Heat transfer engineering an international journal, tập 31, số 10, 2010

Heat Transfer Engineering, 31(10):799–808, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903547461

Film Condensation of R-134a and
R-236fa, Part 1: Experimental
Results and Predictive Correlation
for Single-Row Condensation on
Enhanced Tubes
MARCEL CHRISTIANS, MATHIEU HABERT, and JOHN R. THOME
Laboratory of Heat and Mass Transfer (LTCM), Faculty of Engineering Science Ecole Polytechnique F´ed´erale de Lausanne
(EPFL), Lausanne, Switzerland

New predictive methods for falling film condensation on vertical arrays of horizontal tubes using different refrigerants are
proposed, based on visual observations revealing that condensate is slung off the array of tubes sideways and significantly
affects condensate inundation and thus the heat transfer process. For two types of three-dimensional enhanced tubes,
advanced versions of the Wolverine Turbo-C and Wieland Gewa-C tubes, the local heat flux is correlated as a function of
condensation temperature difference, the film Reynolds number, the tube spacing, and liquid slinging effect. The proposed
methods work best when using R-134a, as these tubes were designed with this refrigerant in mind.

INTRODUCTION

PREVIOUS HEAT TRANSFER COEFFICIENT STUDIES

Tubes in shell-and-tube condensers, widely used in refrigeration, heat pumps, and chemical process industries, are subjected to condensate inundation from the neighboring upper
tubes. In order to increase the efficiency of these systems, plain
tubes were replaced by all types of enhanced tubes, from finned
tubes to tubes with advanced two-dimensional (2D) and threedimensional (3D) enhancement geometries. However, it is necessary to characterize the performance of new tubes, so that
design engineers have a solid foundation on which to base their

designs. Furthermore, it is of interest to test the performance
of these tubes with several refrigerants, such that the differing
behavior may be quantified and taken into account during the
design stage itself.

Jung et al. [1–3] performed falling film condensation tests
using plain, low-fin and enhanced tubes and pure refrigerants R-11, R-12, R-123, R-22, and R-134a, and zeotropic
and azeotropic refrigerant mixtures R-407C, R-410A, R-32/R134a, and R-134a/R-123 on a test section comprised of a
single tube at a saturation temperature of 39◦ C. The finned
tubes had 1,024 fins per meter, while the enhanced tube tested
was the Turbo-C. Chang et al. [4] performed tests on single tubes connected by a U-bend, at a saturation temperature of 39◦ C on low-fin and 3D enhanced tubes, using refrigerant R-134a. The finned tubes had 1,024 and 1,574 fins
per meter, while the two 3D enhanced tubes had T- and Yshape fins. Kumar et al. [5, 6] tested plain and finned tubes
with refrigerant R-134a on single tubes, at a saturation temperature of 39.3◦ C. The finned tubes had fin densities of 472
(rectangular), 934, 1,250, 1,560, and 1,875 fins per meter.
Sreepathi et al. [7] tested several proprietary finned tubes,
commercial finned tubes (748 and 1,574 fins per meter), and
the enhanced tubes Thermoexcel-C and Thermoexcel-CC1 in a
single tube configuration, using R-11 and R-123, at saturation
temperatures of 23.5 and 27.4◦ C. Wen et al. [8] studied the performance of four tubes (667 and 1000 fpm, with and without

The authors thank the laboratory’s industrial sponsors Johnson Controls,
Trane, Wieland Werke, and Wolverine Tube, Inc., for funding this study. Special
thanks to the tube manufacturers, Wieland Werke and Wolverine Tube, Inc., for
supplying the tubes utilized.
Address correspondence to Prof. John R. Thome, Laboratory of Heat and
Mass Transfer (LTCM), Faculty of Engineering Science, Ecole Polytechnique
F´ed´erale de Lausanne (EPFL), Station 9, Lausanne CH-1015, Switzerland.
E-mail:

799

800

M. CHRISTIANS ET AL.

filled fin-roots) in a single tube test section using R-113 at a
saturation temperature of 47.6◦ C.
Kang et al. [9] tested low-fin and 3D enhanced tubes in a test
section consisting of five horizontal tubes placed on a single
horizontal plane (i.e., side by side), at a saturation temperature
of 60◦ C, using refrigerant R-134a. The tested tubes included
one low-fin tube and three Turbo-C variants. Gst¨ohl and Thome
[10, 11] performed tests on a single column of several tubes
(varying the pitch between tubes), as well as plain, low-fin, and
3D enhanced tubes at a saturation temperature of 31◦ C. In these
tests, it was possible to vary the overfeed onto the first tube
of the column to simulate flow deeper in a bundle. The tubes
tested were a Turbo-Chil low-fin tube, and both Wolverine and
Wieland enhanced condensation tubes (Turbo-CSL and GewaC) using only R-134a. As a continuation of this work, Habert
et al. [12] presented additional flow regime transition criteria
for Wieland and Wolverine enhanced tubes using an additional
refrigerant (R-236fa). However, in this study, no heat transfer
measurements were presented.
As such, the aim of this article is to present and discuss the
results obtained in the LTCM’s falling film facility for advanced
versions of the Turbo C and Gewa C 3D enhanced tubes, using
both R-134a and R-236fa. R-236fa was chosen as a second
test fluid because of its compatibility with the experimental test
stand. In addition to the preceding, prediction methods based on

Gst¨ohl and Thome’s [11] original R-134a data-only predictive
model are developed and presented.

EXPERIMENTAL FACILITY
The experimental setup is comprised of three circuits,
namely, the refrigerant, water–glycol, and water circuits. The
refrigerant circuit is shown schematically in Figure 1. It comprises an electrically heated evaporator (Figure 1, (1) flooded
evaporator) to maintain the desired saturation condition, a condenser (Figure 1, (5) auxiliary overhead condenser) to condense

Figure 1 Schematic of the refrigerant circuit in the Falling Film Facility.

heat transfer engineering

any vapor not condensed in the test section, and the test section
itself (Figure 1, (4) test section).
In the refrigerant circuit, starting from the flooded evaporator (Figure 1, (1) flooded evaporator), the refrigerant flows
through the filter (not shown) and the subcooler (Figure 1, (6)
liquid subcooler) to the gear pump (self-lubricating without oil:
Figure 1, (7) overfeed pump). Parallel to the pump, bypass piping is installed so that, together with a frequency controller on
the pump, the desired liquid flow rate can be accurately set. A
Coriolis mass flow meter (Figure 1, (8) Coriolis mass flow meter) follows, after which an electric heater (Figure 1, (9) liquid
heater) is installed to bring the liquid close to saturation conditions at the test section inlet. At this point, the liquid enters
the test section and is distributed uniformly on the top row of
the heated tubes. Special care has been taken in the distributor
design in order to achieve uniform liquid distribution on the top
tube. Once the liquid leaves the distributor, it falls onto the top
of the cooled tube array, on which the vapor in the test section is partially condensed; the residual liquid leaves the test
section by gravity. From the exit of the test section, the liquid
flows back to the flooded evaporator by the effect of gravity.
The vapor that runs through the test section is generated in the

flooded evaporator, where by natural convection it rises to the
top of the test facility. It flows in to the top of the test section,
where the vapor flow is uniformly distributed over its length,
and any remaining vapor is sucked out at the bottom of the test
section. After exiting the test section from the bottom, it flows
back into the condenser, and the liquid drops by gravity back to
the flooded evaporator. The amount of vapor flow can be controlled by increasing the heat input in the flooded evaporator,
which in turn generates more vapor. Consequently, to maintain
a constant system pressure, the cooling load on the auxiliary
condenser is greater. In these tests, it was attempted to maintain the vapor velocity as low as possible, such that vapor shear
effects were minimized.
The water circuit (not shown) is responsible for the cooling
effect in the test section. The water is driven through the test
tubes by a centrifugal pump. An electronic speed-controller,
together with a bypass line, ensures good precision in any water
mass flow adjustment. The water flows through two liquid–
liquid heat exchangers; the first is cooled with industrial water
sourced from Lake Geneva at a constant temperature of 7◦ C,
while the second is heated with hot water from a closed-loop
circuit heated by a heat pump. This water has its flow rate set by
a computer-controlled valve. The water temperature at the test
section inlet is thus automatically maintained constant. The total
water mass flow rate is measured with a Coriolis flow meter (not
shown). Before entering the test section, the test-line water flow
is split into three subcircuits, each supplying to two tubes in the
test section. Each subcircuit has two tube passes; i.e., water goes
in a copper tube in one direction (left to right) and comes back
through the copper tube just above in the opposite direction. A
water–glycol mixture from a network installation is used as a
cold source for the auxiliary condenser.

vol. 31 no. 10 2010


M. CHRISTIANS ET AL.

The test section is a rectangular stainless-steel vessel with six
large windows situated at the front and rear in order to have full
visual access into the experimental setup, to observe the flow on
the tubes. The copper test tubes had a nominal outer diameter of
18.38 mm and are arranged horizontally in a vertical array. The
length of the tubes was 554 mm. In total, six tubes (i.e., three
subcircuits) were installed, at a industry-standard pitch of 38.5
mm.
Furthermore, a stainless-steel tube with an external diameter
of 8 mm was inserted inside each copper test tube. Pairs of
thermocouples were located at three positions axially along the
tube, protruding out through holes to measure the temperature
of the water in the annulus between the stainless steel tube and
the copper tubes. At every location, one thermocouple is facing
upward and one is facing downward. A copper wire with a
rectangular cross section wound helically around the stainlesssteel tube promoted mixing, and further increased the water-side
heat transfer coefficient.
Pressure transducers connected to the test section above and
below the array of tubes were used to measure the vapor pressure
in the test section. The vapor temperature in the test section was
measured above and below the tube array using sheathed thermocouples. The temperatures of the liquid entering and leaving
the test section, as well as the vapor leaving the test section,
were measured.
EXPERIMENTAL ERRORS AND PROCEDURES
The internally mounted thermocouples measuring the water

temperature within the tube annulus along the axial length of
the tubes provide the water temperature profile as a function of
the distance x along the tubes. Assuming only heat flow in the
radial direction, the local heat flux on the outside of the tube,
qo , may thus be expressed as
qo =

˙ water cp,water
m
π Do

dTwater
dx

(1)

where Do is the outside diameter. The value (dTwater /dx) is obtained by differentiating a second-order polynomial fit of the
water temperature profile. Nearly identical temperatures for the
pairs of thermocouples located at each location indicate good
mixing of the water (the temperatures were within thermocouple uncertainty), which helps increase the accuracy of the data
reduction method.
To determine the external local heat transfer coefficient, ho ,
between the outside surface of the copper tubes and the refrigerant, a modified Wilson plot procedure using nucleate pool
boiling (as in Robinson and Thome [13]) on the outside of
the tubes was implemented. The modified Wilson plot method
takes into account slight variations in the heat flux by assuming a relation for the external heat transfer coefficient given by
ho = Co qo0.7 . The internal heat transfer coefficient is the one
given by the Gnielinski [14] correlation, hgni , multiplied by a
constant Ci that takes into account the increase in heat transfer
heat transfer engineering

801

Table 1 Calculated values for the internal heat transfer multiplier Ci
Tube
Wolverine Turbo (condensing)
Wieland Gewa (condensing)

Ci [—]

δCi [—]

δCi /Ci [%]

7.38
4.78

±0.41
±0.40

±5.42
±8.37

due to any internal enhancement, the reduced flow area, and increased turbulence due to the inserted helical tape. The Wilson
plot expression for the tubes is thus
1
1
− Rw qo0.7 =
Uo
Ci

qo0.7
hgni

Do
Di

+

1
Co

(2)

With changes of the water velocity and temperature rise to
maintain a fixed heat flux qo , the values in the square brackets
are altered. The resulting inverse slope of a line plotted through
a plot of the values in the brackets on the left versus the values in
the brackets on the right gives the value of Ci , while the inverse
of the abscissa intercept yields Co . Thus, the heat transfer on the
outside of the tube at any location along its axis can be calculated
with the value of Ci , along with the measured water temperature
profile, the water mass flow rate, and the saturation temperature
of the refrigerant. However, in this study the local coefficient
is only evaluated at the midpoint of every tube. This calculated
value is a perimeter-averaged heat transfer coefficient based on
the external tube diameter. The modified Wilson tests were conducted over a water-side Reynolds number range varying from
6,000 to 16,000. Table 1 shows the values of Ci obtained by this
study. It can be seen that the Ci value obtained for the Wolverine
Turbo-C enhanced condensing tube of 7.38 is higher than for

the other tube, due to its 3D internal enhancement structure.
To eliminate all traces of non-condensable gases that might
have been introduced into the facility (i.e., during tube or refrigerant changes), a vacuum pump (not shown in Figure 1) is
connected to the system and is run until the two low-pressure
reference pressure transducers show no more than 100 Pa (absolute). Once the vacuum pump is stopped, the system pressure
is monitored to make sure that no leaks are present. Only once
these two steps have been accomplished is the system refilled
with refrigerant to proceed with testing. Any remaining traces of
non-condensable gases in the system will migrate to the overhead condenser, where they remain. The measured saturation
temperature using thermocouples and that obtained from the
pressure sensors and REFPROP v8 [15] differed by 0.1 K, a
value within the uncertainty of both measurements.
For experiments involving overfeed, the film flow rate of the
liquid arriving on the first tube was evaluated from the measured
mass flow rate and the tube length, assuming that the refrigerant
is at saturation conditions. The mass flow of refrigerant condensing on the first tube is calculated by an energy balance on
differential elements and added to the film flow rate arriving on
the first tube to obtain the film flow rate at the top of the second
tube and so on. This means an ideal one-dimensional downward flow is assumed on the tube rows and assumes that all the
condensate flows from one tube to the next without leaving the
vol. 31 no. 10 2010


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M. CHRISTIANS ET AL.

