Upload
john-urdaneta
View
245
Download
1
Embed Size (px)
Citation preview
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
1/10
Designing
Spiral-Plate
Heat Exchangers
Spiral-p,late e x ~ h n g e r s offer compactness, a variety of f,low arrangements,
efficient heat transfer, and low maintenance costs. lihese
and other features are described, along with a shortcut design method.
P. E. MINTON, Union Carbide Corp.
Spirall heat exchangers have a number of advan
tages over conventional shell-and-tube exchangers:
centrifugal forces increase heat transfer; the compact
configuration results in a shorter undisturbed flow
lengtH; relatively easy cleaning; and resistance to foul
ing: These curved-flow units (spiral plate and spiral
tube ) are particularly
useful1
for handing viscous
or .solids-containing fluids .
Spiral-Plate-Exchanger Fabrication
A spiral-plate excHanger is fabt icated from two
relatively long strips of plate, which, are spaced apart
and wound around an
open1
split center to form a
pair of concentric spiral
1
passages. Spacing is main
tained uniformly along the length of the spiral by
spacer· studs welded to the. plates.
For most services, both, fluid-flow channels are
closed by alternate channels welded
at
both sides of
the spiral plate (Fig. 1
..
In some applications, one
of the channels is left completely open (Fig. 4)
,.
the other closed at both sides of the plate
.
These
two types of construction prevent the fluids from,
mixing.
Spiral-plate exchangers are fabricated from any
material that can be cold worked and welded, such
as:
carbon steelj stainless steels, Hastelloy m and: C,
nickel and nickel alloys, aluminum alloys, titanium,
and copper alloys.. Baked phenolic-resin coatings,,
among others, protecti against corrosion from· cooling
• Although the spiral-plate and spiral-tutJe exchangers
or•
aimHar
their applications. and methods of· fobricaticm ore. quit• different;
T h i ~
article i• devoted
wholly.
to the
spital-plate
exchanger; an article in
tiM Ml ly
18 i1we of hemical
fnginH ;ng wilt
take up the
1-piral tul:Je
exchanger. ·
For
infonnation
on
aheU-and-tvbe exchangen
se. Ref. 8
9
The desion method presented is
used:
bf, Union Carbide Corp, for the
thermal and hydraulic det ign of· IP irat-p ate exchangers, and is lOme·
wllot,dilfe,...nt from that used by
the
fabricator.
water. Electrodes may also be wound into the assem.
bly
to
ano.dlcally protect surfaces a g ~ i n s t corrosion.
Spiral-plate exchangers are normally designed
for,
the full pressure of each passage. Because the turns
of the spirall are of relatively large diameter, each
turn must. contain its design pressure,, and plate thick
ness is somewhat restricted-for these three reasons,
the maximum design pressure is 150 psi.,. although
foX smaller diameters the pressure. may sometimes be
higher.
J.:.imitations
of materials of construction gov•
ern design temperature.
Flow
Arrangements
and
Applications
The spiral assembly can be fitted with covers to
provide three flow patterns:
:1)
both fluids in spiral
flows;
(2) one fluid in spiral
flow
andi the other in
· axial flow across the spiral; ( 3), one fluid: in spiral
flow and the other in a combination of axial and
spiral flow.
For spiral flow in both channels . the spiral assem.
bly includes flat covers at both sides (Fig. 1). In
this arrangement, the fluids usually
flow·
countercur
rently., with the cold fluid entering at the periphery
and Bowing toward the core; and the hot fluid enter
ing at the core andi flowing toward the periphery.
11his
type of exchanger can
be
mounted with the
axis either vertical or horizontal. It finds wide
application in liquid-to-liquid service,. and for gases
or condensing vapors if the volumes are not too large
for. the maximum flow area of 72 sq. in.
or spiral flow in one channel and axial
low
in
the other the spiral assembly contains conical covers,
diShed heads,
or·
extensions with, flat covers (Fig.
2).
h1 this design, the passage for axial flow
is
open. on,
both sides, and the spiral flow channel is welded on·
both sides.
This type of exchanger
is
suitable for services in·
Reprinted from CHEMICAL
ENGINEERING, May 4,. 1970• Copyright
©• 1970
by McGtaw·Hill I no.
330·
West
42nd
St
New York,
N.Y·. 10036
2030368834
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
2/10
SPI RAL·PLATE
EXCHANGERS
SPIR L
FLOW
in both channels is widely
u s e ~ i g
1
which there is a large difference in the volt.unes
of
the two liquids. This includes liquid-liquid service,
heating or rooling gases, condensing vapors,
or
as
reboilers.
It
may
be
fabricated with one or more
passes on the axial-flow side. And it can
be mounted
with the axis of the spiral either vertical or hori
zontal (usually vertically' for condensing or boiling)'·
For
combiMtion flow a conical cover dist:ibutes
the fluid into its passage (Fig. 3). Part of the spiral
is closed at• the top, and the entering fluid flows
only through the center part
of,
the assembly; A
flat•
cover at the bottom• forces the fluid to ow spirally
before leaving the exchanger.
This type is most· often used for condensing vapors
(mounted
vertically)'· Vapors rst flow axially until
their volume is reduced sufficiently for finali condens
ing and subcooling in spiral flow.
