International Journal of Heat and Mass Transfer 55 (2012) 405–412

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International Journal of Heat and Mass Transfer

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Experimental study of convective condensation in an inclined smooth tube. Part

II: Inclination effect on pressure drops and void fractions
Stéphane Lips, Josua P. Meyer ⇑
Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, Private Box X20, Hatfield 0028, South Africa

a r t i c l e i n f o a b s t r a c t

Article history: This article is the second part of a two-part paper, dealing with an experimental study of convective con-
Available online 12 October 2011 densation of R134a at a saturation temperature of 40 °C in an 8.38 mm inner diameter smooth tube in
inclined orientations. The first part concentrates on the flow pattern and the heat transfer coefficients.
Keywords: This second part presents the pressures drops in the test condenser for different mass fluxes and different
Convective condensation vapour qualities for the whole range of inclination angles (downwards and upwards). Pressures drops in a
Inclined two-phase flow horizontal orientation were compared with correlations available in literature. In a vertical orientation,
Pressure drop
the experimental results were compared with pressure drop correlations associated with void fraction
Void fraction
correlations available in literature. A good agreement was found for vertical upward flows but no corre-
lation predicted correctly the measurements for downward flows. An apparent gravitational pressure
drop and an apparent void fraction were defined in order to study the inclination effect on the flow.
For upward flows, it seems as if the void fraction and the frictional pressure drop are independent of
the inclination angle. Apparent void fractions were successfully compared with correlations in literature.
This was not the case for downward flows. The experimental results for stratified downward flows were
also successfully compared with the model of Taitel and Dukler.
Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction pressure drop model for horizontal tubes. Studies on pressure

drops have also been conducted for enhanced tubes [9,10].
The design of condensers in industrial applications requires pre- Few studies about pressure drop during condensation in verti-
dictive tools for the pressure drop that occurs in the tubes. Pressure cal tubes are available in the literature. Experimental data obtained
drop affects the saturation temperature of the refrigerant and thus for these conditions are often compared with pressure drop corre-
can significantly reduce the efficiency of the system [1]. Pressure lations for adiabatic gas–liquid flow. Kim and No [11] compared
drops during convective condensation or evaporation in horizontal their experimental results with the predictions of the modified
tubes were studied by several research teams in the last 10 years. Nusselt theory [12]. They found that the model underpredicted
Ould Didi et al. [2] compared their experimental pressure drop re- the pressure drop by about 25%. Dalkilic et al. [13] compared 13
sults with different correlations available in the literature. Five dif- two-phase pressure drop correlations with their experimental re-
ferent refrigerants were used for a total of 788 data points obtained sults obtained with condensing R134a in a vertical tube (down-
during the evaporation of refrigerants in smooth horizontal tubes. ward flow) at a high mass flux. They found that the model of
They found that the method of Müller-Steinhagen and Heck [3] Cavallini et al. [5] and the model of Chen et al. [14] predicted the
was the best for annular flows while the method of Grönnerud experimental pressure drop well. Both correlations were devel-
[4] gave the best predictions for both intermittent and stratified- oped for a horizontal orientation. However, the comparison of
wavy flows. All the correlations tested were developed for gas–li- experimental data with pressure drop correlations requires the cal-
quid flow and do not take into account the effect of the phase culation of the gravitational and the momentum pressure drops.
change. To improve these correlations, Cavallini et al. [5] applied Dalkilic et al. [15] showed that the choice of the void fraction mod-
the correction factor of Mickley et al. [6] during the condensation el has a strong effect on the two-phase friction factor.
of a refrigerant inside a tube. More recently, Moreno Quibén and Experimental studies on pressure drops and void fractions in in-
Thome [7,8] published a flow pattern-based two-phase frictional clined tubes are very rare, as indicated in a previous paper by Lips
and Meyer [16]. Würfel et al. [17] presented an experimental study
of two-phase flows inside an inclined tube (20 mm inner diameter,
⇑ Corresponding author. Tel.: +27 0 12 420 3104; fax: +27 0 12 362 5124. angle of inclination: 0°, 11°, 30°, 45°, 90°). They measured two-
E-mail address: josua.meyer@up.ac.za (J.P. Meyer). phase friction coefficients, local thicknesses, void fractions and

0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijheatmasstransfer.2011.09.034
406 S. Lips, J.P. Meyer / International Journal of Heat and Mass Transfer 55 (2012) 405–412