Table 2 Uncertainties of measured heat transfer coefficients at the three
heat flux conditions tested

Array, Turbo C tube, tube spacing 38.5mm, heat flux: 20kW/m2
25000

δho / ho

R−134a

qo = 40 kW/m2

qo = 60 kW/m2

10.40%

7.01%

6.11%

11.62%

7.25%

6.43%

2

qo = 20 kW/m2

Heat transfer coefficient [W/m K]

Tube

EXPERIMENTAL RESULTS WITH THE SINGLE-ROW
TEST SECTION
Tests were performed using the Wolverine Turbo and
Wieland Gewa condensing tubes (both of them have an 18.38mm nominal outer diameter) provided by the manufacturing
companies. Before installation into the test section, the tubes
were thoroughly cleaned. In the column of six tubes (single
vertical row), the center-to-center tube pitch was 38.5 mm, and
tests were performed using refrigerants R-134a and R-236fa, at
a saturation temperature of 31◦ C. Furthermore, tests were performed at constant tube array nominal heat fluxes of 20, 40, and
60 kW/m2 .
In Figures 2–7, it can be seen that the refrigerant in use has
a very large effect on the performance of each tube. For these
tubes, and at all heat fluxes, the R-236fa results show lower
performance over the entire Reynolds number range. Furthermore, when using R-134a, the heat transfer performance of the
first (top) tube is considerably higher than the rest of the array,
something especially true at lower Reynolds numbers. This is
probably related in some manner to the overfeed from the liquid
distributor—the value at the lowest Reynolds number in each
diagram for tube 1 (that is, without overfeed) usually aligns well
with the trend of the rest of the data.
For tests at a constant nominal array heat flux, it can be seen
that there is a very slight or almost no dependence on the tube
row number, a trend that was also evident in the testing presented
by Gst¨ohl and Thome [10].
heat transfer engineering

20000

15000

10000
Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

5000
R−236fa
0

0

500

1000
1500
2000
Film Reynolds number, Re

2500
[−]

3000

3500

bottom

Figure 2 Heat transfer performance of the six Wolverine Turbo C condensing
test tubes at a nominal array heat flux of 20 kW/m2 using both R-134a and
R-236fa.

With the Turbo condensing tube/R-134a combination
(Figures 2–4), the behavior of the tube is similar to the threedimensional enhanced tubes tested originally by Gst¨ohl and
Thome [10]. This similarity is not in terms of the heat transfer coefficient values themselves, since the Turbo-CSL results presented [11] had peaks of roughly 25 kW/m2 -K while
this tube’s peak is at 28 kW/m2 -K, but rather in the general form of the evolution of the heat transfer with increasing
Reynolds number. Also using R-134a, the Wieland Gewa data
(Figures 5–7) show that the top two tubes have a large heat
transfer peak at lower Reynolds numbers. With both tubes, the
data at the highest Reynolds numbers fluctuate and still seem to
form a plateau like that seen in the Turbo-CSL results [11]. In
Array, Turbo C tube, tube spacing 38.5mm, heat flux: 40kW/m2
Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

25000
R−134a
2

tube row. In case of no overfeed, a similar procedure was applied, with the initial flow rate onto the top tube set to 0. The
two-pass water design gives a nearly uniform axial condensate
distribution along the tube array after each pair of tubes. The
saturation temperatures, as well as the transport and thermodynamic properties, are calculated according to REFPROP v8 [15]

from the mean of the pressures measured by pressure transducers above and below the tube array.
Tests were conducted by gradually decreasing the liquid film
flow rate on the top tube at a fixed heat flux. The data were
logged only if steady-state conditions were attained. An error
analysis was performed, and the mean relative errors in the local
heat transfer coefficient at a saturation temperature of 31◦ C are
tabulated in Table 2. A more detailed description of the test
facility, data reduction methods, and measurements accuracies
can be found in Gst¨ohl and Thome [10, 11].

Heat transfer coefficient [W/m K]

Wolverine Turbo
(condensing)
Wieland Gewa
(condensing)

20000

15000

10000

5000
R−236fa
0

0

500

1000
1500
2000
2500
Film Reynolds number, Re

bottom

3000
[−]

3500

4000

Figure 3 Heat transfer performance of the six Wolverine Turbo C condensing
test tubes at a nominal array heat flux of 40 kW/m2 using both R-134a and
R-236fa.

vol. 31 no. 10 2010


M. CHRISTIANS ET AL.
Array, Turbo C tube, tube spacing 38.5mm, heat flux: 60kW/m2

20000

15000

10000

R−134a
2

R−134a

25000

Heat transfer coefficient [W/m K]

2

Heat transfer coefficient [W/m K]

Array, Gewa C tube, tube spacing 38.5mm, heat flux: 40kW/m2

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

25000

803

5000

20000

15000

10000

5000
R−236fa

0

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

0

500

1000
1500
2000
Film Reynolds number, Re

2500
[−]

R−236fa

3000

0

3500

0

500

bottom

1000
1500
2000
2500
Film Reynolds number, Re

bottom

3000
[−]

3500

4000

Figure 4 Heat transfer performance of the six Wolverine Turbo C condensing

test tubes at a nominal array heat flux of 60 kW/m2 using both R-134a and R236fa.

Figure 6 Heat transfer performance of the six Wieland Gewa C condensing
test tubes at a nominal array heat flux of 40 kW/m2 using both R-134a and
R-236fa.

contrast to the results of Gst¨ohl and Thome [10, 11], the heat
transfer degradation with increasing Reynolds number is not
as severe; while it does occur at essentially the same Reynolds
number, and with the same slope, the heat transfer coefficient
stabilizes at ∼50 to 60% of the peak measured heat transfer
coefficient, while for the tubes tested by Gst¨ohl and Thome,
the plateau was found at around 20% of the peak heat transfer
coefficient value. Evidently, this will have a beneficial effect on
condenser performance. For the Wieland tube, tubes 2 through
6 are closely grouped. The general trend for the tubes in the
array is an increase to a stable plateau. Furthermore, tubes 1 and
2 are the only ones to show significant heat transfer degradation
as the film velocity increases. This could be due to a type of en-

trance effect (impingement) only apparent due to the surface’s
geometry.
Using R-236fa, Figures 2–4 show that for the Wolverine
condensing tube, the behavior of the heat transfer coefficient is
vastly different. In this case, the heat transfer coefficient slowly
increases to a band within which the heat transfer fluctuates yet
remains bound. As neither the type of tube, nor the geometric
distribution, nor the measurement technique was changed, it can
be safely concluded that the difference in heat transfer evolution
and the degradation of performance with respect to the R-134a

tests is solely a function of the thermophysical properties of the
refrigerant under consideration. Looking at the Wieland tube
2

Array, Gewa C tube, tube spacing 38.5mm, heat flux: 60kW/m

Array, Gewa C tube, tube spacing 38.5mm, heat flux: 20kW/m2
25000

R−134a

R−134a

Heat transfer coefficient [W/m K]

20000

15000

10000
Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

R−236fa

5000

0

20000

2

2

Heat transfer coefficient [W/m K]

25000

0

500

1000
1500
2000
Film Reynolds number, Re

2500
[−]

3000

15000

10000

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

5000
R−236fa

3500

0

0

500

1000

bottom

Figure 5 Heat transfer performance of the six Wieland Gewa C condensing
test tubes at a nominal array heat flux of 20 kW/m2 using both R-134a and
R-236fa.

heat transfer engineering

1500
2000

2500
Film Reynolds number, Re

3000
[−]

3500

4000

4500

bottom

Figure 7 Heat transfer performance of the six Wieland Gewa C condensing
test tubes at a nominal array heat flux of 60 kW/m2 using both R-134a and
R-236fa.

vol. 31 no. 10 2010


804

M. CHRISTIANS ET AL.

Table 3 Comparison of the physical properties of the two refrigerants at
31◦ C
Property
M [kg/kmol]
pcrit [kPa]

hlv [J/kg]
σ[Nm]
ρl [kg/m3 ]
cpl [J/kg-K]
kl [W/m-K]
µl [Pa s]

underneath it as
θcrit = arcsin

R-134a

R-236fa

102.03
4060
172,000
0.0073
1,184
1,451
0.0780
1.835 × 10−4

152.04
3200
142,000
0.0094
1,340
1,280
0.0711

2.649 × 10−4

data (Figures 5–7), these results differ from the R-134a data
in that they are contained within a small band, and lower in
magnitude. Furthermore, the maximum tube 1 peak using R134a was around 23 kW/m2 -K, while with R-236fa this peak
was found at 12.5 kW/m2 -K.
The large difference in absolute performance (and with respect to increasing Reynolds number) can be attributed to the
geometric design of the tubes themselves; both of these were
optimized for R-134a condensate drainage, and using a different refrigerant is going to have an impact on performance.
Table 3 shows a comparison of the physical properties of the
two refrigerants at 31◦ C. In both falling film evaporation and
condensation, two thermodynamic properties that have large influence are the liquid viscosity and the surface tension. It can
be seen that there is a 36% difference in viscosity and 25%
difference in surface tension between the two refrigerants at a
saturation temperature of 31◦ C. This will primarily affect the
thickness of the liquid film and its interaction with the tube.

UPDATED PREDICTION METHOD

θ = dRe + e

(3)

where the coefficients a, b, and c for the tubes that were tested
are given in Table 1 in [11]. However, it was found that for 3D
enhanced tubes, as the Reynolds number increased, a fraction of
the liquid refrigerant left the tube array sideways [16]. This was
due to the fact that the liquid film did not fall as a stable sheet,
but rather fell with an oscillatory motion. Thus, they calculated
the critical angle (a function of the tube geometry and tube pitch)

for which the liquid film would begin to not reattach the tube
heat transfer engineering

(5)

The portion of liquid that leaves the tube is assumed to be
proportional to the ratio of (θ – θcrit )/θ. This means that the
film Reynolds number on the top of the nth tube in the array can
be expressed as
θcrit
Rebottom,n−1
(6)
θ
Once the actual amount of liquid that falls on the top of the
tube is known, Eq. (3) can be used to determine the heat flux on
the tube. Thus, the heat flux of the nth tube becomes
Retop,n =

qo = a + c

θcrit
Retop,n
θ

Tb

(7)

To apply, the calculation is started on the top tube of the array.
As long as there is no slinging (i.e., θ ≤ θcrit ), Eq. (3) is used

to determine the heat transferred by the tube, and the amount of
liquid leaving the bottom of the tube can be calculated. In this
case, all the liquid flowing off the bottom of the tube is assumed
to fall on top of the tube below (Retop,n = Rebottom,n−1 ). As
soon as the liquid starts to sling out (i.e., when θ > θcrit ), Eq.
(6) can be used to determine the amount of liquid that arrives on
the tube below. Equation (7) is used to determine the heat flux
transferred by the tube. To determine the heat transfer coefficient
from the preceding equation, it suffices to divide the heat flux
by the temperature difference, that is,

Background

qo = (a + cRetop ) T b

(4)

where ro is the tube radius and p is the tube pitch. Then, the
slinging angle is defined as a linear function of the Reynolds
number

hc,o = a + c

Gst¨ohl and Thome [11] presented two heat transfer models
for 3D enhanced condensing tubes: the first for when there is
no slinging (of condensate off the side of the tube), while the
second one takes into account the reduction of the Reynolds
number due to the slinging. They first correlated the heat flux to
the Reynolds number on top of the tube by

ro
p − ro

θcrit
Retop
θ

T b−1

(8)

The empirical constants for the slinging-heat transfer correlation for the tubes tested by Gst¨ohl and Thome are given in
Table 2 of [11], but are also reproduced in Table 4 of this article
for completeness.