A modification of this type:
the
column-mounted
condenser (Fig. 4). A bottom extension
is
flanged
to· mate wi th the column. flange. Vapo r flows
upward
through a large central tube and:
then
axially across
the spiral, where t is condensed. Subcooling may
be
by f a l l i n g ~ f i l m cooling or by controlling a level
of condensate in the channel. In
the
latter case, the
vent• stream leaves in
spiraf
flow. This type is also
designed to allow condensate to dropointo
an
accumu
lator without appreciable subcooling.
lOW
is spiral in one channel axial in other .-Fig. 2
The spiral-plate exchanger offers
many
advantages
over
the
shell-and-tube exchanger·:
(1) Single-flow passage makes
it
ideal for· cooling
or heating sludges or slurries. Slurries can. be proc·
essed in the spiral at velocities as low as 2 ft./sec.
For
some sizes and: design pressures, eliminating the
spacer studs enables the exchanger to handle liquids
having a h igh content. of fioers.
(2) Distribution is good because of the single-Bow
channel.
{3) The spiraHplate exchanger. generally fouls at
much lower rates tlian the shell-and-tube exchanger
because of the single-How passage and curved-How.
path. If it fouls, it can be effectively cleaned chemi
cally because of the single-How path
and
reduced
bypassing. Because the spiral can also be fabricated:
with identical passages, it
is
used for services in•
which the switching of fluids allows one fluid to
remove the scale deposited by the
other .
Also, be
cause the maximum' plate
width is
6
ft. .
it is easily
cleaned with. High-pressure water or steam.
(4). This exchanger is well suited for heating or
cooling viscous fluids because its LID ratio is lower·
than. that; of tubular exchangers. Consequently, lam•
inar-flow heat .transfer is much higher for spiral plates.
When' heat ing or cooling a viscous fluid,
the
spiral
should be oriented with the axis horizontal.
With
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
3/10
COMBIN nON
FLOW
is
used
to condense vapors Fig. 3
the
uis
verticaL the viscous fluid stratifies and
t is
reduces heat transfer
as
much
as
50%.
(5)' With both fluids fl.owing spirally, flow can
be countercurrent (although not truly so, because,
throughout the unit, each channel is adjoined
by
an
ascending and a· descending turn of the other
chan-
nel and because heat-transfer areas are not equal
for each side of the channel, the diameters. being
different). A correction factor may be applied;l
o w ~
ever, it
is
so
small' it can generally be ignored.
Countercurrent flow and' long passages make pos
sible clbse temperature approaches and precise tem
perature control.
{6) The spiral-plate exchanger avoids problems
associated with differential thennal expansion in non
cyclic service.
7) In axial flow, a large_flow area affords a low
pressure. drop, which becomes especially important
when condensing under vacuum.
(8) This exchanger
is
compact:
2;000
sq. ft.
of
heat-transfer· surface in a 58-in.-dia. unit' with a 72-
in.-wide plate .
Umitations
Besides
Pressure
In addition to the pressure limitation· noted earlier,
the spiral-plate exchanger also
has
the followimg
disadvantages:
{1 ) Repairing it in the field
is
difficult. A leak
cannot
be
plugged
as
in a s h e l l ~ a n d t u b e exchanger
(however, the possibility of; leakage in a spiral is less
because it is fabricated from' plate generally much
thicker than tube walls). Should a spiral need repair
ing, removing the covers exposes most of the welding
CHEMICAL ENGINEERING/MAY
4
1970
MODifiiED
combination flow serves on c o l u m ~ g 4
of the spiral assembly. However, repairs on the inner
parts of the plates are complicated. ·
(2) The spiral•plate exchanger
is
sometimes pre
cluded
from
serviee in which thennal eyclmg
is
frequent. When used in cycling services, its mechani-.
cal. design sometimes must• be altered to provide. for
much higher stresses. Full-faced gaskets of com
pressed asl:lestos are not generally acceptable for
cycling services because the growth' of the spiral
plates. cuts the g a s k e t ~ which results in' excessive
bypassing and; in some cases,. erosion of the cover.
Metal-to-metal seals are generally necessary.
(3)
This
exchanger · usually should not
be
used
when a hard deposit forms during operation,
be- ·
cause the spacer studs prevent such' deposits hom
being easily· removed by drilling. When
1
as £or
some
pressures,. sucli studs can be omitted, this .imitatiOn
is
not present'
(
4)
For spiral-axial' flow, the temperature difference
must be corrected. The conventionali correction for
cross
flow
applies. Fluids are not mixed\ flows are
generally single pass. Axial B ow may be multipass.
SHORT tUT RATING METHOD
The shortcut rating method for spiral-plate ex-
changers depends on the same technique as that
2030368836
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
4/10
SPIRAL-PLATE EXCHANGERS
• • •
Empirical Heat-Transfer
and
Pressure-Drop Rel ationshi .p
Eq.