Nomenclature

A cross-sectional area (m2) fric frictional

g gravitational acceleration (m/s2) grav gravitational
G mass flux (kg/m2 s) h homogeneous
L length of the tube (m) i interface
LDP distance between the pressure taps (m) in inlet
P pressure (Pa) l liquid
S length of the interface (m2) lines lines between pressure taps and transducer
x vapour quality (–) meas measurement
mom momentum
Greek symbols rh Rouhani and Axelsson
b inclination angle (>0: upward) (rad) out outlet
e void fraction (–) sat saturation
q density (kg/m3) test test condenser
r surface tension (N/m) v vapour
s shear stress (Pa) w wall

Subscripts Superscripts
eq equivalent ⁄ apparent

entrainments for a gas–vapour flow (air-n-heptane) and heat DPmeas, and a correction DPlines, which depends on the inclination
transfer coefficients during condensation of n-heptane in down- angle:
ward flows. They concluded that the inclination angle has no effect
on the pressure drop. Beggs and Brill [18] proposed a correlation to
predict the void fraction for all inclination angles (both downward DPtest ¼ DPmeas þ DPlines ð1Þ
and upward flows). However, data were collected for air-water As the refrigerant is fully vapour in the pressure lines, the pres-
flow in 25 mm and 38 mm diameter tubes and thus the proposed sure drop in the lines can be depicted as:
correlation cannot be extrapolated for condensation of refrigerant
in an 8.38 mm inner diameter tube.
In conclusion, there is a lack of predictive models to determine DPlines ¼ qv gLDp sin b ð2Þ
the pressure drops in inclined tubes during convective condensa-
tion of refrigerant, especially because of the need to know the void
fraction as a function of the inclination angle. The effect of the con- where b is the inclination angle of the test condenser. b is positive
densation process is not clear as most of the correlations presented for upward flows and negative for downward flows.
in the literature were developed for adiabatic gas–liquid flows. The pressure drops in the test condenser were recorded for the
The purpose of this paper is to get a better understanding of the same experimental conditions summarised in Part I (Fig. 2) of this
different phenomena that affect the pressure drops during convec- paper in terms of mass fluxes G and vapour qualities x. In horizon-
tive condensation of refrigerant in inclined tubes. In the first part tal orientation, the conditions correspond to intermittent and
[19] of this two-part paper, an experimental study of flow patterns annular flow patterns at the boundary of the stratified flow regime
and heat transfer coefficients during convective condensation in an of the Thome–El Hajal–Cavallini [20] map. For each data point, the
inclined tube was presented. This second part is dedicated to the measurements were realised for different inclination angles. The
study of the pressure drops and void fractions in the same experi- FP2000 Sensotec differential pressure transducer was calibrated
mental set-up at the same conditions reported in the first part. to an accuracy of 50 Pa. During all the experiments, the saturation
temperature and the heat transfer rate in the test condenser were
2. Data reduction and experimental procedure kept constant at 40 ± 0.5 °C and 200 ± 5 W respectively.

The details of the experimental facility and test condenser were

discussed in detail in Part I by Lips and Meyer [19] and will not be
repeated here. Pressure taps were inserted between the test con-
denser and the sight glasses at each end of the test condenser,
which is described in Part I (Fig. 1) of this paper. The distance be-
tween the two pressure taps was equal to LDP = 1704 ± 2 mm. An
FP2000 Sensotec differential pressure transducer, calibrated to an
accuracy of 50 Pa, was used to measure the pressure drops inside
the inner tube of the test condenser. The pressure lines between
the taps and the transducer were heated with a heating wire to
avoid condensation in the lines. The electrical power dissipated
in the heating wire was controlled by four thermocouples and a
Labview program, which ensured that the temperature of the lines
was between 5 °C and 10 °C higher than the saturation tempera-
ture of the refrigerant in the test condenser.
The actual pressure drops in the test condenser, DPtest, can be
deduced for the raw measurements of the pressure transducer, Fig. 1. Measured pressure drops for different vapour qualities (G = 300 kg/m2 s).
 S. Lips, J.P. Meyer / International Journal of Heat and Mass Transfer 55 (2012) 405–412 407

The frictional pressure drop depends on the flow pattern and

thus can also depend on the inclination angle of the pipe.
The determination of the gravitational, momentum and fric-
tional pressure drops from the measurements requires knowing
the void fraction in the flow. However, measuring directly and
accurately the void fraction in two-phase flows is complicated
and has not been done in this study. According to Thome [21],
the momentum pressure drop can be calculated using Steiner’s
[22] version of the Rouhani and Axelsson [23] drift flux model:

