che designing spiral heat exchanger - may 1970

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


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


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


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


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


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


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


8/10

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


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


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

che designing spiral heat exchanger - may 1970

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