APTD-1554
HEAT TRANSFER
AND FLOW FRICTION
PERFORMANCE OF HEATED
PERFORATED FLAT PLATES
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Water Programs
Office of Mobile Source Air Pollution Control
Advanced Automotive Power Systems Development Division
Ann Arbor, Michigan 48105
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APTD-1554
HEAT TRANSFER AND FLOW FRICTION
PERFORMANCE OF HEATED
PERFORATED FLAT PLATES
Prepared By
Dr. Wen-Jei Yang
University of Michigan
Department of Mechanical Engineering
Ann Arbor, Michigan 48105
Contract No. 68-04-0019
EPA Project Officers:
William B. Zeber, Paul Kerwin
Prepared For
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Water Programs
Office of Mobile Source Air Pollution Control
Advanced Automotive Power Systems Development Division
Ann Arbor, Michigan 48105
June 1973
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The APTD (Air Pollution Technical Data) series of reports is issued by
the Office of Air Quality Planning and Standards, Office of Air and
Water Programs, Environmental Protection Agency, to report technical
data of interest to a limited number of readers. Copies of APTD reports
are available free of charge to Federal employees, current contractors
and grantees, and non-profit organizations - as supplies permit - from
the Air Pollution Technical Information Center, Environmental Protection
Agency, Research Triangle Park, North Carolina 27711 or may be obtained,
for a nominal cost, from the National Technical Information Service,
5285 Port Royal Road, Springfield, Virginia 22151.
This report was furnished to the U.S. Environmental Protection Agency
by The University of Michigan in fulfillment of Contract No. 68-04-0019
and has been reviewed and approved for publication by the Environmental
Protection Agency. Approval does not signify that the contents necessarily
reflect the views and policies of the agency. The material presented in
this report may be based on an extrapolation of the "State-of-the-art."
Each assumption must be carefully analyzed by the reader to assure that it
is acceptable for his purpose. Results and conclusions should be viewed
correspondingly. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
Publication No. APTD - 1554
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ACKNOWLEDGMENTS
The support of the Advanced Automotive Power Systems Development Divi-
sion, Office of Air Programs, Environmental Protection Agency for this work
is gratefully acknowledged. The study was carried out under contract number
68-04-0019. The author wishes to express his appreciation to Messrs. W.B. Zeber
and Paul Kerwin, Contract Monitors, for their assistance and encouragement.
During the first phase of the study, Dr. I.C. Macedo designed and tested
the experimental apparatus and Dr. J.W. Ou developed a computer program for
correlating test data. Professor John A. Clark and Mr. K.H. Choy had parti-
cipated in the study. Messrs. C.Y. Liang and T.L. Tsai also helped take some
test data. The author wishes to. extend his thanks to them for having helped
to complete this study.
ill
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TABLE OF CONTENTS
Page
LIST OF TABLES Vi
LIST OF FIGURES vii
NOMENCLATURE ix
ABSTRACT 1
INTRODUCTION 2
EXPERIMENTAL APPARATUS AND PROCEDURE 5
TEST RESULTS AND DISCUSSION 10
CONCLUSIONS 20
REFERENCES 21
FIGURES
COMPUTER PROGRAM FOR CORRELATING TEST DATA
V
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LIST OF TABLES
Table Page
1 Geometrical Dimensions and Arrangement of Oval-Slotted Surfaces 13
2 Uncertainty Intervals 19
VI
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LIST OF FIGURES
Figure Caption
1. Heat exchanger test core and position of thermocouples
2. Plate-rectangular perforated fin surface
3. Wind tunnel
4. Schematic of electric power supply loop
5. Schematic of test core installation in wind tunnel
6. Perforation geometry
7. (a) f and j versus Re, (b) f/j versus ฃ" , (c) f versus <$"s,
(d) j versus
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LIST OF FIGURES (continued)
23. f and j versus Re for t/b = 0.0665, slots; (a) through (e) for
6T = 5.7, 12.8, 17.4, 22.8 and 28.8%, respectively.
s
24. f and j versus Re for t/b = 0.0321, slots; (a) through (e) for
6T
25. (a) f versus Re, (b) f/j versus ST , (c) f versus 5" , and
5.7, 12.8, 17.4, 22.8, and 28.8%, respectively.
(d) J versus ^ for t/b = 0.141, staggered round holes
S
26. for t/b = 0.0665, staggered round holes
27. for t/b = 0.0321, staggered round holes
28. Performance parameters 22 FPI perforated fin [5]
Vlll
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NOMENCLATURE
A total heat transfer area
A free flow area inside test core
c
A. free flow area at core entrance
A cross-sectional area of test plate in the flow direction
A wetted surface area
w
a slot spacing, see Fig. 6
A* slot overlap (in flow direction), see Fig. 6
b plate spacing
C specific heat of air
DL hydraulic diameter of the flow channel, =4A L/A ; D, ,, for friction
loss; D. . for heat transfer
hj
d diameter of round hole
d slot width (in flow direction)
s
f fanning friction factor
G mass velocity
g conversion factor
h heat transfer coefficient
j heat transfer factor
K pressure drop coefficient; Ke, at core exit; K., at core entrance
k thermal conductivity of test plate
L flow length
I center-to-center distance between two adjacent holes, see Fig. 6
m rate of air flow
A? pressure drop; APT__, total-to-static; AP _ , static-to-static
1. o S S
p pitch; p , longitudinal; p , transverse
q rate of heat generation in test section
ix
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q rate of heat conduction into test section
K
Re Reynolds number based on hydraulic diameter; R ,., based on D ..;
R . , based on D, .
ej hj
r. hydraulic radius
T temperature; T , or air; T , or-air at core exit; T , of air
at core entrance; T , of plate surface
AT temperature increase of air in test core
t plate thickness
V air flow velocity; Vc, inside core; V^, at core entrance
w plate width or height of rectangular fin
w slot length (normal to flow direction)
S
M absolute viscosity of air
p air density, Pe, at core exit; p^, at core entrance, p , inside core
o porosity, OTJ, frontal; a , surface (or percent open area)
J. 5
Subscripts
F core front
f for friction loss
j for heat transfer
s nlate surface or slot
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-1-
ABSTRACT
A large scale modelling technique is developed to examine the effects of
perforation geometry on the heat transfer and friction loss performance of compact
heat exchanger fins. The test core consists of an electrically heated metal plate
and several unheated dummy plates forming flow channels. Both test and dummy
plates are identically perforated in a staggered pattern. The cores were
tested in a subsonic wind tunnel designed specifically for testing automobile
radiators, environmental system condensers, and liquid-to-air heat exchangers.
The plate surface porosity,the core frontal porosity, and the perforation size
and arrangement were varied. The Reynolds numbers ranged from those corresponding
to both laminar and turbulent flow. The heat transfer factor (j), friction
factor (f) and their ratio (f/j) for a single plate-channel system are obtained
as functions of the Reynolds number, the plate surface porosity and the core
frontal porosity. These results represent qualitatively those of a compact
plate-fin heat exchanger having the same geometric scaling factors when these
systems are represented by appropriate geometric, dynamic and thermodynamic
similarity parameters. The technique can be used to understand the performance
of compact fin surfaces in order to determine an optimum performation geometry
and to form a basis for rational design of compact-heat exchangers.
It is found that under certain circumstances plate perforation will pro-
duce significant improvement in heat transfer for the same pressure drop. These
studies are directed to the design of air-cooled condensers for Rankine cycle auto-
motive engines, marine power propulsion systems and the dry cooling towers of
extra-high capacity electric power plants.
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-2-
INTRODUCTTON
The cycle efficiency of a steam or gas turbine power plant may be considerably
enchanced by the use of a waste heat exchanger. In order to exploit'the small size
and low weight advantages of the power plant, the compactness of the heat exchanger
is an imperative objective in design, with proper considerations given to heat
recovery and pressure drop. The need for compactness in such heat exchangers has
prompted the use of extended surfaces, surface roughness, boundary layer promoters,
and boundary layer interrupters to augment the heat transfer coefficient.
