Latent heat recovery from a counterflow direct contact falling droplet heat exchanger
by Stephen Edward Izbicki
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Mechanical Engineering
Montana State University
© Copyright by Stephen Edward Izbicki (1986)
Abstract:
Heat recovery in one configuration of a direct contact counterflow, falling droplet heat exchanger
(DCHX), from natural gas combustion products was evaluated in terms of sensible and latent
effectiveness. Effectiveness was found for uniform and nonuniform water droplet streams, and high
and low inlet gas humidity ratios over a range of droplet flow rates and inlet gas temperatures. A
droplet generator was built and tested to characterize droplet uniformity under various operating
conditions. Uniform droplets were produced by vibrating the droplet generator at a fixed frequency and
amplitude. Results agree well with those predicted by Rayleigh's theory on the instability of liquid jets.
A stream of nonuniform drops, having standard deviations two to four times higher than the uniform
stream, was produced when the generator was not vibrated. Preliminary heat exchange studies show
single phase energy and two phase mass balances within about 6 %, indicating reasonable accuracy of
temperature and flow measuring apparatus. DCHS effectiveness, defined in sensible heat recovery
terms, is. shown to be further from its thermodynamic limit than that of a standard (no direct contact)
counterflow heat exchanger in the same range of NTU values. A modified effectiveness is defined
which includes the latent heat availability of the inlet gas stream. Modified effectiveness values were
about 50% of their sensible counterparts indicating that latent heat recovery could be significantly
improved. L AT E NT HEAT RECOVERY FROM A COUNTERFLOW D I R E C T
CONTACT F A L L I N G
DR OP L E T HEAT EXCHANGER
by
Stepben
Edward
Izbicki
A th esis submitted in p a r tia l fu lfillm e n t
of t he r e q u i r e m e n t s f o r the d e g r e e
of
Master
of
Science
in
Mechanical
-
Engineering
MONTANA S TATE U N I V E R S I T Y
Bozeman, Montana
June
1986
MAIN LIB.
ii
J T i- I
AP P ROVAL
of
a
thesis
Stephen
submitted
Edward
by
Izbicki
T h i s t h e s i s h a s b e e n r e a d by e a c h m e m b e r of t h e t h e s i s
c o m m i t t e e a n d h a s b e e n f o u n d t o be s a t i s f a c t o r y r e g a r d i n g
content,
English usage,
format,
c ita tio n s,
b ib lio g rap h ic
s t y l e , and c o n s i s t e n c y , and is re a d y fo r s u b m i s s i o n to the
C o l l e g e of G r a d u a t e S t u d i e s .
Chairperson,
A p p r ov e d
for
the
Major
Graduate
Committee
Department
S~— 0 c
Date
Head,
Approved
Date
for
the
College
of
Major
department
Graduate
Graduate
Dean
Studies
iii
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copying
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it
Brief
source
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professor,
use
of
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not
be
allowed
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is
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made.
reproduction
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available
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quotation
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my
thesis
written
-
Date
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use
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ACKNOWLEDGEMENT
The
author
guidance
Dr .
as
also
a committee
This
State
to
Dr .
to. Dr.
Thomas
investigation.
for
his
William
Reihman
Special
suggestions
Martindale
and
for
for
thanks
his
to
encourage­
his
support
member.
study
Engineering
this
Demetriades
Thanks
Montana
indebted
throughout
A nthony
ment.
is
and
was
the
funded
by
the
Engineering
University.
Department
Experim ent
of
Mechanical
Station
of
I
V
TABLE
OF
CONTENTS
Page
LIST
OF T A B L E S ..................................................................................................
LIST
OF F I G U R E S
vi
...........................................................................' ......................................v i i
N O M E N C L A T U R E ......................... .......................................... ......
.
.
..................................... v i i i
A B S T R A C T .............................................................................................................................................. x i
1.
I NT R ODUC T I ON
.
I
2.
MONODI S P E R SE DR OP L E T S T U D Y . ..........................................................................
Background
. .
A p p a r a t u s . . ................................................................................................................
Experimental Procedure
................................................. . . . . .
R e s u l t s a n d D i s c u s s i o n ..........................................................................
.
U n i f o r m D r o p l e t s .............................................................
Nonuniform D ro p le ts
.............................................................. . . .
7
7
9
13
14
15
18
3.
DCHX S T U D I E S ............................................................................................................................23
Background
. ..................................... ...................................................................2 3
F l ow R a t e s ............................................................................................
23
Droplet C haracteristics
....................................................................
24
Effectiveness
...................................................................................................2 6
A p p a r a t u s .................................................................................................... . . . .
28
C o u n t e r f l o w H e a t E x c h a n g e r ..............................................................
28
G a s a n d F l u i d D e l i v e r y ................................................................................. 3 4
Experimental Procedure
................................................................................
36
R e s u l t s and D i s c u s s i o n
: ................................................................................. 3 8
E n e r g y a n d M a s s B a l a n c e s ........................................................................... 3 8
Primary Studies
.................................................................................................... 4 1
4 .
C O N C L U S I O N ...........................................................................................
RE F E RE NCE S
51
....................................................................................................................................... 5 4
A P P E N D I C E S ........................................................ .
APPENDI X A -
.
.
.
'
................................................ 57
DR O P L E T D A T A .................................................................................5 8
APPENDI X B - E F F E CT I VE NE S S
APPENDIX C -
.
D A T A ................................................................. 5 9
B A L A N C E DAT A R E D U C T I O N
C O D E ...........................
60
v i
LIST
OF T ABL E S
Table
1.
Page
Droplet Diameter Standard Deviation for Vibrating
a n d N o n V i b r a t i n g C a p i l l a r y J e t s ....................................
21
2.
S i n g l e Phase E n e r g y B a l a n c e of P r e d i c t e d v s .
M e a s u r e d DCHX H e a t L o s s ........................................................................................3 9
3.
Two P h a s e
DCHX M a s s
Balance
Data
.
.
.-
.
. .............................4 0
vii
LIST
OF F I G U R E S
Figure
Page
1.
Simplified
Sketch
of
2.
S c h e m a t i c of D r o p l e t G e n e r a t o r Power
D e liv e r y Subsystems and P h o to g rap h ic
Falling
Droplet
DCHX
. . . .
and L i q u i d
Diagnostics
.
10
Droplet
4.
Droplet Diameter vs. Je t V elocity (Magnification
R a t i o - 7 : I ) ...........................................................................................................................1 6
5.
T h e o r e t i c a l and E x p e r im e n ta l D r o p l e t Diam eter vs.
J e t V e l o c i t y .....................................................................................................................1 7
6.
T h e o r e t i c a l and E x p e r i m e n t a l D r o p l e t Diame te r vs.
V i b r a t i o n F r e q u e n c y ............................................................................................ 1 9
7.
Experimentally Determined Droplet Diameter vs.
I n p u t P o w e r ..................................... ' ...................................... .................................... 2 0
8.
D r o p l e t S i z e D i s p e r s i o n f o r V i b r a t i n g a n d No n
Vibrating Capillary
Jets(Magnification Ratip-S:!)
. Direct
C h a m b e r ...............................
.
5
3.
9.
Generating
a
Contact
Heat
and
Temperature
Facility
Thermocouple
.
.
.
.
.
.
.
.
12
.
. I.
.
.
Probes
.
.
.
10.
Liquid
11.
DCHX S e n s i b l e E f f e c t i v e n e s s v s . N u m b e r o f T r a n s f e r
U n i t s ................................................................................................................................... 4 2
12.
DCHX L a t e n t E f f e c t i v e n e s s v s . N u m b e r o f T r a n s f e r
U n i t s ................................................................................................................I .
.
.13.
Gas
Exchange
.
T h e o r e t i c a l and E x p e r i m e n t a l S e n s i b l e
E f f e c t i v e n e s s for a Counterflow HeatExchange r
.
29
33
.
. . .
43
46
14.
DCHX S e n s i b l e E f f e c t i v e n e s s v s .
I n l e t L i q u i d Flow
Rate . . .
.............................................................. ...... . .
........................ 4 8
15.
DCHX S e n s i b l e E f f e c t i v e n e s s v s .
I n l e t Ga s
Temperature
. ■ ....................................................................................................
.
21
.
49
Viii
NOMENCLATURE
Symbol
Description
CD
drag, c o e f f i c i e n t
Cp
specific
CR
thermal
Cco
jet,
F
vibration
g
gravitational
^1 C
tube
latent
thermal,
>
L
c o l urn n
length,
NTU
number
of
ML / M d g
liquid,
O O
BI > BI
wet,
dry
Pv
vapor
q
heat
R
thermal
T
temperature,
V
tR
gas
transfer
units
flow
weight,
rate,
kg/kg-mole
kg/s
kPa
rate,
resistance,
W
° K/ W
0K
contact,
veloc ity ,
WZm2 - 0 K
WZ m - 0 K
molecular
mass
pressure,
droplet
coefficient,
m
transfer
gas
kJ/kg
convective
conductivity,
dry
m/s2
vaporization,
diffusion
thermal
t O
Hz
acceleration,
k
g
mm
frequency,
of
kg/m3
mm
diameter,
heat
concentration,
m2 / s
diameter,
dJ ' dt
hf g
ratio
f r e e s t r ear n m a s s
diffusivity,
droplet
D d
k J Z k g - 0K
capacitance
droplet,
mass
d AB
heat,
cm/s
residence
time,
s
i x
NOMENCLATURE— c o n t i n u e d
SvmboI
Letters
surface
tension,
sensible,
X
wavelength,
H
dynamic
V
kinematic
p
mass
r
to
CO
to
Greek
8
Description
standard
(I)
gas
Non
Bi
latent
effectiveness
mm
viscosity,
k g / m —s
viscosity,
density,
C
N/ m
m2/ s
kg/m3
deviation
humidity
ratio,
kgL/kgdg
Dimensional Parameters
B i o t n u m b e r , h. CL
Le
Lewis
Nu
Nusselt
number,
h cL c / k g
Pr
Prandtl
number,
C^^/kg
Re
Reynolds
Sc
Schmidt
Sh
Sherwood
number,
k g / ( p C p ) g DAB
number,
number,
number,
VLc / v
p/pD^g
h ^ L c / DAg
Subscript s
I
DCHX i n l e t
2
DCHX o u t l e t
d
dr ople t
dg
dry
g
gas
i n
test
gas
section
inlet
X
NOMENCLATURE— C o n t i n u e d
Symbol
Descrintion
j
jet
L
liquid
Im
log
m
mea s u r e d
min
minimum
nc
natural
opt
o p t i mu m
out
test
P
pr ed ie te d
r
radiative
S
inne r
T
t erminal
tot
total
mean
convection
section
exit
s u r f ace
f r e e s t r e am
conditions
xi
AB S T RACT
Heat recovery
i n one c o n f i g u r a t i o n of a d i r e c t c o n t a c t
counterflow ,
f a llin g
d r o p l e t h e a t e x c h a n g e r ( D CHX), f r o m
n a t u r a l gas c o m b u s t i o n p r o d u c t s was e v a l u a t e d in t e r m s of
s e n s i b l e and l a t e n t
effectiveness.
E f f e c t i v e n e s s was f o u n d
f o r u n i f o r m and n o n u n i f o r m w a t e r d r o p l e t
streams,
and h i g h
and low i n l e t gas h u m i d i t y r a t i o s over a r a n g e of d r o p l e t
flo w r a t e s and i n l e t gas t e m p e r a t u r e s .
A droplet generator
was b u i l t
and t e s t e d to c h a r a c t e r i z e
droplet
uniform ity
under various
operating
conditions.
Uniform d ro p le ts were
produced
by v i b r a t i n g
the
droplet
generator
at
a fixed
frequency
and a m p l i t u d e .
R esults
agree well
with those
p r e d i c t e d by R a y l e i g h ' s t h e o r y on t h e i n s t a b i l i t y
of l i q u i d
jets.
A s t r e a m of n o n u n i f o r m d r o p s ,
having standard devia­
t i o n s two to f o u r t i m e s h i g h e r t h a n the u n i f o r m s t r e a m ,
was
produced when the
g e n e r a t o r was n o t v i b r a t e d .
Preliminary
h e a t e x c h a n g e s t u d i e s show s i n g l e p h a s e e n e r g y and two p h a s e
m a s s b a l a n c e s w i t h i n a b o u t 6 %, i n d i c a t i n g r e a s o n a b l e a c ­
cu ra c y of t e m p e r a t u r e and flow m e a s u r in g a p p a r a t u s .
DC HS
effectiveness,
defined in sensible heat
recovery
terms,
is.
shown t o be f u r t h e r f r o m i t s
thermodynamic l i m i t
than that
of a s t a n d a r d (no d i r e c t c o n t a c t ) c o u n t e r f l o w h e a t e x c h a n g e r
i n t h e s a m e r a n g e o f NTU v a l u e s . A m o d i f i e d e f f e c t i v e n e s s i s
defined which includes
the
latent
heat a v a ila b ility
of t h e
inlet
gas st re a m .
Modified e f f e c t i v e n e s s v a lu e s were about
50% o f t h e i r s e n s i b l e c o u n t e r p a r t s i n d i c a t i n g t h a t l a t e n t
h e a t r e c o v e r y c o u l d be s i g n i f i c a n t l y i m p r o v e d .
I
CHAP TER
I
I NT R OD UC T I ON
Substantial
potential
to
combustion
are
its
gas
and
exit
usually
sate
in
the
over
exchangers,
the
which
problems
do
c o e ffic ie n ts
favor
of
This
to
avoid
through
domestic
hot
escalate
and
technology
consider
This
forming
the
situations
increasingly
4 0 0 - 4 2 O0 K.
need
heat
exchangers
intermediate
thereby
surfaces
Since
not
ten
conventional
geometry
is
For
to
re ­
more
im­
minimum
flue
temperature
is
acidic
conden­
affo rd
several
prone
DCHX
is
higher
conventional
exchange
therm al
It
times
types.
heat
are
the
exist.
( DC HX)
decreasing
in creases
maintenance.
for
become
conventional
these
fu rth e r
need
lost
such
costs
with
exchanger. [1,2]
resistance
addition,
the
being
of
fuel
methods
be
energy,
exhausts,
As
the
recovery
contact
advantages
thermal
by
heat
D irect
turbine
will
to
are
Examples
stoves.
energy
temperatures
limited
gas
decreases,
E xisting
temperature
streams.
wood
wasted
portant.
low
consumption,
boilers,
a v a il a b il i t y
this
of
fuel
exhaust
h eaters
cover
gas
reduce
industrial
water
amounts
surfaces
system
to
has
no
such
estim ated
are
that
possible
increase
efficiency.
corrosion
re sista n c e
heat
and
and
In
scaling
requires
surface
these
heat
tra n sfe r
using
a DCHX i n
t y p e s . [3]
also
known
to
be
effective
in
removing
2
particulate
product
is
be
as
S C>2 ,
driving
the
force
p a r tia l
gas
pressure
(pollutant)
for
It
S O2
is
and
in
w ill
be
This
tion
a
closed
(p ollutant)
p r e s s u r e
This
a
device
DCHX
loop
remove
the
in
Fair
spray
[6]
column
vary
heat
Drop
from
Of
seven
the
a
1922
[7]
to
heat
data
the
gas
and
the
H 2 S.
DCHX
exchanger.
other
and
presents
exchangers
sizes
wide
p u b licatio n s
on
purifica­
particulate
range
on
to
transfer
using
hollow
uniform
over
one
for
been
design
are
solid
of
heat
cone
nozzles
designed
size.
hundred
dealing
is
correlations
these
drop
condensation
c ite d
and
and
from
they
long
performance
heat
since
not
has
analysis
d eliv ered
examined
1979
exchange
pertaining
works
application,
M o a l e m —M a r o n
lish ed
He
over
uniform
contact
review s
DC HX' s .
in
favorable
NC>2
heat
acid
between
is
unit,
or
The
fluid.
specific
nozzles.
typically
provide
d ire c t
industry,
industrial
spray
working
secondary
filte r
gases
s o lu te
for
useable
require
from
the
favorable
a
to
of
difference
commercially
at
absorption.
gas
will
the
pollutant
soluble
configuration
in
by
fa llin g
difference
moderately
a
. 5mm
e f f i ­
number,
the
with
lim ited .
and
in
whose
Reynolds
to
removed
combustion
is
vapor
and
that
Although
for
the
from
soluble
system
buildup
used
be
l i q u i d . [5]
absorbtion
assumed
of
up
Water
mechanism
the
the
droplet
diam eters
S can
this
gases
co llec tio n ,
by
[4].
and
for
m ix tu re
p a r tic le
drop
velocity
N C> 2
soluble
influenced
with
terminal
water
Fine
strongly
achieved
their
such
certain
em issions.
ciency
can
and
to
Sideman
works
pub­
exchangers.
w ith
droplet
3
formity.
drops
Goren
on
which
Thayer
[9]
4 8% f o r
I mm
comment
sults
of
in
from
silicon
of
5%
that
increased
recently
drops
and
,
how
Sekins
of
and
around
airflow.
drops
drop
Mussulman
which
reducing
Aroclor
They
i.
o s c illa tio n s )
large
model
the
in
imposed
show
computer
sized
effec tiv en e ss
oil
small
however,
a
Mor e
exchanger
of 2.1mm,
of
the
changes
fectiveness
proposed
that
transfer
for
large
surface
column
range
written
aim
fluence
the
steam.
uniform ly
[10].
size
and
size
effectiveness
of
None
variation
W arrington
shows,
the
re ­
for
a
mean
d is tr ib u tio n
an
air
cooling
1 0 0%.
The
by
used
D CH X e f f e c t i v e n e s s .
to
by
[8]
b r e a k u p (no
studies
size
50%
tower
natural
above
droplet
heat
mono d i s p e r s e
a wide
have
Wilke
condense
report
influences
[11]
to
that
the
and
area
in
over
a
present
droplet
a
range
study
of
for
diameter,
a
of
small
given
the
determine
operating
droplet
configuration.
number
to
monodispersity
mo no d i s p e r s e
this
is
water
optimum
gas
exchange
rate.
flow
DCHX
ef­
is
is
heat
is
enhanced
heat
transfer
F or
rate
It
maximizes
increasing
flow
on
in­
conditions.
stream
Heat
drops,
have
the
a
fixed
DCHX
determined
by
.
the
term inal
v elo city
not
the
the
DCHX
case,
column
by
sm allest
the
gas
requirements.