Updated Model
The preceding method is fluid/enhanced tube specific, and
hence, to update its validity for the new tubes, it is evident that
the coefficients utilized should be modified to better fit the new
data. This is also required, since no general model accounting
for the enhancement geometry and its dimensions is available
for these fluid/enhanced tubes combinations in the literature.
A nonlinear least-squares optimization method was utilized to
minimize the difference between the prediction method and
the measured heat transfer data. The optimization process was
started from multiple initial positions (spread from the upper to
vol. 31 no. 10 2010


M. CHRISTIANS ET AL.

805

Table 4 Coefficients in Eqs. (7) and (8) and relative errors of the prediction methods for the single row data
Tube

Refrigerant

Turbo
Turbo
Gewa
Gewa
TurboCSL
Gewa C

R-134a
R-236fa
R-134a
R-236fa
R-134a
R-134a

a [W/m2 -K]

c [W/m2 -K]

b[—]

25,700
11,100

19,250
10,850
25,500
25,200

0.8599
0.7738
0.9042
0.7314
0.91
0.87

d[—]
10−4

3.08 ×
0
0
0
0.00027
0.00018

–6.0805
−0.5938
−0.607
1.2548
−9.7
−6.5

the lower bounds of the parameter constraints), and all arrived

either at the presented solution or very close, showing that the
minimum found is a global minimum rather a local minimum.
The coefficients for use in Eqs. (7) and (8) are shown in Table 4.
There are four sets of coefficients, one for each tube/refrigerant
combination tested.
Figure 8 shows a comparison of the prediction method found
using the nonlinear least-squares optimization and the measured
heat transfer coefficient data obtained using the Turbo enhanced
condensing tube and R-134a. This method predicts 87% of the
results within an error range of ±15%, while 100% of the data
are within a ±30% error band. Comparing the obtained coefficients to those found by Gst¨ohl and Thome (Table 2 of [11]), it
is found that the resulting coefficients are similar in magnitude
(a = ∼25,000, b = ∼0.8, c = ∼−6.5, d = ∼0.0004, e = 0).
Continuing the analysis of the results obtained with the Turbo
enhanced tube (now using R-236fa), the same optimization algorithm was implemented (using Gst¨ohl and Thome’s model),
even though the data do not show a pronounced degradation
in heat transfer. The prediction method (using the coefficients
shown in Table 4), plotted on the same figure as the results, is
shown in Figure 9. For R-236fa, this method only predicts 70%
of the data within ±15%, and 95% of the data to within 30%.

ε [%]

0
0.005
0.005
0.005
0.08
0.14

−0.78
2.85
−0.85
2.76
−2.4
−1.9

σ [%]
9.17
17.07
9.49
17.48
12.9
10.1

However, the R-236fa data are, for most of the tube/refrigerant
configurations, relatively constant, showing little influence with
respect to Reynolds number. The optimization algorithm shifted
the onset of the plateau region to a smaller Reynolds number
by first suppressing the slinging angle (θ) such that it has almost no effect. It also flattened the prediction by setting a yintercept 50% lower than has been previously calculated (for
R-134a and the different tubes tested), and slightly decreasing the power of the exponent b that affects the temperature
difference T. Furthermore, for R-236fa, the multiplier c acts
to suppress the influence of both the slinging angle and the
Reynolds number, rather than to amplify it as seen in the R-134a
results.
Applying the method to the Wieland Gewa C enhanced condensing tube and test refrigerant R-134a results in the prediction
shown in Figure 10. The method predicts 90% of the results
within an error range of ±15%, while 100% of the data are
within a ±30% error band. Comparing the empirical coefficients
to those found by Gst¨ohl and Thome for the Gewa-C, it is found

that the resulting (a) y-intercept coefficient and (b) temperature
difference exponent are similar in magnitude (a = ∼20,000,
b = ∼0.9, c = ∼−0.6, d = ∼0, e = ∼0). However, there is
a relatively large change for the Reynolds number multiplier c,

R−236fa, Turbo, tube spacing 38.50mm

R−134a, Turbo, tube spacing 38.50mm
Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6
Model

25000

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6
Model

25000

20000

2

Heat transfer coefficient [W/m K]

20000

2

Heat transfer coefficient [W/m K]

e[—]

15000

10000

10000

5000

5000

0

15000

0

500

1000
1500
2000
Film Reynolds number, Re

bottom,n−1

2500
[−]

3000

3500

Figure 8 Prediction method for the single-row Turbo condensing tube data
using R-134a.

heat transfer engineering

0

0

500

1000
1500
Film Reynolds number, Re

2000

[−]

2500

3000

bottom,n−1

Figure 9 Prediction method for the single-row Turbo condensing tube data
using R-236fa.

vol. 31 no. 10 2010


806

M. CHRISTIANS ET AL.

perform this is as explained for the R-134a results. The c multiplier acts to slightly amplify the Reynolds number effect, as
was the case with the previous results obtained by Gst¨ohl and
Thome.
Presently, it is not possible to present one set of constants a–
e that works for all the fluid/enhanced tubes combinations. To
achieve this, one needs first to develop a theory-based 3D condensation model, and then a predictive-based slinging model;
such a model requires local film flow measurements and is a
good topic of research for the future.

CONCLUSIONS

Figure 10 Prediction method for the single-row Gewa condensing tube data

using R-134a.

which in this case acts to suppress the the influence of both the
slinging angle and the Reynolds number, rather than amplify it
(that is, this tube slings less). The optimization algorithm shifted
the onset of the plateau region to a much smaller Reynolds
number by suppressing the slinging angle (θ) such that it has
almost no effect.
The prediction method for the Gewa condensing tube/R236fa configuration (using the coefficients shown in Table 4)
is plotted on the same figure as the results in Figure 11. For
R-236fa, this method predicts 70% of the data within ±15%
and 90% of the data to within 30%. As with the R-134a data,
the optimization algorithm shifted the onset of the plateau region to a smaller Reynolds number. The method utilized to

The heat transfer performance of the new versions of the
Wolverine Turbo C and Wieland Gewa C condensing tubes, using refrigerants R-134a and R-236fa, has been measured. Using
R-134a, the heat transfer coefficient of the two enhanced tubes
varied as a function of the film Reynolds number, and was characterized by two distinct zones. At low film Reynolds numbers,
the top tubes of the array showed a large peak in the measured
heat transfer coefficients (most probably, this is an impingement
effect due to the surface geometry), after which the heat transfer coefficient decreased almost linearly. Above a certain film
Reynolds number, the heat transfer coefficient decreases much
more slowly and achieves an almost constant value (that is,
reaches a plateau). Using R-236fa, this large degradation in heat
transfer with increasing film Reynolds number was not seen;
in fact, there was almost no change in the heat transfer performance with increasing film Reynolds number (only fluctuation
within a bound region). For both 3D enhanced tubes, as well
as both refrigerants, the local heat flux on a tube in the array
was correlated as a function of the condensation temperature
difference and the condensate inundation in the form of the film

Reynolds number falling on the tube. The coefficients in the
correlation were found to be close for both tubes apart from the
coefficient c, which corresponds to the slope in the deterioration in heat transfer performance with increasing film Reynolds
number. When using R-134a, the heat transfer coefficient of the
Gewa-C condensing tube decreases less rapidly with increasing
film Reynolds number; however, the peak reached is not as large
as that found using the Turbo-C tube. Using R-134a, the mean
relative error of the fluid/enhanced tube specific method was
less than 1%, with a standard deviation of less than 10%. Using
R-236fa, the measurements were predicted by their respective
methods with mean relative errors of less than 3% and standard
deviations of less than 18%.

NOMENCLATURE

Figure 11 Prediction method for the single-row Gewa condensing tube data
using R-236fa.

heat transfer engineering

a
b
C

prediction method constant, W/m2 -K
prediction method constant
Wilson plot method constant
vol. 31 no. 10 2010

M. CHRISTIANS ET AL.

c
cp
d
D
e
h
hlv
k
M
˙
m
p
pcrit
q
R
r
Re
T
U
x

prediction method constant, W/m2 -K
specific heat at constant pressure, J/(kg-K)
prediction method constant
diameter, m
prediction method constant
local heat transfer coefficient, W/(m2 -K)
heat of vaporization (J/kg)

thermal conductivity, W/(m-K)
molar mass (kg/kmol)
mass flow rate, kg/s
center to center tube pitch, m
critical pressure, kPa
local heat flux relative to a surface, W/m2
thermal resistance m2 K/W
tube radius, m
film Reynolds number, 4 /µ
temperature, K
overall thermal resistance, K/W
coordinate in axial direction, m

Greek Symbols
T
ε

θ
θcrit
ρ
σ
µ

condensation temperature difference, Tsat − Tw
mean relative error
film mass flow rate on one side per unit length of
tube, kg/(m-s)
slinging angle, rad
critical deflection angle, defined by Eq. (4), rad
density, kg/m3

standard deviation
kinematic viscosity, Pa-s

Subscripts
bottom
i
gni
l
n
o
sat
top
v
w

at the bottom of the tube
internal side of tube
Gnielinski (heat transfer coefficient)
saturated liquid
number of rows measured from top row
external side at fin tip
saturated conditions
at the top of the tube
saturated vapor
wall

REFERENCES
[1] Jung, D., Chae, S., Bae, D., and Yoo, G., Condensation Heat
Transfer Coefficients of Binary HFC Mixtures on Low Fin and
Turbo-C Tubes, International Journal of Refrigeration, vol. 28,

no. 2, pp. 212–217, 2005.

heat transfer engineering

807

[2] Jung, D., Kim, C.-B., Cho, S., and Song, K., Condensation Heat
Transfer Coefficients of Enhanced Tubes With Alternative Refrigerants for CFC11 and CFC12, International Journal of Refrigeration, vol. 22, no. 7, pp. 548–557, 1999.
[3] Jung, D., Kim, C.-B., Hwang, S.-M., and Kim K.-K., Condensation Heat Transfer Coefficients of R22, R407C, and R410a
on a Horizontal Plain, Low Fin, and Turbo-C Tubes, International Journal of Refrigeration, vol. 26, no. 4, pp. 485–491,
2003.
[4] Chang, Y.-J., Hsu, C. T., and Wang, C.-C., Single-Tube Performance of Condensation of R-134a on Horizontal Enhanced
Tubes, ASHRAE Transactions, vol. 102, no. 1, pp. 821–829,
1996.
[5] Kumar, R., Varma, H. K., Mohanty, B., and Agrawal, K. N.,
Condensation of R-134a Vapor Over Single Horizontal Circular
Integral-Fin Tubes With Trapezoidal Fins, Heat Transfer Engineering, vol. 21, no. 2, p. 29, 2000.
[6] Kumar, R., Gupta, A., and Vishvakarma, S., Condensation of R134a Vapour Over Single Horizontal Integral-Fin Tubes: Effect of
Fin Height, International Journal of Refrigeration, vol. 28, no. 3,
pp. 428–435, 2005.
[7] Sreepathi, L. K., Bapat, S. L., and Sukhatme, S. P., Heat Transfer During Film Condensation of R-123 Vapour on Horizontal
Integral-Fin Tubes, Journal of Enhanced Heat Transfer, vol. 3,
no. 2, pp. 147–164, 1996.
[8] Wen, X. L., Briggs, A., and Rose, J. W., Enhancement of Condensation Heat Transfer on Integral-Fin Tubes Using Radiused
Fin-Root Fillets, Journal of Enhanced Heat Transfer, vol. 1, no.
2, pp. 211–217, 1994.
[9] Kang, Y. T., Hong, H., and Lee, Y. S., Experimental Correlation of
Falling Film Condensation on Enhanced Tubes With HFC134a;
Low-Fin and Turbo-C Tubes, International Journal of Refrigeration, vol. 30, no. 5, pp. 805–811, 2007.
[10] Gst¨ohl, D., and Thome, J. R., Film Condensation of R-134a on

