Stéphane Lips

Josua P Meyer
email: josua.meyer@up.ac.za

Experimental study of convective condensation in an inclined smooth tube. Part I: Inclination effect on flow pattern and heat transfer coefficient

Keywords:

An experimental study of convective condensation of R134a in an 8.38 mm inner diameter smooth tube in inclined orientations is presented. This article, being the first of a two-part paper (the second part concentrates on the pressure drops and void fractions), presents flow patterns and heat transfer coefficients during condensation for different mass fluxes and vapour qualities for the whole range of inclination angles (from vertical downwards to vertical upwards). The results were compared with three flow pattern maps available in literature. It was found that for low mass fluxes and/or low vapour qualities, the flow pattern is strongly dependent on the inclination angle whereas it remains annular for high mass fluxes and high vapour qualities, whatever the tube orientation. The models of flow pattern maps available in the literature did not predict the experimental data well. In the inclination-dependent zone, experiments showed that there is an optimum inclination angle that leads to the highest heat transfer coefficient for downward flow. The heat transfer coefficient is strongly affected by the liquid and vapour distributions and especially by the liquid thickness at the bottom of the tube for stratified flows. Thus developing a mechanistic model of flow pattern maps is the first step in achieving a predictive tool for the heat transfer coefficient in convective condensation in inclined tubes.

Introduction

Convective condensation occurs in many industrial applications such as air-conditioning, refrigeration, automotive and process industries. Increasing the condenser efficiency in these applications saves space and material and limits the refrigerant load. Higher efficiencies of these systems also reduce the running cost and environmental impact.

Convective condensation in horizontal smooth and enhanced tubes [START_REF] Cavallini | Condensation inside and outside smooth and enhanced tubes -a review of recent research[END_REF][START_REF] Liebenberg | A review of flow pattern-based predictive correlations during refrigerant condensation in horizontally smooth and enhanced tubes[END_REF][START_REF] Miyara | Condensation of hydrocarbons -A review[END_REF][START_REF] Dalkilic | Intensive literature review of condensation inside smooth and enhanced tubes[END_REF] has been widely studied and reviewed in the past. However, Lips and Meyer [START_REF] Lips | Two-phase flow in inclined tubes with specific reference to condensation: A review[END_REF] showed in a previous paper that only a few studies deal with condensation in inclined tubes. Some of them are dedicated to the study of thermosyphons or reflux condensers [START_REF] Wang | Condensation heat transfer inside vertical and inclined thermosyphons[END_REF][START_REF] Noie | Effect of inclination angle and filling ratio on thermal performance of a two-phase closed thermosyphon under normal operating conditions[END_REF]. In these systems, vapour and liquid are flowing upwards and downwards respectively. It appears that there is an optimal inclination angle, found to be in the range of 30-45°, which leads to the highest heat transfer coefficients.

An inclination effect on heat transfer coefficients during convective condensation was first noticed by Chato [START_REF] Chato | Laminar condensation inside horizontal and inclined tubes[END_REF]. For downward flows in slightly inclined tubes, increasing the inclination increased the heat transfer coefficient because of the decrease of the liquid depth in the tube. More recently, Wang and Du [START_REF] Wang | Study on laminar film-wise condensation for vapor flow in an inclined small/mini-diameter tube[END_REF] conducted a theoretical and experimental study on laminar film-wise condensation of steam in small inclined tubes (downward flow in tubes with inner diameter between 1.94 and 4.98 mm). They found that the heat transfer coefficients can be increased or decreased when the tube is tilted, depending on the tube diameter, the vapour quality and the mass flux. They explained their results as the effect of the gravity on the thickness of the liquid film. They developed an analytical model to predict the shape of the liquid-vapour interface for a stratified flow pattern and compared their model in terms of heat transfer coefficients with experimental results. The deviations were within a range of -28 to + 20%.

Würfel et al. [START_REF] Würfel | Turbulence transfer processes in adiabatic and condensing film flow in an inclined tube[END_REF] presented an experimental study of two-phase flows inside a 20 mm inner diameter inclined tube. They measured the heat transfer coefficients during condensation of n-heptane in downward flows. They concluded that the heat transfer coefficients increased continuously with increasing inclinations and they developed a correlation taking into account the inclination angle.

According to this correlation, an inclination angle of 35° and one of 90° increased the heat transfer coefficient with 10% and 16% respectively, compared with the horizontal orientation.

Akhavan-Behabadi et al. [START_REF] Akhavan-Behabadi | Condensation heat transfer of R-134a inside a microfin tube with different tube inclinations[END_REF] studied experimentally the effect of the inclination angle of an 8.92 mm inner diameter microfin tube for condensing flow of R134a. They found that the heat transfer coefficients were higher for downward flows than for upward flows. During their experiments, they found that the inclination angle that led to the highest heat transfer coefficient was 30° downwards.

They developed a correlation based on their experimental data.

The different authors explained that the heat transfer coefficients depend on the distribution of the two phases inside the tube. Thus a study of the flow patterns during convective condensation in inclined tubes is required. Nitheanandan and Soliman [START_REF] Nitheanandan | Influence of tube inclination on the flow regime boundaries of condensing steam[END_REF] conducted an experimental study of the effect of the tube inclination on the flow regime boundaries during condensation of steam. They used a 13.8 mm inner diameter copper tube with small angles of inclination (from 10° downwards to 10° upwards). The range of mass fluxes was 20-280 kg/m²s. They found that the influence of the angle of inclination on the annular flow regime boundary was almost insignificant. However, even a small inclination angle has a strong influence on wavy and slug flow regime boundaries. In a following article [START_REF] Nitheanandan | Analysis of the stratified/nonstratified transitional boundary in horizontal and slightly inclined condensing flows[END_REF], they proposed a mechanistic model to predict the transition between stratified and nonstratified flow in their experiments.

Wang et al. [START_REF] Wang | Two-phase flow patterns and transition characteristics for in-tube condensation with different surface inclinations[END_REF] carried out an experimental study of the flow pattern transitions during condensation of R11 in a 6 mm inner diameter tube for the whole range of inclination angles. The mass fluxes ranged from 9 to 123.2 kg/m²s. The authors described the different flow patterns present as a function of the inclination angle and proposed some correlations for the transition characteristics.

As a conclusion, we can note that the inclination effect depends strongly on the mass flux, vapour quality and flow pattern. However, the experimental studies on flow patterns and heat transfer coefficients during convective condensation in inclined tubes are strongly limited in terms of experimental conditions. Thus, more experimental studies are necessary to achieve a good understanding of this kind of flow and to develop predictive tools.

This article presents some experimental results obtained during the convective condensation of R134a in an inclined smooth tube. The first part is dedicated to the description of the experimental set-up and the experimental procedure. In the second part, the experimental results are presented, in terms of flow pattern maps and heat transfer coefficients for different experimental conditions (the varying parameters being the vapour quality, the mass flux and the inclination angle). A comparison of the results with predictions from different models available in the literature is also presented. This paper is part of a two-part paper and focuses on the heat transfer, while the second paper [START_REF] Lips | Experimental study of convective condensation in an inclined smooth tube. Part II: Inclination effect on pressure drop and void fraction[END_REF] focuses on the pressure drops and void fractions.

Experimental set-up

The experimental facility used in this study was adapted from the one already presented in previous work [START_REF] Van Rooyen | Probabilistic flow pattern-based heat transfer correlation for condensing intermittent flow of refrigerants in smooth horizontal tubes[END_REF][START_REF] Suliman | Improved flow pattern map for accurate prediction of the heat transfer coefficients during condensation of R-134a in smooth horizontal tubes and within the low-mass flux range[END_REF], and is therefore only briefly described. The set-up consisted of a vapourcompression cycle circulating the refrigerant R134a with a nominal cooling capacity of 10 kW and with two high-pressure condensation lines: the test line and the bypass line (Fig. 1). Each line had its own electronic expansion valve (EEV). The bypass line was used to control the mass flow through the test line and the test pressure and temperature. The bypass line had one water-cooled heat exchanger whereas the test line was constituted by three water-cooled condensers: a pre-condenser, to control the inlet vapour quality, the test condenser, where the measurements were performed, and the postcondenser, to ensure that the fluid is fully liquid before the EEV. After the EEVs, the lines combined and entered a water-heated evaporator, followed by a suction accumulator and a scroll compressor.

