Condensate Retention Effects on the Air-Side Heat Transfer Performance of Automotive Evaporator Coils
ACRCCR-32
For additional information:
Air Conditioning and Refrigeration Center University of Illinois Mechanical & Industrial Engineering Dept. 1206 West Green Street Urbana, IL 61801
(217) 333-3115
J. M. Kaiser and A. M. Jacobi
July 2000
The Air Conditioning and Refrigeration Center was founded in 1988 with a grant from the estate of Richard W. Kritzer, the founder of Peerless of America Inc. A State of Illinois Technology Challenge Grant helped build the laboratory facilities. The ACRC receives continuing support from the Richard W. Kritzer Endowment and the National Science Foundation. Thefollowing organizations have also become sponsors of the Center.
Amana Refrigeration, Inc. Ar~elik A. S. Brazeway, Inc. Carrier Corporation Copeland Corporation DaimlerChrysler Corporation Delphi Harrison Thermal Systems Frigidaire Company General Electric Company General Motors Corporation Hill PHOENIX Honeywell, Inc. Hussmann Corporation Hydro Aluminum Adrian, Inc. Indiana Tube Corporation Invensys Climate Controls Lennox International, Inc. Modine Manufacturing Co. Parker Hannifin Corporation Peerless of America, Inc. The Trane Company Thermo King Corporation Valeo, Inc. Visteon Automotive Systems Whirlpool Corporation Wolverine Tube, Inc. York International, Inc.
For additional information:
Air Conditioning & Refrigeration Center Mechanical & Industrial Engineering Dept. University of Illinois 1206 West Green Street Urbana,IL 61801
217 3333115
Abstract
The effect of condensate accumulation and shedding on the air-side thennal
perfonnance of automotive evaporator coils has been studied. Experiments under wet and
dry conditions were conducted to expose the impact of condensate on five different coils.
Condensate retention data were collected in both real-time and at steady-state to
quantitatively detennine how condensate load up on a coil surface. Sensible Colburn j
factors and friction factors were calculated from the experimental data, and the relative
perfonnance of different coils was discussed. A dynamic drainage test was developed to
study the nature of water draining out of a heat exchanger. It was found the simple
drainage test qualitatively predicted how much condensate would be retained by different
coils under operating conditions. Current retention modeling techniques were adapted to
include automotive evaporators.
111
Table of Contents
Page
List of Tables .................................................................................................................... vii
List of Figures .................................................................................................................. viii
Nomenclature ...................................................................................................................... x
Chapter 1 Introduction and Literature Review ................................................................... 1
1.1 Introduction .......................................................................................................... 1
1.2 Literature Review ................................................................................................. 2
1.2.1 Early Studies ........................................................................................... 2
1.2.2 Automotive Evaporator Condensate Drainage and Thermal
Performance ............................................................................................ 7
1.2.3 Modeling Condensate Retention ............................................................ 9
1.3 Objectives .......................................................................................................... 11
Chapter 2 Experimental Apparatus and Methods ............................................................. 12
2.1 Experimental Apparatus ..................................................................................... 12
2.1.1Wind Tunnel .......................................................................................... 12
2.1.2 Condensate Visualization ..................................................................... 16
2.1.3 Dynamic Drainage ................................................................................ 17
2.1.4 Contact Angle Measurements ............................................................... 19
2.1.5 Heat Exchanger Specifications ............................................................. 19
2.2 Experimental Conditions and Procedures .......................................................... 20
2.2.1 Thermal Performance ........................................................................... 20
2.2.2 Steady-state Condensate Retention ...................................................... 20
2.2.3 Real-time Condensate Retention .......................................................... 21
2.2.4 Dynamic Drainage ................................................................................ 23
Chapter 3 Results and Discussion ..................................................................................... 30
3.1 Thermal Performance ......................................................................................... 30
3.2 Condensate Retention ........................................................................................ 35
IV
3.2.1 Real-time Retention .............................................................................. 36
3.2.2 Steady-state Retention .......................................................................... 40
3.3 Dynamic Drainage ............................................................................................. 41
Chapter 4 Conclusions and Recommendations ................................................................. 61
4.1 Conclusions ........................................................................................................ 61
4.1.1 Thermal-Hydraulic Performance .......................................................... 61
4.1.2 Condensate Retention ........................................................................... 62
4.1.3 Dynamic Drainage ................................................................................ 63
4.2 Design Guidelines .............................................................................................. 63
4.3 Recommendations for Future Studies ................................................................ 65
Appendix A Data Reduction ............................................................................................. 68
A.l Mass Fluxes ....................................................................................................... 68
A.2 Heat Transfer Rates ........................................................................................... 69
A.3 Fin Efficiency .................................................................................................... 69
AA Heat Transfer Coefficients ................................................................................ 72
Appendix B Uncertainty Analysis .................................................................................... 81
B.l Uncertainty in Measured Parameters ................................................................ 81
B.2 Uncertainty in Calculated Values ...................................................................... 82
B.2.1 Tube-side ............................................................................................. 82
A. Heat Transfer Rate ............................................................................... 82
B.2.2 Air-side ................................................................................................ 83
A. Vmax .........•............•....•.......................................................................... 83
B. Reynolds Number ................................................................................. 84
C. Friction Factor ...................................................................................... 84
D. Heat Transfer Coefficient.. ................................................................... 85
E. Sensible j factor .................................................................................... 86
B.3 Uncertainty in Measured Condensate Retention ............................................... 86
BA Uncertainity in Dynamic Drainage Tests .......................................................... 87
Appendix C Condensate Retention Model ....................................................................... 89
v
C.l Prior Work ......................................................................................................... 89
C.2 Adaptations ........................................................................................................ 92
References ......................................................................................................................... 98
VI
List of Tables
Page
Table 2.1 Tested coil descriptions .................................................................................... 29
Table 3.1 Tilt test and vertical test comparison ................................................................ 60
Table A.1 Friction factor and Wilson plot data EES code listing ..................................... 77
Table A.2 j factor EES code listing .................................................................................. 79
Table B.1 Uncertainties in measured parameters ............................................................. 88
Table C.1 Relative surface areas and maximum droplet size constraints for Coil 4 ........ 95
Table C.2 Summary of model results for Coil 4 ............................................................... 96
Table C.3 EES code for computing mass per unit area for different surfaces .................. 97
Vll
List of Figures
Page
Figure 2.1 Horizontal flow wind tunnel. (A) 36-cm diameter round sheet metal duct.
(B) Thermal mixing chamber. (C) Screens and honeycomb flow straighteners.
(D) 9:1 contraction. (E) Test heat exchanger. (F) Inlet/ outlet measurement
sections. (G) Strip resistance heaters. (H) Steam injection tube. (I) Axial
blower. .............................................................................................................. 25
Figure 2.2 Test Section for Wet and Dry Runs. (A) Pressure taps (top and bottom). (B)
Chilled mirror hygrometer sensors. (C) Insulated clear acrylic. (D) Drainage
tray. (E) Thermocouple grid (inlet and outlet) ................................................. 25
Figure 2.3 Air velocity measurement locations ................................................................ 26
Figure 2.4 Closed environment glove box apparatus for examining condensing fin
samples. (A) Beaker with water. (B) Fin stock. (C) Peltier device and liquid
heat exchanger. (D) Glove. (E) Fan ................................................................. 26
Figure 2.5 Dynamic drainage apparatus ........................................................................... 27
Figure 2.6 Attaching mechanism for drainage test coils ................................................... 27
Figure 2.7 Real time retention apparatus. (A) Wind tunnel. (B) Suspension mechanism
components. (C) Balance. (D) Inlet! outlet coolant lines. (E) Test heat
exchanger. (F) Drain ........................................................................................ 28
Figure 2.8 Contact angle measurement apparatus ............................................................ 28
Figure 3.1 Coil 1 air-side sensible heat transfer coefficient versus face velocity ............. 47
Figure 3.2 Coil 2 air-side sensible heat transfer coefficient versus face velocity ............. 47
Figure 3.3 Coil 3 air-side sensible heat transfer coefficient versus face velocity ............. 48
Figure 3.4 Coil 4 air-side sensible heat transfer coefficient versus face velocity ............. 48
Figure 3.5 Coil 5 air-side sensible heat transfer coefficient versus face velocity ............. 49
Figure 3.6 Coil 1 air-side pressure drop in mm of water versus face velocity ................. 49
Figure 3.7 Coil 2 air-side pressure drop in mm of water versus face velocity ................. 50
Figure 3.8 Coil 3 air-side pressure drop in mm of water versus face velocity ................. 50
Figure 3.9 Coil 4 air-side pressure drop in mm of water versus face velocity ................. 51
Figure 3.10 Coil 5 air-side pressure drop in mm of water versus face velocity ............... 51
V111
Figure 3.11 Coil 1 j and ffactors versus air-side Reynolds number ................................. 52
Figure 3.12 Coil2j and ffactors versus air-side Reynolds number ................................. 52
Figure 3.13 Coil 3 j and f factors versus air-side Reynolds number ................................. 53
Figure 3.14 Coil 4 j and ffactors versus air-side Reynolds number ................................. 53
Figure 3.15 Coil 5 j and ffactors versus air-side Reynolds number ................................. 54
Figure 3.16 Real time condensate retention and humidity ratio for Coil 5 versus time ... 54
Figure 3.17 Real time condensate retention repeatability for Coil 4 ................................ 55
Figure 3.18 Real time plot for Coil 4 showing overshoot at higher velocity .................... 55
Figure 3.19 Steady state retention for all coils versus face velocity ................................. 56
Figure 3.20 Steady state retention per unit of heat transfer area versus face velocity ...... 56
Figure 3.21 Drainage test plot for Coil 3 illustrating the repeatability of the
experimental technique .................................................................................... 57
Figure 3.22 Partial plot of the repeatability test results showing the area of maximum
error .................................................................................................................. 57
Figure 3.23 Dynamic test results for the fast draining coils ............................................. 58
Figure 3.24 Dynamic test results for the sustained draining coils .................................... 58
Figure 3.25 Extended time drainage test results ............................................................... 59
Figure 3.26 Comparison plot between a vertical coil and a coil tilted 10° ....................... 59
Figure 3.27 Droplet forces and bridges ............................................................................. 60
Figure A.1 Example of Modified Wilson-plot.. ................................................................ 76
Figure C.1 Forces acting on a droplet on an inclined surface due to gravity,
air-flow, and surface tension ............................................................................ 95
Figure C.2 Measured and predicted values of steady-state condensate retention
for Coil 4 .......................................................................................................... 96
IX
Nomenclature
A area (m2)
Adrop area of a droplet (cm2)
Afr frontal area (m2)
b intercept of least squares fit line
C constant of integration
Cd drag coefficient
Cp specific heat at constant pressure (kJ/kg-K)
D diameter (m)
DAB binary mass diffusion coefficient (m2/s)
Ddrop diameter of droplet (m)
Dh hydraulic diameter (m)
L1PHx heat exchanger differential pressure (kPa)
f friction factor
Is fin spacing (rom)
Fd air drag force (N)
Fg gravitational force (N)
Fs surface tension force (N)
g gravitational acceleration (9.81 m1s2)
G mass velocity based on minimum free flow area (kg/m2 -s)
h enthalpy (kJ/kg)
ho air-side heat transfer coefficient (W/m2-K)
hi coolant-side heat transfer coefficient (W/m2 -K)
hm mass transfer coefficient (kg/m2-s)
j sensible j factor
k thermal conductivity (W/m-K)
Lf length or depth of fin (m)
Le Lewis number
m mass flux (kg/s)
mo fin efficiency parameter
x
Nu Nusselt number
Pr Prandtl number
q heat transfer rate (KW)
R thennal resistance (K/W)
Rc coolant flow meter output (pulse/s)
Re Reynolds number
T temperature (OC)
t time (s)
V velocity (mls)
Greek symbols
a angle of inclination (radians)
8 fin thickness (m)
~ relative humidity
y surface tension (mN/m)
" fin efficiency, surface effectiveness
Il dynamic viscosity (N-s/m2)
8 dimensionless temperature
8A advancing contact angle (radians)
8M mean contact angle (radians)
8R receding contact angle (radians)
p density (kg/m3)
cr contraction ratio (Amini Afr)
Subscripts
air aIr
atm atmospheric pressure (atm)
ave average
c coolant
cali calibrated
dp dewpoint
Xl
dry dry condition
f fin
fr frontal
i tube-side
in inlet
I liquid
mair mean aIr
min minimum
max maXImum
a air-side
out outlet
sens sensible
t total
wet wet condition
XlI
Chapter 1 Introduction and Literature Review
1.1 Introduction
In automotive air-conditioning systems, the air-side surface temperature of the
vapor-compression evaporator is usually below the dew point of the conditioned air, and
it is common for water to condense onto the air-side heat-transfer surface. Condensate
accumulates on the surface and is retained by surface tension until it is removed by either
gravitational or flow forces. Retained condensate plays an important role in the overall
performance of the air-conditioning system; it can profoundly affect the heat transfer and
pressure drop performance, but there is disagreement on the overall impact in some heat
exchanger geometries. Condensate retention also has important implications on air
quality. Condensate that blows off with the conditioned air stream can affect comfort, and
water provides a medium for biological activity on air-handling surfaces. The post
operation (off-cycle) condensate draining behavior is extremely important in this respect,
because the warm, moist conditions prevailing after system shut down are conducive to
biological growth.
The focus of this project was on the effect of condensate on air-side thermal
hydraulic performance, with an overall goal to develop new fin-design guidelines that
maximize performance under dehumidifying conditions. A wind tunnel was designed and
constructed for testing heat exchangers under dry and condensing conditions.
Experiments were conducted to obtain steady state and real-time measurements of
condensate retention. Furthermore, heat transfer and pressure drop data for heat
exchangers under dry and condensing conditions were recorded. Extensive drainage tests
1
were conducted using a dynamic drainage test apparatus. The data from the experiments
were used to aid in development and validation of a retention model.
1.2 Literature Review
The majority of the work on air-side thermal performance under dehumidifying
conditions has concentrated on heat exchangers with round tubes, as opposed to the flat
tube, brazed-plate geometry of this study. Nevertheless, the prior work is helpful in
developing an understanding of the impact of condensate retention and shedding. This
section includes a discussion of past work on flat plates, finned-tube coils with plain and
enhanced fins, and the limited work in the open literature on automotive-style
evaporators. Finally, a discussion of condensate retention, drainage, and modeling is
presented.
1.2.1 Early Studies
Bettanini (1970) performed numerous experiments in heat and mass transfer for a
vertical plate and reported an enhancement in sensible performance under condensing
conditions. Bettanini postulated the effect was caused (in part) by an increase in surface
roughness caused by condensation on the surface. Two types of experiments were
conducted to verify this effect. A soap and water solution was sprayed on the surface to
temporarily cause filmwise condensation, and heat transfer measurements were taken
until the condensation turned to dropwise, thus increasing surface roughness. The
sensible heat transfer coefficient increased by approximately 20% when the condensation
turned to dropwise, supporting the roughness effect idea. Additional experiments were
done using gypsum chips to simulate water droplets on the surface. The results from these
tests showed approximately a 10% increase in performance. While these tests do show an
2
impact from surface roughness, the experimental apparatus and procedure used was
simple and not well controlled (as noted by Bettanini), and the extension of these results
to more complicated heat exchangers and flow regimes is unclear.
Yoshii et al. (1973) examined the effects of dropwise condensation on the
pressure drop and heat transfer performance of wavy-fin heat exchangers. It was found
that pressure drop for wet heat exchangers was 50 to 100% higher than for dry
exchangers. Under wet conditions, a 20 to 40% enhancement in heat transfer coefficient
was found for the heat exchangers. To investigate the effect of condensate on the flow
dynamics, scale-up models of the heat exchangers with simulated condensate were made
and tested in a water channel at similar Reynolds numbers. Y oshii and coworkers
reported that drops on the flat fin surface promoted turbulence when the droplet adhered
on the ridge or valley in the wavy fin, but caused separation when adhered to the area
between bends. Additionally, water bridges between the tube and fins significantly
increased the wake region downstream of the tube, but downstream droplets can direct
flow into the wake region. From these observations Y oshii and coworkers concluded the
overall impact on condensate depends on both location and shape of the droplets.
Guillory and McQuiston (1973) and McQuiston (1976) studied developing flow
between horizontal flat plates and found a heat transfer enhancement of about 30% for
wet surface conditions. In agreement with Bettanini, Guillory and McQuiston explained
that the condensate that formed on the heat exchanger increased the surface roughness of
the exchanger walls and this increased roughness explained the increase in heat transfer
and pressure drop found under wet conditions. Tree and Helmer (1976) also studied a
parallel plate heat exchanger under condensing conditions. Unlike Guillory and
3
McQuiston, they found that condensation did not affect the sensible heat transfer and
pressure drop during laminar flow. However, agreement was found in the transitional and
turbulent regime, where condensate was found to increase heat transfer and pressure drop.
For plain-fin-and-tube geometries, Myers (1967), Elmahdy (1975), and Ekels and Rabas
(1987) have reported a sensible enhancement under wet conditions.
