Kuppan T. Heat Exchanger Design Handbook
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L
184
Chapter
4
-7-
pt
FLOW
..
..
.
..
..
..
0
!O
Figure
19
Continuous flat fin-tube heat exchanger: (a) inline layout; and
(b)
staggered layout.
In
Eq.
32
Z"
is
defined
as
'f
=
2x"
if
2x"
c
2y"
2''
=
2y"
if 2y"
<
k"
where
2x"
and
y"
are given
by
2x"
=
(Pt
-
dr)
-
(Pt
-
d,)ffNf
y"
=
[(P,/2)2
+
(PJ2p5
-
d,
-
(Pt
-
d,)t,N,
185
Compact Heat Exchangers
Minimum Free Flow Area for Pressure Drop
For the determination of entrance and exit pressure losses, the area contraction and expansion
ratio
0'
is needed at the leading and trailing fin edges (Fig.
19).
It is given by
[
14,201:
3.3
Compact Plate-Fin Exchangers
The following geometrical properties on each side
are
needed for the heat-transfer and pres-
sure-drop analysis of plate-fin heat exchanger (PFHE):
1.
The primary and secondary surface area (if any)
A,
and A,, respectively
2.
Minimum free
flow
area
A,
3.
Frontal areaAfr
4.
Hydraulic diameter
Dh
and
5.
Flow
length
L
6.
Fin dimensions-thickness and length (height)
The information not specified directly is computed based on the specified surface geome-
tries and core dimensions. Consider a PFHE as shown in Fig.
20
in which
L,
and
L.,
are the
flow
lengths,
Np
and
Np
+
1
are the number
of
flow passages on sides
1
and
2,
respectively, and
V
is the total core volume. The following formulas define some of the geometrical properties on
any one side of the
PF'HE.
These geometrical relations are derived in Refs.
17,
23,
and
24.
The volume between plates on each side
is
given by
Vp.1
=
LIWlNp)
vp,2
=
LI&?b2(Np
+
1)
(36)
Heat transfer area on each side is given by
AI
=
Plvp.1
A2
=
P2vp.2
(37)
where
PI
and
P?
are the surface area density on each side per unit volume between plates.
I
I
I-L
_I
Figure
20
Crossflow plate-fin heat exchanger.
I86
Chapter
4
The ratio of minimum free flow area to frontal area
(0)
on side
1
is given by
where
a
is the thickness of parting plates. The ratio is given similarly for side
2.
Here, the last
approximate equality is for the case when
Np
P
1
or the numbers of passages on the two sides
are the same.
The heat-transfer surface area on one side divided by the total volume
V
of
the exchanger,
designated as
a,,
is
a
-_-I-
A,
-
40
-
bIP1
1-
v
Dh.I
b,
+b2+2a
Similarly,
a?
is given by
4
FACTORS INFLUENCING TUBE-FIN
HEAT EXCHANGER PERFORMANCE
Important factors that influence the heat-transfer performance of tube-fin heat exchangers in-
clude the following:
1.
Tube layout (staggered vs. in-line arrangement)
2.
Equilateral layout versus equivelocity layout
3.
Number of rows
4.
Tube pitch
5.
Finned tube variables (fin height, spacing, thickness)
6.
Fin tubes with surface modifications
7.
Side leakage
8.
Boundary-layer disturbances and characteristic flow length
9.
Contact resistance in finned tube heat exchangers
10.
Induced draft versus forced draft
Johnson
[5]
and Rabas and Taborek
[7]
discuss the effect of various tube-fin parameters
on thermohydraulic performance.
4.1
Tube Layout
The two basic arrangements of the tubes in a tube bank are
(1)
staggered arrangement with
equilateral triangular pitch, and
(2)
in-line arrangement. The extent
of
transverse flow
in
the
inline layout is small in comparison to the staggered arrangement. The most commonly used
is the staggered layout. There are very few applications of low-finned tubes with the in-line
arrangement. It may be used when air-side fouling problems are encountered. For identical
operating conditions, the in-line arrangement has low heat transfer, of the order of
70%,
and
pressure drop
is
also of this order.
287
Compact Heat Exchangers
Figure
21
Equivelocity layout
of
a heat exchanger
[25].