In recent years, a number of studies have been published on the heat transfer
and friction loss performance of compact heat exchangers, notably the work of
Kays and London [1]. Since this type of heat exchangers deals with low density
fluids the friction characteristics of the surface is as important as the heat
transfer behavior.
Among the extended surfaces of the plate-fin and tubular types, the louvered-
plate-fin surface has been favored because of its high area-to-volume ratio and
its higher heat transfer coefficient resulting from boundary layer interruptions.
However, the high heat transfer performance is accompanied by high resistance to
flow. The perforated-plate-fin surface has heat transfer and friction loss perfor-
mance comparable to the louvered-plate fin surface. However, the compactness of
the louvered fin type heat exchangers is limited by the geometry of the louvers.
If very high compactness is required, such as for the condenser in the Rankine-
cycle automotive steam power plant, perhaps only the plain-plate-fin surface or
perforated-plate-fin surface can serve the purpose. The excellence of the latter
surface over the former has been demonstrated in Reference [1].
By virtue of its high heat transfer and low friction loss performance, the
perforated fin tubular heat exchangers can be made either in small size and light
weight as air-cooled condensers in marine [2,3] and automotive [A] propulsion
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systems or in large size as air-cooled heat exchangers in dry cooling towers of
extra-high capacity electric power plant [5]. Kays [6] has reported that perfora-
tion results in a substantial increase in heat transfer performance without intro-
ducing a pronounced form drag. This observation was later confirmed by Pucci et al.
[2] and Shah and Osborn [3]. Wong et^ al. [4] have tested very compact (22 fins
per in.) perforated-fin air-cooled condenser cores for Rankine-cycle automotive
propulsion systems. Their test data supported the Kays observation. However, a
recent work of Mondt and Siegla [7] have indicated some conflict in the generality
of these observations. Over a range of area densities (heat transfer area divided
by core volume), no significant improvement in heat transfer was observed for the
same pressure drop. Miller and Leeman [8] have also concluded no beneficial effect
due to perforations.
The present study serves two main purposes: (1) to determine the effects of
the system parameters and the Reynolds number on the heat transfer and friction
factors of perforated plate surfaces and to rationalize the conflicting performance
data previously reported [1,4,7,8]; (2) to determine the system parameters for
the optimum performance in the operating range of the Reynolds number. The system
parameters include perforation geometry and arrangement, plate thickness-to-spacing
ratio, channel length-to-hydraulic diameter ratio, plate surface porosity and
frontal core porosity. In order to achieve fine detail, a large scale was chosen,
with individual units approximately eight times larger than those fins used in
compact condensers. The perforated test and dummy plates have been arranged in
parallel to form a test core with rectangular channels for the flow of cooling
air. The test plate can be considered a section of rectangular fins attached
between two plates in a compact heat exchanger.
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-4-
In the present study, only one out of four walls of the rectangular test
channel is heated for studying heat transfer performance using the steady state
method. As a result, some test results expressed in terms of the f/j ratio take
values even less than the theoretical limit of 2 for a flow channel with all xvalls
being heated. Detailed discussion is addressed to the question of very low f/j
values. With the use of an appropriate Reynolds number for single-wall heated
flow channels,the f/j ratios agree well with those for all-wall heated flow channel
obtained by the single-blow(transient) method [9]. The effects of plate (or fin)
thickness on the heat transfer and pressure drop performance are also discussed.
The reasons for no beneficial effect due to perforations [7,8] are explained.
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-5-
EXPERIMENTAL APPARATUS AND PROCEDURE
The experimental setup used to investigate the heat transfer and friction
loss performance of perforated plates consisted of a heat exchanger test core
situated in a subsonic wind tunnel.
The heat exchanger test core, as schematically illustrated in Fig. 1, was
constructed for large scale testing of the plate-rectangular fin surface, Fig. 2.
It consisted of an electrically heated aluminum plate and several dummy plates
made of. fiberglass. All the plates were 1/32-inch thick (t) and identically
perforated with round or slotted holes of a staggered arrangement. The number
and size of the round or slotted holes determine the surface porosity or percent
open area. The plates were arranged in parallel with the test plate as the
center piece. Wood slabs were used to space the plates for air flow passages.
The thickness of the wood slabs was varied to have different values of the plate
thickness-to-spacing ratio or the frontal porosity. The plates and wood slabs
were stacked together by lA-inch bolts. The total number of the plates and
slabs determines the frontal area of the test core: 6-inch width, W , by H-inch
height. Thus, the W/t ratio for the test core was 192. This may be compared
with 80 , the W/t ratio, for a fin of 0.00^-inch thickness and 0.320-inch height,
which is that of a prototype heat exchanger used -as a reference. For both
systems, the ratios were large enough to warrent the neglect of side effects
on the flows through the channels. The test core was 6 inches long in the
flow direction.
Aluminum was selected as the material for the test plate mainly for several
reasons: (i) its high thermal conductivity which tends to uniformize the
temperature distribution, (ii) sufficiently high electric resistance to warrent
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-6-
for electrical heating, (iii) easy for perforation by drilling or punching,
and (iv) the Garrett condenser for low-pollution potential steam engine is made
of the same material. Fiberglas was used as the dummy plates. Only the test
plate was heated for the investigation .of convective heat transfer to the air,
while the unheated dummy plates were used for the study of friction loss of
air flow over the plates.
The wind tunnel consisted of a contraction section, test section, diffuser,
fan, and discharge ducting as shown in Fig. 3. It was originally designed with
the capability for testing both scale models and full size automotive radiators
and condensers over a range of vehicle speeds and air-side pressure drops
comparable to automotive application [10] .
Three flow control methods may be used to meet the air flow requirements
of the tunnel: (l) a 2:1 fan speed reduction by means of switching the volt-
age of the electric motor which reduces fan air flow by this same ratio;
(2) variable inlet guide vane geometry capable of producing a continuous variation
in fan air flow from 15$ to 100% of maximum air flow; and (3) a bypass around
the test section which can produce a continuous variation in test section air
flow from 10 to 100$ of maximum test section air flow. The change in fan
speed and the inlet guide vane geometry produce changes in fan characteristics
while the tunnel bypass alters the total system flow characteristic to vary the
test section air flow. The bypass also allows the fan to operate in a surge-
free region at all times. The bypass is accomplished by constructing the
contraction section and the test section as a single unit and then translating
this unit forward relative to the fixed diffuser and fan.
In order to obtain the information on the uniformity of the air flow in
the test section of the wind tunnel, horizontal and vertical Pitot tube traverses
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-7-
were made in a plane normal to the tunnel longitudial axis and located near the
middle of the test section. The traverses were made at 3-inch intervals except
near the walls where the spacing was reduced to 1.5 and then to 0.25 inches
from the walls. Using the velocity at the center of the tunnel as the reference
velocity (at 77-1 ft/sec), it was found that at a distance of 1.5 inches velocities
were generally within 1;5$ of the reference value. These results indicated
the uniformity of air flow in the test, section of the wind tunnel.
The test core was installed in the test section of the wind tunnel.
Electric power was supplied to the test plate through cables from a low-voltage
M-G power supply (36 Kw, 0-12v, 0-3000 amp). In order to insure flexibility
of operation, the power source and the test plate were arranged in series with
a stainless steel pipe to form a power supply loop, Fig. ^. The pipe which
was internally cooled by water from municipal supply was designed to dissipate
excess electric power. By varying the length of the pipe and/or by adjusting
the water flow rate through the pipe, the electric power dissipated in the test
plate was adjusted so that the plate surface temperature was set in a desired
range. Because of relatively low electrical resistance, only a fraction of
electric power from the power supply was consumed by the test section. A shunt
of known electrical resistance was installed in the power supply loop. The voltage
drop across the shunt and the test plate (only the portion that was exposed
to the air stream) were measured by a Weston Model 622 Millivoltmeter. The
electric power that dissipated in the test section was transmitted to the air
stream.