Tube Arrays With Plain and Enhanced Surfaces: Part I, Experimental Heat Transfer Coefficients, Journal of Heat Transfer, vol.
128, pp. 21–32, 2006.
[11] Gst¨ohl, D., and Thome, J. R., Film Condensation of R-134a on
Tube Arrays With Plain and Enhanced Surfaces: Part II, Prediction Methods, Journal of Heat Transfer, vol. 128, pp. 33–43,
2006.
[12] Habert, M., Ribatski, G., and Thome, J. R., Experimental Study
on Falling Film Flow Pattern Map and Intercolumn Distance With
R-236fa, ECI International Conference on Boiling Heat Transfer,
Spoleto, Italy, 2006.
[13] Robinson, D. M., and Thome, J. R., Local Bundle Boiling Heat
Transfer Coefficients on a Plain Tube Bundle (RP-1089), HVAC
and R Research, vol. 10, no. 1, pp 33–51, 2004.
[14] Gnielinski, V., New Equations for Heat and Mass Transfer in
Turbulent Flow Through Pipes and Ducts, Forschung Im. Ingenieurwessen, vol. 41, no. 1, pp. 359–368, 1975.
[15] NIST, NIST Thermodynamic Properties of Refrigerants and
Refrigerant Mixtures Database, ver. 8.0, Gaithersburg, MD,
2007.
[16] Gst¨ohl, D., and Thome, J. R., Visualization of R-134a Flowing on
Tube Arrays With Plain and Enhanced Surfaces Under Adiabatic
and Condensing Conditions, Heat Transfer Engineering, vol. 27,
pp. 44–62, 2006.

vol. 31 no. 10 2010


808

M. CHRISTIANS ET AL.
Marcel Christians is a Ph.D. student at the Laboratory of Heat and Mass Transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL),
Switzerland. He received his B.Eng. and M.Eng. (mechanical) degrees at the University of Pretoria, South

Africa, where his thesis topic covered in-tube condensation of refrigerants in the intermittent flow regime.
His current research is on falling film flow visualization, as well as falling film evaporation and condensation heat transfer on bundles of enhanced tubes.

Mathieu Habert performed his Ph.D. thesis on
falling film evaporation on single rows and bundles
of plain and enhanced tubes at the Laboratory of Heat
and Mass Transfer at the Swiss Federal Institute of
Technology in Lausanne (EPFL), Switzerland, completing his degree in February 2009. Currently, he is
chief technical officer of CHS in Gland, Switzerland.

heat transfer engineering

John. R. Thome has been a professor of heat and
mass transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, since 1998.
His primary interests of research are two-phase flow
and heat transfer, covering boiling and condensation
of internal and external flows, two-phase flow patterns and maps, experimental techniques on flow visualization and void fraction measurement, and more
recently two-phase flow and boiling in microchannels. He received his Ph.D. at Oxford University,
England, in 1978, and was formerly an assistant and associate professor
at Michigan State University. He left in 1984 to set up his own international engineering consulting company. He is the author of four books, Enhanced Boiling Heat Transfer (Taylor & Francis, 1990), Convective Boiling
and Condensation (Oxford University Press, 1994, 3rd ed., with J. G. Collier), Wolverine Engineering Databook III (2004), and Nucleate Boiling on
Micro-Structured Surfaces (with M. E. Poniewski, 2008), which are now available free at and
He received the ASME
Heat Transfer Division’s Best Paper Award in 1998 for a three-part paper on
flow boiling heat transfer published in the Journal of Heat Transfer. He also
authored the chapter “Boiling” in the new Heat Transfer Handbook (2003). He
is an associate editor of Heat Transfer Engineering and is chair of ALEPMA
(the Aluminum Plate Fin Heat Exchanger Manufacturers Association).

vol. 31 no. 10 2010

Heat Transfer Engineering, 31(10):809–820, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903547487

Film Condensation of R-134a and
R-236fa, Part 2: Experimental
Results and Predictive Correlation
for Bundle Condensation on
Enhanced Tubes
MARCEL CHRISTIANS, MATHIEU HABERT, and JOHN R. THOME
Laboratory of Heat and Mass Transfer (LTCM), Faculty of Engineering Science Ecole Polytechnique F´ed´erale de Lausanne
(EPFL), Lausanne, Switzerland

Local test results for two enhanced condensing tubes (next-generation versions of the Wieland Gewa and Wolverine Turbo
enhanced condensing tubes) are obtained for refrigerants R-134a and R-236fa on the center row of a three row-wide tube
bundle. The “bundle effect” on the heat transfer performance of the test section is observed and described. New predictive
methods for falling film condensation on bundles are proposed, based on a modification of the previous vertical singlerow method with condensate slinging. The modifications performed to the experimental setup to allow for bundle tests are
described. For two types of enhanced tubes and two refrigerants, the local heat flux is correlated as a function of condensation
temperature difference, the film Reynolds number, the tube spacing, and liquid slinging effect.

INTRODUCTION
The heat transfer performance of tubes in shell-and-tube condensers is a function of a large amount of variables. Not only is
it dependent on the condensate inundation from the tubes above,
but the geometric distribution of the tubes can also affect the
performance. In order to increase the efficiency of falling film
condensers, it is necessary to accurately characterize the performance of new enhanced tubes in a test section that attempts to
approximate actual conditions in a bundle. This is not to say that

single-row condensing tests are not necessary; on the contrary,
they are necessary to understand the fundamental flow around
these tubes before trying to understand the more complex flow
that occurs in a bundle. Furthermore, it is of interest to test the
The authors thank the laboratory’s industrial sponsors Johnson Controls,
Trane, Wieland Werke, and Wolverine Tube, Inc., for funding this study. Special
thanks to the tube manufacturers, Wieland Werke and Wolverine Tube, Inc., for
supplying the tubes utilized.
Address correspondence to Prof. John R. Thome, Laboratory of Heat and
Mass Transfer (LTCM), Faculty of Engineering Science, Ecole Polytechnique
F´ed´erale de Lausanne (EPFL), Station 9, Lausanne CH-1015, Switzerland.
E-mail:

performance of these tubes with several refrigerants, such that
the effect of the thermophysical properties of each fluid may be
quantified and taken into account during the design stage.

PREVIOUS HEAT TRANSFER COEFFICIENT STUDIES
In 1994, Huber et al. [1–3] tested a 5 × 5 bundle using finned
and three-dimensional (3D) enhanced tubes using R-134a and R12 as test refrigerants. The bundle was arranged using horizontal
tubes with a vertical pitch of 19.1 mm and a horizontal pitch
of 22.2 mm. The finned tubes tested had 1,024 fins per meter
and 1,574 fins per meter, while the two 3D enhanced tubes
tested were the Gewa-SC and the Turbo-Cii. The saturation
temperature for these tests was 35◦ C. In their test section, all
tubes were cooled with water, only the middle tubes of each row
were instrumented, and the tube length-averaged heat transfer
coefficients were measured. Concurrently with [1–3], Cheng and
Wang [4] tested plain, finned, and 3D enhanced tubes in a three
rows wide by two columns deep bundle. Adjacent tubes were

connected by U-bends. The horizontal pitch used was 30 mm
with a vertical pitch of 50 mm. R-134a was tested at a saturation

809


810

M. CHRISTIANS ET AL.

temperature of 38◦ C. They used finned tubes with 1,024, 1,260,
and 1,614 fins per meter, and three types of 3D enhanced tubes.
The measured heat transfer coefficients were the average values
of the two-pass axial length. Rewerts et al. [5] used the same test
section and the same tubes as in their previous research [1–3].
They also tested at the same saturation temperature with R-134a.
Again, only the middle tubes of each row were instrumented
and the heat transfer coefficients measured were tube lengthaveraged. All the tubes were cooled with water.
Belghazi et al. [6–8] used plain, commercially available
finned tubes and enhanced tubes in a staggered bundle comprising of 33 tubes distributed in 13 horizontal rows. The horizontal spacing was 24 mm and the vertical spacing was 20 mm.
There was one cooled tube on each odd row, and there were two
cooled tubes on even rows. They tested several refrigerants and
refrigerant mixtures, namely, R-134a and mixtures of R-23 and
R-134a, with the concentration of R-23 varying from 0 up to
11%. The finned tubes had 433, 748, 1,024, 1,260, and 1,574 fins
per meter. The enhanced tube tested as the Gewa-C+. The saturation temperature for these tests was 40◦ C. The researchers
measured average tube heat transfer coefficients using a Wilson plot method. In [6], the authors presented a tube-specific
(Gewa-C+) method that took into account the drainage around
the enhancement structure of the tube.
Honda et al. [9–13] tested finned tubes with several refrigerants for both in-line and staggered tube bundles. The bundle was

comprised of 38 tubes distributed in 15 rows and three columns,
with a horizontal spacing of 22 mm and a vertical spacing of 22
mm. The tubes tested had 1,040, 1,923, and 2,000 fins per meter.
They tested R-123, and a mixture of R-134a (14%) and R-123.
The heat transfer coefficients were calculated according to the
average row heat flux based on a water-side energy balance.
As such, the aim of this article is to first detail the modifications performed on the LTCM installation allowing for condensation bundle tests to be performed, and second, to present
and discuss the results obtained in the LTCM’s bundle falling
film facility for advanced versions of the Turbo C and Gewa C
3D enhanced tubes, using both R-134a and R-236fa. The heat
transfer coefficients measured here are local values rather than

1
2
3
4
5

1. Liquid distributor
2. Side overfeed tubes
3. Half-tube
4. Side-array tubes
5. Test tubes

Figure 2 Top part of the test section as modified to run bundle tests.

tube length-averaged values and hence are more useful for the
development of prediction methods. Finally, a bundle prediction
method based on the single-row method presented in Part 1 of
this article (this issue) and in [14] is proposed.

EXPERIMENTAL FACILITY
The basics of the experimental setup utilized in this study
are unchanged from those described in Part 1 of this article
(this issue) and [15]. The modifications that were required to
convert the single-row test section to a bundle are discussed in
this section.
A part of the original test section is shown in Figure 1.
Instead of using only the single distributor on top of the center
tube array (single equi-spaced column of tubes), two sets of two
high-performance condensing tubes were installed on both sides
of the distributor, through which cold glycol is run regardless of
whether condensation or evaporation is being studied (Figure 2).
These four tubes provide the condensate overfeed for the side
rows. The glycol mass flow rate can be controlled to regulate
the amount of condensate being generated. To further fine tune
the amount of heat exchanged, a three-way valve is installed.
Figure 3 shows the additional circuit installed that feeds the
two side-row overfeed circuits. The glycol flow rate through

1

2

3

1. Pre-distributor tube
2. Polyurethane foam
3. Polyethylene foam
4. In-line distribution holes

5. Half tube
6. First test tube

4
5
6

Figure 1 Original test section as used by Gst¨ohl and Thome [14, 15].

heat transfer engineering

Figure 3 Side overfeed circuits (glycol).

vol. 31 no. 10 2010


M. CHRISTIANS ET AL.

Figure 4 Auxiliary side-array circuits (water).

each side can be manually controlled such that there will be no
imbalance in the heat extraction between the two sides.
To better simulate conditions in real condensers, tubes were
also installed around the center column of tubes arranged in a
staggered equilateral triangle layout. In total, there are 22 peripheral tubes around the six center column instrumented tubes, with
a vertical pitch of 38.5 mm and a horizontal pitch of 22.3 mm (as
recommended by our industrial sponsors). The side-array tubes
are also partially shown in Figure 2. Water is pumped through
these tubes; however, unlike the center column, the water goes
through all the side tubes in 11 passes (rather than the two passes

in the center column for each pair of tubes). The water flow rate
through each side-array can be controlled in a similar fashion to
the glycol overfeed circuit, such that the water-cooled side-array
condensate flow remains balanced. The auxiliary water circuit
installed for the bundle tests is shown in Figure 4.