A,
is
transverse area available for
flow;
A?
is diagonal area available for
flow.
4.2
Equilateral Layout versus Equivelocity Layout
[25]
In the conventional equilateral staggered layout, the area available for air flow in the transverse
direction
is
half of that available in the diagonal direction; therefore, energy is lost in accelerat-
ing and decelerating the air stream as it
flows
through the bank. In the equivelocity layout
(shown in Fig.
21),
these two areas are made equal by adjusting the transverse
(P,)
and longitu-
dinal
(PI)
pitches, thus minimizing these losses. For the tube bank examined in Ref.
25,
the
transverse pitch increases from
2.5
to
3.625
in
(63.5
to
92.1
mm), while the longitudinal pitch
decreases from
2.165
to
1.6
in
(55.0
to
40.60
mm). The layout angle for the equilateral case
is
30°,
and it becomes around
50"
for high-finned tubes in the equivelocity arrangement (the
exact value of this angle depends on the specific
fin
geometry).
The thermal hydraulic performance of the equivelocity layout (Fig.
22)
has been compared
1.2
1
4
Figure
22
Performance
of
an equivelocity unit
[z].
188
Chapter
4
with that of an equilateral bank of high-finned tubes typical of air-cooler heat exchanger
(ACHE) design with the following results
[25]:
At the same Reynolds number, the equivelocity layout shows,
on
the average, a
7%
lower
j
factor and a
4%
lower Fanning friction factor than the equilateral factor.
At the same face velocity, the equivelocity layout shows average reductions of
19%
in pressure
drop per row over the equilateral layout.
In each of the layouts, the
j
and
f
factors for a three-row bundle have essentially the same
value
(95-98%)
of that for a five-row bundle, indicating that only three rows
of
tubes are
necessary to obtain uniform surface characteristics for high finned tubes.
In general, for applications where horsepower is evaluated at a high premium and a re-
duced pressure drop is attractive, even at the expense of some loss
of
thermal performance, an
expanded pitch layout type should
be
strongly considered.
4.3
Number
of
Tube
Rows
The addition of tube rows in the crossflow direction is the common way of increasing heat-
transfer area when the frontal area of the tube bank is fixed. Such
an
addition of tube rows
increases the flow length for the air and may affect the fluid dynamics with a possible effect
on heat transfer and pressure drop. Pressure drop through the tube bundle increases with the
number of tube rows. The temperature drop through the tube bundle also increases with the
number of tube rows, though the effect is very large with the first few tube rows and for
a
very large number
of
tube rows the effect is small. Temperature drop through a multirow tube
bank is shown in Fig.
23
[26].
The row effect on heat transfer coefficient is discussed
by
Johnson
[5].
A basic difference exists between the row effects for the in-line and the staggered
arrangements. For an in-line arrangement, the heat-transfer coefficient decreases with an in-
175
150
0
cb
Q)
125
E"
0)
-w
L
100
Coolinq
water temp
I
75
1
2 3
4
5
6
7
8
9
101112
Number
of
tube rows
Figure
23
Temperature
drop
through a multi-tube row heat exchanger.
Compact
Heat Exchangers
189
crease in the number of rows. Brauer
[27]
shows that the one-row tube bank heat-transfer
coefficient is approximately
50430%
higher than the average for four rows, whereas for a
staggered arrangement the four-row tube bank has approximately
30%
higher heat-transfer
coefficient (average) than a one-row tube bank.
4.4 Tube Pitch
Tube pitch is commonly used in heat-exchanger design to affect compactness of the core and
flow conditions. The hydraulic diameter increases with the pitch. Based on comparable air
velocities, the pitch has no effect on the heat-transfer coefficient. However, increasing the pitch
strongly affects the pressure drop, as it decreases the pressure drop through the bundle
[5].
4.5 Fin-Tube Variables
The fin-tube variables that affect the thermal performance include fin height, fin spacing, and
thickness and thermal conductivity of the
fin
material. Surface area of the tube bank can be
increased by employing fin tubes with high (longer) fins and denser spacing. However, increas-
ing the fin height will decrease the fin effectiveness, and may lower heat transfer compared
with the short fins. Denser fins may lower the heat transfer because of laminarization of the
flow conditions between the fins
[5].
