s u l f u r , and potassium
seed c o n ta in e d in an MHD exh a u st gas, would r e q u i r e an expensive c le a n
b u rn in g f u e l
e ffic ie n c y .
such as n a t u r a l gas'a n d w ould lo w e r th e o v e r a l l p l a n t
T h e r e f o r e , th e f u l l
e x p l o i t a t i o n o f the e f f i c i e n c y
advantages o f an MHD power . p la n t i s dependent on th e employment o f h ig h
te m p e ra tu re d i r e c t l y f i r e d a i r p r e h e a te r s .
Four types o f p r e h e a te r designs have in th e p a s t been c o n s id e re d
f o r coal f i r e d MHD a p p l i c a t i o n s :
- 2 1)
th e chequerwork packed bed p r e h e a te r
2)
th e packed pebble bed p r e h e a te r
3)
th e cored b r i c k packed bed p r e h e a te r
4)
th e f a l l i n g bed p r e h e a te r
Al I o f the se are r e g e n e r a tiv e ty p e h e a t e xch a n g e rs.
P o lis h r e s e a r c h e r s . have s iz e d th e chequerwork ty p e p r e h e a te r and
found th e dim ensions q u i t e l a r g e ( I ) .
Creep o f th e ceram ic b r ic k s a t
th e bottom o f such a massive chequerwork i s a s e r io u s problem .
The
packed pebble bed ty p e p re h e a te rs have th e in h e r e n t problem o f
p lu g g in g up from th e coal s la g d e p o s it s , though th e y are f e a s i b l e in
an i n d i r e c t l y f i r e d f a c i l i t y
(2 ).
The cored b r i c k p r e h e a te r o f f e r s
X
both th e p o s s i b i l i t y o f n o t p lu g g in g from th e exhaust gas coal s la g
d e p o s its and good therm al e f f e c t i v e n e s s
A ll
(3 ).
packed bed ty p e p r e h e a te rs (chequ erw ork, pebble bed and
cored b r i c k ) o p e ra te in a c y c l i c mode o f h e a t-u p and blow-down.
This
r e q u ir e s la r g e gas v a lv e s i n t h e MHD exh a u st gas f lo w stream o p e r a tin g
p e r i o d i c a l l y and s e a l in g a g a in s t th e d i f f e r e n t i a l
i n l e t and o u t l e t o f th e MHD channel
h ig h te m p e ra tu re s (around 2000K ).
p re s s u re between th e
( a p p r o x im a te ly 7 atmospheres) a t
These v a lv e s r e p r e s e n t Targe c a p i t a l
c o s ts and r a is e s e r io u s r e l i a b i l i t y q u e s t i o n s .
T h is problem , teamed
w i t h th e problems o f f i n d i n g a d u ra b le bed m a t e r ia l and r e d u c in g
p lu g g in g and f o u l i n g t o an a c c e p ta b le l e v e l , has caused p r e h e a te r
desig n t o la g behind development o f o t h e r MHD components.
- 3 The f a l l i n g
bed conce pt re p r e s e n ts one s o l u t i o n t o th e problems
o f o t h e r d i r e c t l y f i r e d MHD p r e h e a te r design c o n c e p ts .. T h is design
employs h e a t t r a n s f e r fro m p a r t i c l e s f a l l i n g
gas.
thro ugh a c o u n t e r f lo w o f
In th e MHD a p p l i c a t i o n th e p a r t i c l e s would be heated in one s e t
o f chambers by th e e xha ust from th e MHD c h a n n e l.
p a r t i c l e s would then f a l l
second chamber.
These heated
th ro u g h a c o u n t e r f lo w o f com bustion a i r i n a
F ig u re 1.1 shows th e f lo w process i n v o lv e d .
Continuous
r e c y c l i n g o f t h e bed m a t e r i a ls e l im in a t e s any v a lv e s i n th e exhaust
gas f l o w .
The la r g e s u r fa c e - a r e a - t o - m a s s r a t i o o f th e p a r t i c l e s
f a l l i n g bed p r e h e a te r g iv e i t
\
p o te n tia l
f o r h ig h hea t t r a n s f e r r a t e s .
Two typ e s o f bed m a t e r i a l ' f o r t h e f a l l i n g
been proposed; s o l i d p a r t i c l e s o f a m a t e r ia l
l i q u i d d ro p le ts o f a m a te ria l l i k e
i n th e
coal s la g .
p a r t i c l e p r e h e a te r have
l i k e alum ina ( 4 , 5) and
E x te n s iv e research was
done on th e a t o m iz a t io n o f l i q u i d s la g by a team o f E n g lis h eng ine ers
( 6) .
These s t u d ie s were focused on th e use o f t w in j e t a to m iz e r s ,
b r e a k in g .u p a j e t o f l i q u i d s la g w i t h a j e t o f a i r .
T h is ty p e o f
a to m iz e r had th e d isa d va n ta g e o f a w ide d i s p e r s io n o f d r o p l e t s iz e s ,
c a u sin g la r g e chamber le n g t h r e q u ire m e n ts .
I f th e d r o p l e t s are m ono-disperse in s i z e , th e y can be p a r t i a l l y
" f l o a t e d " by th e gas and th e chambers can be v e ry compact.
As the
d r o p l e t s iz e d is p e r s io n in c re a s e s th e v e l o c i t y o f th e gas m ust.be
decreased to a v o id e l u t r a t i o n o f th e s m a ll e r p a r t i c l e s and th e chamber
le n g t h must be in c re a s e d to p r o v id e adequate re s id e n c e tim e f o r heat
SLAG
(1650K)
EXHAUST
GAS
( 1 8 1 GK)
i r
~
1.1X10
PASCALS
MHD
___ !
EXHAUST
GAS
( 2 2 00K)
SLAG
< 1 9 2 0 K)
1.2X10
PREHEATED
Al R
( I BOOK)
A I R
( I 2 OOK )
FIGURE 1.1
FALLING LIQUID SLAG DROPLET AIR PREHEATER
- 5 “
t r a n s f e r to o r from th e l a r g e r d r o p l e t s .
o f a fa llin g
T h e r e fo r e , th e f e a s i b i l i t y
bed hea t exchanger u s in g l i q u i d s la g as th e bed m a te r ia l
i s dependent on a narrow d is p e r s io n o f th e d r o p l e t d ia m e t e r s .
M ono-disperse sprays have been a ch ie ve d by v i b r a t i o n induced
a t o m iz a t io n .
W ith t h i s method th e d r o p l e t s a re fo rm e d .by d i s t u r b i n g
a l i q u i d c a p i l l a r y j e t by e i t h e r v i b r a t i o n
sound p re s s u re waves ( 9 , 1 0 ).
(7 , 8) o r w i t h e x te rn a l
E xp erim e ntal data has shown t h a t drops
u n ifo r m i n d ia m e te r t o w i t h i n f i v e p e r c e n t o f th e mean can be o b ta in e d
u s in g l i q u i d s
as i n v i s c i d as w a te r and as v is c o u s as g l y c e r i n .
The co n ce p t o f th e above d e s c rib e d d r o p l e t g e n e r a to r and the f a l l i n g
bed h e a t exchanger u s in g l i q u i d s la g as th e hea t t r a n s f e r media are
combined in th e f o l l o w i n g p r e h e a te r d e s ig n .
d r o p l e t s iz e d i s t r i b u t i o n s
I t i s shown, t h a t narrow
o b t a in a b le w i t h the d r o p l e t g e n e r a to r can
r e n d e r an e f f i c i e n t and compact d i r e c t l y f i r e d , h i g h te m p e ra tu re
p r e h e a te r f o r open c y c le f o s s i l
f u e le d MHD a p p l i c a t i o n s .
Some o f th e
o f f design o p e r a t io n a l c h a r a c t e r i s t i c s are a ls o c o n s id e r e d .
.
CHAPTER I I
ANALYTICAL MODEL
The d i f f e r e n t i a l e q u a tio n s f o r th e h e a t t r a n s f e r w i t h i n th e heat
exchanger were o b ta in e d from b a s ic p r i n c i p l e s .
R a d ia tiv e T r a n s f e r
R a d ia tiv e energy exchange between any two d r o p l e t s in th e chamber
depends upon th e s o l i d a n g le subtended by one d r o p l e t as viewed from
th e o t h e r .
T h e re fo re ,
it
i s necessary to d e r iv e an e x p re s s io n f o r
th e shadowing e f f e c t o f t h e p a r t i c l e s . .