"   #1
0:25
x x 1x 1:18ð1  xÞ½g rðql  qv Þ
erh ¼ ð1 þ 0:12ð1  xÞÞ þ þ
qv qv ql Gq0:5
l

ð7Þ
For the experimental conditions in the present study, the
momentum pressure drop calculated with this correlation was al-
Fig. 2. Measured pressure drops for different mass fluxes (x = 0.5). ways lower than 10% of the frictional pressure drop, so the choice
of void fraction correlation is not of great importance for the
momentum pressure drop determination. Note that, as stated by
3. Effect of inclination angle on pressure drops and void Dalkilic et al. [15], the choice of the void fraction correlation is of
fractions great importance for determining the gravitational pressure drop.
For the horizontal orientation, the gravitational pressure drop is
3.1. Experimental study of pressure drops equal to zero, whatever the void fraction, so it is possible to deter-
mine the frictional pressure drops. Fig. 3 represents a comparison
The pressure drops measured in the test condenser as a function between the experimental frictional pressure drops in horizontal
of the inclination angle are plotted in Fig. 1 for G = 300 kg/m2 s and orientation and the predictions of several correlations and models
for different vapour qualities. An angle of 90° is for vertical down- published in the literature. The model of Moreno Quibén and
ward flow, 0° is for horizontal flow and +90° is for vertical upward Thome [8] best represents the experimental results. This model
flow. The pressure drops increase when the inclination angle in- is a flow pattern-based correlation and was developed for adiabatic
creases because of the gravitational pressure drop. We can note flows and for convective evaporation in smooth tubes. In this
that the increase is stronger for upward flows than for downward study, it was used with the flow pattern map of El Hajal et al.
flows. Furthermore, the smaller the vapour quality, the stronger [20] to predict the flow pattern during convective condensation.
the increase of the pressure drops with the inclination angle. For The other correlations presented in Fig. 3 were developed for adi-
the horizontal and vertical downward orientations, the pressure abatic flows and mostly for annular flow patterns. The correlation
drops increase when the vapour quality increases. However, for of Friedel [24] and the one of Grönnerud [4] agree well with the
vertical upward orientation, the pressure drops decrease when experiments whereas the correlation of Chisholm [25] gives good
the vapour quality increases. results for high pressure drops only, which correspond to annular
Fig. 2 gives the pressure drops as a function of the inclination flow pattern. The homogeneous model, the correlations of
angle for different mass fluxes and for x = 0.5. The different curves Müller-Steinhagen and Heck [3] and those of Lockart–Martinelli
follow the same trend for different mass fluxes. The pressure drops [26] show a higher discrepancy between the predictions and the
increase when the mass flux increases and for upward flows. How- measurements.
ever, the relative inclination effect on the pressure drop is almost Several correlations were developed to predict the pressure
independent of the mass flow. drops in vertical tubes, especially for upward flows. However, to
It is commonly admitted in the literature that the measured be able to compare the experimental results with these correla-
pressure drops, DPtest , are the sum of three different terms: the tions, we have to determine the gravitational pressure drops and
gravitational pressure drop, DP grav , the momentum pressure drop, thus choose a void fraction correlation. Fig. 4 represents the
DPmom , and the frictional pressure drop, DP fric :
DPtest ¼ DPmom þ DPgrav þ DPfric ð3Þ
The momentum pressure drop depends on the kinetic energy at
the inlet and outlet of the tube and thus on the void fraction as a
function of the vapour quality, which depends on the inclination
angle:
" ! ! #
2 ð1  xÞ2 x2 ð1  xÞ2 x2
DPmom ¼ G þ  þ ð4Þ
ql ð1  eÞ qv out
ql ð1  eÞ qv in

The subscripts in and out refer to the inlet and outlet of the tube
respectively. The gravitational pressure drop is directly linked to
the inclination angle b of the tube
DPgrav ¼ qeq gLDp sin b ð5Þ

where qeq is the equivalent density of the fluid. Considering the

homogeneous model, it can be written as:
Fig. 3. Comparison of experimental pressure drops with different correlations for
qeq ¼ ql ð1  Þ þ qv ð6Þ horizontal flow.
408 S. Lips, J.P. Meyer / International Journal of Heat and Mass Transfer 55 (2012) 405–412

an apparent gravitational pressure drop, DP grav , which is the differ-

ence between the pressure drops in inclined and horizontal
orientation:
DPgrav ¼ DPtest  ðDPtest Þb¼0 ð8Þ