Since the frontal area of all of the test cores was considerably less than
the wind tunnel test section area, the cores were mounted on a support which was
fixed to the bottom of the test section, Fig. 5- Baffles of constant area section
were installed immediately upstream as well as downstream of the core. A bellmouth
in the inlet end of the constant area section was used to insure proper inlet
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-8-
flow conditions. Sealing was used to insure proper inlet flov conditions.
Sealing was used around the core-baffle joint and also the baffle-test section
wall joint to insure that all of the airflow which entered the constant area
section flowed through the core.
Two Pitot tubes were inserted into the constant area sections, one at
upstream and the other at downstream. The Pitot tubes were connected to a CGS 5-23-1
Type (Range 0.1 psi) Barocel pressure sensor. The following four pressure
differences were read from a CGS Class I barocel electronic manometer: total
to static pressure differences at both upstream and downstream and total to
total and static to static pressure differences between upstream and downstream.
The air velocities at the inlet and exit of the test core and the static,
dynamic and total friction losses in the test core were measured by copper-
constantan thermocouples and read on a L & N 8662 precision potentiometer.
The inlet air temperature was read by a thermocouple located near the tip of
the upstream Pitot tube. Nine thermocouples were mounted on the test
plate surface at 1/2" back from the downstream edge, Fig. 1. One was on the
center line of the test plate and the other eight were installed symmetrically,
four on .each side spaced at 0", 1/V, 1/2" and 1-1/2" from the wall. The tips
of these thermocouples, electrically insulated from the test plate by very
thin mica films, were cramped tightly on the plate surface. The readings of
these nine thermo-couples were used to determine the tempaature gradients of
the test plate at the wall. Their geometrical average was used as the plate
surface temperature. Two copper rods were erected vertically at 1-inch distance
downstream from the edge of the test plate at 1.5-inch from the center of the
constant area section on each side. Six thermocouples were mounted on the
rods, two on the left rod and four on the right rod. They measured the distri-
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bution of the outlet air temperatures at six different vertical locations down-
stream from the test plate, Fig. 1. One thermocouple was iinea up wicu tuซ=
test plate, while the vertical location of the other five thermocouples was varied:
at 1/8", 1/4", 1/2", 1" downward and 1/4" upward from the test plate, ine in-
tegrated mean value of the measured temperature distribution was employed as the
average outlet temperature of the air stream ..from ,the channels heated by the test
plate. During adiabatic runs for pressure drop measurements tne copper roas were
removed.
For testing, the fan was started. The desired, air velocity through the
test section was set "by means of adjusting bypass opening. Water to the power
dissipating tube was turned on. Power supply was turned on and adjusted to
bring the plate surface temperature to about 200ฐF. When steady state values
had been established, air and plate surface temperatures and voltage drops
were recorded. After these measurements, the two copper rods with six air
thermocouples were removed. The same test was repeated without heating the
test plate and pressure drops were measured. This extra step was taken in order
i
to eliminate the effect of the copper rods on the pressure drop readings. These
steps were repeated for successive data points.
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TEST RESULTS AND DISCUSSION
The electric power dissipated as heat (at the rate of q ) in the test plate
is equal to the product of the voltage drop across the test plate and the cur-
rent flowing in the power supply loop. Because of high thermal conductivity
of the aluminum test plate, a substantial amount of the heat being generated
in the portions of the test plate which protruded out of the baffle was trans-
mitted into the test core by conduction. The amount of heat q transferred into
the test core by conduction is given as 'ฃr&4J(Tx// \AX) \ where k is the
thermal conductivity of aluminum, f\p is the cross sectional area of the test
plate normal to air flow, and [~'^X 1 and (^/,-J are the temperature grad-
ients at the baffle walls in the direction normal to air flow. These two com-
ponents of heat q and q, , were then transmitted to the air stream in the chan-
e K
nels wetting the test plate by convection. Therefore, the heat transfer co-
efficient between the test plate and the air stream, h can be evaluated using
the equation q +q, = hA(T -T ), where A is the heat transfer surface area, T
6 K. S ci S
is the plate surface temperature and T is the mean bulk temperature (average
3.
of the inlet and the outlet) of the air stream. As a result of convective
heat transfer, the enthalpy of the air streams has increased by mC (T -T . ) ,
p 3G ell.
where m is the flow rate of the air streams in the channels wetting the test
plate, C is the specific heat of the air at constant pressure and T. and T
are the air temperatures at the inlet and exit, respectively. Good agreement
between the enthalpy change of the air stream and the power input was obtained
in the tests.
All physical properties of the air were evaluated at the mean bulk temper-
ture. The flow velocity entering the core V is calculated using the Bernoulli's
equation:
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where (-4 /I- ) is the total-to-static pressure difference measured by the up-
stream Pitot tube, J- is the density of the fluid entering the core and g"
is the conversion factor. The flow velocity is not different appreciably from
that leaving the core based on (d/j-* ) measured by the downstream Pitot tube.
This indicates virtually no change in the fluid density from the core entrance
to the core outlet, i.e., R f^sjL in which the subscripts i, m and e de-
/ i ftn *ig.
note the core entrance, the average value in the core and the core outlet,
respectively. Due to flow area change the flow velocity inside the core V
is calculated from
wherein A and A represent the free flow areas at the core entrance and inside
the core, respectively.
The Reynolds number which indicates flow conditions in the test core is
defined based on the hydraulic radius r, of the flow channels in the core as
where U is the absolute viscosity and G is the mass velocity defined as G=?m\ฃ
The hydraulic radius is defined as the minimum flow area inside the core A
divided by the wetted perimeter. For the present system, it is equal to
wb
2(vป/+b) wnere b is the plate spacing and w is the width of the channel.
The friction factor f is defined based on the static pressure drop across
the test core A P* and determined by the pressure drop equation (2-26a) of
Reference [1]:
t?
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in which the effect of flow acceleration on pressure drop is neglected and the
entrance and exit loss coefficients K and K are determined by Fig. 5-3 of
Reference [1]. Both the j and f factors are functions of the frontal porosity
of the test core, the plate surface porosity (percent open area) and the Rey-
nolds number.
The heat transfer performance is expressed by the heat transfer factor j,
which is defined as
in which Pr is the Prandtl number.
The frontal porosity ฃ*p is the ratio of the free flow to frontal area.
It is related to the ratio of the plate thickness to spacing as
*-7T^
The plate surface porosity ฃ1 can be expressed as
for the round hole pattern in a staggered arrangement, where d is the hole
diameter and 1 is the center-to-center distance between two adjacent holes,
Fig. 6. It is a function of only one dimension less parameter d/1. In the
case of the oval slotted pattern
2
(8)
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for *L-^ 1, where w is the slot length, d is the slot width, p is the
longitudinal pitch (the center- to-center distance between two adjacent trans-
verse rows measured in the flow direction) , and p is the traverse pitch (the
distance between centers of the slots in adjacent longitudinal rows measured
perpendicularly to the direction of flow) . It is functions of three dimension-
less parameters: w /d , p /d and p./d . For the case of w /d = 1, 65
SSฃS tS SS
of the oval shotted pattern reduces to that of the round circle pattern.
a/d = 0 corresponds to the case of an infinite slot.
s
Both the round hole patterns and the oval slotted patterns, each having
five plate surface porosities of 5.7, 12.8, 17.4, 22.8, and 28.8%, were fabri-
cated and tested. The round-hole surface was tested in the first phase of the
project (from May, 1971 to December, 1971). In the second phase (from January,
1972 to August, 1972), five different oval-slotted surfaces were tested whose
geometrical dimensions and arrangement are given in Table 1. The number of
figures illustrating the test results for the slotted surfaces is also listed
in Table 1.
Test Results
Surface
1
2
3
4
5
Vin>
1/2
1/2
2
2
1/2
ds(in)
1/8
1/8
1/8
1/8
1/16
a*(in)
0
1/8
0
1/2
0
in Figures
7
10
13
16
19
- 9
- 12
- 15
- 18
- 21
Table 1. Geometrical Dimensions and Arrangement of Oval-Slotted Surfaces
Here, a* is defined as the slot overlapping width in the flow direction. Sur-
face 1 was tested during the first phase of the project and it was repeated in
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the second phase. The surface porosity was changed by varying the center-to-
center distance d, or p .