No. Mechanism or Restriction
EmpiricaliEquation-HeatTransfer
Spiral Flow
l ) No phase change
( l i q u i d ~ ' •
N ••
>
N
11
u
h
=
(11 + 3:54.D, Du) 0 ~ 0 2 3 c G
(NM.)-• ~ P r ) - '
{2)
No phase change (gas),N11. > N
11
h =
(11
+ 3.54 D /D
} 0.0144
cG• •(D,)
-•.:
(3)
No phase change ( liquid), NR., < N
< • · ·
Spiral
or
Axial Flow
(4) Condensing vapor, vertical,
Na.
< 2,100
k
= 0.925
k
[gcpL'IJ 10,000
1
n
No phase change
(gas). NRe
>
10,000
(8) Condensing vapor, horizontaH N
R•
< 2,100
(9) Nucleate boiling, vertical
Plate
(10)
Plate , sensible heat
transfer
(11)
Flate,
latent
heat
transfer
Fouling
(12)
Fouling, sensible
heat transfer
(13)
Fouling, latent hea t transfer
Eq.
No.
Mechanism or Restriction
Spiral Flow
(14)
No phase change, N > N
11..-
1 5 ~ ,
No phase change, 100 <
N
11
, <
Nt..c
(Hi)
No phase change,
N11. < 100
(17)
Condensing
AxiaJIFiow
(18) No phase change, N
11
, > 10,000
(19)
Condensing
Notes:
1. NR..- =
20,000(D,/D/1)
0
"
2
. G
=
W.pd(Ap,,)
h
=
0.0144 c G · .
(D.)
-• :
I t= 12 k ./p
h =
12 k. /p
h
=assumed
h
=assumed
E Tlpirical E q u a t i o n > - ~ r e s s u r e Drop
aP
=
0:0011
[ d ~ r Ld,
1
1
- ; ; 5 )
( ~ r · + 1.5
+ ~ ]
L [-W Jl
[
1.035 Z '· ( ~ ) . · (.#-)'
,-
,1
t> P
=
0
·
001
s
d ~ H -t; 0.125)
W
+ 1.;>
-
t> P
= 3 , 3 8 ~ ~ ~ , :
(i;J (
L [ W ]• [ 1.3
z•;•
/,H)\ 1 6]
t> P
=
0;0005
-;
d H
(d,
+
0.125)
\w
'
+
1 .5
+
L
t> P = 4 x 10-' (w)u 0.0115 z•' ..
+
1 + 0.03 H
s d ~ '
L d,
t> P
=
2
: d ~ ? ~ - . ( ~ ) '
• [
Oi0115,zo' ~
+
1
+
0.03 HJ
3. Surface-condition factor ( ~ ' ) for copper and
steel=
LO; fo r stainless steel= 1.7; for pol.ished surfaces= 2.5.
M A 2 0 ~ E E R I N G
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
5/10
for
Rating
Spiral Plate
Heat Exchangers Table I
Physical
Work
MecHanical
Factor
Property Factor Factor
Design
Factor
= 20.6
z•·• M•·•••
W ..
(T;,-TL)
X
d,
(See Note 1
)
X
.....
X
fl T
11
LH•·•
:,,
= 19.6
X
W .. (T -T,,)
X
d,
(See Note 1)
.
flT11
LH•·•
..
M'''(z,)•·
X
W
2
3
(T
11
-TL}
X
d,
(See Note
1)
=32.6
X
s '' (,z.p.u
flT
11
LH i7•
II
= 3.8
M'' Z'',
X
W'',A
X
1
X
cs•
ll.T•
£-I•H
M'' Zl'
11
W•
11
(T Td
1
1.18
X
X
X
8
. .
l l T ~ r
H•t•L•t•
= 167
z•·•4•M•· '
X
W
0
· (TH-TL)
X
d,
X
8
ll.T.
HL•·•
J
=
158 X
W•·•(TH-TL)
X
d,
ll T11
H£0·
•
11
z•l•M•ts
W''
3
A
X
1
=
16.1
X
X
ll.T.
L•t3H•r•
'
C8
2
M•··•z•·•a•·'
Pt·o r
w···A
X
d, ·'I'
(See Notes 2
and
3)
~ =
0.619
X
P ···
X
ll T11
L•·•H•·•
r .
cs•·•••
500
c
X
W ~ T H T d
X
p
X
k,
ATM
1Ii
=
278
1
X
WA
X
_.1?._
I
x·
k .
ll T11
LH
=
6 000
c
X
W(Tit-Td
X
1
,
X
h. flT11
LH
=3,333
1 WA
1
X
h
X
ll T11
X
LH
Note 1)
Note 1:)
CHEMICAL ENGINEERING/MAY 4 1970
1
2 3 368838
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
6/10
SPIRAL·Pl.ATE
. EXCHANGERS •
for
s h e U . a n d ~ t u b e
heat exchangers (which were
dis-
cussed oy Lord, Minton
and
Slusser ).