Mi ni mum
let
time.
residence
surface
term inal
area
to
of
volume
v e lo c itie s.
the
sm allest
drops
w o u l d be
stream,
column
Large
drops
As
a
have
high
a re s u lt,
is
Biot
large
If
carried
leading
length
ra tio s ,
drop.
to
this
out
were
of
makeup
function
water
of
drop­
com paratively
numbers
drops
and
have
the
low
high
higher
4
term inal
v e lo c itie s .
As
residence
times,
contact
transfer
rates
the
size
drop
The
a
than
present
size
ating
study
dispersion
exchanger,
uated.
In
•falling
Next
utilizing
this
droplets
gas
combustion
tioned
previously,
lik e ly
be
the
a closed
present
nearly
which
cing
let
a
jets,
removed.
group
and
nonuniform
an
droplet
equally
a range
open
of
from
for
operating
I).
unit
can
is
be
this
was
w ill
most
sake,
that
a
tubes,
drop­
determined
gas
by
produ­
disturbance
for
a
plate
sized
natural
of
men­
produced
randomly
and
of
As
shown
conditions,
air
eval­
stream
frequency,
effec tiv en e ss
for
was
tube
a c o u n t e r f I ow
c a p illa ry
if
oper­
a vertical
It
specified
re s u lt
and
various
sim p lic ity 's
( 0 =5 %)
a
First
characterize
figure
one.
spaced
w ill
droplets,
a
pf
useable
Conversely,
exchange r
under
(see
stream
at -
to
generator,
energy
heat
narrowing
parts.
m o no d i s p e r s e
However
is
attached.
Heat
DCHX . o v e r
tion
of
a
com m ercially
( o = 1 0- 20- %)
the
droplet
products
disturbing,
are
stream
the
overall
two
tested
effectiveness
system.
mo no d i s p e r s e
in
produced
extracts
DCHX s y s t e m
mechanically
to
a
lower
higher
effectiveness.
out
was
configuration,
water
natural-
carried
the
have
Consequently
improve
droplets
drops
and
drops.
generator
of
large
times
should
was
droplet
conditions.
heat
smaller
dispersion
monodis.perse
the
lower
a re su lt,
is
for
uniform
combus­
pro duet s .
In
light
organize
remaining
this
of
the
above
discussion,
paper
in
a
s im ila r
discussion
is
comprised
it
seemed
manner.
of
three
logical
Therefore
parts.
to
the
Chapter
5
combustion
product —
outlet oort
monodisparse
droplet
generator
I iquid
inlet'
droplet
i njectors
f a llin g .
droplets
counter flowing
heat transfer
chamber
gas
stream!ines
gas in le t/
— liquid outlet
manifold
combustion
product---inlet port
_1 iquid
outlet
Figure
I:
Simplified
Sketch
of
a
Falling
Droplet
DCHX
6
II
describes
techniques
monodisperse
droplet
uniform
droplet
characterization
the
f i r s t
drop
size
droplet
study
d isp ersio n
DCHX e x p e r i m e n t a l
Chapter
III,
ground
sions
both
and
along
the
are
in
with
Chapter
monodisperse
producing
This
production
used
the
as
In
the
I V,
and
the
Chapter
basis
for
and
procedure
of
p e rtin e n t
is
droplet
the
and
of
results
of
results
v a ria tio n s
in
experiments.
reviewed
theoretical
with
a
report
III,
are
re su lts.
concerned
measuring
a
DCHX p e r f o r m a n c e
development
of
and
includes
theory
studies.
apparatus
a d iscu ssio n
section.
in
stream.
current
from
used
The
back­
conclu­
re s u lts
DCHX p e r f o r m a n c e
in
from
studies.
7
CHAP TER
MONODI S P E R S E
II
D R OP L E T STUDY
Ba ^ k _ g r _ p u i i d
It
is
tion
to
show
size
and
spacing
lary
jet.
This
ture.
are
critical
that
based
that
the
a
is
water
to
jets
[12]
hy
is
for
the
a x ia lly
such
a
of
vibration
disintegration
of
a
liquid
the
in
is
a
c a p il­
the
in
lite ra ­
this
manner
i n s t a b i l i t y
Rayleigh
leads
column
uniform
v ib ra tin g
liquid.
which
investiga­
nearly
stream
on
inviscid
frequency
of
documented
a n a ly sis
an
current
stream
well
produce
R ayleigh's
in
droplet
produced
used
on
importance
phenomenon
Devices
capillary
the
of
most
given
showed
rapidly
sized
drops
column
are
X,
correspond
( 3 . 5 d j <X<7dj ) by
lin e a riz e d
Linblad
overcome
v e lo c ity
have
over
varies
closely
a
and
shown
BtSdj
those
th at
Schneider
[15]
the
uniform ly
range
and
found
Hendricks
p re d ic ts
that
frequency
between
to
(2.01)
in
6.Sdj .
which
These
exp erim en tally
[14].
lower
Rayleigh's
l i m i t
should
be
order
to
[9] *
and
viscous
to
[13]
Schneider
theory
Xm i n = ( n ) d j
Tien
produced
wavelength
lim its
liq u id
and
to
by:
F o p t = Vj / 4 . 5 OSdj
Rajagopalon
of
be
density,
forces,
capillary
estab lish ed .
surface
This
tension,
report
jets
that,
must
minimum
and
je t
in
have
is
a
minimum
a function
diam eter.
It
of
is
8
given
by:
(Vj , m i n > 2 = 8 8 / P d d j
However
to
Dabora
35%
lower
By
[16]
than
has
equation
conservation
the
volume
the
ratio
of
of
found
of
a water
drop
(2.02)
mass,
jet
minimum
velocities
one
volume
of
wavelength
diameter
is
found
one
drop
long,
within
ity
by
Rajagopalon
3% o f
with
l i t t l e
Several
the
tube
tube
equation
cause
due
je t
velocity
distribution,
termines
that
in d ic a te s
meter
At
actually
higher
creases
which
as:
at
cause
a
A
a
unity.
Schneider
assumed
this
ratio
and
to
j e t
and
Reynolds
Their
unity
formulations
in
[14]
of
momentum
de­
and
Wronski
their
je t
[19]
d ia­
(Rej<17).
numbers.
diam eter
higher
than
analysis
They
d j / d t
Dabora
de­
that
does
viscous
ra tio
and
than
jet
effects.
the
a
less
at
laminar
this
slightly
drive
uniform­
p ro file ,
v e lo c itie s ,
Hendricks
be
Goren
dissipation
high
p ro file ,
assumes
( 1 7 (Re j <100)
value
to
effects
somewhat
v e lo c ity
low
drop
contracta
be
by
( dj / d t = .885).
viscous
s u f f i c ie n t ly
Mathematical
to
to
agreement
formation.
conservation
study
at
numbers
predicts
f l a t t e r
by
good
vena
[18]
Harmon
increases
include
that
diam eters
and
showed
satellite
a p arab o lic
m o n o to n ical Iy
however,
that
for
Reynolds
Harmon
to
dj = . 8 6 6 d ^ .
that,
[13]
which
(2.03)
indicating
indicate
[15,17].
diameters
Tien
(2.03),
waste
authors
exit
and
equals
from
Dd / d j = l . 1 4 5 ( V j / F d j ) 1 / 3
R esults
up
predicts.
the
column
to
actual
(2.02)
not
suggest
effec ts
toward
[16]
have
investigations.
describing
the
production
of
9
no m i n i f o r m I y
expression
to
be
the
produced
at
the
previously
ever,
are
drop
size,
order
vibration
cited
in
attempt
in
to
of
for
the
to
maximum
analysis.
that
jet
insta­
of
the
droplets
They
of
an
droplets
Most
nonuniform
degree
derives
oscillations,
re fe rs
o s c illa tio n s .
characterize
[20]
imposed
Dd j 0 p t
frequency
confirm
absence
Levich
without
R ayleigh's
works
the
sparse.
Dd ~ D d > o p t .
p red icted
produced
drops
showing
of
b i l i t y
sized
do
not
are
how­
nonuniformity.
Ajijd ar.a_tu._s
The
develop
first
a
droplet
characterize
Liquid
at
head
from
that
water
is
source
and
to
an
of
the
proper
the
f i l t e r e d
and
monitored
ber.
MB
isothermal
water
An
set
through
through
the
flow
the
Jet
to
am plitude
P M5 0 0
in stru m e n ta tio n
to
2
the
for
and
rate
the
is
manner.
constant
rate
s lig h tly
higher
generator
chamber.
Excess
outlet,
having
The
flow
a
rate
the
combination
the
constant
and
is
supplies
a
by m ean s
by
then
pressure
generator
a
head
varied
source
chamber
Exci tor.
providing
were
water
entering
Vibramate
flow
to
v e lo c itie s
to
schematic).
following
supplied
jets
tem perature,
and
in
flow
elevation.
prior
to
Figure
overflow
o s c i l l a t o r —a m p l i f i e r
E lectro n ics
a
the
rate.
immediately
frequency
is
capillary
reservoir
its
at
was
pressure
chamber
2)
investigation
with
(see
source
(Figure
to
along
formation
generator
drained
this
tem perature,
passing
adjusting
of
the
conducting
generator
droplet
re s e rv o ir
x than
in
constant
delivered
Water
step
are
cham­
signal
of
D iagnostics
an
to
frequency
counter
osci11oscope
voltmeter
x
water supply
y
-e
overflow
outlet
-WW-
constant head
reservoir
P
I ohm
resistor
power
supply
signal
generator
amplifier
manometer
vibrator
ammeter
generator
chamber
d if fuser
screen
2:
thermocouple
flow meter
camera
strobo Iume
Figure
fiI ter
S c h e m a t i c of D r o p l e t G e n e r a t o r Power
D e l i v e r y S ub s ys te ms and P h o t o g r a p h i c
movable
stroboscope
and L i q u i d
Diagnostics
11
monitor
signal
The
generator
num
chamber
with
an
set
equally
tubes
were
burrs
or
Each
tube
carefully
were
sized
i . d. x . 4 7 mm
was
These
Nineteen
jets
were
Droplet
with
a
size
camera
9 Omm
turn
used
in
body
and
bellows.
camera
1 532 A S tro b o lu m e
which
of
the
the
'stop'
to
were
that
a
6. 4mm
flash
stream
the
of
s ta in le s s
reference,
the
steel
1 3 mm
for
Radio
motion
by
e x c ita tio n
coplanar
of
with
the
the
ends.
that
of
was
i.d.
plate.
lens
w ith
fitted
a General
flash
film
f e ll
( AS A 1 2 5 )
sheet
1 5 3 1 AB S t r o b o t a c
each
the
through
observation
was
Strobotac
used
to
frequency
negative
appeared
stream.
source.
between
visual
In
L i e t z—
approximately
acrylic
diam eter
ori­
. 47mm
a 35mm
f/2.0
stream
the
all
( 2 8mm
bottom
duration)
For
no
studies.
5 Omm
droplet
the
of
a
AlI
that
jets
frequency.
known
at
show
P lus-X-Pan
setting
tubes.
capillary
into
diffused.
bottom
ensure
lengths
translucent
was
the
inside
synchronized
Kodak
alumi­
accommodate
to
consisted
flash
included.
required
these
droplet
thick
tube
ps
with
a General
droplet
was
The
source
to
magnification
(15
taken
The
Summicron
sh u tter
b acklighting.
and
a
Image
Radio
camera
all
to
present
epoxying
instrumentation
The
using
were
epoxied
on
capillary
polished
inside
in
2:1.
Photographs
by
long)
were
drilled
uniformly.
are
cylindrical
f i t t e d
steel
and
a
m icro sco p ic ally
achieved
o. d. x 2 3 mm
tubing.
Wetzlar
machined
finished
diameter
is
thick)
stainless
inspected
3)
long)
i r r e g u l a r i t i e s
and
consumption
(Figure
(.3cm
spaced
was
power
i . d . x 2.2 c m
plate
other
and
its e lf
(9.5cm
aluminum
of
fice
frequency
a
for
size
Drops
were
12
Figure
3:
Droplet
Generating
Chamber
13
measured
stereo
from
the
measuring
negatives
with
been
characterizing
f i r s t
droplet
data
to
(jet
v elo city ,
param eter
vibration
The
15
data
operating
frequency
For
were
Photographs
the
data
grid
all
the
several
droplet
the
absence
je ts
uniformity
above
cleaned,
sumption
a
at
the
constant
from
frequency
data
forced
range
of
the
data
was
mass
recorded,
holding
j e t
center
20%
at
the
was
v e lo c itie s .
In
the
DCHX
v elo city
20%
above
point
droplet
v ib ra tio n
and
to
each
on
to
a
conditions,
below
taken
center,
below
forma­
obtained
th is
the
on
for
manner,
influence
of
determined.
head
and
for
data
power)
and
predicted
a
the
the
input
above
Inform ation
p h o to g ra p h in g ,
determined
vibration
of
parameters
B efore
city
over
jets.
from
corresponds
data
from
center.
in
at
varied
data
tion
case
example,
constant
was
percent
center
its
for
40
conditions
III.
power
to
the
devise
away
and
case.
v ib ra tio n
v a ria tio n s
has
for
to
frequency
center
and
was
v ib ra tio n
data
Chapter
Next
defining
individually
in
conditions
parameters
varied
studies
( . 7 x - 3 x)
procedure
The
were
droplet
the
operating
DCHX t e s t s .
conditions.
optimum
Lomb
P r o c e dure
formation,
the
during
p re s c rib in g
DCHX o p e r a t i n g
grid
droplet
determ ine
generator
grid
and
microscope.
Experimental
In
a Bausch
tu b e s
reservoir
flow
Next
were
d ro p let
ul t r a s o n i c a l l y
adjusted
data.
amplitude
and
were
a
and
velo­
predetermined
imposed,
motion
jet
power
'stopped'
con­
using
14
the
Strobotac.
ted
to
Jet
insure
disintegration
the
droplet
depth
of
field.
taken
at
this
meter
was
varied
ment,
the
negatives
taken
at
each
sharpest
frame
A
and
of
Drop
w ith in
At
this
the
Of
measurements
were
three
only
those
of
three
ca me
then
one
After
the
a minimum
inspec­
camera's
point
repeated.
condition,
showing
v i s u a l Iy
photographs
inspected.
operating
used.
three
process
were
then
fe ll
condition.
the
boundaries,
were
stream
series
operating
was
para­
develop­
negatives
with
the
droplets
directly
from
per
these
negatives.
To
find
actual
m a g n ifica tio n
ratio
is
the
diam eter
tio n
is
The
(cr)
graph)
ra tio
ratio
had
of
s ta in le s s
diameter
sions.
drop
the
for
for
specified
steel
operating
be
known.
to
tube
of
the
size
d ro p lets
j e t s
developed
developed
drop
all
all
to
average
given
size,
the
major
measured
size
of
the
negative.
is
minor
the
(three
(maximum
of
and
m ag n ificatio n
size
and
variation
measured
The
actual
in
drop
known
Droplet
axes
dimen­
standard
devia­
drops
per
photo­
nineteen)
at
a
condition.
Rjj j>uJ^jtjs _and Dj._s_c u_s_s_i_pn
The
purpose
concerned
produced
showing
by
operating
and
also
of
power)
the
that
important
a
droplet
conditions
used
th is
in
to
nearly
generator
(jet
the
study
was
uniform
DCHX s t u d i e s
the
and
of
The
droplet
described
velocities
determine
twofold.
stream
earlier,
vibration
Chapter
sensitivity
of
f i r s t
at
was
the
frequency
III.
It
droplet
was
dia­
15
meter
to
son
of
are
made
change s
in
experimentally
to
Since
the
it
is
proposed
most
the
other
goal
of
the
degree
to
which
ing
from
percent
e f f ic ie n t
a
of
velocities
droplets
heat
in
the
Compari­
droplet
diameters
earlier.
droplet
e x tra c tio n
nonuniform
R esults
the
the
was
find
emanat­
presented
over
the
is
D C H X,
to
when
are
mean,
stream
for
investigation
become
from
power.
derived
a uniform
je t.
deviation
used
uniform
particular
nonvibrating
and
prediction
th at
method
this
standard
frequency
determined
theoretical
the
jet
vibration
range
as
of
DCHX s t u d i e s .
TJnj-JEorm Dr.ojgJL_ej:.s
The
dependence
v e lo c ity
is
shown
streams
pictured
a
vibration
fixed
and
spacing
agreement
drop
shown
in
that
6%
tal
This
one
p lo tte d
5.
It
is
to
the
lie
a
4
5.
(2.03)
a
and
and
of
the
knowing
the
tube's
error
four
je t
for
by
all
size,
deter­
is
figure,
lie
within
experimen­
counterparts.
u n ce rtain ty
droplet
m ag n ifica tio n
actual
this
values
causes
Good
v elo city ,
examining
at
diameter
v elo city .
th e o re tic a l
r a tio
how,
experimentally
of
je t
droplet
droplet
je t
introduced
m a g n ific a tio n
D eterm ination
in
on
qualitatively
experimental
th e ir
ments.
The
function
be
spacing
frequency,
apparent
may
and
increasin g
as
above
reference
and
indicate
systematic
erro r
size
and
with
theoretical
system atic
c a lc u la tin g
4
equation
another,
values
Figure
amplitude
size,
Figure
d ro p let
Figures
increase
although
of
in
in
between
mined
of
r a tio
the
in
measure­
req u ires
m icroscope's
16
V ; = 1 . 3 5 m/s
Figure
4:
V i=I.50m/s
V j= I.65m/s
V i b r a t i o n F r e q u e n c y = 850
In p u t Power = 1.5 W
Droplet Diameter
(Magnification
vs. Jet
Ratio -
Vj
Hz
l-SOm/s
Velocity
7:1)
17
Droplet
D i a m e ter
vs.
Jet V e l o c i t y
F r e q u e n c y = 850 Hz
Power =
I .5 LU
Diameter
.950
.350
Droplet
(mm)
Input
.650
Key
□
- Experimental
----
Equation
(2.03)
.750
□
□
.550
I .40
1.50
1.60
Jet V e l o c i t y
Figure
5:
1.70
I .30
(m/s)
T h e o r e t i c a l and E x p e r i m e n t a l
D roplet Diameter vs. J e t V elocity
18
magnification
ratio
and
ence
tube.