The test condenser consisted of a tube-in-tube counterflow heat exchanger, with water in the annulus and refrigerant on the inside. Its length was L = 1 488 ± 3 mm and the inside channel was a copper tube with an inner diameter of di = 8.38 mm. Cylindrical sight glasses were positioned at the inlet and outlet of the test condenser. They permitted flow visualisation and acted as insulators against axial heat conduction. The glass tube was chosen carefully to have the same inner diameter as the copper tube. The copper tube was connected to the glass tube with a brass housing and a Teflon U-seal to avoid any disturbance of the flow. A high-speed camera (200 fps) was used to record the flow at the exit of the sight glass. On each side of the test section, three pressure taps were inserted between the sight glasses and the test section. A bush was installed over the outside of the tube and was soldered at both ends. It had three fittings into which the capillary tubes could slide and be soldered. It ensured that the size of the taps was not too large and eased the pressure transducer and capillary piping installation. On each side, two of the pressure taps were connected to two different Gems Sensor pressure transducers for the measurements of the refrigerant absolute pressures at the inlet and outlet of the test section. The two remaining pressure taps were connected to an FP2000 Sensotec differential pressure transducer. The distance between the two pressure taps was 1 704 mm. Straight calming sections were positioned before and after the sight glasses. They were 500 mm and 400 mm long respectively and ensured that the flow was fully developed at the inlet of the test condenser and also minimised disturbance of the exit sight glass. The test condenser could be inclined from 90° upwards to 90° downwards by using flexible hoses at the inlet and outlet of the test section. The outer-wall temperature of the inner tube of the test condenser was measured at seven stations, equally spaced. At each station, four holes were drilled on the outside of the inner tube at the bottom, the top and the sides of the tube respectively. In each hole, a thermocouple was placed and soldered. Thermocouples wires went of the test section through T-junctions placed regularly on the outer tube. The refrigerant temperatures were taken at four stations: inlet and outlet of the test section, inlet of the pre-condenser and outlet of the post-condenser. These measurements were taken on the outside of the refrigerant tube. At each station, thermocouple measurements were taken with four T-type thermocouples, equally spaced and soldered onto the tube perimeter. At the inlet and outlet of the test section, the consistency was checked between the refrigerant saturation temperature measured by the thermocouples and the saturation temperature determined with the absolute pressure sensors. On the water side, the water temperature was measured at six stations: the inlet and outlet of the pre-, test (i.e. test condenser) and post-condenser. At each station, thermocouple measurements were taken with three T-type thermocouples, equally spaced and soldered onto the tube perimeter. The temperature measurements were made on an adiabatic and insulated copper tube separated from the test-section with a 10 cm long plastic tube. The mixing of the water with a swirler was sufficient to ensure an accurate bulk temperature measurement. All the thermocouples were calibrated together to an accuracy of 0.1°C.

The refrigerant and water mass flows through the pre-, test and post-condensers were measured with

Coriolis mass flow meters.

Data reduction and experimental procedure

Steady-state conditions were assumed when the energy balance (Eq. ( 1)) was less than 3%, and the temperatures, pressures and mass flows of the system were considered as constant. The temperature stabilization was the limiting parameter and the criterion used was a variation of the mean wall temperature lower than 0.1 K for 10 minutes. Note that a good energy balance ensures that the heat losses to the surroundings are low compared to the heat transfer rates in the three condensers. It also ensures that the temperature measurements are correct on both the refrigerant and water sides. It was unfortunately not possible to check the energy balance for each condenser separately and a fortiori for the test condenser. However, it is reasonable to assume that the heat losses are roughly homogeneous in the three condensers. The fluctuation of the measurements and other calculated properties were statistical monitored for stability.

𝐸𝐵 = |𝑄 𝑟𝑒𝑓 -𝑄 𝑤𝑎𝑡𝑒𝑟 | 𝑄 𝑟𝑒𝑓 (1)
The properties of the refrigerant at the inlet of the pre-condenser and the outlet of the postcondenser were determined by temperature and pressure measurements. From these measurements, the thermophysical properties of the condensing refrigerant were determined by utilising data from a refrigerant property database [START_REF] Refprop | NIST thermodynamic properties of refrigerants and refrigerant mixtures (REFPROP), Version 8.0, NIST Standard Reference Database 23[END_REF]. The heat transfer rate of the refrigerant was determined from the mass flow rate and change in enthalpy between the inlet of the pre-condenser and the outlet of the post-condenser. The heat transfer rate on the water side was obtained from the mass flow rates of the water in the three condensers and the average inlet and outlet temperatures at the inlet and outlet of the condensers.

The inlet vapour quality xin of the test condenser was calculated from the enthalpy of the refrigerant at the inlet of the test condenser htest,in and the enthalpy of the liquid hl and the vapour hv at the same temperature and pressure:

𝑥 𝑖𝑛 = ℎ 𝑡𝑒𝑠𝑡,𝑖𝑛 -ℎ 𝑙 ℎ 𝑣 -ℎ 𝑙 (2)
The enthalpy of the refrigerant at the inlet of the test condenser htest,in was calculated from the enthalpy of the refrigerant at the inlet of the pre-condenser hpre,in (calculated from the pressure and the temperature at the inlet of the pre-condenser), the mass flow of the refrigerant 𝑚̇𝑟 𝑒𝑓 and the heat transfer rate in the pre-condenser Qpre:

ℎ 𝑡𝑒𝑠𝑡,𝑖𝑛 = ℎ 𝑝𝑟𝑒,𝑖𝑛 - |𝑄 pre | 𝑚̇𝑟 𝑒𝑓 (3)
The heat transfer rate through the pre-condenser was calculated from the water mass flow, specific heat capacity and water temperatures at the inlet and outlet. The vapour quality at the exit of the test section was also calculated from Eq. ( 2) except that the enthalpy at the outlet of the test condenser was used instead of the inlet enthalpy, calculated as:

ℎ 𝑡𝑒𝑠𝑡,𝑜𝑢𝑡 = ℎ 𝑡𝑒𝑠𝑡,𝑖𝑛 - |𝑄 test | 𝑚̇𝑟 𝑒𝑓 (4)
The heat transfer rate through the test condenser was calculated from the water mass flow, specific heat capacity and water temperatures at the inlet and outlet. The average vapour quality of the test section was calculated by doing the arithmetic mean of the inlet and outlet vapour qualities: x = (xin + xout)/2. The heat transfer coefficient αcond was calculated by re-arranging Newton's law for condensation considering a constant heat transfer coefficient in the test condenser:

𝛼 𝑐𝑜𝑛𝑑 = | 𝑄 𝑡𝑒𝑠𝑡 𝐴(𝑇 𝑤,𝑖 ̅̅̅̅̅ -𝑇 𝑠𝑎𝑡 ) | ( 5
)
where A is the area of the inner surface of the test condenser inner tube.

where zj is the j th measurement location along the test condenser.

The experimental set-up does not allow the determination of the local heat transfer coefficient.

Averaging the wall and saturation temperature leads to smoothing the variation of the heat transfer coefficient with the vapour quality (that varies between 3.4 % and 11 % across the test-section), with the temperature difference between the wall and the fluid at saturation (that varies with a few Kelvin because of the water temperature variation on the annulus) and with the position on the tube (the wall temperature difference is about 0.2 K between the top and the bottom of the tube). It also hides the saturation temperature variation due to the pressure drop (typically 0.5 K across the test-section).

However, the average heat transfer coefficient on the test-section is a characteristic parameter of the flow and can be studied and compared to correlations. For each experimental condition, the heat transfer coefficient was determined and the flow pattern was visualised for different inclination angles from 90° upwards to 90° downwards. Table 1 summarises the range of the experimental parameters and their fluctuations. The fluctuations represent the range of variation of the parameter for a certain mass flux and vapour quality and for different angles of inclination. After steady-state conditions were assumed to be reached, the different sensor signals were recorded continuously over a period of five minutes (200 points). To avoid any noise measurement, the average of the points was used for the calculation of the fluid properties and the heat transfer coefficients. The experimental uncertainties of the heat transfer coefficients were calculated using the method of propagation of the errors applied to Eq. ( 5). The main part of the uncertainty came from the temperature measurements on the water side for the heat transfer rate uncertainty and on the refrigerant sides for saturation and wall temperature uncertainties. The uncertainties on the averaged temperature measurement were estimated to be 0.1 K for each station on both the refrigerant and temperature sides. It led to an uncertainty of the temperature difference of condensation 𝑇 𝑤,𝑖 ̅̅̅̅̅ -𝑇 𝑠𝑎𝑡 slightly lower to 0.1 K due to the propagation of the errors for the summations and averaging.

Uncertainties induced by the mass flow meters were negligible. Depending on the experimental conditions, the relative uncertainties of the heat transfer coefficients were found to be between 4% and 9%. The experimental uncertainty of the vapour quality is directly linked to the energy balance and is lower than 0.03, which is also lower than the vapour quality variation across the test section. The flow is stratified-wavy (Fig. 3a) when the liquid is mostly located at the bottom of the tube.

Waves occur at the liquid-vapour interface and a thin liquid film can be located at the top of the tube, with small ripples or without. The annular-wavy flow (Fig. 3b) occurs when the thickness of the liquid film at the top of the tube increases: small waves can be present at the surface of this liquid film, but the main part of the liquid is still located at the bottom of the tube. The intermittent flow (Fig. 3c) occurs when the waves in the bottom part of the tube are big enough to reach the top of the tube. The flow is annular (Fig. 3d) when the liquid is located uniformly at the perimeter of the tube and the vapour flows in the tube central core. The churn flow (Fig. 3e) is a highly turbulent flow where slugs of liquid regularly collapse in the central vapour core, leading to dispersed bubbles in the tail of the slugs.

