Kuppan T. Heat Exchanger Design Handbook
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174
Chapter
4
IAMINAR
BOUNDARY LAYER
\
LAMINAR
Figure
13
Offset strip
fin:
(a) schematic; and
(b)
laminar
flow
on
the fins and
in
the wakes.
1.
The perforated holes promote turbulence, which increases the local heat-transfer coeffi-
cient compared to plain fins, but as the percentage of perforated holes increase, the loss
of heat transfer surface offsets this advantage
[
131.
2.
The perforated surface is prone to flow-induced noise and vibration.
Applications.
Perforated fins are now used in only a limited number of applications [14].
Typical applications include:
1.
“Turbulators” in oil coolers.
2.
In boiling applications to maintain a wetted surface and minimize depositionskoncentra-
tions
[
131. Perforated corrugations permit interchannel fluid migration, which evens out
surges and vibration and avoids localized concentrations or depositions.
3.
Perforated fins were once used in two-phase cryogenic air separation exchangers, but now
they have been replaced by offset strip fins.
Shah
[
151 provides a very detailed evaluation of the perforated fin geometries.
Offset Strip Fin
The offset strip fin (OSF) is commonly used geometry in plate-fin heat exchangers. The offset
strip
fin
is
designated as the serrated fin in Ref. 13. The fin has a rectangular cross section; it
is cut into small strips
of
length
I,
and every alternate strip is offset by about
50%
of the fin
pitch
in
the transverse direction as schematically shown in Fig. 13. Fin spacing, fin height,
fin
thickness, and strip length in the flow direction are the major variables of offset strip fins.
Offset strip fin geometry is characterized by high heat-transfer area per unit volume, and
high heat-transfer coefficients. The heat-transfer mechanism
in
offset strip fins is described by
Joshi and Webb
[
161 and is as follows. The heat-transfer enhancement is obtained
by
periodic
growth of laminar boundary layers on the fin length, and their dissipation in the fin wakes as
shown schematically in Fig. 13b. This enhancement is accompanied by an increase in pressure
drop because of increased friction factor.
A
form drag force, due to the finite thickness of the
fins, also contributes to the pressure drop. Fluid interchange between channels is possible.
Offset strip fins are used
in
the approximate Reynolds number range of 500-10,000
[
141.
Salient features pertaining to thermal performance include the following
[
131:
1. Commonly used in air separation plants where high thermal effectiveness at low mass
velocities is required
[
131.
2.
The heat-transfer performance of offset strip fins is increased by a factor of about
1.5
to
4 over plain fins of similar geometry, but at the expense
of
higher pressure drop
[
141,
Compact Heat Exchangers
I75
3.
At high Reynolds numbers, thej factor decreases, while the friction factor remains constant
because of the high form drag. Therefore offset fins are used less frequently for very high
Reynolds number applications.
4.
They are used at low Reynolds number applications calling for accurate performance pre-
dictions, such as some aerospace applications; other
fin
performance data are not
as
repeat-
able.
Herringbone or Wavy Fin
Since wavy fins have noninterrupted walls in each flow channel, they are less likely to catch
particulates and foul than are offset strip fins. Their performance is competitive with that of
the offset strip fin, but the friction factor continues to fall with increasing Reynolds numbers
[
131. The waveform in the flow direction provides effective interruptions to flow and induces
very complex flows. The augmentation is due to Goertler vortices, which form as the fluid
passes over the concave wave surfaces. These are counterrotating vortices, which produce a
corkscrew-like pattern and probable local flow separation that will occur on the downstream
side of the convex surface [8,14]. In the low-turbulence regime (Re of about
6000
to
8000),
the wall corrugations increase the heat transfer by about nearly three times compared with the
smooth wall channel. Therefore, wavy fins are often a better choice at the higher Reynolds
numbers typical of the hydrocarbon industry; the smooth surface allows the friction factor to
fall with increasing Reynolds number. Kays and London
[
171
provide curves of
j
and
f
versus
Re for two wavy-fin geometries.
Louver Fins
The louvers are essentially formed by cutting the sheet metal of the fin at intervals and by
rotating the strips of metal thus formed out of the plane of the fin. Louvers can be made in
many different geometries, some of which
is
shown in Fig. 14. Note that the parallel louver
fin and offset strip fin both have small strips aligned parallel to the flow. The louvered fin
geometry of Fig. 14 bears a similarity to the offset strip. Rather than offsetting slit strips, the
entire slit fin is rotated
20-60"
relative to the airflow direction. As such, they are similar
in
principle to the offset strip fin. Louvered fins enhance heat transfer by providing multiple flat
plate leading edges with their associated high values of heat-transfer coefficient. Salient fea-
tures of louver fins are:
The louvered fin strip length is usually longer than the OSF, e.g., 6-18 mm, versus 3-9 mm
for the
OSF
[8]; the louvered fin gage is generally thinner than that of an offset strip of
the fin.