The apparent gravitational pressure drop is equal to the actual

gravitational pressure drop only if the frictional and momentum
pressure drops remain constant, whatever the angle of inclination.
Fig. 6 represents the apparent gravitational pressure drop as a
function of the sinus of the inclination angle for G = 300 kg/m2 s
and for different vapour qualities. For upward flows, the apparent
gravitational pressure drops increase linearly with the sinus of the
inclination angles. If we assume that the frictional pressure drop
remains constant in these conditions and according to Eq. (5), it
can mean that the void fraction remains constant, whatever the
Fig. 4. Comparison of experimental pressure drops with different correlations for
inclination angle. However, it is not possible to verify this assump-
vertical upward flow.
tion with the present experimental set-up and it is also possible
that the frictional pressure drop variation compensates the void
comparison of the experimental results for the vertical upward ori- fraction variation. A void fraction sensor is required to confirm this
entation with five different models. The homogeneous model [21] assumption. The apparent gravitational pressure drop also logically
predicts both the void fraction and the pressure drops. The correla- increases when the vapour quality decreases as it leads to a de-
tion of Friedel for vertical upward flow [24] is used with the void crease of the void fraction. For downward flows, the evolution of
fraction correlation of Rouhani and Axelsson [23]. The void fraction the apparent gravitational pressure drops is no longer linear with
correlation of Chisholm [25] is used with the pressure drop corre- the sinus of the inclination angle. It shows that the frictional pres-
lations of Chisholm [25], Chen et al. [14] and Cavallini et al. [5]. All sure drops and/or the void fraction are dependent on the angle of
the correlations represent the experimental results well, except the inclination. Note also that the lowest vapour quality (x = 0.1) does
homogeneous model, which is not valid for flows with a slip ratio not lead to the highest apparent gravitational pressure drop (in
not equal to one, which is the case in the present study. The good absolute value).
agreement shows that the gravitational pressure drops, and thus Fig. 7 represents the effect of the mass fluxes on the apparent
the void fraction, for upward flows are predicted well by the void gravitational pressure drops: the apparent gravitational pressure
fraction correlations. drop as a function of the sinus of the inclination angle is plotted
There are few studies dealing with vertical downward flows, for 3 mass fluxes and for 3 vapour qualities. As for Fig. 6, the behav-
comparatively to vertical upward flows. Fig. 5 represents the com- iour of the flow is different for upward and downward flows: for
parison between the experimental results and the same correla- upward flows, the apparent gravitational pressure drops are al-
tions as those presented in Fig. 4. Only the Friedel correlation most insensitive to the mass flux. On the contrary, for downward
was adapted to the one developed for downward vertical flows flows, the mass flux has a noticeable effect on the pressure drops.
[24]. The Friedel and Chisholm correlations predict quite well the The difference of behaviour between downward and upward
experimental results for high-pressure drops (i.e. high mass fluxes flows can be explained by the flow pattern analysis presented in
and high vapour qualities), but none of the correlations are able to the first part of the article. For upward flows, the flow pattern is
predict the whole range of pressure drops encountered in the mainly intermittent or annular. For intermittent flows, there is a
experiments. The correlations underestimate the pressure drops: strong interaction between the liquid and the vapour phase: the
it means that they overestimate the gravitational pressure and inclination angle has a weak effect on this interaction and the fric-
they underestimate the void fraction for two-phase flow in vertical tional pressure drops and the void fraction remain constant. Annu-
downward tubes. lar flows are mainly lead by shear forces and the gravitational
It has previously been noticed that it is not possible to separate forces are negligible. As a consequence, the inclination angle has
the frictional pressure drop and the gravitational pressure drop also almost no effect on the flow properties. Furthermore, for these
from the experimental measurements. However, we can define two flow patterns, the void fraction is almost insensitive to the