Inconsistent with a simple roughness effect, McQuiston (1978a,b) found the
enhancement in plain finned-tubes to be strongly dependent on fin spacing. For circular
finned tubes, Jacobi and Goldschmidt (1990) found the enhancement to be Reynolds
number dependent. A degradation was observed at low Reynolds numbers, and an
enhancement was found at high Reynolds numbers. Jacobi and Goldschmidt suggested
that their results, and those of McQuiston, were due to condensate retention. At low
Reynolds numbers, retained condensate would occupy heat exchanger area with a
deleterious effect, but at high Reynolds numbers, vapor shear would remove retained
condensate and roughness effects of the remaining condensate would dominate. This
explanation has since been supported by the work ofUv and Sonju (1992).
Further complicating the issue, spatial variations of the dry-surface local heat
transfer coefficient mayor may not have a significant impact on the fin efficiency (Huang
and Shah, 1991; and Kearney and Jacobi, 1996), and the same could be true for a wet fin.
Hu et al. (1994) conducted detailed local heat transfer experiments with simulated
condensate. Their results indicate that for circular fins the effect on fin efficiency is small,
as did Kearney and Jacobi, but the overall impact of condensate retention on average heat
transfer can be significant. For circular fins, the average sensible heat transfer coefficient
4
can be increased by as much as 30% due to condensate effects at high Reynolds numbers.
The impact in other geometries (e.g., louvered fins) remains unclear.
Hong (1996) examined the use of hydrophilic coatings to improve wettability and
thereby decrease the pressure drop associated with wet-fin operation. Wavy, lanced, and
louvered fins were studied, and at fixed face velocity of 2.5 mis, the ratio of wet-to-dry
pressure drop was 1.2 for each geometry tested. A model to predict the carry-over
velocity was developed and compared to experimental data. Carry-over velocity is
dependent on surface tension forces that depend on contact angle. Hong presented contact
angle data obtained from a sessile drop goniometer test; however, because a static test
procedure was adopted, no measure of contact angle hysterisis was obtained-a result
between the advancing and receding is all that can be achieved through such an approach.
Hong found that after approximately 1,000 wetting cycles the coated and uncoated test
surfaces all exhibited contact angles of approximately 60 degrees.
Korte and Jacobi (1997) studied the effects of condensate retention on the air-side
performance of plain-fin-and-tube heat exchangers. Experiments were conducted under
dry conditions and then repeated under condensing conditions. It was found that the heat
transfer performance under condensing conditions was dependent on the fin spacing. An
enhancement in heat transfer for wet conditions was seen for a 6.35 mm fin pitch heat
exchanger but not for a 3.18 mm fin pitch heat exchanger. The results for the heat
exchanger with a 3.18 mm fin pitch showed the heat transfer performance under wet
conditions to sometimes be better and sometimes worse than for dry conditions. It was
also found that the effect of condensation on friction factor was dependent on fin spacing.
Similar friction factors were observed for a 6.35 mm fin pitch heat exchanger under wet
5
and dry conditions. At 3.18 mm fin pitch, there was a significant increase in friction
factor under wet conditions. However, with increasing air-flow rates the quantity of
retained condensate and the increase in friction factor decreased.
Wang et al. (1997) studied the performance of plain finned-tube heat exchangers
under dehumidifying conditions. The effects of fin spacing, number of tube rows, and
inlet conditions were investigated. Nine plain-fin-and tube heat exchangers were tested
with fin spacing ranging from 1.82 mm to 3.2 mm and 2, 4, and 6 tube rows. Heat
transfer performance and friction factors were observed for the exchangers at a relative
humidity of 50% and 90%. The friction factors for wet coils were found to be much
larger than those of dry coils. For fully wet conditions, the friction factors were found to
be 60 to 120% higher than for dry conditions and insensitive to change in inlet air relative
humidity, fin spacing, and the number of tube rows. Sensible j factors under
dehumidifying conditions were not found to be dependent on the inlet air conditions.
Under wet conditions, a degradation in sensible heat transfer was seen at low Reynolds
numbers. At high Reynolds numbers, a small enhancement in heat transfer performance
was observed under wet conditions but the enhancement disappeared as the number of
tube rows increased.
Ha et al. (1999) studied the hydraulic performance of wet fin-and-tube heat
exchangers with various wettability coatings. Contact angle measurements obtained were
used to characterize each ofthe different surfaces. For all surfaces, an increase in pressure
drop was found for heat exchangers under wet conditions. The increase in pressure drop
was greater with increasing contact angles. It was also found that surfaces with smaller
contact angles retained less condensate and required less time to reach a steady value of
6
retained condensate. Furthennore, pressure drop models for dry and wet heat exchangers
with dropwise condensation were developed.
Yin and Jacobi (1999) studied the effect of condensate retention on thennal
perfonnance for plain-fin and wavy-louvered fin heat exchangers exposed to air frontal
velocities from 0.8 mls to 2.0 mls. They reported the amount of condensate was
independent of face velocity for these geometries and air-flow rates, but dependent on fin
geometry and contact angles. A greater amount of condensate was retained in the wavy
louvered coils. Under wet conditions, Colburn j factor decreased, and this degradation
was greater at greater fin densities--consistent with a greater amount of water being
retained. Additionally, under dry conditions, the wavy-louvered had a higher j factor
relative to the plain fin coil, but the enhancement disappeared under wet conditions. The
work of Kim and Jacobi (1999) similarly showed a decrease in thennal perfonnance for
both plain and enhanced fins (slit-fin) round tube evaporators. The increased pressure
drop was concluded to be caused by the blockage effect of retained condensate and the
decrease in wet heat transfer due to fouling of the air-side heat transfer surface in plain
fins, and additional fouling of the louvers or slits by condensate bridging.
1.2.2 Automotive Evaporator Condensate Drainage and Thermal Performance
Little work has been reported in the open literature to address condensate drainage
on automotive-style evaporator coils; however, a few studies addressing the thennal
perfonnance of such coils have been reported. Wang et al. (1994) found an increased air
side heat transfer coefficient under wet conditions and surmised condensate on the fins
acted as an enhancement by increasing surface roughness. Their study included only two
7
different heat exchangers, giving useful but limited results. Osada et al. (1999) performed
heat transfer and visualization experiments on single fin columns of flat tube evaporators.
They investigated the effects of surface wettability, louver geometry, and inclination
angle on condensate drainage. Osada and co-workers concluded that fin surface
characteristics near the air-flow-exit face of the heat exchanger were an important factor
in condensate drainage. This region of the fin is important because airflow forces push
condensate toward that part of the fin-it accumulates there until it is drained by gravity.
Osada and co-workers found that decreasing the non-louvered length on the fin promotes
better drainage; they suggest that increasing the louver cut length decreases the amount of
louver blockage caused by condensate bridging within the inter-louver space.
Very recently, McLaughlin and Webb (2000a) studied the impact of fin geometry
on drainage characteristics and retention using a table-top test cell for experiments with a
single-fin column. They undertook several methods to validate their test methods, and
they argued that this approach with a single fin specimen provides results representative
of a full-scale heat exchanger. Single-fin tests were conducted with an air flow of 2.5m1s
and an entering relative humidity greater than 95%. During these experiments, tube-side
cooling was provided by cold water circulated through a tube brazed to one side of the
fin. This simplification allowed optical access through glass on the other side of the fin,
but it certainly compromised the thermal boundary conditions, and the fin-glass interface
modified the geometry and surface tension boundary conditions on retained condensate
as recognized by McLaughlin and Webb. Their results suggest louver pitch is the single
most important parameter determining drainage characteristics of louver fin evaporators.
They state that a critical louver pitch between 1.1 mm and 1.3 mm exists for a louver
8
angle of 30°, where condensate retention increases by 26%. In a related study, they found
up to a 40% decrease in air-side heat transfer coefficient under wet conditions for the 1.1-
mm-Iouver-pitch evaporator, no change under wet conditions for the 1.33-louver-pitch
coil (McLaughlin and Webb, 2000b). They conclude that condensate bridging within the
louvers is responsible for the increase in retention and degradation of perfonnance.
1.2.3 Modeling Condensate Retention
Several models of condensate retention have been proposed. Rudy and Webb
(1981) reported a method for measuring condensate retention for the condensation of pure
fluids on integral low-finned tubes. They found that condensate retention was intensified
for a close fin spacing and suggested that the gravity-drained model of Beatty and Katz
(1948) was inadequate because it neglected surface tension effects; they later developed
their own models (Webb, et aI., 1985a,b). Unfortunately, there is little hope of
generalizing these geometrically specific results. Jacobi and Goldschmidt (1990)
presented a simplified model of condensate retention in the "bridges" fonned between
neighboring fins. Their model was qualitatively successful in predicting heat transfer
effects; unfortunately, it is not possible to trivially generalize this model for other
condensate geometries or more complex fins.
Korte and Jacobi· (1997) developed a model to predict the quantity of retained
condensate for uncoated aluminum plain-fin-and-tube heat exchangers with a fin spacing
of 6.35 mm. The quantity of retained condensate was detennined by calculating the
volume of retained condensate and multiplying this volume by the density of the water.
Unlike previous studies, the model incorporated advancing and receding contact angles
9
that were used to detennine surface tension forces. Modeling techniques were relatively
successful in predicting the quantity of retained condensate for the 6.35 mm fin pitch heat
exchanger, but many higher order effects were not included. The model of Korte and
Jacobi incorporated only droplets adhering to the surface, other features such as bridges
occurring between fins, fillets and bridges at the fin-tube junction, or other condensate
geometries were not included. However, they developed initial force balances to assist in
detennining the sizes of some simple bridges. The droplet size distributions used in the
model were based on the work of Graham (1969). Air-flow forces were included by
assuming a constant drag coefficient and approximating the local velocity using laminar
flow approximations. Gross surface coverage values were estimated from experimental
observations and, as noted by Korte and Jacobi, there may be variations in area covered
through the length of the fin due to sweeping effects.
The retention model of Korte and Jacobi was adapted to include condensate
bridging at the fin-tube junction by Yin and Jacobi (1999). Furthennore, the modeling
technique was applied to a heat exchanger with over twice the fin density. The decreased
fin spacing made it difficult to detennine the droplet size distributions on the heat
exchanger. Therefore, a stock fin sample was studied in the controlled environment of a
glove box. Using image analysis software, Yin and Jacobi detennined not only the
droplet size distribution (still based on the concepts developed by Graham), but also
investigated the vertical variations of droplet size density due to sweeping along the fin.
The model successfully predicted the amount of condensate retention in a 2.13 mm fin
pitch coil, but over predicted the mass in heat exchangers with 1.59 mm and 1.27 fin
pitches. This discrepancy was attributed to the assumption in the model of zero
10
interaction between droplets on adjacent fins. It is likely that in a heat exchanger with
tighter fin spacing for two droplets on adjacent fins would coalesce, creating a fin bridge,
and cause a greater sweeping effect as the larger fin bridge is shed. A similar approach in
modeling was studied by Kim and Jacobi (1999), and a corresponding over-prediction of
mass as heat exchanger geometry became more complex was reported.
1.3 Objectives
The objectives of this project were to determine the effect of condensate retention
on air-side heat transfer performance of automotive evaporator coils, to investigate the
drainage characteristics during operation and after system shutdown, and finally to
develop a condensate retention model to predict the amount of condensate retention based
on prior modeling efforts for plain-fin-and-tube heat exchangers. Air-side heat transfer
performance under and condensing conditions were measured, and condensate retention
measurements were taken in real-time and at steady state. A dynamic drainage test rig
was developed and the results were used to aid in the understanding of retention and
shedding of condensate. A model was developed to predict total condensate retention
under normal operating conditions.
11
Chapter 2 Experimental Apparatus and Methods
A closed-loop wind tunnel was designed and constructed for testing heat
exchangers under condensing conditions. Heat exchanger perfonnance and condensate
retention measurements were obtained using the apparatus. A condensate visualization
chamber was built to study retention on small pieces of fin stock. A water drainage test
apparatus was constructed to test drainage behavior of heat exchangers. This chapter
describes the experimental apparatus, instruments, experimental procedures, and heat
exchangers tested for this research.
2.1 Experimental Apparatus
2.1.1 Wind Tunnel
The thennal perfonnance and condensate retention apparatus consisted of a
closed-loop wind tunnel, a test section for testing heat exchangers exposed to horizontal
air-flow, and a coolant loop that circulates a single-phase coolant. The wind tunnel is
shown schematically in Figure 2.1. It was used to obtain measurements of retained
condensate and heat transfer perfonnance for various types of heat exchanger geometries.
Experiments were conducted with a horizontal flow of air, and specimens were tested at
various air flow rates typical to mobile air-conditioning applications. The closed-loop
wind tunnel allowed control of temperature, humidity, and air flow rate. Air temperature
was controlled by varying the power supplied to ten electrical resistance heaters using a
PID controller; the total capacity of these heaters was 7.5 kW. A feedback Type-K
thennocouple was located just downstream of the main tunnel contraction. The heaters
were located in two banks, one upstream of the blower and the other downstream of the
blower. The second bank was used only during testing at the highest heat duties. Evenly
12
spaced Type-T thennocouples were used both upstream and downstream of the test
section to measure the inlet and outlet air temperature. A six-thennocouple grid was used
upstream and a twelve-thennocouple grid was used downstream to measure the average
inlet and outlet air temperatures. The upstream temperature readings for all
thennocouples varied from the mean less than O.8°C at the lowest air velocity and less
than O.3°C at the highest velocity, with the upper row always reading higher than the
lower row. The relatively large variation at the low flow rates was caused by improper
mixing in the thennal-mixing chamber. The upper duct discharged directly into the top of
the chamber and caused excessive stratification. Each thennocouple was individually
referenced to a thennocouple located in an ice bath, and calibrated to a NIST traceable
mercury-in-glass thennometer using a thennostatic bath. Calibration data were fit with
fifth order polynomials for each thennocouple. The dewpoints of the air were measured
by chilled mirror hygrometers with a measurement uncertainty of ±O.2°C. Air was
supplied to the chilled mirrors through sampling tubes located 30-cm upstream and
downstream of the test section. A small, medical diaphragm air pump drew air through
the sampling tubes. The dewpoint of the incoming air was maintained using a steam
injection system. The humidifier was a boiler capable of providing 11.5 kglhr of steam.
The output of the humidifier was controlled by varying the input heater power using a
PID controller. The upstream dewpoint monitor provided the control signal for the steam
injector. The steam was injected into the tunnel through a perforated pipe 50-cm
downstream of the first bank of heaters. An axial fan, belt driven by a DC motor, mixed
the airstream and provided volumetric flow rates up to 8.5 m3/min. Upstream of the test
section, air was drawn from a thennal mixing chamber and passed through a set of
13
screens, honeycomb flow straighteners, and a 9: 1 contraction to obtain steady laminar
flow before passing through the test section. Additional, smaller contractions were
required just upstream of the test coil to match the flow to each geometry. These elliptical
contractions were cut from Styrofoam, covered with aluminum tape, and attached to the
wind tunnel walls with adhesive.
The test section, shown In Figure 2.2, was designed for testing wet heat
exchangers. The design allowed for both real-time and steady-state measurements of the
mass of retained condensate. The test section was constructed using clear acrylic to allow
for optical access. In order to limit conduction losses when observations were not being
made, the test section was insulated with 1.27 cm thick polyethylene foam insulation with
an insulation factor of 0.08 W/m2K. Upstream and downstream pressure taps were
located on the upper and lower walls of the rectangular test section for measuring the
pressure drop across the heat exchanger. The pressure taps were located approximately
7.5 cm upstream and downstream of the heat exchanger, with two taps at each location
spaced 7.5 em apart centered on each side of the test section. An electric manometer with
an uncertainty of ±0.124 Pa was used to measure the air-side pressure drop across the
heat exchanger. Face velocities were measured at the test section using a constant
temperature thermal anemometer. The face velocity was determined by taking twelve
equally spaced measurements traversing the height of the heat exchanger in three places
at each of the four velocity measurement locations shown in Figure 2.3. The twelve
measurements were recorded and an average face velocity was determined. The velocity
measurements were within 11 % of the average at the lowest velocity and 8% at the
highest velocity. Turbulence intensity measurements were taken using a hot wire
14
anemometer at the velocity measurement locations, with a plain-fin-and-tube installed in
the test section. Measurements were made at three locations and except for the small
wake region behind the thermocouples, the turbulence intensity was less than 2.5%.
A single-phase ethylene glycol (DOWTHERM 4000) and water mixture was
circulated on the tube side of the heat exchanger. Over the course of this project, two
different concentrations of ethylene glycol were used, 32.6% and 40.0%. The
concentrations were mixed and maintained by measuring the specific gravity of the
mixture using a NIST traceable hydrometer. The required specific gravity was obtained
by interpolating on manufacturer provided tables. Coolant-side temperatures were
measured using type-T immersion thermocouples located approximately two meters
upstream and downstream of the heat exchanger. Each thermocouple was individually
referenced to a thermocouple located in an ice bath, and calibrated in the same manner as
the wind tunnel grid thermocouples. An R-502 liquid-to-liquid, variable-speed chiller was
used to control the coolant temperature. Temperature of the solution was controlled using
an immersion temperature probe on the supply line as the control signal for a proportional
controller driving the compressor. The mixture was circulated through a copper tubing
loop by two pumps. An integral, centrifugal, recirculation pump provided a 200-kPa head
to a positive displacement rotary gear pump. The gear pump was belt driven to minimize
vibrations by a two horsepower motor. The coolant flow was controlled by using an
inverter to vary the drive motor speed. The test heat exchanger was connected to the
copper tubing with flexible, reinforced, PVC tubing that terminated with quick
disconnect couplings to facilitate removal of the coil. All tubing was insulated with 9.5
mm polyethylene foam insulation with an insulation factor of 0.05 W/m2K. Coolant flow
15
rate was measured on the return line using a positive displacement disc flow meter with a
measurement uncertainty of ±1.0%. A transmitter attached to the flow meter provided a
1-5V pulse with a frequency proportional to the volumetric flow rate. A Philips
programmable timer/counter was used to count the number of pulses over a timed cycle
with an uncertainty of ±2 pulses. Mixing cups were not used in the coolant lines prior to
the thermocouples to help minimize line pressure losses, but the flow is well mixed. The
supply line was insulated and typical flow Reynolds numbers were from 4000 to 7000
which should maintain a flat temperature profile. The return line was also well insulated
and the highly interrupted internal geometry of the tubes of the tested coils is such that it
mixes the coolant.