Figure
14
Flow pattern through a typical louvred fin showing limiting flow directions where
F
is
louvre pitch,
L,
louvre length and
a
the louvre angle.
176
Chapter
4
The
fin
corrugations normally form a triangular passage. Hence, it is generally not as strong
as
an
offset strip
fin,
since the latter has a “large” flat area for brazing, thus providing
strength
[
141.
The louver fins may have a slightly higher potential of fouling compared to the offset strip
fins [14].
The louvered fin can provide heat-transfer coefficients comparable to the
OSF.
However, the
ratio of
j/f
tends to
be
lower because of the considerable form drag on the
bent
fins
[S].
Louver fins can enhance heat transfer by a factor
of
two or three compared with the equivalent
unlouvered surfaces
[
131.
A wide range in performance can be achieved by varying the louver angle, louver width, and
louver form.
The operating Reynolds number range is 100-5000, depending upon the type of louver geome-
try
employed
[
141.
Applications.
Their attractive thermal performance characteristics in terms
of
compactness,
light weight and low pumping power for a given heat-transfer duty make louver fins a potential
candidate for aerospace applications
[
181. They are recognized as very effective heat-transfer
surfaces, leading to compact solutions to cooling problems. Louvered fin surfaces are now
used widely
for
engine cooling equipment, air-conditioning heat exchangers (evaporators and
condensers), and aircraft oil and air coolers. They share this quality with the offset strip fin
surfaces
[
191. The louvered surface is the standard geometry for automotive radiators. For the
same strip width the louvered
fin
geometry provides heat-transfer coefficients comparable to
the OSF.
Pin Fins
An array of wall-attached cylinders (e.g., rods, wires) mounted perpendicular to the wall
is
known as pin fins. They can be manufactured at a very high speed continuously from a thin
wire. After the wire is formed into rectangular passages, the top and bottom horizontal wire
portions are flattened for brazing or soldering with the plates. Pins can be of circular or el-
liptical shapes. The enhancement mechanism due to a pin array is the same as that
of
the
offset strip
fin,
namely, repeated boundary layer growth and wake dissipation
[8].
The poten-
tial application for pin fins is at very low Reynolds number (Re
<
500)
for which the pressure
drop is of no major concern. Present applications for pin fins include [14]:
(1)
electronic
cooling devices with generally free convective flows over the pin fins and
(2)
to cool turbine
blades.
Limitations
of
Pin Fins.
1.
The surface compactness achieved by the pin
fin
geometry is much lower than that
achieved by the strip fin or louver
fin
surfaces.
2.
Due
to
vortex shedding behind the circular pins, noise and flow-induced vibrations can
take place.
2.9.1
FIN
Corrugation Code
A
commonly encountered code for fin corrugation is [13]: 350S1808. The first three digits
give the
fin
height
in
thousandths
of
an inch
(350=0.35
inches). The letter gives the
type
of
corrugation
(S
=
serrated). Other types are
P
=
plain, R
=
perforated,
H
=
herringbone. The next
two digits give the fins per inch (18
=
18 fpi). The following two digits give the
fin
thickness
in
thousandths of an inch
(08
=
0.008 in). The time following the oblique stroke
(if
any) is
used only for perforated fin and
it
is the porosity,
0.
Compact Heat Exchangers
I77
2.1
0
Corrugation Selection
Corrugations, edge bars, and parting sheets are chosen primarily to contain the appropriate
pressure. Corrugation selection depends on factors such as
[
131
compactness, pressure, me-
chanical integrity, manufacture, performance, velocity limits, and fouling.
2.1
1
Materials of Construction
PFHEs
are made in a variety of materials to suit a wide range of process streams, temperatures
and pressures. Material specifications should comply with the appropriate section of the
ASME
or
to other applicable codes.
Aluminum
Aluminum is preferred for cryogenic duties, because of its relatively high thermal conductivity,
strength at low temperatures, and low cost. For cryogenic services, aluminum alloy
3003
is
generally used for the parting sheets, fins, and edge bars that form the rectangular PFHE block.
Headers and nozzles are made from aluminum alloy
3003, 5154, 5083,
5086,
or
5454
[13].
Above ambient temperature, with increase in temperature, most aluminum alloys rapidly lose
their strength. For land-based transport vehicles, aluminum PFHEs are used up to
170-1
80°C
to cool supercharged engine intake air.