Fig. 5. Comparison of experimental pressure drops with different correlations for Fig. 6. Apparent gravitational pressure drops for different vapour qualities as a
vertical downward flow. function of inclination angle (G = 300 kg/m2 s).
 S. Lips, J.P. Meyer / International Journal of Heat and Mass Transfer 55 (2012) 405–412 409

plotted in Fig. 8 for G = 300 kg/m2 s and for different vapour qual-
ities. For upward flows, the apparent void fraction can be consid-
ered constant, at least for a void fraction higher than 0.25. For
downward flows, the apparent void fraction increases when the
inclination angle increases. For each curve, three markers repre-
senting different correlations are plotted. For b = 0°, the marker
represent the value of the Steiner [22] version of the correlation
of Rouhani and Axelsson [23]. This correlation was developed for
horizontal flows. The void fraction correlation of Chisholm [25],
which is supposed to be independent of the tube orientation, is
plotted for b = 45°. Lastly, the Rouhani and Axelsson correlation
for vertical tubes [23] is plotted for b = 90°. Note that the different
correlations and the apparent void fraction for upward flows fol-
low the same trends. Thus, it would be interesting to further inves-
tigate the link between the apparent and the actual void fraction.
In the same figure is plotted in thick lines the mean apparent void
fraction for upward flows, which is determined by doing a linear
Fig. 7. Effect of the mass flux on the apparent gravitational pressure drop as a regression of the apparent gravitational pressure drop as a function
function of inclination angle. of the sinus of the inclination angle. The range of inclination angles
used for the linear regression is 5–90°, which corresponds to the
range where the curves can be considered as linear. Eqs. (9) and
mass flux. On the contrary, for downward flows, stratified flows oc- (10) are then used to calculate the mean apparent void fraction.
cur: this kind of flow is strongly dependent on the gravitational Fig. 9 represents the same type of curve than that in Fig. 8 but
forces and thus on the inclination angle of the tube. As a conse- for three different mass fluxes and three different vapour qualities.
quence, the slip ratio between the phases, the void fraction and This graph confirms the fact that the mass flux has almost no influ-
the frictional pressure drops strongly depend on the inclination ence on the apparent void fraction as well as on the void fractions
angle. predicted by the correlations.
As for the apparent gravitational pressure drop, different behav-
3.2. Theoretical study of the void fraction iours can be distinguished in terms of apparent void fractions: for
upward flows, the apparent void fraction is almost independent of
From the apparent gravitational pressure drop, it is possible to the inclination angle whereas it depends strongly on the inclina-
determine an apparent void fraction, which is defined as the void tion angle for downward flows and low vapour qualities. For high
fraction that would have led to the apparent gravitational pressure vapour qualities, the apparent void fractions remain almost con-
drop: stant whatever the tube orientation. By means of the observations
ql  q presented in Part I of the present article, it is possible to link these
 ¼ ð9Þ three types of behaviour to the three main types of flow patterns,
ql  qv
namely intermittent, stratified and annular flows respectively. The
where q is the apparent density of the flow: strongest variation of the apparent void fraction is encountered for
low mass fluxes when the tube orientation varies from slightly
DPgrav
q ¼ ð10Þ downwards to slightly upwards. It corresponds to the modification
gLDP sin b of the flow pattern from stratified to intermittent (Fig. 4, Part I).
The apparent void fraction is equal to the actual void fraction The experimental mean apparent void fractions for upward
only if the frictional pressure drops for the inclined orientation flows are plotted in Fig. 10 as a function of the vapour quality for
are the same as those for the horizontal orientation. However, G = 300 kg/m2. The void fractions predicted by different correla-
keeping this limitation in mind, it is interesting to study the tions are also presented. A good agreement is observed between
apparent void fraction as a function of the inclination angle. It is the experimental results and the correlations of Friedel [24] and

Fig. 8. Effect of inclination angle on the apparent void fraction and comparison with
different correlations (G = 300 kg/m2 s). The thick horizontal lines represent the Fig. 9. Effect of the mass flux on the apparent void fraction. The thick horizontal
mean apparent void fraction between 5° and 90°. lines represent the mean apparent void fraction between 5° and 90°.
410 S. Lips, J.P. Meyer / International Journal of Heat and Mass Transfer 55 (2012) 405–412

Fig. 10. Apparent void fraction for horizontal and upward flows and comparison Fig. 11. Pressure drops predicted by the model of Taitel and Dukler compared with
with different correlations (G = 300 kg/m2 s). experimental results (G = 200 kg/m2 s; x = 0.25).