Flow pattern is the result of a balance between gravitational, frictional and capillary forces.

Thus it depends on the fluid properties, the mass flux and the vapour quality, but also on the inclination angle of the tube. Fig. 4 shows some photos of the flow for different vapour qualities and different angles of inclination for a mass flux of 300 kg/m²s. An angle of -90° is for vertical flow downwards, 0° is for horizontal flow and +90° is for vertical flow upwards. For high vapour qualities, the flow becomes more and more annular and is insensitive to the inclination angle. For low vapour qualities, the flow is highly sensitive to the angle of inclination. Stratified flow occurs for slightly downward orientations (negative angles in Fig. 4). For higher inclination angle, intermittent flow is present, whatever the direction of the flow and we observe churn flows for the downward and upward vertical orientations.

Fig. 5 represents the effect of the inclination angle for a constant vapour quality (x = 0.5) and for different mass fluxes. For low mass fluxes, the flow pattern is dependent on the inclination angle but for high mass fluxes, the flow is annular, whatever the tube orientation. To conclude, the inclination effect is strongly dependent on both the mass flux and the vapour quality. [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] for horizontal orientation.

Comparison with Thome-El Hajal-Cavallini flow pattern map

El Hajal et al. [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] proposed a widely used flow pattern map for convective condensation in horizontal tubes. Fig. 6 represents the comparison of the experimental results and our observations of the flow regimes with the Thome-El Hajal-Cavallini flow pattern map [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] for the horizontal orientation. Considering that the experimental points are close to the transitions between the different flow patterns, a good agreement is found between the experimental data and the Thome-El Hajal-Cavallini flow pattern map.

Comparison with flow pattern maps for inclined orientations.

Several flow pattern maps for two-phase flows in inclined tubes have been published in the literature. It is interesting to compare their prediction with the experimental results obtained with condensing R134a.

The Barnea [START_REF] Barnea | A unified model for predicting flow-pattern transitions for the whole range of pipe inclinations[END_REF] flow pattern map is a mechanistic model that aims to predict the transitions between smooth-stratified (SS), stratified-wavy (SW), annular (A), churn (Ch), slug (Sl), bubbly (B), elongated bubbly (EB) and dispersed bubbly (DB) flow patterns for the whole range of inclination angles. However, in order to simplify the map, we considered in this study only the distinction between stratified (S = SS + SW), annular (A) and intermittent (I = Ch + Sl + B + EB + DB) flows.

The Barnea [START_REF] Barnea | A unified model for predicting flow-pattern transitions for the whole range of pipe inclinations[END_REF] flow pattern map has to be built pixel by pixel thanks to a logical path proposed by the author. In conclusion, more experiments are necessary to estimate the accuracy of flow pattern maps as a function of the inclination angles presented in the literature. These maps were developed for adiabatic flow and thus do not take into account the condensation phenomenon. However, we can certainly say that the Barnea [START_REF] Barnea | A unified model for predicting flow-pattern transitions for the whole range of pipe inclinations[END_REF] flow pattern map obviously needs to be adapted for refrigerant flows, whose properties differ strongly from air-water flows. A more comprehensive experimental database is required to build a flow pattern map dedicated specifically to condensing refrigerants in inclined tubes and the Crawford et al. flow pattern map can be a good start to reach this objective.

Effect of inclination angle on heat transfer coefficients

The condensation heat transfer coefficient in the test section was measured for a range of mass fluxes and inclination angles. Fig. 9 shows the comparison of experimental results obtained for the horizontal orientation with three different correlations available in the literature. The correlation of Thome et al. [START_REF] Thome | Condensation in horizontal tubes. Part 2: new heat transfer model based on flow regimes[END_REF] comes from a flow pattern-based model. The Cavallini et al. [START_REF] Cavallini | Condensation in horizontal smooth tubes: a new heat transfer model for heat exchanger design[END_REF] correlation is based on two different regimes, depending on whether the heat transfer coefficient is dependent on the condensation heat flux (ΔT-dependent regime) or not (ΔT-independent flow regime). These two correlations were developed for convective condensation in horizontal tubes only. The correlation of Shah [START_REF] Shah | A general correlation for heat transfer during film condensation inside pipes[END_REF] aims to predict the heat transfer coefficient, whatever the tube orientation. A relatively good agreement is observed between the experimental results and the prediction of the correlations, even if the correlations overestimate the experimental data by about 25%. Some correlations were developed for vertical flows. The correlation of Shah [START_REF] Shah | A general correlation for heat transfer during film condensation inside pipes[END_REF] and the correlation of Dobson and Chato [START_REF] Dobson | Condensation in smooth horizontal tubes[END_REF] were developed for annular flow regimes and are thus independent of the tube orientations. Fig. 10 and Fig. 11 compare the experimental results and the correlations of Shah [START_REF] Shah | A general correlation for heat transfer during film condensation inside pipes[END_REF] and Dobson and Chato [START_REF] Dobson | Condensation in smooth horizontal tubes[END_REF] for upward vertical and downward vertical orientation respectively. The correlations overestimate the data by about 25%, which is the same as that for the horizontal orientation. This deviation may be partially explained by the presence of oil in the refrigerant that tends to decrease the heat transfer coefficient in the condenser. According to previous studies [START_REF] Van Rooyen | Probabilistic flow pattern-based heat transfer correlation for condensing intermittent flow of refrigerants in smooth horizontal tubes[END_REF][START_REF] Suliman | Improved flow pattern map for accurate prediction of the heat transfer coefficients during condensation of R-134a in smooth horizontal tubes and within the low-mass flux range[END_REF] performed on the experimental set-up, the amount of oil can be estimated between 0.5 % and 3%. Another cause of the deviation can come from the temperature measurement uncertainties (especially on the water side because of the low water velocities) and the correlation uncertainties. However, the similarity between the comparisons in horizontal and vertical orientation explains why very few studies have been conducted on the heat transfer in inclined tubes: the difference in terms of heat transfer coefficients between the two types of orientations is lower than the accuracy of the correlations and the discrepancy between the experimental results.

The thermal resistance in a condensation process is mainly induced by the thermal resistance of heat conduction in the liquid film. Thus, the heat transfer coefficient is strongly dependent on the distribution of the liquid in the tube and, as a consequence, on the flow pattern, which can be influenced by the inclination angle. Fig. 12 shows the heat transfer coefficient as a function of the inclination angle for different vapour qualities and a mass flux of 300 kg/m²s. Fig. 13 is a similar graph for different mass fluxes and a vapour quality of 0.5. At high mass fluxes and high vapour qualities, the heat transfer coefficient is independent of the inclination angle. However, for low mass fluxes and low vapour qualities, the heat transfer coefficient is dependent on the inclination angle.

There is an optimum inclination angle that leads to the highest heat transfer coefficient. Depending on experimental conditions, this optimum inclination angle is between -15° and -30° downwards. For low vapour qualities, there is also a specific inclination angle (about 15°) that leads to the lowest heat transfer coefficient for upward flows.

For example, with reference to Fig. 12, for x = 0.1 and G = 300 kg/m²s, αcond,max = 2370 W/m²K (at β = -15°), αcond,min = 1570 W/m²K (at β = -90°) and αcond,β=0° = 1880 W/m²K (at β = 0°). The inclination effect I is equal to 43%.

With this kind of map, we can define a gravity-independent zone where the heat transfer coefficient is independent of the inclination angle (for high x and G), and a gravity-dependent zone where the inclination effect is significant (low x and low G).

The shape of the curves plotted in Fig. 12 and 13 for low vapour qualities and low mass fluxes and especially the presence of minimum and maximum heat transfer coefficient show that the average heat transfer coefficient is the result of several different phenomena, which influence the flow pattern as a function of the inclination angle. Increasing the inclination angle leads to a decrease of the average void fraction in the system because of the gravitational forces that decrease the liquid velocity.

This leads to an increase of the liquid film conduction resistance in the system and thus to a decrease of the heat transfer coefficient. For G = 300 kg/m²s and for low vapour qualities (x = 0.1 and x = 0.25), we observed a plug and slug flow pattern for slightly inclined upward flows. For sharper inclination angles, the flow is more and more turbulent and churn flow pattern appears. Churn flow leads to a better heat transfer coefficient than plug and slug flows because of the instabilities that increase the heat transfer.

For slightly downward flows, the gravitational forces lead to an increase in the liquid velocity and thus to an increase of the void fraction: the flow becomes stratified. The stratified flow pattern leads to the highest heat transfer coefficient because of the presence of the liquid film at the top of the tube. The more the tube is inclined, the thinner the liquid film is at the bottom of the tube and the higher the heat transfer coefficient is. However, the more the tube is inclined, the more the liquidvapour interface is curved. This leads to an increase of the wetted perimeter at the bottom of the tube.