EXPERIMENTAL ERRORS AND PROCEDURES
As the central row of tubes was not changed with the installation of the additional tubes, the internal enhancement coefficients calculated using the Wilson plot method also remained
unchanged. This means that both the values calculated and the
uncertainties tabulated in Table 1 of Part 1 remain valid and
are not presented in this section. Furthermore, since the measurement method utilized in the center column of tubes has not
changed either, and neither were the tubes, the uncertainties tabulated in Table 2 of Part 1 are also valid and not repeated here.
The saturation temperature was kept unchanged at 31◦ C.
For experiments involving condensate overfeed, the film flow
rate of the liquid arriving on the first tube was evaluated from
the measured mass flow rate and the tube length, assuming that
the refrigerant is at saturation conditions. The mass flow of refrigerant condensing on the first tube is calculated by an energy
balance on differential elements and added to the film flow rate
heat transfer engineering

811

arriving on the first tube to obtain the film flow rate at the top
of the second tube and so on. This means, however, that it is
assumed that there is an ideal flow on the central row, without
slinging onto or from the side rows. In the case of no overfeed, a similar procedure was applied, with the initial flow rate
onto the top tube set to 0. Any slinging from the side-overfeed
or top side-array tubes onto the first tube are ignored. Again,
as in Part 1, the saturation temperatures, as well as the transport and thermodynamic properties, are calculated according to
REFPROP v8 [16] from the mean of the pressures measured by

pressure transducers above and below the tube array. The pressure drops from top to bottom of the bundle were in fact quite
small, and the subsequent change in thermal properties therefore
negligible.
Due to the fact that there are now two additional controllable
operating conditions or states (i.e., the heat transferred from
the glycol-cooled side-overfeed circuits and the water-cooled
side-row circuits) in the test section, and the fact that we are
only acquiring data for the center column, it was required that
the influence of these conditions on the heat transfer behavior
be quantified. A further objective was to identify the results
for which a true “bundle effect” could be distinguished and
thus use those to establish our “bundle database” for use in
building such a prediction method. Thus, the presentation of
the bundle heat transfer results is presented first by refrigerant,
and then the state. A test state (condition) is defined as any
combination of the glycol side-overfeed condensate flow and
water side-array condensate flow that will create a distinctly
different environment for the center tube row. There are four
distinct states achievable in the bundle, namely, both glycol and
water flow rates at maximum values, zero for both circuits (i.e.,
at 0 kg/s), the glycol flow rate at its maximum with no water
flow rate, and vice versa. These four conditions are illustrated
in an approximate schematic of each in Figure 5. The notion
that specific inundation rates on the central vertical row are still
achieved by using the overfeed pump (which goes on to the
multi-part distributor and the half-tube) should be clear. Refer
to Part 1 of this article for a schematic of the test facility.
These four states will be mentioned often; for brevity’s
sake, in all graphs they will be indicated as mOmSA (maximum side-overfeed, maximum side-array), mOnSA (maximum

Maximum Side-overfeed flow
Maximum Side-array flow
(mOmSA)

Figure 5
loops.

Maximum Side-overfeed flow
No Side-array flow
(mOnSA)

No side-overfeed flow
Maximum side-array flow
(nOmSA)

No side-overfeed flow
No side-array flow
(nOnSA)

Flow variable states for the glycol and water side-array auxiliary

vol. 31 no. 10 2010


M. CHRISTIANS ET AL.
2

R−134a, Bundle, Turbo condensing, tube spacing 38.5mm, heat flux: 40kW/m , mOmSA

25000

20000
2

side-overfeed, no side-array), nOmSA (no side-overfeed, maximum side-array), and nOnSA (no side-overfeed, no side-array).
Tests were conducted by gradually decreasing the liquid overfeed flow rate (from the pump) on the center top tube at a fixed
heat flux. This liquid overfeed is completely independent of
the previously mentioned bundle states. This liquid flow rate
is measured using a Coriolis flow meter and can be very accurately controlled. The data were logged only once steady-state
conditions were attained. A more detailed description of the test
facility, data reduction methods and measurements accuracies
can be found in Gst¨ohl and Thome [14, 15], as well as in Part 1
of this two-part article.

Heat transfer coefficient [W/m K]

812

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

15000

10000

5000

EXPERIMENTAL RESULTS WITH THE BUNDLE TEST
SECTION
Search for the “Bundle Effect”

0

0

500

1000
1500
2000
2500
3000
Film Reynolds number, Rebottom [ − ]

3500

4000

Figure 6 Turbo performance using R-134a in the tube bundle at a nominal
bundle heat flux of 40 kW (mOmSA), representative of all heat fluxes and tubes.

Tests were performed using the Wolverine Turbo and
Wieland Gewa condensing tubes (both of them have 18.38 mm
nominal outer diameter) provided by the tube manufacturers.
Before installation into the test section, the tubes were thoroughly cleaned. The film flow rate (per unit length) was varied
from 0.25 kg/m-s to 0 kg/m-s. Tests were performed at constant

tube array nominal heat fluxes of 20, 40, and 60 kW/m2 . The
tests were repeated for each variable state condition, such that a
comparison could be made.
Due to the large amount of data obtained (two tubes, two
refrigerants, and four state combinations), representative figures
are presented to advance the discussion of the appearance of a
“bundle effect.” Unless stated otherwise, the trends presented are
indicative of the behavior at all heat fluxes, for both refrigerants,
and for both tubes. Once the comparison of the four states is
finished, the results independent of the variable states will be
shown.
mOmSA
Figure 6 presents the heat transfer performance of the six
center tubes in the bundle with the side-overfeed and side-row
circuits exchanging the largest amount of heat possible. It is
immediately clear that there is a large difference for the bundle
heat transfer coefficients measured as opposed to the single-row
results of Figures 2–7 of Part 1. The first significant aspect is that
the bundle seems to have completely flattened out the peak that
was present in the single-row results. This is advantageous for
condenser performance since tubes 4 through 6 have flattened
out at quite high values. Furthermore, it is also clear that the
results are no longer grouped together on more or less one
“curve.”
In addition, starting from the first (top) tube in the center row
of the bundle, the measured heat transfer coefficient is very low
and then rises monotonically from tube to tube up to the fifth
heat transfer engineering

tube, after which there is a decrease in the measured heat transfer values of the sixth tube. This trend seems to be attributable

to “entrance” and “exit” effects on tubes 1–3 and tube 6, respectively. Instead, comparing the bundle performance of tubes 4, 5,
and 6 to those of the single row at a film Reynolds number of
1,000 shows that the performances are comparable to the values
presented in Part 1 of this article. A reason that might explain
the decrease in the performance of the sixth tube with respect to
the fifth tube is the fact that due to the geometric constraints imposed by the test section vessel itself, it is the lowermost tube in
the bundle, and is not completely surrounded by the side-array
tubes, as shown in Figure 7. Thus, not having other tubes for the
condensate to fall onto would also affect the heat transfer due
to the change in the liquid film flow characteristics (i.e., more
of the condensate will flow onto tube 6 than tube 5).
In this configuration, the heat transfer performance of the
bundle is essentially constant as a function of the heat flux.
There is some variation on tubes 1, 5, and 6 at low Reynolds
numbers, but as this increases, the results quickly collapse into
a similar range. For the top tube rows, the overfeed condensate
needs to get distributed and may create a “flooding” effect that
reduces their heat transfer coefficients.

1. Tube 5
2. Tube 6
3. Machining limit

1
2

3

Figure 7 Cut-away view of the bottom of the bundle test section.

vol. 31 no. 10 2010


M. CHRISTIANS ET AL.

mOnSA

813
2

R−134a, Bundle, Gewa condensing, tube spacing 38.5mm, heat flux: 60kW/m , nOmSA

2

R−134a, Bundle, Gewa condensing, tube spacing 38.5mm, heat flux: 40kW/m , mOnSA

25000

20000
2

Heat transfer coefficient [W/m K]

In essence, the general trends spotted in the results for
the mOmSA results are also found in this subsection’s results.
Figure 8 shows that there is a large separation between the heat
transfer results of the first tube and the rest of the tubes of the
center column. The entrance effects on the first tube are easily visible, as there is a constant increase in the heat transfer
coefficient with increasing mass flow. This was not seen in the
previous section’s results.

Apart from the first tube, which has an increasing trend, the
rest of the tubes behave in a very constant fashion, and only the
fifth shows a small decrease in heat transfer performance at the
highest Reynolds numbers. The sixth tube again has an “exit”
effect.
In comparison with the previous results, it can be seen that
the first tube has lower heat transfer coefficients throughout the
entire Reynolds number range, as well as at the different heat
fluxes. It is proposed that there are two main reasons for this
phenomenon; first, this may be due to the variability in the heat
flux when testing at a nominal bundle heat flux—i.e., each tube
has its own midpoint so reporting here the nominal heat flux
does not show this effect (the actual heat fluxes are used later
for the prediction method). However, this effect alone will not
decrease the heat transfer coefficient of the first tube so drastically. Second, as noted earlier, it is possible that in the bundle
test section, liquid is retained both above and around the first
tube, in a flooding effect, which would lead to decreased performance throughout the Reynolds number range. This would also
depend on the enhanced tube utilized and its particular drainage
characteristics. This phenomenon is found for both Wieland and
Wolverine’s tubes.

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

15000

10000

5000

0

0

500

1000

1500
2000
2500
3000
3500
Film Reynolds number, Rebottom [ − ]

4000

4500

Figure 9 Gewa performance using R-134a in the tube bundle at a nominal
bundle heat flux of 6 0kW (nOmSA).

nOmSA
As shown in Figure 9, due to the absence of the side-overfeed,
the first three tubes show a tendency to decrease the heat transfer
coefficient with an increase in Reynolds number, much like

the single-array tests shown in Part 1. There is a noticeable
difference between the top three tubes and the bottom three
tubes of the bundle. The top three tubes show a very slight
decrease in measured heat transfer coefficient, while the bottom
three show an equally slight increase. There is a very large
difference (between 60 and 100%) between the top and bottom
tubes. In all probability, this is a “bundle effect” acting on the
three bottom tubes, which receive the redistributed film flow
on them, as opposed to the top three, which again appear to
have a flooding effect created by the configuration of the test
section.

25000

nOnSA

2

Heat transfer coefficient [W/m K]

20000

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6
show

15000

10000

5000

0

0

500

1000
1500
2000
2500
3000
Film Reynolds number, Rebottom [ − ]

3500

4000

Figure 8 Gewa performance using R-236fa in the tube bundle at a nominal
bundle heat flux of 20 kW (mOnSA).

heat transfer engineering

The results found when neither the side-overfeed nor the
side-array circuits are active show that the heat transfer of the

top three tubes degrades as a function of Reynolds number;
however, as can be seen in Figure 10, this degradation only
happens at higher Reynolds numbers (tubes 2 and 3), while tube
1 degrades almost immediately. However, unlike the single-row
or the nOmSA bundle tests, there is a heat transfer recovery
that essentially increases the heat transfer coefficient back to
pre-degradation levels.
Of further interest is that over the three heat fluxes, the heat
transfer performance of the center column in the bundle increases as the tube number increases (except tubes 2 and 3; they
have essentially the same performance), which was not the case
when the side-overfeed circuits were active. What is more, the
fifth tube (which was the better performing tube in the mOmSA
vol. 31 no. 10 2010


814

M. CHRISTIANS ET AL.
2

2

R−134a, Bundle, Turbo Condensing Tube, tube spacing 38.5mm, heat flux: 60kW/m

25000

20000

20000

Tube 1
Tube 2
Tube 3
Tube 4
Tube 5
Tube 6

15000

10000

5000

0

Heat transfer coefficient [W/m2 K]

25000

2

Heat transfer coefficient [W/m K]

R−134a, Bundle, Turbo condensing, tube spacing 38.5mm, heat flux: 20kW/m , nOnSA

mOmSA T4
mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4

nOmSA T5
nOnSA T4
nOnSA T5

15000

10000

5000

0

500

1000
1500
2000
2500
Film Reynolds number, Rebottom [ − ]

3000

3500

Figure 10 Turbo performance using R-236fa in the tube bundle at a nominal
bundle heat flux of 20 kW (nOnSA).

and mOnSA cases) is not the best performing tube any longer,
which serves to show that in the nOnSA case, the heat transfer
degradation effect on the sixth tube caused by having installed

the auxiliary tubes is diminished (yet not negligible).