The data acquisition system consisted of a control unit, programmable
timer/counter, and personal computer. The control unit contained an 20 bit analog-to
digital converter and samples 23 channels. The channel outputs are read twice a second,
averaged over 11 measurements, and recorded every 45 seconds. The personal computer
receives the recorded outputs and stores them in a data text file for subsequent analysis.
The temperatures, dewpoints, and coolant flow meter readings are recorded by the data
acquisition system. The air velocity, barometric pressure, and core pressure drop are
manually recorded during a test.
2.1.2 Condensate Visualization
A condensate retention visualization apparatus was built to quantify the nature of
retained condensate on small pieces of fin stock. The apparatus is an acrylic box with
volume of approximately 0.07 m3 containing a humidity source and test section. The
clear acrylic provides optical access for taking photographs from a variety of orientations.
16
A plastic glove is mounted around an access hole in one side to allow non-intrusive
manipulation of the test section. The visualization apparatus is shown in Figure 2.4. The
test section consists of a sample fin (or fin stock) mounted to a Peltier thermoelectric
device. The Peltier device is water-cooled and capable of removing 50 Watts using a DC
power supply. The sample is bonded to a piece of aluminum stock using thermal epoxy
and then clamped to the Peltier device. A submersible pump with a 0.2 Lis capacity
circulates water from an icebath through a heat exchanger connected to the hot side of the
Peltier device. A beaker of hot water provides water vapor and a small fan mixes the air
to provide a uniform distribution of water vapor.
2.1.3 Dynamic Drainage
A schematic diagram of the drainage apparatus is shown in Figure 2.5. The
apparatus consists of a moving water reservoir and mechanism to suspend and weigh the
heat exchanger. The moving reservoir has a volume of 68 liters and is positioned using a
hydraulic jack. This simple arrangement allows a smooth, consistent lowering of the
water reservoir. The heat exchanger is suspended from a balance using an acrylic frame
and attaching mechanism. The frame is large enough to accommodate both the balance
and the width of any coil (see Fig 2.5). The attaching mechanism depends on the
particular heat exchanger being tested. In this study, nine coils were tested. Four coils
were attached to the weighing mechanism by permanently fixing aluminum "wings" to
the outside as detailed in Figure 2.6a. The wings are 58mm x 90mm rectangles attached
to a two-piece narrow aluminum strap. The lower strap is connected by a pin and clamp
to the wing, allowing angular adjustment, and the upper strap is connected to the frame
by a bolt. The two pieces of the strap are connected by a clamp to allow height
17
adjustments. In this way a test coil that can be tilted in two directions during a test,
allowing experiments on orientation effects on water drainage. The other coils did not
have an external attachment site for the same wings, so heavy gauge wire was looped
under the upper tube row or manifold as shown in Figure 2.6b. The wire was then bent
into a rectangle, interlocked with the frame and heat exchanger providing a stable
support. Adjustments were done by lengthening or shortening the wire loop until proper
orientation was obtained.
A precision balance was used for the mass measurements. It has a readability of
0.1 grams and a reported uncertainty of <0.1 grams. An adjustable base that allows the
balance to be leveled or moved vertically if required supports the balance. The balance
has an RS-232 port and a personal computer could be used to record mass readings.
Based on initial repeatability of experimental data, it was decided for this study to
manually read and record all data.
The dynamic drainage apparatus was modified to obtain real-time condensate
retention measurements as shown in Figure 2.7. A frame was built to support the balance
and suspension mechanism over the test section. The aforementioned adjustable attaching
technique allowed the minute adjustments required to align the test coil with the
incoming airstream. The metal hanging straps acted as springs to offset the moment
created by the coolant lines and airflow forces. The coolant lines were securely clamped
to the wind tunnel frame as far as possible from the heat exchanger. This long, horizontal
run after the sturdy support helped eliminate measurement errors created by fluid
momentum and vibrations. The apparatus was tested by operating under dry conditions to
assess the measurement errors and the observed mass varied less than three grams at a
18
face velocity of approximately 3.0 mls. It is impossible in this test set-up to operate in a
closed system and record real-time measurements since the evaporator has to be free
floating. Side plates of thin acrylic and an aluminum bottom tray were constructed to
minimize air losses. The gap between the test section and the coil was also made as small
as possible.
2.1.4 Contact Angle Measurements
Most studies use a goniometer to measure contact angles, whether advancing,
receding, or solely static angles are measured. A new method using digital photography
and image analysis software was developed for this study. Initial results were compared
to values recorded with a goniometer and found to be in close agreement. The test set-up
is outlined in Figure 2.8. A syringe of distilled water and a test specimen platform are
mounted on a ring stand. A CCD camera with a 1-6.5 zoom lens is oriented horizontally,
focused on the test specimen. Scion Image Acquisition and Analysis software is used to
acquire a video clip at 20 frames per second while water is added and removed from the
sample with the syringe. Individual frames are extracted from the video and the contact
angles are measured with built-in image analysis tools. The advancing contact angle is
the angle between the substrate and water the moment before the droplet contact line
moves as water is added. Alternatively, the receding contact angle is the angle just before
the droplet contact line moves as water is removed.
2.1.5 Heat Exchanger Specifications
The specifications for the tested heat exchangers are displayed in Table 2.1. The
evaporators are numbered 1 through 7 and are referred to by number throughout this
document. Coils 1 through 5 were tested for thermal performance and steady-state
19
retention. Real-time condensate retention tests were performed on Coils 4 and 5.
Dynamic drainage test data were collected on Coils 2 through 7, with additional drainage
tests completed on Coils 3 through 5 with the coil face tilted.
2.2 Experimental Conditions and Procedures
2.2.1 Thermal Performance
Experiments were conducted under both dry and wet conditions. Dry experiments
were conducted by setting the inlet coolant temperature so that the temperature at the tube
wall is above the dewpoint of the air throughout the heat exchanger. Dry conditions were
verified by comparing the inlet and outlet dewpoints. The heat duty of the some of the
evaporators in this study is high enough to require the inlet air temperature to be elevated
above 45° C to avoid "pinching-off' part of the coil. During the dry experiments the inlet
temperatures were used to determine when the system had reached steady-state and data
are recorded and averaged for at least three minutes in the steady-state condition while
pressure drop and airflow are measured and recorded manually.
Wet experiment procedures are very similar to the dry experiments. The operating
conditions are set so that the entire heat exchanger is wet by ensuring the outlet coolant
temperature is below the outlet dewpoint. Steady-state in wet experiments is determined
by the air inlet temperature and inlet air dewpoint, and to ensure the condensate retention
has reached steady-state the test is allowed to run for at least one hour. Once the system
has reached steady-state data are recorded and averaged over at least a three-minute
interval while pressure drop and airflow are measured and recorded manually.
2.2.2 Steady-state Condensate Retention
Steady-state condensate retention measurements were recorded either after
thermal performance data is recorded or during test runs solely for retention
20
measurements . The procedure is identical in either case. The wind tunnel is operated at
steady-state for a minimum of one hour to ensure condensate retention is also at steady
state. The wind tunnel is shut down and a small tray is inserted under the test heat
exchanger to catch any condensate that is knocked off during the removal process. The
heat exchanger is removed from the wind tunnel and disconnected from the coolant lines.
The inlet and outlet tubes are sealed off by the quick release couplings with automatic
valves that are used to connect the coolant lines to the heat exchanger. The heat
exchanger and tray are weighed and the total mass is recorded. The heat exchanger and
tray are then allowed to thoroughly dry and are weighed again. The difference between
these two weights is the mass of the retained condensate. To hasten the drying process
(normally at least 24 hours) compressed air was used to blow off a large amount of the
water from the coil, and a heat gun was used to further dry the heat exchanger. In
instances when these rapid drying techniques were employed, the evaporator was often
weighed again after several hours to ensure the recorded dry weight was accurate.
2.2.3 Real-time Condensate Retention
Real-time condensate retention measurements required usmg two heat
exchangers--the test coil, and a 'dummy' coil. The dummy coil was necessary to
minimize the transient response of the inlet conditions during a test. The wind tunnel
system requires about one to two hours to reach steady state. However, a test coil only
requires approximately fifteen minutes to reach a maximum retention mass.
Before system start up, the test coil is placed in the test section on the weighing
system and adjusted for proper orientation. By removing the lower adjustment clamp the
coil could be pivoted and removed from the tunnel without changing any other
21
adjustments. The dummy coil is then inserted and the wind tunnel is turned on and
allowed to reach steady state. Once the tunnel reaches steady state it is shut down and the
coils are rapidly changed. Timing and experience are the essential elements to how the
tunnel is turned back on and the resulting quality of data recorded. The two most
important considerations are when to turn the steam on and zero the balance. The steam
injection is the slowest responding element of the wind tunnel system (heaters, chiller,
blower, etc.). The steam could not be left on during changeover because it likely would
saturate both the tunnel and the dewpoint monitors. If the steam were turned on too late,
the coil would dehumidify the air quicker than the humidifier could respond, resulting in
a lag in the retention measurements and a large overshoot of the dewpoint set point and
subsequent oscillations. Through repetition, the timing was refined so the transient
response of inlet dewpoint was less than three minutes.
The balance needed to be zeroed prior to deposition of condensate but after the
coolant pump and blower were operating. Once the entire system is running and the data
acquisition program is started, mass measurements are recorded every ten seconds for
900 seconds then every 60 seconds for an additional 360 seconds. To assist in
synchronizing the mass measurements with the inlet air conditions, the inlet dewpoint is
recorded manually approximately once a minute. This also served as a check of the steam
injection system response. The time at which the first condensate drips from the bottom
of the coil is also recorded. After the amount of condensate retained on the coil reaches a
steady value, the system is shut down and the steady-state value is recorded as previously
described. Checking the steady-state value helped verify the test procedures and results.
22
2.2.4 Dynamic Drainage
For each experimental drainage test run, a dry test coil was suspended over the
water reservoir, the orientation was checked using a standard bubble level, and
adjustments were made to ensure proper alignment on two axes. Test runs were also
conducted with the test specimen tilted 10 degrees. Alignment in these tests was achieved
using a plumb bob and adjusting the heat exchanger until the plumb string intersected
marks scribed on the external surface, producing the proper degree of tilt.
The balance was turned on and zeroed, and a final alignment check was
performed. Zeroing the balance at this stage allowed direct reading of the mass of water
retained on the coil. The water reservoir was raised until the entire test coil was
submerged. Due to the large amount of horizontal fin surface in the coils, there was
concern that a significant amount of trapped air might remain in the submerged coil. This
possibility was investigated by conducting tests during which the water was vigorously
agitated and the coil turned through 1800 while submerged. It was found that a dry coil
when submerged contains a negligible amount of trapped air and simply agitating the
water and causing flow through the coil could remove this small amount of air. However,
if a coil is partially removed from the water after a "false start" and needs to be
resubmerged (say if an alignment problem is noticed as the coil starts to drain), a large
amount of air will be trapped upon re-submerging the wet coil. This increased amount of
air is the result of isolated areas within the coil that are surrounded by water bridges, and
care must be taken to avoid re-submerging a wet coil.
Additional verification of this potential test problem was attained by performing
desktop tests on single fins (similar to those of McLaughlin and Webb). The fin sample
23
was placed between two pieces of clear acrylic and clamped in place. An initially dry fin
was placed into a clear glass container and observed. As expected very few air bubbles
remained on the fin. Then the fin was removed and replaced after it had begun to drain.
Large air bubbles, bridging five to ten louvers, were easily observed. As a result of these
tests it is recommended that dip testing should not include the re-submerging of any coil
as part of the test procedure.
With an initially dry test specimen fully submerged in the reservoir, testing was
initiated by lowering the reservoir and starting a stopwatch at the instant the bottom of
the coil cleared the water. Weight readings were recorded at five-second intervals for
ninety seconds, then at 3D-second intervals for an additional 240 seconds. Other data
points of longer duration were also recorded during various tests to help fully
characterize the nature of water drainage. Repeated observations of the test coil were
obtained, with special attention to the early drainage behavior (in the first thirty seconds),
to ensure orientation remains correct and the heat exchanger remains stable.
24
~ ® ~
I' "\
® © @
'-Q)®® ®
~ ® ~
(v/
Figure 2.1 Horizontal flow wind tunnel. (A) 36-cm diameter round sheet metal duct. (B) Thermal mixing chamber. (C) Screens and honeycomb flow straighteners. (D) 9: 1 contraction. (E) Test heat exchanger. (F) Inlet! outlet measurement sections. (G) Strip resistance heaters. (H) Steam injection tube. (I) Axial blower.
®
Figure 2.2 Test Section for Wet and Dry Runs. (A) Pressure taps (top and bottom). (B) Chilled mirror hygrometer sensors. (C) Insulated clear acrylic. (D) Drainage tray. (E) Thermocouple grid (inlet and outlet).
25
VELOCITY MEASUREMENT LOCATIONS l (THREE VERT. READINGS EACH)
f
HEAT EXCHANGER 111+--< -
TOP VIEW
Figure 2.3 Air velocity measurement locations.
6.5 em.
AIRFLOW
Figure 2.4 Closed environment glove box apparatus for exammmg condensing fin samples. (A) Beaker with water. (B) Fin stock. (C) Peltier device and liquid heat exchanger. (D) Glove. (E) Fan.
26
Figure 2.5 Dynamic drainage apparatus.
Vertical AdjUstment!
Clamp (
HX Body
(a)
Figure 2.6 Attaching mechanism for drainage test coils.
27
Adjustable Base
/" Acrylic Frame
Wire threaded between header and
HX Body
(b)
Figure 2.7 Real time retention apparatus. (A) Wind tunnel. (B) Suspension mechanism components. (C) Balance. (D) Inlet! outlet coolant lines. (E) Test heat exchanger. (F) Drain.
Syringe
Light Source \ CCD camera Specimen
Figure 2.8 Contact angle measurement apparatus.
28
Table 2.1 Tested coil descriptions.
Extemal Dim Louver Louver Louver Fin Fin Fin OF Strip Contact Angle Coil
(HxWxD) Fin type
pitch angle width width thickness pitch Height Advancing Receding
1 213 219 92 Louver 5.08 N/A 6.35 9.14 0.13 2.12 64 35
2 209.6 203.2 76.2 Louver 1.59 N/A 6.35 9.53 0.13 2.12 60 30
3 215.9 228.6 58.0 Louver 1.20 30 6.35 8.00 0.10 1.81 68 44
4 215.9 228.6 58.0 Louver 1.00 36 6.35 8.00 0.10 1.81 68 44
5 215.9 228.6 58.0 Louver 1.00 42 6.35 8.00 0.10 1.81 68 44
6 242.9 292.1 58.0 Offset 1.19 0 8.51 9.73 0.09 1.81 0.64 46 30
7 190.5 247.7 76.2 Offset 1.27 0 6.35 9.40 0.10 1.69 0.85 48 31
All dimensions in mm except contact angles in degrees
29
Chapter 3 Results and Discussion
Condensate retention affects air-side heat transfer and pressure drop
characteristics of heat exchangers; however, the direction of the effect is heavily
dependent on geometry and operating conditions. The main objective of this work is to
quantify these effects on the performance of automotive evaporators. The experimental
approach was to establish the impact of retained condensate by performing thermal
performance experiments under dry and wet conditions, and then record both steady-state
and real-time condensate retention measurements to begin understanding how condensate
is retained on the surface. Additionally, extensive drainage tests were completed that
assist in developing how the condensate affects performance. Furthermore, these drainage
tests show the geometrical dependence of the post operation drainage that affects long
term air quality, another important parameter in measuring overall system performance.