Beyond a certain inclination angle, the heat transfer coefficient decreases because of the decrease of the perimeter occupied by the thin film of condensation at the top of the tube, where most of the condensation occurs. This is highlighted in Fig. 15, which shows flow patterns and heat transfer coefficients for x = 0.1 and G = 300 kg/m²s and for x = 0.25 and G = 200 kg/m²s for downward orientations. A minimum in the wetted perimeter can be observed for an angle of about 45° for both cases. It does not correspond exactly to a maximum for the heat transfer coefficient, which means that the thickness of the condensation film at the top of the tube is also affected by the inclination angle.

The heat transfer coefficient mainly depends on the perimeter occupied by the condensation film and its thickness. For vertical downward orientation, we observed churn flows, which leads to low heat transfer coefficients compared with stratified flows.

In conclusion, the prediction of the heat transfer coefficients for condensing flows in inclined tubes requires a mechanistic model to predict the flow patterns. Then, specific models have to be developed, which depend on the flow pattern. For annular flows, the heat transfer coefficient is not dependent on the inclination angle but for stratified flows, it is important to take into account the inclination effect on the liquid distribution around the perimeter of the tube: three major parameters were highlighted in this study: the void fraction, the curvature of the liquid-vapour interface and the condensation film thickness.

Conclusions

Convective condensation experiments were conducted in a smooth inclined tube for the whole range of inclination angles from vertical downward flow to vertical upward flow. R134a at a saturation temperature of 40°C was used, mass fluxes and vapour qualities ranging from 200 to 600 kg/m²s and 0.1 to 0.9 respectively.

The inclination effect on the flow pattern and heat transfer coefficient was studied. The distribution of the fluids in the tube is the result of a balance between gravitational, shear and capillary forces. It appears that the inclination angle has a strong effect on the liquid distribution in the tube and thus affects the flow patterns and the condensation heat transfer coefficients. An optimal inclination angle that leads to the highest heat transfer coefficient can be found: the increase of heat transfer can be up to 20% for an inclination angle of -15° (downward flow) but the heat transfer coefficient can also be decreased for upward flows. For high mass fluxes and high vapour qualities, the shear forces are predominant: the flow remains annular and the condensation heat transfer coefficient is constant, whatever the angle of inclination.

A comparison of the flow patterns of this study were made with two models available in the literature. It shows that none of them is able to predict correctly the flow pattern transitions for R134a condensing in an inclined 8.38 mm inner diameter smooth tube. It was also shown that the heat transfer coefficient is closely dependent on the flow pattern. These results highlight the necessity to develop new predictive tools, in terms of flow pattern maps and heat transfer correlations, to try to optimise the heat transfer in industrial processes just by inclining the condenser tubes. However, more experimental studies are required to fully understand the different phenomena that influence convective condensation in inclined tubes.

List of figure captions

List of table captions

Table 1 Range of experimental parameters and fluctuations.

  The experiments were conducted for different mass fluxes G, mean vapour qualities x and inclination angles β. The average saturation temperature was kept constant at 40°C and for all the experiments the heat transfer rate in the test condenser was kept constant at Qtest = 200 W by changing the mass flow rate of the water. This heat transfer rate led to a maximum vapour quality difference across the test condenser of 0.11 for the lowest mass flux (G = 200 kg/m²s) to 0.034 for the highest mass flux (G = 600 kg/m²s). Fig.2summarises the matrix of the 13 experimental conditions (mass flux and vapour quality) on the Thome-El Hajal-Cavallini[START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] flow pattern map. For a horizontal orientation, the experimental conditions mainly correspond to intermittent and annular flow patterns at the boundary of the stratified flow regime.

4. Effect of inclination angle on flow patterns 4 . 1 .

 41 Experimental flow visualisationExcept for the recordings made by the high-speed video camera, visual observations were also made. However, no uniform flow pattern identification procedure exists at present and the definition of the flow patterns changes from one author to another. For the present study, five flow patterns have been identified: stratified-wavy, annular-wavy, annular, intermittent and churn. This classification is based on that of Kim and Ghajar[START_REF] Kim | Heat transfer measurements and correlations for air-water flow of different flow patterns in a horizontal pipe[END_REF]. Even if this classification was developed for air-water flow, the same types of flow pattern were observed with R134a. Churn flow pattern regroups the flow patterns named bubbly/slug and annular/bubbly/slug by Kim and Ghajar. Smooth stratified and plug flows have not been encountered during the experiments. Intermittent flows regroup slug and plug flows. In the present paper, churn flow is not included in intermittent flow because it appears only for vertical and near vertical orientations.

Fig. 3

 3 Fig. 3 summarises the different types of flow patterns considered in this study. It represents a concatenation of a small part of several photos recorded in a short period of time. Thus, it is both a spatial and temporal image of the flow pattern. The time length of the sequences in Fig. 3 is 0.15 s.

Fig. 7

 7 shows a comparison of our experimental flow patterns with the Barnea[START_REF] Barnea | A unified model for predicting flow-pattern transitions for the whole range of pipe inclinations[END_REF] flow pattern map for different angles of inclination. The Barnea[START_REF] Barnea | A unified model for predicting flow-pattern transitions for the whole range of pipe inclinations[END_REF] flow pattern map was developed for adiabatic air-water flows and it appears that it fails to predict the flow pattern during the condensation of R134a in an 8.38 inner diameter tube: for downward flows, the model underestimates the mass flux that leads to the transition from stratified to annular flow regimes. For upward flows, a better agreement is observed but more experiments are required to estimate the accuracy of the model.A second flow pattern map available in the literature is that of Crawford et al.[START_REF] Weisman | Flow pattern transitions in vertical and upwardly inclined lines[END_REF][START_REF] Crawford | Two-phase flow patterns and void fractions in downward flow. Part I: steady-state flow patterns[END_REF]. In their map, transitions between annular (An), intermittent (I), bubbly (B) and stratified (S) flows are predicted for adiabatic flow of R113 in 25 mm and 38 mm inner diameter tubes. Fig.8shows a comparison of experimental flow patterns with the Crawford et al. flow pattern map for different inclination angles. A relatively good agreement is found between the experiments and the theoretical flow pattern map for the annular transition. However, the predictions in terms of stratified/intermittent transition do not reflect the experiments. No bubbly flow has been observed during the experiments but according to the Crawford et al. flow pattern map, this kind of flow pattern occurs only for very low vapour qualities.

Fig. 12

 12 Fig.12also shows that for x = 0.1 and G = 300 kg/m²s, the heat transfer coefficient is increased by about 20% at the optimum inclination angle of about -15° compared with the horizontal orientation. However, the inclination effect depends on the vapour quality and the mass flux and the gain becomes negligible at high vapour qualities and mass fluxes.

Fig. 14

 14 Fig. 14 presents a map of the inclination effect on the heat transfer coefficient. The map is drawn on the Thome-El Hajal-Cavallini [19] flow pattern map. The size of the circle represents the inclination effect I, which is defined as the ratio of the difference between the maximum and minimum heat transfer coefficient and the heat transfer coefficient obtained in horizontal orientation: 𝐼 = 𝛼 𝑐𝑜𝑛𝑑,𝑚𝑎𝑥 -𝛼 𝑐𝑜𝑛𝑑,𝑚𝑖𝑛 𝛼 𝑐𝑜𝑛𝑑,𝛽=0°(8)

Fig. 1 .

 1 Fig. 1. Schematic diagram of the experimental set-up (EEV = electronic expansion valve).

Fig. 2 .

 2 Fig. 2. Experimental test points on the Thome-El Hajal-Cavallini [19] flow pattern map (R134a; di = 8.38 mm; Tsat = 40°C).

Fig. 3 .

 3 Fig. 3. The different types of flow patterns considered in this study (R134a, the time length of the sequence is 0.15 s).

Fig. 4 .

 4 Fig. 4. Effect of the inclination angle on the flow pattern for different vapour qualities (R134a, G = 300 kg/m²s).

Fig. 5 .Fig. 6 .

 56 Fig. 5. Effect of the inclination angle on the flow pattern for different mass fluxes (R134a, x = 0.5).Fig. 6. Comparison of experimental flow patterns for the horizontal orientation with the Thome-El Hajal-Cavallini flow pattern map [19]; (a)-(f) refer to the flow patterns in Fig. 4 at an inclination angle of 0° and a mass flux of 300 kg/m²s.

Fig. 7 .

 7 Fig. 7. Comparison of experimental flow patterns with the Barnea [21] flow pattern map (An = Annular, I = Intermittent, S = Stratified).

Fig. 8 .

 8 Fig. 8. Comparison of experimental flow patterns with the Crawford et al. [22,23] flow pattern map (An = Annular, B = Bubbly, I = Intermittent, S = Stratified).

Fig. 9 .

 9 Fig.9. Experimental heat transfer results for horizontal orientation compared with the correlations of Thome et al.[START_REF] Thome | Condensation in horizontal tubes. Part 2: new heat transfer model based on flow regimes[END_REF], Cavallini et al.[START_REF] Cavallini | Condensation in horizontal smooth tubes: a new heat transfer model for heat exchanger design[END_REF] and Shah[START_REF] Shah | A general correlation for heat transfer during film condensation inside pipes[END_REF].

Fig. 10 .

