CHAPTER 5

DESIGN FUNDAMENTALS OF GASKETED-PLATE HEAT

EXCHANGERS

5.1 INTRODUCTION

Manufacturers of gasketed-plate heat exchangers have, until recently, been

criticised for not publishing their heat transfer and pressure loss correlations.

Information which was published usually related to only one plate model or was

of a generalized nature. The plates are mass-produced but the design of each plate

pattern requires considerable research and investment, plus sound technical and

commercial judgement, to achieve market success. As the market is highly

competitive the manufacturer’s attitude is not unreasonable.

Some secrecy was lifted when Kumar [26] published dimensionless

correlations for Chevron plates of APV manufacture. The Chevron plate is the

most common type in use today. If additional geometrical data are available from

the makers, the correlation enables a thermal design engineer to calculate heat

transfer and pressure drop for a variety of Chevron plates. Although the data have

been provided by one manufacturer, and should only be applicable to these plates,

it is reasonable to assume that all well-designed plates of the Chevron pattern

behave in a similar manner.

Whatever function is required from a gasketed-plate heat exchanger,

ultimately the manufacturers must be consulted to ensure guaranteed

127

performance. Only they can examine all the design parameters of their plates to

achieve the optimum solution.

As a result, the design of gasketed-plate heat exchangers is highly

specialized in nature considering the variety of designs available for the plates and

arrangements that are possible to suit varied duties. Unlike tubular heat

exchangers for which design data and methods are easily available, a gasketed-

plate heat exchanger design continues to be proprietary in nature. Manufacturers

have developed their own computerized design procedures applicable to the

exchangers marketed by them. Attempts have been made to develop heat transfer

and pressure drop correlations for use with plate heat exchangers, but most of the

correlations cannot be generalized to give a high degree of prediction ability. In

these exchangers, the fluids are much closer to countercurrent flow than in shell-

and-tube heat exchangers. In recent years, some design methods have been

reported. These methods are mostly approximate in nature to suit preliminary

sizing of the plate units for a given duty. No published information is available on

the design of gasketed-plate heat exchangers. [7, 4]

5.2 PLATE GEOMETRY

5.2.1 Chevron Angle

This important factor, usually termed β , is shown in Figure 5.1 [7, 4], the

usual range of β being 25°-65°.

128

Figure 5.1 Main dimensions of a Chevron plate

5.2.2 Effective Plate Length

The corrugations increase the flat or projected plate area, the extent

depending on the corrugation pitch and depth. To express the increase of the

developed length, in relation to the projected length (see Figure 5.2 [7, 4]), an

enlargement factor φ is used. The enlargement factor varies between 1.1 and

1.25, with 1.17 being a typical average [7, 30], i.e.

(5.1) length projectedlength developed

=φ

129

Figure 5.2

Chevron p

troughs

The value of φ as

specified by the ma

where can be apA1

and and ca

diameter as:

pL wL

pD

Developed and projected dimensions of a

late and cross-section normal to the direction of

given by Eq. (5.1) is the ratio of the actual effective area as

nufacturer, , to the projected plate area : [7, 4, 30] 1A pA1

(5.2) A

pA11=φ

pproximated from Figure 5.1 as:

(5.3) LL ⋅ wppA =1

n be estimated from the port distance and and port vL hL

(5.4) D− pvp LL ≈

(5.5) D+ phw LL ≈

130

5.2.3 Mean Channel Flow Gap

Flow channel is the conduit formed by two adjacent plates between the

gaskets. Despite the complex flow area created by Chevron plates, the mean flow

channel gap b , shown in Figure 5.2 by convention, is given as: [7, 4, 30]

(5.6) tp −b =

where p is the plate pitch or the outside depth of the corrugated plate and t is the

plate thickness, b is also the thickness of a fully compressed gasket, as the plate

corrugations are in metallic contact. Plate pitch should not be confused with the

corrugation pitch. Mean flow channel gap b is required for calculation of the

mass velocity and Reynolds number and is therefore a very important value that is

usually not specified by the manufacturer. If not known or for existing units, the

plate pitch p can be determined from the compressed plate pack (between the

head plates) , which is usually specified on drawings. Then cL p is determined as

[4, 30]

(5.7) L

t

c

Np =

where is the total number of plates. tN

5.2.4 Channel Flow Area

One channel flow area is given by [7, 4, 30] xA

(5.8) bLwxA =

where is the effective plate width. wL

131

5.2.5 Channel Equivalent Diameter

The channel equivalent diameter is given by [7, 4] eD

(5.9) ( )w

xe P

AD 4surface wetted

area flow channel4==

as ( ww LbP )φ+= 2 . Therefore, Eq. (5.9) can be written as

(5.10) ( )( )w

we Lb

bLDφ+

=2

4

In a typical plate, b is small in relation to , hence: wL

(5.11) 2= φbDe

5.3 HEAT TRANSFER AND PRESSURE DROP CALCULATIONS

5.3.1 Heat Transfer Coefficient

With gasketed-plate heat exchangers, heat transfer is enhanced. The heat

transfer enhancement will strongly depend on the Chevron inclination angle β ,

relative to flow direction, influences the heat transfer and the friction factor that

increase with β . On the other hand, the performance of a Chevron plate will also

depend upon the surface enlargement factor φ , corrugation profile, gap b , and

the temperature dependent physical properties especially on the variable viscosity

effects. In spite of extensive research on plate heat exchangers, generalized

correlations for heat transfer and friction factor are not available.