Actual
ratio
were
constant
about
2 %.
U ncertainty
size
was
around
tube
boundaries
t a i n t ie s
leads
exhibited
in
The
quency
ly
and
range
Figure
the
study
measuring
to
in
of
the
known
to
within
photographed
slig h t
'fu zzin ess'
Therefore
measuring
refer­
m ag n ificatio n
and
the
the
the
error
of
typical
above
of
tube
the
uncer­
q u a n titie s
the
magnitude
5.
of
in
to
droplet
Figure
the
to
cube
7 shows
is
of
to
as
As
of
is
frequency,
r e la tio n
power.
vibration
diameter
changes,
independent
this
Since
root
the
input
diameter
6.
frequency
v ib ra tio n
in
in
size
microscope
system atic
Figure
covered
and
negatives.
a
diameter
size
due
the
sensitive
figure.
droplet
on
indicated
slightly
meter
4 %,
sensitivity
is
photographed
throughout
to
p ro p o rtio n al
the
tube
encountered
re a d ily
the
is
inverse­
it
is
only
evidenced
between
might
power,
fre­
be
at
drop
in
dia­
expected,
least
for
the
study.
N_qnun_i_f_q_rm Dr_qp>_l.e_t_s
The
through
8.
nonuniform ity
a
Four
and
droplet
two
tie s
from
are
four
of
times
Also
capillary
streams,
two
nonvibrating
shown.
deviation
to
nonvibrating
ex h ib ited
drops
It
in
droplets
jet
is
emanating
jets,
seen
produced
higher
included
is
by
in
by
all
depicted
from
with
Table
I,
nonvibrating
than
those
under
the
table
is
the
when
that
jet
the
jets
sample
in
Figure
vibrating
equal
induced
forced
is
jets
veloci­
standard
from
two
vibration.
mean
or
aver—
19
Droplet
Vibration
D i a m e ter
Frequency
Jet V e l o c i t y =
Droplet
Diameter
(mm)
Input
Power =
1.5 m,
I .5 U
.30 0
.750
.700
O - Experimental
Equation
(2.03)
.650
.600
.550
1000
Imposed V i b r a t i o n
Figure
6:
F r equency
(Hz)
T h e o r e t i c a l and E x p e r i m e n t a l
Droplet Diameter vs. V ib ra tio n Frequency
20
Droplet
Diameter
(mm)
Droplet
Diameter
vs.
Input
Jet
.900
Powe r
V e lo c ity = 1.5 m/s
F r e q u e n c y = 8 5 0 Hz
.300
.700
□
□
O
O
0
.600
1.00
1.50
Vibration
Figure
7:
Input
2.00
Power
(W)
Experimentally Determined
Droplet Diameter vs.
I n p u t Power
21
I:
D roplet Size D is p e rsio n for V i b ra tin g
Non V i b r a t i n g C a p i l l a r y J e t s
(M a g n if ic a tio n Ratio - 8:1)
Droplet Diameter
V i b r a t i n g a n d Non
Standard Deviation for
Vibrating Capillary Jets
No n V i b r a t i n g
(Ifs)
I .77
1.63
I . 47
1.31
^mean
( mm)
^mode
( mm)
.49
.4 9
.53
.56
.47
.45
.45
.4 8
and
Vib r a t i n g
a
( %)
13
11
20
17
Dm e a n
( mm)
Dmo d e
( mm)
a
( %)
.65
.64
.62
.61
.65
.64
.62
.61
5 .5
5 .1
5 .5
00
Table
8:
4X
Figure
22
age
droplet
diameter
occurring
included
rather
uted
show
the
and
j e t s
larger
are
mode
or
sample
nonuniform
and
mode
are
This
standard
droplets
most
For
equal.
not
equal
are
important
to
a
said
shown
d istrib ­
by
to
it
the
other
are
skewed
Samples
since
something
These
normally
are
is
frequently-
exhibit
mode
deviations
a t t r i b u t a b l e
the
population.
distribution.
mean
distribution.
the
sampling
mean
each
size
the
sample
for
that
normal
samples,
skewed
ing
to
than
which
that
diam eter
and
for
have
a
indicates
nonvibrat­
than
random
error; '
Droplet
part
by
same
order
form
droplet
measurement
negative
as
the
accuracy,
determined
c la r ity ,
was
standard
d ev iatio n
stream.
around
5%.
for
This
ex h ib ited
the
is
by
of
the
most
the
uni­
23
CHAP TER
III
DCHX S T U D I E S
Background
Design
large
as
of
number
eith er
tional
a
of
operational
and
generally
lim ited
o u tlin es
heat
exchange
or
include
physical
tion
droplet
variables.
variables
atu res
falling
These
geom etric
flow
column
and
typically
particle
and
provides
a
b asis
for
for
Opera­
temper­
v a ria b le s
diameter.
equations
a
classified
sizes,
Geometric
length
optimizing
v a r i a b l e s [21].
rates,
governing
involves
are
p ro p e rtie s.
to
the
DCHX
This
d ire c t
are
sec­
contact
evaluating
DCHX
effectiveness.
F J1P w
R a j t _e_s
Combustion
composition,
addition,
products
excess
since
to
or
induced,
to
induce
The
product
must
a
DCHX
be
a
is
air
and
sufficient
present.
using
rate
configuration
upwards,
draft
thermal
combustion
the
flow
flow
In
low
capacitance
the
the
ra tio
liquid
and
of
mass
gas
flow
power
streams.
rate
This
by
size.
In
combustion
either
it
fuel
was
natural
necessary
fan.
C^ ,
defined
as:
g
times
is
requires
study
Cr = (m Cp ) L Z ( m C p )
is
combustor
draft,
this
ratio,
determ ined
an
(
the
sp e c ific
important
3 . 01)
heat
of
parameter
24
in
heat
exchanger
of
each
stream's
change.
Sekins
1.0
th eir
for
thermal
energy
and
Thermal
since
storage
[10]
experim ents
with
ratio
model
of
capacitance
of
air
it
rate
Thayer
capacitance
Mussulman's
sent
operation
unit
th is
silic o n
3.6
was
a r e la t iv e
per
keep
was
cooling
ratio
is
temperature
r a tio
oil
used
via
of
constant
drops
in
water
approximately
measure
in
at
air.
Warrington
dro p lets
2.0
in
A
and
[11].
the
pre­
study.
D_r.OpJLjijt ^ h a r j i j:_t_erj.j;Jb_ij:_s
DCHX
size
and
area,
e ffe c tiv e n e ss
physical
convective
resistance
city,
Vj,
and
is
drag
others
are
are
assumed
to
Terminal
internal
to
by
fu n ctio n
fa ll
at
by
at
droplet
v elo city ,
surface
and
these
th e ir
around
balancing
of
mixing
controlled
in je c tio n
determ ined
forces
complex
p ro p e rtie s.
a fte r
v e lo c ity
a
coefficient,
among
Droplets
is
conduction
variables.
term inal
V j = .7 5 V
droplet
Terminal
g ra v ita tio n a l
yield:
V T= [ 4 D d g ( p d - p g ) / 3 C Dp g ] 1 / 2
The
drag
numbers
c o e ffic ie n t,
( 2<Re ^ <5 00)
Cp,
v a rie s
approximately
for
(3.02)
moderate
Reynold's
as:
CD= 1 8 . 5 / R e d ‘ 6
The
stream
assumes
time
is
period
d ire c tly
uniform
contact
time,
velocity
and
gas
t
velo­
,
column
for
which
re la te d
flow
is
to
and
as:
droplets
to ta l
a
re la te d
length
(3.03)
heat
fixed
to
contact
the
tra n s fe r.
c o l u mn
term inal
If
diameter.
v eI d e i t y .
gas
one
then
gas
t c=L/ (Vx- V g )
Yao
[22]
d ro p let
mass
complexity
its
of
a
w rite s
exact
energy
tra n sp o rt
the
problem
however,
of
A dimensional
velocity,
temperature
of
form ulation
and
solution.
number
an
vapor
of
the
equation.
no
analysis
and
dimensionless
(3.04)
Due
attem pt
reveals
the
(defined
to
was
concentration
parameters
coupled
the
made
at
dependence
profiles
in
the
on
nomen­
clature):
Re,
From
these
The
of
fin a l
Lewis
the
to
An
tion,
and
It
thermal
Le,
and
is
mass
the
a measure
S h = S h ( R e ,Sc), the
transfer
ratio
of
concentration
energy
of
the
[23].
q r / q t o t ^^^
Permits
the
equation,
groups
thermal
to
r e la tiv e
boundary
is
d ro p lets
number
and
( B K . 04),
low
of
the
nonsteady
internal
For
omitting
for
this
the
a
mixing,
the
p re s e n t
the
radiation
droplet,
present
evidenced
conduction
approximation.
ders
in
layers.
the
equation
The
ra tio
of
transport
is
derived
equa­
by
s tu d y ,th e
term.
by
of
d ifficu lt
Ya o
r a t i o
This
leaves
as:
study,
high
resistance
Coupling
mass
th ick ­
d T d / d t = 6 / P d Cp D d [ h c ( T d - T 00) + h d h f g ( C s - C 00) ]
For
are
transfer.
model
complete
Schrock
and
and
^ f g ( C d - C ro) Z p d C p ( T d - T 00) ,
approximate
assuming
heat
provides
sensible
energy
I f g ( C d - C 09) Z p d Cp ( T d - T aj )
Nu=Nu(Re,Pr)
number,
param eter,
latent
Le,
convective
d iffu s iv ity .
ness
Sc,
param eters,
dimensionless
found.
Pr,
the
low
Reynold's
make
this
droplet
number
model
mass
and
energy
to
solve.
As
(3.05)
a
( Re d > 1 0 )
reasonable
transport
a
Biot
firs t
ren­
approxi—
26
mation
mass
one
transfer
which
ted
tend
that
spheres
of
is
stant
in
under
the
This
assumption
cancel
each
other.
surface
the
heat
from
addition.
reasonable
the
test
above
residence
hand
assume
section
[25].
to
repor­
lower
has
that
is
a
a
heat
r e la tiv e ly
large
evaporate.
drop
diam eter
the
solid
enhanced
to
Solving
the
errors
been
transfer
water
a
two
has
acts
energy
yields
exclnding
nonevaporating
dro p lets
assumptions
time
it
(h .£ g ~ 2 4 0 0 k J / k g ) ,
cause
to
of
Since
by
introduces
First,
those
other
to
t R,
evaporation
v a p o riz a tio n
required
th erefo re
time,
term.
On
la te n t
heat
input
residence
c o e ffic ie n ts
[24].
to
high
to
estimate
droplet
tra n s fe r
due
can
energy
theoretical
energy
It
is
is
con­
equation
or
expected
as:
t R = P d c P 1V
6 h Cl n K T d , ^
t - T ro) / ( T d j i n - T 03) ]
(3.06)
E_f_f_e_c_t j .yje n_e_s_s
The
e ffe c tiv e n e s s
defined
as
maximum
possible
er,
the
defined
this
r a tio
in
rate
terms
hypothetical
would
be
liquid.
cooled
Since
to
the
in
liz e s
droplet
'sensible'
of
this
a
heat
actual
achieved
of
infinite
importance
the
of
the
heat
in
sen sib le
area
same
exchanger
an
the
S g,
change
effectiveness
change
is
in
the
defined
area
the
as
ty p ic a lly
rate
recovery
tem perature
study,
effectiveness,
infinite
exchanger,
temperature
energy
tra n s fe r
heat
liquid
is
hot
the
is
to
the
exchang­
[26].
inlet
cool
of
gas
in le t
primary
definition
numerator.
In
u ti­
This
as:
= S - ( S cp ) L ( t L i 2 - T l 1I ) / ( S c p ) g ( i g i l - i L i l )
(3.07)
27
Since
the
la te n t
heat
define
a
case,
a
present
from
heat
hypothetical
th is
case,
presumed
The
to
outlet
^l ,!
and
and
products,
is
of
a v a il a b il i t y
of
the
r e la tiv e
humidity
e L = ( ™Cp ) L ( T L , Z -
again
tL
,
, I >1
to
recovering
necessary
in
the
that
energy
of
to
However
in
stream
is
gas
the
water
leave
the
vapor.
DCHX a t
e ffec tiv en e ss,
are
as:
defined
( 3 . 0 8)
U)T L , 1 =ML / M g [ P v , T L , I z <P » - P v , T L , 1 ) ]
transfer
size,
q u an tity
is
actual
behavior
and
in
NTH,
a
size.
is
plotted
or
which
approaches
of
of
larger.
values
can
formulated
fer
difference,
units
and
a
For
AT ^ m ,
log
its
two
heat
This
exchanger's
N TH e x h i b i t s
asym ptotic
low
NTH v a l u e s ,
of
for
small
heat
the
streams.
temperature
N™ - < a V L < T L . 2 - TL . i m
l
heat
units.
thermodynamic
terms
the
ATl » - l < T g , l - T L , 2 > - < T g , I - T
transfer
p a r tic u la r
is
(3 - 0 ^
nondimensional
counterflow
in
of
mean
a
a
heat
e s versus
asymptotically
become
ture
of
effectiveness
values
be
against
number
measure
A plot
e^ ,
I
[ ( m C p ) g ( T g> 1 - T L j 2 ) + m d g (ti)l - t i , T L , l ) l l f g, T L , I j
Effectiveness
from
Latent
^,
to
sensible
possible
size.
in le t
assumed
to^
was
the
hum idity.
ratio
with
As
infinite
la te n t
is
it
e^.
compared
exchanger
stream
100%
outlet
transfer
include
gas
concerned
effe c tiv e n e ss,
heat
the
was
combustion
'la te n t'
actual
study
are
log
lim it
as
NTH
exchanger,
NTH
mean
Number
defined
» V g ATl m
as
tempera­
of
trans­
follows:
( 3 ' 10)
. V J /
l n J t T g 1I - T L l 2 ) / ^ , , , Z - T l i i l H
(3.11)
28
Aj3j) J i r j i J t J i s
nent
Th e
apparatus
test
fa cility
at
The
apparatus
oratory.
tems,
they
The
entire
attached
sketch
test
are
combustion
the
gas
and
a
Cojunjt e r f l o w
The
Liquid
inflow/gas
in
center
greatest
gas
inside
the
is
plastic
8 p.F
droplet
4.5
duct
is
a perma­
Ryon
meters
subsys­
unit,
and
tall,
the
systems.
is
platform.
and
Lab —
major
delivery
A
rigidly
detailed
in stru m e n ta tio n
section
outflow
(36
capacitor
fan
comprises
input
duty
fan
duct
t h r ee
sub­
sections.
uppe r
section.
and
the
lower
section
i.d .
(125
x
an
the
to
operating
Housed
unit
induction,
in
assembly.
t e s t
at
long)
generating
draft
to
cm
section.
droplet
with
43
watts
upper
fixed
this
and
DCHX
th e
for
voltage
for
of
the
i n
cm
the
speed,
stand,
support
is
capabilities.
Fan
A heavy
the
place
I.
varying
b etw een
take
monodisperse
by
unit
con s i s t s
the
controlled
provides
It
duct
attached
part
made
three
exchange
exchange
test
in flo w /liq u id
in
platform,
heat
subsystems
heat
the
discussed
reg u lato r.
of
observation
outflow
lie s
Rotatron
conditions)
of
University's
consists
i n t e r e s t.
A cylindrical
a
p art
Eteajt E x c h a n g e r
of
which
is
9.
counterflow
provides
State
stands
platform ,
s y s tern
the
study
m ono d i s p e r s e
which
Figure
this
Montana
multilevel
showing
in
for
counter flow
system,
to
appears
used
line
is
voltage
observation
Connection
s e c ti o n
by
is
means
29
L... 2
rubber
skirt
variable
area
flowmeter
upper
transition
platform level II
low vel oci t y
flow column
di gi t al
thermometer
middle
t ransition
thermocouple
switches
platform level I
heating
element
high v el o c i t y
flow column
on" f i c e
meter
lower
t ransi tion
igas i n l e t /
liquid o u tl e t
manifold
heater
control
dual
manometers
outl e t
fluid
co l l ec ti o n
thermocouple
t ype s:
• - surface
• - liquid i n l e t / o u t l e t
A
Figure
9:
Direct
~
liquid instream
gas instream
Contact
Heat
Exchange
Facility
30
of
a
flexible
rubber
Tke
section
test
sectio n al
conical
area,
sheet
tra n sp a re n t
section
about
upon
to
metal
flow
is
bottom
top
from
40
cm/s
cm/s,
test
wetted.
To
a c celerated
and
column
serves
part
I,
velocity
th is
the
column
Average
long)
gas
was
increase
low
contact
a major
p ortion
sectio n
since
of
DCHX
to
This
falling
at
radially
sidewalls
e ffe c ts,
inside
w ater
in
the
by
total
the
18 0 c m /s
the
to ta l
its
two
the
flow
gas
in
the
(Dd = . 50
loss
lower
gas
was
by
mm)
transfer.
contact
adjacent
(7
It
time
is
transition
cm
to
The
long,
From
term inal
50
at
i.d.
in
cm/s
the
in
top.
x 71
cm
th is
column
instream
longer,
is
tran sfer
cm
a
below
'blowout'
droplets
96
region.
has
kept
v e lo c itie s
heat
by
entry
column
columns
in te ra c tio n s .
diameter
droplet
holding
heat
in
d ro p let-g as
velocity
High
8 0% o f
and
cm
Gas
time
increasing
of
droplet
cm/s.
column
region.
the
cm/s
are
velocity
deflected
entrance
20
gases
droplets,
causing
used
v e lo c ity
v e lo c ity
thereby
velocity
water
in su lated
Ga s
top
significantly
was
15
prevent
175
in
cross
uninsulated
the
cm/s
around
ac ry lic
cm/s.
to
two
10
minimize
sm allest
170
and
regions.
section,
measures
a
regions
prevent
from
e x te rn a lly
transition
o b serv atio n
as
of
to
varying
section.
Transparent
upper
three
of
Combustion
being
the
visual
of
column
columns.
two
to
from
transition
perm it
flow
necessary
become
vertical
transition
the
entering
a
co n sistin g
in
is
200
is
a c ry lic
decelerated
decreases
skirt.
expected
occurs
spent
in
regions.
that
in
th is
the
high
31
A sp e c ia lly
entrance
to,
section.