 10 Fig. 10. A comparison between the experimental heat transfer results and different correlations for vertical upward flow.

Fig. 11 .

 11 Fig. 11. A comparison between the experimental heat transfer results and different correlations for vertical downward flow.

Fig. 12 .

 12 Fig. 12. Inclination effect on heat transfer coefficients for different vapour qualities (G = 300 kg/m²s).

Fig. 13 .

 13 Fig. 13. Inclination effect on heat transfer coefficients for different mass fluxes (x = 0.5).

Fig. 14 .

 14 Fig. 14. Map of the inclination effect on heat transfer coefficients drawn on the Thome-El Hajal-Cavallini [19] flow pattern map.

Fig. 15 .

 15 Fig. 15. Flow patterns and heat transfer coefficients for downward flows at low mass fluxes and low vapour qualities.

Fig. 1 .

 1 Fig. 1. Schematic diagram of the experimental set-up (EEV = electronic expansion valve).

Fig. 2 .

 2 Fig. 2. Experimental test points on the Thome-El Hajal-Cavallini [19] flow pattern map (R134a; di = 8.38 mm; Tsat = 40°C).

Fig. 3 .

 3 Fig. 3. The different types of flow patterns considered in this study (R134a, the time length of the sequence is 0.15 s).

Fig. 4 .

 4 Fig. 4. Effect of the inclination angle on the flow pattern for different vapour qualities (R134a, G = 300 kg/m²s).

Fig. 5 .

 5 Fig. 5. Effect of the inclination angle on the flow pattern for different mass fluxes (R134a, x = 0.5).

Fig. 6 .

 6 Fig. 6. Comparison of experimental flow patterns for the horizontal orientation with the Thome-El Hajal-Cavallini flow pattern map [19]; (a)-(f) refer to the flow patterns in Fig. 4 at an inclination angle of 0° and a mass flux of 300 kg/m²s.

Fig. 7 .

 7 Fig. 7. Comparison of experimental flow patterns with the Barnea [21] flow pattern map (An = Annular, I = Intermittent, S = Stratified).

Fig. 8 .

 8 Fig. 8. Comparison of experimental flow patterns with the Crawford et al. [22,23] flow pattern map (An = Annular, B = Bubbly, I = Intermittent, S = Stratified).

Fig. 9 .

 9 Fig. 9. Experimental heat transfer results for horizontal orientation compared with the correlations of Thome et al. [24],Cavallini et al.[START_REF] Cavallini | Condensation in horizontal smooth tubes: a new heat transfer model for heat exchanger design[END_REF] and Shah[START_REF] Shah | A general correlation for heat transfer during film condensation inside pipes[END_REF].

Fig. 10 .

 10 Fig. 10. A comparison between the experimental heat transfer results and different correlations for vertical upward flow.

Fig. 11 .

 11 Fig. 11. A comparison between the experimental heat transfer results and different correlations for vertical downward flow.

Fig. 12 .

 12 Fig. 12. Inclination effect on heat transfer coefficients for different vapour qualities (G = 300 kg/m²s).

Fig. 13 .

 13 Fig. 13. Inclination effect on heat transfer coefficients for different mass fluxes (x = 0.5).

Fig. 14 .

 14 Fig. 14. Map of the inclination effect on heat transfer coefficients drawn on the Thome-El Hajal-Cavallini [19] flow pattern map.

Fig. 15 .

 15 Fig. 15. Flow patterns and heat transfer coefficients for downward flows at low mass fluxes and low vapour qualities.

  Tsat, is the mean saturation temperature of the refrigerant in the test condenser and was obtained by averaging the saturation temperature measured at the inlet and outlet of the test condenser. 𝑇 𝑤,𝑖 ̅̅̅̅̅ , is the mean inner-wall temperature. It is linked to the mean outer-wall temperature of the tube, 𝑇 𝑤,𝑜 ̅̅̅̅̅ , through the thermal resistance of the wall of the copper tube, Rw:

	𝑇 𝑤,𝑜 ̅̅̅̅̅ =	1 𝐿	∑ [( 𝑇 𝑤,𝑜 6 𝑗 + 𝑇 𝑤,𝑜 𝑗+1 2 𝑗=1	) (𝑧 𝑗+1 -𝑧 𝑗 )]
			𝑇 𝑤,𝑖 ̅̅̅̅̅ = 𝑇 𝑤,𝑜 ̅̅̅̅̅ + |𝑄 𝑡𝑒𝑠𝑡 𝑅 𝑤 |	(6)
	with 𝑅 𝑤 = ln(𝑑 𝑜 𝑑 𝑖 ⁄ ) 2𝜋𝑘 𝐶𝑢 𝐿 ⁄	.

𝑇 𝑤,𝑜 ̅̅̅̅̅ was calculated by averaging the outer-wall temperature 𝑇 𝑤,𝑜 𝑗 measured at the seven different stations along the test condenser by means of a trapezoidal numerical integration method:

Table 1

 1 Range of experimental parameters and fluctuations.

	Parameter	Range	Fluctuations
	Tsat	40°C	± 0.5°C
	G	200-600 kg/m²s	± 5 kg/m²s
	x	0.1-0.9	± 0.01
	Qtest	200 W	± 5 W

Acknowledgements

The funding obtained from the NRF, TESP, University of Stellenbosch/University of Pretoria, SANERI/SANEDI, CSIR, EEDSM Hub and NAC is acknowledged and duly appreciated.


Stéphane Lips

Josua P Meyer
email: josua.meyer@up.ac.za

Experimental study of convective condensation in an inclined smooth tube. Part II: Inclination effect on pressure drops and void fractions

Keywords:

This article is the second part of a two-part paper, dealing with an experimental study of convective condensation 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. This second part presents the pressures drops in the test condenser for different mass fluxes and different vapour qualities for the whole range of inclination angles (downwards and upwards). Pressures drops in a horizontal orientation were compared with correlations available in literature. In a vertical orientation, the experimental results were compared with pressure drop correlations associated with void fraction correlations available in literature. A good agreement was found for vertical upward flows but no correlation 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.

Introduction

The design of condensers in industrial applications requires predictive tools for the pressure drop that occurs in the tubes. Pressure drop affects the saturation temperature of the refrigerant and thus can significantly reduce the efficiency of the system [START_REF] Cavallini | In-tube condensation performance of refrigerants considering penalization terms (exergy losses) for heat transfer and pressure drop[END_REF]. Pressure drops during convective condensation or evaporation in horizontal tubes were studied by several research teams in the last 10 years. Ould Didi et al. [START_REF] Ould Didi | Prediction of two-phase pressure gradients of refrigerants in horizontal tubes[END_REF] compared their experimental pressure drop results with different correlations available in the literature. Five different refrigerants were used for a total of 788 data points obtained during the evaporation of refrigerants in smooth horizontal tubes. They found that the method of Müller-Steinhagen and Heck [START_REF] Müller-Steinhagen | A simple friction pressure drop correlation for two-phase flow in pipes[END_REF] was the best for annular flows while the method of Grönnerud [START_REF] Grönnerud | Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators. Part IV: Two-phase flow resistance in boiling refrigerants[END_REF] gave the best predictions for both intermittent and stratified-wavy flows. All the correlations tested were developed for gas-liquid flow and do not take into account the effect of the phase change. To improve these correlations, Cavallini et al. [START_REF] Cavallini | Experimental investigation on condensation heat transfer and pressure drop of new HFC refrigerants (R134a, R125, R32, R410A, R236ea) in a horizontal smooth tube[END_REF] applied the correction factor of Mickley [START_REF] Mickley | Heat, mass, and momentum transfer for flow over a flat plate with blowing or suction[END_REF] during the condensation of a refrigerant inside a tube. More recently, Moreno Quibén and Thome [START_REF] Moreno Quibén | Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part I: Diabatic and adiabatic experimental study[END_REF][START_REF] Moreno Quibén | Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part II: New phenomenological model[END_REF] published a flow pattern-based two-phase frictional pressure drop model for horizontal tubes. Studies on pressure drops have also been conducted for enhanced tubes [START_REF] Cavallini | Heat transfer and pressure drop during condensation of refrigerants inside horizontal enhanced tubes[END_REF][START_REF] Olivier | Pressure Drop During Refrigerant Condensation Inside Horizontal Smooth, Helical Microfin, and Herringbone Microfin Tubes[END_REF].