Primarily; the method combines into one relation
ship• the classical' empirical equations for fihn, heat
transfer coefficients with• heat'-ballmce equations and
with correlations tHat describe
tHe
geometry of the
heat e x c ~ g e r The resulting .overall; equation• is
recast into three separate groups.
that
contain• factors
relating to the physical properties of the fluid, the
performance or
duty
of the exchanger,
and
the
mechanical design or arrangement of the heat-transfer·
surface. These groups are then multiplied tbgether'
with• a numerical factor to obtain a product that is
equal: to' the fraction of the total driving force-or
log mean temperature difference b.Tll
or
LMTD)
that
is dissipated across each element of resistance
in the. heat-How path1
When the sum
of the products for
the
individual
resistance equa15 1,
the
trial design may be assumed
to be satisfactory for heat: transfer. The physical
significance is that the sum of the temperature drops.
across each· resistance
is
equal to the total available
t .Tll· The pressure. drops for both' f l u i d ~ flow paths
must be checked: to ensure that: both are within
acceptable limits
.
Usually, several trials are necessary
to get a satisfactbry balance between heat transfer
and pressure drop.
Table I summarizes the equations used with the
method for heat transfer and: pressure drop
The
columns on the left list the conditions to which each
equation applies,
and
the second columns. gives the
standard forms of the correlations for
.6hn
coefficients
that are found in texts.
The
remaining columns in
Table
I:
tabulate the numericaL physical property,
work and mechanical design factors-all of which
together. form tlie recast dimensional equation. 1'he
product of these factors gives. the fraction of total
temperature drop' or driving force ( J T
1
/b.T
1
)
across
the. resistance.
As stated, the sum of
t .Thl
t .T
11 (the
hot-fluid
factor),
tJ.T./tJ.TM (the
cold-fluid factor)', b.T,/b.TJI.
(the fouling factor), and AT..,/ti.T
11
(the plate factor)
determines the adequacy of: heat transfer. Any com
binations of b.T
1
/
b.T 1
may
be
used, as long as
the
orientation specified: by the equation matches that
of the exchanger's flowpath .
The units in
tHe
pressure-drop
eq1.1ations
are con
sistent with those used for heat transfer. Pressure drop
is calculated directly in psi.
Approximations and Assumptions
For
many organic liquids, thermal conductivity
data
are either· not available
or
difficult to obtain.
JSecause molecular weights ('M) are known, the
Weber equation, which, follows,. yields thermal con
ductivities. whose accuracies are quite satisfactory
for most design purposes: · ·
k -
0.86
(q#'/M ')
u;
on the other hand, the thermal conductivity
is lrnown, a pseudomolecular weight may be used:
M = 0.636 c / k ) l ~
In what follows, each of
tHe
equations in Table I'
r e v i e w ~ d ,
and the conditions in· which each equa
tion apphes, as well as its limitations, are given
1
Jn, several' cases, numerical factors are inserted or
a p p r ? x i m ~ t i o n s made,
so
as to
adapt
the empirlcal
relationshtps to the. design of spiral-plate exchangers.
Such modifications have been• made to increase the
accuracy, to simplify, or to Broaden the use of
the
~ e t h o d . Rather than by any simplifying approxima
tions,.
the
accuracy of the method is limited
by.
that
with which fouling factors, fluid properties and fab
rication tolerances
can be
predicted.
Eq:uations tor: Heat; Transfer-Spiral Flow
. Eq; 1):.-No Phase Change Liquid), NR.. > Na • --
for.
liquids with Reynolds numbers greater
than
the critical Reynolds number. Because the term
(1
+
3.54
D,IDH)
is
not constant for any given
heat, exchanger, a weighted average of 1.11 has oeen
used for• this method. If a design is selected with
a different value, the numerical factor can be. adjusted
to reflect the new value.
Eq. (2):..-No Phase Change ~ G a s ) , N
, >
NR.rc-is
for gases with Reynolds numbers greater than the
critical
ReynoiCis
number;. Because tlie Prandtl number
of common• gases
is
appromately eq)Ja) to
0178: and
the viscosity enters only as
l-'o.2,
the relationship of
physical' properties for gases is essentially a constant.
This constant, when combined with the numerical
coefficient in Eq. (I) to eliminate the physical prop.
erty factors for gases, results ih Eq. (2). As in Eq. l ).,
the term
•1
+
3.54 D,/D'H) has been taken•
·as
l L
Eq. 3)-No Phase Change
,Liquid), N
, < N
11
-
is for liquids in laminar
Bow,
at moderate ~ and
with' large kinematic viscosity
p.Lfp). The
accuracy
of the correlation, decreases as the operating conditions
or the geometry of, the heat-transfer surface are
changed
tQ
increase the effect of natural convection.
For a spiral
plate:n
(D/L)1
11
= [12
112
D,j(DHd,) •J '
= 2 '
(d,/dn)•
The value
of
(d,/d; )1 6 varies from 0.4 to 0;6. A value
of o s for
d.ldH)
1
'
8
has been used for this method.
Heat Tramsfer
Equations-Spirator
Axial Flow
Eq. 4}-Cond.ensing Vapor,. Vertical, NR..
<
2,100
- is for film condensation of vapors on a vertical
plate with a terminal Reynolds number
( 4 1 J / ~ )
of·
less than'
2,l00.
Condensate loading
(or)
for veftical
plates is II =
W/2L.
For Reynolds numbers above
2,100,. or fbr high Ptandtl numbers, the equation
should be • adjusted
by
means of the Dukler plot,
as discussed by Lord, Minton, andi Slusser.s
To
use
Eq. (4) most conveniently, the constant in it should
be multiplied by the ratio of the value obtained
by
the Nusselt equation to the Dukler plot.