0
500

1000

1500
2000
2500
3000
3500
Film Reynolds number, Rebottom [ − ]

4000

4500

Figure 11 Comparison of the four variable states on tubes 4 and 5 for the
Turbo condensing tube and R-134a at a heat flux of 40 kW/m2 , representative
of both tubes and all heat fluxes.

were considerably lower than the rest were those found when
testing the nOnSA case.

R-236fa Variable State Comparison
R-134a Variable State Comparison
As has been shown in the preceding subsection, the first three
tubes appear to be heavily influenced by the variation in the side
flow conditions, while for the sixth tube results are influenced

by its position as the bottom-most tube in the bundle. Plotting
the results obtained for the fourth and fifth tubes for all four
states tested together (separated by heat flux), it may thus be
possible to satisfactorily conclude whether these tubes show
true “deep-in-the-bundle” heat transfer behavior.
Turning to Figure 11 (which is representative of both tubes
at all heat fluxes for R-134a), the effect of the side conditions
is evident, especially as the results from the nOnSA case are
compared to the results found when one or both of the side
circuits are active. Over the entire range of Reynolds number,
the heat transfer performances of the fourth and fifth tubes when
in nOnSA conditions are either the lowest or among the lowest
measured. This is not only seen in the 20-kW/m2 results, but
also in the 40- and 60-kW/m2 data.
Of particular interest is that one of the definitive “bundle effects” is that the degradation found in the single-row results is
not present any longer. This is very probably due to the redistribution of the flow normally incoming to tubes 4 and 5 to the
side-array tubes. This effect is seen repeated in the results taken
at 40 and 60 kW/m2 (not shown for brevity).
Finally, over the three heat fluxes tested, almost constant heat
transfer coefficients were measured on the fifth tube, with any
or both of the side circuits active (i.e., mOmSA, mOnSA, or
nOmSA cases). The only measurements from the fifth tube that
heat transfer engineering

For a heat flux of 20 kW/m2 , the comparison is plotted in
Figure 12. At this heat flux, it can be seen that the majority of the results are relatively constant. For tube 5, the results found when using mOnSA, nOmSA, and nOnSA are almost
identical, and only deviate at larger Reynolds numbers. However, the mOmSA data are found to be consistently ±15% lower
than the rest. This is contrary to the expected result in which
the conditions with any of the side circuits active would perform similarly, with the nOnSA data being the odd ones out.
The reason why this occurred is not clear, except that these

tubes’ enhancement was not optimized by the manufacturers for
R-236fa condensate drainage. The results that were obtained
from tube 4 also vary much more from case to case than when
R-134a was utilized.
At 40 kW/m2 in Figure 13, the results presented are representative for the two tubes and the test heat fluxes of 40 and
60 kW/m2 (the results shown in Figure 12 were the exception).
The results on the fifth tube show the same trends as when using
R-134a, namely, that regardless of the side-state status, all the
data are grouped. The results for the fourth tube show that the
data from mOmSA and the nOmSA cases exhibit very similar
trends, while the results from the mOnSA and nOnSA cases are
similar.
The bundle configuration showed much larger gains in performance for R-236fa, and particularly the Wieland condensing tube/R-236fa results achieved almost the same performance
as when using R-134a, which was an unexpected result. This
phenomenon is seen repeated in the results taken at 40 and
vol. 31 no. 10 2010


M. CHRISTIANS ET AL.
2

R−236fa, Bundle, Gewa Condensing Tube, tube spacing 38.5mm, heat flux: 20kW/m

25000

Heat transfer coefficient [W/m2 K]

20000

mOmSA T4

mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4
nOmSA T5
nOnSA T4
nOnSA T5

15000

10000

5000

0

0

500

1000
1500
2000
Film Reynolds number, Rebottom [ − ]

2500

Figure 12 Comparison of the four variable states on tubes 4 and 5 for the
Gewa condensing tube and R-236fa at a heat flux of 20 kW/m2 .

60 kW/m2 . This was seen for the Wolverine Turbo condensing
tube as well.
Results Independent From Variable State Conditions
The preceding results showed that to obtain results independent of the variation in the side states, the top three tubes and
the sixth tube could not be used as it is evident that they were
influenced by entrance and exit effects, respectively. Isolating
the fourth and fifth tubes, it was found that the results were
independent of the side states as long as one or both of the side
circuits were active.

815

Using the Turbo enhanced condensing tube and R-134a, at a
heat flux of 20 kW/m2 (all Reynolds numbers) the average heat
transfer coefficient measured is roughly 17–19 kW/m2 -K (tubes
4 and 5). This can be compared to the results found in the singlerow results (Figure 2 of Part 1), in which the average heat transfer
coefficient before degradation (Re < ∼1,000) is an average of
22 kW/m2 -K. Of particular interest is that one of the definitive
“bundle effects” is that the progressive degradation found in the
single-row results with increasing film Reynolds number is no
longer present. However, while there is no degradation, there is
no sharp peak either. The absence of the peak is probably due
to the redistribution of the flow between tubes 4 and 5 and the
side-array tubes. This effect is seen repeated in the results taken
at 40 and 60 kW/m2 . The results obtained for all heat fluxes,
using the Turbo condensing tube and R-134a, are shown in
Figure 14.
Utilizing the Wieland Gewa condensing tube and R-134a,
the average heat transfer coefficient measured is roughly
15–15.5 kW/m2 -K (tubes 4 and 5). In the single-row results

(Figure 5 of Part 1), the average heat transfer coefficient before
degradation (Re < ∼1,000), and excluding the first tube results,
was an average of 17 kW/m2 -K. The same bundle effect described earlier is thus also present in Wieland’s tube data, and
again the degradation in heat transfer coefficient with increasing
Reynolds number is not present anymore and neither is the peak.
The heat transfer data (all heat fluxes) for the Gewa condensing
tube are presented in Figure 15.
Going back to the Turbo condensing tube, using R-236fa, the
average heat transfer coefficient measured is roughly 13 kW/m2 K (tubes 4 and 5, all heat fluxes). In the single-row results (again,
Figures 2–4 of Part 1), the average heat transfer coefficient
(excluding tube 1) was 7–7.5 kW/m2 -K. Unlike R-134a, there
was no worsening of the heat transfer peak performance—in
fact, the bundle testing resulted in higher measured heat transfer

2

R−236fa, Bundle, Gewa Condensing Tube, tube spacing 38.5mm, heat flux: 40kW/m

R−134a, Bundle, Turbo Condensing Tube, tube spacing 38.5mm

25000
25000

20000

mOmSA T4
mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4

nOmSA T5
nOnSA T4
nOnSA T5

15000

10000

Heat transfer coefficient [W/m2 K]

Heat transfer coefficient [W/m2 K]

20000

mOmSA T4
mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4
nOmSA T5

15000

10000

5000
5000

0
500

1000

1500
2000
Film Reynolds number, Re

bottom

2500

3000

[−]

Figure 13 Comparison of the four variable states on tubes 4 and 5 for the
Gewa condensing tube and R-236fa at a heat flux of 40 kW/m2 , representative
of both tubes and all heat fluxes.

heat transfer engineering

0
500

1000

1500
2000
2500
3000

Film Reynolds number, Re

bottom

3500
[−]

4000

4500

Figure 14 Variable state independent results found on tubes 4 and 5 of the
test section: Turbo condensing tube, all heat fluxes for R-134a.

vol. 31 no. 10 2010


816

M. CHRISTIANS ET AL.

heat fluxes since the trends and magnitudes are the same. It is
possible that, due to the increased surface tension of R-236fa
(with respect to R-134a) and to the relatively tight spacing of
the tubes, the redistribution of refrigerant was more pronounced.
Redistribution, in our opinion, has an effect of thinning out the
average thickness of the film over the tubes, thus increasing the
heat transfer coefficient.

R−134a, Bundle, Gewa Condensing Tube, tube spacing 38.5mm

25000

2

Heat transfer coefficient [W/m K]

20000

mOmSA T4
mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4
nOmSA T5

15000

10000

The method formulated in [14] and used in Part 1 of this
article, for single-row falling film condensation on plain and
enhanced tubes, correlated the heat flux as a function of the film
Reynolds number and the wall temperature difference, when
there was no slinging, as

5000

0

0

500

1000

1500
2000
2500
3000
3500
Film Reynolds number, Re
[−]

4000

BUNDLE PREDICTION METHOD

4500

bottom

qo = (a + cRetop ) T b

Figure 15 Variable state independent results found on tubes 4 and 5 of the
test section: Gewa condensing tube, all heat fluxes for R-134a.

coefficients throughout the Reynolds number range, especially
on tubes 4 and 5, which can be seen in Figure 16. The fact
that this tube was designed for use with R-134a affects the

condensate drainage from the enhancement; this effect coupled
to the redistribution of the flow around tubes 4 and 5 is the
reason why there is an increase in performance. Again, since
the results are relatively heat flux independent, the results for all
heat fluxes have been presented on the same figure.
Finally, for the Gewa tube with R-236fa, the average heat
transfer coefficient measured for tubes 4 and 5 is roughly 13–
13.5 kW/m2 . In the single-row R-236fa results, the average
(without the first [top] tube) was 9 kW/m2 -K (Figures 5–7 of Part
1). Again, the bundle configuration showed a large performance
gain when using R-236fa. Figure 17 shows the results for all

To include the effect of the fraction of condensate that would
be slung off the tubes defined with respect to the critical slinging
angle, the heat flux when there was slinging and the maximum
slinging angle are determined as follows:
θcrit = arcsin

(2)

Retop,n =

(3)

θcrit
Rebottom,n−1
θ

qo = a + c

(4)

θcrit
Retop,n
θ

Tb

(5)

R−236fa, Bundle, Gewa Condensing Tube, tube spacing 38.5mm

25000

20000

20000

mOmSA T4
mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4
nOmSA T5

15000

10000

5000

Heat transfer coefficient [W/m2 K]

25000

2

Heat transfer coefficient [W/m K]

ro
p − ro

θ = d Re + e

R−236fa, Bundle, Turbo Condensing Tube, tube spacing 38.5mm

0

(1)

mOmSA T4
mOmSA T5
mOnSA T4
mOnSA T5
nOmSA T4
nOmSA T5

15000

10000

5000

0

500

1000
1500
2000
Film Reynolds number, Re

bottom

2500
[−]

3000

3500

0

0

500

1000
1500
2000

Film Reynolds number, Re

bottom

Figure 16 Variable state independent results found on tubes 4 and 5 of the
test section: Turbo condensing tube, all heat fluxes for R-236fa.

heat transfer engineering

2500
[−]

3000

3500

Figure 17 Variable state independent results found on tubes 4 and 5 of the
test section: Gewa condensing tube, all heat fluxes for R-236fa.

vol. 31 no. 10 2010


M. CHRISTIANS ET AL.

817

Table 1 Coefficients in Eqs. (1)–(5) and relative errors of the prediction
method (using the first set of parameter constraints) for the bundle data

R-134a

R-236fa
R-134a
R-236fa

22,000
11,800
14,350
24,050

0.8199 −0.1605
0
0.9588
2.4303
0
1.112
−0.409
0
0.886 −33.671 0.0023

0
0
0
0

1.63
3.90
0.96
2.21

σ

[%]
13.80
22.00
10.2
15.40

A more detailed overview of this method is given in both Part
1 and [14].