Three plate spacings were tested: 0.974", 0.47" and 0.221". For the plate
thickness of 1/32", the thickness-spacing ratios were 0.0321, 0.0665, and 0.141,
respectively, or equivalently, S = 0.970, 0.937 and 0.875, respectively. The
t/b ratios for a plate-^fin heat exchanger with rectangular fins of 0.004-in
thickness are 0.046 and 0.0962 for the fin pitches of 11 and 22 fins per inch,
respectively.
The test results were correlated for the j and f factors and their ratio
against (i) the Reynolds number with plate porosity as parameter in the a series
of Figs. 7 through 21, (ii) against the plate surface porosity with the Reynolds
number as parameter in the b, c and d series, and (iii) the Reynolds number with
a", w and d as parameters in Figs. 22 through 24. The test results for the
s s
round hole surface are included in the report in Figs. 25 through 27. These
results were obtained by correlating the test results using the flow velocity
at the core entrance.
The variables to be examined include hole or slot size (d , w or d), de-
S S
gree of slot overlapping a*, plate surface porosity & and frontal porosity
S
tf'p or t/b).
1) Effects of slot length
Two slot lengths had been studied, w = 2" and w = 1/2". Referring to
S o
Table 1, the comparisons were made between surfaces 1 and 3 for the in line
arrangements and between surfaces 2 and 4 for the overlapping arrangements.
In each case, w is the only variable with d being held constant at 1/8 inch.
s s
Figures 22 through 24 illustrate the effects of slot length on the f and j
factor. It is disclosed that the f factor for the slot length of 2" is con-
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sistently lower than that for the slot length of 1/2". In general, the j fac-
tor for the slot length of 2" is higher than that for the slot length of 1/2".
Consequently, the longer slots (w = 2") have lower f/j ratios than the shorter
s
ones (w = 1/2") for both the in-line arrangement and the overlapping arrange-
men t.
2) Effects of slot width
The effects of slot width (d ) on the friction loss and heat transfer per-
formance of the perforated plates were studied by comparing a slot width of
1/8" with that of 1/16". Referring to Table 1 again, this is a comparison
between surfaces 1 and 5 both being the in-line arrangements with a* = 0 and
w = 1/2". The results indicated that for the slot width of 1/16", the j fac-
S
tor is consistently higher than that of the slot width of 1/8", and the f factor
is slightly lower for the narrower slot than that of the wider one. Conse-
quently, the narrower slot (d = 1/16") has a lower f/j ratio than the wider
S
one.
3) Effects of slot overlapping
Two overlapping arrangements were studied: surface 4 with
a* = 1/2" and surface 2 with a* = 1/8". The effects of slot overlapping were
evaluated by comparing the results for surfaces 2 and 4 with those for sur-
faces 1 and 3 with the in-line arrangements having identical slot width and
slot length. An examination of these results shows that there is no appreciable
difference in f, j, or f/j between the two slot arrangements. This is an in-
dication that slot arrangement plays an insignificant role on both the heat
transfer and flow friction performance.
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4) Effects of Reynolds number
The effects of the Reynolds number on the f and j factors depend largely
on the t/b ratio as can be seen by comparing Figs. 22, 23 and 24. For the
value of t/b equal to 0.141, the f factor decreased with an increase in the
Reynolds number until the latter reached the value of approximately 4,000 at
which high-pitch noise generated in the test core was heard. A further increase
in the Reynolds number was marked by a sudden upturn in the value of f which
was evidenced by the generation of high-pitch noises (those test data encircled
by a dotted line). This increase in the f factor had eventually resulted in
a high f/j ratio when the Reynolds number exceeded 4,000. For the value of
t/b equal to 0.0665, the value of f decreased with an increase in the Reynolds
number. It reached a minimum value at the Reynolds number of approximately
8,000 and then increased for a further increase in the Reynolds number. How-
ever, noise was detected only at the highest Reynolds number in the test ser-
ies, approximately 15,200. At the t/b ratio of 0.0321, no noise was ever de-
4
tected up to the Reynolds number of approximately 3 x 10 . The effect of the
Reynolds number on the f factor was found to be very minor. For all values
of the t/b ratio, the j factor was found to decrease with an increase in the
Reynolds number.
5) Effects of plate surface porosity
A solid plate and five perforated plates were tested. The plate surface
porosities correspond to 0, 5.7, 12.8, 17.4, 22.8 and 28.8%. Regardless of
perforation size and geometry, generally, both the f and j factors increased
with an increase in the plate surface porosity. But because of the problem
of noise generation which becomes more severe as the surface Is more perforated,
the optimum plate surface porosity is taken to be between 15 to 22 percent.
-------
-17-
As the surface porosity is increased beyond 22 percent, the problem of noise
becomes quite serious. This can be realized in the plots of f versus Re for
the surface porosity of 28.8 percent. Especially at the highest Reynolds
number, the intensity of noise generated in the test core was very high, and
the f factor increased sharply. These phenomena were especially pronounced
at the t/b ratio of 0.141.
6) Effects of frontal porosity
A comparison of the test data for three t/b ratios 0.141, 0.0665 and 0.0321,
revealed that the t/b ratio of 0.0665 gives the best f/j ratio. Noise gener-
ated by the test core is related to the t/b ratio. No noise was detected at
the t/b ratio of 0.0321 even at high Reynolds number and high plate surface
porosity. At the t/b ratio of 0.0665, noise was heard only when the Reynolds
number exceeded approximately 11,400. Therefore, the optimum t/b ratio is
between 0.0665 and 0.141.
7) Error analysis of test data
An error analysis was carried out to evaluate the uncertainty intervals
for the experimental results using the method described in Reference [H]ซ The
95 percent confidence limits for both the f and j factors were evaluated at
three representative Reynolds numbers and three t/b ratios: 0.141, 0.0665 and
0.0321, respectively. Only the test plate having w = 1/2", d = 1/8", a* = 0
s s
and surface porosity of 5.7 percent was used in the error analysis. However,
the results which vary only with the Reynolds number apply to any test plates
irrespective of their perforation size and geometry and surface porosity. The
percentage of error for the f and j factors increases with a decrease in the
Reynolds number. The average percentage of error for the j factor is around
14 percent and that for the f factor is about 13 percent. The results of the
-------
-18-
error analysis were tabulated in Table 2 and the uncertainty intervals were
marked in Fig. 7a, 8a, and 9a.
It is important to note that the test results have confirmed the geometric
and dynamic similarities through the following two observations. First, the
"transition" of air flow patterns is delayed from Re=2,000 to about 3,500 as
t/b decreases from 0.2 to 0.0964, as illustrated in Fig. 28. The same pheno-
menon is observed in the present results. The "transition" is delayed from
Re of approximately 5,000 to 9,000 to 17,000 (which is disclosed from the plot
of j versus Re) as t/b decreases from 0.141 to 0.0665 to 0.0321. Second, the
values of f/j for the plate surface porosities of 12.5% and 25% in Reference
[5] are practically the same. The equal values of f/j for the two porosities
is confirmed in the present results for both perforated patterns.