The
plate,
has
upper
through
m
the
a
mass
kg
upper
d ro p lets
and
temperature
test
rate.
A water
liquid
outlet.
Test
tored
run
to
trap
section
therm ocouple
in
each
them.
placement
fabrication
inconsistencies.
an
temperature
made
length
tions
such
bath.
that
of
as
Argon
a
of
20
wire
diameters)
the
bead
ju n ctio n .
region
adjacent
isotherm al
from
Al I
the
the
chamber.
by
in
lead
to
flow
were
in
exercised
all
type
and
T,
constant
cases,
wire
the
in
errors
were
a
the
moni­
re s is ta n c e
arrangement
ju n ctio n
for
through
m inim ize
checked
two
liquid
average
was
contact
This
through
co llec te d
its
to
exposed
te s t
outlet
thermocouples
was
the
lower
is
.021
wall
continuous
care
uninsulated
a
inner
into
escaping
placement,
enters
into
tem peratures
and
gas
chamber
determine
loss,
to
gas
flu id
assembly
environm ent
section
in
Great
Thermocouple
wall
that
run.
conduction
wall
way
gas
and
double
a
a
surface
test
of
manifold
accurately
and
steel
the
O utlet
with
in
upper
test
mm
at
such
asso c ia te d
welded
the
DCHX
6.4
chamber's
of
co lle c te d
prevents
gas
the
gas
from
outer
stream
bypass
measured
past
throughout
in
the
Combustion
insulated
are
immersed
allowed
entire
is
welded
chamber.
d is tr ib u te d
section,
the
lower
combustion
from,
co n sists
Perforations
its
is
and
chamber's
uniform ly
thermocouples
35
wall
Water
flow
of
perm its
ex it
manifold,
section.
Fluid
flu id
cylindrical
region.
inner
m anifold
working
single
annular
allow
and
a
and
designed
(minimum
same
condi­
provided
whose
was
an
purpose
32
was
to
eliminate
Al I
fold)
insulating
had
Steady
evaluated
from
information.
the
line.
Good
surements
face,
tion
by
and
ature
detector.
couple
probes
and
the
gas
mm
from
angle,
stream,
a
at
one
this
attempt
probe
the
such
axial
gas
gas
were
from
a
end.
sleeve
(7
that
a water
was
made
location
for
to
is
shown
in
ac ry lic
sur­
Bead j u n c ­
into
this
in
a
bead
of
lead
junctions
with
acrylic
of
the
was
Figure
were
10.
epoxied
steel
exposed
to
x 19
to
9.5
a right
mm l o n g )
formed.
column.
is
from
located
tube
droplet
which
thermo­
were
wire
of
temper­
s ta in le s s
mm o . d .
seal
series
ju n ctio n s
mm
x 4
groove.
resistance
3.2
determine
probes,
the
Thermocouples
tig h t
construction
mea­
m onitored
bending
center-
surface
were
i.d.
design,
stream
checked
of
occurred
for
in
epozied
bead
each
gas
was
resistan c e
directio n .
length
mm
surfaces
measurement
prevent
After
outer
type,
lengths
thermocouple
and
foil
10).
sufficient
inner
thermal
groove
was
to
mani­
achieved
then
platinum,
and
these
and
flow
accuracy
(Figure
tube's
teflo n
f i t t e d
An
of
allow
the
the
configured
in su la te d
To
small
tem peratures
droplets
and
surface
a
wire
single
stream
contacting
tube.
a
through
was
regions
th eir
temperature
outer
to
tem perature
using
loss
contact
lead
on
tem peratures
machining
bare
Gas
heat
and
thermal
(transition
lo cated
column
inner
tests
was
these
perpendicular
Surface
to
state
Flow
column
losses.
surfaces
therm ocouples
surfaces.
at
conduction
temperatures
A sketch
similar
The
to
droplet
of
that
probe
33
Figure
10:
Liquid
and
Gas
Temperature
Thermocouple
Probes
34
was
constructed
mm
tube,
is
turned
a
1.3
also
by
bent
upwards
mm
hole
through.
fittin g
to
to
a
plastic
angle.
In
droplets.
i t s
sleeve
small
fight
catch
along
The
a
side
to
re s e rv o ir
has
sleeve
this
The
a
a 2.5
the
probe
case
plastic
allow
over
sleeve
continuous
capacity
of
has
flow
around
40
dropl ets.
G_as
and
FiI u J . d DiBiI iJ y iBr y
A 4 0,000
p lie s
natural
section.
long,
gas
cases
test
it
section.
to
the
atmosphere,
to
be
drawn
by
the
necessary
to
Since
HWH
flange
shutting
level.
tap
orifice
pair
U -tube
of
the
from
and
thermocouple
had
no
these
mercury
bulb
and
water
flow meter
single
flow
rig h t
probes
cm
to
the
the
DCHX
probes.
angle
agree
thermometer.
the
DCHX
te s t
i.d.
by
Gas
DCHX i n l e t
or
6kW
w ith in
A radial
air
chamber
is
permitted
were
at
made
.5 5
gas
1 % ( 0 K)
probe
of
with
with
stream
a
with
probes
Readings
those
traverse
a
upstream
found
shields.
the
m^/min).
temperature
each
air
heater
at
measured
were
open
lim ited,
immersion
were
In
through
tem perature
other
bead
meters
DCHX m a n i f o l d .
cm -^O
pressure
Unlike
4.5
tem perature
in le t
( A P = 2 .5
bends
to
to
measurements
inlet
the
sup­
c o mb u s t or
A
manometers.
at
( HVH)
atmospheric
Chromalox
rate
heater
combustion
fan.
flowmeter
differential
these
suction
Gas
7.9
run
down
controlled,
Orifice
of
the
water
products
port
HWH e x i t , m a i n t a i n e d
desired
hot
pipe,
HWH e x i t
the
therm ostatically
at
steel
the
was
dom estic
combustion
In su lated
connects
some
the
B TU/ h r
with
a
revealed
35
only
a minimal
Fluid
in je c to r
is
temperature
delivery
housed
m onitored
F lo w m e t er
in
with
of
water
exchange
studies,
flow
to
dry
For
these
area
=1.8
the
the
the
te s ts
a
A
wet
fying
the
vapor
content.
a
Using
and
equation
pair
all
thermocouples
for
temperature
type
to
flow
meter.
rate
to
be
thermocouple
in le t.
to
rate
For
heat
provide
adequate
psychrometers
measured
of
DCHX
of
a
suction
on
balance
a Fluke
determination.
rod
were
(surface
to
the
rod,
located
in
DC
to
v o lt
pump
draws
gas
product
provided
of
position
model
outlet.
fan
psychrometer
natural
determination
24
4.5
inlet
combustion
Ome ga
copper
psychrometer,
The
data
and
ju n ctio n s
secured
used
a
inlet
bead
wick,
outlet
which
rate
the
length
section,
psychrometric
Finally,
cm
The
through
flow
at
transport.
measurement.
used
droplet
flow
flow
single
DCHX
d ig ita l
.95
b u lb .
ples
A
thermocouple
sock
unit,
s to ic h io m e tric
were
the
area
in je c to r
the
of
section.
t r a n s i t i o n
and
at
locations.
In je c to r
v a ria b le
frequency.
temperatures
inside
duct.
show
injectors
separate
s itio n
fan
co n stru cted
convective
for
means
T ri-F la t
test
cm^).
upper
provide
by
psychrom eters,
soldered
as
accomplished
upper
a
31
bulb
lead
served
these
tem perature
S pecially
and
at
vibration
measures
wet
the
c a lib r a tio n
independent
water
is
gradient
gas
fuel
flow
2168A d i g i ta l
compo­
of
combustion
a
sam­
rate,
a means
switches
is
a
v e r i ­
product
connected
thermometer
36
ExjD_e r j. m_e n_t_a_l
Historically,
characterizing
considered
an
individual
phase
subject
considerable
in
a
to
fu ll
'insecure
conduct
single
ried
out
Inlet
gas
center
coupled
th is
point
with
the
ducted.
Another
place
most
on
determine
temperature,
to
steady
start
up
and
carrying
allow
state
and
equilibrium .
a
inlet
out
for
these
being
sensitivity
these
conditions.
parameter
Conservative
phase
flow
This
data
provided
were
tests
changes
con­
dispersion.
air
effec t
were
was
exten­
heated
the
of
in
gas
designed
to
in
inlet
gas
great
care
was
rate.
in v e stig a tio n s
time
the
tests
size
using
to
(air).
generator
studies
find
Other
liquid
two
involved
car­
measurement.
droplet
to
about
droplet
of
products
s u ffic ie n t
for
temperature
f i r s t
only
information
se rie s
v a r ia tio n
system's
slightly
to
were
phase
is
assessing
tests
gaseous
mono d i s p e r s e
of
of
engaging
prudent
end,
been
system,
Before
purpose
balance
and
e ffec tiv en e ss.
the
a
varied
variations
combustion
hum idity
In
the
flow
the
has
measurement
[27].
this
energy
s ig n ific a n t
im portant
of
were
DCHX a n d
Parameter
the
taken
gas
To
flows
m ulti-phase
seemed
for
using
Subsequent
concerning
At
DCHX
temperatures
case.
insight
sive,
the
a
it
te sts,
performance.
with
in
study,
phase
Accurate
uncertainty
DCHX
phase
instrumentation
science'.
p ro p e rtie s,
fledged
two
for
is
the
apparatus
true
variations
estim ates
after
of
for
to
both
reaching
system
reach
i n i t i a l
in itial
time
con—
37
sta n ts
for
these
th ir ty
minutes
during
test
S tart
up
includes
to
the
because
ature
to
Since
period
case
of
to
account
prescribed
these
code,
a
this,
set
were
by
hum idity,
consists
for
of
the
of
te st
gas
including
for
th is
it
DCHX w a s
in itia l
property
brought
conditions
provided
the
author.
BALANCE
flow
vapor
energy
flow
and
documentation
to
to
first.
rate
data
rates,
mass
deemed
a
ade­
over
a
control
effects.
code
DCHX
as
balance.
in
manual
To
at
a
collected
control.
single
appears
Due
p ro p e rtie s
Data
computer
receives
runs.
equilibrium
necessary
the
test
have
change
so
temper­
occurred
necessary
is
studies.
was
experim ent
was
temper­
Therefore
intervals,
it
addition
to
remaining
system
using
sectio n
brought
reached.
times
This
in
was
in
mass.
flu c tu a tio n s
reduced
and
is
and
since
smaller
both
minute
and
system
in
atmospheric
pressure
higher
much
the
up
respectively.
minutes
five
the
hour
thermal
system
twenty
months,
conditions
Data
w ritten
te s ts
one
involve
s ta r t
equilibrium
delivery
sm aller
equilibrium
at
and
throughout
mass,
several
accom plish
and
once
gas
delivery
was
for
Typical
changes
change
acquisition,
quate.
at
not
hours
s ig n if ic a n tly
entire
gas
thermal
minimal
data
the
five
hours
is
a much
duration
a high
was
and
does
Test
the
Parameter
once
it
eight
constant
changes
are
v a ria tio n s .
were
heating
DCHX.
ature
for
runs
time
changes
the
BALANCE,
temperature,
input.
phase
Output
heat
A copy
appendix.
of
loss
the
3 8
ILl-SJl-Ijt-S _an d
Results
divided
phase
of
into
energy
included
the
two
The
the
and
of
gas
in
defined
e a rlie r,
(NTU).
Comparison
conventional
re s u lts
mass
balances.
various
the
is
of
sensible
made
co u n t e r f low
with
of
between
unit
was
liq u id
to
flow
of
par­
uniformity
are
pre­
effe c tiv e n e ss
tra n s fe r
present
by
latent
Of
R esults
described
are
determine
to
size
la te n t
the
single
results
conditions.
number
are
limits.
droplet
and
are
respect
performance.
a fu n ctio n
and
study
operating
effect
on
gas
DCHX
studies
These
acceptable
primary
the
as
P relim in ary
within
hum idity
of
exchange
effectiveness,
were
terms
heat
tem perature,
the
under
interest
in le t
sented
that
exchanger's
recovery,
ticular
phase
operated
purpose
heat
heat
two
show
instrumentation
contact
parts.
and
to
direct
Discussion
system
Kays
units
and
a
and London
[26] .
E nergy
and
Mayy
Single
Table
2
as
DCHX h e a t
B aiancyy
phase
percent
loss,
energy
balance
deviation
defined
as
re s u lts
between
are
predicted
presented
and
in
measured
follows:
(3.12)
4p=(Ts-T.)/<*w+Be)
where:
R e=
(3.13)
Du e
and
the
to
uncertainties
determination
of
in
calculating
meaningful
thermal
radiation
resistances
em issivities
for
the
6% i n
acrylic
Table
2
Table
sections,
are
2:
within
the
Single
Predicted
( 0 K)
product
and
l i s t s
mass
basis.
The
mass
air
balance
effec t
of
in le t
on
a
percent
vals
for
flow
rate
mass
balance
flow
measurement
liq u id
4%
from
to
at
vary
ent
from
ing
3
the
gives
true
outlet
the
was
outside
gas
would
of
and
could
humidity
6%.
and
the
DCHX
Mas s
bal­
of
through
flow
nonunif or—
readings
even
be
last
ratio
differ­
though
airtight,
thereby
column
as
the
vapor
humidity
occurred,
condensed
vapor
outlet
Flow
Also,
to
inter­
in le t
to
caused
The
percent
m ajo rity
incurred
found
ratio.
w ater
2%
indicated
have
on
shows
Confidence
The
have
the
and
show n.
dilution.
reading.
tested
air
amount
gas
making
average
was
table
rate
attributed
Error
outlet
also
w ithin
be
combustion
absolute
values.
can
22
The
flow
is
are
possible
location,
an
within
given
error.
and
section
by
the
DCHX
the
DCHX t e s t
dilution
the
with
rates
discrepancy
nonuniformities
mi t i e s
flow
on
for
runs.
liq u id
fa lls
I .6
2.3
6.2
data
process
basis
about
B a l a n c e of
DCHX H e a t L o s s
te s t
re s u lts
within
acceptability.
125
133
145
phase
condensation/ evaporation
ance
of
balance
two
balances
Me a s u r e d
P e r c e nt
Loss
Deviation
( W)
( %)
123
130
136
four
ty p ical
lim its
Phase Energy
vs. Measured
3 86
394
401
3
energy
Predicted
Loss
(W)
g, i n
Table
the
a
the
some
lower­
in
Table
percent
of
40
inlet
liquid
indicates
Column
from
one
net
is
gain
p o sitiv e
for
rate.
A positive
increase
arranged,
low est
liq u id
rates
a
flow
to
liquid
in
terms
highest.
column
toward
higher
Table
in
3:
the
in
Thus
going
bottom
inlet
Tw o
quantity
liquid
P h a se
water
of
the
from
inlet
Ma s s
Liquid
out
Ma s s
Vapor
i n
Ma s s
Vapor
out
(gm/s)
(gm/s)
(gm/s)
(gm/s)
this
the
liquid
negative
test
flow
shown
at
higher
column
the
run.
rate,
by
top
Balance
Data
Per ce nt
Ma s s
Bal ance
( %)
( %)
Combustion Product Values
2.45
2.44
.3 1 6
.264
2.50
2.45
.317
.27 7
2.63
2.60
.328
.198
2.63
2.56
.325
.217
2.68
2.63
.315
.229
2.70
2.66
.324
.233
2.72
2.67
.323
.248
2.76
2.71
.318
.249
2.76
2.70
.321
.298
2.79
2.74
. 3 02
.314
2 .99
3 .06
.330
.170
2.99
3 . 02
.329
.185
3.01
.312
3.04
.179
3 .01
. 3.04
.230
.327
3.01
3.02
.325
.226
3 .03
.332
3.04
.189
3 .06
.3 2 1
3 .03
.166
3.10
3 .08
.315
.235
3.19
3.18
.319
.224
3.19
3.21
.323
.150
3.19
3 .23
.323
.173
3 .21
.232
3.24
.3 1 4
.062
.090
.160
.17 8
.136
.131
.125
.119
.083
. 061
.089
.114
.103
. 068
.089
.133
.125
.1 0 0
.105
.153
.110
.051
2.3
3 .3
5.6
6 .2
4.6
4 .4
4 .2
4 .0
2.7
2 .0
2.7
3 .5
3 .1
2.0
2.7
4 .0
3 .8
3 .0
3 .0
4 .5
3 .2
I .5
-0.41
-2.00
-1 .1 4
-2.66
-1.87
-1.48
-1 .8 4
- I . 81
-2 .1 7
-1.79
2.34
1.00
1.00
1.00
0.33
0.33
1.00
-0.65
-0.31
0.63
1.25
0.93
Air Values
2.97
2.85
2.99
2.87
2 .99
2.88
3 . 01
2.91
.051
.022
.048
.013
I .7
0.7
1.6
0 .4
-4.04
-4.01
-3 .68
-3 .32
.100
.1 2 8
.093
.1 1 8
to
condensation
Ma s s
• Water
Not
Balanced
(gm/s)
.0 3 1
. 031
.031
. 031
the
rates.
DCHX M a s s
Ma s s
Liquid
in
for
tendency
in d ic a te s
flow
in
Percent
Liquid
Gained
41
P r im a r y ;
S tu d ie s.
The
variation
combustion
uniform
of
sensible
products
droplets
observations
and
is
air
shown
concerning
and
latent
with
both
in
Figures
DCHX
effectiveness
uniform
11
and
effectiveness
and
12.
are
for
non-
Several
immediately
clear.
A linear
droplet
1%
in
data
the
F irs t
DCHX
droplet
third
of
is
for
with
even
the
th is
for
large
not
ex h ib it
than
the
that
cause
skewed
mean
droplet
by
5%
radial
size
an
to
was
in­
increase
the
1. 0
to
of
2 0%
cause
a
measura­
other
hand,
nonuniform
often
in
realized
by
made
velocity
dispersion
in
a few
the
large
jets.
A
designing
be
a x ially
gradients.