1 he preceding only applies to the condensation
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
7/10
of
condensable vapors. Noncondensable gases in, the
vapor decrease the 1m coefficient, the reduction
depending on the relative sizes a£ the gas-cooling
load and the total cooling and condensing duty.
(A method for analyzing condensing in the presence
of noncondensable g ~ ~ e s
is discussed
by Lord, Minton
and S l u s s e r ~ }
Eq
5)-Condensate Subcooling, Vertical,.
Na.
<
2,100-is fbr laminar films flowing in layer form down
vertical plates.
ThiS
equation is used when, the. con
densate
from a vertical condenser is tb be cooled
below the bubble point. In, such cases, it
is
con
venient to treat the condenser-subcooler as two
separate heat exchangers-the first operating only as
a condenser, (no subcooling), and the second as a
liquid cooler
only.
Fig. 5 shows the assumptions that
must be made to determine the height of each section,
so
as to calculate intermediate temperatures that will
permit in, fum the calculation of the LMTID. ·
Eq. (4)
is
used in combination with appropriate
expressions for other resistances to heat transfer, tb
calirulate the height of the subcooling section. In tlle
case of the subcooling section only (See Fig. 5), the
arithmetic mean temperature · difference,, [ (
Thm -
T..,.) + ThL - T.L)]/2, of the two fluids should
be used instead of the log mean temperature dif-
ference .
Equations for Heat
Transfer-Axial
Flow
Eq.
6)-No
Phase Change Liquid)l NR., > 10;000
- is for liquids. with Reynoltls numbers greater than
Hl OOO;.
Eq. 7)-No Phase Change Gas),. NR., > 10,000-
is for. gases with Reynolds numbero greater than
10,000 Again, because the physical property factor
for common, gases is essentially a constant,
thiS
con
stant
is
combined with the numerical factor in
Eq.
:6)
to get Eq,
7).
stiBCOOUNG·ZONE calculations
depend on arittlmetic·mean tem·
perature difference of, the tWo
fluids instead of log·mean tem·
perature differenoes-Fig. 5
CHEMICAL ENGINEERING/MAY 4,
1970
Condensing
zone
Eq.
8)-CondenMg
Vapor . HorU:ontal Na. <
2,100-is for 1m condensation on spiral plates ar-
ranged for horizontal axial flow witli a terminal
Reynolds number a£ less than 2,100. For a spiral
plate, eondensate loading
r)
depends on the length
of the plate and spacing between adjacent plates.
For
any given plate length and channel spacing, the
heat-transfer
area
for each 360-deg. winding of the
spiral fucreases with the diameter
of
the spiral. The
number of revolutions affects the eondensate load
ing in two ways: (
1
the heat-transfer area changes,.
resulting in more condensate being formed in the
outer spirals; and (2) the effective length over which
the condensate
is
formed is.determiiled by the number
of revolutions and the plate width. Ilhe. equations
presented depend: on a value for the effective number
of spirals
of: L/7.
Therefore,. the eondensate load
ing is given by:.
W (1,000) 7 12)/4HL- 21,000 W/HL
This equation can be corrected
i f
a design is. obtained
with a significantly dilferent condensate loading.
It
does not include allowances for turbulence due
to vapor-liquid sHearing or splashing
of
the con
densate. At high condensate loadings, the liquid
condensate on the bottom of the spiral channels may
blanket part of the exchanger, s effective heat-transfer
surface.
Eq. 9)-Nucleate Boiling, Vertical-is for nucleate
boiling on vertical plates. In a rigorous analysis of
a thermosyphon reboiler, the calculation of heat
transfer
is
combined with the hydrodynamics of the
system to determine the circulating rate through the
reboiler. How.ever,
for
most design purposes,
tliis
calculation is not necessary. For atmospheric pres
sure and higher, the assumption, of nucleate boiling
over the full height of the plate gives. satisfactory
results.
The
assumption of nucleate boiling over the
entire height of the plate in. vacuum service produces
overly optimistic results. (The mechanism of thermo-
2 3 36884
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
8/10
SPIRAL·Pl.ATE EXCHANGERS • • •
syphon reboilers has been already discussed by Lord,
Minton and
Slt1sser.s.
)
A surface condition factor, I, appears. in the empiri·
cal
correlations for boiling coefficients. This. is a
measure
of,
the number of nucleation sites for, bubble
formation on the heated surface. The equations
for
t .Tt/tl.TII contaim,I' (the reciprocal of I) , which
Has
values of 1.0 for copper and steel, 1.7 for stainless
steel or chrome.nickel alloys, and 2.5 for polished
surfaces.
Equations for Heat Transfer-Plate
Eq. ~ 1 0
and
llrHeat Transfer Through the
Plate-are for calculating the plate factor. The inte
grated form of the Fourier equation
is QlfJ =
k..,A
tl.'Pw)/X, with X the plate thickness. Expressed in
the form of a heat-transfer coefficient;
hw
= 12k..,/p.
Eq. (10) is used whenever sensible heat transfer
i. i
involved for either fluid. Eq. (H) is usedi when
there is latent heat transfer for each fluidl
Equations for Heat Transfer-Fouling
Eq.