Fin efficiency increases with a reduction in
fin
height
and an increase in fin thickness. Thermal conductivity is usually not a problem in selecting the
material of a primary surface, but it is important in extended surfaces because of the relatively
long and narrow heat flow path, which affects their heat-transfer performance
[6].
Fin Height and Fin Pitch
The fin height and fin pitch that can be used effectively are fundamentally related to the
boundary-layer thickness
[6].
Wen-Jei Yang
[6]
states the rule of thumb:
(I)
For large thermal
boundary layer thickness, the heat-transfer coefficient,
h,
is low and thus high fins are em-
ployed;
(2)
low fins are employed in the case of a thin boundary layer where
h
is high; and
(3)
if the fin spacing is too small, the main stream cannot penetrate the spaces between the
fins, resulting in no increase in thermal boundary area and an excessive pressure drop.
4.6
Finned Tubes with Surface Modifications
The term “surface modification” refers to fin
tubes
that have extended surfaces that are me-
chanically deformed to various shapes by crimping, corrugating, cutting, slotting, or serrating
the fins; for continuous plate fins, surface interruptions constitute surface modification
[5].
Any surface modification will increase the heat transfer and pressure drop as compared with
the identical smooth fin. Common surface modifications for circular fins are discussed further
in Chapter
8.
4.7 Side Leakage
The heat-transfer and pressure-drop performance of a tube bank is affected by the leakage flow
between the outermost tube and the side walls. This is equivalent
to
the bundle-to-shell bypass
stream (C-stream) leakage in a shell and tube exchanger. The effect of bypass flow can be
minimized by attaching side seals to the exchanger in every even row as shown in Fig. 24a.
Clearance between the core and the housing can be minimized by welding metal strips to the
housing or attaching metal strips to the header as shown in Fig. 24b.
I
90
Chapter
4
Figure
24
Sealing strips
to
arrest bypass flow: (a) between the core and the housing; and (b) between
the tubes and side sheets.
4.8
Boundary-Layer Disturbances and Characteristic
Flow
Length
Periodic interruption of the boundary layer is achieved by breaking the total flow length into
many characteristic lengths by means of offset strip fins, louvered fins, wavy fins, etc.
1281.
The characteristic
flow
length,
1
is illustrated in Fig.
25.
The characteristic flow length and the
hydraulic diameter,
Dh,
are responsible for the numerical merits of a surface geometry. The
representative length of finned heat exchangers as parameters to represent their performance
suggests that it would be possible to enhance their performance by shortening the representative
length of the fin and using finer segmentation than the regions of louvered or offset strip fins
[29].
The application of the pin finned surface can be considered one of the best candidates.
4.9
Contact Resistance in Finned
Tube
Heat Exchangers
Continuous Finned Tube Exchanger
In the design of finned tube heat exchangers, the contribution of contact resistance at the
interface between the tube and fin collar is not always negligible compared with the total heat
transfer resistance (Fig.
26).
This is particularly true for mechanically bonded tube-fin ex-
changers used in low-pressure applications such as air-conditioning industries and air coolers
for supercharged engine intake air. In the heat exchanger assembly process, the initial interfer-
ence, the microhardness of the softer material at the interface, contact area, and contact pressure
are parameters that determine the contact resistance
1301.
Selection of the proper bullet size
can optimize the degree of contact at the interface. During the last three decades, many re-
searchers have developed experimental methods to measure thermal contact resistance accu-
rately. An experimental method to measure contact resistance in a vacuum environment
is
described by Nho et al.
[30].
In a typical experimental setup, they found that the contact
resistance at the tube and fin interface was
17.6-31.5%
of the overall resistance
in
a
vacuum
environment,
Compact Heat Exchangers
I91
Qo
0
00
Tube$
with
Circular
fins
%
00
Straight
continuous
.Fins
f
Strip
fins
Figure
25
Characteristic flow length between major boundary layer disturbance for various heat
exchanger surfaces.
[From
Ref.