C o nsid er an in c re m e n ta l sphere o f r a d iu s £ and th ic k n e s s . d£
c e n te re d about a d r o p l e t o f d ia m e te r d / as shown in F ig u re 2 . 1 .
Assume,
th e sphere i s o ccu p ie d by d r o p l e t s o f d ia m e te r dm lo c a te d randomly w i t h
an average number d e n s it y n.
subtended by a l l
Let
( £ ) r e p r e s e n t t h e t o t a l s o l i d ang le
o f th e d r o p l e t s w i t h i n th e sphe re .
The f r a c t i o n o f
s o l i d ang le n o t y e t shadowed by these d r o p l e t s i s
f (£■) = (4fn - fi(£))/4TT
2.01
Then th e s o l i d ang le subtended by th e d r o p l e t s w i t h i n th e in c re m e n ta l
sphere is
dO(&) = (-------9— ) (4Tr£2d£.) f (£)
2.02
4A
T h is y i e l d s th e d i f f e r e n t i a l e q u a tio n
+
2.03
/
-
I
-
With- th e boundary c o n d i t i o n
f i( o ) = 0 ,
th e s o l u t i o n is
B(Jl) = 4ir( I - B - m d J y 4
2 .04
T h e re fo re ,
2.05
To d e r iv e th e e q u a tio n s f o r th e n e t r a d i a t i o n i t was assumed t h a t
th e d r o p l e t s are b la c k b o d ie s .
I t was f u r t h e r assumed t h a t the
d r o p l e t s form an o p t i c a l l y dense c lo u d and th e r a d i a t i o n p e n e t r a t io n
d is ta n c e i s sm all compared w i t h th e d is ta n c e o v e r which s i g n i f i c a n t
te m p e ra tu re changes o c c u r .
Thus th e gas was c o n s i d e r e d . t r a n s p a r e n t .
A f t e r th e e q u a tio n s were s o lv e d , t h i s l a t t e r assum ption was checked-and
th e a b s o r p tio n by th e gases was found to be small
(1 1 ).
The r a d i a t i v e
t r a n s f e r fro m a d r o p l e t o f d ia m e te r dm i n th e annul us to th e d r o p l e t
o f d ia m e te r d- as shown i n F ig u re 2 .2 is
2 .0 6
where
2 .07
and
2
Jr =
2
+ r
2
2 .0 8
I
- 8 -
FIGURE 2.1
INCREMENTAL SPHERE FOR DERIVATION OF SHADOWING EFFECT
2
I
FIGURE.2 .2
INCREMENTAL ANNULUS FOR DERIVATION OF RADIATIVE TRANSFER
- 9 The t o t a l r a d i a t i v e t r a n s f e r from a l l
x= °°
2 2 2
now d, dm
8
I
r—
o f th e d r o p le t s i s then
r
re-(,n7rdnl2(x 2+ r2) ’5
4
X=- 00
dr
dx
x2 + r 2
r= o
2.09
I n t e g r a t i n g w i t h re s p e c t t o r y i e l d s
X= CO
2 2 2
now d. dm
2+1
8
J
2.10
Tsm4(x) El ( IotxD dx
X--
CO
where
2.11
a = 1/4 nnd
and
( x ) is the f i r s t exponential in te g ra l fun ction
E1( X)
2.12
The i n t e g r a t i o n o f e q u a tio n ( 2 .1 0 ) r e q u ir e s th e te m p e ra tu re o f th e s la g
d r o p l e t s to be s p e c i f i e d as a f u n c t i o n o f x .
Since t h i s
i s n o t known,
a T a y l o r ' s s e r ie s expansion about x=0 t r u n c a te d a f t e r th e f i r s t f o u r
terms o f the s e r ie s i s employed.
sm
g (x ) - g ( o ) + x g ' ( o ) +
g" (o) +
Qm i (O)
2 .1 3
- 10 S u b s titu tin g
( 2 .1 3 ) i n t o
( 2 .1 0 ) and u s in g th e r e l a t i o n s h i p
0,
n
J x nE1 ( | x | ) d x
OO
2
y ie ld s
odd
9 9 9
ncnr d.. a_
Ji
m
Qr2+1 = —
JJ
I
x " E1( x ) d x ,
n even
2.14
g ( o ) E 1 (ax)+%x 2g " ( o ) E 1(a x )
2.15
I n t e g r a t i o n o f e q u a tio n ( 2 .1 5 ) g iv e s
,
Qr^ 1 = a-rrd_.2T. 4 +
Ji l Sm "
16a d.2
i
9
Sm d
2.16
4'
Since th e r a t e o f therm al em ission from th e d r o p l e t d^ is
Q r 1 = OTTd12I 5 . 4
,
2.17
th e n e t r a d i a t i v e h e a tin g r a t e o f th e d r o p l e t is
IGod1
io o o :2
Qr
net
T T zr
Sm d_
d2<Tsm4 >
+ =TTd1 (Tsm - Ts1'
2.18
E q uation (2 .1 8 ) re p re s e n ts th e n e t r a d i a t i v e h e a tin g o f a d r o p l e t
o f d ia m e te r d 1 by the s u r ro u n d in g d r o p l e t s o f d ia m e te r d ^.
in c lu d e d in th e energy balance f o r th e f a l l i n g d r o p l e t s .
energy balance f o r th e c o n t r o l volume i s a p p li e d , i t
T h is i s
When th e
i s necessary to
- 11 r e p r e s e n t th e n e t r a d i a t i v e h e a t f l u x .
I f th e average mean f r e e path
o f a photon e m it te d by a d r o p l e t is sm all compared w i t h th e d is ta n c e
o v e r w hich s i g n i f i c a n t te m p e ra tu re changes o c c u r , then th e n e t r a d i a t i v e
h e a t f l u x i s o b t a in e d by use o f th e Rosseland d i f f u s i o n e q u a tio n ( 1 2 ) .
qr
-IGoT
3
3a_
dT
dx
2.19
where ar i s th e Rosseland- mean a b s o r p tio n c o e f f i c i e n t .
In t h i s case
a ^ would equal a d e fin e d in e q u a tio n ( 2 . 11) and T th e lo c a l mean s la g
te m p e ra tu r e .
Then
64oTsm
d (Tsm)
2.20
Smclm2.!
E q uation ( 2 .2 0 ) r e p r e s e n ts th e r a d i a t i v e d i f f u s i o n th ro u g h the s la g
d r o p l e t c lo u d .
D r o p le t Energy Balance
Fine (13) has found th e therm al d i f f u s i v i t y o f s la g s s i m i l a r to
coal s la g a t te m p e ra tu re s o f 1600K t o be on th e o r d e r o f 5 x 10- / (m / s e c )
The r e s u l t i n g B i o t modulus f o r th e d ia m e te rs c o n s id e re d i s between
0 .3 and 0 . 8 .
Based on th e s e low B i o t numbers and th e i n t e r n a l m ix in g
w i t h i n th e d r o p l e t , an is o th e rm a l sphere i s assumed.
C o n sid e r a d r o p l e t o f d ia m e te r d. f a l l i n g th ro u g h a c o u n te r f lo w o f
gas as shown i n F ig u re 2 . 3 .
TTdi 3
ps cs i
(
6
Then
d(Ts . )
^
dt
~ ^cov + ^ r n e t
2 ‘ 21
- 12 but
d (L ,)
d (T . )
d (L ,.)
2.22
and
qCOV = - h I dI
2 .2 3
(Tg - Ts 1 >
24 it,.
2.24
- 2vSmdSdm30,-n2
Combining e q u a tio n s ( 2 .2 1 ) th ro u g h ( 2 .2 4 ) and ( 2 .1 8 )
si
_
dx
6M
W
,
qds ( ^ s m dmDi n 2 ) 2
ds cs i d i Vs i
d^
O
+
18cS id1-vS iltS
ps cs i d i v s i
2.25
(T=m4 - L , 4 )
sm
s1
E q uation ( 2 .2 5 ) re p re s e n ts th e d e r i v a t i v e w i t h r e s p e c t t o p o s i t i o n o f
th e te m p e ra tu re o f th e p a r t i c l e s o f d ia m e te r d^ as th e y f a l l
chamber.
through th e
For the i d e a l i z e o case o f one d r o p l e t d ia m e te r (m o n o -d isp e rse )
t h e r e i s one e q u a tio n o f t h i s fo rm , and d. equals d , I . equ als I
,
•
III
Ol
oIII
e tc .