Few studies about pressure drop during condensation in vertical tubes are available in the literature. Experimental data obtained for these conditions are often compared with pressure drop correlations for adiabatic gas-liquid flow. Kim and No [START_REF] Kim | Turbulent film condensation of high pressure steam in a vertical tube[END_REF] compared their experimental results with the predictions of the modified Nusselt theory [START_REF] Carey | Liquid-vapor phase-change phenomena[END_REF]. They found that the model underpredicted the pressure drop by about 25%. Dalkilic et al. [START_REF] Dalkilic | Comparison of frictional pressure drop models during annular flow condensation of R600a in a horizontal tube at low mass flux and of R134a in a vertical tube at high mass flux[END_REF] compared 13 two-phase pressure drop correlations with their experimental results obtained with condensing R134a in a vertical tube (downward flow) at a high mass flux. They found that the model of Cavallini et al. [START_REF] Cavallini | Experimental investigation on condensation heat transfer and pressure drop of new HFC refrigerants (R134a, R125, R32, R410A, R236ea) in a horizontal smooth tube[END_REF] and the model of Chen et al. [START_REF] Chen | Two-phase pressure drop of air-water and R-410A in small horizontal tubes[END_REF] predicted the experimental pressure drop well. Both correlations were developed for a horizontal orientation. However, the comparison of experimental data with pressure drop correlations requires the calculation of the gravitational and the momentum pressure drops. Dalkilic et al. [START_REF] Dalkilic | Effect of void fraction models on the two-phase friction factor of R134a during condensation in vertical downward flow in a smooth tube[END_REF] showed that the choice of the void fraction model has a strong effect on the two-phase friction factor.

Experimental studies on pressure drops and void fractions in inclined tubes are very rare, as indicated in a previous paper by Lips and Meyer [START_REF] Lips | Two-phase flow in inclined tubes with specific reference to condensation: A review[END_REF]. Würfel et al. [START_REF] Würfel | Turbulence transfer processes in adiabatic and condensing film flow in an inclined tube[END_REF] presented an experimental study of two-phase flows inside an inclined tube (20 mm inner diameter, angle of inclination: 0°, 11°, 30°, 45°, 90°). They measured two-phase friction coefficients, local thicknesses, void fractions and entrainments for a gas-vapour flow (air-n-heptane) and heat transfer coefficients during condensation of n-heptane in downward flows. They concluded that the inclination angle has no effect on the pressure drop. Beggs and Brill [START_REF] Beggs | A study of two-phase flow in inclined pipes[END_REF] proposed a correlation to predict the void fraction for all inclination angles (both downward and upward flows). However, data were collected for air-water flow in 25 mm and 38 mm diameter tubes and thus the proposed 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 the pressure drops in inclined tubes during convective condensation of refrigerant, especially because of the need to know the void fraction as a function of the inclination angle. The effect of the condensation process is not clear as most of the correlations presented in the literature were developed for adiabatic gas-liquid flows.

The purpose of this paper is to get a better understanding of the different phenomena that affect the pressure drops during convective condensation of refrigerant in inclined tubes. In the first part [START_REF] Lips | Experimental study of convective condensation in an inclined smooth tube. Part I: Inclination effect on flow pattern and heat transfer coefficient[END_REF] of this two-part paper, an experimental study of flow patterns and heat transfer coefficients during convective condensation in an inclined tube was presented. This second part is dedicated to the study of the pressure drops and void fractions in the same experimental set-up at the same conditions reported in the first part.

Data reduction and experimental procedure

The details of the experimental facility and test condenser were discussed in detail in Part I by Lips and Meyer [START_REF] Lips | Experimental study of convective condensation in an inclined smooth tube. Part I: Inclination effect on flow pattern and heat transfer coefficient[END_REF] and will not be repeated here. Pressure taps were inserted between the test condenser and the sight glasses at each end of the test condenser, which is described in Part I (Fig. 1) of this paper. The distance between the two pressure taps was equal to LΔP = 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 temperature of the refrigerant in the test condenser.

The actual pressure drops in the test condenser, ΔPtest, can be deduced for the raw measurements of the pressure transducer, ΔPmeas, and a correction ΔPlines, which depends on the inclination angle:

∆𝑃 𝑡𝑒𝑠𝑡 = ∆𝑃 𝑚𝑒𝑎𝑠 + ∆𝑃 𝑙𝑖𝑛𝑒𝑠 (1)
As the refrigerant is fully vapour in the pressure lines, the pressure drop in the lines can be depicted as:

∆𝑃 𝑙𝑖𝑛𝑒𝑠 = 𝜌 𝑣 𝑔𝐿 ∆𝑃 sin 𝛽 ( 2
)
where β is the inclination angle of the test condenser. β is positive for upward flows and negative for downward flows.

The pressure drops in the test condenser were recorded for the same experimental conditions summarised in part I (Fig. 2) of this paper in terms of mass fluxes G and vapour qualities x. In horizontal orientation, the conditions correspond to intermittent and annular flow patterns at the boundary of the stratified flow regime of the Thome-El Hajal-Cavallini [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] map. For each data point, the measurements were realised for different inclination angles. The FP2000 Sensotec differential pressure transducer was calibrated to an accuracy of 50 Pa. During all the experiments, the saturation temperature and the heat transfer rate in the test condenser were kept constant at 40±0.5°C and 200±5 W respectively.

Effect of inclination angle on pressure drops and void fractions

Experimental study of pressure drops

The pressure drops measured in the test condenser as a function of the inclination angle are plotted in Fig. 1 for G = 300 kg/m²s and for different vapour qualities. An angle of -90° is for vertical downward flow, 0° is for horizontal flow and +90° is for vertical upward flow. The pressure drops increase when the inclination angle increases because of the gravitational pressure drop. We can note that the increase is stronger for upward flows than for downward flows. Furthermore, the smaller the vapour quality, the stronger the increase of the pressure drops with the inclination angle. For the horizontal and vertical downward orientations, the pressure drops increase when the vapour quality increases. However, for vertical upward orientation, the pressure drops decrease when the vapour quality increases. It is commonly admitted in the literature that the measured pressure drops, ∆𝑃 𝑡𝑒𝑠𝑡 , are the sum of three different terms: the gravitational pressure drop, ∆𝑃 𝑔𝑟𝑎𝑣 , the momentum pressure drop, ∆𝑃 𝑚𝑜𝑚 , and the frictional pressure drop, ∆𝑃 𝑓𝑟𝑖𝑐 :

∆𝑃 𝑡𝑒𝑠𝑡 = ∆𝑃 𝑚𝑜𝑚 + ∆𝑃 𝑔𝑟𝑎𝑣 + ∆𝑃 𝑓𝑟𝑖𝑐 (3)
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:

∆𝑃 𝑚𝑜𝑚 = 𝐺 2 [( (1 -𝑥) 2 𝜌 𝑙 (1 -𝜀) + 𝑥 2 𝜌 𝑣 𝜀 ) 𝑜𝑢𝑡 -( (1 -𝑥) 2 𝜌 𝑙 (1 -𝜀) + 𝑥 2 𝜌 𝑣 𝜀 ) 𝑖𝑛 ] (4)
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 𝛽 of the tube.

∆𝑃 𝑔𝑟𝑎𝑣 = 𝜌 𝑒𝑞 𝑔𝐿 ∆𝑃 sin 𝛽 (5)
where 𝜌 𝑒𝑞 is the equivalent density of the fluid. Considering the homogeneous model, it can be written as:

𝜌 𝑒𝑞 = 𝜌 𝑙 (1 -𝜀) + 𝜌 𝑣 𝜀 (6)
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 frictional 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 [START_REF] Thome | Engineering Data Book III[END_REF], the momentum pressure drop can be calculated using Steiner's [START_REF] Steiner | Heat transfer to boiling saturated liquids, VDI-Wārmeatlas (VDI Heat Atlas)[END_REF] version of the Rouhani and Axelsson [START_REF] Rouhani | Calculation of void volume fraction in the subcooled and quality boiling regions[END_REF] drift flux model:

𝜀 𝑟ℎ = 𝑥 𝜌 𝑣 [(1 + 0.12(1 -𝑥)) ( 𝑥 𝜌 𝑣 + 1 -𝑥 𝜌 𝑙 ) + 1.18(1 -𝑥)[𝑔𝜎(𝜌 𝑙 -𝜌 𝑣 )] 0.25 𝐺𝜌 𝑙 0.5 ] -1 (7)
For the experimental conditions in the present study, the momentum pressure drop calculated with this correlation was always 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 Dalkilic et al. [START_REF] Dalkilic | Effect of void fraction models on the two-phase friction factor of R134a during condensation in vertical downward flow in a smooth tube[END_REF], the choice of the void fraction correlation is of great importance for determining the gravitational pressure drop.

For the horizontal orientation, the gravitational pressure drop is equal to zero, whatever the void fraction, so it is possible to determine the frictional pressure drops. Fig. 3 represents a comparison between the experimental frictional pressure drops in horizontal orientation and the predictions of several correlations and models published in the literature. The model of Moreno Quibén and Thome [START_REF] Moreno Quibén | Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part II: New phenomenological model[END_REF] best represents the experimental results. This model is a flow pattern-based correlation and was developed for adiabatic flows and for convective evaporation in smooth tubes. In this study, it was used with the flow pattern map of El Hajal at al. [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] to predict the flow pattern during convective condensation. The other correlations presented in Fig. 3 were developed for adiabatic flows and mostly for annular flow patterns. The correlation of Friedel [START_REF] Friedel | Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow[END_REF] and the one of Grönnerud [START_REF] Grönnerud | Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators. Part IV: Two-phase flow resistance in boiling refrigerants[END_REF] agree well with the experiments whereas the correlation of Chisholm [START_REF] Chisholm | Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels[END_REF] gives good results for high pressure drops only, which correspond to annular flow pattern. The homogeneous model, the correlations of Müller-Steinhagen and Heck [START_REF] Müller-Steinhagen | A simple friction pressure drop correlation for two-phase flow in pipes[END_REF] and those of Lockart-Martinelli [START_REF] Lockhart | Proposed correlation of data for isothermal two-phase, two-component flow in pipes[END_REF] show a higher discrepancy between the predictions and the measurements.

Several correlations were developed to predict the pressure drops in vertical tubes, especially for upward flows. However, to be able to compare the experimental results with these correlations, we have to determine the gravitational pressure drops and thus choose a void fraction correlation. Fig. 4 represents the comparison of the experimental results for the vertical upward orientation with five different models. The homogeneous model [START_REF] Thome | Engineering Data Book III[END_REF] predicts both the void fraction and the pressure drops.

The correlation of Friedel for vertical upward flow [START_REF] Friedel | Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow[END_REF] is used with the void fraction correlation of Rouhani and Axelsson [START_REF] Rouhani | Calculation of void volume fraction in the subcooled and quality boiling regions[END_REF]. The void fraction correlation of Chisholm [START_REF] Chisholm | Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels[END_REF] is used with the pressure drop correlations of Chisholm [START_REF] Chisholm | Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels[END_REF], Chen et al. [START_REF] Chen | Two-phase pressure drop of air-water and R-410A in small horizontal tubes[END_REF] and Cavallini et al. [START_REF] Cavallini | Experimental investigation on condensation heat transfer and pressure drop of new HFC refrigerants (R134a, R125, R32, R410A, R236ea) in a horizontal smooth tube[END_REF]. All the correlations represent the experimental results well, except the homogeneous model, which is not valid for flows with a slip ratio not equal to one, which is the case in the present study. The good agreement shows that the gravitational pressure drops, and thus the void fraction, for upward flows are predicted well by the void fraction correlations.

There are few studies dealing with vertical downward flows, comparatively to vertical upward flows. Fig. 5 represents the comparison between the experimental results and the same correlations as those presented in Fig. 4. Only the Friedel correlation was adapted to the one developed for downward vertical flows [START_REF] Friedel | Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow[END_REF]. The Friedel and Chisholm correlations predict quite well the experimental results

for high-pressure drops (i.e. high mass fluxes and high vapour qualities), but none of the correlations are able to predict the whole range of pressure drops encountered in the experiments. The correlations underestimate the pressure drops: it means that they overestimate the gravitational pressure and they underestimate the void fraction for two-phase flow in vertical downward tubes.

It has previously been noticed that it is not possible to separate the frictional pressure drop and the gravitational pressure drop from the experimental measurements. However, we can define an apparent gravitational pressure drop, ∆𝑃 𝑔𝑟𝑎𝑣 *

, which is the difference between the pressure drops in inclined and horizontal orientation:

∆𝑃 𝑔𝑟𝑎𝑣 * = ∆𝑃 𝑡𝑒𝑠𝑡 -(∆𝑃 𝑡𝑒𝑠𝑡 ) 𝛽=0° (8)
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/m²s 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 inclination angle. However, it is not possible to verify this assumption with the present experimental set-up and it is also possible that the frictional pressure drop variation compensates the void fraction variation. A void fraction sensor is required to confirm this assumption. The apparent gravitational pressure drop also logically increases when the vapour quality decreases as it leads to a decrease of the void fraction. For downward flows, the evolution of the apparent gravitational pressure drops is no longer linear with the sinus of the inclination angle. It

shows that the frictional pressure drops and/or the void fraction are dependent on the angle of inclination. Note also that the lowest vapour quality (x = 0.1) does not lead to the highest apparent gravitational pressure drop (in absolute value). Fig. 7 represents the effect of the mass fluxes on the apparent gravitational pressure drops: the apparent gravitational pressure drop as a function of the sinus of the inclination angle is plotted for 3 mass fluxes and for 3 vapour qualities. As for Fig. 6, the behaviour of the flow is different for upward and downward flows: for upward flows, the apparent gravitational pressure drops are almost insensitive to the mass flux. On the contrary, for downward flows, the mass flux has a noticeable effect on the pressure drops.

The difference of behaviour between downward and upward flows can be explained by the flow pattern analysis presented in the first part of the article. For upward flows, the flow pattern is mainly intermittent or annular. For intermittent flows, there is a strong interaction between the liquid and the vapour phase: the inclination angle has a weak effect on this interaction and the frictional pressure drops and the void fraction remain constant. Annular flows are mainly lead by shear forces and the gravitational forces are negligible. As a consequence, the inclination angle has also almost no effect on the flow properties. Furthermore, for these two flow patterns, the void fraction is almost insensitive to the mass flux. On the contrary, for downward flows, stratified flows occur: this kind of flow is strongly dependent on the gravitational forces and thus on the inclination angle of the tube. As a consequence, the slip ratio between the phases, the void fraction and the frictional pressure drops strongly depend on the inclination angle.

Theoretical study of the void fraction

From the apparent gravitational pressure drop, it is possible to determine an apparent void fraction, which is defined as the void fraction that would have led to the apparent gravitational pressure drop:

𝜀 * = 𝜌 𝑙 -𝜌 * 𝜌 𝑙 -𝜌 𝑣 (9)
where 𝜌 * is the apparent density of the flow:

𝜌 * = ∆𝑃 𝑔𝑟𝑎𝑣 * 𝑔𝐿 ∆𝑃 sin 𝛽 (10)
The apparent void fraction is equal to the actual void fraction only if the frictional pressure drops for the inclined orientation are the same as those for the horizontal orientation. However, keeping this limitation in mind, it is interesting to study the apparent void fraction as a function of the inclination angle. It is plotted in Fig. 8 for G = 300 kg/m²s and for different vapour qualities. For upward flows, the apparent void fraction can be considered 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 representing different correlations are plotted. For β = 0°, the marker represent the value of the Steiner [START_REF] Steiner | Heat transfer to boiling saturated liquids, VDI-Wārmeatlas (VDI Heat Atlas)[END_REF] version of the correlation of Rouhani and Axelsson [START_REF] Rouhani | Calculation of void volume fraction in the subcooled and quality boiling regions[END_REF].

This correlation was developed for horizontal flows. The void fraction correlation of Chisholm [START_REF] Chisholm | Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels[END_REF],

which is supposed to be independent of the tube orientation, is plotted for β = 45°. Lastly, the Rouhani and Axelsson correlation for vertical tubes [START_REF] Rouhani | Calculation of void volume fraction in the subcooled and quality boiling regions[END_REF] is plotted for β = 90°. Note that the different correlations and the apparent void fraction for upward flows follow the same trends. Thus, it would be interesting to further investigate 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 regression of the apparent gravitational pressure drop as a function of the sinus of the inclination angle. The range of inclination angles used for the linear regression is -5° to 90°, which corresponds to the range where the curves can be considered as linear. Equations ( 9) and ( 10) are then used to calculate the mean apparent void fraction. Fig. 9 represents the same type of curve than that in The experimental mean apparent void fractions for upward flows are plotted in Fig. 10 as a function of the vapour quality for G = 300 kg/m². The void fractions predicted by different correlations are also presented. A good agreement is observed between the experimental results and the correlations of Friedel [START_REF] Friedel | Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow[END_REF] and Chisholm [START_REF] Chisholm | Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels[END_REF]. Note that the LMTD void fraction correlation [START_REF] Thome | Engineering Data Book III[END_REF],

used by El Hajal et al. [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] for the flow pattern and heat transfer [START_REF] Thome | Condensation in horizontal tubes. Part 2: new heat transfer model based on flow regimes[END_REF] models of convective condensation in horizontal tubes, does not represent the measurements well.

In conclusion, the apparent void fraction may be a possible estimation 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.

Specification of stratified flows

The most-used model for stratified flows in inclined tubes is that of Taitel and Dukler [START_REF] Taitel | A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow[END_REF].

The model assumes a smooth stratified flow with a flat liquid-vapour interface. The momentum balance on the vapour phase yields:

𝐴 𝑣 (- 𝑑𝑃 𝑑𝐿 ) 𝑣 = 𝜏 𝑣𝑤 𝑆 𝑣 + 𝜏 𝑖 𝑆 𝑖 + 𝐴 𝑣 𝜌 𝑣 𝑔 sin 𝛽 (11)
and for the liquid phase, it gives:

𝐴 𝑙 (- 𝑑𝑃 𝑑𝐿 ) 𝑙 = 𝜏 𝑙𝑤 𝑆 𝑙 -𝜏 𝑖 𝑆 𝑖 + 𝐴 𝑙 𝜌 𝑙 𝑔 sin 𝛽 (12)
Taitel and Dukler [START_REF] Taitel | A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow[END_REF] showed that it is possible to solve these equations considering that the Fig. 14 represents a comparison between the model (Eq. ( 9)) and the experimental apparent void fraction determined for the data points corresponding to stratified flows. Although the pressure drops (Fig. 11 and Fig. 12) and the liquid hold-up predictions (Fig. 13) agree with the experiments, the apparent void fraction and the predicted void fractions do not correspond well. This can be due to the fact that the apparent void fraction does not represent the actual void fraction in the flow. The frictional pressure drop cannot be considered independent of the inclination angle. Note that no distinction can be made between frictional and gravitational pressure drop in the Taitel and Dukler model as the two phases are considered separate and the gravitational forces applied differently for each phase. This highlights the necessity to implement a void fraction sensor in the test section in order to further study pressure drops for two-phase flows in inclined tubes.

Conclusions

Convective condensation experiments were conducted in a smooth inclined tube for a range of inclination angles. R134a at a saturation temperature of 40°C was used, mass fluxes and vapour qualities ranging from 200 to 600 kg/m²s and 0.1 to 0.9 respectively.

The inclination effect on the pressure drops was studied experimentally and the results were compared with different correlations available in the literature for the horizontal and vertical orientations. For horizontal orientation, the model of Moreno Quibén and Thome [START_REF] Moreno Quibén | Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part II: New phenomenological model[END_REF] used with the flow pattern map of El-Hajal et al. [START_REF] Hajal | Condensation in horizontal tubes. Part 1: two-phase flow pattern map[END_REF] for convective condensation best represents the experimental results. The correlation of Friedel [START_REF] Friedel | Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow[END_REF] and that of Grönnerud [START_REF] Grönnerud | Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators. Part IV: Two-phase flow resistance in boiling refrigerants[END_REF] also gave good results. For the comparison of pressure drops in vertical tubes, a void fraction correlation had to be chosen. The determination of the momentum and gravitational pressure drop requires the knowledge of the void fraction. The different correlations tested gave a good agreement with experimental data for 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 gravitational 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 downward 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 [START_REF] Taitel | A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow[END_REF] in terms of pressure drops.

However, this model is limited to stratified flows.

This article highlights the necessity to insert a void fraction sensor in the experimental set-up in order to have a better comprehension of the effect of the inclination angle on the pressure drops and void fractions during convective condensation in inclined tubes. Dukler model [START_REF] Taitel | A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow[END_REF].

List of figure captions

Fig. 2

 2 Fig. 2 gives the pressure drops as a function of the inclination angle for different mass fluxes and for x = 0.5. The different curves follow the same trend for different mass fluxes. The pressure drops increase when the mass flux increases and for upward flows. However, the relative inclination effect on the pressure drop is almost independent of the mass flow.

Fig. 8

 8 Fig. 8 but for three different mass fluxes and three different vapour qualities. This graph confirms the fact that the mass flux has almost no influence on the apparent void fraction as well as on the void fractions predicted by the correlations.As for the apparent gravitational pressure drop, different behaviours can be distinguished in terms of apparent void fractions: for upward flows, the apparent void fraction is almost independent of the inclination angle whereas it depends strongly on the inclination angle for downward flows and low vapour qualities. For high vapour qualities, the apparent void fractions remain almost constant whatever the tube orientation. By means of the observations presented in part I of the present article, it is possible to link these three types of behaviour to the three main types of flow patterns, namely intermittent, stratified and annular flows respectively. The strongest variation of the apparent void fraction is encountered for low mass fluxes when the tube orientation varies from slightly downwards to slightly upwards. It corresponds to the modification of the flow pattern from stratified to intermittent (Fig.4, part I).

  liquid is immobile compared to the vapour, which leads to 𝜏 𝑖 = 𝜏 𝑣𝑤 . 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 results 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/m²s with x = 0.25 for -45° ≤ β ≤ -5° and G = 300 kg/m²s with x = 0.1 for -20° ≤ β ≤ -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/m²s and x = 0.25 and in Fig. 12 for G = 300 kg/m²s and x = 0.1. The experimental pressure drop is the sum of the gravitational and frictional pressure drops, i.e. the measured pressure drop minus the momentum pressure drop. Although the model has not been developed for condensing flows, there is a good agreement between the model and the experiments for the data point situated in the stratified flow regime.The model of Taitel and Dukler[START_REF] Taitel | A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow[END_REF] also allows determining the liquid hold-up and the void fraction in the tube. The liquid hold-up is defined as the ratio between the height of liquid in the tube and the tube diameter. A comparison between the flow visualisation and the liquid hold-up predicted by the model of Taitel and Dukler is represented in Fig.13. The pictures represent an image of the average height of liquid in the tube and the lines represent the prediction of the model between β = -60° and β = 15°. Although the liquid-vapour interface is wavy, we can note a good agreement between the model and the visualisations. Note that for β = 15°, the flow is intermittent (the model of Taitel and Dukler is not valid anymore as it was developed for stratified flows) and the images do not represent the average liquid height in the tube well, as can be expected. For β = -60°, the liquid-vapour interface is curved and thus the assumption of a flat interface in the Taitel and Dukler 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 would allow the prediction of a smooth transition between stratified and annular flow patterns.

Fig. 1 .

 1 Fig. 1. Measured pressure drops for different vapour qualities (G = 300 kg/m²s).

Fig. 2 .

 2 Fig. 2. Measured pressure drops for different mass fluxes (x=0.5).

Fig. 3 .

 3 Fig. 3. Comparison of experimental pressure drops with different correlations for horizontal flow.

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Comparison of experimental pressure drops with different correlations for vertical upward flow. Fig. 5. Comparison of experimental pressure drops with different correlations for vertical downward flow.Fig. 6. Apparent gravitational pressure drops for different vapour qualities as a function of inclination angle (G = 300 kg/m²s).

Fig. 7 .Fig. 8 .

 78 Fig. 7. Effect of the mass flux on the apparent gravitational pressure drop as a function of inclination angle.Fig. 8. Effect of inclination angle on the apparent void fraction and comparison with different correlations (G = 300 kg/m²s). The thick horizontal lines represent the mean apparent void fraction between -5° and 90°.

Fig. 9 .

 9 Fig. 9. Effect of the mass flux on the apparent void fraction. The thick horizontal lines represent the mean apparent void fraction between -5° and 90°.

Fig. 10 .

 10 Fig. 10. Apparent void fraction for horizontal and upward flows and comparison with different correlations (G = 300 kg/m²s).

Fig. 11 .

 11 Fig. 11. Pressure drops predicted by the model of Taitel and Dukler compared with experimental results (G = 200 kg/m²s; x = 0.25).

Fig. 12 .

 12 Fig. 12. Pressure drops predicted by the model of Taitel and Dukler compared with experimental results (G = 300 kg/m²s; x = 0.1).

Fig. 13 .

 13 Fig. 13. Comparison between the flow visualisation and the liquid-hold-up predicted by the Taitel and

Fig. 14 .

 14 Fig. 14. Comparison between the apparent void fraction and the void fraction predicted by the model of Taitel and Dukler [28] for stratified flow.

Fig. 1 .

 1 Fig. 1. Measured pressure drops for different vapour qualities (G = 300 kg/m²s).

Fig. 2 .

 2 Fig. 2. Measured pressure drops for different mass fluxes (x=0.5).

Fig. 3 .

 3 Fig. 3. Comparison of experimental pressure drops with different correlations for horizontal flow.

Fig. 4 .

 4 Fig. 4. Comparison of experimental pressure drops with different correlations for vertical upward flow.

Fig. 5 .

 5 Fig. 5. Comparison of experimental pressure drops with different correlations for vertical downward flow.

Fig. 6 .

 6 Fig. 6. Apparent gravitational pressure drops for different vapour qualities as a function of inclination angle (G = 300 kg/m²s).

Fig. 8 .

 8 Fig. 8. Effect of inclination angle on the apparent void fraction and comparison with different correlations (G = 300 kg/m²s).The thick horizontal lines represent the mean apparent void fraction between -5° and 90°.

Fig. 9 .

 9 Fig. 9. Effect of the mass flux on the apparent void fraction. The thick horizontal lines represent the mean apparent void fraction between -5° and 90°.

Fig. 10 .

 10 Fig. 10. Apparent void fraction for horizontal and upward flows and comparison with different correlations (G = 300 kg/m²s).

Fig. 11 .

 11 Fig. 11. Pressure drops predicted by the model of Taitel and Dukler compared with experimental results (G = 200 kg/m²s; x = 0.25).

Fig. 12 .

 12 Fig. 12. Pressure drops predicted by the model of Taitel and Dukler compared with experimental results (G = 300 kg/m²s; x = 0.1).

Fig. 13 .

 13 Fig. 13. Comparison between the flow visualisation and the liquid-hold-up predicted by the Taitel and Dukler model [28].

Fig. 14 .

 14 Fig. 14. Comparison between the apparent void fraction and the void fraction predicted by the model of Taitel and Dukler [28] for stratified flow.

Acknowledgements

The funding obtained from the NRF, TESP, University of Stellenbosch/University of Pretoria, SANERI/SANEDI, CSIR, EEDSM Hub and NAC is acknowledged and duly appreciated.