Table 2 Coefficients in Eqs. (1)–(5) and relative errors of the prediction
method (using the second set of parameter constraints) for the bundle data

Turbo
Turbo
Gewa
Gewa

R-134a
R-236fa
R-134a
R-236fa

a
b
c
[W/m2 -K] [ — ] [W/m2 Kb ]
25,350
21,500
24,510
23,950

10000

0.8160
0.9650
1.092
0.866

−14.01
−43.95
−26.43
−44.579

d
[—]

e
[—]

ε
[%]

σ
[%]

0.002 −0.155 1.63 13.70
0.003 −0.605 4.36 23.60
0.001
0.041 1.34 10.64
0.0024 −0.27 1.86 14.80

heat transfer engineering

0

0

500

1000

1500
2000
Film Reynolds number, Re

2500

bottom,n−1

3000

3500

4000

[−]

Figure 18 Comparison of the prediction (method 1) with the bundle T4 and
T5 Turbo condensing tube data using R-134a.

acts to suppress the influence of an increase in the Reynolds
number. For R-236fa (first method) and for the second method
(both R-134a and R-236fa), it is used to magnify the effect of
an increase in the film Reynolds number. The constant a gives
the “height” of the performance plateau, while the temperature
difference exponent b is relatively close to 1 and decreases
the effect of the temperature drop (the resultant b−1 leads to
an exponent both small and negative), by shallowing-out the
prediction. For the same tube (and both refrigerants), the second
method utilizes a nonzero slinging angle constant e (in radians,
equivalent to an angle of –9◦ off the y-axis for R-134a, –35◦ for
R-236fa) to offset the onset of slinging. The small multiplier d in
front of the Reynolds number decreases the effect of the increase
with Reynolds number, and is also used to effectively retard
the onset of slinging. The temperature difference exponent b
R−236fa, Turbo condensing tube, tube spacing 38.50mm
Tube 4
Tube 5
Model

25000

20000

2

Heat transfer coefficient [W/m K]

The preceding method was shown to correctly predict the
results obtained by Gst¨ohl and Thome [14] with the previous

tubes and the same test section and refrigerant; it also performed
well with the new tubes tested, R-134a and R-236fa. Due to this
previous empirical success, it was decided to attempt to fit the
data found with the bundle test section to the same form of
equation.
Using the same nonlinear least-squares algorithm developed
for the single-row results on the data obtained on the fourth and
fifth tubes of the test facility, the resulting empirical coefficients
are presented in Tables 1 and 2. In each table, a set of empirical
coefficients for each tube/refrigerant combination is presented,
with each showing essentially the same goodness of fit.
The main difference between the two methods stems from
the assumptions utilized to run the optimization. For the first
(method 1), it was assumed that the slinging angle should be
equal to 0 for a Reynolds number of 0 (i.e., e = 0), while the
second (method 2) allowed it to find a minimum for a non-null
value by penalizing a zero value of e. For the methods in Table 1
for which both d and e are equal to 0, the prediction method
utilized collapses to the form shown in Eq. (1).
For the Turbo condensing tube/R-134a combination, the fit
predicted 75% of the data within a ±15% error band and 95%
of the data within ±30%. When using R-236fa, the Turbo condensing method predicted only 60% of the data within a ±15%
error band but 90% of the data within ±30%. A comparison of
the first method against the R-134a and R-236fa data is shown
in Figures 18 and 19, respectively.
In the case of the Turbo condensing tube (R-134a data), the
multiplier in front of the Reynolds number c (in the first method)

Ref.

15000

5000

Updated Model

Tube

20000

2

Turbo
Turbo
Gewa
Gewa

Tube 4
Tube 5
Model

25000

Heat transfer coefficient [W/m K]

a
b
c
d
e

ε
Tube Refrigerant [W/m2 -K] [ — ] [W/m2 Kb ] [ — ] [ — ] [%]

R−134a, Turbo condensing tube, tube spacing 38.50mm

15000

10000

5000

0

0

500

1000
1500
Film Reynolds number, Re

2000
[−]

2500

3000

bottom,n−1

Figure 19 Comparison of the prediction (method 1) with the bundle T4 and
T5 Turbo condensing tube data using R-236fa.

vol. 31 no. 10 2010


818

M. CHRISTIANS ET AL.
R−134a, Gewa condensing tube, tube spacing 38.50mm
Tube 4
Tube 5
Model

20000

2

Heat transfer coefficient [W/m K]

25000

15000

10000

5000

0

0

500

1000

1500
2000
Film Reynolds number, Re

2500

bottom,n−1

3000

3500

4000

[−]

Figure 20 Comparison of the prediction (method 1) with the bundle T4 and
T5 Gewa condensing tube data using R-134a.

essentially stays unchanged, as in the first method. Furthermore,
although a is larger in the second method than in the first, the
much larger c increases the effect of the Reynolds number,
producing a difference between the two terms in the parentheses
(a + cRe) that is on the order of the first method.

Turning to the Wieland Gewa condensing tube, the R-134a
fits (shown in Tables 1 and 2) predict 86% of the data within
a ±15% error band and 100% of the data within ±30%. Using
R-236fa, both of the fits presented predict 80% within a ±15%
error band and 95% within ±30%. The assumptions utilized to
run the optimization were the same as those delineated earlier.
A comparison of the first method against the use of R-134a and
R-236fa is shown in Figures 20 and 21, respectively.
The multiplier in front of the Reynolds number, c, in the first
method, again acts to suppress the influence of an increase in the
R−236fa, Gewa condensing tube, tube spacing 38.50mm
Tube 4
Tube 5
Model

20000

2

Heat transfer coefficient [W/m K]

25000

15000

10000

5000

0

0

500

1000
1500
Film Reynolds number, Re

2000
[−]

2500

3000

bottom,n−1

Figure 21 Comparison of the prediction (method 1) with the bundle T4 and
T5 Gewa condensing tube data using R-236fa.

heat transfer engineering

Reynolds number for R-134a. However, for R-236fa (method
1), or both refrigerants in method 2, c is used to magnify the
effect of the Reynolds number, since it is also being simultaneously decreased by the slinging angle multiplier. The constant
a again gives the “height” of the performance plateau, while the
temperature difference exponent b is close to 1 and decreases
the effect of the temperature drop by shallowing-out the prediction. In fact, since the exponent is positive (for R-134a, both
methods), this shows that there is a very slight increase in heat

transfer performance with increase temperature difference (the
exponent corresponds to more or less taking the ninth root of
the temperature difference).
The second method utilizes a nonzero slinging angle constant
e (in radians, equivalent to an angle of 2◦ off the y-axis for R134a, and –15◦ for R-236fa) to offset the onset of slinging. The
small multiplier d in front of the Reynolds number decreases
the effect of any increase in Reynolds number, and is also used
to effectively retard the onset of slinging. The temperature difference exponent b essentially stays unchanged as in the first
method. Furthermore, although a is larger in the second method
than in the first, the much larger c increases the effect of the
Reynolds number.
In summary, for the two tubes test, both methods developed
resulted in essentially the same mean relative error and standard
deviation of the prediction. However, method 1 is recommended
for use, as the fact that e is set to 0 has physical meaning.

CONCLUSIONS
Modifications were made to the falling film facility such that
a bundle configuration of tubes could be tested under condensation conditions. A large database of results was gathered from
the ensuing experimental campaign. It was found that for this
particular tubes and bundle configuration, R-134a performs better than R-236fa, since these tubes have been optimized for use
with R-134a. However, for the Turbo condensing tube, the difference in performance between the two refrigerants was only
around ±2.5 kW/m2 -K on average for tubes 4 and 5; the large
increase in performance compared to the single-row data of Part
1, when using R-236fa, was not expected. The difference in performance when using the Gewa enhanced condensing tube also
was remarkably lower than expected. Furthermore, it was found
that when using R-134a as the test refrigerant, the largest bundle
effect was experienced when both the auxiliary water side-array
circuits and the glycol side-overfeed circuits were active, although tubes 4 and 5 were shown to be essentially independent
of the side flow states. The first tubes of the bundle showed a

performance decrease when using R-134a, while with R-236fa
it was found that the results measured were of the same order
as the original single-row data. In the case of R-134a, it seems
plausible that there is condensate holdup (flooding) around the
first tube.
Visual comparison of these bundle data with the results found
in the single-row test section experimentation shows that the
vol. 31 no. 10 2010


M. CHRISTIANS ET AL.

method proposed by [14] involving slinging of the liquid film
off the tube could be modified to predict the R-134a data best.
In particular, the trends of the bundle results (when viewed as
an ensemble) more closely resemble those found for the TurboChil low-fin tube, which had a flatter performance over a large
Reynolds number range, but where results were dependent on
the position in the column itself [15].
The heat transfer method developed by Gst¨ohl and Thome
[14] was modified to fit the data gathered for the bundle configuration. The measured results from all six tubes were used
when developing the single-row prediction in Part 1, while only
the fourth and fifth tube data were utilized in the bundle configuration, due to “entrance” and “exit” effects on the other tube
rows.
The complexity of the trends in tubes from 1 to 6 in the
bundle suggests that local observation of the flows between the
tubes would be valuable to gain a physical insight into the liquid
distribution process.

NOMENCLATURE
a

b
c
d
e
p
q
r
Re
T

prediction method constant, W/m2 -K
prediction method constant
prediction method constant, W/m2 -K
prediction method constant
prediction method constant
center to center tube pitch, m
local heat flux relative to a surface, W/m2
tube radius, m
film Reynolds number, 4 /µ
temperature, K

Greek Symbols
T
ε

θ
θcrit
σ
µ

condensation temperature difference, Tsat − Tw
mean relative error
film mass flow rate on one side per unit length of tube,
kg/(m s)
slinging angle, rad
critical slinging angle, rad
standard deviation
kinematic viscosity, Pa-s

Subscripts
bottom
n
o
sat
top
w

at the bottom of the tube
number of rows measured from top row
external side at fin tip
saturated conditions
at the top of the tube
wall
heat transfer engineering

819

REFERENCES
[1] Huber, J. B., Rewerts, L. E., and Patee, M. B., Shell-Side Condensation Heat Transfer of R-134a—Part II: Enhanced Tube Performance, Proceedings of the ASHRAE Annual Meeting, Jun 25–29
1994, Atlanta, GA, vol. 100, pp. 248–256, 1994.

[2] Huber, J. B., Rewerts, L. E., and Patee, M. B., Shell-Side Condensation Heat Transfer of R-134a—Part III: Comparison With
R-12, Proceedings of the ASHRAE Annual Meeting, June 25–29
1994, Atlanta, GA, vol. 100, pp. 257–264, 1994.
[3] Huber, J. B., Rewerts, L. E., and Patee, M. B., Shell-Side Condensation Heat Transfer of R-134a—Part I: Finned-Tube Performance, Proceedings of the ASHRAE Annual Meeting, June 25–29
1994, Atlanta, GA, vol. 100, pp. 239–247, 1994.
[4] Cheng, W.-Y., and Wange, C.-C., Condensation of R-134a on
Enhanced Tubes, Proceedings of the ASHRAE Annual Meeting,
June 25–29 1994, Orlando, FL, USA, vol. 100, pp. 809–817, 1994.
[5] Huber, J. B., Rewerts, L. E., and Patee, M. B., Effect of R-134a Inundation on Enhanced Tube Geometries, ASHRAE Transactions,
vol. 102, no. 2, pp. 285–296, 1996.
[6] Belghazi, M., Bontemps, A., and Marvillet C., Condensation Heat
Transfer on Enhanced Surface Tubes: Experimental Results and
Predictive Theory, Journal of Heat Transfer, vol. 124, no. 4, pp.
754–761, 2002.
[7] Belghazi, M., Bontemps, A., and Marvillet, C., Experimental
Study and Modelling of Heat Transfer During Condensation of
Pure Fluid and Binary Mixture on a Bundle of Horizontal Finned
Tubes, International Journal of Refrigeration, vol. 26, no. 2, pp.
214–223, 2003.
[8] Belghazi, M., Bontemps, A., Signe, J. C., and Marvillet, C., Condensation Heat Transfer of a Pure Fluid and Binary Mixture Outside a Bundle of Smooth Horizontal Tubes. Comparison of Experimental Results and a Classical Model, International Journal
of Refrigeration, vol. 24, no. 8, pp. 841–855, 2001.
[9] Honda, H., Fujii, T., Uchima, B., Nozu, S., and Nakata, H., Condensation of Downward Flowing R-114 Vapor on Bundles of
Horizontal Smooth Tubes, Heat Transfer Japanese Research, vol.
18, pp. 31–52, 1989.
[10] Honda, H., Takamatsu, H., Takada, N., and Makishi, O., Condensation of HCFC123 in Bundles of Horizontal Finned Tubes:
Effects of Fin Geometry and Tube Arrangement, International
Journal of Refrigeration, vol. 19, no. 1, pp. 1–9, 1996.
[11] Honda, H., Takamatsu, H., and Takada, N., Experimental Measurements for Condensation of Downward-Flowing R123/R134a
in a Staggered Bundle of Horizontal Low-Finned Tubes With Four
Fin Geometries, International Journal of Refrigeration, vol. 22,

no. 8, pp. 615–624, 1999.
[12] Honda, H., Takamatsu, H., and Kim, K., Condensation of CFC-11
and HCFC-123 in In-Line Bundles of Horizontal Finned Tubes;
Effect of Fin Geometry, Journal of Enhanced Heat Transfer, vol.
1, no. 2, pp. 197–209, 1994.
[13] Honda, H., Takata, N., Takamatsu, H., Kim, J. C., and Usami, K.,
Condensation of Downward-Flowing HFC134a in a Staggered
Bundle of Horizontal Finned Tubes: Effect of Fin Geometry, International Journal of Refrigeration, vol. 25, no. 1, pp. 3–10,
2002.
[14] Gst¨ohl, D., and Thome, J. R., Film Condensation of R-134a on
Tube Arrays With Plain and Enhanced Surfaces: Part II, Prediction Methods, Journal of Heat Transfer, vol. 128, pp. 33–
43, 2006.

vol. 31 no. 10 2010


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M. CHRISTIANS ET AL.