When t h e r e i s d i s p e r s io n in th e d r o p l e t d ia m e te r s , t h i s is
accounted f o r by l e t t i n g
d^ denote th e d ia m e te r o f th e d r o p l e t s o f the
i t h d i s c r e t e s i z e ; i = l denotes th e s m a ll e s t d r o p le t s and i=N denotes
th e l a r g e s t d r o p l e t s .
Thus, t h e r e a re N e q u a tio n s o f th e above form
13 (one f o r each d i s c r e t e s i z e ) .
C o n tro l Volume Energy Balance
The e q u a tio n f o r th e heat exchange between the d r o p l e t s and the
gas i s d e r iv e d u s in g th e c o n t r o l volume shown in F ig u re 2 . 4 .
The
h e a t lo s s fro m th e w a ll s per u n i t area i s re p re s e n te d by qw .
The
r a d i a t i v e d i f f u s i o n te rm , q r? is p resen ted in e q u a tio n ( 2 . 2 0 ) .
energy b alance f o r th e c o n t r o l
volume y i e l d s
^lflS icS i1Si Ix " rflS icS i1Si I x+ax
+ ( c gltgT9 l x+Ax " W
An
n
g l Xl " V
0Oi x
“ qJx+Ax^
2.26
= 0
R e arran ging and u s in g e q u a tio n ( 2 .2 0 )
lflS icSl
i= 1
d fx S i1
2lj2opSV i n 4vSm
9V g cg
V g
d
fT
Av
' sm
3
d fx Sm1 ' .
dx
qWll0O
2.27
'
cg%
Heat Loss From th e Wall
B e fore th e h e a t lo s s can be c a l c u l a t e d , th e i n s u l a t i o n m a te r ia l
and t h ic k n e s s has to be d e te rm in e d .
i n s u l a t i o n c o n s id e re d are l i s t e d
The e i g h t ty p e s o f ceram ic
in Table 2 . 1 .
The in n e r w a ll
- 14 -
I
FIGURE 2 .3
DROPLET ENERGY BALANCE
ltS
FIGURE 2.4
V
Ag
CONTROL VOLUME FOR ENERGY BALANCE
- 15 -
TABLE 2 .1
M a n u fa c tu re r
PROPERTIES OF THE INSULATING MATERIALS
Type
Thermal
C o n d u c t ! v it y
( j/ m - s e c - K )
Upper
Temperature
L i m i t (K)
Standard
S ize (cm)
Norton
AN-599
1.290
2140
7.62
J o h n s -M a n v ille
JM-3200
0.503
2030
11.43
Johns-Manvi l i e
JM-3000
0.475
1920
11.43
J o h n s -M a n v ille
JM-2800
0.424
1810
11.43
J o h n s -M a n v llIe
JM-2600
0.338
1700
11.43
J o h n s -M a n v ille
JM-2500
0.308
1640
11.43
J o h n s -M a n v ille
JM-2300
0.144
1530
11.43
Johns-M anvil Ie
Cerawool
0.078
1140
5.08
- 16 te m p e ra tu re i s assumed to be equal t o th e lo c a l mean s la g d r o p l e t
te m p e ra tu re and th e o u t e r w a ll
i s s p e c i f i e d a t 370K.
Because o f th e
c o r r o s iv e e n viro n m e n t w i t h i n th e e xcha nger, Norton AN-599 bubble
alum ina b r i c k i s used as th e f i r s t l a y e r o f i n s u l a t i o n .
t o be 7.62 cm. t h i c k .
The o u t e r l a y e r o f i n s u l a t i n g m a t e r i a l ,
J o h n s -M a n v ille C eraw ool, i s chosen because o f i t s
c o n d u c t i v i t y and i t s
lo w e r therm al
a b i l i t y to absorb any co nd ensatio n which m ig h t
o c c u r on th e i n n e r w a ll o f th e e n c lo s in g p re ssu re v e s s e l.
i s t o be 5 .08 cm t h i c k .
ig n o r e d .
T h is l a y e r
R e spective th ic k n e s s e s o f th e re m a in in g
i n s u l a t i o n s a re chosen by a computer t r i a l
o u t l i n e d below .
T h is l a y e r i s
and e r r o r te c h n iq u e as
Thermal r e s is t a n c e o f t h e metal p re s s u re vessel i s '
=»
To d e te rm in e th e c o n v e c tiv e f i l m
n a t u r a l c o n v e c tio n i s assumed.
c o e f f i c i e n t on th e o u t s id e w a l l ,
For an am bient a i r te m p e ra tu re o f
295K and a c h a r a c t e r i s t i c le n g t h o f e i g h t meters th e G rashof number
P r a n d tl number p r o d u c t i s
GrPr = 2 .5 x 10
Since t h i s
12
i s i n t h e t u r b u l e n t range f o r n a t u r a l c o n v e c t i o n ,. the
r e s u l t i n g N u s s e lt number i s
Nu = . I S ( G r P r ) ' 333
(14)
Then
k
a
2.28
- 17
The o p t i m i z i n g c r i t e r i o n
f o r d e t e r m in in g th e i n s u l a t i o n th ic k n e s s e s
i s th e o u t e r chamber d ia rtie te r; th e id e a b e in g t o maxim ize th e th ic k n e s s
o f t h e lo w e r c o n d u c t i v i t y m a t e r i a ls and thus m in im iz e t h e o u t e r
d ia m e te r.
The desig n c o n s t r a i n t s are t o keep th e te m p e ra tu re s a t th e
i n t e r f a c e s w i t h i n th e l i m i t s o f th e r e s p e c t iv e i n s u l a t i o n s .
The com puter
r o u t i n e t h a t chooses and s iz e s th e r e s p e c t iv e i n s u l a t i o n s begins by
t r y i n g o n ly th e h ig h therm al r e s is t a n c e m a t e r i a l between t h e s p e c i f i e d
i n n e r and o u t e r la y e r s . .
I f th e i n t e r f a c e te m p e ra tu re s a re to o h ig h ,-
s u c c e s s iv e la y e r s o f t h e lo w e r r e s i s t a n t i n s u l a t i o n s a r e added u n t i l
th e i n t e r f a c e te m p e ra tu re s a re w i t h i n th e l i m i t s o f th e r e s p e c t iv e
in s u la tio n s .
\
C o n sid e r th e case where o n ly one ty p e o f i n s u l a t i n g m a te r ia l
between th e s p e c i f i e d o u t e r and i n n e r la y e r s o f i n s u l a t i o n s
as shown i n F ig u re 2 . 5 .
From th e s o l u t i o n o f t h e c o n d u c tio n e q u a tio n s
f o r r a d ia l heat t r a n s fe r w ith c y lin d r ic a l
T
i s used
Ro ( To - Ta ,h1,,(R2/ R l>
2
Ro ( To - Ta>h1n<R3/R 2>
T3 ’ T2
symmetry
2 .2 9
2 .30
E q uating th e h e a t i n and o u t o f each fa c e
R, =
( A
- T s i^ V V h R ,
2.31
- 18 These are s o lv e d by use o f s u c c e s s iv e s u b s t i t u t i o n and the
i n t e r f a c e te m p e ra tu re s are checked a g a in s t th e upper te m p e ra tu re l i m i t
s p e c i f i c a t i o n s o f th e i n s u l a t i o n m a t e r i a l s .
I f these are t o o h ig h ,
a l a y e r o f th e n e x t h i g h e r r a te d te m p e ra tu re i n s u l a t i n g m a t e r i a l i s
added, and th e i n t e r f a c e te m p e ra tu re s are c a l c u la t e d and checked.
Each l a y e r o f i n s u l a t i o n added i s
a v a ila b le .
T h is method i s
11.4 cm t h i c k - - t h e s iz e c o m m e rc ia lly
repeated u n t i l a l l o f th e tem p e ra tu re s
were w i t h i n th e l i m i t s o f th e r e s p e c t iv e m a t e r i a l s .
A f t e r these ste p s are co m p le te d , a n o th e r check i s made t o see
i f any o f th e i n t e r f a c e te m p e ra tu re s a re low enough t o r e p la c e a l a y e r
o f i n s u l a t i o n w i t h th e n e x t lo w e r c o n d u c tiv e i n s u l a t i o n .
For in s t a n c e ,
th e above method c o u ld r e s u l t w i t h a l a y e r o f JM-2300, a l a y e r o f
JM-2500, and a l a y e r o f JM-2600, when th e te m p e ra tu re between th e
JM-2500 and th e JM-2600 i s low enough t o r e p la c e t h e JM-2500 w i t h
JM-2300.
'
.