Chisholm [25]. Note that the LMTD void fraction correlation [21],
used by El Hajal et al. [20] for the flow pattern and heat transfer
[27] models of convective condensation in horizontal tubes, does
not represent the measurements well.
In conclusion, the apparent void fraction may be a possible esti-
mation of the actual void fraction for upward flows. The linearity of
the apparent gravitational pressure drops as a function of the sinus
of the inclination angle tends to show that the frictional pressure
drops and the void fraction can be considered constant in these
conditions. This is not the case for downward flows where the
inclination angle has a stronger influence on the flow pattern and
thus on the frictional pressure drop and void fraction. Thus, for
downward flows, the apparent void fraction has not really any
physical significance. A specific analysis has to be conducted for
these configurations, especially to understand the inclination effect
on stratified flows.
Fig. 12. Pressure drops predicted by the model of Taitel and Dukler compared with
experimental results (G = 300 kg/m2 s; x = 0.1).
3.3. Specification of stratified flows

The most-used model for stratified flows in inclined tubes is model has not been developed for condensing flows, there is a good
that of Taitel and Dukler [28]. The model assumes a smooth strat- agreement between the model and the experiments for the data
ified flow with a flat liquid–vapour interface. The momentum bal- point situated in the stratified flow regime.
ance on the vapour phase yields: The model of Taitel and Dukler [28] also allows determining the
  liquid hold-up and the void fraction in the tube. The liquid hold-up
dP is defined as the ratio between the height of liquid in the tube and
AV  ¼ sv w Sv þ si Si þ Av qv g sin b ð11Þ
dL v the tube diameter. A comparison between the flow visualisation
and the liquid hold-up predicted by the model of Taitel and Dukler
and for the liquid phase, it gives: is represented in Fig. 13. The pictures represent an image of the
average height of liquid in the tube and the lines represent the pre-
 
dP diction of the model between b = 60° and b = 15°. Although the li-
Al  ¼ slw Sl þ si Si þ Al ql g sin b ð12Þ quid–vapour interface is wavy, we can note a good agreement
dL l
Taitel and Dukler [28] showed that it is possible to solve these
equations considering that the liquid is immobile compared to
the vapour, which leads to si sv w . This model allows the calculation
of the pressure drop for two-phase flows in slightly inclined tubes.
We can compare the prediction of the model with experimental re-
sults only for stratified flows, i.e. for low vapour qualities and low
mass fluxes. In our experimental database, two sets of conditions
led to stratified flows: G = 200 kg/m2 s with x = 0.25 for 45° 6
b 6 5° and G = 300 kg/m2 s with x = 0.1 for 20° 6 b 6 5°. The
comparison between the experimental pressure drops and the
ones calculated by the Taitel and Dukler model is presented in
Fig. 11 for G = 200 kg/m2 s and x = 0.25 and in Fig. 12 for G = 300
kg/m2 s and x = 0.1. The experimental pressure drop is the sum of
the gravitational and frictional pressure drops, i.e. the measured Fig. 13. Comparison between the flow visualisation and the liquid-hold-up
pressure drop minus the momentum pressure drop. Although the predicted by the Taitel and Dukler model [28].
 S. Lips, J.P. Meyer / International Journal of Heat and Mass Transfer 55 (2012) 405–412 411

upward flows but failed to predict the pressure drops during

downward flows.
A theoretical analysis of the void fraction was also conducted.
An apparent void fraction was calculated from the apparent grav-
itational pressure drops. It appears that for upward flows the void
fraction can be considered constant and the correlations available
in the literature represent the experimental results well. For down-
ward flows, the apparent void fraction cannot be considered an
estimation of the actual void fraction as the frictional pressure
drops seem to depend on the inclination angle.
For slightly inclined orientations and especially for downward
flows, the experimental results were compared successfully with
the model of Taitel and Dukler [28] in terms of pressure drops.
However, this model is limited to stratified flows.
This article highlights the necessity to insert a void fraction sen-
sor in the experimental set-up in order to have a better compre-
Fig. 14. Comparison between the apparent void fraction and the void fraction
predicted by the model of Taitel and Dukler [28] for stratified flow. hension of the effect of the inclination angle on the pressure
drops and void fractions during convective condensation in in-
clined tubes.
between the model and the visualisations. Note that for b = 15°, the
flow is intermittent (the model of Taitel and Dukler is not valid Acknowledgements
anymore as it was developed for stratified flows) and the images
do not represent the average liquid height in the tube well, as The funding obtained from the NRF, TESP, University of Stel-
can be expected. For b = 60°, the liquid–vapour interface is curved lenbosch/University of Pretoria, SANERI/SANEDI, CSIR, EEDSM
and thus the assumption of a flat interface in the Taitel and Dukler Hub and NAC is acknowledged and duly appreciated.
model is not verified. The extension of this model for the whole
range of inclination angles by taking into account the curvature
of the liquid–vapour interface would be a real improvement. This References
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