Any attempt for the estimation of film coefficient of heat transfer in

gasketed-plate heat exchangers involves extension of correlations that are

132

available for heat transfer between flat flow passages. The conventional approach

for such passages employs correlations applicable for tubes by defining an

equivalent diameter for the noncircular passage, which is substituted for diameter,

. [4] d

For gasketed-plate heat exchangers with Chevron plates, some of selected

correlations for the friction factor , and the Nusselt number , are listed in

Table 5.1. [15] In these correlations, Nusselt and Reynolds numbers are based on

the equivalent diameter (

f

)

Nu

bDe 2= of the Chevron plate.

As can be seen from Table 5.1, except the correlation given by Savostin

and Tikhonov [16] and Tovazhnyanski et al. [20], all the other correlations give

separate equations for different values of β and do not take into account

specifically the effects of the different parameters of the corrugated passage.

The channel flow geometry in Chevron plate pack is quite complex, that is

why, most of the correlations are generally presented for a fixed value of β in

symmetric ( β = 30 deg/30 deg or β = 60 deg/60 deg ) plate arrangements and

mixed ( β = 30 deg/ 60 deg ) plate arrangements. The various correlations are

compared by Manglik [15] and discrepancies have been found. These

discrepancies originated from the differences of plate surface geometries which

include the surface enlargement factor φ , the metal-to-metal contact pitch , and

the wavelength , amplitude , and profile or shape of the surface corrugation

and other factors such as port orientation, flow distribution channels, plate width

and length. It should be noted that in some correlations, variable viscosity effects

have not been taken into account.

P

cP b

133

134

As can be seen from Table 5.1, both heat transfer coefficient and friction

factor increase with β . From the experimental data base, Muley et al [14] and

Muley and Manglik [13,33] proposed the following correlation for various values

of β :

For 400Re ≤

14.03/15.0

38.0

PrRe30

44.02

==

w

b

khbNu

µµβ

(5.12)

2.05

5.0

583.0

Re28.6

Re2.30

30

+

=βf (5.13)

For 800Re ≥

[ ]( )[ ]

14.0317.390/2sin0543.0728.025 PrRe10244.7006967.02668.0

×+−= ++−

w

bNuµµββ πβ

(5.14)

(5.15) [ ] [ ]{ }1.290/2sin0577.02.023 Re10016.21277.0917.2 ++−−×+−= πβββf

The heat transfer coefficient and the Reynolds number are based on the

equivalent diameter . To evaluate the enhanced performance of Chevron

plates, prediction from the following flat-plate channel equations [13] is compared

with the results of the Chevron plates for

( bDe 2= )

29.1=φ (surface enlargement factor)

and 59.0=γ (channel aspect ratio, cPb2 ).

( ) ( ) ( )( )

>

≤=

−

4000Re PrRe023.0

2000Re PrRe849.114.0318.0

14.03131

wb

wbedLNuµµ

µµ (5.16)

(5.17) ≤ 2000

>=

2000Re 0.1268ReRe Re24

0.3-f

135

Depending on β and Reynolds number, Chevron plates produce up to five

times higher Nusselt numbers than those in flat-plate channels. The corresponding

pressure drop penalty, however, is considerably higher: Depending on the

Reynolds number, from 1.3 to 44 times higher friction factors than those in an

equivalent flate-plate channel equations. [13]

A correlation in the form of Eq. (5.18) has been also proposed by Kumar.