Once th e i n s u l a t i o n s iz e s are d e te rm in e d , th e hea t f l u x term is
c a l c u l a t e d u s in g an 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
where qw r e p r e s e n ts the h e a t lo s s fro m th e w a ll as used in Equation
( 2 .2 7 ) and
H = I/
"
+
E
i
(15)
2 .32
F a l l i n g D r o p le t Dynamics
■.
The e x p re s s io n f o r th e dynamics o f a s p h e r ic a l d r o p l e t o f
d ia m e te r d^ f a l l i n g
th ro u g h a c o u n t e r f lo w o f gas i s d e r iv e d by use o f
t h e f r e e body diagram i l l u s t r a t e d
buoyant f o r c e
i n F ig u re 2 . 6 .
I g n o r in g th e
(p / ps« 1 )
3
4
CDpgVr i
2.33
d iP s ^ s i
As w i t h e q u a tio n ( 2 . 2 5 ) , th e r e are N e q u a tio n s o f t h i s
form (one
e q u a tio n f o r each d i s c r e t e d r o p l e t s i z e ) .
The d ia m e te r o f th e chamber depends on th e t e r m in a l v e l o c i t y o f
X
t h e s m a ll e s t p a r t i c l e .
The t e r m in a l
v e l o c i t y i s c a l c u l a t e d from the
e x p re s s io n
4ap d.
-V
term
.(
is
■)
2 .34
D im ensionless R e la tio n s
To f a c i l i t a t e
ease o f s o l u t i o n and use o f d im e n s io n le s s em perical
c o r r e l a t i o n s , th e above e q u a tio n s .w e re n o rm a liz e d u s in g th e f o l l o w i n g
param eters
— 20 -
FIGURE 2 .5
FIGURE 2 .6
GEOMETRY FOR THE CASE OF THREE LAYERS OF
INSULATION
DROPLET FREE BODY DIAGRAM
V r l" i
M9
= Reynolds Number
h ,-di
Nu,
N u s s e lt Number
Pr = — p—^—
E q u a tio n s ( 2 .2 5 ) ,
= P ra n d tl Number
( 2 .2 7 ) , and (2 .3 3 ) tra n s fo rm r e s p e c t iv e ly in to
th e f o llo w in g :
d<pS i
_
6Nu . U. ( m
*
+ ¥2 - (J)si.)
*
( Pr p C1
d,
*
(U1 - U )
d2< V )
1
+
du2
< C
- +si )
dtp,
9
- ( i m ) ( Z c' i , X i *
i= l
A & n + ¥6
dn
d<J>c
3 c DuI 1
W
where
V
4 p * d .* ( U .-U
+ ¥8
)
- 23 - I 0V
V
T2gpsdmDin 4vsmTl , s 4
18 D0 * s
=g(T2 , g- T 1>g)
qWn 0 O_____________
V g
(T2,g " Tl,g>
T7 ' aV v L r
W
Y8
W
PAV
l, r
The va lu e s f o r th e N u s s e lt number were c o r r e la te d fro m p u b lis h e d data
as
Nu. = ^ g R e V 630P r - 333
(1 5 )
2.3 8
The drag c o e f f ic ie n t was d eterm ined fro m th e Reynolds number
Il
O
O
1 8 .5 /R e -600
5 .7 4 /R e -372
0 .44
Re<200
200<Re<1000
Re>1000
(1 6 )
2 .39
- 24 The above param eters and e q u a tio n s a p p ly to t h e . to p chamber b u t
w o uld be id e n t ic a l f o r th e .lo w e r chamber w ith th e e x c e p tio n t h a t
T2 ’ V1 anc* V2 w ould be re p la c e d by T3 , T ^, V3 and
r e s p e c t iv e ly .
Method o f S o lu tio n
The n o n - lin e a r s e t o f o r d in a r y d i f f e r e n t i a l e q u a tio n s (2 .3 5 )
th ro u g h (2 .3 7 ) re p re s e n t a boundary v a lu e system w ith one known
b o u ndary.
unknown.
A lth o u g h th e boundary va lu e s a re known a t x= L, L i t s e l t is
Assuming th e e q u a tio n s a re w e ll behaved, th e system can be
s o lv e d by an i n i t i a l
v a lu e n u m e rica l m ethod.
An ene rg y balance o f th e
e n t ir e h e a t exchanger system is used, to f in d th e te m p e ra tu re s a t th e
to p o f th e chambers and th e mass flo w r a te s .
Thus (.2N+1) i n i t i a l
va lu e s a re known, le a v in g o n ly one t o be a p p ro x im a te d --th e f i r s t
d e r iv a t iv e o f th e mean s la g te m p e ra tu re .
The problem a r is e s fro m th e form o f e q u a tio n ( 2 .2 5 ) .
For th e
mean s la g te m p e ra tu re th e e q u a tio n is
d2(Tsm
d <Tsm>
C1 (Tg-Tsm) + c2
where C l and C2 re p re s e n t th e v a r ia b le c o e f f ic ie n t s .
I f th e system is
s o lv e d w ith th e second term to th e r i g h t o f th e equal s ig n equal to
z e ro , th e te m p e ra tu re p r o f ile s a re n e a r ly li n e a r .
The a d d it io n o f th e
second te rm re nde rs th e te m p e ra tu re s o lu t io n , and i t s
d e r iv a t iv e s ,
e x p o n e n tia l in n a tu re and e x tre m e ly s e n s it iv e to th e i n i t i a l
ft'
v a lu e
- 25 a p p ro x im a tio n and n u m e rica l tr u n c a tio n e r r o r .
Any s l i g h t e r r o r w i l l
compound i t s e l f e x p o n e n tia lly and dom inate th e e q u a tio n s , re n d e rin g
th e s o lu t io n m e a n in g le s s .
The second d e r iv a t iv e term re p re s e n ts a p o r tio n o f th e r a d ia t iv e
t r a n s f e r w h ile th e f i r s t term to th e r i g h t o f th e equal s ig n re p re s e n ts
th e c o n v e c tiv e t r a n s f e r .
D e fin in g e as th e r a t i o o f th e se two terms
and e m plo ying an o rd e r o f m agnitude a n a ly s is y ie ld s
d2< C >
C2 1 2 L
dx^
C1 t V
sm
■) + 4 T
3
Sm
d2<Tsm>
dx2
T r g-T smT
V
wI th
AT
L
2
and
Cf
For th e upper chamber
AT
L
u s in g q u a n t it ie s from a n u m e rica l s o lu tio n
o b ta in e d w ith th e r a d ia t iv e term n e g le c te d r e s u lt s in
E = 0.030
and f o r th e lo w e r chamber
E = 0.002
S ince th e s e r a t io s a re much le s s th a n one, th e r a d ia t io n term is
sm a ll in com parison to th e c o n v e c tio n te rm .
T h e re fo re , th e r a d ia tio n
I
- 26 second d e r iv a t iv e term in e q u a tio n
th e e q u a tio n s .
(2 .3 5 ) was ig n o r e d .in o r d e r to s o lv e
T h is is n o t to say t h a t th e rm a l r a d ia t io n
is
ig n o re d
in th e a n a ly s is ; b u t r a t h e r , th e second d e r iv a t iv e te rm in e q u a tio n
(2..18) was dropped.
The i n i t i a l
c o n d itio n s a t th e to p o f th e chamber a re
♦st - V 1
V
The i n i t i a l
0
va lu e f o r th e second d e r iv a t iv e term in e q u a tio n (2 .3 6 )
had to be a p p ro xim a te d in o rd e r to i n i t i a t e
S ince t h is
te rm had l i t t l e
th e n u m e rica l i t e r a t i o n .
e f f e c t on th e r e s u lt s
( le s s th a n one p e rc e n t)
th e a p p ro x im a tio n d id n o t have to be v e ry a c c u ra te . •
A f o u r th o rd e r R unge-K utta in t e g r a t io n te c h n iq u e was employed to
s o lv e th e system o f e q u a tio n s .
In th e bottom chamber th e le n g th was
de te rm in e d by in t e g r a t in g u n t i l ^
equ ale d
one, w h ile in th e to p
chamber th e p re d e te rm in e d s la g e x i t te m p e ra tu re was used as th e
p a ram eter to d e te rm in e th e le n g th .
E r r o r a n a ly s is f o r h ig h e r o r d e r R unge-Kutta schemes is
ve ry
d i f f i c u l t o r im p o s s ib le to im plem ent f o r systems o f n o n lin e a r d i f f e r e n t ia l
e q u a tio n s o f t h i s ty p e ( 1 7 ) .
To check th e convergence and s t a b i l i t y
s e v e ra l d i f f e r e n t s te p s iz e s were used.
No a p p a re n t problem s a ro s e .
CHAPTER I I I
DROPLET FORMATION
A c r i t i c a l elem e nt in th e d e sig n o f a f a l l i n g
bed c o u n te rflo w
h e a t exchanger is c o n tr o l o f the, d is p e r s io n o f t h e . d r o p le t d ia m e te rs .
To p re v e n t any o f th e p a r t ic le s fro m b e in g blown o u t o f th e to p ,
th e v e lo c it y o f th e gas th ro u g h th e chamber must be li m i t e d by th e
te rm in a l v e lo c it y o f th e s m a lle s t p a r t ic le s .
I f th e d r o p le t s iz e s
a re c h a r a c te r iz e d .b y a w ide d is p e r s io n , th e la r g e r p a r t ic le s w i l l f a l l
much f a s t e r than th e s m a lle r ones and th e le n g th o f th e chamber w i l l
become u n fe a s ib ly la r g e .
For exam ple, th e p a r t ic le s iz e d i s t r ib u t i o n
o b ta in e d fro m Heywood and Womack (6 ) u s in g a tw in j e t a to m iz e r would
r e q u ir e chamber le n g th s in excess o f 100 m eters f o r an MHD p re h e a te r.
F ig u re 3 .1 f u r t h e r i l l u s t r a t e s
th e chamber d im e n s io n s .
th e e f f e c t o f p a r t ic le d is p e r s io n on
One c o n ce p tu a l s o lu t io n to t h i s
problem
is th e fo rm a tio n o f th e s la g d r o p le ts by v ib r a t io n a to m iz a tio n .
In th e proposed a to m ize r,, r e fe r r e d to as a drop g e n e ra to r, th e
l i q u i d is fo rc e d th ro u g h a c a p i ll a r y w h ich is v ib r a te d a t a p re ­
d e te rm in e d fre q u e n c y to produce u n ifo r m ly s iz e d d ro p s .
T h is te c h n iq u e
has been used p r im a r ily in re s e a rc h a p p lic a tio n s such as com bustion (.8)
and drop co a lescen ce s t u d ie s . ( 1 8 ) .
The f i r s t q u a n t it a t iv e a n a ly s is o f
l i q u i d j e t d i s in t e g r a t io n was made in 1878 by Lord R a y le ig h ( 1 9 ) .
His
r e s u lt s , w h ich a re a p p lic a b le to an in v is c i d f l u i d w ith o u t any a e ro ­
dynamic fo rc e s a c t in g on i t ,
showed t h a t th e fre q u e n c y f o r maximum
i n s t a b i l i t y , and hence th e optimum fre q u e n c y f o r u n ifo r m ly s iz e d d ro p s .
- 28 —
- 3.25mm
M hameter
length
O u te r Chamber D iam eter (m e te rs )
d
P e rc e n t V a r ia tio n Between Mean and Minimum D iam eter
FIGURE 3 .1
EFFECT OF PARTICLE DISPERSION ON LENGTH AND DIAMETER
OF THE UPPER CHAMBER FOR A SOOOMWt MHD FACILITY
- 29 is
g iv e n by
3.01
Fopt - Y 4-508 Do
T h is a n a ly s is was extended by L e v ic h ( 2 0 ) - to in c lu d e th e e f f e c t s o f
f l u i d v is c o s it y and s u rfa c e te n s io n fo rc e s r e s u lt in g in
'V 1Fo p t = (
13
S o p
) (
%
r~ T 3
y_.
3.0 2
)
U j
The minimum fre q u e n c y f o r th e fo rm a tio n o f n e a rly u n ifo r m ly s iz e d
drops was d e te r m in e d .e m p ir ic a lly by R ajogopalan and T ie n (7 ) as
Fmin
3 .0 3
0 -4 Fo p t
These same re s e a rc h e rs a ls o d e te rm in e d th e t h e o r e t ic a l e x p re s s io n f o r .
th e drop s iz e r e s u lt in g fro m th e j e t d is in t e g r a t io n
V,
1 /3
d = 1.145 ( - J l H
2 /3
D-
3 .04
The minimum average v e lo c it y in th e c a p i ll a r y nece ssary to form a
s ta b le j e t , as de te rm in e d by L in d b a ld and S ch neider (1 8 ) is
8 or
Vc,min = ( - T
. %
-1
3-05
Harmon (2 1 ) has r e la te d th e c a p i ll a r y d ia m e te r to th e f r e e stream j e t
d ia m e te r by.
D- = 0.867 D„
3.06
- 30 The above e q u a tio n s were used to s im u la te th e drop g e n e ra to r
th e h e a t exchanger a p p lic a t io n .
fo r
There a re two methods o f d is tu r b in g
th e l i q u i d j e t :
1)
F lo w in g th e l i q u i d
th ro u g h c a p i l l a r i e s
in a p la te w hich
is v ib r a te d w it h in a p re d e te rm in e d fre q u e n c y range
2)
F lo w in g th e l i q u i d
th ro u g h c a p i ll a r ie s
in a s t a tio n a r y
p la te w ith th e d is tu rb a n c e produced by e x te rn a l sound
p re s s u re waves.
U n ifo rm ly s iz e d drops ( to w it h in f i v e p e rc e n t o f th e mean) have
been a ch ie ve d by th e f i r s t method ( 7 , 8 ) .
The second method was
in v e s tig a te d by Miesse (9 ) b u t no s iz e d i s t r ib u t i o n s were p u b lis h e d .
A m a jo r f a c t o r in th e v a r ia t io n o f d r o p le t d ia m e te rs is th e
v a r ia t io n
in th e c a p i l l a r y d ia m e te rs .
c a p illa r ie s
is
The re q u ire d number o f
in th e d i s t r i b u t o r p la t e at. th e chamber to p is
4 til
Number o f C a p illa r ie s = ---------------------- p—
pSvC T Dc,m
3 .0 7
■
Because o f th e h ig h te m p e ra tu re s , e x tru d e d ceram ic tu b in g is
suggested f o r th e c a p i l l a r i e s .
The s ta n d a rd to le ra n c e s f o r t h is
tu b in g w ith in s id e d ia m e te rs ra n g in g fro m 1 .3 x 10
is
±3% o r 1 .3 x 10 4 m e te rs , w h ic h e v e r is
g r e a te r .
to 1 .3 x IO "'3 m ete rs
These to le ra n c e s
were used to f in d th e minimum c a p i l l a r y d ia m e te r f o r a s p e c ifie d
mean c a p i l l a r y d ia m e te r.
For la m in a r flo w th e p re s s u re d ro p .a c ro s s
th e s m a lle s t c a p i ll a r y is g iv e n by
I
- 31 3 2 ]i
AP
£
C
s
TT
Vc , min
3.0 8
c ,m in
where Vc mi- n is th e minimum v e l o c it y re q u ire d to form a j e t in th e
s m a lle s t c a p i l l a r y .
S ince th e c a p i l l a r y le n g th s a re equal j, th e
v e l o c it y in th e mean c a p i ll a r y d ia m e te r is g ive n by
V
=
V
.
D
Cjl In m
c,m
c ,m
n
2
2
3.09
c ,m in
The optimum o p e ra tin g fre q u e n c y is c a lc u la te d u s in g e q u a tio n ( 3 .0 2 ) .
From e q u a tio n (3 .0 4 ) th e mean d r o p le t d ia m e te r fro m th e s m a lle s t
c a p i ll a r y and th e mean d r o p le t, d ia m e te r from th e mean c a p i l l a r y are
o b ta in e d .
Assuming th e d r o p le t d ia m e te rs from any c a p i l l a r y va ry
w it h in 5% o f th e mean d r o p le t d ia m e te r o f t h a t c a p i l l a r y , th e s m a lle s t
d r o p le t w it h in th e exchanger is c a lc u la te d from th e mean d r o p le t
d ia m e te r o f th e s m a lle s t c a p i l l a r y .
min
dm
T hat is
.95 d
m,min
dm,m
The c a p i l l a r y d ia m e te rs and th e d r o p le t d is p e rs io n s a re assumed
t o f o llo w a normal d i s t r i b u t i o n .
d e v ia t io n , i t was f u r t h e r assumed
In o rd e r to c a lc u la te th e sta n d a rd
t h a t 99% o f a l l o f th e d ro p le ts
w i t h in th e chamber a re w i t h in th e d ia m e te r range a s .c a lc u la te d above
T h is r e s u lt s in a s ta n d a rd d e v ia tio n o f
-
Sd "
dmin
;-------- 27576
32
-
( 22)
3 .1 0
The fre q u e n c y fu n c t io n f o r th e p a r t i c l e d i s t r i b u t i o n was then g e n erate d
by
/
,( d r dn. ) 2
f(d .)