28.1
Tension-Wound Fins on Circular Tubes
For round-fin tubes with aluminum fins wrapped on steel tubes under tension, the contact
resistance increases quickly with the operating temperature
so
that their application is limited
to temperatures of
100°C
or less
[31].
Otherwise, the tension would be reduced, leading to fin
loosening, due to the higher thermal expansion of aluminum.
Integral Finned Tube
With an integral finned tube, there is no concern at the fin bond about heat-transfer resistance
and the integrity of tubing, regardless of temperature and pressure levels. However, only certain
fin geometries can be obtained with an extrusion process.
4.10
Induced Draft Versus Forced Draft
The heat transfer and pressure drop depend
on
the method used to generate the flow on the
tube bank, namely, induced draft or forced draft. When a fluid enters the tube bank, the level
of turbulence can change with penetration into the bundle. The tube bundle heat-transfer coeffi-
cient and pressure-drop performance
vary
for each additional row for a shallow exchanger, and
become independent of the number of rows only for the deep bundles with a very large number
of tube rows
[7].
Common practice is to apply a row correction multiplier to the deep bundle
correlations (ideal bundle) to account for these variations. Recommendations by Rabas et al.
[7]
for the mode of flow are discussed next.
I92
Chapter
4
Figure
26
Metal-to-metal contact between tube and fin.
Induced Draft
For induced draft, the recommended approach is to use the heat-transfer row correction
for
plain tube banks. Table
1
presents the plain tube bundle row corrections from two different
sources, Giedt
[32]
and ESDU
[33]
with values for more than five-tube rows. The bundle
pressure drop variation with row number is smaller than the heat-transfer coefficient variation
and hence the row effect is usually ignored.
Forced Draft
A
conservative approach suggested is to neglect the row correction for the forced draft mode
of operation for low-finned tube banks
[7].
5
THERMOHYDRAULIC FUNDAMENTALS OF
FINNED TUBE HEAT EXCHANGERS
It
is
a common practice to use the Colburnj factor to characterize the heat-transfer performance
and the Fanning friction factorfto characterize the pressure drop
of
the tube banks as functions
Table
1
Tube Bundle Heat Transfer Row Corrections
Number
of
rows
1
2
3
4
5
6
7
8
~~~~~
Giedt
0.65
0.71
0.80
0.85
0.90
0.94 0.96
0.98
ESDU
0.65
0.77
0.84
0.90
0.94 0.97
0.99
1.00
Source:
Ref.
7.
Compact Heat Exchangers
193
of
Reynolds number.
This
section provides empirical correlations for
j
andffactors. With these
correlations, the performance of geometrically similar heat exchangers can
be
predicted, within
the parameter range
of
the correlations.
5.1
Heat Transfer and Friction Factor Correlations
for Crossflow over Staggered Finned
Tube
Banks
During the last
50
years many investigations have been carried out to determine the heat
transfer and pressure drop over the tube banks. One of the first correlations was established by
Grimson
[34]
for bare tube banks.
A
standard reference for the heat-transfer and fraction data
of plate-fin heat exchanger surfaces is the book by Kays and London
[
171.
This book presents
j
andfversus Reynolds number plots for tube banks, tube-fin heat exchangers, and
52
different
plate-fin surface geometries. Some of these data were published in
Transactions
of
the
ASME.
Shah and Bhatti
[35]
summarize important theoretical solutions and correlations for simple
geometries that are common in compact heat exchangers. Most
of
the experimental data have
been obtained with air as the test fluid. The
j
factor and fanning
f
factor are defined rather
consistently in the literature by the following equations.
j=-
h(Pr)
u3
Gc,
=T)”’
Gc,
k
Nuk
or
h=-
Dh
where
G,,,
is given by
and is based on the minimum free
flow
area within the tube bundle. This minimum free flow
area includes the gaps between the outermost tubes and the side walls of the tube bundle. In
Eq.
44,
contraction and expansion losses and momentum losses are neglected; only flow fric-
tion effect is taken into account.
The Reynolds number is defined
as
where
d,
is the fin root diameter or the tube outside diameter, which depends on the tube
manufacturing techniques, and
Dh
is the hydraulic diameter.
Thej
factor is related to Stanton
number and Prandtl number by
j
=
st(pry3
(47)
where the Stanton number is given by