(12)
and
13)-Fouling-is
for conduction of,
heati through scale or solids deposits.. Fouling co•
efficients are selected by the designer,. based upon
his experience. Fouling coefficients of 1,000 to 500
(fouling factors ofi 0.001 to 0.002) normally require
exchangers 10 to' 30% larger than for
clean
service;
The selection of, a fouling factor is arbitrary be-
cause there is usually insufficient data for accurately
assessing the degree of fouling that should
be
assumed
for a
(itiven
design. Generally, fouling for a spiral
plate exchanger' is considerably less than for shell
and-tube exchangers. Because fouling varies with
material. velocities and temperature, the extent to
which this influences design depends on operating
conditions and,
to
a great degree, the design· itself.
Eq. (12)
iS
used for sensible heat transfer for
either fluid, and Eq . (
13)
when latent heat is
trans
ferred' on both sides ofi the. plate;
Equations for; Pressure
r o ~ S p i r a l Flow
Eq
.
U)-No
PhDse
Change Nth > N
a
..
iS
based
on equations proposed by Sander.
4
•
12
'Ilerm A in
Sander's equation €an be closely approximated by.
the value of 28/(d.
+
0.125). Term
B
in Sander's
equation accounts for the spacer studs. The factor
1.5 assumes 18 studs/sq. ft. and a stud dia. of
5/16
in.
Eq. 15)-No Phase Change 100 < Na, <
Na,.
again is based upon the equation proposed by Sander.
For, this flow regime, the. term
A can
be closely
approximated' by the 'lalue of
103.5/(d, +
0.125).
As in Eq (14h the factor of
1.5
accounts for the
spacer studs.
Eq. 16)-No Phase Ch4nge N
2
,
<
JOO:..aJso
is
based on the Sander eq1.1ations. For this flow regime,,
term
A
can be closely approximated by the value of
2,170
d
1
I.'f5. For this flow regime, the studs have
A
B
c
c
D.
D.
D.
d
I
G
g.
H
h
k
L
M
p
p
t:J
Q
s
u
w
r
z
6
Nomenclature
Heat-transfer area,
sq.
ft.
Filln thickness (:0J00187,
z r/g
r
11
,.ft.
Core dia., in.
Specific liea.t, l3tu./ (lb.) ("F.)
Equivalent dia.,
ft.
Helix
or
spi.ral dia ., R
Exchanger
outside
dia.,in .
Channel spacing, in.
Fanning friction
facto r, dimensionless
Mass
veloeity,lb./(hr.H Iq.
Gravitational constant,
ft,./. (hr.)• (4.18
x
1:0 )
Channel plate wi.dtli, in.
Film coefficient
of heat
t:ransfer.,.
Btu./
(hr.) (sq. ft.) (•F.)
Thermal conductiVity, Btu./{hr.) (sq ft.)
(•F;fft.)
Plate
length,
ft.
Molecular weight, dimensionless
Pressure, psia.
Plate
thickness; in.
Pressure
drop,.psi.
Heat transferred,
Btu.
Specific
gravity (referred
to water
at
20 C.)
Logarithmic mean
temperature
difference
·· (LM'IlD),
•c.
Overalll
heat-transfer
coefficient, Btu./.
(hr.)
(sq.
ft.) eF.)·
Flowrate,
(lb./hr.) /1,000
Condensate loading, lb./.
(hr.) (ft.)
Viscosity, op.
Time,
hr.
A
I
Heat of
vaporization,
Btu./lb.
Viscosity, lb./.(hr.)
(ft.)
Liquidldensity, ll:L/cu1ft.
Vapor density, lb.f.cu.ft.
I
P•
I:, I:
IT
Surface
condition factor, dimensionli ss
Surface
tension, dynes/em.
Subscripts
Built fluid propertie s
c
Cold
stream
I Film
fluid properties
. H
High temperature
h
Hot
stream
L
.IJ.ow temperature
m Median
temperature 1see
Fig. 5)
s Scale or fouling
material
w
Wall, plate material
Dimensionless Groups
N
•• Reynolds number
N
Critical Reynolds number
Nr.r Prandtl number
little effect· on the pressure drop,. and any such effect
is included' in the Sander equation.
Eq;
17rCondensing-is
for calculating the pres
sure drop
for·
condensing vapors and is identical to
that for
no
phase change, except for
a
facto11 of
0.5 used with the condensing equation. For total
condensers, the weight rate of
flow
used
in
the
calculation should be the inlet flowrate. Because the
average
Bow
for partial condensers is greater than
MAY 4,.1970/CHEMICAL ENGINEERING
2 3 368841
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
9/10
far total condensers,. the multip]ymg factor should
be 0.7 instead of 0.5. Because the estimation of the
pressure drop for condensing vapors is not clear-cut,
the equation should be used only to approximate
the. pressure drop, so
as
to prevent the design of
exchangers with, excessive. pressure losses.
Equations for Pressure Drop--Axiali Flow
Eq :18}-No Phase Change
N., >
10,000-is
an
expression• of the Fanning equation for
n o n c o m p r e s s i ~
ble fluids,.in which the friction factOr f in, the Fanning
equation = 0.046/N.,u.