3.11
- S d VZTr
For th e d is c r e t e number o f d r o p le t s iz e s as modeled in th e com puter code
th e r e s p e c tiv e number f r a c t io n s were o b ta in e d by in t e g r a t io n o f th e
fre q u e n c y f u n c t io n .
y
CHAPTER IV
RESULTS
The e q u a tio n s p re se n te d in C hapter I I and C hapter I I I w e re .a p p lie d
to th e d e sig n o f an MHD a i r p re h e a te r system .
The’ com puter program
o u t lin e d in Appendix I I was used to n u m e r ic a lly in te g r a te th e e q u a tio n s .
The o p e ra tin g c o n d itio n s f o r th e 3000 MW therm al open c y c le f a c i l i t y
c o n s id e re d were s im il a r to th o s e o f th e ECAS Base Case One Open C ycle
s tu d y (2 3 ) b u t w ith h ig h e r o p e ra tin g te m p e ra tu re s .
in c re a s e th e th e rm a l e f f i c ie n c y o f th e p la n t .
H ig h e r te m p e ra tu re s
The p re s s u re a t th e
in g re s s o f th e channel was a ls o h ig h e r than t h a t o f th e ECAS s tu d y ; t h is
b e in g a p p ro p ria te f o r th e h ig h e r o p e ra tin g te m p e ra tu re s
(2 4 ).
A fte r
th e chambers were s iz e d u s in g th e se o p e ra tin g c o n d it io n s , p a r t ia l
\
lo a d
o p e ra tio n was s tu d ie d .
F u ll Load Design
The d ia m e te rs o f th e chambers a re dependent on th e mass flo w r a te
o f th e gas th ro u g h th e chamber and th e te rm in a l v e lo c it y o f th e s m a lle s t
d r o p le t .
In o r d e r to keep these d ia m e te rs re a s o n a b le , i t was nece ssary
to use th re e , s e ts o f p re h e a te rs .
Each o f these s e ts c o n s is ts o f th re e
upper chambers and one lo w e r chamber as shown in F ig u re 1 .1 .
p a ra m e te rs -T9
T9
, T1
, Iiiri, and rh. were s p e c if ie d .
g
b
The
Chamber
le n g th , s la g mass flo w r a t e , and p re s s u re drop th ro u g h , th e c a p i ll a r ie s
were th e d e sig n c r i t e r i a w h ile th e s la g te m p e ra tu re s , c a p i ll a r y
d ia m e te r and d is tu rb a n c e fre q u e n c y were th e v a r ia b le d e sig n p a ra m e te rs.
.I
-
34 -
The e f f e c t s o f th e o p e ra tin g s la g te m p e ra tu re s on th e d esign
c r it e r ia
a re shown in F ig u re 4 .1 , F ig u re 4 .2 , and F ig u re 4 .3 .
F ig u re 4 .1 was o b ta in e d by a r b i t r a r i l y ch o o sin g a c a p i l l a r y d ia m e te r o f
2mm and th e o p e ra tin g fre q u e n c y a t th e c o rre s p o n d in g ,o p tim u m d is tu rb a n c e "
fre q u e n c y .
The mass flo w r a te o f th e s la g was o b ta in e d by an energy
ba la n ce on th e lo w e r chamber w ith th e h e a t lo s s from th e chamber w a lls
assumed n e g lig ib le .
I t was a ls o assumed t h a t th e h e a t lo s s from th e
p ip in g t h a t tr a n s p o r ts th e s la g from one h e a t t r a n s f e r chamber to
a n o th e r was n e g lig ib le ; t h a t
i s , T1 c e q u a ls T„
Xjb
4jS
and T9 _ e qu als T9
£jS
djS
The e xh a u st gas. te m p e ra tu re a t th e e x i t o f th e upper exchanger was
c a lc u la te d fro m an energy balance f o r the. e n t ir e system and checked
to be s u re t h a t i t was h ig h e r than th e dew p o in t o f th e potassium
s u lf a t e
(a b o u t 1600 K ).
D e creasing th e te m p e ra tu re v a r ia t io n o f th e s la g in c re a s e s th e
s la g mass flo w
r a te re q u ire d and decreases th e ag g re g a te chamber le n g th .
(The a g g re g a te
le n g th r e fe r s to th e le n g th
th e le n g th o f th e lo w e r cham ber).
o f one upper chamber p lu s
In o rd e r to keep th e le n g th s
re a so n a b le w ith o u t th e flo w r a te o f th e s la g becoming e x c e s s iv e , th e
t o t a l te m p e ra tu re d iff e r e n c e f o r th e s la g media was chosen a t 270K.
S ince th e .s la g becomes v e ry v is c o u s a t lo w e r te m p e ra tu re s , th e p re s s u re
drop th ro u g h th e c a p i l l a r i e s a t th e to p o f th e upper chamber is c r i t i c a l .
T h e re fo re , th e lo w e s t w o rk in g s la g te m p e ra tu re was. chosen a t 1650K.
Though th e p re s s u re drop would be le s s i f a h ig h e r te m p e ra tu re were
P ressure Drop (MPas/cm)
- 35 -
CAPILLARY DIAMETER (mm)
700
1800
19
Slag Tem perature ( K e lv in s )
FIGURE 4 .1
EFFECT OF SLAG TEMPERATURE AND CAPILLARY DIAMETER ON
THE PRESSURE DROP THROUGH THE CAPILLARY
- 36 -
HIGHEST SLAG TEMPERATURE ( K e l v i n s )
—
1900
1920
1940
950
1960
/
1
I8 6 0
260K
900
280K
850'
8001
300%
750
320%
1700
1650J
700
1600
Temperature ( K e lv
Lowest S la g
SVAC MASS
o f SLW T
effect
f I GORt
in s )
B
^
ure
0N
fLOVl RATE
A ggregate Chamber Length (m e te rs)
- 37 -
AT = 260K
HIGHEST SLAG TEMPERATURE
(Kel v in s )
2.0mm
1600
1650
Lowest Slag Tem perature ( K e lv in s )
FIGURE 4 .3
EFFECT OF SLAG TEMPERATURE ON CHAMBER LENGTH
- 38 ch ose n, th e chamber le n g th in c re a s e s r a p id ly above t h i s
te m p e ra tu re .
The n e x t d e sig n v a r ia b le c o n s id e re d was th e mean c a p i ll a r y
d ia m e te r .. F ig u re 4 .4 and F ig u re 4 .5 i l l u s t r a t e
th e e f f e c t o f th e
c a p i l l a r y d ia m e te r on th e r e s p e c tiv e chamber le n g th s .
F ig u re 4 .6 g iv e s
th e optimum d is tu rb a n c e fre q u e n c ie s f o r th e upper and lo w e r chamber
a t th e v a rio u s c a p i l l a r y d ia m e te rs .
c a p i ll a r ie s
The p re ssu re drop th ro u g h the
and c lo g g in g a g a in become c r i t i c a l .
To keep these a t a
minimum, th e mean c a p i ll a r y d ia m e te r f o r th e upper chamber was chosen
a t 2.2mm.
In th e case o f th e lo w e r h e a t exchange chamber, th e s m a lle r
c a p i l l a r y d ia m e te rs r e q u ir e h ig h d is tu rb a n c e fre q u e n c ie s because o f
th e lo w e r s la g v is c o s it y .
Because th e le n g th o f th e lo w e r chamber
x
1
■
v a r ie s by le s s than two m eters a t optimum fre q u e n c y f o r th e c a p i ll a r y
d ia m e te rs c o n s id e re d , a la r g e r c a p i l l a r y d ia m e te r o f 2.5mm was s e le c te d .
The optimum fre q u e n c y r e fe r s to th e fo rm a tio n o f th e d r o p le ts by
th e d ro p .g e n e ra to r.a n d n o t th e d e s ig n o f th e h ea t e xcha nger.
The
optimum fre q u e n c y f o r j e t d is in t e g r a t io n is n o t n e c e s s a r ily th e b e s t
c h o ic e f o r th e o p e ra tin g fre q u e n c y o f th e d e s ig n .
U n ifo rm ly s iz e d drops
have been produced by fre q u e n c ie s h ig h e r and lo w e r th e n th e optimum
d is tu rb a n c e fre q u e n c y .