-------
Table 2. Uncertainty Intervals
Slot-Size: 1/2" x 1/8"
Perforation Geometry: in-line, a*=0
t/b
O.lUl
O.lUl
O.lUl
0.0665
0.0665
0.0665
0.0321
0.0321
0.0321
Re
7883
3153
788
15156
6062
1516
28137
11255
28lU
j
0.0066
0.0076
0.0117
0.0066
0.0081
0.013^
0.0061
0.0082
0.0115
+^ x 100$
J ,
12.0$
13.^$
27-2$
12.3$
lU.O$
28.0$
13.0$
15-0$
27.0$
f
O.OlUO
0.0108
0.0223
0.0112
0.0095
0.0150
0.0121
0.0126
0.0133
f> f
f
5.0$
12.6$
50.8$
5.0$
12.7$
57.0$
5-1$
13.0$
7^.0$
VO
I
-------
DISCUSSION
Figure 2 shows: the f/j ratio :at some values less than two. This may appear
at first to be at variance with certain established vievfs. However, one may
recall that for laminar flow inside tubes or ducts, the ratio f/j=8.6 (L/Dft/Re)
may take any values depending "upon the magnitude of L/D, and Re. Hence, in this
case there is no reason why a value of 2^is aclower limit for this ratio. The
presence of perforated holes should not -change'the order of magnitude of f/j
substantially. Secondly, the present study deals with the case of asymmetrical
heating. That is heat transfer from one wall (of the test plate), while the fluid
flow wets all four channel walls. Therefore, the hydraulic diameter, defined
as AA L/A , will have two different values: D^ .=4b f of !heat transfer and
c.' w .:.- .' . to -t- chj
D =2wb/(w-Kb) for friction^ loss. ;As a result; the characterizing Reynolds'-,
n r > * *r >^ *
number takes two different forms: Re. = 4bG/y for heat transfer and Re,=2wbG;/y
(w+b) for friction loss. For the same flow velocity-, Re. is about two times
Re,: when the channel width is much greater than the channel height. Sincecboth
the j and f factors dependiupon both the'Reynolds number and the hydraulic;-
cdiameter, the relationships of- j=j(Re., -L/D, .)-.and f=f(Re>f, L/D,f) should 6e
',' ' ' ' '^
employed in an asymmetrical heating case. Under this circumstance, the ratio of
I :' '. 'I I;
f/j will lead to a physical situation which is entirely different from that for
a symmetrical heating case. For convenience, both f:and j are plotted against
Ref here,/ .-_ In the event all plates are heated (as vindicated by the sub-
script 2) ,;: the hydraulic diameter D, . will be exactly 2b,i since the two vertical
walls of a\ 'ฃlow channel are unheated. Then, the corresponding Reynolds number
" * ' : I I ^ '^'
is one hali that of the one-plate heated case (as denoted! by .the 'subscript 1)
.'j 'i f j i ^.( . -'-
;:. I ' i r, ;.: :=-
for the same flow velocity. A. preliminary result in*[9] indicated that jn (in
;-; ^ . ; : y '^ \ j . U) . j .., I 3 ฃ 7 1
"Ithe present; study) at Re.^jis approximately equal to! j?^(6btaa.ned';bya the Single
Blow Technique) at Re._ for the!same flow velocity or for;Re '=2R'e.?, see Fig.
7-a for j. With this approximation, all test results for j.. for o=0 case were
-------
-21-
recalculated in terms of j-, when t-, = fj anc* Ref=Re-2- In so doin8 all ^?^2
ratios have become either equal to or greater than 2, within experimental un-
certainty. Hence, it should be recognized that the f/j ratio has been employed
merely for convenience to indicate the overall behavior of a symmetrically heated
flow channel. One should not extend its implications, particularly the concept
of f/j=2, to an asymmetrical heating case.
Another item of importance is the problem of noise generation in the per-
forated surfaces. As was noted in the previous section, noise intensity increases
with an increase in the surface porosity at high Reynolds number. It is shown
in [9] that noise is edge tone in nature and high intensity occurs when the
vortex shedding frequency coincides with a natural frequency of either the plate
or the air column in the test core. This noise may be removed or eliminated
by inserting plate supports to increase the natural frequency of both the plates
and the air column.
As disclosed by the visualization study in Reference [3], several different
flow patterns are generated inside and downstream from the cavities (round
holes and slots) depending upon the slot width (or the diameter in case of a
round-hole cavity) to plate thickness ratio, ds/t or d/t. As a result, both the
pressure drop and heat transfer performance (also noise generation and plate
vibration) are significantly affected by the ratio. For low values of the ratios
as were the cases in References 7 and 8, the fluid produces neither circulation
inside the cavity nor cross flow through the cavity into the stream on the
other side of the plate. In other words, the fluid experiences very little or
no disturbance when it flows over the cavities as if no cavities are there.
This leads to no merit due to perforations as concluded in References [7] and
[8]. On the other hand, when the ds/t ratio exceeds a value of 2.00 in case of
slot perforation or 2.75 in case of round-hole perforation, either a counter-
-------
-22-
clockwise circulation inside the cavity and/or cross flow through the cavity
into the stream on the other side of the plate occurs, resulting in a rigorous
turbulence and mixing downstream from the cavity. Significant improvement in
heat transfer accompanied by an increase in pressure drop is observed.
-------
-23-
CONCLUSIONS
A large scale technique is developed to examine the effects of perforation
geometry on the heat transfer and friction loss performance of compact heat
exchangers of the plate-perforated rectangular fin surfaces. Through the com-
parison of the test results with those of the compact heat exchangers of dif-
ferent scale, the geometric and dynamic similarities of both systems are con-
firmed, thus establishing the validity of the large scale technique.
The technique is simple and quick to carry out and may also be employed to
determine the optimum perforation geometry and to understand or interpret
the test data of the compact heat exchanger. It is concluded from the
study
1. Plates perforated with smaller slots seem to give the better overall heat
transfer-friction loss performance, i.e.lower f/j, than those with larger slots.
2. The optimum plate thickness to plate spacing ratio, t/b, is found to be
between 0.0665 and 0.141.
3. With noise problems taken into consideration, the optimum surface porosity
for all slotted plates appears to be between 15 and 22 percent.
4. Noise generation becomes a serious problem under the conditions of high
Reynolds numbers when the plates with high surface porosity are arranged in a
high t/b ratio.
5. An increase in the slot length results in a slight decrease in the f fac-
tor but an increase in the j factor.
6. The degree of slot overlapping in the flow direction has little effect
on the f/j ratio.
-------
-24-
REFERENCES
1. W. M. Kays and A. L. London, Compact Heat Exchangers, 2nd Ed., McGraw-Hill
Book Co., New York (1964).
2. P. F. Pucci, C. P. Howard and C. 11. Piersall, Jr., "The Single Blow Tran-
sient Testing Technique for Compact Heat Exchangers Surfaces," Journal
of Engineering for Power, Trans. ASME, Ser. A, 89, pp. 29-40 (1967).
3. R. 11. Shah and H. H. Osborn, "Final Report-Advanced Heat Exchanger Design
of Compact Heat Exchangers When Operating in a Marine Environment," Air
Preheater Company, Wellsville, New York (May 1967).
4. S. Wong, J. D. Duncan, D. W. Graumann, J. C. Gibson and J. J. Killackey,
''Compact Condenser for Rankine Cycle Engine," Final Report 71-7464 (pre-
pared for Office of Air Programs, Environmental Protection Agency, Ann
Arbor, Michigan), AiResearch Manufacturing Co., Los Angeles, California
(June 1971).
5. L. Forgo, :'Some Extra High Capacity Heat Exchangers of Special Design,"
Proc. 1972 International Seminar on Recent Developments in Heat Exchangers,
International Center for Heat and Mass Transfer, Trogir, Yugoslavia (1972).
6. W. M. Kays, "The Heat Transfer and Flow Friction Characteristics of a
Wavy Fin, and a Perforated Fin Heat Transfer," TR No. 39, Department of
Mechanical Engineering, Stanford University, Stanford, California (1958).
7. J. R. Mondt and D. C. Sigela, "Performance of Perforated Heat Exchanger
Surfaces," ASME Paper No. 72-WA/HT-52 (1972).
8. 11. L. Miller and C. A. Leeman, "Heat Transfer and Pressure Drop Charac-
teristics of Several Compact Plate Surfaces,1: AIChE Preprint 9, 13th
National Heat Transfer Conf., Denver, Colorado (1972).
9. C. Y. Liang, "Heat Transfer and Friction Loss Performance of Perforated
Surfaces," Ph.D. thesis in progress, Department of Mechanical Engineering,
University of Michigan, Ann Arbor, Michigan (1973).
10. J. A. Clark, C. A. Siebert, R. B. Keller, M. Borden, and J. C. Hoo,
"Automotive Radiators Manufactured by the Electroforming Process," Final
Report of ORA Project 05335 (under contract with International Copper
Research Association, Inc., Mew York), University of Michigan, Ann Arbor,
Michigan (December 1964).