Conse­
was
to
It
of
nonvibrating
assumed
which
produced.
e ffe c tiv e n e ss
the
non-
to
assumptions
flow
and
s ig n ific a n tly
most
in
appar­
conditions,
d is tr ib u tio n
increase
involves
Gas
are
loss
the
negligible
if
a
the
are
uniform
words,
around
than
operation.
flow
to
less
of
effe c t
between
other
On
produced
section.
of
sufficient
the
by
drops
lack
nonuniform
of
modes
ex istin g
In
and
difference
enough
from
was
uniform
two
dispersion
not
offset
small
DCHX t e s t
symmetric
shows
effectiveness.
then,
possible
quently,
II,
smaller
possible
num ber
a
d isp ersio n
in
drops
11
that,
size
diam eters
droplets
be
is
Chapter
change
large
in
on
effectiveness.
size
in
droplet
the
may
analysis
between
causes
droplets
fluence
is
it
difference
shown
Figure
possible
uniform
ble
from
e ffe c tiv e n e s s
Several
ent.
regression
theoretically
42
I
.30
C o mbustion
to
Effectiveness,
□ I
□ - u n i f o r m drops
W
Sensible
Products
9 - non-uni form drops
.70
_
.60
—
.50
_
A t m o s p h e r ic Air
.40
“
O
%
1.00
1.20
Number
Figure
11:
<)
- uniform drops
^
-
1.40
of T r a n s f e r
n o n - u n i f o r m drops
1.60
1.30
Units (NTU)
DCHX S e n s i b l e E f f e c t i v e n e s s
Number of T r a n s f e r U n i t s
vs.
43
A t m o s p h e r ic Air
.50
O - u n i f o r m drops
^ - n o n - u n i f o r m drops
i-4
U
Ul
Ul
40
*
C
Oi
%
a
Q
D 3
30
U
Cd
Ol
M-
Laten
LU
.20
Combu s t i o n
Products
d - u n i f o r m drops
. 10
® - n o n - u n i f o r m drops
1.00
1.20
Nu m b e r
Figure
12:
1.30
1.60
of T r a n s f e r
DCHX L a t e n t
Nur nher of
Units
I .SO
(NTU)
Effectiveness vs.
Transfer Units
44
large
enough
variations
in
d isp ersio n
the
DCHX
in
wall.
uniform
difference
It
for
modes
area
Ss
is
for
air
not
e f f e c t i v e n e s s
explained
are
an
order
products
test
and
stream
in itial
at
is
the
to
As
densation
of
for
gas
have
of
the
droplet
is
that
the
liq u id
test
section
appreciably
reduced
thus
th at
both
the
m inim izing
the
than
as
shown
in
the
lower
high
its
up
air
the
other
found
tem perature.
This
combustion
in
its
in
be
ratios
enters
is
from
order
the
large,
the
air
to
bring
s a tu ra tio n
pres­
hand,
a
in
combustion
air
energy
to
on
for
pressure
of w ater
s S~ S £
can
humidity
temperature
close
while
of
and
discrepancy
those
sensible
11
p ro d u c ts
saturation
of
those
Figures
products
inlet
than
from
in
co m b u stio n
that
e ffec tiv en e sses
apparent
that
from
the
considerably
evaporation
products
vapor
axial
conditions.
tra n s fe r
cases,
This
the
pressure
content
down
combustion
fo r
amount
the
Combustion
o u tlet
S^
clear.
3).
a p ortion
heat
why,
magnitude
vapor
vapor
d iffe r
( T g ^ ~ 3 9 5 0K ) ,
lo st
for
the
optimum
flowed
may
negated
and
im p lic a tio n
than
fig u re s
noting
considerable
a ir's
sure.
first
of
and
the
v a lu e s
(Table
section
a
the
by
be
the
operation
reasons
th an
case
droplet
products
the
have
radial
two.
from
higher
may
the
may
less
av a ila b le
clear
However
12,
of
nonuniform
combustion
air.
at
phenomenon
between
is
th is
contacted
This
and
In
operating
all
surface
DCHX p e r f o r m a n c e ,
conditions
e ffec ts.
unavoidably
inner
the
influence
flow
was
F in ally ,
flow
to
a
higher
saturated
stream
re s u lts
products.
have
in
a
net
The
con­
energy
gained
able
is
in
to
condensing
raise
droplet
consequently
the
droplet
As
which
for
to
and
however
energy
in
doing
are
the
a
with
for
and
having
described
by
should
firs t
in
heat
the
ience
of
an
Kays
be
an
expected
and
noted
of
the
In
mean
having
of
flow
that
the
Since
losses,
the
the
latent
values
re s u lts
the
s a m e NTU
Figure
assumes
system
not
fall
ratio ,
13.
It
no
losses
does
exper­
corrected
would
to
energy.
capacitance
curve
are
liquid
p o te n tia l
in
in
DCHX
energy.
outlet
is
of
combus­
that
latent
appears
present
which
s^ f o r
the
unit,
thermal
ideal
effectiveness
of
pro­
amount
e ffe c tiv e n e ss
count e r f low
[26]
of
there
sen sib le
from
d ifference
higher
more
vapor
Combustion
indicate
rates
inlet
the
recovering
recovering
London
exchanger.
that
air,
equivalent
since
p o te n tia l
values
products,
BCHX
ideal
irrecoverable
is
and
by
l i t t l e
n eg lig ib le .
job
effectiveness
the
Therefore
The low
poor
avail­
products
since
has
to
is
higher.
s ig n ific a n tly
form.
effectiveness
from
range
a
combustion
those
is
comparison
comparison
is
air
air
contain
in
combustion
energy.
temperatures
higher
A
for
relatively
though
increase
low,
water
Sensible
effectiveness,
la te n t
ss
evaporating
for
change
so
la te n t
products,
Even
is
recover
ducts,
is
higher
latent
a ir
between
tion
much
the
than
temperatures.
temperature
for
content
rather
for,
below
it
th o se
ideal.
addition,
tem perature
the
with
regard
d ifferen ce,
greatest
uncertainty
to
the
the
d eterm in atio n
tem perature
was
that
of
the
of
log
measurement
outlet
gas.
46
Effectiveness
K ays and London
Sensible
DCHX Resu I ts
(figure
11)
I .60
Number
Figure
13:
of T r a n s f e r
T h e o r e t i c a l and
Effectiveness for a
Units
I .80
(NTU)
Experimental Sensible
Counterflow Heat Exchanger
D uu ee
gt2 ’
to
temperature,
ble
of
axial
and
the
temperature
T_ o
was
general
as
the
This
gas
tem perature
of
net
DCHX
gas
o v erp red ictio n
fluences
ting
be
the
it
the
the
tially
linear
curve.
Since
is
with
lim it
F in a lly
of
a
s vs.
the
Figures
flow
rate
and
ness.
With
all
other
liquid
flow
rate
flow
system
which
makes
hot
energy,
is
gas.
In
its
gas
gas
it
15
show
15
tem perature.
is
in
Figure
Kays
from
the
on
i t s
in­
shif­
may
shown.
13
is
is
essen­
and
London
behavior,
thermody­
effec t
sensible
extract
the
outlet
and
dem onstrates
though
an
gas
that
in le t
effective­
is
in
because
capacity
more
latent
of
increase
T his
storage
to
lower
even
curve
asym ptotic
constant,
energy
since
by
an
exchanger.
possible
addition
13
the
the
effectiveness.
the
This
DCHX c u r v e
fu rth e r
temperature
raises
Figure
ex h ib it
and
by
than
in
effectiveness
made
the
param eters
temperature
enhanced.
in le t
14
be
slope
heat
increases
liquid
shown,
DCHX i s
ideal
liquid
the
NTU
to
the
3 % ( 0K)
results
Figure
words,
surface
of
1 0% ( 0 K ) .
in
value
than
order
T his
NTU v a l u e s ,
steeper
the
higher
other
NTU p l o t s
that
than
given
the
the
less
gas
re lia­
in n er
was
around
curve
observation
range
apparent
namic
for
In
on
o u tle t
flows,
outlet's
change.
of
in
obtaining
phase
amount
temperature
im portant
for
an
right.
in
tem perature
effectiveness
underpredicted,
that,
two
section
NTTJ v a l u e s
DCHX
toward
The
it
of
in
test
by
v a ria tio n s
difficulty
surface
o u tlet
the
rad ial
measurements
taken
tem perature.
and
of
the
energy
from
contains
less
energy
an
providing
recovery
increase
a
in
g reater
48
Combustion
.70
U
Effectiveness
- u n i f o r m drops
S — n o n — u n i form drops
M
Sensible
□
Products
.60
a sea
□
□
□
M
B3
□
.50
.40
A t m o s p h e r i c Air
,O
</" - u n i f o r m drops
.30
^
- n o n - u n i f o r m drops
2.35
2.55
Inlet
Figure
14:
2.75
Liquid Flow Rate
2.95
(kg/s)
3.15
x IOa -S
DCHX S e n s i b l e E f f e c t i v e n e s s
I n l e t L i q u i d Flow Rate
vs.
a
49
I
I
l
I
I
I
I
I
I
-
a
.70
*D
-
—
Sensible
Effectiven
33
.60
-
G
3
Combustion
a
Products
□
- uni form drops
3
— n o n - u n iform drops
.50
.40
+
A t m o s p h e r ic Air
&
—
.30
O
- uniform drops
—
f
- n o n - u n iform drops
—
!
I
l
380
l
390
Inlet
Figure
15:
l
I
400
Ga s T e m p e r a t u r e
I
I
410
I
420
(K)
DCHX Sensible E f f e c t i v e n e s s vs.
Inlet Gas T e m p e r a t u r e
50
amount
of
s e n s i b l e
effectiven ess.
Thus,
increased
inlet
gas
crease
in
outlet
latent
energy
e n e r g y ,
for
fixed
temperature
temperature,
recovery.
c a u s e s
gas
and
causes
and
a
d e c r e a s e
liquid
a
flow
rates,
corresponding
subsequent
in
decrease
in­
in
51
CHAPTER
IV
CONC LUS ION
The
present
uniform
droplet
operational
In
f i r s t
to
jet
is
axially
effect
is
are
vibrated.
droplet
shown
of
to
be
but
therefore
reasonable
to
It
has
droplets
ator
to
is
small
also
been
produced
without
being
when
velocity.
Variations
in
and
certain
power
in
that
water
is
on j e t
40%
parameters.
of
nonuniform
the
standard
deviations
that
to
be
somewhat
and
is
drops
appears
dia­
uniformity
through
The
no
is
nonuniform
value.
had
drop
The
mean
15%,
It
above
forced
of
power.
droplet
stream
genera­
velo city
input
the
a
velocity
of
power
standard
droplet
addition,
of
that
and
with
input
In
was
characteristics
the
jet
dependent
vibrated.
th e ir
drops
of
generator
droplets,
when
shown
10
of
regarding
frequencies
produced
changes
around
nonuniform
uniform
conclude
and
of
production
independent
distribution
20%
a droplet
vibration
20%
skewed
to
study
weakly
frequency
data
influence
m onodispersity.
v ib ra tio n
in se n sitiv e
the
droplet
that
frequency
on
this
its
5%,
provided
DCHX p e r f o r m a n c e .
of
show
has
and
velocities,
around
v ib ra tio n
meter
part
Results
deviations
tor
on
determine
various
inputs.
production
variables
the
tested
for
investigation
size
gener­
exhibit
vary
a
from
dispersion
dependent
on
jet
52
The
number
second
of
part
in le t
rate
and
heat
exchanger
gas
gas
vapor
it
is
droplet
size
the
Consequently
t i y e to
uniform ity
a
strong
proximately
tical
heat
those
tial
for
to
a
Tendencies
flow
the
rate
present
tiveness
is
one
would
higher
inlet
. , Overall,
available
could
inlet
for
shows
data
way
be
by
gas
the
energy
to
to
the
vapor
at
product
in
has
by
re­
energy.
liquid
recovery
increasing
the
test
section
of
poten­
inlet
energy
iden­
below
the
la te n t
increasing
ap­
terms
effectivenesses
av ailab le
in
is
results
of
decrease
effective­
evaluated
la te n t
have
content.
means
increase
sensi-
otherw ise
therefore,
t ha t
increase
Another
less
otherwise
the
i n. d i c a t e
condi­
for
higher
of
flow'
products
system
p ortion
attained.
expected,
air
that
droplet
combustion
combustion
present
on
were
might
gas
flow
indicate
actual
be
effectiveness
system.
suggested
of
they
a
nonuniform ities,
results
DCHX
greater
is
as
s i g n i f i c a n t l.y
the
the
attained
The
in
for
that
rec ov e ry
attain
covering
show,
liquid
d isp ersio n s
flow
of
uniformity
dependent
to
than
effectiveness
air.
not
due
in le t
Results
size
that,
function
conditions.
latent
is
consisted
droplet
with
varied.
of
e ffe c ts
twice
which
effectiveness
results
Sensible
were
not.optim ized
tions.
is
in
along
range
possible
was
Other
tests
effec tiv en e ss
for
However
in v e s tig a tio n
content
temperature
uniform ity
ness
this
DCHX p e r f o r m a n c e
and
been.
of
I
i n-
DCHX e f f e c ­
length.
effe c tiv e n e ss
This
shown
at
temperatures.
present
despite
system
shows
indications
the
excellent
system
recovery
was
of
operated
53
at
less
s t i l l
-than
b e tte r
d rople t
f I ow
optimum
recovery
rate
and
conditions.
could
contact
be
It
seems
accomplished
time.
apparent
by
that
increasing
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18.
D. B. H a r m o n , ' D r o p S i z e s f r o m L o w S p e e d J e t s ' ,
of th e F r a n k l i n I n s t i t u t e ,
v o l. 259, 1955,
pp.
19.
S.L. G o r e n a n d S . W r o n s k i ,
'The Shape
o f Low
Speed
Capillary Jets
of N ew tonian L iq u id s',
Journal
of F l u i d
Mechanics,
v o l . 25, 1966,
pp. 1 8 5 - 1 9 8 .
2 0.
V. G. L e v i c h . ,
P h v s i c o c h e m i c a l Hv d r o d v n a m i c s ,
H a l l , E n g l e w o o d C l i f f s , N . J . , 1 9 6 2 ) p g. 6 3 3 .
21.
R. L e t a n , ' D e s i g n o f a P a r t i c u l a t e
Exchange r : Uniform
Countercurrent
27, 1976.
22.
S . C . Ya o ,
Berkeley,
23.
S.C. Y a o a n d V. E . S c h r o c k , ' H e a t a n d M a s s T r a n s f e r
F r e e l y F a l l i n g D r o p s ' , AS ME, 7 5 - W A / H T - 3 7 , 1 9 7 5 .
24.
M. C. Y u e n a n d L. W. C h e n ,
'Heat T ra n sfer Measurements
E v a p o ra tin g
D ro p le ts ',
I n t e r n a t i o n a l
J o u rn a l
H eat and Mass T r a n s f e r ,
v o l . 2 1 , 1 9 7 8 , p p . 5 3 7 —5 4 2 .
Ph.D.
1974.
'On th e I n s t a b i l i t y of J e t s ' ,
Proceed­
L ondon
M ath
S o c i e t y ,
v o l.
10,
4-13.
Thesis,
U niversity
D irect
Flow',
of
Journal
519-522.
(Prentice-
Contact Heat
AS ME,
76-Ht—
C a lifo rn ia
at
from
of
of
57
25.
S.C.
Y a o a n d A.
Ra n e , ' H e a t
D r o p l e t F l o w i n Low P r e s s u r e
10, 19 7 9 .
T ransfer
Systems',
of E v a p o r a t i n g
AS ME, 7 9 - W A / H T -
26.
W. M.
Kays
and
A. L.
London, Compact
Heat
( M c G r a w - H i l l , New Y o r k , 1 9 5 5 ) p p . 1 3 - 6 3 .
27.
G. B. W a l l i s , ' R e v i e w - T h e o r e t i c a l M o d e l s o f G a s - L i q u i d
F lo w s ', J o u r n a l of F l u i d s E n g i n e e r i n g , v o l . 104, S ept.
1 9 8 2 , p p . 2 7 9 - 2 83 .
Exchangers,
58
APPENDICES
i
59
APPENDIX A
DR OP L E T DATA
Uniform
Frequency
680
765
850
935
1020
Data
D
mean
( mm)
a
( %)
^max
( mm)
^min
( mm)
Sample
Size
.650
.622
.607
.597
.577
5 .9
5 .0
4.7
4 .3
3 .3
.742
.696
.676
.655
.615
. 5 89
.556
.523
.523
.518
32
54
47
54
51
.605
.615
.610
.605
.605
4.3
3 .8
3 .7
3 .9
4.3
. 6 8 8
.665
.671
.650
. 6 88
.543
. 572
.566
.559
.554
45
47
54
54
50
(m/s)
.648
. 63 8
.622
.607
5 .5
5 .1
5 .5
4 .8
.721
.711
.691
.665
.572
. 566
.5 41
.551
36
33
36
36
(Hz)
In p u t Power
0.9
1.1
1.5
1.9
2.2
Jet
Droplet
V elocity
1.79
1.65
1.52
1.38
(W)
NonZUni form
Jet
Velocity
(m/s)
^mean
Dm o d e
( mm)
( mm)
1.77
1.63
1.47
I .31
.486
.490
.527
.559
.468
.451
.451
.485
Droplet
Cf.
( %)
13.
11
2 0
17
Data
Dm a x
Dm i n
( mm)
( mm)
Sample
Size
(-)
.635
.635
.802
. 819
.401
.434
.418
.434
48
50
48
40
60
APPENDIX B
EFFECTIVENESS
Tg,l
(
0
F)
Tg
(
0
,2
F)
Tl , I Tl ,
( 0 F)
( 0 F)
O
m
2
(kg/s)
DATA
O
L, I
x10 5
(kg/s)
mL , 2
Xl03
(kg/ s )
2.63
2.63
2.76
2.79
3.19
2.45
2.60
2.56
2.70
2.74
3.18
2.44
C o m b u s t i on P r o d u c t V a l u e s
251
102
51
119
5.98
251
106
49
119
6.03
248
1 0 2
50
117
6.05
249
105
51
118
6 . 02
245
1 0 2
49
117
5.92
249
104
51
117
6.06
246
104
49
117
6.04
247
50
104
118
6 . 1 0
250
50
104
118
6.09
249
1 0 2
50
117
6.04
251
106
50
118
6 . 0 1
253
105
49
119
6.09
253
1 0 1
52
118
6 . 1 0
254
1 0 2
52
118
6.06
251
1 0 0
52
116
6 . 1 0
252
1 0 2
52
118
6.09
251
1 0 0
52
119
6.05
252
1 0 0
53
6
. 01
119
252
1 0 2
52
1 2 2
5.44
251
104
53
1 2 1
5 .43
253
52
105
119
6.5 8
252
103
52
1 2 0
6 .55
226
1 0 0
51
115
6.19
228
1 0 1
51
116
6.15
253
103
49
118
6.71
253
103
49
6 . 73
117
225
51
97
115
6.14.