The l i m i t on lo w e r fre q u e n c ie s has been found to
be 40% o f optimum b u t no upper l i m i t has been s e t ( 7 ) .
t h a t in c re a s in g th e fre q u e n c ie s by 50% s t i l l
d r o p le t s .
I t was assumed
r e s u lt s in u n if o r m ily s iz e d
To decrease th e le n g th o f th e upper cham ber, th e o p e ra tin g
fre q u e n c y was s e le c te d a t 50% above th e optimum d is tu rb a n c e fre q u e n c y ,
O
MINIMUM FREQUENCY
(40* V
OPTIMUM FREQUENCY-
-150% OPTIMUM FREQUENCY
C a p illa r y D iam eter (mm)
FIGURE 4 .4
EFFECT OF CAPILLARY DIAMETER AND DISTURBANCE FREQUENCY ON THE UPPER
CHAMBER LENGTH
Chamber Length (m e te rs )
•MINIMUM FREQUENCY
OPTIMUM FREQUENCY'
150% OPTIMUM FREQUENCY
C a p illa r y D iam eter (mm)
FIGURE 4 .5
EFFECT OF CAPILLARY DIAMETER AND DISTURBANCE FREQUENCY ON THE
LOWER CHAMBER LENGTH
Frequency ( H e rtz )
■LOWER CHAMBER ( I
UPPER CHAMBER (T
= 1920K)
= 1650K)
2.0
2.2
C a p illa r y D iam ter (mm)
FIGURE 4 .6
OPTIMUM DISTURBANCE FREQUENCIES FOR VARIOUS CAPILLARY DIAMETERS
\
I
- 42 In th e lo w e r cham ber, th e o p e ra tin g fre q u e n c y was chosen as th e
optimum d is tu rb a n c e fre q u e n c y .
The d e sig n s p e c if ic a t io n s f o r th e upper and lo w e r chambers and
t h e i r r e s p e c tiv e dim en sion s f o r th e SOOOMWt MHD f a c i l i t y
p re se n te d in T ab le 4 .1 and T a b le 4 .2 .
s tu d ie d a re
F ig u re 4 .1 and F ig u re 4 .8 show
th e te m p e ra tu re and v e lo c it y p r o f ile s w it h in th e r e s p e c tiv e chambers.
The d r o p le ts in th e upper chamber a c c e le r a te f o r about th e f i r s t h a l f
o f th e chamber th e n d e c e le ra te in th e bottom h a l f .
in c re a s in g v e l o c it y o f th e gas. as i t
T h is is
due to th e
r is e s th ro u g h th e chamber.
The s la g is pumped to th e to p o f th e upper chamber by th e p re s s u re
from th e lo w e r chamber.
Assuming t h a t each upper chamber is fe d by
th re e 20cm d ia m e te r s la g l i n e s , th e t o t a l f r i c t i o n
lo s s .is on th e o rd e r
o f 2 x IO4 p a s c a ls .
The head lo s s , assum ing a t o t a l h e ig h t o f 30 m e te rs ,
5
is 7 .7 x 10 p a sca ls and th e p re s s u re drop th ro u g h th e c a p i ll a r ie s is
1.1 x 10
p a s c a ls .
T h e re fo r e , th e t o t a l p re s s u re re q u ire d , to push
th e s la g th ro u g h th e p ip in g and c a p i l l a r i e s
p a s c a ls .
is a p p ro x im a te ly 9 .0 x IO5
S ince th e p re s s u re d iff e r e n c e between th e upper and lo w e r
chambers is
1.09 x 10®, n o .s la g pumps a re r e q u ire d .
T r a n s fe r r in g th e s la g fro m th e upper chamber to th e lo w e r is
a c h ie v e d by use o f th re e r e s e r v o ir s as shown in
one r e s e r v o ir is b e in g f i l l e d
by i t s
F ig u re 1 .1 .
re s p e c tiv e upper h e a t exchange
chamber, th e second is b e in g p re s s u riz e d and th e t h i r d
in t o th e lo w e r h e a t e xcha nger.
W hile
is
b e in g em ptied
In t h i s manner a c o n tin u o u s flo w o f s la g
- 43 TABLE 4 .1
DESIGN SPECIFICATIONS FOR 3000 MWt MHD PREHEATER
Upper Chamber
Number o f Chambers
9
Lower Chamber
3
Gas I n l e t Tem perature
2200K
1200K
Gas O u tle t Tem perature
1816K
1800K
Slag I n l e t Tem perature
1650K
1920K
Slag O u tle t Tem perature
1920K
1650K
Gas Mass Flow Rate
150 k g /s e c
375 kg/sec
Slag Mass Flow Rate
288 kg /se c
864 kg/sec
Chamber P ressure
.11 MPas
1 .2 MPas
Chamber In n e r D iam eter
6 .6 5 m
5.3 1 m
Chamber O u te r D iam eter
8 .2 8 m
6 .9 3 m
16.80 m
4 .3 2 m
Mean C a p illa r y D iam eter
2 .2 mm
2 .5 mm
O p e ra tin g Frequency
245 H e rtz
411 H e rtz
Mean D ro p le t D iam eter
3.0 2 mm
2 .7 0 mm
.022 MPas/cm
.002 MPas/cm
Chamber Length
C a p illa r y P ressure Drop
- 44 -
TABLE
4 .2
INSULATION SPECIFICATIONS FOR HEAT EXCHANGER
CHAMBERS
Type
Upper Chamber
Lower Chamber
T h ickness
Thickness
N o rtra n AN-599
.076 m
.076 m
Johns M a n v ille JM-3000
. 114 m
.114 m
Johns M a n v ille JM-2800
.114 m
.114 m
Johns M a n v ille JM-2600
.229 m
.114 m
Johns M a n v ille JM-2300
.229 m
.342 m
Johns M a n v ille Cerawool
.051 m
.051 m
I
- 45 -
MEAN DROPLET
VELOCITY
GAS TEMPERATURE
MEAN SLAG
TEMPERATURE
Length (m e te rs )
FIGURE 4 .7
VARIATION IN PROPERTIES FROM THE TOP OF THE
UPPER CHAMBER
V e lo c ity (m /sec)
Tem perature ( K e lv in s )
'
- 46 3 .5
MEAN SLAG
TEMPERATURE
2 .5
GAS TEMPERATURE
2.0
MEAN DROPLET
VELOCITY
1.5
1.0
Length (m e te rs )
FIGURE 4 .8
VARIATION IN PROPERTIES FROM THE TOP OF THE LOWER
CHAMBER
V e lo c ity (m /sec)
Tem perature ( K e lv in s )
3 .0
- 47 is s u p p lie d to th e lo w e r cham ber.
P a r t ia l Load O p e ra tio n
I t may be necessary a t tim e s to o p e ra te an MHD f a c i l i t y
than f u l l
lo a d .
a t le s s
The o p e ra tin g c h a r a c t e r is t ic s o f an MHD channel a t
p a r t ia l lo a d has been s tu d ie d by Rosa ( 2 5 ) .
As an example o f how th e
p re h e a te r w o uld o p e ra te in such a ca se, a th r e e - q u a r te r lo a d o p e ra tio n
was c o n s id e re d .
The a i r te m p e ra tu re s in th e lo w e r exchanger a re th e same as in
th e f u l l
lo a d s it u a t io n , w h ile th e te m p e ra tu re o f th e e xh a u st from
th e MHD channel is s l i g h t l y h ig h e r .
Was k e p t th e same as in th e f u l l
The mass f lo w r a te o f th e s la g
lo a d s i t u a t i o n .
An energy balance
was employed to f in d th e te m p e ra tu re o f th e s la g a t th e bottom o f th e
lo w e r chamber.
Since th e le n g th o f th e ch a m b e r.is s p e c if ie d , i t was
necessary to c o n tr o l th e h e a t t r a n s f e r by c o n t r o ll in g th e d r o p le t
d ia m e te r.
The c o r r e c t o p e ra tin g fre q u e n c y o f th e drop g e n e ra to r was
determ ined by t r i a l
and e r r o r u s in g a com puter p r o g r a m " s im ila r to th e
one employed in th e f u l l lo a d d e s ig n .
The fre q u e n c y was v a r ie d , and
thus th e drop, d ia m e te rs , u n t i l th e s p e c ifie d te m p e ra tu re s a t th e
bottom o f th e exchanger were reache d.
The p ro ce d u re f o r th e upper chamber was much th e same.
The
e xh a u st gas te m p e ra tu re a t th e e x i t o f th e h e a t exchanger was d e te rm in e d
by an energy bala n ce and th e d is tu rb a n c e fre q u e n c y was fo u n d by t r i a l
. /
- 48 and e r r o r .