The
equation
has
been
revised
to•
account for pressure lbsses in the inlet
and outlet nozzles, and the irnlet and outlet
heads.
The equation also, includes the correction for the
spacer studs in
the flow. eliannels.
Eq. (19}-Conden.ring-again
is
identical
to, that
for no phase change, except for a factor of 0.5. Again.
for partial condensers,. a value of 0.7 should be used
instead of 0.5. For condensing pressure drop, only
approximate results. should:
be
expected, which them
selves should be used only to prevent designs that
would result
in
excessive pressure losses.
For overhead condensers, the pressure drop in
the center tube must
be
added to the pressure drop
calculated from
Eq.
(19).
SAMPLE CALCUlATIONS
This example applies the rating method to the
design of a
l i q u i d ~ J i q u i d
spiral-plate heat exchanger
under the following conditions:
ConditiODs
Hot Side Coldi Side
Flowrate,
lb. /hr . . . . . . . . . . . . . . . . .
6,225 5,,925
Inlet temperature,
•c.. . . . . . . . .
200 60
Outlet temperature, •c..
. . . . .
I20 I
50.4
V:iscoeity, cp. . . . . . . . . . . . . . . . . . .
3.
35' . 8
Specific heat, Btu./lb.;oF.... ... . ... 0.71
0.66
Molecular, weight.... . . . . . . . . . . . . . 200.4 200.4
Specific ~ V f o v i t y ... 0 843
liL843
Allowable yressure
drop,
psi.. . . . . . I I'
Material o construction
. . . . . . . . . . .
stainless steel
(k
-
Ul)
Z,/z.)u•:
. . . . . . . . . . . . . . . . . . . . . I I
Preliminary Calculations
Heat transferred
= 6
1
225 X (200-120) X 1.8 X
0,11: = 636,400 Btu./hr.
t.T
11
(or LMTD)
• -
49.4)/ln 60/4U) •
54.5
C.
For a flrst trial, the approximate surface can be
calculated' using an assumed overall heat-transfer
coefficient,
U
of
50
:Btu./(hr.)
sq .
ft.)
°F.):
A -
636,400/(50 X I.8 X 54.5)
=
I30
sq. ft.
Because this is a small exchanger, a plate
width
of 24 in.
is assumed. Therefore,
L = i30/
2 X
2). =
3 2 ~ 5
ft.
A channel spacing of
in.
for both. fluids
is also assumed. The Reynolds number for spiral flow
can be calculated from the expressiont
N
•• '
IO,OOO (JV/HZ)
Therefore:
CHEMICAL ENGINEERING/MAY 4, 1970
Hot side
Na. • (10,( )()()
X 6.225/ 24 X 3.35) •
714
CoiC I
aide
Na, •
(lOiOOO X 5.925)/(24 X 8) • 309
Because the ftuids willi be in· lamimar flow, spiral
flow is selected for the heat exchanger design. From
Table I, the appropriate expressions for rating are:
Eq.
(3)
for both fluids, Eq.
(10).
for the plate,
Eq, (12) for fouling
and
Eq. 15) far pressure drop.
Heat-Transfer Calculations
Now; substitute values:
Hot side, Eq. 3):
~ T . . .
-
32.6[ ~ ] .
X
aTJI 0:843 ..
,
[
· ~ 5 ~
80
J
~ · ~ ~ 2 5 ]
• 32.6 X3.775
X
4.967
X
0.001387, • 0.848
Colli side, Eq.
3):
aT
_ ·[ 200.4
1
111
] 5.925
111
X9C:U ] X
t: TM
32.6 0.843' ... . 54.5
[
0.375
J
24111
X
32.5,
=
32.6
X
3.775
X
5.431
X
0.001387 • 0.927
Foulin.g, Eq. ( 12):
t:.T,
_
6
OOO f.
0J66
J [ 5.925
X
90.4 J [ . I J
t TJI
- ,
L
,000 54.5 32.5
X 24
• 6,000 X 0;00066 X 9.828 X 0.001282 • 0.050
Flate,. Eq. (10):
E ·
..
500
[ ~ 6 6 - J f
5.925 X
9CMJ
[ O.I25 ]
t:. /111 10
•
L
54.5 32.5
X 24
= 500
X
01066
X
9.828
X
0.0001603 • 0.052
Some Spi,r,ai-Piate
Exchanger;
Standar;ds-Table
Ill
Plate
Outside 018.,
Core
Widths,, lin.
Maximum, .lin.
Dia.,ln
.
4
32
8
6
32
8
12
32
8
12 58
l2
18
32
8
18
58
12
24
32 8
24
58 12
30
58
12
36
58
12
48
58
12
6C 58 12
72
58
12
ahannel spacings, in.: 3/16 (12 in. maximum width.),
114 48 ;n.
maximum width),
5/16,
. . .
3f4
and:
l
Plate thiCknesses: stainless steel) 14-3 U.S. gage; car·
bon steel, 3/16, 114 and 5/16 in.
o3oasss4
8/17/2019 CHE Designing Spiral Heat Exchanger - May 1970
10/10
SPIRAL·PLATE EXCHANGERS
Sum of Products
(SOP):
SOP
=
0.848
+
0.927
+
0.050
+
0.052
=
1.877
Because S0P
is
greater than
1,
the assumed: heat
_xchanger is inadequate. The smface • area must
be enlarged by increasing the plate width or the
plate .length. Because, in all the equations
1
L applles
directly, the follbwing new length is adopted:
1.877 X 32.5 -
61i
ft.