11. S. J. Kline and F. A. McClintock, "Describing Uncertainties in Single-
Sample Experiments," Mechanical Engineering, 75, pp. 3-8 (1953).
-------
BOLT
WOOD PLATE
PERFORATED
DUMMY
PLATE
COPPER ^,
CONNECTORSN
PERFORATED
TEST PLATE
WOOD SLAB
Fig.l Heat exchanger test core and posicton
(not exact location) of thermocouples
ts)
en
* HORIZONTAL .POSITION OF
PLATE THERMOCOUPLES
ป VERTICAL POSITION OF
OUTLET AIT
THERMOCOUPLES
-------
PLATE
\\ \ \\\\\\\^\\\\\\\\\\
/ / /
'
t
1
V
1
1
V
'
/
t
/
f / / /
/
/
\
t
SJ_
;
^
/
^J-U
^-\
F
PERFORATED
RECTANGULAR
FIN
i
N>
VSAVSA \\^:\\ \\\\\\\\
PLATE
Fig.2 Plate-rectangular perforated fin surface
-------
CONTRACTION CONE
9:1 RATIO
WESTINGHOUSE 8O3O
25 HP MOTOR
IOOOO RPM at 7"SP
INLET VANE FLOW CONTROL
2x2-4'LONG
22'-
Pig.3 Wind tunnel
-------
WATER IN
COPPER
CONNECTORS
TEST
PLATE
5/8-OD BWG
16 STAINLESS STEEL
TUBE
COPPER
CONNECTORS
*WATER OUT
i
to
00
SHUNT
POWER
SUPPLY
(12V, 3000 A MG SET)
Fijr,.4 Schematic of electric power supply loop
-------
BY-PASS
FLOW
PITOT TUBES
DIFFUSER
CONSTANT
AREA INLET
r-n
\ i 1
X
RODS
\ ^
/
ft
^
^
^ปTEST
CORE
SUP-
PORT
-f
!
u
^
*k
/
1
\
\
\
\
\
/SECTION J
1, ^m^y
t
t
t
BELLMOUTH
_^ C0f
AIR
FLOW
* ^a
ซ
t
BAFFLE
*
*
t
\COPPER
CONNECTOR
^ITRAC
CON
(
Tf ~ >
) -J- wL.
TION
E
i
N)
vo
1
)
CABLES FROM
POWER SUPPY
Fir,. 5 Schematic of test core installntion in wind tunnel (elevation view)
-------
(b) OVAL SLOTTED
PATTERN
C ) ( )
dEE)(EEirD
3
( ) . ( )
AIR FLOW
Perforation
(a) ROUND HOLE
PATTERN
o o o o
o
o
o
i4
o
o o o
O
I
AIR FLOW
-------
-31-
i rj i i
*.J
X ;- '
* i*
TrG) -rA
7 :
i * It,- 1
J
-2
U 10
-i
3*10 ,
i
"... .'... .
SYMBOL
7 V "t '
S! T ' ^ ' : T
.. T... .. .? .:.Dฐ .i' :
: : . *? ; ,
- --; -''v , o--- ; ' ,q /
7" ' ; v .'; i r - "
i
^ - * ^ v ;
o- ซ v ; ;;; ^ ; :
10
10"
Fig. 7a. f and j versus Re, for t/b=0.141, 1/2" (length) x 1/8" (width) slots
in in-line arrangement.
-------
2 IB
: A
-ts-
P '
iKe.
01
D-
i i
T
- -I
JQBA
_
10
15
20
25
O
' i _ 4 _ _ j _
f - I f
Fig. 7b. f/j versus CTS, for t/b=0.141, 1/2" (length) x 1/8" (width) slots in in-line arrangement
-------
: ' : i . '
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0 A t
A i B J B i
k i
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Fig. 7c. f versus tfg, for t/b=0.141, 1/2" (length) x 1/8" (width) slots in in-line arra
t
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Fig. 8c. f versus 0~s, for t/b=0.0665, 1/2" x 1/8" slots in in-line arrangement
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Fig. 9b. f/j versus
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arrangement.
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Fig. lla. f and J versus Re, for t/b=0.0665, 1/2" x 1/8" slots in
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overlap arrangement.
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Fig.. 19c.- f .versus (J^, for t/b=0.141, 1/2" x 1/16" slots in inrline arrangement.
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Fig. 22a. f and j versus Re for t/b=O.Ul, slots; for 5g=5.7%
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"t' -. i TTT
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Fig. 25c. ฃ versus ^_ for t/b=0.1Al, staggered round'holes.
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A ' A A -, - l~^-
'1 V A ' ' , L
AI | i V 1
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Fig. 26c. f versus fl* , for t/b=0'.0665, staggered round holes.
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i O
O :
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; ^> &>
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A *
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Fig. 27a. ฃ versus Re, for t/bฐ0.0321, staggered round holes.
' 'Hf
LuAnrlilimlr. 'i s V. <:;<:lซ>
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A
ฉ
''&
! I AC
!:'i5456
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20
25
Fig. 27b. f/j versus (f , for t/b=0.0321, staggered round holes.
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Fig. 27c. f versus (ys, for t/b=0.0321, staggered round holes.
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0.020
j
0.005
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L
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Fig. 27d. j versus (fs for t/b=0.0321, staggered round holes.
-------
-118-
TEST DATA
[AIRESEARCH SURFACE 22R-.326-PERF
- .004 (A/)]
O BASE LINE DATA
[KAYS AND LONDON PERFORATED
FIN 13.95(P)]
.iiun.i ..iii'iinr:;!. :an
DATA FROM WATER-TO-AIR TEST
TEST AIR SURFACE: 22.0 RECTANGULAR FINS PER IN
0.326 IN. PLATE SPACING, .004 IN. ALUMINUM FIN
MATERIAL PERFORATED WITH 0.079 IN. DIA. HOLES
SPACED 32 PER SO.. IN. IN SQ. PATTERN (15.9 PERCENT
OPEN AREA), 3.38 IN. FIN FLOW LENGTH
D = 0.0826 IN.
B = 524 FT2/FTS
Af/A = 0.872
RIM AREA OF HOLES INCLUDED IN FIN AREA.
FIN EFFICIENCY BASED ON FIN AS A SOLID FIN.
100
200
400
600 800 1000
2000
4000 6000
REYNOLDS NUMBER
F1g. 28. Performance parameters 22 FPI perforated fin [5].
-------
-119-
in,-: yp ( Q ) , j A ( - ) , f ,:,r. 1 ( ^ , 6. ) , TT ( ? '>, \ ) , X ( 1 -
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PK,A|-!|-) = K --'=: d/M'. S ( TP ( i ) -TH ( ? ) ) +.AHS ( TP ( H ) -TP ( 9 ) ) ) /I.. 1 A
PI i'..i hi'; ='~>\n M,. T-S^'i'L T* . "-i^-'i '^
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y. ,-:=TA (<)) -:--(;/> i' / \f- .
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T'J.::| .:< = . .S=:- ( T I^-r Tf|i:T
i;Fl. T= 'IP-; -T'-a.'LK
H = '; . ---f p "I ! T :\ L / : 1 1-; i . T '
p i. "i =^ . 7n;:-:=PX i 1
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-------
-120-
P F R C = ( R F - 2.'1'"' r' > / H n r, r, .
AKOF.ACl (I',!. )'+('FACT CI ,3 l-^CTI I , 1 ) )*P!-wr
'"> < t = F AC T ( I , ? ) + ( F AC, T ( I , 4 ) -F.'.\r, T ( I , 2 ) ) -P FP C
M:(KF . r;T. i.'" n n :~> , ) AKC=FaCT(I,3) :
IFIRF .GT. 1.0HOO .) IปKr: = FACU I f4)
P I.. O S S = . r> o O f! <". o 0 ft 1 H * ( V C HK F -.= * 2 ) == ( A K C- '> K F )
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=,F1?.4,2X,ซHARFA
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-121-
SMP.kOl 'T I i iR S Il-.'TRK ( i>-i\/, TT-, T'Fi" )
15. F i: I. '-i'\/ ( ?M )
i ii ;,IR-!.S 1 n;.i TT ( ? 3 1. ) '
no ]f,;-:,-: T = 1. ,??i.
I H ( TRi-' .1. R . i-V (11) KM If! I HI p
/rii'i f.fii\i Tl '"v! !h
10 ,1 = 1-1.
T P >: = T T ( . I) + ( T t l-i- ,'' V ( .)))/( 1-1V ( f ) - R V ( J ) )
H R 71 IK I"
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SSTONON K?F4 . T~10 CAR 05=750
STGNT-N IvAS : 09:15.15 04-22-72
"K?F4" 'SIGNED QM AT 09:26.40 ON 04-22-72
SI 1ST DATA
1
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V
4
5
6
7
R
a
' 10
11
I?'
13
14
1^ :
16
1 7
1"
19
20
21
22.'
23
74
25
26
27
,28
20
.30
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32
33
34
35
1
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5.5
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70.
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161 .
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139.
196.
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2.17.
224.
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259.
266.
273.
280.
287.
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1.012
1. 171
1. 332
1.494
1. 657
1. 321
1 . 987
2. 154
2. 322
2.491
2. 663
2.R35
3.007
3. 182
3. 357
3.534
3.712
3.890
4.C7C
4. 251
4.^34
4.617
A. 801
4.987
5. 174
5.361
5.55G
5.739
5.930
6. 122
6. 314
6.5G8
16.!
3 16.0 19.0 19.0 19.0
44.0 .305 .375
71.
73.
95.
92.
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106.
113.
120.
127.
134.
141.
148.
155.
162.
169.
176.
183.
190.
197.
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2 1 1 .
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?25.
232.
239.
246.
253.
260.
267.
274.
2R1.
288.
295.
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1.035
1.194
1.355
1.517
1.680
1.345
2.011
2.178
2.346
2.516
2.687
2*859
3.032
3. 207
3.332
3.559
3.737
3.915
4.096
4.277
4.46C
4.643
4.R27
5.014
5.200
5.388
5.577
5.766
5.957
6.149
6.342
6.536
72.
79.
86.
93.
ICO.
107.
114.
1 ?1 ,
123.
135.
142.
149.
156.
163.
170.
177.
184.
191.
198.
205.
212.
2 19.
226.
233.
240.
247.
254.
261.
268.
275.
282.
289.
296.
.399
1.G57
1.217
1.378
1.540
1.704
1. 869
2 . 03 5
2,202
2.37C
2.540
2.711
2.884
3.057
3.232
3.407
3.584
3. 762
3o941
4. 122
4.303
4,486
4.670
4.854
5.04C
5.227
5.415
5.604
5.794
5.985
6. 177
6.370
6.564
73.
80.
37.
94.
101.
108.
115.
122.
129.
136.
143.
150.
157.
164.
171.
178.
185.
192.
199.
206.
213.
220.
227.
234.
241 .
248.
255.
262.
269.
276.
283.
290.
297.
.922
1.080
1.240
1.401
1.563
1.727
1.893
2.059
2.226
2.394
2.565
2.736
2.908
3.082
3.257
3.433
3.610
3.787
3.967
4.148
4.329
4.512
4.696
4.880
5.067
5.254
5.442
5.631
5.821
6.012
6.204
6.397
6.592
74.
81.
88.
95.
102.
109.
116.
123.
130.
137.
144.
151.
158.
165.
172.
179.
186.
193.
200.
207.
214.
221.
228.
235.
242.
249.
256.
263.
270.
277.
284.
291.
293.
.944
1.103
1.263
1.424
1.587
1.751
i.916
2.083
2.250
2.418
2.589
2.760
2.933
3.107
3.282
3.458
3.635
3.813
3.993
4.174
4.355
4.538
4.722
4.9C7
5.094
5.280
5.469
5.658
5.848
6.040
6.232
6.425
6.620
75.
82.
89.
96.
103.
110.
117.
124.
131.
138.
145.
152.
159.
166.
173.
180.
187.
194.
201.
208.
215.
222.
229.
236.
243.
250.
257.
264.
271.
278.
285.
292.
299.
.967
1.126
1.286
1.448
1.610
1.774
1.940
2.107
2.274
2.443
2.614
2.785
2.958
3.132
3.307
3.483
3.661
3.839
4.018
4.199
4.381
4.564
4.749
4.934
5.120
5.307
5.496
5.685
5.875
6.067
6.259
6.453
6.647
76.
83.
90.
97.
104.
111.
118.
125.
132.
139.
146.
153.
160.
167.
1 f ^t o
181.
168.
195.
202.
209.
216.
223.
230.
237.
244.
251.
258.
265.
272.
279.
286.
293.
300.
ro
END nr FI.LF
-------
-123-
NOMENCLATURE
TP (9)
TA (5)
FACT (3,4)
Z (14)
TT (231)
MV (231)
L16
L25
L34
K
GAP
GAPP
TIN
PX11
SVOLT
PVOLT
V
T
SIGMA
temperature of plate at points 1-9 MN, F
temperature of air at points 9,10,1,2,3 MV, F
coefficients of expansion and contraction
through an opening
values read from first two lines of data
fill, which have no meaning to program
temperature readings corresponding to
millivolts in MV (231) F
millivolt readings corresponding to
temps in TT (231)
distance between plate thermocouples
1 & 2; 2& 3, 7 & *, and 8 & 9
distance between plate thermocouples
3 & 4; 6 & 7
distance between plate thermocouples
4 & 5; 5 & 6
thermal conductivity of plate
1) center to center distance
between plates '
2) actual distance between plates
center to center distance between plates
inlet temperature of air
pressure at point 1-1 PSIxlO
shunt voltage VOLTSxlO
voltage from power source VOLTSxlO
velocity FT/MIN
thickness of plate FT
area reduction factor due to plates
in core
MV
FT
FT
FT
BTU/HR-FT-F
IN
FT
FT
MV, F
-1
-2
-2
hydraulic radius
FT
-------
-124-
VCORE
ANU
RE
TPA
A
PRADD
POWER
PTOTAL
AREA
TOUT
TBULK
DELT
H
FJ
Pll
PERC
AKC
AKE
PLOSS
PCORE
F
HJ
corrected velocity due to area reduc-
tion in core
viscosity of air SQFT/MIN
Reynolds number
average plate temperature F
cross sectional area of plate SQFT
power added from ends of plate BTU/HR
power supplied to plate BTU/HR
power supplied to plate plus power
from ends BTU/HR
area under curve of air temperature
vs. gap F-FT
temperature of air at outlet F
average temperature of air F
difference between average temperature
of plate and average temperature of air F
heat transfer coefficient
ratio of F to HJ
pressure at point 1-1
percentage between Reynolds numbers
for coefficient of expansion and
contraction
coefficient of contraction
coefficient of expansion
pressure loss in core
core pressure
Fanning friction factor
heat transfer factor
BTU/HR-SQFT-F
"H20
"H20
"H20
-------
-125-
LOGIC PROG
(' O INPUT
HYDRAULIC RADIUS
1 '
; 3) CORE VELOCITY
{'A") REYNOLDS NUMBER
1
(T) AVERAGE PLATE TEMPERATURE
,-, r
(6J TOTAL POWER IN PLATE
(7) AREA UNDER CURVE OF GAS vs. T
i
(T) AVERAGE AIR TEMPERATURE
i
(T) HEAT TRANSFER COEFFICIENT
(lO] HEAT TRANSFER FACTOR
ATO
AIR
I
11) CORE PRESSURE
FANNING FRICTION FACTOR
F/HJ RATIO
i
r
OUTPUT
GO TO (1
-------
-126-
OPERATING INSTRUCTIONS . PROG
( ASSUMES PROG IS STORED IN COMPILED FORM CALLED PROG1; AND FILE 'DATA' IS
ALSO STORED)
(ASSUMED OPERATOR HAS WORKING KNOWLEDGE OF TELETYPE AND MICHIGAN TERMINAL SYSTEM)
(T) SIGN ON TO TELETYPE
WHEN TERMINAL IS READY TYPE 'THE FOLLOWING:
#RUN PRpGl 5 = DATA
(T) TERMINAL WILL TYPE:
(/EXECUTION' BEGINS^ '
GAP (IN)*
USER WILL TYPE IN A GAP AND HIT 'RETURN' BUTTON. TERMINAL WILL TYPE:
TP(;1)-TP(9) - (MV) ;,.;
(T) USER WILL TYPE IN TP(1)-TP(9) IN MILLIVOLTS, WITH A COMMA BETWEEN
EACH PIECE OF DATA. THIS WILL ALLOW..THE USER TO AVOID FORMATTED ;'~
INPUT. USER WILL THEN HIT 'RETURN1.
THE REMAINING DATA IS- TYPED;. IN AS: THE TERMINAL ASKS FOR IT. WHEN
ALL THE DATA IS IN, THE TERMINAL WILL PRINT THE OUTPUT AND RETURN
TO ASK FOR A NEW GAP AND MORE DATA.
IF THERE IS MORE DATA, INPUT IT; IF NOT, HIT 'BREAK', AFTER
MESSAGE, HIT 'BRK-RLS', THEN SIGN OFF.
ALL DATA IS REAL, AND DECIMAL POINTS MUST BE TYPED.
-------
ฉ
-127-
DATA FILES PROG
DATA
The first two lines of 'DATA1 contain information used
for another program. They have.no use here, but are by-
passed by reading into array Z by the following format:
FORMAT (8F6.2.MF6.2, 2F6.4)
The rest of the file contains a conversion chart for
changing millivolt readings of temperature to Fahrenheit.
All temperatures inputted are done so in millivolts, and
the program converts them to ฐF. The chart starts at
70ฐF and goes to 300ฐF. Each line is stored in the
following format:
MV ฐF
FORMAT (7(F6.3, F5.0))
There are 33 lines in this chart and 35 in the complete file.
-------
-128-
EXPLANATION OF LOGIC
PROG
ฉ
INPUT
The program begins by setting up the array FACT and
then reads the file 'DATA'. The program will then
ask for the following information which should be
typed on separate lines.
1) GAP (IN)
2) TP(1)-TP(9) (MV)
3) TA(9) , TA(10) , TA(1) , TA(2);, TA(3) (MV)
A) TIN(MV), PX11, SVOLT, PVOLT, V(FT/MIN)
The information is read in and all temperatures are
converted to ฐF.
(T) HYDRAULIC RADIUS (R)
1) K-118.
2) T=l/384.
- ~:" '3) GAP=GAPP-T
4) SIGMA=1/(1+T/GAP)
5) , 4*W*GAP
2*(W+GAP)
GAP
4*(.5+GAP)
W=.5 FT
BTU/HR-FT-F
FT
FT
FT
0
CORE VELOCITY (VCORE)
i\ AMTT i-> m- 3
1) ANU-. 17x10 3
x
60SEC
_.
= .0102
2) VCORE=
SIGMA
REYNOLDS NUMBER
4* R* VCORE
1) Re=
ANU
FT
MIN
FT/MIN
-------
-129-
ฉ
ฉ
AVERAGE PLATE TEMPERATURE
TPA is calculated taking the area under the curve
of TP(9) VS. LENGTH of plate, and dividing it by
the length of the plate.
TPA
TOTAL POWER IN PLATE
1) A=T*L=.(1/384)*(l/2)=l/768 FT"
2) PRADD=K*A*(LTP(l)-TP(2)/+/TP(8)-TP(9)/)/L16
BTU/HR
x 3.412
BTU
HR WATT
BTU
HR
BTU
HR
BTU*
HR
3) POWERปPVOLT*SVOLTX.3412
. VOLTX10+2 xVOLTxlO*2
10+5OHM
4) PTOTAL=POWER -ซ PRADD
AREA UNDER CURVE OF GAP VS. TATO
AIK
1) IF GAPP=l/48 FT (t/b=0.141)
AREA - (TA(1) + 2TA(4) -f TA(2)) * GAP/4. FT-F
IF GAPP=l/24 FT (t/b=0.0665)
AREA + (TA(1) + 2TA(4) + 3TA(2) + 2TA(5)) * GAP/8 FT-F
IF GAPP-1/12 FT (t/b=0.0321)
AREA =(TA(1) + 2TA(4) + 3TA(2) +6TA(5) +4TA(3))x GAP/16
AVERAGE AIR TEMPERATURE
1) TOUT AREA/GAP
2) TBULK = (TOUT + TIN) x .5
F
F
FT-F
-------
-130-
(?) HEAT TRANSFER COEFFICIENT
1) DELT=TPA-TBULK
2) H=PTOTAL/ (A*DELT) , A=L *2 , L= . 5
- 2JPTOTAL _BTU^ BT-U/HR-Fr'-F
DELT FT2HR F
TTTp (PR)2/3 H PR=.72 ?
HJ= -^ ^Q^ , c - 2A BTU/-LBM.F
-> p i'
(.72)2/3 H
.074x.24x60 VCORE
CORE PRESSURE
1) Pll=2.768xPXllx "H20 "H20
2) PLOSS=.0000000618 x (VCORE**2%)" * (AKC-AKE) "H20
3) PCORE=P11-PLOSS "H20
. PCORE L=.5 FT
= l/2Gx.?xVCORE2(fe ^ :G=32,2 .LBMxFT/LBFxSEe2
PCORExRx64.4 "H20 x FT2 x MIN
.074x.5x(VCORE**2) LBFxSEC2
64.4x3600xl44xPCORExR
7.4x5.x2.768x(VCORE**2)
32500000.*PCORE*R
(VCORE**2)
1) FJ = F/HJ
(14) OUTPUT
Program prints output sheet showing input .and ,answers.
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
APTD-1554
3. RECIPIENT'S ACCESSION NO.
4. TITLE ANDSUBTITLE
Heat Transfer and Flow Friction Performance of Heated
Perforated Flat Plates
5. REPORT DATE
June 1975
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Dr. Wen-Jei Yang
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Michigan
Department of Mechanical Engineering
Ann Arbor, Michigan 48105
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-04-0019
12. SPONSORJNG AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air and Water Programs
Office of Mobile Source Air Pollution Control
Ann Arbor, Michigan 48105
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
is. ABSTRACT
large scale modelling technique is developed to examine the effects of
perforation geometry on the heat transfer and friction loss performance of compact heat
exchanger fins. The test core consists of an electrically heated matal plate and
several unheated dummy plates forming flow channels. Both test and dummy plates are
identically perforated in a staggered pattern. The cores were tested in a subsonic
wind tunnel designed specifically for testing automobile radiators, environmental
system condensers, and liquid-to-air heat exchangers. The plate surface porosity, the
core frontal porosity, and the perforation size and arrangement were varied. The
Reynolds numbers ranged from those corresponding to both laminar and turbulent flow.
The heat transfer factor M), friction factor (f) and their ratio (f/j) for a single
plate-channel system are obtained as functions of the Reynolds number, the plate sur-
face porosity and the core frontal porosity. These results represent qualitatively
those of a compact plate-fin heat exchanger having the same geometric scaling factors
when these systems are represented by appropriate geometric, dynamic and thermodynamic
similarity parameters. The technique can be used to understand the performance of com-
pact fin surfaces in order to determine an optimum performation geometry and to form a
basis for rational design of compact-heat exchangers.
it is found that under certain circumstances plate perforation will produce signi-
ficant improvement in heat transfer for the same pressure drop. These studies are
directed to the design of air-cooled condensers for Rankine cycle automotive engines,
marine power propulsion systems and the dry cooling towers of extra-high capacity
electric power plants.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
13. DISTRIBUTION STATEMENT
Jnlimited
19. SECURITY CLASS (This Report>
Unclassified
21. NO. OF PAGES
126
2O. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
- 131 -
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