225
98
51
116
6.08
250
1 0 1
51
118
6 . 1 0
103
251
51
119
6.07
274
51
1 2 1
104
6.08
1 2 1
274
104
51
5 . 90
252
1 0 0
50
118
6 . 1 2
252
103
51
118
6.13
252
103
51
1 2 0
5.49
2 82
52
1 2 2
107
6.04
2 . 6 8
2 . 6 8
2 . 76
2.50
3 .10
2.70
2.72
3 .01
3 . 03
3.19
3 .19
3 .03
2.99
2.99
2 .99
3 .03
3 . 01
3 .01
2.99
2.97
2.97
3 .01
2.97
2.99
3 . 01
2.99
2 . 97
3.21
3 . 01
2.99
3 .05
2.71
2.45
3 .08
2.67
3.04
3 . 04
3 .21
3.23
3 .06
3.06
3 .03
3 . 07
3 .03
3 .02
3 .06
3 . 01
2.95
2.95
3 .09
3 . 02
3 .02
3 .04
2.97
2.99
3 .24
3 .02
3.04
3.04
Al r
253
252
248
251
2.99
3 . 01
2.97
2.99
2.91
2.85
2.87
Values
80
81
80
82
54
55
53
52
94
94
93
93
6.26
6.26
6 . 2
8
6.14
2 . 6 6
2 . 8 8
O
m V,
O
Xl03
(kg/s)
mv, 2
xlO3
(kg/s)
Tinif arm
i ty
.328
.325
.321
.314
.319
.316
.315
.318
.317
.315
.324
.323
.312
.332
.323
.323
.321
.330
.313
.322
.331
.341
.339
.332
.33 8
.339
.331
.328
.329
.327
.322
.329
.314
.325
.316
.337
.198
.217
. 2 98
.302
.224
.264
.229
.249
.277
.235
.233
.248
.179
.189
.150
.173
.166
. 171
.128
.164
.244
.224
.181
.169
.229
.249
.163
. 178
. 1 85
.230
.219
.223
.232
.226
.181
.228
nu
.031
.031
.031
.031
.093
.118
nu
. 1 0 0
nu
.128
U
I
U
Tl
nu
U
U
nu
U
U
U
U
nu
nu
U
nu
U
nu
U
nu
U
nu
U
nu
U
nu
U
nu
U
nu
U
nu
U
nu
nu
nu
nu
U
61
APPENDIX C
BALANCE
10 "
20
"
30
"
DATA R E DUC T I ON
B A L A N C E .............. DCHX D a t a
Reduction
CODE
Program
This
program
receiv es
DCHX t e m p e r a t u r e ,
hum idity,
pressure
40 '
and f l o w r a t e d a t a as i n p u t
5 0 ' BALANCE c a n b e u s e d t o p e r f o r m
single
or two phase
a n a I y se s
60 "
Output o p tio n s in clu d e:
70 "
I. mass f l o w , en e rg y and mass b a l a n c e s
80 '
and e f f e c t i v e n e s s r e s u l t s only
90 "
2 . DCHX t h e r m a l r e s i s t a n c e s a n d h e a t t r a n s f e r
plus #1
100'
3 . DCHX g a s p r o p e r t i e s a n d n o n d i m e n s i o n a l
param eters plus #1,2
HO
120
'
'
130 '
140 '
150 '
I NP UT VARI ABLE L I S T
160 '
1 7 0 ' GAS M A S S F L O W ..........................................
180 ' P A ( i n - H g ) - a t m o s p h e r i c p r e s s u r e
190 ' TA(F ) - a t m o s p h e r i c t e m p e r a t u r e
200 ' T 2 4 ( F ) - o r i f i c e i n l e t gas t e m p e r a t u r e
210 ' DP( i n - H 2 0 ) - d i f f e r e n t i a l
orifice
pressure
220 ' P I ( i n - H 2 0 ) - or i f i c e i n i e t g a s p r e s s u r e / b e l o w
atmospheric
230
240
'
VAPOR
MASS
F L O W ............................
250
WI ( - ) - i n i e t h u r n i d i t y r a t i o
260
WO( - ) - o u t l e t h u m i d i t y r a t i o
27 0
MG(kg/ k g - m o I e ) - d r y g a s m o l e c u l a r w e i g h t
280
2 9 0 ' M A S S B A L A N C E .......................................
300
MLlCkg/s e c ) - i n l e t w a te r mass flow
ML O - o u t l e t
310
3 20 '
E N E R G Y B A L A N C E ................................
330
T G l(F )- in le t gas te m p e r a tu r e
TGO-outlet
340
TL I ( F ) - i n l e t
liquid tem perature
TLO-outlet
3 50
3 6 0 ' H E A T T R A N S F E R .....................................
370
T I(F )-In tern al flu id bulk tem perature
380
TS l ( F ) - i n t e r n a I
surface temperature
390
TSO(F)-external
surface tem perature
400
TCP( F ) - i n t e r n a I g a s t e m p e r a t u r e ; f o r s p e c i f i c h e a t
determination
410
62
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
PRI NT
P R I N T " I M P O S E D O S C I L L A T I O N ? - YES ( Z l = 0 ) - N O ( Z I = I ) "
I N P U T " Z1
: ",Zl
PRINT
P R I N T "GAS FLOW V A R I A B L E S "
: ", PA5 TA5 T24
I NPUT " P A , T A5 T 2 4
I NPUT " D P 5P l
:
DP5 P l
: " , T G I , TGO
I NP UT " T G I 5TGO
I N P U T " T L I 5TLO
: " , TL I , TL O
P R I N T " VAPOR FLOW V A R I A B L E S "
I N P U T " WI , WO , M G
: " , W I , W O , MG
P R I N T " MASS BALANCE V A R I A B L E S "
I N P U T " M L I , MLO
M L I 5 MLO
PRI NT
P R I N T "DO YOU WANT A HEAT LOS S ANAL YS I S ? - Y E S ( W l = O )
NO(Wl=I)"
5 7 0 I N P U T "W I
:
Wl
5 8 0 PRI NT
5 9 0 I F WI < . 1 THEN 6 0 0 E L S E 7 3 0
6 0 0 P R I N T " HEAT T R ANS F E R V A R I A B L E S "
6 1 0 FOR I = I TO 9
6 2 0 PRI NT
63 0 PRINT " I = " ; I
64 0 INPUT " T I , T S I , T S O
T I ( I ) , T S l ( I ) 5TSO( I )
6 5 0 NEXT I
6 6 0 PRI NT
6 7 0 P R I N T " S P E C I F I C HEAT DATA"
6 8 0 FOR I = I TO 5
6 9 0 PRI NT
7 0 0 PRINT " I - C P = " ; I
7 1 0 I NPUT "TCP
:",TCP(I)
7 2 0 NEXT I
7 3 0 PRI NT
740
PRINT
"TO
OUTPUT
RESISTANCES
AND H . T - - Y E S ( X l = O ) NO(Xl=I)"
750
PRINT
"TO
OUTPUT
GAS
PROPERTIES
ETC.
-YES(Yl=O)
NO(Yl=I)"
7 6 0 I N P U T " X l 5Y l
: " , X l , Yl
7 7 0 GOSUB 5 4 7 0
7 8 0 GOSUB 9 3 0
7 9 0 GOSUB 1 1 6 0
8 0 0 GOSUB 1 6 1 0
8 1 0 GOSUB 1 7 2 0
8 2 0 I F W K . l THEN 8 3 0 E L S E 8 6 0
8 3 0 GOSUB 2 2 2 0
8 4 0 GOSUB 3 7 9 0
8 5 0 GOSUB 6 7 6 0
8 6 0 GOSUB 6 9 7 0
8 7 0 I F X l < . I THEN 8 8 0 E L S E 8 9 0
8 8 0 GOSUB 6 5 5 0
8 9 0 I F Y l < . 1 THEN 9 0 0 E L S E 9 1 0
9 0 0 GOSUB 5 6 8 0
9 1 0 END
63
920
"
9 3 0 ' S UB R O UT I NE TO CONVERT I N P U T DATA UN I T S
9 4 0 " ............C o n v e r s i o n F a c t o r s
950 ' 3 .3 7 1 5 k P a / i n - H g @ 294 K
960 ' .2484
kPa/in-H20@ 294 K
97 0 ' 1.8 R/K
98 0 '
9 9 0 P A= 3 . 3 7 1 5 * P A
1000 DP=.2484*DP
1010 P l= .2 4 8 4 * P l
1 0 2 0 TA=( TA + 4 5 9 . 6 7 ) / I .8
1030 T24 = ( T 2 4 + 4 5 9 . 6 7 ) / 1 . 8
1 0 4 0 T G I = ( TC 1 + 4 5 9 . 6 7 ) / ! . 8
1 0 5 0 TGO=(TGO +4 5 9 . 6 7 ) / 1 . 8
1 0 6 0 TL I = ( TL 1 + 4 5 9 . 6 7 ) / l . 8
107 0 TLO=(TLO +4 5 9 . 6 7 ) / 1.8
1 0 8 0 FOR I = I TO 9
1 0 9 0 T l ( l ) = ( T I ( l ) + 4 5 9 .6 7 ) / 1 .8
1 1 0 0 T S I ( I ) = CTS K l ) + 4 5 9 . 6 7 ) / I . 8
1110 TSO(l) = (T S O (l) +459.67)/1.8
1 1 2 0 T C P ( I ) = ( T C P ( l ) + 4 5 9 . 6 7 ) / I .8
1 1 3 0 NEXT I
1 1 4 0 RETURN
1150 "
1 1 6 0 ' S UB ROUT I NE TO CALCULATE GAS MASS FLOW RATE
1170 "
B-diameter ra tio
DENS( k g / s ) - g a s d e n s i t y
P 2 4 , T24
1180 "
Y-expansion fa c to r K-flow c o e ffic ie n t
1190
'
MF A( k g / s ) - g a s m a s s f l o w r a t e
RE-ReynoIds number
1200
"
Dl ( m ) - p i p e d i a m e t e r
D2(m) - o r i f i c e d i a m e t e r
1210
'
D l l ( i n ) - p i pe d i a m e t e r
D 2l(in)-orifice
diameter
1220
"
M (k g /k g -m o le )-to ta l gas m o le c u la r w eight
1230 "
P 24(kP a)-orifice in le t
gas p re ssu re
1240 '
1250 D l= .07899
1260 D2=.025959
1 2 7 0 B=D2/D1
1280 P24=PA-Pl
1
1 2 9 0 M= ( 1 + W I ) / ( ( W I / 1 8 . 0 1 6 ) + ( 1 / MG) )
1 3 0 0 DENS = P 2 4 * M / ( 8 . 3 1 4 3 4 * T 2 4 )
1 3 1 0 WGAS = WI
1 3 2 0 TGAS=T24
1 3 3 0 GOSUB 4 2 8 0
1 3 4 0 U24=UT
1 3 5 0 K24=KT
1360 Y = l-(.41+.35*(B "4))*((D P/P 24)/K 24)
1370 MFA=I!
13 80 R E l = ( 1 .27 3 2 * M F A ) / ( U 2 4 * D 2 )
1 3 9 0 " CALCULATE FLOW C O E F F I C I E N T . . . K
1 4 0 0 D 1 1 = 3 . 11
1410 D21=1.002
1 4 2 0 A= D 2 I * ( 8 3 0 - 5 0 0 0 * B + 9 0 0 0 * B ~ 2 - 4 2 0 0 * B ' ' 3 + 53 0 / S Q R ( D l I ) )
1 4 3 0 KE1 = ( . 3 6 4 + . 0 7 6 / S Q R ( D l I ) ) * ( B ' ' 4 )
1 4 4 0 I F B > ( . 0 7 + . 5 / D l l ) THEN KE2 = 0 : G O T O 1 4 6 0
64
1450
1460
147 0
1480
14 9 0
1 5 00
1510
1520
1530
154 0
1550
1560
1570
1580
1 590
1600
1610
1620
1630
1640
1650
1660
1670
1680
1690
17 00
1710
1720
1730
1740
K E 2 = . 4 * ( ( 1 . 6 - l / D l I ) ~ 5 ) * ( ( ( . 0 7 + . 5 / D l I ) - B ) '',2.5)
I F B > . 5 THEN K E 3 = 0 : G O T O 1 4 8 0
KE3 = - ( 8 . 9 9 9 9 9 9 E - 0 3 + . 0 3 4 / D l ! ) * ( ( . 5 - B ) ~ l . 5 )
I F B < . 7 THEN KE4 = 0 : GOT O 1 5 0 0
KE4 = ( 6 5 / ( D 1 I ^ 2 ) + 3 ) * ( B - . 7 ) /v2 . 5
KE = . 5 9 9 3 + . 0 0 7 / D 1 I + K E 1 + K E 2 + K E 3 + K E 4
KO = KE * ( D. 2 1 * 1 0 ^ 6 ) / ( D 2 1 * I 0 ^ 6 + ( I 5 *A ) )
R E l = C l .2732*MFA)/(U24*D2)
K=K0*(1+A/RE1)
MF A= 3 5 . 1 2 4 * K * Y * D 2 " 2 * S Q R ( D E N S * D P )
R E 2 = ( 1 . 2 7 3 2 * MF A) / ( U 2 4 * D 2 )
I F A B S ( R E 2 - R E I ) < 2 5 THEN I 5 8 0
GOTO 1 3 8 0
RETURN
"
"
" S UB R O UT I NE TO CALCULATE VAPOR FLOW RATES
"
MVlCkg/ s ) - i n l e t v a p o r f l o w r a t e
MVO-outlet
'
"
I n l e t Vapor Flow
M V I = W I * M F A / ( I +W I )
"
"
O u t l e t Vapor Flow
MV0 = W 0 * M F A / ( 1 + W l )
RETURN
"
"
' S U B R O U T I N E TO CALCULATE DCHX E F F E C T I V E N E S S AND
' MA S S AND ENERGY BALANCES
QlCkW) - e n t h a l p y
change
DM(kg/ s ) - I i q u i d m a s s b a l a n c e
17 5 0 '
HAlCk J / k g ) - g a s i n l e t e n t h a l p y
HAO-outlet
1760 '
HVI Ck J / k g ) - v a p o r
"
"
HVO- • "
1770'
HLlCkJ/ k g ) - I iq u id
"
"
HLO-"
1780 '
CRl(-)-inlet
thermal
capacitance
C RO"
1790 '
W S C- ) - s a t u r a t i o n
humidity
ratio
at o u t l e t
gas te m p e r a tu r e
1800 '
DTLM(K)-Iog m ean t e m p e r a t u r e d i f f e r e n c e
1810 '
NTU (-)-number of t r a n s f e r u n i t s
1820 '
EFFI ( - ) - s e n s i b l e e f f e c t i v e n e s s
1830 '
EFF2(-)-latent
effectiveness
1840 '
1 850 '
1
860 '
1870 ' Mass B a la n c e
1 8 8 0 DM= CMV0+ MLO) - ( MVI + MLI )
1 8 9 0 MAVG=C ML 0 + ML I + MV 0 + MVI ) / 2
I 9 0 0 D D M = I O O * D M / MAVG
1910 ' Energy B a l a n c e
1 9 2 0 TGH=TGI
1 9 3 0 GOSUB 3 9 3 0
1 9 4 0 HAI =HA. : HV I = HV
1 9 5 0 TGH=TLI
65
,1 9 6 0
1970
1980
1990
2000
2010
2020
2030
20 40
2050
2060
2070
2080
20 90
2100
2110
2120
2130
2140
2150
2160
2170
2180
2190
2200
2210
2220
2230
2240
2250
2260
2270
2280
2290
2300
2310
23 20
233 0
2340
2350
2360
2370
23 80
23 90
2400
2410
2420
GOSUB 3 9 3 0
HLI=HL
TGH=TGO
GOSUB 3 9 3 0
HAO=HAr HVO=HV
TGH=TLO
GOSUB 3 9 3 0
HLO=HL
Ql = ( MLO* HLO+ MV 0 * HV 0+ M F A / ( I +W I ) * H A O ) ( ML I * H L I + MVI * HV I + MFA/ ( I +WI ) * H A l )
" Effectiveness
Calculations
TGC=TGI
GOSUB 5 1 2 0
CPI=CPT
C R I = ( M L I * 4 . 1 9) / ( MF A* CPI )
CRO= ( ML 0 * 4 . 1 8 ) / ( M F A * C P l )
EFF I = C R 0 * ( T L 0 - T L I ) / (T G I - T L I )
GOSUB 5 3 7 0
WS = C 1 8 . 0 2 / M G ) * P V / ( P A - P V )
I F W K W S THEN 2 1 5 0 E L S E 2 1 6 0
WS = WI
QFG=HF* M F A * ( W I - W S ) / ( 1 + W I )
QFAC=QFG/( M F A *C PI * ( T G I - T L I ) )
E F F 2 = E F F l / ( I +QFAC)
D T L M = ( ( T C I - T L 0 ) - ( T G O - T L I ) ) / L OG ( ( T G I - T L O ) / ( T G O - T L I ) )
NTUl = E F F I * ( T G I - T L T ) / D T L M
RETURN
J
' S UB R O UT I NE TO CALCULATE I N T E R N A L , WALL
AND EXTERNAL HEAT T R ANS F E R
GOSUB 2 2 9 0
GOSUB 2 4 2 0
GOSUB 2 9 0 0
GOSUB 3 0 2 0
GOSUB 3 5 3 0
RETURN
" S UB R O UT I NE TO READ S E C T I O N A L DATA
"
R C D ( K / W) - s e c t i o n c o n d u c t i o n t h e r m a l r e s i s t a n c e
L(m)11
length
D0(m)11
outside
diameter
"
E(-) 11
m aterial
em issivity
'
FOR I = I TO 9
READ R C D ( I ) , L ( I ) , D O ( I ) , E ( I )
NEXT I
DATA 4 . 5 4 , . 3 2 , . 2 8 2 , . 9 5 , 2 . 5 8 , . 2 3 , . 5 6 6 , . 9 5 , 6 . 2 3 ,
. 0 7 1 ,. 8 4 8 , .95
DATA 3 . 1 4 , . 0 7 1 , . 8 4 8 , . 9 5 , 4 . 7 1 , . 3 7 , . 2 4 4 , . 8 , . 2 7 ,
. 71 , . 0 8 9 1 , . 95
DATA 3 . 4 I , . 6 0 5 , . 2 7 2 , . 8 , . 0 3 3 , . 9 6 , . 1 5 3 , . 9 5 , I . 2 8 ,
. 4 8 , . 3 3 3 , . 95
RETURN
" S U B R O U T I N E TO CALCULATE I NT E R NAL CONVECTI VE
HEAT T R A N S F E R '
66
2430
2440
2450
2460
2470
2480
2490
2500
2510
2520
2530
2540
2550
2560
257 0
2580
2590
2600
2610
2620
2630
2640
2650
2660
2670
2680
2690
27 00
2710
27 20
2730
2740
2750
27 60
2770
2780
2790
2800
2810
2820
2830
2840
2850
2860
2870
2880
DTl(K)-Internal tem perature difference
TMI(K)-mean i n t e r n a l te m p e r a tu r e
Ul(kg/m -s)-internal
abs. v is e .