Pr essur;e-Drop
Cal.culations
Hot side, Eq. (15):
p . .
[
0.001 X.61 ] [ - 6 · ~ ] X
0;843 0.375 X 24
[
1.035 X 3.35
112
X 1 X 24
112
16 J
(0.375+
0.125) 6.225
1
12 +
1.
5
+ 6f
t:.P
· 0.07236
X
0.6917
X
9.202
=- 0J461i
psi.
Cold side, Eq . (,15):
t:.P
.. [1).(101 X 61
J [ - - 5 . 9 ~ ]
X
0.843 0.375 X 24
f 1.035 X 8
11
: X 1 X 24
112
, 16]
t
(0.375
+
€1.125) 5.925112
+
LS+ 61
t:.P = 0.07236 X 0.6583 X 13.55 = 0.645 psi.
Because the pressure drop
is
less than the allowal:lle;
the spacing
can•
be decreased. For the second trial,
¥ in. spacing for
botH
channels
is
adoptedl
Because the Heat-transfer· equation for every factor
except the plate varies directly witH
d
a new SOP·
can be
c a l c u l a t e d ~
t:.Tl/llTM
""
0.848 (0.25/0.375) = 0.565
tJ.T;/tJ.7 M
=
0.927 (0;25/0.375) = 0.618
t:.T /ATII
=
0.052 (0;25/0.375)
=
0.035
tJ.T,./tJ.TM
= 0.050
SOP - 0;565 + 0.618 + 0.050 + 0.052 == 1.285
L
=
1.285 X 32.5
=
41.8
ft.
A =
41.8 X 2 X 2
=
167 sq.
ft.
The new pressure drop becomes:
Hot side:
l l
[' 0.001 X41.8 J [ - · 6 · ~ ~ ~ - ] X
0.843 0.25 X 24
[
1.035 X 3.35
112
X 1 X
24
112
16 ]
M75
X 6.225112
+ ·1.
5
+
411:8-
tJ.P
- 0;04958 X 1.037 X 11.80 = 0.607 psi.
Colo· side:
tJ.P _ [·
o . o o ~ _ 4 h 8 ~ ]
5.925_.]
x
0.843 ' 0.25 X 24
[
D.035 X 8
112
X 1 X 24
112
16 .]
--o37sx 5.92511··- -- + 1.
5
+ ·us
AP
=
0.04958 X 0.9875•X 17.59
=
0.8611
The pressure drops are less than the maximum
allowable.
The
plate spacing cannot be less than
¥ in. for a 24 .in. plate width; decreasing the width
would result:
in
a higher than allowable pressure drop.
Therefore, the design is accept:able.
The diameter of the outside spiral can now be
calculated with Table and the following equation:
Ds = [15.36 X L (d,.
-t
d;, + 2p) +
Q2jtl•
Ds
=
115,36
4L8)
[0,25 + 0:25 + 2 (0.125)) + 8
1
11
2
Ds-=
23.4 in.
For a spiral-plate exchanger, the best design• is
often• that•
in.
which• the outside diameter approximately
equals the plate width.
Design summary:
Plate
width..
. . . . .. .
..
. .. . 24 in.
Plate
length..............
. . . 41.8 f t
Channel
spacing... . . . . . . . . . 1/4
in
.
(both sides)
Spiral diameter.. .. . . . . . . . 23.4 in .
Heat-transfer area... . . . . . . 167 sq. ft.
Hot-side pressure drop . . . . . 0.607 psi.
C o l d ~ s i d e pressure drop
. . . .
0. 861 psi.
U... ... . . . . . . ... . . . . . . ... . . . 38.8 Btu./(hr.)(sq.ft.)("F.)•
•
Acknowledgements
The author thanks American
Heat
Reclaiming Corp.
for.
providing figures and for permission to use certain
design.standards. He
is
also grateful to the Union Car
bide Corp
.
for permission
to
publish this article.
References
H Baird, M. H. I..
MoCrae,
W .. Rumford. F .. and S l e .
C. G. M.. Some Consldera.tlon"
on
Heat Tm.naofer
In
SpLI"al Plate Heat
Exchangers, Chem. Eng.
Science., 7,
1 and 2, 1957, p. 112.
2.
BLasius,
H..
Dae .\hnlichkeit.sgesets bel Rlebunpvor
gangzen
in
Flussigkeiten, Fonol uug81 e/t.
Ul,
1913.
3.
C o l b u ~ n , . A . P .. A Method of CoJ:TelaUng F o r c e d • C o n W ~ e
tlon
Heat
TTansfer
Da.ta
and
e.
Comparison
With
Fluid
F'rlot.lon, A.ICI F: TMM., 9, 1'933, p. 1174.
4: HargiS, A. M ...
Beok.mann, A.
T.
and Lola.oonoa., JL J.,.
Applica.tion6 of
Spiral'
Plate
Heat: Ex