[15] Gst¨ohl, D., and Thome, J. R., Film Condensation of R-134a on
Tube Arrays With Plain and Enhanced Surfaces: Part I, Experimental Heat Transfer Coefficients, Journal of Heat Transfer, vol.
128, pp. 21–32, 2006.
[16] NIST, NIST Thermodynamic Properties of Refrigerants and Refrigerant Mixtures Database, ver. 8.0, Gaithersburg, MD, 2007.
Marcel Christians is a Ph.D. student at the Laboratory of Heat and Mass Transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL),
Switzerland. He received his B.Eng. and M.Eng. (mechanical) degrees at the University of Pretoria, South
Africa, where his thesis topic covered in-tube condensation of refrigerants in the intermittent flow regime.
His current research is on falling film flow visualization, as well as falling film evaporation and condensation heat transfer on bundles of enhanced tubes.
Mathieu Habert performed his Ph.D. thesis on
falling film evaporation on single rows and bundles

of plain and enhanced tubes at the Laboratory of Heat
and Mass Transfer at the Swiss Federal Institute of
Technology in Lausanne (EPFL), Switzerland, completing his degree in February 2009. Currently, he is
chief technical officer of CHS in Gland, Switzerland.

heat transfer engineering

John R. Thome has been a professor of heat and
mass transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, since 1998.
His primary interests of research are two-phase flow
and heat transfer, covering boiling and condensation of internal and external flows, two-phase flow
patterns and maps, experimental techniques on flow
visualization and void fraction measurement, and
more recently two-phase flow and boiling in microchannels. He received his Ph.D. at Oxford University, England, in 1978 and was formerly an assistant and associate professor at Michigan State University. He left in 1984 to set up his own international engineering consulting company. He is the author of four books,
Enhanced Boiling Heat Transfer (Taylor & Francis, 1990), Convective Boiling
and Condensation (Oxford University Press, 1994, 3rd ed., with J. G. Collier), Wolverine Engineering Databook III (2004), and Nucleate Boiling on
Micro-Structured Surfaces (with M. E. Poniewski, 2008), which are now available free at and
He received the ASME
Heat Transfer Division’s Best Paper Award in 1998 for a three-part paper on flow boiling heat transfer published in the Journal of Heat Transfer. He also authored the chapter “Boiling” in the new Heat Transfer Handbook (2003). He is an associate editor of Heat Transfer Engineering and is
chair of ALEPMA (the Aluminum Plate Fin Heat Exchanger Manufacturers
Association).

vol. 31 no. 10 2010


Heat Transfer Engineering, 31(10):821–828, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903547545

Dropwise Condensation Heat
Transfer on Plasma-Ion-Implanted
Small Horizontal Tube Bundles
ALI BANI KANANEH, MICHAEL HEINRICH RAUSCH, ALFRED LEIPERTZ,
¨
and ANDREAS PAUL FROBA
Lehrstuhl f¨ur Technische Thermodynamik, Universit¨at Erlangen-N¨urnberg, Erlangen, Germany

Stable dropwise condensation of saturated steam was achieved on stainless-steel tube bundles implanted with nitrogen ions
by plasma ion implantation. For the investigation of the condensation heat transfer enhancement by plasma ion implantation,
a condenser was constructed in order to measure the heat flow and the overall heat transfer coefficient for the condensation
of steam on the outside surface of tube bundles. For a horizontal tube bundle of nine tubes implanted with a nitrogen ion dose
of 1016 cm−2 , the enhancement ratio, which represents the ratio of the overall heat transfer coefficient of the implanted tube
bundle to that of the unimplanted one, was found to be 1.12 for a cooling-water Reynolds number of about 21,000. The heat
flow and the overall heat transfer coefficient were increased by increasing the steam pressure. The maximum overall heat
transfer coefficient of 2.22 kW·m−2 ·K−1 was measured at a steam pressure of 2 bar and a cooling-water Reynolds number
of about 2,000. At these conditions, more dropwise condensation was formed on the upper tube rows, while the lowest row
received more condensate, which converted the condensation form to filmwise condensation.

INTRODUCTION
Dropwise condensation (DWC) can be described as a phenomenon of incomplete wettability of a surface. The wettability
of a surface is mostly responsible for the formation of a certain type of condensation and has a very strong effect on the
performance of the respective heat transfer process. As firstly
discovered by Schmidt et al. [1], the heat transfer coefficient for
DWC of steam can be up to one order of magnitude larger in
comparison with filmwise condensation (FWC). This can result
in a reduction of the condenser size and thus in a decrease of
capital costs. Furthermore, the operating costs are also lower
due to the reduction of the pressure losses on both the cooling
and condensation side. Although the conditions necessary for

promoting DWC have been well known for several decades and
experiments with coatings as promoters have been carried out
successfully, at least in part, the application of DWC is currently
The authors gratefully acknowledge the financial support for parts of this
work by the German National Science Foundation (DFG, Deutsche Forschungsgemeinschaft).
Address correspondence to Prof. Dr.-Ing. Andreas Paul Fr¨oba, Lehrstuhl f¨ur
Technische Thermodynamik, Universit¨at Erlangen-N¨urnberg, Am Weichselgarten 8, D-91058 Erlangen, Germany. E-mail:

still in a testing phase. The reason for this is, on the one hand,
that the implementation of condensers with DWC surfaces is
connected with a large financial expenditure, and on the other
hand, that long time stability of DWC has not been achieved
with most of the tested methods so far.
Different methods were already examined to reduce the wettability of the condenser surface by applying fatty acids or oils
[2, 3] or coatings with low surface free energy materials like
organics [4, 5] and polymers [6]. At LTT-Erlangen, diamondlike carbon (DLC) coatings and direct modification of the metal
surfaces by ion implantation are studied [7]. The latter method
is considered to reduce the surface free energy of the metal and
was applied for the first time by Zhao et al. [8, 9] using ion
implantation of N, Ar, He, H, and Cr in copper tubes. In another
work by Choi [10], stable DWC could be generated on metallic
surfaces by an appropriately implemented ion beam implantation process with ion doses of 1015 up to 1017 cm−2 , using nitrogen ions. In the same work, measurements on ion-implanted
condenser plates resulted in condensation heat transfer coefficients up to 17 times larger than those predicted by Nußelt’s
theory for FWC. Recent work points out that an enhancement
factor between 2 and 6 depending on the surface subcooling
and the condenser material seems to be a more realistic value
[11, 12].

821

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A. B. KANANEH ET AL.

DWC on tube bundles was also examined by different authors
using the method of ion plating technology and ion beam implantation. A horizontal tube bundle condenser was constructed
in the year 1987 in Dalian Power Station by Zhao et al. [9] to
maintain DWC using a combined method consisting of ion plating and ion beam treatment with Cr and N on the outer surface
of the tubes. The condenser was operated for about 2 years,
after which some of the tubes at the steam entrance were damaged due to a mechanical constructional defect [13]. Zhao et al.
[14] studied FWC and DWC of steam in vertical and horizontal U-type condensers with a steam pressure of 1.2 to 1.8 bar.
Each condenser contained 7 U-type 70Cu-Ni30 white copper
tubes with an outside diameter of 16 mm and a length of 1 m
treated with activated reactive-magnetron sputtering ion plating
of Cr+ , N+ , and C2 H6 . A small bundle of magnetron sputtering
ion plating-treated tubes was investigated by Burnside and Zhao
[15]. The overall heat transfer coefficients for the treated tubes
were 62 to 81% larger in comparison with the untreated ones.
The implementation of the method of plasma ion implantation represents a further development of previously investigated
surface treatment methods, particularly aiming at technical applications. Plasma ion implantation is a pulsed process and induced by surrounding the sample with plasma, which has been
created using a high voltage, and accelerating the cations in
the plasma onto the substrate by charging it negatively. The
advantage of this technique is the possibility of achieving simultaneous implantation of the tube surface from all directions
more easily than by directed ion beam implantation. In an earlier
work [16], stable DWC was achieved on plasma-ion-implanted
single horizontal stainless-steel tubes implanted with nitrogen
ion doses of 1015 and 1016 cm−2 . In this work, plasma ion implantation is used for achieving stable DWC on condenser tube
bundles. The increase in the heat flow and in the overall heat
transfer coefficient for the condensation of saturated steam on

these tubes is determined experimentally.

Figure 1 Equilibrium droplet and contact angle on a horizontal surface.

energy γsurf is given by
γsurf = Usurf − T Ssurf

(1)

which can be decreased both by reducing the internal energy of
the surface Usurf and by increasing its entropy Ssurf . A fundamental approach for explaining the effects of ion implantation
concerning the adjustment of DWC by Zhao and Burnside [13]
suggests that implantation of foreign elements into the surface
can increase Ssurf . Furthermore, if the implanted elements have
higher energy, the bonding energy in the surface layers will
be decreased and hence Usurf will be reduced. The higher the
energy of the elements implanted, the larger is the decrease in
the surface free energy of the implanted surface. Several other
approaches are provided by the same authors, all of them resulting in a reduced surface free energy of the metal. In contrast,
recent experimental results with titanium surfaces show that the
surface free energy criterion often fails in predicting DWC. Instead, nucleation processes on places with locally altered surface
chemistry and induced microscopic surface roughness seem to
be another possible reason for the appearance of DWC [12, 18].

EXPERIMENTAL

WETTABILITY OF THE SURFACE AND ION
IMPLANTATION
In general, the wettability of a solid surface depends on the
interfacial tensions of the phase boundaries between solid and

liquid, solid and gas, and liquid and gas. A liquid droplet on
a plane horizontal solid surface attains an equilibrium shape
characterized by the equilibrium contact angle as shown in
Figure 1.
From the surface free energy of a solid, which is equivalent to
the interfacial tension of the phase boundary between solid and
vacuum, it can be estimated whether a liquid wets a surface or
not. When the surface free energy of a solid is below 40 mN. m−1 ,
it is relatively unwettable by water. If its surface free energy is
larger than 60 mN. m−1 , the surface will be wettable and a water
drop will spread with a low contact angle [17]. The surface free
heat transfer engineering

Experiments have been executed to quantitatively describe
the heat transfer enhancement caused by the adjustment of stable
DWC of steam on ion implanted horizontal tube bundles. For
this, an experimental condenser has been constructed to measure
the heat flow and the overall heat transfer coefficient on bundles
with different numbers of tubes and tube arrangements. The
experimental apparatus consists of four main parts, namely, an
electric evaporator with automatic water supply, a condenser
test cell, a cooling-water cycle, and a condensate collection
and recycling system. A schematic diagram of the experimental
apparatus is shown in Figure 2.
The tubular condenser used in this work can contain a bundle
of nine horizontal tubes (3 rows × 3 columns). The condenser
tubes have a length of 500 mm, an outer diameter of 20 mm, and
a wall thickness of 2 mm. For multiple tube experiments, the vertical and horizontal tube pitches are 60 mm. Because of its high
stability against corrosion, stainless steel X10CrNiMo18-9 (material no. 1.4571, thermal conductivity 16.3 W. m−1. K−1 ) was
vol. 31 no. 10 2010