Nonaluminum
Stainless steels and most nickel alloys are used for
PFHEs,
particularly for high-temperature
services. Stainless steels have poor thermal conductivity, but their higher strength allows thin-
ner parting plates and fins than with aluminum, which offsets some of the reduction in heat
transfer.
2.1
2
Mechanical Design
The
PFHE
is a pressure vessel. It is required to be designed and constructed in accordance
with a recognized Pressure Vessel Code. The mechanical design
of
a PFHE can be divided
into the conventional pressure vessel area of header tanks, nozzle, nozzle reinforcements, lifting
devices, pipe loads, etc., and the less familiar area of the block itself.
2.1
3
Manufacture, Inspection, and Quality
Control
PFHEs
are manufactured by brazing. Heat exchanger manufacture by brazing is described in
Chapter
15.
The manufacturer is responsible for the mechanical design and for the thermal
design where the latter is not specified by the purchaser. Salient features
of
quality control and
inspection of
PFHE
are detailed in Ref.
13.
3 SURFACE GEOMETRICAL RELATIONS
3.1
Surface
Geometrical Parameters-General
The following are some of the basic relationships between the surface and core geometries on
one side of the compact heat exchangers,
Hydraulic Diameter, Dh
The
generalized relation for hydraulic diameter is given by
&=-
4A,L
A
I
78
Chapter
4
where
A
is total heat transfer area,
A,,
is free flow area, and
L
is
flow
length. The hydraulic
radius
rh
is given by
Dh/4.
Surface Area Density
a
and
CJ
For
a
compact heat exchanger with secondary surface on one side, it is customary
to
designate
the ratio of the total heat-transfer surface area on one side of the exchanger to total volume
of
the exchanger by
a,
and the ratio of the free flow area to the frontal area by
U.
Thus,
AI
A2
a,
=-
and
a,=-
V
V
From the definition of hydraulic diameter Dh, the relation between hydraulic diameter,
surface area density
a,
and
U
is given by
and
3.2
Tubular
Heat
Exchangers
Geometrical relations are derived for the in-line and staggered tube arrangements with bare
tubes, individually finned circular tubes, and circular tubes with plain continuous fins. The
header dimensions for the tube bank is
Lz
x
L3,
the core length for flow normal to the
tube
bank
is
L.,
and the no-flow dimension is
L3.
The lateral pitch
is
given by
P,
and longitudinal
pitch by
PI.
Flow
is idealized as being normal to the tube bank on the outside. Surface geornet-
rical relations for tube-fin heat exchangers are derived from first principles by Shah
[20,21],
and for individually finned tubes by Idem et al.
[22].
The surface geometrical relations given
here are based on Shah
[20].
Tube Inside
Tubes have inside diameter
di,
length between headers
L,,
header thickness
Th,
and total length
including header plates thickness as
L,
+
2Th.
The total number
of
tubes, N,,
is
given by
The geometrical properties of interest for analysis are
Total heat transfer area
A
=
nd,L,N,
Minimum free
flow
area
A,,
=
(n/4)d:N,
Compact Heat Exchangers I79
Hydraulic diameter
Dh
=
d,
Tube length for heat transfer
=
L,
Tube length for pressure drop
=
L,
+
2Th
The geometrical properties given by
Eqs.
(7) to
(1
1)
also hold good for other types of
arrangements discussed next
.
Tube Outside
Bare Tube Bank.
In-Line Arrangement.
The geometrical properties of the in-line tube bank as shown in
Fig.
15
are summarized here. The number of tubes in one row (in the flow direction) are
The total heat-transfer area consists of the area consists of the area associated with the tube
outside surface, given by
A
=
Rd,,L1
N,
(13)
The minimum free flow area
A,,
frontal area
Afr,
the ratio of free flow area to frontal area
0,
and hydraulic diameter
Dh
are given by
4
A&
L)h
=
___
A
Flow length for pressure drop calculation
=
L2
Heat exchanger volume
V
=
L
I
L2L3
It must be emphasized that the foregoing definition of the hydraulic diameter is used by
Kays and London [17] for tube banks. However, many correlations use the tube outside diame-
I-
Pt
L
.
FLOW
-
Figure
15
Inline tube bank geometry.
I80
Chapter
4
ter or fin root diameter as the characteristic dimension in the heat-transfer and pressure-drop
correlations.
So
it is essential to find out first the specific definition of the characteristic length
before using a particular correlation.
The geometrical properties given by
Eqs.
14
to
18
also hold good for other types
of
arrangements discussed later.
Staggered Arrangement. A staggered tube bank and its unit cell are shown in Fig.
16.