[26-29] This correlation is in the Nusselt form. Provided the appropriate value of

, channel flow area, and channel equivalent diameter, are used, calculations are

similar to single-phase flow inside tubes, i.e.

hJ

(5.18) µ17.0

3/1Pr

==w

bh

e JkhDNu

µ

or

(5.19) w ( )

e

bh

D

kJh

17.03/1Pr

=µµ

where is the equivalent diameter defined by Eq. (5.9), eD bµ is the dynamic

viscosity at bulk temperature, wµ is the dynamic viscosity at wall temperature,

( ) kc /Pr pµ= and . Values of C and depend on flow characteristics and Chevron angles. The transition to turbulence occurs at low

Reynolds numbers and, as a result, the gasketed-plate heat exchangers give high

heat transfer coefficients. The Reynolds number, Re , based on channel mass

velocity and the equivalent diameter, , of the channel is defined as

yhh CJ Re= h y

eD

(5.20) Gµ

ecD=Re

The channel mass velocity is given by

136

(5.21) m

wcpc bLNG =

where is the number of channel per pass and is obtained from cpN

(5.22) tN −=p

cp NN

21

where is the total number of plates and is the number of passes. tN pN

In Eq. (5.18), values of and versus for various Chevron angles

are given in Table 5.2. [7, 26, 27, 28] In the literature, various correlations are

available for plate heat exchangers for various fluids depending on flow

characteristics and the geometry of plates. [14, 17, 18, 22, 30, 31, 32]

hC y Re

Table 5.2 Constants for single-phase heat transfer and pressure loss calculations for gasketed-plate heat exchangers

137

5.3.2 Channel Pressure Drop

The total pressure drop in gasketed-plate heat exchangers consists of the

frictional channel pressure drop, cp∆ and the port pressure drop ∆ . The

following correlation is given for the frictional channel pressure drop [4, 7, 26,

30]:

pp

(5.23) µ17.02

24 −

=∆

w

b

e

cpeffc D

GNfLp

µρ

where is the effective length of the fluid flow path between inlet and outlet

ports and it must take into account the corrugation enlargement factor

effL

φ ; this

effect is included in the definition of friction factor. Therefore , which is

the vertical port distance. The Fanning friction factor (which is defined as τ

veff LL =

f w/

( ρu2) and is equal to times the Moody friction factor which is equal to

(dP/dx)L/( ρu2)) in Eq. (5.23) is given by

(5.24)

zpKf

Re=

Values of and pK z versus for various Chevron angles are given in

Table 5.2. For various plate surface configurations, friction coefficient vs.

Reynolds number must be provided by the manufacturer.

Re

5.3.3 Port Pressure Drop

The total port pressure loss may be taken as 1.3 velocity heads per pass

based on the velocity in the port, i.e. [4, 7, 26, 30]

(5.25) p

pp N

Gp

ρ23.1

2

=∆

138

where

(5.26)

4

2p

p DmG

π=

where is the total flow rate in the port opening and is the port diameter. m pD

The total pressure drop is then:

(5.27) pctot ppp ∆+∆=∆

5.4 EFFECTIVE TEMPERATURE DIFFERENCE

One of the features of plate-type units is that countercurrent flow is

achieved. However, the logarithmic mean temperature difference requires

correction due to two factors: (a) the end plates, where heat is transferred from

one side only, and (b) the central plate of two-pass/two-pass flow arrangements,

where the flow is cocurrent. However, unless the number of channels per pass is

less than about 20, the effect on temperature difference is negligible. Hence, in

many applications, for counter flow arrangement which is given below may

be used.

( lmT∆ )

lmT∆

(5.28) ∆−∆

2

1

21,

lnTTTTT cflm

∆∆

=∆

1T∆ and 2T∆ in Eq. (5.28) are the terminal temperature differences at the inlet

and outlet.

If countercurrent flow does not apply, then a correction factor must be

applied to

F

lmT∆ exactly as for shell-and-tube heat exchangers. [28, 30, 34, 35]

Values of for a two-pass/one-pass system are shown in Figure 5.3. [35] F

139

Figure 5.3 Temperature difference correction factor ( )F for gasketed-plate heat exchangers – two-pass/one-pass system (applicable to 20 or more plates)

5.5 OVERALL HEAT TRANSFER COEFFICIENT

Once both film heat transfer coefficients have been determined from

section 5.3.1 the overall heat transfer coefficient is calculated:

(5.29) fcfh

wchf

RRkt

hhU++++=

111

where U is the fouled or service heat transfer coefficient, and h are the heat

transfer coefficients of hot and cold fluids, respectively, and are the

fouling factors for hot and cold fluids, and

f hh

R

c

fh fcR

( )wkt is the plate wall resistance.

Sometimes a cleanliness factor is used instead of fouling factors. [4, 7] In

this case a ‘clean’ overall heat transfer coefficient U is calculated from c

wchc kt

hhU++=

111 (5.30)

140

The service or fouled overall heat transfer coefficient, when the

cleanliness factor is CF, is given by

(5.31) ( )fcfh

c

cf

RRU

CFUU++

== 11

5.6 HEAT TRANSFER SURFACE AREA

The heat balance relations in gasketed-plate heat exchangers are the same

as for tubular heat exchangers. The required heat duty, Q , for cold and hot

streams is

r

(5.32) )−( ) ( ) ( ) ( 2112 hhhpcccpr TTcmTTcmQ =−=

On the other hand, the actually obtained heat duty, , for fouled

conditions is defined as:

fQ

(5.33) cflmeff TFAUQ ,∆=

where is the total developed area of all thermally effective plates, that is,

that accounts for the two plates adjoining the head plates.

eA

2−tN

A comparison between Q and defines the safety factor, , of the

design: [4]

r fQ sC

(5.34) Q

r

fs QC =

These analyses will be applied to the thermal design of a gasketed-plate heat

exchanger for a set of given conditions.