3.1 Thermal Performance
Thermal performance data were collected for five different heat exchangers under
dry and condensing conditions. The results are presented in both dimensional and non
dimensional forms. Data reduction and interpretation follows the methods detailed by the
ARI Standard for condensing heat exchangers, with special attention to related recent
work (e.g., Jacobi and Goldschmidt, 1990; Korte, 1997; Hong and Webb, 1996). A
combination of FORTRAN and Engineering Equation Solver (EES) routines were used
to reduce the data. Dimensional plots of the sensible air-side heat transfer coefficient
versus frontal velocity are given in Figures 3.1 through 3.5 and air-side core pressure
drop in millimeters of water versus frontal velocity are shown in Figures 3.6 through
3.10. The data reduction procedure used to calculate the heat transfer coefficients is
30
discussed in Appendix A, Data Reduction. The pressure drop is recorded manually during
the experimental test using an electronic manometer. The experimental results are non-
dimensionalized by calculating the sensible Colburn} factors and the Fanning friction
factors for the data sets. These parameters are determined from temperature, mass flow,
pressure drop, and geometrical data using the following equations:
} = StPr% = Nu = hPr% Re prX' GCp
Dh
(3.1)
(3.2)
Plots of} andffactors versus air-side Reynolds number are given in Figures 3.11
through 3.15. The sensible heat transfer coefficient for all coils decreased under
condensing conditions, an effect that has been contributed in recent literature (Osada et
ai. (1999), and McLaughlin and Webb(2000» to condensate bridges in the inter-louver
space. While the relative performance of a coil under dry and wet conditions is of interest
in understanding the impact of condensate retention on performance, the absolute
performance is of paramount importance in application. The experimental results will be
presented and discussed giving exposure to both the relative performance of wet versus
dry conditions for a single coil and comparative performances of different coils.
The heat transfer results for Coils 1 and 2 shown in Figures 3.1 and 3 .2,
respectively, are lower under both wet and dry conditions than the performance of Coils 3
31
through 5 shown in Figures 3.3-3.5, but they clearly demonstrate the effect of geometry
on wet performance. The sensible heat transfer coefficient for Coil 2 decreased 30%
when the coil was fully wet, compared to a 12% decrease for Coil 1. The main
differences between Coil 1 and Coil 2 are louver design and louver pitch. Coil 1 has a
complex 'scoop' louver design while Coil 2 is more of a standard louver design. Coil 2
has a much smaller louver pitch, 1.59 mm, than the 5.08 mm louver pitch of Coil 1. The
impact of these geometrical differences under dehumidifying conditions is to give a
larger relative amount of surface area where retained condensate acts not as performance
enhancements, but as flow interruptions. The condensate sticking on the Coil 2 surface
interacts with the flow such that the flow is redirected into duct or channel flow, probably
through the formation of louver bridges. When condensate ceases to exist as droplets and
totally blocks a flow passage, the enhancement due to boundary layer tripping and vortex
shedding disappears. The highly compact design of these coils can also cause the pressure
drop across the coil to increase even in duct flow as the condensate on the fin surface
decreases the minimum flow area, especially in the instances where fin bridges are
formed. This effect is consistent with the findings of McLaughlin and Webb (1999)
where it was observed that a coil with a smaller louver pitch (a critical louver pitch
between 1.1 and 1.3 mm for their study) had a larger propensity for inter-louver bridging
by condensate. The pressure drop performance shown in Figures 3.6 and 3.7 for Coils 1
and 2 are consistent with the condensate interrupting the flow in Coil 2 more then Coil 1.
Coil 1 had a much larger (>30%) pressure drop across the coil at all air velocities, likely
caused by the greater core depth, thicker tubes, and higher effective louver angle of the
scoop louver. However, the pressure drop increase under wet conditions of Coil 1 is
32
considerably smaller than the increase in Coil 2. Coil 2 had a >25% increase over the
entire velocity test range while Coil 1 had <10% increase at lower velocities and <20% at
higher velocities. Both the heat transfer and pressure drop performance trends are also
presented for Coils 1 and 2 in non-dimensional j and f factor plots in Figures 3.11 and
3.12, where the same trends are seen over the entire Reynolds number range.
As previously stated, the heat transfer performance for Coils 3 through 5 is higher
than the corresponding performance of Coils 1 and 2. This increase in heat transfer
coefficient does result in the expected higher pressure drop across the coils from the
higher louver angles, smaller louver pitch, and decreased fin spacing. The flow over each
louver (or offset strip) can be viewed as flow over a flat plate. The Reynolds analogy for
flat-plate flows from White (1991) states,
C 2/ .--L = 2Pr73
Ch
(3.3)
or alternately, friction is proportional to heat transfer. It should be stressed Equation 3.3
is reliable only for certain flow conditions such as low pressure gradients. Thus, by
increasing the number of louvers a streamline flows over (by decreasing louver pitch or
by increasing louver angle) in an array to achieve increased heat transfer will also
increase pressure drop.
Both Coils 4 and 5 had higher sensible heat transfer coefficients than Coil 3 under
both wet and dry conditions; in fact, the wet performance of Coils 4 and 5 is the same as
the dry performance of Coil 3 within the experimental uncertainty. The main geometrical
differences between the coils are louver pitch, louver angle, and number of louver banks.
Coil 3 has a 1.2 mm louver pitch compared to the 1.0 mm louver pitch in Coils 4 and 5.
Coil 3 also had a louver angle of 30° versus the 36° and 42° louver angles for Coils 4 and
33
5 respectively. Coil 3 also has four louver banks (three turnaround louvers) while Coils 4
and 5 each have two relatively long louver banks with only a single turnaround section.
Under dry operating conditions (and to a lesser degree wet) the net result of the
geometry differences is a higher heat transfer coefficient and larger pressure drop. The
heat transfer results are shown in Figures 3.3-3.5 and the pressure drop in Figures 3.8-
3.1 O. The main contributor to both effects is the smaller louver pitch, which causes a
greater number of louvers for the same coil depth, and thus a greater number of boundary
layer restarts, resulting in a higher average Nusselt number and friction factor. This
geometrical effect partially explains the greater pressure drop across Coils 4 and 5
relative to Coil 3. The greater louver angles also cause an increase in pressure drop, as
evidenced in the distinctly greater pressure drop in Coil 5 with a 42° louver angle versus
Coil 4 with a 36° louver angle. Increasing the louver angle increases the effective flow
depth of the coil. Under wet operating conditions Coils 3 and 5 performed similarly to
Coil 2 with a 25-30% increase from dry to wet for Coil 3 and a 20% increase in pressure
drop for Coil 5. Coil 4 responded to wet conditions with only a 10% increase in core
pressure drop, similar to Coil 1, though for a different reason. Coil 1 had a lower increase
in pressure drop because the geometry is much more open with wider fin spacing and
larger louver pitch. The reason for the wet pressure drop performance in Coil 4 will be
seen in the next section-at steady-state it retained considerably less condensate than the
other coils.
34
3.2 Condensate Retention
Condensate retention data were recorded under transient and steady-state
conditions. The transient, real-time retention experiments were conducted for several
reasons. Yin and Jacobi (1999) and Kim and Jacobi (1999) reported an overshoot in
condensate retention for some geometries, where the quantity of condensate retained
reached a maximum, then decreased to a steady-state value. This behavior existed at all
tested face velocities, and at some velocities there was a 15% difference between the
maximum and steady-state values. Since there were no other discernible oscillations
present after the initial overshoot, the dynamics that caused the behavior were not
addressed. Korte and Jacobi (1997) discussed two possible scenarios for condensate
retention. (1) Condensate may accumulate until deposition is balanced with shedding,
resulting in a steady value under a given operating condition. (2) Condensate retention
could be cyclic and oscillate between a maximum and minimum value due to contact
angle hysterisis and shedding characteristics.
Condensate accumulates on a surface by condensation and coalescence, and is
retained by surface tension forces. The water droplets are held until they are shed either
when flow and gravitational forces overcome the surface tension forces, or the droplet is
swept by another droplet being shed. This sweeping is likely an important shedding
mechanism, especially under the fully wetted operating conditions of interest. Potentially,
for certain geometries, sweeping could remove a considerable amount of water,
essentially resetting the heat exchanger surface to a partially loaded condition. The
surface would then start the loading process again, resulting in condensate retention
oscillations in time. A caveat to this idea is the latent load the coil is operating under that
35
could offset the sweeping effect by causing the heat transfer surfaces to effectively be
constantly shedding water. If the water mass flux onto the surface is high enough, then as
soon as a droplet is swept another droplet condenses on the now clean surface and little
oscillation would be observed. Yin and Jacobi (1999) noticed a difference in droplet size
distribution vertically on a flat plate, but it was observed in a very low latent load
environment in a glove box that caused only a relatively small frequency of sweeping.
For the heat exchangers in this study, a droplet drains from the coil through one
(or a combination) of three main drainage routes. (1) Flow forces push the water toward
the downstream edge of the fin array and the droplet drains down the edge of the fins. (2)
The droplet drains through the fins until it reaches the bottom. (3) The droplet moves
down the channels along the tube wall to the bottom of the coil. Both geometry and flow
conditions will affect the relative quantity of condensate draining through each of the
different modes. Osada et at. (1999) studied the effects of surface condition, louver cut
length, and a dividing section on drainage. Osada and coworkers found a 2.0 mm center
dividing section promoted drainage along the tube wall in the center of the array versus
the water moving along the fin length to the trailing edge before draining. This finding is
an important point regarding the performance of Coils 4 and 5, which have a relatively
large open turnaround section in the center of the array that may behave similar to an
actual division.
3.2.1 Real-time Retention
Condensate retention has been shown to have a large impact on heat transfer, and
therefore the actual amount of water on the surface at a given time affects interpretation
of performance data. The existence of oscillations in condensate retention would affect
36
the validity of the thennal perfonnance and steady-state retention data, dependent on the
frequency of the oscillations. Additionally, the overall time required for the condensate
on the heat exchanger to reach a steady-state value was initially unknown, and the actual
test duration required could affect experimental procedures. In summary, real-time
retention experiments were conducted to investigate condensate loading characteristics,
to validate the thennal perfonnance and steady-state retention data, and to detennine any
required changes to experimental procedures.
A plot showing condensate retention and humidity ratio versus time for Coil 5 is
shown in Figure 3.16. The retention data were recorded over a 45 minute interval, longer
than any other test run. The humidity ratio is shown to verify the operating conditions and
validate the experimental apparatus and procedure. Inlet air temperatures were also
recorded and showed less than 1.0°C variation over the course of a test due to the
relatively large thennal mass of the tunnel. The approximately three minute transient
period in the humidity ratio is caused by the humidifier controller adjusting the steam
injection rate after restarting the wind tunnel as discussed in Chapter 2. The quantity of
condensate retained increased asymptotically to a steady value. There were virtually no
oscillations in the mass after twenty minutes, and what small fluctuations that were noted
are likely caused by system vibrations and not an unsteadiness in the quantity of retained
condensate.
The repeatability of the experimental technique is shown in the plot of two test
runs with Coil 4 in Figure 3.17. The two data sets were collected at face velocities that
were within the experimental uncertainty of each other. The large uncertainty in the
velocity measurement is caused by the necessity to leave the coil free floating and not
37
seal the wind tunnel while recording the data. As discussed in the experimental
procedure, the real time retention measurement apparatus is set-up as consistently as
possible to mitigate the velocity measurement error.
The results in Figure 3.17 show a similar trend to that of CoilS (see Figure 3.16),
but there is an abrupt flattening of the curves for several minutes, then a gradual climbing
to a steady-state value. This flat region is in the same area where previous studies (Yin
and Jacobi (1999), Kim and Jacobi (1999» observed an overshoot in condensate
retention, and the effect is more pronounced in the VI = 1.4 mls test. Actual overshoot
was observed for the same coil (Coil 3) at a face velocity of 1.5 mls as displayed in
Figure 3.18. Also shown in Figure 3.18 is a test run with VI = 0.8m1s where neither an
overshoot nor flattening trend is observed, only a gradual climb to a steady-state value.
The steady-state values measured by removing the heat exchanger from the wind tunnel
and weighing as described for steady-state tests are also plotted for the two runs in Figure
3.18. Unlike the plain-fin-round-tube heat exchangers studied by Yin and Jacobi (1999)
where the overshoot was dependent only on geometry, operating conditions appear to
affect the transient retention behavior of automotive style evaporators.
The real-time condensate retention behaviors of the tested evaporators were well
behaved in the sense that there were no substantial oscillations in time that would effect
data acquisition or interpretation. Under some operating conditions, there was a single
oscillation where the mass of condensate overshoot the final steady-state value by 10%
and then smoothly decreased to the steady value. This overshot was only observed at face
velocities of approximately 1.4 - 1.5 mls. The likely cause of the overshoot existing only
at certain velocities is the drainage dynamics of the coil. As stated, a surface will load up
38
with condensate until the water is shed through gravitational or flow forces. The rate of
deposition depends on the prevailing operating conditions of both the incoming moist air
stream and the fin surface. The difference in this deposition rate is clearly seen in Figure
3.18. The slopes of the graphs between 100 and 300 seconds is the rate condensate is
being deposited on the surface (there was no observed drainage during this phase). This
may also be calculated from the following,
• m = m (mIn -mOUI ) , (3.6)
Conti Air
and at steady-state this quantity is also equal to the drainage rate of condensate, since the
quantity of water removed from the airstream also must leave the heat exchanger at
steady-state.
An overshoot in condensate retention would be expected in only the following
special case. For a given coil at different operating conditions, the relative amount of
drainage occurring through the aforementioned drainage routes will vary. For instance, at
higher velocities, one would expect more drainage along the downstream edge because of
the increased shear forces. Additionally, the order in which the drainage modes occur will
also depend on operating conditions, at lower velocities, drainage along the tube walls
will likely will occur before any condensate is pushed to the back of the coil by the air
flow. However, each of these drainage modes, especially the pure gravity driven ones,
necessarily has a maximum rate constrained by the geometrical parameters that create the
routes through which condensate can drain. Thus, the circ*mstances where an overshoot
in condensate retention could occur can now be identified. If the maximum drainage rate
for drainage along the tube wall or through the fin is reached before airflow forces have
pushed enough condensate to the back of the fin for drainage, then an overshoot could
39
occur. This overshoot would be temporary because as the condensate effectively 'backs
up' on the fin surface, higher shear forces will occur on the larger droplets, and they will
be forced to the downstream edge and a balance will be eventually reached. At higher
flow rates, shear forces would dominate from the beginning, and at lower velocities the
gravity drainage modes would be dominant. It should be stressed here that this
explanation is only a hypothesis, and would be difficult to directly verify with the
existing test set-up. Also, since the resulting effect of this overshoot is minimal with no
long-term effect on heat transfer, it isn't likely that the transient nature of condensate
retention is an important design consideration. However, these drainage modes will effect
steady-state retention, a very important design consideration.
3.2.2 Steady-state Retention
Steady-state retention measurements on all five coils are shown in Figures 3.19
and 3.20. Total condensate retained is plotted in Figure 3.19 versus frontal velocity and
quantity of condensate retained per unit of total heat transfer area versus frontal velocity
is plotted in Figure 3.20. Condensate retention for all five coils displays a heavy
dependence on frontal velocity, though the magnitUde of the impact varies with
geometry. Coil 2 had a 50% increase in retention when the frontal velocity changed from
2.0 mls to 1.0 mls. By comparison, Coil 4 retention only increased 25% with the same
velocity change. Similar data trends were reported by Korte and Jacobi (1997) for
uncoated, plain-fin-and-tube heat exchangers in a downward flow wind tunnel with
velocities in the range of 1.5 mls to 8.0 mls based on minimum free flow area. Yin and
Jacobi (1999) observed condensate retention to be independent of air velocity over the
40
range of face velocities from 0.8 mls to 2.0 mls for plain-fin-and-tube coils m a
horizontal flow wind tunnel.
The large influence of air-flow rate on the quantity of retained condensate for the
studied automotive evaporators studied is likely caused mainly by geometry and not
surface condition, though surface condition is a contributing factor in general for
condensate retention. Kim and Jacobi (1999) observed almost a 50% decrease in
condensate retention for a heat exchanger treated with a hydrophilic coating over an
uncoated coil. Korte and Jacobi (1997) reported condensate retention on a hydrophilic
surface coil had little dependence on air velocity. Three of the five coils (coils 3-5) tested
in this study had virtually identical surfaces. They were manufactured at roughly the
same time by the same laboratory and had been exposed to testing conditions the same
number of times. The other two coils were older and tested more frequently, and as a
result, though they initially had moderately hydrophilic surfaces, by the time steady-state
retention tests were conducted the advancing and receding contact angle were similar to
the other three coils. Therefore, the differences in the condensate retention between the
coils are caused by geometric differences.
3.3 Dynamic Drainage
Dynamic drainage tests were completed for coils 2 through 5 and two additional
coils that were not tested in the wind tunnel for this study. Most of the research on
condensate retention has focused on its effects on thermal performance. Korte and Jacobi
(1997,2000), Yin and Jacobi (1999), and Kim and Jacobi (1999) state that the effects on
thermal performance depend directly on the nature and quantity of retained condensate,
and that such retention can be modeled if the flow forces, gravitational force, and surface
41
tension forces (and surface condition) are considered. They have developed retention
models to predict the quantity of condensate retained on a coil during operation.
Unfortunately, none of this work addresses the important issue of post-operation
drainage. Condensate drainage must be understood if designers are to develop fast
draining coils to mitigate biological activity on the air-handling surfaces and improve air
quality. The automotive industry typically relies on the "dip test" to provide drainage
information. In this test, the coil is submerged in a reservoir of water, withdrawn and
weighed. There is little consistency in how this test is conducted, namely in the time
delay between dipping and weighing and in heat exchanger handling during the dip test.
The dynamic drainage test developed during this study alleviates some of the potential
misinterpretation due to differences in dip test techniques. This new variation to the
standard dip test is used to develop a deeper understanding of post-operation condensate
drainage behavior, which is linked to the actual condensate retention during operation.
Multiple test runs were conducted for most coils, initially to ascertain the
repeatability of the test procedures, and finally for periodic verification of results. Figure
3.21 shows the results from three different tests on one heat exchanger demonstrating the
repeatability of the experimental results. As expected, the maximum error occurs during
the rapid draining phase in the first 60 seconds as illustrated in the partial chart of the
results in Figure 3.22. Overall, the differences between tests are within the experimental
uncertainty, and this repeatability served as an additional check of test conditions.
Drainage test results for the six heat exchangers are depicted in Figures 3.23 and
3.24. Unless otherwise noted, all mass values are on per unit heat transfer area basis. The
basic behavior shown in the figures resembles an exponential-like decrease in retained
42
water, with one group of coils (in Fig. 3.23) showing a short time constant (lOW-i), and
one group exhibiting a long time constant (high-i). The low-icoils are the three coils that
reach within 20% of their final value (based on a 300 second total test time) in the first 20
seconds, and high- i coils are the remaining three coils that show distinctly different
drainage patterns.
Test runs over an extended time interval were completed on a selection of coils
and are presented in Figure 3.25. Data were recorded at one-hour intervals after initial
data points were collected to verify proper orientation by comparison to other test runs.
Lab conditions were not controlled in regards to temperature and humidity so there was
initially concern that evaporation could lead to a misinterpretation of the results. A tray
was placed between the test heat exchanger and the water reservoir after fifteen minutes
and by observing the amount of water that drained into the tray it was concluded that
evaporation accounted for a negligible amount of the mass change during a four-hour
test. Coils 6 and 7 continued to drain a significant amount of water, especially during the
first hour of the test, although they appeared to have very slow drainage rates in the
shorter tests. In comparison, Coils 3 through 5 drained rapidly in the first five minutes,
then lost only 13% more, whereas Coil 6 lost an additional 26% over the extended time
period.
Data were also recorded for Coils 3 through 5 with the coil face tilted 10° from
vertical. A representative graph in Figure 3.26 displays the results for a single coil and
Table 3.1 outlines the effects on each coil. The tilt tests were conducted using exactly the
same procedure as the vertical tests. Multiple experiments were again performed to
ensure the repeatability of the test results. The results typically varied less then 4% over
43
the entire test. Coils 3 and 4 each drained approximately an additional 25% when tilted,
but Coil 5 was distinctly different, draining only 15% more. This difference is likely due
to the way water is being retained on each coil rather than just the quantity.
Examination of the tilt test results in conjunction with the extended time results
provides information about where water is being held in the heat exchangers. Germane to
the discussion is a comment on the different areas water can be held in a fin array.
Essentially, water can stick on the fin surface, on the tube surface, or as a bridge between
louvers, fins, or fin-tube junctions. Water contained on the fin surface is held In
equilibrium by surface tension and gravitation forces as shown in Figure 3.27a,b. In
Figure 3.27a, the droplet is on a horizontal section and in Figure 3.27b, the droplet is on
an inclined surface, such as a louver. In both of these cases, tilting the heat exchanger
potentially can cause the droplet to move, depending on the actual surface tension forces
and degree of tilt. Likewise, water held along the fin-tube junction as a fillet, also will be
affected by an orientation change. Furthermore, water in the channels formed by the fin
tube junction and the fold of the fin itself will not exist as droplets, but as a film that may
extend the entire fin depth, and may be easily displaced from a tilted coil. However, a
water bridge in a louver is a very stable entity as pictured in Figure 3.27c. The water
bridge is held in the louver space predominantly by surface tension forces, and has a
maximum size constrained by geometry. Louver angle likely also contributes to louver
bridge stability by changing the effective height of the bridge. The higher the angle,
subject to limit of probably around 60° where gravity can begin to dominate, the more
stable a bridge will be because of the ability of the solid-liquid-gas interface to be closer
to the proper contact angle, and thus have the surface tension holding force as large as
44
possible. It is unlikely that any degree of orientation change will affect a louver bridge.
This was verified by desk-top experiments on a piece of fin stock, and indeed, a fin could
be rotated through an entire 360° and a louver bridge remained. Bridges between offset
strips, as shown in Figure 3.27d, appear to be less stable because of the significantly
larger space, relative to a louver, that the water occupies in an offset strip, thus gravity is
a large factor in displacing the bridge. The susceptibility of larger bridges to be shed by
gravity agrees with the results of McLaughlin and Webb (2000) where a larger louver
pitch, and thus larger bridges, had substantially less louver bridging.
The tilt results presented in Table 3.1 show that Coil 5 significantly differed in
response from the other two coils tested. All three coils are identical except for fin
design, so it may be stated with confidence that the fin geometry of Coil 5 accounted for
the difference. From the preceding argument, louver bridging is the likely reason Coil 5
retains more water when tilted relatively to the other three coils. The louver angle in Coil
5 is 42°, higher than Coil 4, which has only 36° louvers. Coil 5 likely has a greater
amount of water retained as louver bridges than Coil 4, up to 11 % more, or at least louver
bridges that are more stable and less apt to swept out during drainage. The extended time
drainage results support this stable louver bridge idea. Between the one and four hour
data points Coil 6 drained an additional 26% while Coil 5 only drained 13%, consistent
with the idea that louver bridges in Coil 5 are locked in and have less tendency to drain.
The tilt test can help determine how condensate is retained by showing how much
water is 'easily' removed from the coil by gravity forces. Furthermore, under actual
operating conditions, flow forces coupled with gravitational forces may create a resultant
force on retained condensate that is similar to the tilt test, and thus both vertical and tilt
45
test results give insights into how much condensate is retained on in a coil under
operation. Indeed, the steady-state retention results in Figure 3.19 show qualitatively that
Coil 4 drained better and also held less condensate over the entire range of tested
velocities. Osada and coworkers (1999) found that coil inclination greatly influenced the
thermal performance of an evaporator, and further investigation of this effect could be a
valuable tool in future fin development.
46
0.2 I I I I I I I I I I I I I I I I I I I I I
1 ~ I 0 Coil 1 dry
I ~
0 Coil 1 wet -i ~
0.15 I
I
2' j N l < 0 E 0 - 0.1 0
~ r ° 0 l 0 r 00 -I ..c 0 0 ...
i I- -< I !
0.05 f- --1 ! J r ~ ~ , ~ :-
r J 0 I I I I I I I I I I I I I I I I I I I
0 1 2 3 4 5 Face Velocity (m/s)
Figure 3.1 Coil 1 air-side sensible heat transfer coefficient versus face velocity.
0.2 I I I I I I I I I I I I I I I I I I I I I I I I J r-
I i 0 Coil 2 dry I
:-
~ t 0 Coil 2 wet
0.15 f- 0° 1 t 2'
0 l
N o 0 ...j < L ! E 1
~ 0.1 c- o 0 --1
I
~ l 0 ~ 0 l ..c 0
0 j 0 0
0.05
1 -I
0 1 2 3 4 5 Face Velocity (m/s)
Figure 3.2 Coil 2 air-side sensible heat transfer coefficient versus face velocity.
47
~ N < E -~ -
.J:. 0
~ N <
0.2 L ~
015~ l f-
0.1 r-
0.05
1 i-
0 0
0.2
0.15
E ~ 0.1 ~
o .J:.
0.05
~ ~ I-
1 1 I 1 1 1 1 ,
0 Coil 3 wet
0 Coil 3 dry
0 0
0 0
1 i 1 1 , 1 1 1 1 1 1 1 1 1 I 1
1 2 3 4
Face Velocity (m/s)
Figure 3.3 Coil 3 air-side sensible heat transfer coefficient versus face velocity.
1 1 1
I
I ~
J 1
--!
..i
I
~ -j
j ~ ~
1 --<
~ j
1 , 1 I
5
I I I I I i I I i I I I 10 1 1 1 1 J o Coil 4 dry o Coil 4 wet
o
o
o
o o
o
o
~ l ~
I
1 -j
-l I
I ~
~ ~ ~ 1
o L! --'-I -,1'--.11'--.11---1---1.1---1.1 ---1.1 ----'-I ----'---1..1 --'-, ---,-I --'-.1 --'-_''--.1'---11---1.1---1.---1.1 ----'-I ----'-I ----'-, ---1j
o 1 2 3 4 Face Velocity (m/s)
Figure 3.4 Coil 4 air-side sensible heat transfer coefficient versus face velocity.
48
5
0.2 I i i i i i i I i i i ! i i i
r Coil 5 dry
~ 0
0 Coil 5 wet 0
0.15 - 00
2' 0 0
N < E 0 - 0.1 f-
~ 0
0 0 I-.=
t I
0.05 r I
I I-
0 !
i i I i i i i I i i i i I i i i i i i i
0 1 2 3 4 Face Velocity (m/s)
Figure 3.5 Coil 5 air-side sensible heat transfer coefficient versus face velocity.
20 i i I i i i i i i
f
i i I I I I I i i I i i
I 0 Coil 1 dry
I 0 Coil 1 wet
15 f- 0
~ 0
Q t- o 0 N I-
::I: I
E ~ I 0
.5. 10 ~ 0
a.. "C ~
00 i
I- m I 0 r 0
5 f- a
~
o o 1 2 3 4
Face Velocity (m/s)
Figure 3.6 Coil 1 air-side pressure drop in mm of water versus face velocity.
49
I
l
1 -I
~ ~ !
-< I
~ -j
I
J ~ I
-j
-I ,
1
5
'] j ~ -1 l ~
i
-1
5
20
~ I I I I I I i ! I
-j
0 Coil 2 dry i
I -j
t 0 Coil 2 wet 1 ~
I ~ 15 --l
i - 0
o 1 0 N
:I: l-E E 10 r- 0 0 -i -
l 0
~ c. 0 0 "C 0
0 0 ! 0 5 ~
I- 0 -j ,
I f- 0 1
~ 0 ~ 0 I ,
i -j
0 , i I I i I I i I I I i I I I I I I
0 1 2 3 4 5 Face Velocity (m/s)
Figure 3.7 Coil 2 air-side pressure drop in mm of water versus face velocity.
20 I I I i I I I I I I I I I I I I I I I
J ~
I 0 Coil 3 dry
I I-
~ 0 Coil 3 wet
~ 15 0
-I 0 i
N I-
j :I: I
0 0 f-E
10 ~ .§. 0
c. r 0 0 "C r
~ 0 -j
:- 0 ~ 5 ~
,
0 1 f0-
r ~
t i
-j
0 I I I I I I I I I I I I I I I I I I I I j
0 1 2 3 4 5
Face Velocity em/s)
Figure 3.8 Coil 3 air-side pressure drop in mm of water versus face velocity.
50
-0 N
:J: E E -Q. 'tJ
Q N
:J: E .5. Q. 'tJ
20 ,I I I
0 Coil 4 dry 0 Coil 4 wet 0
15 - 0
~ 0
~ 10 0
l- 0 I
0 r ~ 0
i 0 r-
5 i
CP '-e- o ; 0 ~ 0 L !
0 [
I I I I I I I I I I I I I
0 1 2 3 4 Face Velocity (m/s)
Figure 3.9 Coil 4 air-side pressure drop in mm of water versus face velocity.
20 I I I I I I I I I I I I I I I I I I I
f I 0 Coil 5 dry
I 0 Coil 5 wet 0
I-15 f- 0
~ 0 0
l-
i Do 10 f---
I
f 0
~ 0
5 0
o o 1 2 3 4
Face Velocity (m/s)
Figure 3.10 Coil 5 air-side pressure drop in mm of water versus face velocity.
51
...,
1 l -i
j I
-: -i l ...i
I
-.j
~ I j 5
I l
~ ~
J I
-1
j
5
0 0 - 0.1 ! o cPo 0 t- o 0 c- o
'"" L 0
;- 0 Coil 1 dry j I- 0 Coil 1 wet j i ...
0 0 Coil 1 dry f , f... .., I 0 Coil 1 wet f I I I
I -I
I ,
I 0
~ 0
r 0 0
0 0 0
I DO
0 0 0
0 I I 0 , 0
I 0.01
200 400 600 800 1000 1200 Re
Oh
Figure 3.11 Coil 1 j and f factors versus air-side Reynolds number.
I
I I - I 0
~ 0.1 c-D 0 -'
0 ~ 0 0 ~ 0 0 a l 0
0 0 o 0
1 ... 0 0 Coil 2 dry j
0 Coil 2 wet j 0 Coil 2 dry f
I 0 Coil 2 wet f !
I 0
I I- 0 -] I 0
0 00
Cb 0 0 0 0
0.01 200 400 600 800 1000 1200
Re Oh
Figure 3.12 Coil 2 j and f factors versus air-side Reynolds number.
52
i I
.... I
0.1
~ I .. I
0 ! f-I
~ i
;-
:
0.01
200
I ....
0.1 I-
.. 0
0.01
200
0 Coil 3 j dry 0 Coil3j wet 0 Coil 3 fdry
0 0 0 Coil 3 fwet 0 0
0 0
0 0
0 0
0 c 0
0 0
400 600 800 1000 ReOh
Figure 3.13 Coil 3 j and f factors versus air-side Reynolds number.
I I I 0 Coil 4 dry j 0 Coil 4 wetj 0 Coil 4 dry f
0 0 Coil 4 wet f ° 0 0 0
0° 0 0
° 0 0 0 0 0
o o o o
o o o
400 600 800 1000 ReOh
Figure 3.14 Coil 4 j and ffactors versus air-side Reynolds number.
53
I
J ..J
I
1 "1
] i I
1 I
-I i I I
! -;
I
1200
l
1 1 ~
1200
....
... 0
I
o 0
00 o I 0.1 '-
t o 0
0.01
I
I :-
I
~ I
t I
I , I
200
o
o
o
Coil 5 dry j Coil 5 wetj Coil 5 dry f Coil 5 wet f
o
o
400
o o 0
o o 0 o o o o
600 800 1000 ReOh
Figure 3.15 Coil 5 j and f factors versus air-side Reynolds number.
350 ~ I' " '" o V,=1.31
300 '--___ ---I.
, , I
o 0 o
00
250 -< 000
: 200 r ,,-o-/a-<> O-o~ ~o~ O-o~ ~o_ ~ 150 ~ i I
l 1
l -j I I
l l I
j 1200
0.03
o 0.025
0.02
0.015
-i :-
100 f 50 ~
t ~
~ ~ v,=l'l ]
0.01
0.005
O~-L~~~~-L~~~~~~~~~~~~~~~ o 3000 o 500 1000 1500
Time (5)
2000 2500
Figure 3.16 Real time condensate retention and humidity ratio for Coil 5 versus time.
54
::I: c 3 ~ = 0
350
300
250
-en 200 -IS co :E 150
100
50
350
300
250
- 200 en -IS co :E 150
100
50
o o
i i
~ I ~ !->-f-
i
• I j iii I I I I Iii I I f iii Iii
-i 0.03 V=1.4 , V=1.3 , 6~
-1 0.025
j -1
~~~~6*-~;le..~e:...~-6-6 j 0.02
0.015
500 1000
Time (s)
0.01
- - V,=1.4 0.005 - - 6 - - V,=1.3 ~
o 1500
Figure 3.17 Real time condensate retention repeatability for Coil 4.
• V=1.5 , 6 V,=O.8
200
-{;- to -IS -6- -{;- to -IS -/r -{;- -6- 6-6 ._- ....... __ ..
6
•
- - V,=1.5
- - 6 - - V=O.8 ,
i 1
400 600 time (s)
800 1000 1200
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
o
Figure 3.18 Real time plot for Coil 4 showing overshoot at higher velocity.
55
::I: c 3 1I cr. 0
::I: c 3 1I cr. 0
§ "C Q) c S ~ IS CIS
:::lE
-5 ~
-N
E -.9 CIS
~ <C :: c
:::J ... Q) c..
"C Q) C
s ~ IS CIS
:::lE
SOO E i i i I i i I i i i I i i i I i i i r I i i i
i~ f- 0 Coil 1
4S0 ~ /::, -~ Coil 2 I- ---£l - Coil 3
[j ~
- - (> - - Coil 4 i~ 400 ~ "- T-
~i151 0 ~ /::,
3S0
300 /::, ~
---.f1 +0- + "'---
2S0 <>- -,+-+-
----- _0_ -E <Y-_ -0_ --B-
~
200 ~ -0 []
1S0 ~ f--
r-100 t i i i I i i i i I i i i i I i i i i I , i i i I
0 O.S 1.S 2 2.S Face Velocity (m/s)
Figure 3.19 Steady state retention for all coils versus face velocity.
Coil 1 Coil 2
160 r -[] - Coil 3 - - (> - - Coil 4
- + - - Coil5
140 t \
! \ i ~ I "-
120 r /::, 0 ~/::,
+0- + "-
~ ""-- - ~ 100 r <>-9
~-+ .+- , /;:,
~/::, t - _0 "-.
I <Y - ----- _0 --g
80 ti - -0
D
i i i I i i i i I i i i i I i i i i I i i i i I i i i
0 O.S 1 1.S 2 2.S Face Velocity (m/s)
Figure 3.20 Steady state retention per unit of heat transfer area versus face velocity.
56
--i
j ~ ~
-j ]
i -;
3
-i
'~ j 1 1 -1 -i
j -i
I
J j
3
iii 1 Iii ill 1 i i i , i
Run 1 Run 2 Run 3 I :
r
200 ~ o t I Iii Iii iii iii Iii iii iii iii iii I
450
440
430
-420 S IB ~ 410
400
390
380
o 50 100 150 200 250 300 Time (5)
Figure 3.21 Drainage test plot for Coil 3 illustrating the repeatability of the experimental technique.
I I i i I ! i I 16 1 I i I i !
i i I
f 0
0 ° Run 1 >-
Run2 !- 60 0 >- °0 >- 6 Run 3 ~ 60
°
~ 6 0 S 6 C
I 6 (,)6
~ 6 ~go
1:16 00 6 00 0
6 0 666~
0 ° 6 bl
~ 6 g
6 0
~
I
L i i i I i i i I i i i i I i i i i I i i i
0 50 100 150 200 Time (5)
Figure 3.22 Partial plot of the repeatability test results showing the area of maximum error.
57
i I i l l l l
I
] I
-1 -j
-1 i I
350
-, --<
~ ---J
~ j
~ -1 J
-1 -:1 ~
~ J 4
--< -I
i j
250
400 r i I i I i i i i i ! I i i i I l ...,
0 Coil 3 ~ t-
350 c- D Coil 4 l l-i- t:;. Coil 5 r J
~300 t -j
1 - ~ .9250 -1 CIS j f 0
~ 200 -1
1 G) 0eo .. r ~=- 0 0 0 0 0 0 0 i ~ 150 ~D.A~ t:;. t:;. t:;. t:;. t:;. I 'L[u~, 0 0 0 0 0
100 ~
~i ~ ~
i I II! I ! ! I 1 i ! J
50 I ! ! i I i i i I I i i
0 50 100 150 200 250 300 350
Time (s)
Figure 3.23 Dynamic test results for the fast draining coils.
450 I I I I I I
0 Coil 2 400 - -
0 Coil 6 350 - t:;. Coil 7 --N
< ~ E 300 f-Ooo --CD Cb~COCOooo -CIS f 250 - 0
0 -0 « ~6t:;.~
0 0 ... 0 0 j G) Co 200 -1 IS
~Mt:;. t:;.
-j
6 -I
CIS t:;.
:E 150 0 t:;. t:;.
~ t:;.
100 0 0 0 0 0 0 0
50 0 50 100 150 200 250 300 350
Time (s)
Figure 3.24 Dynamic test results for the sustained draining coils.
58
250
_ 200 N < E S co 150 e
<C ... G) Q.
II! 100 co :!
8 Coil 3
-El-- Coil 4
--<> - Coil 5
----6---- Coil 6
,
"1 ,
-,
- - + - - Coil 7 ~
~~~-~-~~~~-----~--~~~~ l 6- __ -+------ ]
- - - -Lot - _ _ _ _ - + - - • - _ _ _ _ ~ 50 -'-'------6 +- - - •• - - - oj----j
~ • -. - -- - - -. - - - -Lot - - - - •• - • -. - _. ____ " -6 i
f-r ~ o L[ ---"--'-' ---L' ---"--'-' ----'-' ---1'--'-' ----'-' ---11--,-, ----'-' ---1'--'-' ----,-, ---'---'-'----'-' ---,,--,-1----,-, ---"--'-'----'-' ---"---'-'----'-' -'---'-'--"
500
450
400
350
c; - 300 II! co :!
250
200
150
100
o 5000 Time (s)
Figure 3.25 Extended time drainage test results.
l i i i I i i i i i i i i i I i i i I i i i
'1 I
• Vertical 6 Tilted
1 r· F···-..-..... • 1 • • • • ~6 -i
E- 6l1l1l1
-j ~ -i J
~ ~6 6 6 6 6 ~ r- 6 6 6 -l I
~ r-
~ j r-
~
[, i i i I i i i i I i i i I i i i i I i i i i I i i i i I i i I J
0 50 100 150 200 250 300 Time (s)
Figure 3.26 Comparison plot between a vertical coil and a coil tilted 10°.
59
350
Table 3.1. Tilt test and vertical test comparison.
Coil Orientation Mass
20 secs
3 Vertical 414 Tilted 325
4 Vertical 348 Tilted 276
5 Vertical 365 Tilted 323
(a) Horizontal Surface
(c) Louver Bridge
% change Mass
% change Mass
60 secs 180 secs
24
23
12
390 304 342 263 364 312
Fsr
sr= receding angle surface tensioo force
sa= advancing ange surface tensioo force
25 374 284
26 335 254
15 362 304
(b) Tilted Surface
Larger relatil.e bridge, more affected i:1{ gravity
(d) Offset Strip Bridge
Figure 3.27 Droplet forces and bridges.
60
% change
27
27
17
Chapter 4 Conclusions and Recommendations
Heat transfer, pressure drop, and retention data have been collected and presented
for five automotive evaporators. The thermal performance tests were conducted under dry
and wet conditions and both steady-state and transient retention data were recorded.
Additionally, a dynamic drainage test was developed and a variety of coils tested. This
chapter contains general conclusions about the effects of condensate on the overall
performance of an automotive air-conditioning system, and a recommendation for the
focus of future work in this area.
4.1 Conclusions
4.1.1 Thermal-Hydraulic Performance
The heat transfer coefficient decreased and the pressure drop increased for all
coils tested. Condensate retention causes the decrease in heat transfer coefficient by
forming bridges in the inter-louver space and redirecting the flow from the desired
louver-directed flow to duct-directed flow. Additionally, condensate may also form
bridges between fins effectively creating a dead region on the fin. Larger louver pitches
helped prevent louver bridging, but decreased absolute performance of the coil due to
reduced boundary layer restarting (and resulting thicker boundary layers).
The pressure drop increases under wet conditions even though the flow is
redirected into duct flow and that would seem to decrease pressure drop. The presence of
condensate on the fin surface decreases the effective minimum flow area and causes
increased pressure drop. This effect will be even greater with the presence of fin bridges.
Coil 4 was shown to have only a slight increase in pressure drop from dry to wet
conditions, and a corresponding lower quantity of retained condensate.
61
4.1.2 Condensate Retention
A highly repeatable method of measuring condensate load-up on evaporators was
developed. The quantity of retained condensate reached a steady value in 15-25 minutes
depending on operating conditions. The greater the water mass-flux the shorter the time
to reach steady-state, as expected. At some specific air-flow rates, an initial 10%
overshoot in condensate retention was observed. This effect may be important in
determining the drainage characteristics of a coil. It was hypothesized the relative
quantity of condensate draining through different modes causes the overshoot, though
further experiments are required. Extended test runs were done to investigate the
possibility of oscillations in retention caused by shedding mechanisms that may impact
the performance characteristics and data interpretation methods. However, the quantity of
condensate remained within 1.5% over a 45 minute test, once a steady value was attained.
Steady-state retention results showed a large influence of frontal velocity on the
quantity of retained condensate for all the tested coils. The impact of the airflow shear
forces varied with geometry over the tested range of face velocities. At the highest
velocities the quantity of retained condensate for similar geometries (same heat transfer
area, different louver designs) showed a slight tendency to converge, indicating that shear
forces start to dominate gravity forces and geometrical influences on retention. A large
turnaround section, similar to the centerline divide investigated by Osada and coworkers
(1999), resulted in lower condensate retention in Coil 4 compared to Coil 5, though the
impact of the higher louver angle is unclear. However, heat transfer was observed to
decrease by a greater amount in Coil 4 under wet conditions, likely due to a lower
absolute number of louvers without condensate bridging.
62
4.1.3 Dynamic Drainage
A dynamic drainage test apparatus was built to test the drainage of a variety of
coils. Initial drainage response (in a 300 second interval), 10ng-teInl drainage, and
orientation effects were investigated. Two distinct drainage patterns were observed; fast
draining coils that reached a steady-state value within about 120 seconds, and sustained
drainage coils that continued to substantially drain water for up to four hours. The long
teInl results, and the results of the tests with the coil face tilted 100 from vertical show the
influence of louver bridging on drainage. When a louver bridge exists, gravitational
forces are not sufficient to remove the bridge unless the bridge is very large, such as one
that may exist between offset strips. Thus, in 10ng-teInl testing, louvered fins drain much
slower than offset strip fins. This drainage behavior is potentially important to biological
growth on the fin surface.
The drainage tests also qualitatively predicted the condensate retention in the
wind tunnel for Coils 2 through 5; that is, the rank-order for condensate retention in
wind-tunnel testing was congruent with the drainage test results. The drainage test over
predicted the absolute quantity of retention, but with the large influence of shear forces
on retention this result would be expected. The drainage test reflects retention at the zero
velocity operating condition. Furthermore, the test procedure developed is more accurate
than traditional 'dip-test' methods, because the relative rates of drainage are important.
4.2 Design Guidelines
In order to compare two fin designs and one design declared 'better', it is
necessary to define the objective function as it relates to system perfomlance. The
optimized design attributes can be any combination of the following parameters.
63
1) Higher heat transfer coefficient, under either dry, wet, or wet compared to dry.
2) Lower pressure drop across the coil, again under either dry, wet, or wet
compared to dry.
3) Lower quantity of condensate retention, under operation or post-operation.
A higher heat transfer coefficient is obviously desirable to either increase the heat duty of
a heat exchanger or alternatively and perhaps more importantly, decrease the size of the
coil while maintaining the same capacity. A lower pressure drop is beneficial because of
pumping power and noise. Overall system efficiency will be improved if less pumping
power (the blower fan in automotive applications) is required. Increased blower speed
also generally causes increased noise levels. As discussed in the introduction, water
remaining on the air-side surface of an evaporator coil after system shutdown is a prime
environment for biological activity, and the result is a degradation of air quality through
odor and thermal performance through fouling. In summary, care must be taken when
rating heat exchangers and developing design guidelines, as it is critical to define the
proper objective function based on the focus of the optimization. From the results of this
study, the following are recommended design guidelines for improved fin design:
• Keep louver angle at or below 36°. The comparative results of Coils 4 and 5
showed only a slight increase in heat transfer coefficient from using a 42°
louver and large increase in core pressure drop.
• Increase the effect of the turnaround section on condensate drainage by
increasing the length or openness of the turnaround section, effectively
dividing the fin. One interesting possibility is to actually remove part of the
heat transfer surface in the center. This may allow a smaller 'drainage' section
64
to obtain the same benefits, thus leaving more area for the high heat transfer
louvers.
• Offset-strip fins appear to drain condensate better than louver fins over the
long-term, such as after system shutdown (a tentative conclusion based on
limited test results), and as discussed should form less condensate bridges.
Thermal-hydraulic performance data for offset strip arrays would be required
to further quantify potential benefits of that design.
4.3 Recommendations for Future Studies
There are several areas where additional research can either enhance the ideas
generated in this study, further the condensate retention modeling efforts, or refine the
design guidelines for developing improved fins. Three specific research directions are
discussed in this section.
Drainage and sweeping effects for automotive evaporators are substantially
different from plain-fin coils, there are important interactions between fins and fins and
fins and tubes in the automotive evaporator. As a result, it is expected the wet
performance of the fins vary will vertically in the fin column due to condensate
distribution. The variance in heat transfer coefficient from top to bottom in the fin array
would be important to determine both the impact of condensate on performance and
refine the retention model by indirectly predicting how much louver and fin bridging
exists. McLaughlin and Webb (2000) suggested that lower header design is key to
determining how much condensate will 'back-up' vertically in a coil, and vertically
resolved performance data would also develop this idea. A heat exchanger could be
partitioned into thirds or fourths vertically by embedding thermocouples in the tube at
65
specific points depending on circuiting, and matching the downstream air temperature
thennocouples to the tube locations.
Related to vertical partitioning, is more sophisticated single fin column testing
with optical access. One of the keys to condensate modeling is predicting the droplet
distribution on the surface, and the highly compact geometry of automotive evaporators
make it virtually impossible to observe the fins during operation. Previous efforts at
single column testing (Osada et aI., 1999, and McLaughlin and Webb, 2000) used only
single-sided cooling of the fin, which could affect the distribution on the fin, and
definitely affects the distribution on what would be the outer tube surface. The tube-side
geometry also needs to be closely matched; however, this will be difficult to accomplish
while maintaining optical access, as will cooling both sides of the fin. However, one
solution may be to treat the inside of the glass to make it hydrophilic, and then make
observations through the water film. This would at least allow a better approximation of
drainage routes. Cooling the tube surface would be easier, as dry, refrigerated air could
be blown across the outer surface. Results of single column tests would yield important
observations required to model droplet, and more importantly, bridge distributions along
the fin depth and height.
The final recommended research focus is in asymmetric fin design. All the fins
tested in this study (and in the open literature), are symmetric along the fin depth
centerline. The large influence of shear forces on condensate retention necessarily means
there exists a condensate distribution along the fin depth. Fin designs that have good heat
transfer characteristics do not necessarily manage condensate effectively, and by
designing the fin to promote high heat transfer in the front of the fin and better
condensate drainage in the back, overall perfonnance can be increased. The larger gaps
66
within an offset strip array may have a tendency to form less condensate bridges.
McLaughlin and Webb (2000) noted the louver cut end provides an area where a
condensate meniscus can easily grow into a louver bridge. A true offset strip would have
no narrowing at the cut end. Offset strips though, do not have the heat transfer
performance for the same fin depth as louvers. So a potentially superior fin design is to
use small pitch high angle louvers for the highest possible heat transfer in the front of the
array and offset strips or larger pitched louvers in the rear of the fin to decrease bridging
and promote drainage. The actual configuration of the design would be a primary
objective. Initial experiments on scale-up models would be an efficient technique to
determine a starting point for an optimal design. Single fin column testing would also be
useful, and a modular type test specimen could be built with partial fins that are different
types of louvers and offset strips could be built and different configurations could be
easily tested.
67
Appendix A Data Reduction
This appendix describes the data reduction techniques used for this study. Many
of the parameters are straightforward calculations. Further discussion of the calculations
is presented as needed. The output file from the data acquisition system and the manually
recorded data described in Chapter 2 are used as the input variables for the main data
reduction routine maintained on a commercial equation solver, Engineering Equation
Solver (EES). The advantages of using EES are the thermophysical property functions for
moist air are built in and a parametric table can be used to manage multiple test runs. The
EES code used for the data reduction is shown in Tables A.I and A.2
A.1 Mass Fluxes
The coolant-side mass flow rate was calculated from the density and volumetric
flow rate; measured with a flow meter that provided a 5-volt dc pulse with 1.849xI06
pulses per cubic meter of liquid. Equation A.I was used to calculate the coolant mass
flow rate where Re is the number of pulses per second. The outlet coolant temperature
was used to calculate the coolant density since the meter was located on the return line.
. R ( I ) me = ePe I.849xI06
(A.I)
The air-side mass flow rate was calculated from the frontal velocity, flow area,
and density. The velocity of the air at the heat exchanger face was measured using a
constant temperature thermal anemometer. The anemometer was calibrated by the
manufacturer at standard temperature and pressure so the measured velocity needed to be
corrected based on the temperature and pressure at the heat exchanger face. The actual
velocity was calculated using Equation A.2.
68
v = V (273 + Tfr J(101.325J fr,c fr 294.1 Patm
(A.2)
The atmospheric pressure is measured with a NOV A laboratory barometer and the air
temperature is from the upstream thermocouples. All other air properties were computed
using thermophysical property functions that were built into EES.
A.2 Heat Transfer Rates
Equations A.3 through A.5 were used to calculate the heat transfer rates.
Calculations were based on measurements made at the test section inlet and outlet. The
data used for this study required that air-side and coolant-side heat transfer rates were
within 10% including the bias error discussed in Appendix B.
(A.3)
qrol = rh air (hin,air - houl,air) (A.4)
(A.5)
A.3 Fin Efficiency
The fin geometry in the tested automotive evaporator coils can be modeled for fin
efficiency calculations as a straight fin with an adiabatic tip. Furthermore, the adiabat for
each fin is taken as the centerline due to circuiting and coolant flow rates. Most of the
heat exchangers tested use a parallel flow manifold with three coolant passes so each side
of the fin is at the same temperature with the exception of the two fins that are along the
turnarounds. Additionally, the coolant flow rate is such that the temperature change is
between 1.5 and 5.0 degrees Celsius, so any deviation of the adiabat from the centerline
for any fin will be much smaller than the fin width.
69
Fin efficiency for the dry condition tests was computed using a standard equation
commonly found in heat transfer texts (for example Incoprera and Dewitt, 1990). The
expression for a straight fin with adiabatic tip is,
(A. 6)
where,
(A. 7)
For fins where the fin width is much greater than fin thickness ma reduces to
(A.8)
For calculating the fin efficiency under condensing conditions when the fin
surface is full wetted, the method presented by Wu and Bong (1994) is used. They
consider the driving forces for heat and mass transfer separately. Wu and Bong assumed
a linear relationship between OJ s' the humidity ratio of the saturated air at the wet surface,
and 1'., the surface temperature. This assumption allowed them to analytically solve the
governing fin surface temperature differential equation when the Colburn-Chilton heat
and mass analogy holds. Namely, the heat transfer coefficient and the mass transfer
coefficient are related by
h 2/ _0 = CpLe/3 hm
(A.9)
With the fin surface temperature distribution known expressions for the heat transfer
from the fin and the maximum heat transfer (occurring if the entire fin was at the fin base
temperature) are derived.
70
(A.lO)
(A. 1 1 )
Where m is related to ma in the dry fin equation by,
(A.12)
(A.13)
and b is the average slope of the saturation line on the psychometric chart from
0) -0) b = s,t s,b
1; -Tb (A. 14)
The fin efficiency is defined as the ratio of heat transfer to maximum possible heat
transfer. Hence,
tanh(mL) 17f =
mL (A.15)
which is same as the expression for fin efficiency in the dry case with ma modified by Eq
A.12. The fully wet fin efficiency of Wu and Bong is relatively independent of the
humidity ratio of the incoming air,
With the fin efficiency known, the overall surface effectiveness for both wet and
dry conditions can be calculated from,
Af n =1--(1-n ) 'ft A 'If
I
(A. 16)
71
A.4 Heat Transfer Coefficients
A modified Wilson-plot methodology was used to calculate the air-side heat
transfer coefficient. The technique used was an adaptation of the ideas discussed by
Briggs and Young (1969), and presented by Rohnsenow et al. (1985). Wilson (1915)
devised a technique whereby individual thermal resistances could be extracted from the
overall system thermal resistance. The general thermal circuit for the studied heat
exchangers neglecting air-side and tube-side fouling and no tube-side enhancements is:
I I I I I = = = +--+R UA (UA)c (UA)o (17hA)o (hA)c W
(A17)
The basic idea behind building a data set for the Wilson-plot method is to hold one side
of the heat exchanger (the air, or hot side in this study) constant and systematically vary
the flow on the other side. Solving Equation A.I7 for _1_ and grouping terms yields Uc
Equation A18.
(A18)
For turbulent flow through constant cross-sectional ducts, the Nusselt number correlation
has the form of
Nu - C ReO.8 Pr°.4 - ° and an equivalent form of Equation AI8 is
(AI9)
(A20)
72
A plot of _1_ versus ~o 8 with the air-side temperature and mass flux held constant and U v· c
Equation A.19 being valid is linear and has the form of,
y = mx+b (A.20a)
where,
(A.20b)
The slope and intercept of the resulting data set are calculated by a least squares
fit to the data points. Equation A.18 can be solved for 1]ho directly or iteratively for ho
with a fin efficiency equation and j factors can be computed.
Briggs and Young modified the Wilson-plot routine by incorporating the real
possibility that the fluid temperature on either side of the heat exchanger could vary from
test run to test run. Instead of plotting a velocity function they used the tube-side Nusselt
number directly in the form of
Nu, ~ C, Re" prO'(;: J (A.2l)
and proceeded in a similar manner. A linear regression analysis is carried out to
determine the appropriate Reynolds number exponent that minimizes the least squares fit
to the data points.
For this study, further modification of the Briggs and Young technique is used to
construct the Wilson-plot. The tube-side Nusselt number is calculated using the
Gnielinski correlation for transitional flow in tubes:
Nu = (f 18)(ReD -1000)Pr D 1+12.7(fI8)1/2(Pr2/3 -l)
(A.22)
73
where,
(A.23)
The Reynolds number is based on hydraulic diameter, DH = 4Ac . The Wilson-plot was p
constructed by plotting _1_ versus _1_. Thus the linear relationship is, VA NU D
(A.24)
Where the first term on the right hand side is dependent on tube-side Reynolds number
and the second group is independent and held constant by maintaining the air-side
conditions. Furthermore, the wall resistance for the range of Reynolds numbers in this
study accounted for less than 5% of the total resistance and was neglected. The intercept
of the least squares fit line to a single set of Wilson-plot data is the air-side resistance,
(A.25)
This Wilson-plot technique has effectively allowed the tube-side resistance to be forced
to zero by extrapolating to an infinite tube-side Nusselt number. Equation A.25 and the
fin efficiency equations are then solved iteratively to obtain the air-side heat transfer
coeffi ci ent.
The methodology for building a complete set of data is described next. Since the
focus of this study is air-side heat transfer an effort was made to maximize the amount of
air-side data while maintaining the lowest uncertainty. The slope of the Wilson-plot is
independent of the air-side velocity, so the adopted technique was to collect a baseline
data set at an air-side Reynolds number at approximately the middle of the range of
74
interest (-700 based on hydraulic diameter). This baseline data set consisted of Wilson
plot points generated from tube-side Reynolds numbers from approximately 4,000 to
9,000. Subsequent data sets were recorded for other air-side Reynolds numbers (from
-300-1100) at only three or four tube-side flow rates where the Reynolds number varied
between 5,000 and 8,000. The slope of the linear fit to the baseline data set was induced
on all other data sets and the intercept was calculated from a modified, least squares fit.
This technique was really beneficial in condensing experimental test runs because of the
difficulty in maintaining constant air-side conditions for the extended duration required to
record data for the different tube-side Reynolds numbers. An example modified Wilson
plot is shown in Figure A.I.
75
1 I
1 ~
6 I-
--<
I-
~
L
:t I!I A
~ Z!l Z!l
j II
~ e e
• J
.. • •
4
r • • • :.; :.;
~
~ § )( x
9 !iii !iii
"/
3 >-
f3 !iii
i
-~ >-
...
f:
12 t - • Baseline 8 -Re 1
Re2 - ~~ Re3 - !!'! Re4 0
"1
0 0.005 0.01
0.015 0.02 1/Nuo
Figure A.I Example of MOdified Wilson-plot.
76
"EES code for computing friction factors and data for Wilson plots. 10 input parameters: Air inlet/outlet temperatures Coolant inlet/outlet read voltages Inlet/outlet depoints in F Air velocity Coolant flow meter reading Atmospheric pressure Pressure drop across heat exchanger"
"Heat Exchanger Geometry" A_min=.0252 A_tot = 2. 52 A_fr= .03923 sigma=A_min/ A_fr
"Tube-side Calculations" Tin_cF= Tin_cC*1.8+ 32 TouCcf=TouCcC*1.8+32
"Tube-side Thermocouple calibration curves" Tin_cC= 1.208200E-Ol +2.565600E+Ol *VoICin_ref+4.646300E-Ol *Volt_in_ref/\ 2-1. 170900E+00*VoIUn_ref/\3 Tout_cC= 1.045000E-0 1 + 2.567500E +0 1 *Volt_out_ref+4.694600E-Ol *Volt_out_ref/\ 2-1. 176600E+00*Volt_outJef/\3
"Coolant flowrate" Q...c=R_c/l0/700*0.003785 m_c= Q...c* Rho_c Re_tube=4/(50/1000)*m_c/Vis_c
{mIl3ls} {kg/s}
"Coolant Properties, 40% Concentration" Rho_c=(3. 703704E-7*Tout_cF/\ 3-8.214286E-5*Tout_cF/\ 2-1.150132E-2*Tout_cF+6.789952E+l)/0.06243 {Density Kg/mIl3} Vis_c=(-1.759259E-5*Tin_cF/\3+3.764286E-3*Tin_cF/\2-3.183122E-1 *Tin_cF+ 12.73762)*(lE-03) {Viscosity Ns/mIl2} k_c=(-1.851852E-8*Tin3 F/\3+1.785714E-6*Tin_cF/\2+2.839947E-4*Tin_cF+.2176667)/.5778/1000{Conductivity W/mK} Cp_c=(9.259259E-9*Tin_cF/\3-3.571429E-7*Tin_cF/\2+4.312169E-4*Tin_cF+.7923810)/2.389E-4/1000{Specific Heat KJ/KgK}·
''Tube side heat rate" Q...ref=m_c*Cp_c*(TouccC-Tin_cC)
''Tube-side Nu Calculation using Gniel. correlation" Nu_D=(Ctube/8*(Re_tube-l000)*Pr_tube)/(1+12.7*(sqrt(Ctube/8)*(Pr_tube/\(2/3)-1») Ctube=(. 79*ln(Re_tube)-1.64)/\( -2) Pr _tu be = Cp_c*Vis_c/k_c
"Air-side Calculations"
Table A.I Friction factor and Wilson plot data EES code listing.
77
Tdp_inC=(Tdp_inF-32)/1.8 (degrees F to degrees C) Tdp_outC=(Tdp_outF-32)/1.8 (degrees F to degrees C) Tdp_inC=DewPoint(AirH20,T=Tin_air,P=P _atm,w=wl) {determine absolute humidity} Tdp_outC=DewPoint(AirH20,T = Tout_air,P=P _atm,w=w2) {determine absolute humidity} P _atm=(P _hg)*convert(inHg,kPa) {Pressure conversion} RH_in=ReIHum(AirH20,T=Tin_air,P=P _atm,w=wl) {Relative Humidity} RH_out=ReIHum(AirH20,T=Tout_air,P=P _atm,w=w2) {Relative Humidity} T _mair=(Tin_air+ Tout_air)/2 w_mair=(wl +w2)/2 Rho_airl =Density(AirH20,T = Tin_air,P=P _atm,w=wl) Rho_air2=Density(AirH20,T=TouCair,P=P _atm,w=w2) Rho_air=Density(AirH20,T= T _mair,P=P _atm,w=w_mair) Vis_air=Viscosity(AirH20,T = T _mair,P=P _atm,w=w_mair) k_air=Conductivity(AirH20,T=T_mair,P=P _atm,w=w_mair) Cpin3ir=SpecHeat(AirH20, T = Tin_air,P=P _atm,R=RH_in) Cpout_air=SpecHeat(AirH20,T=Tout_air,P=P _atm, w=w2) Cp_mair=(Cpin_air+Cpout_air)/2 hin_air=Enthalpy(AirH20,T=Tin_air,P=P _atm,w=wl) hout_air=Enthalpy(AirH20,T = Tout_air,P=P _atm,w=w2) h_mair=(hin_air+hout_air)/2
"Air flowrate" m_dot_air=VoLair*Rho_air {Kg/s}
{Kg/m A3} {Kg/m A3} {Kg/m A3} {Nslm A2} {W/mK} {KJ/KgK} {KJ/KgK} {KJ/KgK} {KJ/Kg} {KJ/Kg} {KJ/Kg}
VoLair=VeLair*Flow_area*(273+ Tin_air)/294.1 *101.4/P _atm "Velocity probe correction" Flow_area=8*.0254*12*.0254 {Wind Tunnel geometry}
V _max=V _air*(A_fr/ A_min) G3ir=V _max*Rho_air V _air=VoLair/ A_fr Pr _a=Cp_mair*Vis_air/k_air* 1000 Re3ir=G_air*2.30/1000/Vis_air "2.30=hydraulic diameter"
"Heat Rates" CLsens=m_docair*Cp_mair*(Tin_air-Tout_air) q_tot=m_dot_air*(hin_air-hout_air) q_ave=( q_ref+q_tot)/2 CLerr=( q_ref-q_ave )/CLave LMTD=(Large-Small)/ln(Large/Small) Large= Tin_air-Tout_cC Small=Tout_air-Tin_cC
"Wilson Plot Data" Wilsy=(LMTD/q_sens) Wilsx=l/Nu_D
"ffactor" Cair=2*dp*Rho_air/G_air" 2*A_min/ A_tot-( l-sigma" 2)*(Rho_airl/Rho_air2-1 )*(A_min/ A_tot)*(Rho_air/Rho_airl) dp-deltaP*convert(inH20,pa)
Table A.I (cont.) Friction factor and Wilson plot data EES code listing.
78
"EES code for computing j factors 11 input parameters: Atmospheric pressure Inlet/outlet coolant temperatures air mass flux Wilson plot intercept air Prandtl number air specific heat air density air conductivity inlet/outlet humidity ratios"
st=h/(G*Cp_a) j=st*PrA(2/3)
eta_fin=tanh(m*L)/(m*L) m_O=sqrt(2*h/(k*thickness» m=m_O*sqrt(l +b*xi) thickness= .004*convert(in,m) k=.154 {kWlm K} L=.15625*convert(in,m) eta_o=l-A_fin/A_t*(l-eta_fin) A_t=2.542 2.296=A_fin
\\ Wu and Bong" (theta+theta_p)/(theta_b+theta_p)=cosh(M*(L-finwidth»/cosh(m*L){fin temp. distribution)
finwidth=.15625*convert(in,m) theta=T _a-T_t theta_b= T _a-T_b theta_p=xi*C_O/(l +b*xi)
xi=h_fg/(Cp_a*LeA(2/3» b=(w_s_t-w_s_b)/(T _t-T _b) a=w_s_b-(w_s_t-w_s_b )/(T _t-T _b)*T_b C_O=w_a-a-b*T 3 w_s_t=humrat(AirH20,T=T_t,P=P _atm,D=T_t) {Hum ratio at fin tip} w_s_b=humrat(AirH20,T=T_b,P=P _atm,D=T_b) {Hum ratio at fin base}
Le=k_a/(rho_a*Cp_a*D_AB)/1000 D_AB=( .00143*T _aA 1. 75)/(P _atm*M_ABA .5*(Sigma_nu_AA( 1/3)+Sigma_nu_BA(1/3»)A 2)
Sigma_nu_A= 19.7 Sigma_nu_B= 13.1
M_AB=2*( l/M_A+ l/M_B)A( -1) M_A=MOLARMASS(Air) M B=MOLARMASS(Steam)
Table A.2 j factor EES code listing.
79
rho3=density(airH20,P=P _atm,T=T_a,W=w_a) w3=(wl +w2)j2 h_fg=h3-h2 h2=ENTHALPY(Steam,x=O,P=Pl) h3=ENTHALPY(Steam,x= 1,P=Pl) Pl=PRESSURE(Steam,T=T_a,x=O) 2*T b=Tin C c+ Tout C c
Table A.2 (cont.) j factor EES code listing.
80
Appendix B Uncertainty Analysis
Uncertainties in the experimentally measured and reduced data are presented in
this appendix. The errors in the measured parameters are discussed and propagated to
estimate the uncertainties in the calculated parameters. Most of the uncertainty
calculations are straightforward, but several warrant discussion and clarification.
B.l Uncertainty in Measured Parameters
The errors associated with the various experimental measurements are shown in
Table B.1. The dewpoint of the air was measured by chilled mirror hygrometers at the
inlet and outlet and had a measurement uncertainty of ±0.2°c. Coolant flow rate was
measured using an oscillating disc type flow meter with a measurement uncertainty of
±1.0%. Air-flow velocities were measured using a constant temperature thermal
anemometer with a calibrated uncertainty of ±2.0% of the measured reading. Finally, an
electric manometer with an uncertainty of ±O.l24 Pa was used to measure the air-side
pressure drop across the heat exchanger. Type-T thermocouples were used to measure the
air temperature and the coolant temperature. Each thermocouple was individually
referenced to a thermocouple located in an ice bath and calibrated to a NIST traceable
mercury-in-glass thermometer. Calibration data were fit with fourth order polynomials
for each thermocouple. The uncertainties associated with the thermocouples were ±0.2°c.
A precision electronic balance was used to measure condensate quantities and had an
uncertainty of ±0.1 grams, which is less than 0.05% over the entire range of
measurements and will normally be neglected.
81
B.2 Uncertainty in Calculated Values
The uncertainties in calculated experimental values were detennined usmg
techniques by Kline and McClintock (1953). The propagation of error through the data
reduction equations introduces an uncertainty in calculated parameters. Equation B.l was
used to detennine the uncertainties in the calculated values.
Wy = :t BY W [( J 2]~ m=l BXm m
(B.l)
Where Wm = uncertainty of variable m=I,2,3, ... ,n
W y = propagating uncertainty in result
BY = partial derivative of result with respect to variable m. BXm
When Y is simply related to Xm by the following fonn,
(B.2)
then Equation B.l may be rewritten as,
Wy -:t Xm [ ( w J2]~ Y m=l Xm
(B.3)
B.2.1 Tube-side
A. Heat Transfer Rate
The uncertainty in coolant heat transfer rate is calculated using Equation B.4,
where the first three tenns on the right hand side is uncertainty from the mass flow rate.
As published by the manufacturer, the volumetric mass flow rate meter has an uncertainty
of 1.0%. Using a conservative 2.0% uncertainty in the ethylene glycol mixture properties
82
the uncertainty in tube-side heat transfer rate is estimated to be 10%. However, in the
beginning of this study, it was determined a bias error of approximately 5% existed
where the computed heat transfer rate on the tube-side was lower than the computed heat
transfer rate on the air-side. Different sources of error on both sides of the heat exchanger
were investigated and it was concluded the immersion thermocouples on the tube-side
were the cause. The coolant flow-rate was required to be relatively large to maintain
turbulent flow through the heat exchangers and this caused tube-side temperature
differences ofless than 2.0°C giving an uncertainty of 10% from the thermocouples. The
actual bias error is probably the result of errors in the calibration that are compounded by
the high uncertainty in temperature reading. The errors in the average heat transfer rate
were very consistent and varied less than 4% from the 5% bias, giving an overall
uncertainty within 10%.
Wqc = [(WP<.OUI )2 +(WRc)2 + (l.O%Y +(Wcp)2 +(WtlT)2]h qc Pc.out Rc Cp!1T
(B.4)
B.2.2 Air-side
A. Vrnax
Equation B.5 was used to determine the propagated uncertainty for V max. The
frontal velocity was measured directly using a constant temperature thermal anemometer
with an uncertainty of 2.0% in the measured reading. Heat exchanger dimensions were
measured using a caliper with an uncertainty of 0.025 mm., and the uncertainty for each
parameter is based on number of measurements required. Amin has an additional source of
83
error due to orientation when the coil is placed in the wind tunnel and is approximately
4%. The uncertainty in Vmax was 6% with an uncertainty in Afr of2.0%.
WVmax = [( WV~ir)2 + (WAfr J2 + (W ~io)2 + (Wp~" )2]Yz V max Valr A fr Amm PaIr
(B.5)
B. Reynolds Number
The uncertainty in air-side Reynolds number based on hydraulic diameter is
calculated using Equation B.6. The uncertainty in hydraulic diameter is approximately
1.5%, and the uncertainty in air mass flux is the same as for V max, 6%. Therefore, the
uncertainty in Reynolds number is approximately 6.5%.
~ ~ ~ ~ w. [(W)2 (W )2 (W )2]Yz ReDh = Gair + Dh + Pair
(B.6)
C. Friction Factor
The uncertainty in air-side friction factor is determined by Equation B. 7. With an
uncertainty in A tot of 4.5% the uncertainty in air-side friction factor is calculated to be
12%.
+(WA~in)2 +(WAIOI)2 Amm Atot
(B.7)
84
D. Heat Transfer Coefficient
The difficult factor in determining the uncertainty in heat transfer coefficient is
estimating the error in the Wilson plot intercept. As detailed in Appendix A, the Wilson
plot is constructed by plotting llUA versus 1INutube and fitting a least squares line to the
data for each air-side condition. The variance in the intercept for a single line can be
estimated using an equation from Beers (1957),
(B.8)
Where k is the number of samples and the first term is the estimated variance in y. The
95% interval can now be used to estimate the uncertainty in the y-intercept of a single
Wilson plot line. Several values were computed and the maximum uncertainty for a data
set was 8%. It should be noted that additional statistical analysis would be required to
estimate the added uncertainty of fitting subsequent data sets to the same slope. The
uncertainty in air-side sensible heat transfer coefficient is calculated using Equation B.9
when the coil is wet and is 11 %. For dry coil calculations, only the last three terms in
Equation B.9 are used and the uncertainty is 9%.
~= h
85
(B.9)
E. Sensible j factor
The only significant contributions to the j factor uncertainty are from the mass
velocity and the air-side heat transfer coefficient h. The uncertainty in sensible j factor is
calculated using Equation B.lO and determined to be 15%.
W [ 2 (W: J2 (W: J2 )2]Yz -!-= (Wh) + ~ + CP'~" + (Wpr
) h Galr CP,alr Pr (B.10)
B.3 Uncertainty in Measured Condensate Retention
The major sources of error contributing to the uncertainty in condensate retention
measurements are from the experimental apparatus and procedures. The error associated
with the electronic balance is negligible compared to the other errors. Steady-state
retention measurements were collected after the coil was exposed to condensing
conditions in the closed wind tunnel. When the tunnel is shut off, the coil continues to
drain water and until the catch tray is inserted, the drained amount of condensate is lost.
To ascertain the possible quantity of lost condensate a test run using the real-time
retention apparatus was performed. After the coil had reached steady-state the tunnel was
shut down and mass readings were recorded every 10 seconds for four minutes. It was
found the coil drained 5% of the retained condensate in the first 50 seconds. It normally
took less than 30 seconds to open the test section and insert the catch tray, so 5% is likely
a conservative estimate of the uncertainty in the mass of retained condensate for the
steady-state retention tests. The uncertainty for the mass of condensate in the real-time
retention tests is also less than 5%. The final value recorded in the real-time tests was
86
compared to the value obtained by removing the heat exchanger after the final reading
and proceeding to measure the retained condensate using the same procedure as for the
steady-state tests.
B.4 Uncertainty in Dynamic Drainage Tests
Evaluation of the experimental uncertainty for the drainage experiments requires
further consideration of the techniques used during a test run. The maximum source of
error is synchronizing the mass reading with the stopwatch. The first 18 readings are
recorded at five-second intervals, when the maximum drainage occurs, at rates up to 30
gls. A conservative estimate of the timing error is 0.5 seconds and this translates to a
maximum uncertainty of 5% from data recording. Additional sources of error are coil
orientation and the balance. Tests were conducted to determine the effect of small angular
orientation errors. If the coil is vertical to within two degrees the results varied less than
3% in the initial 60 seconds and less than 2% in the extended-time mass measurements,
and this uncertainty is within the synchronization uncertainty. Equation B.II combines
the three and yields an overall test uncertainty of 6%.
W mDrain (B.ll)
mDrain
87
Table B.I Uncertainties in measured parameters.
Measured Parameter Uncertainty
~PHX ±O.OOI inches of water
Tair, in ±O.2°e
T air,out ±O.2°e
Tc,in ±O.2°e
Tc, out ±O.2°e
Tdp,in ±O.2°e
Tdp, out ±O.2°e
Pulses ±O.5%
Yair ±2%
88
Appendix C Retention Modeling
This section describes condensate modeling work, presents the pertinent
equations, and discusses adaptations of the model to the complex fin designs of this
study. The two essential elements for predicting the volume of water retained on a coil,
and thus the mass, are the distribution of water on the coil surface, and the distribution of
droplet sizes in those wetted areas. Additionally, non-standard accumulation (i.e.
condensate bridges) will be particularly important as the modeling techniques are applied
to more compact geometries.
C.l Prior Work
Much of the foundation for the retention model discussed herein was set forth by
Korte and Jacobi (1997,1999), and a brief synopsis of their methodology will be given.
They started with a droplet with a circular contact line as shown in Figure C.1, and
derived the maximum droplet size by performing a force balance between gravitational,
air-flow, and surface tension forces.
Fg,x + Fd,x + F.,x = 0 (C.1)
The gravitational force is simply
(C.2)
Where the droplet volume is computed from approximating the droplet as a hemi-
spherical cap interfacing the surface at an average contact angle () M •
v = 1fl)3 (2 -3COS()M + cos3 ()M J droplet 24 . 3 () sm M
(C.3)
89
The drag force is computed using the results of AI-Hayes and Winterton (1981) where a
constant drag coefficient of 1.22 was found to apply to bubbles on a submerged surface
for Red = Paud / fLa from 20 to 400. Since the flow regime would not be expected to
change for the Reynolds numbers of this study (and that of Korte and Jacobi) the same Cd
is used. The drag force on a droplet is calculated by,
(C.4)
where Ap is the projected area and u is the local velocity at the droplet mid-height, hd /2.
(C.S)
(C.6)
Korte and Jacobi used a laminar (Blasius) velocity profile midway through the heat
exchanger using a freestream velocity based on the maximum velocity in the coil. A
simplication for the current model is the assumption of a linear velocity profile still
computed at the same height using the maximum velocity in the heat exchanger. The
justification for this simplication is the relatively low droplet heights and comparison of
the results to the more tedious boundary layer results.
The surface tension force was determined by integrating the surface tension force
along the contact line assuming a linear variation in contact angle (for full derivation see
Korte and Jacobi, 1997.)
A maximum retained droplet size can now be estimated by combining Eqs. C.1, C.2, C.4,
and C.7 into:
(C.7)
90
where,
.... -..... 1-PaCAOM -cosOM sin OM )
Ssin 2 OM
(e.S)
(e.9)
(e.1O)
Korte and Jacobi used the ideas developed by Graham (1969) to calculate the
droplet size distribution based on the maximum droplet diameter. Graham conducted
detailed photographic studies of condensation and divided the droplets into two different
groups and used the following power-law fits.
for 10,urn < d < 0.2dmax (e.lla)
for 0.2 dmax < d < dmax (e.llb)
where &V is the number of drops of diameter cL+O.2d per cm2• Through digital image
analysis the constants BJ and B2 were determined to be 2.042(106) /J.m1.73/cm2 and
4.467(109) /J.m2.8/cm2 respectively. Equation C.ll is then recast into a form for the
number of droplets a certain diameter per unit area by using !::.d = 0.4/).}/ .
n(d)=5.l 04(1 06)d"2.73
n(d)=1.117(lOJo)d"3.8
for 1O,urn < d < O.2dmax
for 0.2 dmax < d < dmax
(e.12a)
(C.12b)
The total mass of condensate on a heat exchanger surface can now be calculated by
integrating over all droplet diameters over the entire surface.
M = Pw f fn(~)V(~)d~dA (e.13) Ard
91
Korte and Jacobi (1999) used the model to successfully predict the quantity of
retained condensate on a plain-fin-and-tube heat exchanger with a fin spacing of 6.35
mm, but did not predict the retention for a heat exchanger with a fin spacing of3.18 mm.
Korte and Jacobi concluded interactions between the fins become at smaller fin spacings,
and their model does not account for any fin interactions. Yin and Jacobi (2000) added to
the model by including condensate bridges between fins at the fin-tube junction. The
model of Yin and Jacobi overpredicted the retention for a heat exchanger with a fin
spacing of 2.18 mm, and again it was concluded that interactions between droplets was
changing the distribution of water on the surface.
C.2 Adaptations
The focus of the modeling efforts for the studied automotive evaporator coils is to
attempt to use the model in its current form by separating the heat transfer surface into
four different areas with different orientations and restrictions. While this will still fall
short of accounting for interactions between droplets on adjacent fins, it will show the
applicability of the modeling ideas and give some additional insight into condensate
retention.
The studied coils have vertical, inclined, and horizontal surfaces. The tubes and
the fin-tube interface are vertical. The louver surfaces are inclined at the louver angle.
The turnaround section and the fin area between the louver-end and the tube wall is
horizontal. Each of these areas are treated seperately and slightly different. The mass of
retained condensate is predicted at face velocities of 1.0 to 2.25 mis, encompassing the
tested range of the wind tunnel retention tests. The force balance was used to compute
92
maximum droplet size was altered to investigate the possibility of droplet detachment
from gravity on the underside of the fin surface. It was found that a droplet is removed
from the surface by flow forces prior to gravity for all cases-a result that is especially
dependent on contact angles. The actual size of the droplets on the different surface
sections are constrained by geometry (the smallest computed dmax was 3.3 mm), and two
different ideas were pursued to account for this. The first is to simply set dmax equal to
largest possible droplet size such as louver pitch for the louver area and fin pitch for the
vertical area. However, this artificially modifies the distribution functions-the number
of drops calculated for example at 0.2 mm is dependent on the maximum droplet size
which should be derived from the surface conditions not size. Furthermore, by setting
dmax all dependency on air velocity is lost, which is not accurate for the tested coils. A
more logical approach (and the adopted one) is to compute the maximum droplet size in
the normal fashion and adjust Equation C.13 to integrate only up to maximum allowable
droplet size. Any droplets that are bigger are assumed to be retained in a different manner
or shed. The constraints on the sizes in the different sections are based on observations of
fin stock in the condensate visualization glove-box. It was observed that a droplet larger
than the louver pitch can remain on a louver by being non-axisymmetric.
Table C.l displays the relative area percentages of each of the different sections
and the constraints on dmax. Table C.2 is a summary of the results for applying the model
to Coil 4 showing the mass per unit area for each of the different sections and the total
predicted mass. The model prediction is compared to the experimentally measured value
graphically in Figure C.2, and the EES code is shown in Table C.3.
93
Figure C.2 shows the model underpredicted the retained mass at all frontal
velocities, an opposite trend than observed by Yin and Jacobi (2000) and Kim and Jacobi
(2000). In both those studies the authors concluded interactions between droplets on
adjacent fins caused the discrepancy. A droplet that is shed on one fin and sweeps along
the fin surface could coalesce with a large droplet on a neighboring fin and cause
premature sweeping on that fin, thus decreasing the actual mass by a mechanism not
captured by the model. In this study, the likely cause for the underprediction is bridging
between fins and louvers. The droplets that were larger than the constraint were simply
discarded. It is logical that these large drops would be the first to form bridges. The trend
in Figure C.2 that at higher velocities the prediction and measured quantities are closer
also supports this idea. At higher velocites there should be less bridging as flow forces
clear out the bridges (though this phenomenon has not been experimentally observed in
this study it is logical).
The model developed by Korte and Jacobi has been adapted and applied to a heat
exchanger tested in this study. The model correctly predicts the trends and is within 12%
of the measured value throughout the tested velocity range. The model was also applied
to Coil 5 and underpredicted the retention by 30-40%, a result that does not signify
failure of the model, but rather emphasizes the importance of condensate bridging to the
problem. Coil 5 was concluded to have a larger relative amount of condensate bridging
than Coil 4. The model does not yet include the physics of bridging or the influence of
the vertical variation in condensate retention discussed in Chapter 4, but the limited
succes in applying it to a vastly different goemetry than it was originally developed for
definitely displays its robustness.
94
y
Figure C.I Forces acting on a droplet on an inclined surface due to gravity, air-flow, and surface tension.
Table C.I Relative surface areas and maximum droplet size constraints for Coil 4.
Percent of Restriction on Area Dmax (mm)
Louver 40.9 1.5
Vertical 9.7 1.8
Turnaround 26.8 2.5
Flat 22.6 4
95
"
Table C.2 Summary of model results for Coil 4.
Mass per unit area (g/mA2) Total Area 2.54 (mA2)
Velocity Vertical Louver Turnaround Flat
Total Mass (rn/s) (g)
1 65.1 50.5 82.9 180.7 228.7
1.25 65.3 50.8 78.4 164.8 216.9
1.5 65.6 51.1 76.2 153.6 209.4
1.75 65.8 51.5 75.2 145.1 204.3
2 66.1 52.0 74.8 138.4 200.8
2.25 66.5 52.5 74.9 133.0 198.4
300 r i j
- - - - - Model Prediction ~
J lc. Coil 4
~ I-- l-S l.. 'C
250 ~ j CI) C lc.
S &! .. .. .. lc. .. !a ......... lc.
CIS
200 ~ ......
lc. ~ ::! -- ... ---- ---- --- -1 S
1 0 I-
..j
~
150 0.5 1 1.5 2 2.5
Face Velocity (m/s)
Figure C.2 Measured and predicted values of steady-state condensate retention for Coil 4
96
EES program to calculate maximum droplet diameter and mass of water per unit area"
theta_a = 64*(PI/180) {advancing contact angle in radians} theta_r = 44.0*(PI/180) {receding contact angle in radians} alpha = alpha_d*(PI/180) {angle between fin surface normal and gravity in radians} u_max = u_a/.642 {air-side face velocity, m/s} Cs = 0.00181 {interfin spacing in m} rho = DENSITY(Water, T=20, X=O.O) {density of liquid water, kg/m"3} rho_a = DENSITY (Air, T=2S, P=101) {density of air, kg/m"3} sigma = 0.072 {surface tension, N/m} 9 = 9.8 {gravitational acceleration, m/s"2} C_d = 1.22 {drag coefficient per AI-Hays and Winterton} theta = (theta_a+theta_r)/2 {Average contact angle}
{Force Balance to find d _ max}
XCO=(xLOa+xLOb)*sigma*PI/2 xLOa=(sin(theta_r)-sin(theta_a-PI» / (theta_r - theta_a + PI)
xLOb=(sin(theta_r)-sin(theta3+PI»/ (theta_r - theta_a - PI) XC1=-rho_a*C_d*(theta - cos(theta)*sin(theta»/2 XC2=-( (2-3*cos(theta )+cos(theta)/\ 3)/( sin(theta)'" 3) )*rho*g*PI*sin( alpha )/24
y=d_m*(1-cos(theta»/4 u=u_max*(2*y/Cs) {simplification to the model of Korte and Jacobi}
XC2*(d_m)"'2 + XC1*(d_m)*u/\2 + XCO = 0 d_max=d_m* 1e6
{Integration of droplet size distribution functions}
{d_m is maximum diameter in m} {d_max is maximum diameter in microns}
n_s=(S.104e06)*( d_s)/\( -2.73) n_b=(1.117e10)*( d_b )/\( -3.80)
{number of droplets with d<.2d_max, percm"2} {number of droplets with d>.2d_max, per cm"2}
V _s=(PI*d_s/\ 3)*( (2-3*cos(theta )+cos(theta)'" 3)/(sin(theta)'" 3) )/24 {small droplet volume, microns"3}
V _b=(PI*d_b/\ 3)*( (2-3*cos(theta)+cos(theta)'" 3)/(sin(theta)'" 3) )/24 {big droplet volume, microns"3}
VT_s=INTEGRAL(n_s*V_S, d_s, 10,d_max/S) {total d_s volume in microns"3 per cm"2}
VT _b=INTEGRAL( n_b*V _b, d_b, d_max/S, d_max_constrained) {total d_b volume in microns"3 per cm"2 with max drop size constrained}
MpA=rho*(VT_s+VT_b)*(le-ll) {total retention in g/m"2}
Table C.3 EES code for computing mass per unit area for different surfaces.
97
References
AI-Hayes, RAM. and Winterton, R H. S., 1981, "Bubble Diameter on Detachment in Flowing Liquids," Int. J. Heat Mass Transfer, Vol. 24, pp. 223-230
ARl, 1981, Standardfor Forced-Circulation Air-Cooling and Air-Heating Coils, ARl-410.
Beers, Y, 1953, Introduction to the Theory of Error, Addison-Wesley Pub. Co., Cambridge, MA
Bettanini, E., 1970, "Simultaneous Heat and Mass Transfer on a Vertical Surface," International Institute of Refrigeration Bulletin, Vol. 70, pp. 309-317.
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