CHAPTER 5 DESIGN FUNDAMENTALS OF GASKETED-PLATE HEAT ...web.iitd.ac.in/~pmvs/courses/mel709/CHAPTER...
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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
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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°.
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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
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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
pA1
1=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 ≈
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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
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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
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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 ≥
[ ] ( )[ ]14.0
317.390/2sin0543.0728.025 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
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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
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(5.21) m
wcpc bLNG =
where is the number of channel per pass and is obtained from cpN
(5.22) tN −=
pcp 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
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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
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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 1<R :
(5.39) C=( ) ( ) minmincmcm pcp =
(5.40) ( )
cpcmUA
CUANTU ==
min
and when 1>R :
(5.41) C=( ) ( ) minmincmcm php =
(5.42) UA( )
hpcmCUANTU ==
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.
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Figure 5.4 Mixed theta concept