K(-)- internaI
sp. h e a t r a t i o
K I ( W/ m - K ) - i n t e r n a l t h e r m ,
cond.
PRI( - ) - in te rn a I P randtl
no.
RE l ( - ) - i n t e r n a I R e y n o l d ' s n o .
NUI( - ) - i n t e r n a l N u s s e l t
no.
RI(K/W )-internal
convective therm al re s is t.
Ql(kW)- i n t e r n a l h e a t t r a n s f e r
Dl(m )-internal
section diameter
QI N=O
FOR I = I TO 9
DTI(I)=TI(I)-TSI(I)
TM I(l) = (T I(l) +T S l(l))/2
TGAS=TMI(I)
WGAS=WO
GOSUB 4 2 8 0
UI(I)=UT
KI(I)=KIT
PRI(I)=PRIT
Read s e c t i o n a l i n s i d e d i a m e t e r and w a l l t h i c k n e s s
READ D I ( I ) , T H ( I )
I F I = < 4 THEN 2 6 6 0 E L S E 2 7 0 0
Gas i n l e t / l i q u i d o u t l e t m a n i f o l d
NUI(I) =DI(I)ZTH(I)
R I ( I ) = TH ( I ) Z ( K K l ) * 3 . 1 4 1 6 *D I ( I ) * L ( I ) )
GOTO 2 8 4 0
Test sect ion
REI( I ) = ( 1.27 3 2 * M F A )Z (D l(l)*U l(l))
XD ( 5 ) = 2 . 9 1 : X D ( 6 ) = 1 4 . 7 9 : X D ( 7 ) = 1 3 . 9 3 : X D ( 8 ) = 1 8 : X D ( 9 ) = 1 3 . 0 8
RPI(I)=(REI(I)*PRI(I)ZXD(I))
I F 1 = 6 OR 1 = 8 THEN 2 7 4 0 E L S E 2 8 2 0
I F 1 = 6 THEN 2 7 6 0 E L S E 2 7 9 0
Turbulent entry region
NUI(I)=.0 27*REI(I)*.8*PRI(I)*.3
GOTO 2 8 3 0
Laminar entry region;
q=const.
NUI ( I ) = 4 . 3 6 + ( ( . I * R P I ( I ) ) Z ( I + . 0 1 6 * R P I ( I ) ~ . 8 ) )
GOTO 2 8 3 0
Laminar entry region;
T=const.
NU l ( l ) = 3 . 6 6 + ( ( . 1 0 4 * R P I ( D ) Z U + . 0 1 6 * ( R P I ( I ) ) A . 8 ) )
R I ( I ) = I Z ( 3 . 1 4 1 6 * N U l ( I ) * K I ( I ) *L ( I ))
Q l ( I ) = D T I 1( I ) Z ( R i d ) * 1 0 0 0 )
I F 1 = 9 GOTO 2 8 7 0
QIN=QIN+QI(I)
NEXT I
DAT A . 1 1 1 , . 0 8 3 , . 3 0 2 , . 1 4 6 , . 6 4 1 , . 0 7 6 , . 6 4 1 , . 0 7 6 , . 0 9 3 ,
,.0 7 3 ,,.1 1 3 ,,.1 5 2 ,,.2 6 ,
2 8 9 0 RETURN
2900
' S UB R O UT I NE TO CALCULATE WALL CONDUCTI ON
HEAT T R ANS F E R
67
2 9 1 0 ""
DTW( K) —w a l l t e m p e r a t u r e d i f f e r e n c e
2920 "
QWALL(kW)-walI h e a t t r a n s f e r
2930 "
2 9 4 0 QWALL=O
2 9 5 0 FOR I = I TO 9
2 9 6 0 DTw ( I ) = T S I ( I ) - T S O ( I )
2 97 0 Q W A L L ( I ) = D T W ( I ) / ( R C D ( I ) * ! 0 0 0 )
2 9 8 0 I F 1 = 9 GOTO 3 0 0 0
2 9 9 0 QWALL= QWALL+ QW A L L ( I )
3 0 0 0 NEXT I
3 0 1 0 RETURN
3020
" S UB R O UT I NE TO F I N D EXTERNAL HEAT T R ANS F E R
3030 "
G ( M/ 2 ) - g r a v .
a c c e I I e r a t ion
BC( W / M' ‘2 - K A4 ) - B o l t z m a n n c o n s t .
3040 ^
AO( m ^ 2 ) - s e c t i o n e x t e r n a l s u r f a c e a r e a
3050 "
DT0 ( K ) - e x t e r n a I t e m p e r a t u r e d i f f e r e n c e
3060 "
TFO(K)11
mean f l u i d te m p e r a tu r e
3 0 7 0 " ............ E x t e r n a l D i m e n s i o n l e s s P a r a m e t e r s ( - )
3080 " G R - G r a s h o f no.
RA-R ayl e i g h no.
P R - P r a n d t I no.
N U O - N u s s e l t no.
3090 "
Z - z e t a ; m e a s u re of c y l i n d e r / f l a t p l a t e v a r i a t i o n
3100 '
F F - c o r r e c t s NU0 f o r c y l i n d e r c u r v a t u r e
3 1 1 0 " ............E x t e r n a l T h e r m a l R e s i s t a n c e s ( K / W )
3120 ' RCV-c o n v e c t i o n
RRAD-ra d i a t io n
ROUT-total p a r a l l e l r e s is t a n c e
3 1 3 0 " ............E x t e r n a l H e a t T r a n s f e r ( k W )
3140 " QC-co n v e c t ion
QRradiation
ROtotal
3150 "
3 1 6 0 G= 9 . 8 0 2
3 1 7 0 B C= 5 . 6 7 E - O 8
3 1 8 0 QOUT=O
3 1 9 0 QC=O
3 2 0 0 QR=O
3 2 1 0 FOR I = I TO 9
3 2 2 0 AO( I ) = 3 . 1 4 I 6 * D 0 ( I ) * L ( I )
3230 TFO(l)=(TSO(l)+TA)/2
3240 DTO(I)=TSO(I)-TA
3250 TAIR=TFO(I)
3 2 6 0 GOSUB 4 8 8 0
3 2 7 0 G I ( I ) = ( G * D T 0 ( I ) ) / ( T F 0 ( I ) *V ( I ) ~ 2 )
3280 G R ( I ) = G 1 ( I ) * L ( I ) " 3
3 2 9 0 R A ( I ) = P R ( I ) *GR( I )
3 3 0 0 I F 1 = 3 THEN F F ( I ) = I : G 0 T 0 3 3 8 0
3 3 1 0 I F 1 = 4 THEN F F ( I ) = I : G 0 T 0 3 4 0 0
3320 " V e r t i c a l f l a t p l a t e n a t u r a l c o n v e c t i o n
3330 N U 0 (l)= .4 7 9 * (D 0 (l)/L (l))* G R (l)"(l/4 )
3340 Z ( l ) = ( 5 . 6 6 / D O ( l ) ) * ( L ( l ) / G l ( l ) ) * ( l / 4 )
33 50 F F ( I ) = 1 + Z ( I ) * . 159
3 3 6 0 GOTO 3 4 1 0
3370 " H o r i z o n ta l f l a t p l a t e n a t u r a l co n v e ctio n
3380
I F RA( I ) < I E + 0 7 THEN NU 0 ( I ) = . 5 4 * R A ( I ) ~ .2.5 : G OTO 3 4 1 0
3390
I F RA( l ) > = l E + 0 7 THEN NU0 ( I ) = . I 5 * R A ( I ) ~( I / 3 ) : G OTO 3 4 1 0
3 4 0 0 N U O ( I ) = . 2 7 * R A ( I ) Z1. 2 5
3410
3420
3 43
3440
3450
3460
3470
3480
3490
3500
3510
3520
3530
R C V ( I ) = F F ( I ) / ( 3 . 1 4 1 6 * D O ( l ) * K ( I ) *NUO( I ))
Q C ( I ) = D T O ( I ) / ( R CV ( I ) * 1 0 0 0 )
0 R RAD( I ) = 1 / ( B C * E ( I ) * A 0 ( I ) . * ( T S 0 ( I ) <‘ 2 + T A * 2 ) * ( T S 0 ( I ) + T A ) )
Q R (I)= D T O (I)/(RRAD(I)*1000)
ROUT(I ) = ( r r a d ( i ) * r c v ( i ) ) / ( r r a d ( i ) + r c v ( i ) )
QO(I)=DTO(I)/(ROUT(I)*1000)
I F 1 = 9 GOTO 3 5 1 0
QOUT = Q O U T + Q O( I )
QC=QC+QC(I)
QR= QR h- Q R ( I )
NEXT I
RETURN
" S UB R O UT I NE TO CALCULATE HEAT TRANS F ER BY
S P E C I F I C HEAT
3540 '
CP(kJ/ kg-K)-gas
specific heat
3550 "
QCP(kW)-heat t r a n s f e r from
flu id stream section
3560 "
QC . . ( k W ) - 1 o t a l h e a t
transfer
from s e c t i o n s 5-8
3 5 7 0 FOR I = I TO 5
3580 TGC=TCP(I)
3 5 9 0 GOSUB 5 1 2 0
3600 CP(I)=CPT
3 6 1 0 NEXT I
3620 CPl=(CP(l)+CP(2))/2
3 6 3 0 Q C P ( 5 ) = M F A * C P l * ( T C P ( I ) - T CP ( 2 ) )
3640 CP2=(CP(2)+CP(3))/2
3 6 5 0 Q C P ( 6 ) = MF A * C P 2 * ( T C P ( 2 ) - T CP( 3 ) )
3660 CP3=(CP(3)+CP(4))/2
3 6 7 0 QCP(7) = M F A * C P 3 * ( T C P ( 3 ) - T C P ( 4 ) )
3680 CP4=(CP(4)+CP(5))/2
3 6 90 QC P ( 8 ) = M F A * C P 4 * ( T C P ( 4 ) - T C P ( 5 ) )
3700 CP5=(CP(l)+CP(5))/2
3 7 1 0 QC P 5 = M F A * C P 5 * ( T C P ( I ) - T C P ( 5 ) )
3 7 2 0 QCI N= Or QCW A= 0 : Q CO = O
3 7 3 0 FOR 1 = 5 TO 8
3740 QCIN=QCIN+Ql(l)
3 7 5 0 Q CWA=Q CWA+Q WALL ( I )
3 7 6 0 QCO = QCO h- Q O ( I )
3 7 7 0 NEXT I
3 7 8 0 RETURN
3 7 9 0 ' S U B R O U T I N E TO C A L C U L A T E R T O T A L 5 Q T O T A L AND QC T OT
(SEC. 5 - 9 )
3800 " T h is i s an e n e r g y b a l a n c e f o r the
te s t sectio n only
3 8 1 0 QTOTAL=O
3 8 2 0 FOR I = I TO 9
3830 RT0TAL(I)=RCD(I)+ROUT(I)
3 8 4 0 Q T O T A L d ) = ( T S 1 ( 1 ) - T A ) / ( RT OTAL ( l ) * 1 0 0 0 )
3 8 5 0 I F 1 = 9 GOTO 3 8 7 0
3 8 6 0 QTOTAL = Q T O T A L H - Q T O T A L d )
3 8 7 0 NEXT I
3 8 8 0 QCTOT=O
69
3890
3900
3910
3920
3930
3940
3950
3 960
3970
3 98 0
3990
4000
4010
4020
4030
4040
4050
4060
4070
4080
4 0 90
4100
4110
4120
4130
4140
4150
4160
4170
4180
4190
4200
4210
4220
4230
4240
4250
4260
4270
4280
4290
4300
4310
43 20
4330
4340
4350
4360
4370
4380
43 9 0
4400
FOR 1 = 5 TO 8
QCTOT=QCTOT+QTOTAL(I)
NEXT I
RETURN
" S UB R O UT I NE TO CALCULATE GAS,
VAPOR AND L I Q U I D ENTHALPY
"
TGH(K)- d u m m y g a s e n t h a l p y t e m p e r a t u r e
'
FAC(- ) - i n t e r p o I a t i on f a c t o r
' ............ D u m m y E n t h a l p i e s ( k J / k g )
" HA- g. as
HV-vapor
HL-Iiquid
'
I F T G H < 3 0 3 . 1 5 THEN 4 0 0 0 E L S E 4 0 5 0
FAC=(TGH-273.15)/30 .
HA=FAC*29.6
HV = F A C * 5 5 + 2 5 0 1 . 3
HL=FAC*125.7 9
GOTO 4 2 7 0
I F T G H < 3 3 3 . 1 5 THEN 4 0 6 0 E L S E 4 1 1 0
FAC=( TGH- 3 0 3 . 1 5 ) / 3 0
HA=FAC*30.16 + 29.6
HV=FAC*53 .3 + 2 5 5 6 .3
HL = F A C * ! 2 5 . 3 4 + 1 2 5 . 7 9
GOTO 4 2 7 0
I F T G H < 3 6 3 . 1 5 THEN 4 1 2 0 E L S E 4 1 7 0
FAC=(TGH-333. 1 5 ) / 3 0
HA = F AC *3 0 .24 + 5 9 . 76
HV = F A C * 5 0 . 5 + 2 6 0 9 . 6
HL = F A C * 1 2 5 . 7 9 + 2 5 1 . 1 3
GOTO 4 2 7 0
I F TGH< 3 9 3 . 1 5 THEN 4 1 8 0 E L S E 4 2 3 0
FAC=( T G H - 3 6 3 . 1 5 ) / 3 0
HA= FAC * 3 0 . 3 + 9 0
HV=FAC*46.2 + 2 6 6 0 . I
HL = F A C * ! 2 6 . 7 9 + 3 7 6 . 9 2
GOTO 4 2 7 0
F AC = ( T G H - 3 9 3 . 1 5 ) / 3 0
HA=FAC*30.4 + 1 2 0 . 3
HV = F A C * 4 0 . 2 + 2 7 0 6 . 3
HL = F A C * 1 2 8 . 4 9 + 5 0 3 . 7 1
RETURN
' S UB R O UT I NE TO CALCULATE GAS A B S . V I S C O S I T Y ,
' S P . HEAT R A T I O , THERMAL C ON D U C T I V I T Y AND PRANDTL
"
TGAS ( K ) - d u m m y g a s t e m p e r a t u r e
"
FAC(- ) - i n t e r p o I a t i o n f a c t o r
' ............D u m m y A b s . V i s e , ( k g / m - s )
" UG-gas
UV-vapor
UT-mixture
' ............ D u m m y s p . h e a t r a t i o
(-)
" KG-gas
KV-vapor
KT-mixture
" ...........Du m m y I n t e r n a l
Thermal
Conductivity
(W/m-K)
" KIG-gas KIV-vapor
KIT-mixture
" ............ D u m m y I n t e r n a l P r a n d t l N o . ( - )
' PRIG-gas PRIV-vapor PRIT-m ixture
'
NO.