The total number
of
tubes with half tubes in the alternate row is given by
Eq.
6.
If the half
tubes are eliminated from the alternate intermediate tube rows, then the number
of
tubes in the
first row will
be
L3/X,
and in the second row
L3/X,
-
1.
The minimum free flow area
occurs
either at the front or through the diagonals (refer to Fig. 16b). The minimum free flow area
is
then given by
[20]:
4,
=
-2
-
1
1
z
+
(PI
-
d")
L,
1
where
-0
-I
tc-
FLOW
PL
__r_
...
. . *
..
.
(b)
Figure
16
Staggered tube bank: (a) layout; and
(b)
unit
cell.
Compact Heat Exchangers
I81
z=2x
if
2xc2y (19b)
z=2y
if
2yc2x
(
194
in which
2x
and
y
are defined as
2J
=(Pt-
do)
(204
=
[(~,/2)~
+
(P,)~]O.~
-
do
(206)
In
Eq.
(19a), the last term
(P,
-
d)L,
corresponds to the free flow area between the last tube at
each end in the first row and the exchanger wall.
Circular Fins
on
Circular
Tubes.
The basic core geometry of an idealized single-pass cross-
flow exchanger for an inline arrangement is shown in Fig.
17.
The total number of tubes in
this exchanger is given by
Eq.
6.
It is idealized that the root of a circular fin has an effective
..
d.F
..
t
L
b)
Figure
17
Individually finned circular
fin
tube.
(a)
Layout;
and (b) diagram showing frontal area
(dotted lines) and
free
flow area (hatched area).
I82
Chapter
4
diameter
d,
and the fin tip has a diameter
d,..
Depending upon the manufacturing techniques,
d,
may be the tube outside diameter or tube outside diameter plus two fin collar thickness. The
total heat transfer area consists of the area associated with the exposed tubes (primary area)
and fins (secondary area). The primary area,
A,
is the tube surface area minus the area blocked
by the fins. It is given by
where
ti
is
fin
thickness and
Ni
is number of fins per unit length.
The fin surface area,
Af,
is given by
and therefore, the total heat-transfer surface area
A
is equal to
A,
+
At,
given by:
A
=
nd,(LI
-
tf
Nf L,)N,
+
[2n(df
-
df)/4
+
&ftf]Nf LIN,
(23)
Minimum Free Flow Area for Circular Fins on Circular Tubes-In-Line Arrangement.
The minimum free flow area for the in-line arrangement is that area for a tube bank,
Eq.
13.
minus the area blocked by the fins:
Minimum Free Flow Area for Circular Fins on Circular Tubes-Staggered Arrangement.
The basic core geometry of an idealized single-pass crossflow exchanger for staggered arrange-
ment
is
given
in
Fig.
18.
The total number
of
tubes in this exchanger is given by
Eq.
6.
For
the staggered tube arrangement, the minimum free flow area could occur either through the
transverse pitch or through the diagonals similar to those
of
the
unit
cell shown
in
Fig. 4.18b.
The minimum free flow area is given by
[
19,201:
where
in
which
2x'
and
y'
are given by
Dimensions
2x'
and
y'
cannot be depicted in the figure.
Continuous Plain
Fins
on
Circular
Tubes.
The
tube-fin arrangement is shown in Fig.
19.
The
total heat-transfer area consists
of
the area associated with the exposed tubes (primary area)
and the fins (secondary area). The primary area is the same as that given by Eq.
13,
minus
the
area blocked by the fins. Therefore,
A,
is given by
[
14,201:
The total fin surface area,
Ai,
consists of
(1)
the fin surface area,
dr,
and
(2)
the area with
leading and trailing edges,
d:,
given
by:
183
Compact Heat Exchangers
L3
I
Figure
18
Individually finned tube staggered arrangement. (a) Geometry;
and
(b)
unit cell [after Ref
(2
1
)I.
and
Total heat transfer surface area
A
=
A,
+
Af
(30)
Minimum Free
Flow
Area for the In-Line Arrangement. The minimum free
flow
area
for an in-line arrangement is that area for a tube,
Eq.
13,
minus the area blocked by the fins
[
14,201:
A0
=
[(PI
-
4)b
-
(PI
-
4)tfNf~,I(~,/Pl)
(31)
Minimum Free
Flow
Area for the Staggered Arrangement. For the staggered tube ar-
rangement as shown in Fig.
20,
the minimum free
flow
area could occur either through the
transverse pitch
or
through the diagonals.
The
minimum free
flow
area is given by
[20]:
A,
=
{(&/Pt
-
OZ”
+
[(PI
-
4)
-
(PI-
dJtfNf]}L,
(32)