The r e s u lt s f o r b o th chambers a re p re se n te d in T ab le 4 .3 .
In th e lo w e r chamber th e h ig h e r s la g te m p e ra tu re s compensate f o r
th e decreased a i r mass flo w r a te and th e mean d r o p le t d ia m e te r and
th e d is tu rb a n c e fre q u e n cy a re n e a r ly th e same as in th e f u l l
case.
lo a d
In th e upper chamber th e mean d r o p le t d ia m e te r is s m a lle r and
th e d is tu rb a n c e fre q u e n cy is
la r g e r than th e f u l l
lo a d s it u a t io n .
T h is is due m a in ly to th e decreased flo w r a te o f th e gas.
O th e r o p e ra tin g lo ads a re a chieved by fre q u e n c y v a r ia t io n
in
th e same manner as above o r by rem oving one o r two sets., o f th e p re h e a te r
systems fro m o n - lin e .
For in s ta n c e , h a l f lo a d is o b ta in e d by o p e ra tin g
two s e ts o f th e h e a t exchanger systems a t th r e e - q u a r te r lo a d .
The
o p e ra tin g c h a r a c t e r is t ic s w ould be th e same as in T a b le ,4 .3 e xce p t th e re
would be o n ly s ix upper chambers and two lo w e r chambers in o p e r a tio n .
- 49 -
TABLE 4 .3
OPERATING SPECIFICATIONS FOR 3000 MWt MHD
PREHEATER AT 3 /4 LOAD
Upper Chamber
dumber o f Chambers
Lower Chamber
9
3
Gas I n l e t Tem perature
2230K
1200K
Gas O u tle t Tem perature
1850K
1800K
Slag I n l e t Tem perature
1734K
1935K
Slag O u tle t Tem perature
1935K
1734K
Gas Mass Flow Rate
113 kg /se c
281 kg /se c
Slag Mass Flow Rate
288 k g /se c
864 k g /s e c
Chamber P ressure
O p e ra tin g Frequency
Mean D ro p le t D iam eter
C a p illa r y P ressure Drop
.110 MPas
433 H e rtz
2 .5 0 mm
.010 MPas/cm
1.16 MPas
394 H e rtz
2 .7 4 mm
.002 MPas/cm
CHAPTER.V
SUMMARY
The f a l l i n g
bed h e a t exchanger has many advantages o v e r th e
cored b r ic k h e a t exchanger f o r h ig h te m p e ra tu re d i r e c t f i r e d
a p p lic a t io n s .
MHD
These in c lu d e th e compact s iz e , th e e lim in a t io n o f
m assive h ig h te m p e ra tu re v a lv in g , th e u n in te r r u p te d flo w o f th e e xh a u st
gas and p re h e a te d a i r , and th e a b i l i t y
o p e r a tio n .
U t iliz a t io n o f t h is
to a d ju s t e a s ily to p a r t ia l lo a d
ty p e o f p re h e a te r in a c o r r o s iv e
en viro n m e n t such as coal s la g has th e added advantage o f r e q u ir in g
p e r io d ic re p la ce m e n t o f o n ly th e d i s t r i b u t o r p la te r a th e r th a n
re p la c in g th e e n t ir e bed as w ould be nece ssary w ith th e cored b r ic k
exchanger.
P r e v io u s ly , the f a l l i n g bed p re h e a te r u s in g l i q u i d s la g as th e
h e a t t r a n s f e r media had n o t been c o n s id e re d a v ia b le a lt e r n a t iv e to
th e cored b r ic k h e a t exchanger because o f th e la rg e chamber dim ensions
t h a t w ould be r e q u ire d .
These la r g e chamber s iz e s were due to th e la c k
o f c o n tr o l o f th e drop s iz e s and drop s iz e d i s t r i b u t i o n .
has shown, a t le a s t c o n c e p tu a lI y , t h a t t h i s
problem can be s o lv e d by
em ploying v ib r a t io n a to m iz a tio n o f th e l i q u i d
s iz e d d r o p le t s .
T h is s tu d y
to produce u n ifo r m ly
The r e s u lt in g h e a t exchangers a re e f f i c i e n t and com pact.
The m a jo r problem in h e r e n t w ith t h i s
d i s t r i b u t o r p la t e .
co nce pt is th e d e sig n o f th e
The c re e p and therm al s tre s s a s s o c ia te d w ith a
loaded p la te a t e le v a te d te m p e ra tu re s a re m a jo r c o m p lic a tio n s .
it
W h ile
is p ro b a b le t h a t th e f i r s t g e n e ra tio n o f d i r e c t - f i red p re h e a te rs f o r
- 51 MHD a p p lic a t io n w i l l b e .o f th e cored b r ic k d e s ig n , w ith adva ncin g h ig h
te m p e ra tu re m a te r ia ls te c h n o lo g y th e f a l l i n g bed p re h e a te r w i l l
p ro b a b ly become a v ia b le a lt e r n a t i v e .
B e fo re f u r t h e r work can be done
on th e d e sig n o f a l i q u i d s la g p re h e a te r system , e x p e rim e n ta l s tu d ie s
on th e v ib r a t io n a to m iz a tio n o f l i q u i d s la g a re n e ce ssary to e it h e r
r e in f o r c e o r a l t e r th e assum ptions used in t h i s s tu d y .
,
'
There a re many a d d itio n a l a p p lic a tio n s f o r th e l i q u i d
hea t exchanger w hich sh o u ld be pursued.
d r o p le t
By add in g th e e q u a tio n s f o r
mass t r a n s f e r , compact c o o lin g tow ers c o u ld be designed u s in g a
w a te r to a i r system .
O th e r a p p lic a tio n s can be found in coal
g a s if ic a t io n o r in any area in v o lv in g c o r r o s iv e li q u i d s o r gases.
APPENDIX
- 53 APPENDIX I
MATERIAL PROPERTIES
F o llo w in g are th e p r o p e r t ie s as f u n c t io n s o f te m p e ra tu re f o r a i r ,
exhaust gas, and coal s la g as used in the design o f th e heat exchanger
system.
A ll
tem p e ra tu re s are in K e l v i n s .
A ir
ca = 9 67 .+ 9.60 x IO- 2 T +1.29 x IO- 4 T 2- 4 . 37 x IO- 8 T 3 ( j o u l e s / k g - k ) (26)
a
d
P 3 = 1.62 x ! C f 6! - 513
a
a
( p a s c a l- s e c )
(26)
2.65 x IO3T3^
( jo u le s / m - s e c - K )
(I + - P -
(27)
IO- 1 2 ^ a )
Exhaust Gas
Cg =
917.+.031Tg
(jo u le s /k g -K )
Pg = 7.46 x IO- 7 Tg - 582
k
9
= .029+2.9 x IO- 4 T
g
(28)
( p a s c a l- s e c )
(28)
+ .80 x IO- 8 T 2 ( jo u le s / m - s e c - K )
g
Coal Slag
Cg = 8 7 1 .+ .180Tg
P
(jo u le s /k g -K )
= 1.49(10( 1 -47x 1()4/(1-8Ts - 4 6 0 ) - 6 - 5))
(29)
(30)
(28)
/
.
■
- 54 The v i s c o s i t y o f th e s l a g . i s f o r c o a ls w i t h a h ig h c a lc iu m c o n te n t
and a low s i l i c a
c o a l.
(a b o u t 35) s i m i l a r t o Montana s u b -b itu m in o u s
For b itu m in o u s coal as would b e .fo u n d i n th e e a s te r n U n ite d
S tates th e s i l i c a
by t e n f o l d .
it 's
ra tio
r a t i o i s around 55 and t h e ' v i s c o s i t y i s in c re a s e d
In o r d e r t o use t h i s
ty p e o f s la g i n a drop g e n e r a to r ,
v i s c o s i t y must be lo w ered by th e a d d i t i o n o f CaO.
APPENDIX I I
F o llo w in g i s an o u t l i n e o f th e computer program used in
s i z i n g th e h e a t exchanger chambers.
- 56 -
O utp ut
BIBLIOGRAPHY
- 58 BIBLIOGRAPHY
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G eneration and Use, Babcock and
MONTANA STATE UNIVERSITY LIBRARTFS
3 1762 100 5317 8
N378
P935
cop.2
DATE
Prill, Raymond L
Design of a high
temperature falling bed
air preheater for direct
coal-fired MHD power
generation ...
IS S U E D TO
/J3
X
/