4410
4420
4430
4440
4450
4460
4470
4480
4490
4500
4510
4520
4530
4540
4550
4560
4570
4580
4590
4600
4610
4620
4630
4640
46 50
4660
4670
4680
46 90
4700
4710
4720
4730
4740
47 50
4760
4770
4780
4 7 90
4800
4810
4820
483 0
4840
4850
486 0
4870
4880
4890
4900
4910
4920
4930
IF
T G A S O O O THEN 4 4 2 0 E L S E 4 5 2 0
(tgas-27 5)/25
UG=FAC*!.2 5 E - 0 6 + 1 . 7 2 1 E - 0 5
UV = F A C * . 0 0 0 0 0 1 + 8 . 0 9 E - 0 6
KG=I.4 0 1 - F A C * . 0 008
KV = I . 3 3 0 1 - F A C * . 0 0 0 9
KIG=FAC*.0 0 2 + . 0 2 4 3
KIV = FAC*.0013 + .0183
P R I G= . 71 3 5 - F A C * . 0 06 5
PRIV = FAC*.04 +. 8 17
GOTO 4 8 3 0
I F TGAS < 3 5 0 THEN 4 5 3 0 E L S E 4 6 3 0
f a C=C t g a s - 3 o o ) / s o
UG = F A C * 2 . 3 6 E - O 6 + 1 . 8 4 6 E - O 5
UV=FAC*.0 0 0 0 0 2 + 9 . 0 9 E - 0 6
KG = I . 4 0 0 2 - F A C * . 0 0 1 8
KV=I.3 2 9 2 - F A C * . 0 0 3 4
KIG = FAC*.0037 + .0263
KIV=FAC*.0 0 3 4 + . 0 1 9 6
PRIG = .7 0 7 - F A C * . 007
PRIV=FAC*.0 8 5 + . 8 5 7
GOTO 4 8 3 0
I F TGAS < 4 0 0 THEN 4 6 4 0 E L S E 4 7 4 0
FAC=CTGAS- 3 5 0 ) / 5 0
UG = F A C * 2 . 1 9 E - 0 6 + 2 . 0 8 2 E - 0 5
UV = F A C * 1 . 9 6 E - 0 6 + 1 . 1 0 9 E - 0 5
KG = I . 3 9 8 4 - F A C * . 0 0 3 2
KV=I.3 2 5 8 - F A C * . 005
KI G = F AC* . 0 0 3 8 + .03
KIV=FAC*.0 0 4 2 + . 0 2 3
PRIG = .7-FAC*.01
PRIV=FAC*.0 9 1 + . 9 4 2
GOTO 4 8 3 0
FAC=CTGAS-400)/50
UG = F A C * 2 . 0 6 E - 0 6 + 2 . 3 0 l E - 0 5
UV=FAC*.0 0 0 0 0 1 8 + 1 . 3 0 5 E - 0 5
K G = I.3952-FAC*.0042
KV=I.3 2 0 8 - F A C * . 0 0 5 4
KIG = FAC*.0 0 3 5 + . 0 3 3 8
KIV=FAC*.0 0 5 9 + . 0 2 7 2
PR I G = . 6 9 - F A C * . 0 0 4
PRIV=FAC*.!0 7+ 1.033
U T = U G / C l + W l ) + W GAS * U V / CI + WGAS )
K T = K G / C l + W l ) + WGAS * K V / CI + WGA S )
K I T = K I G / C I + WI ) + WGAS * K I V / C l + WGAS)
P R I T = P R I G / ( 1 + W I ) + W G A S * P R I V / C I + WGAS )
RETURN
' S UB R O UT I NE TO CALCULATE EXTERNAL F L U I D P R O P E R T I E S
"
TA I R ( K ) - d u m m y e x t e r n a l a i r t e m p e r a t u r e
"
FACC- ) - i n t e r p o I a t i o n f a c t o r
"
K(W/m - K ) - e x t e r n a l t h e r m a l c o n d u c t i v i t y
VCm~2/s)"
kinematic v isco sity
"
PTC-)"
Prandtl
no.
fac=
71
4940
4950
4960
4970
4980
4990
5000
5010
5020
5030
5040
5050
5060
5070
5080
5090
5100
5110
5120
5130
5140
5150
5160
5170
5180
5190
5200
5210
5220
5230
5240
5250
5260
5270
5280
5290
5300
5310
5320
5330
5340
5350
5360
5370
5380
5390
5400
5410
542 0
5430
5440
5450
5460
"
I F T A I R O O O THEN 4 9 6 0 E L S E 5 0 1 0
FAC=( T A I R - 2 5 0 ) / 5 0
K ( I ) = FAC*.004 + .0223
V ( I ) = F AC * 4 . 4 5 E - 0 6 + 1 . 1 4 4 E - 0 5
P R ( I ) = . 7 2-FAC*.0 13
GOTO 5 1 1 0
I F T A I R O 5 0 THEN 5 0 2 0 E L S E 5 0 7 0
F A C = ( T A I R - 3 O0 ) / 5 O
K ( I ) = FAC*.0037 + .0263
V ( I ) = FAC*5 . 0 3 E - 0 6 + 1 . 5 8 9 E - 0 5
P R ( I ) = . 7 0 7 -F A C * . 007
GOTO 5 1 1 0
FAC=(TAIR-350)/50
K(I)=FAC*.0038+.03
V ( I ) = F AC * 5 . 4 9 E - 0 6 + 2 . 0 9 2 E - 0 5
P R ( I ) = . 7 - F A C * . 01
RETURN
" S UB R OUT I NE TO CALCULATE GAS S P E C I F I C HEAT
"
FAC(- ) - i n t e r p o I a t i o n f a c t o r
'
C P G( k J / k g - K ) - d u m m y g a s s p e c i f i c h e a t
"
C PV (k J/k g -K) -dummy v a p o r
"
"
'
CPT ( k J / k g - K ) - d u m m y t o t a l
"
"
I F T GC < 3 0 0 THEN 5 1 8 0 E L S E 5 2 2 0
F A C= ( T C C- 2 7 3 . 1 5 ) / 2 6 . 8 5
CPG=FAC*.0 0 0 5 + 1 . 0 0 6 5
CP V = F A C * . 0 1 8 + 1 . 8 5 4
GOTO 5 3 5 0
I F TG C< 3 5 0 THEN 5 2 3 0 E L S E 5 2 7 0
FAC= ( TG C- 3 0 0 ) / 5 0
CPG = F A C * . 0 0 2 + 1 . 0 0 7
CPV=FAC*.0 8 2 + 1 . 8 7 2
GOTO 5 3 5 0
I F T G C < 4 0 0 THEN 5 2 8 0 E L S E 5 3 2 0
F A C = ( T C C- 3 5 0 ) / 5 0
CPG = F A C * . 0 0 5 + 1 . 0 0 9
CPV=FAC*.2 0 4 + 1 . 9 5 4
GOTO 5 3 5 0
FAC=(TGC-400)/50
CPG=FAC*.007 + 1 .0 14
CPV=FAC*.4 0 2 + 2 . 5 6
CPT=CPG/(l+ W l)+ (W l/(l+ W l))* C P V
RETURN
" S UB R O UT I NE TO CALCULATE S AT UR AT I ON P R E S S U R E AND
' AND HEAT OF V A P O R I Z A T I O N
'
PV(kPa)s a t u r a t i o n p r e s s u r e @ TL I
"
H F (k J/k g )-h e at of v a p o r iz a t i o n
@ TL I
I F T L K 2 8 3 . 1 5 THEN 5 4 2 0 E L S E 5 4 4 0
P V = I . 0 1 7 + . 2 I * ( TL I - 2 8 0 . 3 7 ) / 2 . 7 8
GOTO 5 4 5 0
PV = I . 2 2 7 + . 5 4 * ( T L I - 2 8 3 . 1 5 ) / 5 . 5 6
HF=2491-14*(TLI-280.37)/8.34
RETURN
72
5 4 7 0 ' S UB R O UT I NE TO EXAMI NE I N P U T DATA
5480
LPRINT
" .....................................I N P U T
D A T A .......................................... . . "
5 49 0 LPRINT
5 5 0 0 LPRINT " P A ( i n - H g ) TA(F) T 2 4 ( F ) D P ( i n - H 2 0 )
Pl(in-H20)"
5510 LPRINT P A, TA , T2 4 , D P ,P 1
5 5 2 0 LPRINT
5 5 3 0 LPRINT " T G I ( F )
TGO(F)
TLl(F)
TLO(F)"
5 5 4 0 L P R I N T T G I , T G 0 , TL I , TLO
5 5 5 0 LPRINT
5 5 6 0 L P R I N T " WI
WO
MG"
5 5 7 0 L P R I N T W I , W 0 , MG
5 5 8 0 LPRINT
5 5 9 0 LPRINT " M L l ( k g / s )
MLO(kg/s)"
5 6 0 0 L P R I N T M L I 5 MLO
5 6 1 0 LPRINT
5 6 2 0 I F W K . l THEN 5 6 3 0 E L S E 5 6 7 0
5630 LPRINT " I
TI(F)
TSI(F)
TSO(F)
TCP(F)"
5 6 4 0 FOR I = I TO 9
5 6 5 0 L P R I N T I , T I ( I ) , TS I ( I ) , TS O ( I ) , T C P ( I )
5 6 6 0 NEXT I
5 6 7 0 RETURN
^
5 6 8 0 ' S UB R O UT I NE TO O UT P UT - C O NVE R T E D I N P U T , E N T H A L P I E S .
5 6 9 0 ' S E C T I O N DATA, GAS P R O P E R T I E S , N / D P ARAMETERS AND
5700 "
EXTERNAL THERMAL R E S I S T A N C E AND HEAT T R ANS F E R
5710 LPRINT
57 2 0 L P R I N T " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' '
5 7 3 0 L PRI NT " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * a * * * * * * 11
5 7 4 0 LPRINT
5750
GOSUB 5 4 7 0
5760
GOSUB 5 8 0 0
5770
GOSUB 5 9 1 0
5780
GOSUB 6 0 1 0
5 7 9 0 RETURN
5 8 0 0 ' S UB R O UT I NE TO OUTPUT GAS , V A P O R AND L I Q U I D E N T H A L P I E S
5810 LPRINT
5 8 2 0 LPRINT
5 8 3 0 L P R I N T " ----- G A S , V A P O R AND L I Q U I D E N T H A L P I E S ____ "
5840 LPRINT
5850
LPRINT " H A l ( k J / k g )
HVl(kJ/kg)
HLl(kJ/kg)"
5 8 6 0 L P R I N T H A I 1HV I , H L I
5 8 7 0 LPRINT
5880
LPRINT " H A O ( k J / k g )
HVO(kJ/kg)
HLO(kJ/kg)"
5 8 9 0 L P R I N T HAO, HVO, HL O
5 9 0 0 RETURN
5 9 1 0 ' S E C T I O N DATA S UB R OUT I NE
5920 LPRINT
5 9 3 0 LPRINT
5 940
LPRINT
" .................................. S E C T I O N
D A T A ...........................................
5950 LPRINT
5 9 6 0 LPRINT " I
RCD( K/ W)
L(m)
DO( m)
E"
5 9 7 0 FOR I = I TO 9
5 9 8 0 L P R I N T I 1R C D ( I ) 1L ( I ) 1D O ( I ) , E ( I )
5 9 9 0 NEXT I
73
6 0 0 0 RETURN
6 0 1 0 " GAS P R O P E R T I E S AND N / D VALUES OUTPUT S U B R O U T I N E
6 02 0 LPRINT
6 0 3 0 LPRINT
6040
LPRINT
" ........................I N T E R N A L GAS P R O P E R T I E S ...........................
6 0 5 0 LPRINT
6 0 6 0 LPRINT " I
TMl(K)
UI(kg/m-s)
Kl(w/m-K)
PRI(-)"
6 0 7 0 FOR I = I TO 9
6 0 8 0 L P R I N T I , T MI ( I ) , U I ( I ) , K l ( I ) , P R I ( I )
6 0 9 0 NEXT I
6 1 0 0 LPRINT
6 11 0 LPRINT
6120
LPRINT
" .............. E X T E R N A L A I R
P R O P E R T I E S ....................."
6 13 0 LPRINT
6 1 4 0 LPRINT " I
TFO(K)
K(W/m-K)
V(m"2/s)
PR(-)"
6 1 5 0 FOR I = I TO 9
6 1 6 0 L P R I N T I , T F O ( I ) , K ( I ) , V ( I ) 3P R ( I )
6 1 7 0 NEXT I
6 1 8 0 LPRINT
6 19 0 LPRINT
6 2 0 0 L P R I N T " ............ N O N - D I M E N S I O N A L P A R A M E T E R S ................ "
6 21 0 LPRINT
6 2 2 0 LPRINT " I
GR(-)
NUO(-)
REI(-)
NUI ( - ) "
6 2 3 0 FOR I = I TO 9
6 2 4 O wL P R I N T I , G R ( I ) 3 N U O ( I ) 3 RE I ( I ) 3N U K I )
6 2 5 0 NEXT I
6 2 6 0 LPRINT
6 2 7 0 LPRINT
6 2 8 0 LPRINT
" ........................GAS S P E C I F I C H E A T S .........................."
6 29 0 LPRINT
6 3 0 0 LPRINT " C P l ( k J / k g - K ) = " , CPl
6 3 1 0 L P R I N T " C P 2 ( k J / k g - K ) = " , CP2
6320
L P R I N T " C P 3 ( k J / k g - K ) = " , CP3
6 3 3 0 L P R I N T " C P 4 ( k J / k g - K ) = " , CP4
6340
L P R I N T " C P 5 ( K J / K G - K ) = " , CP5
6 3 5 0 RETURN
6 3 6 0 ' S UB R O UT I NE TO OUTPUT EXTERNAL THERMAL R E S I S T A N C E AND
. HEAT T R A N F E R "
6 37 0 LPRINT
6 3 8 0 L PR I N T 11* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * n
6 39 0 LPRINT
6 4 0 0 L P R I N T " ............E X T E R N A L T H E R M A L R E S I S T A N C E ............. "
6 41 0 LPRINT
6 4 2 0 LPRINT " I
RCV( K/ W)
RRAD( K/ f f )
ROUT( K/ W) "
6 4 3 0 FOR I = I TO 9
6 4 4 0 L P R I N T I 3 R C V ( I ) , R R A d ( I ) 3R O U T ( I )
6 4 5 0 NEXT I
6 4 6 0 LPRINT
6 47 0 LPRINT
6480
LPRINT
" ..................... E X T E R N A L H E A T T R A N S F E R ............................"
64 90 LPRINT
6 5 0 0 LPRINT " I
Q C V( k W)
QRAD( k W)
Q O U T ( k W) "
6 5 1 0 FOR I = I TO 9
74
6520
6530
6540
6550
6560
6570
6580
6590
6600
6610
6620
6630
6640
6650
6660
6670
6680
6 6 90
6700
6710
6720
6730
6740
6750
6760
6770
6 7 80
6790
6800
6810
6820
6830
6840
6850
6860
6870
6880
6890
6900
6910
6920
6930
6940
6950
6960
6970
6980
6990
7 000
LPRINT I , QC( I ) , QR( I ) , QO( I )
NEXT I
RETURN
" S UB R OUT I NE TO OUTPUT R A D IA L AND EXTERNAL THERMAL
R E S I S T A N C E AND H . T .
GOSUB 6 3 6 0
GOSUB 6 5 9 0
RETURN
" S UB R O UT I NE TO OUTPUT R A D IA L THERMAL R E S I S T A N C E AND
HEAT TR A N SFER
LPRINT
LPRINT
LPRINT
" ................... R A D I A L
T H E R MA L
R E S I S T A N C E ...................... "
LPRINT
LPRINTnI
RIN(K/W)
R WAL L ( K/ W) .
R O U T ( K / W)
RTOT(K/W)"
FOR I = I TO 9
L P R I N T I , R I ( I ) , R CD ( I ) , ROUT( I ) , RTOTAL ( I )
NEXT I
LPRINT
LPRINT
" .......................... R A D I A L H E A T T R A N S F E R .............................."
LPRINT
LPRINT "I
QI N( kW)
QWAL L ( k W)
QOUTCkW)
QTOTCk W) "
FOR I = I TO 9
L P R I N T I , Q I CI ) , Q WALLC I ) , QOCI ) , QTOTALCI )
NEXT I
RETURN
' S UB R O UT I NE TO OUTPUT ENERGY BALANCE FOR
SECTIONS 5 - 8
LPRINT
L PRINT " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * "
LPRINT
L P R I N T " . . . P A R T I A L E N E R G Y B AL AN C E - S ECT I ONS CS EC. 5 - 8 ) . . "
LPRINT
L P R I N T nQ I N C k W)
QWALLCk W)
QOUTCkW)
QTOT Ck W)
Q C P ( k W) "
LPRINT
FOR 1 = 5 TO 8
LPRINT QI(I),QWALLC I ),QOCl),QTOTALCl),QCPCD
NEXT I
LPRINT
LPRINT
L PR I N T " .............. P A R T I A L E N E R G Y B A L A N C E S U M ( S E C . 5 - 8 ) ..........."
LPRINT
L P R I N T nQ I N C k W ) = " , Q C I N
L P R I N T nQWALCkW) = " , QCWA
L P R I N T nQOUTCkW) = " , QC O
L P R I N T n Q T O T C k W) = " , Q C T O T
L P R I N T nQCP Ck W) = " , QCP5
RETURN
' S UB R O UT I NE TO OUTPUT MASS FLOW, MASS AND
ENERGY BALANCE
' AND E F F E C T I V E N E S S R E S UL T S
LPRINT
L PR I N T ', * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
75
7010
7 020
7030
7040
7050
7060
7070
7080
7090
7100
7110
7120
7130
7140
7150
7160
7170
7180
7190
7200
7210
7220
7230
7240
7250
7260
7270
7280
7 29 0
7300
7310
7320
7330
7340
7350
73 6 0
7370
7 3 80
7390
7400
7410
7420
7430
7440
LPRINT
FLOW
D A T A .............
LPRINT
" .................................. M A S S
LPRINT
I F Z I < . I THEN 7 0 5 0 E L S E 7 0 7 0
L P R I N T " S H A K IN G "
GOTO 7 0 8 0
L P R I N T "NOT S H A K I N G "
LPRINT
L P R I N T " M F A ( k g / s ) = " , MFA
LPRINT " T G I ( K ) = " , T G I
L P R I N T " M L I ( K G / S ) = " , ML I
L P R I N T " C R I ( —) = " , C R I
L P R I N T "W S ( k g / k g ) = " , WS
LPRINT
LPRINT
" ................... MAS S
AND E N E R G Y B A L A N C E
LPRINT
L P R I N T "DMAS ( %) = " , DDM
L G = 1 0 0 * ( 1 - MLO/ ML I )
L P R I N T " M L l ( k g / s ) = " , ML I
L P R I N T " ML O ( I c g Z s ) = " , ML I
L P R I N T " M V l ( k g Z s ) = " , MVI
L P R I N T "MVO ( k g Z s ) = ” , MVO
L P R I N T "ML OS T ( k g Z s ) = " , DM
L P R I N T "MB AL( % ) = " , DDM
LPRINT "LIQUID GAIN(%)=",LG
I F W K . l THEN 7 2 7 0 E L S E 7 3 5 0
L P R I N T " DE NE R GY ( k W ) = " , Ql
LPRINT
LPRINT
" ............................. T O T A L H E A T L O S S ............
LPRINT
L P R I N T " Q I N ( k W ) = " , QI N
L P R I N T " QWAL L ( k W) = " , QWALL
L P R I N T " Q 0 U T ( k W ) = " , QOUT
L P R I N T "Q T O T A L (kW ). = " , QTOTAL
LPRINT
LPRINT
" ........................H 2 0 E N E R G Y G A I N D A T A
LPRINT
LPRINT " E F F l ( - ) = ", E F F l
LPRINT
LPRINT " EF F 2 ( - ) = ", EFF2
LPRINT
L P R I N T " N T U I ( - ) = " , NTUl
LPRINT
RETURN
MONTANA STATE UNIVERSITY LIBRARIES
stks N378.Izl
RL
Latent heat recovery from a counterflow
3 1762 00513708 6
M ain
N37P
Tzl
c o p .?
OATg
I z b i c k i , S t e p h e n E.
la te n t h eat recovery
f v Oy a c o u n t e r b l o w . . /
I g g U g D TO
Main
Tzl
cop. 2