141

5.7 THERMAL PERFORMANCE

In a performance evaluation, the exchanger size and flow arrangement is

known. In a design case considerable skill and experience are required to produce

the optimum design involving the plate size and pattern, flow arrangement,

number of passes, number of channels per pass, etc. Like shell-and-tube heat

exchanger design, many designs may have to be produced before the optimum is

found. The heat transfer and pressure drop calculations described in section 5.3

assume that the plates are identical. However, at the design stage, other variations

are available to the thermal design engineer.

A plate having a low Chevron angle provides high heat transfer combined

with high pressure drop. These plates are long duty or hard plates. Long and

narrow plates belong to this category. On the other hand, a plate having a high

Chevron angle provides the opposite features, i.e. low heat transfer combined with

low pressure drop. These plates are short duty or soft plates. Short and wide plates

are of this type. A low Chevron angle is around 25º - 30º, while a high Chevron

angle is around 60º - 65º. Manufacturers specify the plates having low values of

β as ‘high-θ plates’ and plates having high values of β as ‘low-θ plates’. Theta

is used by manufacturers to denote the number of heat transfer units (NTU),

defined as: [4, 13, 14]

(5.35) ( ) m

cc

cpc T

TTcmUANTU

∆−

=== 12θ

(5.36) ( ) m

hh

hph T

TTcmUANTU

∆−

=== 21θ

The ε - NTU method is described in Chapter 3; the total heat transfer rate from

Eq. (3.35) is

(5.37) ( ) ( )T−= ε 11min chp TcmQ

142

Heat capacity rate ratio is given by Eq. (3.27) as:

(5.38) T −

12

21

cc

hh

h

c

TTT

CCR

−==

When 1R :

(5.41) C=( ) ( ) minmincmcm php =

(5.42) UA( )

hpcmC

UANTU ==min

In calculating the value of NTU for each stream, the total mass flow rates

of each stream must be used.

The heat exchanger effectiveness for pure counter flow and for parallel

flow are given by Eqns. (3.38) and (3.39), respectively. Heat exchanger

effectiveness, ε , for counter flow can be expressed as: [1, 12, 44]

(5.43) [ ][ ]maxminmaxmin

maxmin

-NTU(1exp)(1-NTU(1exp1

CCCCCC

−−−−

=ε

which is useful in rating analysis when outlet temperatures of both streams are not

known.

143

5.8 THERMAL MIXING

A pack of plates may be composed of all high-theta plates (β = 30º for

example), or all low-theta plates (β = 60º for example), or high- and low-theta

plates may be arranged alternately in the pack to provide an intermediate level of

performance. Thus two plate configurations provide three levels of performance.

[7, 9]

A further variation is available to the thermal design engineer. Parallel

groups of two channel types, either (high + mixed) theta plates or (low + mixed)

theta plates, are assembled together in the same pack in the proportions required

to achieve the optimum design.

Thermal mixing provides the thermal design engineer with a better

opportunity to utilise the available pressure drop, without excessive oversurface,

and with fewer standard plate patterns. Figure 5.4 [32] illustrates the effect of

plate mixing.

144

Figure 5.4 Mixed theta concept

One channel flow area � is given by [7, 4, 30]Any attempt for the estimation of film coefficient of heat transfer in gasketed-plate heat exchangers involves extension of correlations that are available for heat transfer between flat flow passages. The conventional approach for such passages employsFor gasketed-plate heat exchangers with Chevron plates, some of selected correlations for the friction factor �, and the Nusselt number �, are listed in Table 5.1. [15] In these correlations, Nusselt and Reynolds numbers are based on the equivalent diameAs can be seen from Table 5.1, both heat transfer coefficient and friction factor increase with �. From the experimental data base, Muley et al [14] and Muley and Manglik [13,33] proposed the following correlation for various values of �:ForDepending on � and Reynolds number, Chevron plates produce up to five times higher Nusselt numbers than those in flat-plate channels. The corresponding pressure drop penalty, however, is considerably higher: Depending on the Reynolds number, from 1.3 toA correlation in the form of Eq. (5.18) has been also proposed by Kumar. [26-29] This correlation is in the Nusselt form. Provided the appropriate value of �, channel flow area, and channel equivalent diameter, are used, calculations are similar to sinOnce both film heat transfer coefficients have been determined from section 5.3.1 the overall heat transfer coefficient is calculated: