Convective condensation at low mass flux: Effect of turbulence and tube orientation on the heat transfer

Convective condensation at low mass flux: Effect of turbulence and tube orientation on the heat transfer

International Journal of Heat and Mass Transfer 144 (2019) 118646 Contents lists available at ScienceDirect International Journal of Heat and Mass T...
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International Journal of Heat and Mass Transfer 144 (2019) 118646

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Convective condensation at low mass flux: Effect of turbulence and tube orientation on the heat transfer Marco Azzolin ⇑, Stefano Bortolin, Davide Del Col Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padova, Italy

a r t i c l e

i n f o

Article history: Received 28 May 2019 Received in revised form 2 August 2019 Accepted 25 August 2019 Available online 10 September 2019

a b s t r a c t It is well proved in the literature that gravity affects in-tube condensation heat transfer at low mass flux. Nevertheless very limited data are taken at low mass flux when changing tube orientation, despite the many practical applications. In this paper, convective condensation inside a 3.4 mm inner diameter tube is investigated in horizontal and vertical downflow using R134a as the working fluid. The experiments are performed at low mass flux, between 50 kg m2 s1 and 200 kg m2 s1, which are usually the less investigated despite the relevance of gravity force at such low velocities. The condensation heat transfer coefficient in vertical downflow can be as low as half the value in horizontal flow at the same operating conditions, since gravity acts for the thinning of the liquid film in the horizontal tube. In vertical downflow, the heat transfer coefficients show an early effect of turbulence, thus a new transition criterion is here proposed. Criteria for predicting the relevance of channel orientation on the heat transfer coefficient are also assessed. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Condensation in small diameter channels can be found in many applications such as compact heat exchangers, heat pipes, thermal control in aeronautical/space applications. In the last years, several studies have been performed during condensation inside channels of around 1 mm diameter [1,2]. Nevertheless the number of studies dealing with condensation in small channels that investigate the low mass flux range [3], the effect of the channel inclination [4] and saturation-to-wall temperature difference [5] is very limited. Even less are the available works that, in these working conditions, correlate the condensation heat transfer process with the corresponding two-phase flow pattern [6,7]. The low mass flux conditions (typically around and below 100 kg m2 s1) are very interesting for practical applications. For example, in vapor compression systems, the adoption of inverter-driven compressors with variable speed leads often the system to work far from its design conditions and thus the condenser can be found to operate at low values of mass velocity. Another example: low values of mass velocity can be found in the condenser section of loop heat pipes (LHPs), capillary pumped loops (CPLs) and two-phase loop thermosyphons (TPLTs) making the availability of experimental data and models essential for their correct design.

⇑ Corresponding author. E-mail address: [email protected] (M. Azzolin). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118646 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

At low mass velocity, results obtained with conventional channels cannot be extended to small diameter channels [5,8]. When considering condensation at low mass velocities in small channels or capillaries, different works [9,10] showed that the surface tension and the viscous effect are greater compared to the gravity effect. Recently, Toninelli et al. [11] showed, by numerical simulations, the relative importance of shear, gravity and surface tension during condensation of R134a in two channels having internal diameters equal to 1 mm and 3.4 mm. Garimella et al. [12] developed a model for the prediction of the heat transfer coefficient considering two zones (shear/gravity dominated and shear/surface tension dominated) with the objective to account for the relations between shear, gravity and surface tension forces. Recently, Meyer and Ewim [13] pointed out the lack of studies at low mass fluxes and they measured R134a condensation heat transfer coefficients in a horizontal tube (8.38 mm inner diameter) ranging the mass flux from 50 to 200 kg m2 s1. They found that an effect of the saturation-to-wall temperature difference on the heat flux can be observed when the mass flux was lower or equal to 100 kg m2 s1. The gravity effect on condensation can be investigated on ground by changing the channel inclination or performing experiments in reduced gravity conditions (e.g. parabolic flights). The effect of gravity during condensation has been studied experimentally on ground by changing the orientation of the channel by Lips and Meyer [14] and Olivier et al. [15]. In their papers, they measured the heat transfer coefficient, the void fraction and performed flow visualizations of condensing R134a at different inclinations

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Nomenclature A c d dp/dz e Eo G  G g h JG _ m Pr q Ra Re T U x Y, Y* We Wec

area specific heat inner diameter pressure drop gradient entrained liquid fraction 2 Eötvös number Eo ¼ Dq g d =r mass velocity transitional mass flux standard acceleration due to gravity specific enthalpy superficial velocity of vapor J G ¼ xG=qG mass flow rate Prandtl number heat flow rate mean roughness according to EN ISO 4287:1998/A1 [33] Reynolds number temperature combined experimental uncertainty thermodynamic vapor quality dimensionless inclination parameter Weber number Weber number defined according to [27]

Greek symbols a heat transfer coefficient b inclination angle

(from vertical downward to vertical upward) inside a tube with an internal diameter of 8.38 mm. The minimum mass velocity investigated in these studies was 100 kg m2 s1. In a later work, Ewim et al. [16] extended the investigation to a lower range of mass velocity reaching 50 kg m2 s1. They reported that channel inclination significantly influenced the flow patterns and the heat transfer coefficients: the maximum inclination effect was found at the lowest mass flux tested. Del Col et al. [17] investigated the effect of inclination during condensation of R134a and R32 in a minichannel with an inner hydraulic diameter of 1.23 mm and square cross section. They found that the effect of the channel inclination on the condensation heat transfer coefficient became noteworthy in downflow, at vapor qualities lower than 0.6 and mass velocities lower than a critical value equal to 150 kg m2 s1 for R134a and equal to 200 kg m2 s1 for R32. They also developed a dimensionless correlation using the inclination parameter Y* (Eq. (1)) to predict a gravity dependent region as a function of the working conditions during condensation. The parameter Y* is calculated as:

Y  ¼ 0:185  Eo0:35

 0:65 Dq

qG

x1:748

ð1Þ

where Eo is the Eötvös number, Dq the density difference between the liquid and the vapor phases, qG is the density of the vapor phase and x the vapor quality. The Y* parameter should be compared with the dimensionless inclination parameter Y as reported in Eq. (2) and firstly defined by Taitel and Dukler [18]:

Y¼

Dq  g  sinðbÞ   dp dz

DT, DT

l q qC r

enthalpy difference density difference between the liquid and the vapor phases temperature difference viscosity density vapor core density according to [27] surface tension

Subscripts eq equivalent f friction F film G vapor i corresponding to i-th sub-sector in inlet L liquid LF liquid film m mean ml mean logarithmic out outlet ref refrigerant sat saturation TR transitional w wall

phase. Given a working condition, if Y > Y* some effect of gravity should be expected. Viceversa, if Y < Y*, the heat transfer coefficient during condensation will be not affected by channel orientation. Considering the condensation investigation in microgravity conditions during parabolic flights, Lee et al. [19] measured the heat transfer coefficient inside tubes and visualized the flow pattern during condensation outside tubes. The authors found that, when condensing inside the tube, with inner diameter equal to 7.12 mm, the effect of gravity was very significant particularly at low mass velocities. Azzolin et al. [20] studied convective condensation inside a 3.4 mm diameter channel in microgravity conditions during the 62nd ESA Parabolic Flight Campaign. The working fluid was HydroFluoroEther HFE-7000 (1-methoxyheptafluoropropane) and the mass flow rate ranged between 70 kg m2 s1 and 170 kg m2 s1. The combination of heat transfer coefficient and flow pattern visualizations showed that gravity had a beneficial effect on the heat transfer coefficient by acting on the liquid distribution along the channel perimeter. The present work is aimed at the investigation of R134a convective condensation inside a 3.4 mm diameter channel at low mass flux and two different channel orientations. This paper tries to extend the limited database available for channel diameter between 2 mm and 4 mm at low mass flux (between 50 kg m2 s1 and 200 kg m2 s1). Measurements of the heat transfer coefficient and visualization of the flow pattern have been performed to get a better understanding of the condensation phenomena, with particular attention to the effect of channel orientation and the turbulence in the liquid film.

ð2Þ

f ;G

where b is equal to 0° in horizontal configuration and 90° in vertical downflow, g indicates the standard acceleration due to gravity and   dp is the single-phase friction pressure gradient for the vapor dz f ;G

Dh Dq

2. Experimental apparatus The test facility used in the present work was already employed in previous experimental heat transfer campaigns [21,22] and it has been modified to accommodate a new test section. A schematic

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

3

a)

b)

1st sub-sector

2nd sub-sector 3rd sub-sector

4th sub-sector

5th sub-sector

Glass window

Fig. 1. (a) Experimental test rig: FD (filter dryer); PV (pressure vessel); CFM (Coriolis-effect mass flow meter); TV (throttling valve); MF (mechanical filter); BV (ball valve); P (pressure transducer); DP (differential pressure transducer); T (thermocouple); DT (thermopile). (b) Layout of the test section and 3-D image of a single sub-sector showing the coolant flow passage.

layout of the test rig is reported in Fig. 1a and a short description is provided below. 2.1. Test rig The test rig is made of a refrigerant loop and three auxiliary water loops. In the refrigerant loop, a post-condenser is used to keep the refrigerant subcooled before it enters the filter dryer and the free-oil magnetic drive gear pump. The refrigerant mass flow rate is measured in the subcooled liquid line by a Corioliseffect mass flow meter placed before a tube-in-tube heat exchanger, which is used to vaporize and superheat the fluid during condensation tests. After the evaporator, the refrigerant enters the heat transfer test section where it is partially or fully condensed and the heat is removed using distilled water as secondary fluid. The experimental test section (Fig. 1b) is composed of two heat exchangers: each heat exchanger is fed by a dedicated water loop and equipped with a flow regulating valve and a Coriolis effect mass flow meter. When necessary, the water temperature level in the two hydraulic loops can be set independently using electrical heaters installed after the thermal bath. On the refrigerant circuit the temperatures at the inlet and outlet of the test section are measured with two T-type thermocouples directly immersed in

the fluid flow and the operative pressure is measured at the inlet of the first heat exchanger by means of a relative pressure transducer, whereas two differential pressure transducers with different full scale (1 kPa and 100 kPa) are employed to measure the pressure drop along the test section. 2.2. Test section The test section is made of a copper tube with an internal diameter of 3.4 mm and internal surface roughness (Ra) equal to 0.18 mm. The test section is composed of three parts: two counter-current heat exchangers for heat transfer measurements and a glass window for flow pattern visualization (Fig. 1b). Each heat exchanger is divided in several sub-sectors: the first heat exchanger is 540 mm long and is divided in three sub-sectors; the second heat exchanger is 480 mm long and is divided in two sub-sectors. The sub-sectors have been machined on the external copper tube surface obtaining an enhanced geometry with nine fins (each fin presents two grooves to create the water channel, Fig. 1b). Between one fin and the following one, the grooves are rotated by 90°. This particular geometry on the coolant side has been designed to decrease the water side heat transfer resistance by increasing the external heat transfer area and disturbing the

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boundary layer changing continuously the flow direction. This means that, for a given saturation temperature and water inlet temperature, the temperature difference between the copper wall and the coolant flow is reduced while the temperature difference is higher on the refrigerant side (between the condensing fluid and the wall) which is favorable for a more precise measurement of the heat transfer coefficient. To create the coolant path, Lexan tubes have been used as containment for the water. Del Col et al. [1] successfully applied and validated a similar technique for two phase heat transfer measurements in a channel with an internal diameter equal to 0.96 mm. In each sub-sector, six thermocouples are embedded in the copper wall, inserting them in the second, fifth and eighth fin, as shown in Fig. 1b. Two holes have been done in each fin, in different angular positions. The accommodation of the wall thermocouples is made so that the thermocouple wires do not cross the coolant path. On the water side, two thermocouples and a triple junction thermopile are used to double check the temperature difference of the water at the inlet and outlet of each sub-sector. Since the measurement of the water temperature at the inlet and outlet of a sub-sector is crucial for a precise evaluation of the heat flow rate, some mixers have been placed on the water path before the inlet and after the outlet. Between the two heat exchangers, a borosilicate glass tube has been placed for the visualization of the flow pattern. The glass tube has an internal diameter equal to 3.4 mm and is 200 mm long. Two pressure ports have been soldered at the inlet and outlet of the test section: one at the inlet of the first heat exchanger and one at the outlet of the second heat exchanger. The distance between the two pressure ports is 1080 mm.

3. Data reduction and uncertainty 3.1. Data reduction The profile of refrigerant, wall and water temperatures measured during a condensation test run of R134a at G = 150 kg m2 s1 is reported in Fig. 2. In this example, the refrigerant R134a enters

_ water;i cwater DT water;i qwater;i ¼ m

55

50

Ref IN/OUT

Saturation (p)

Wall

Water

ai ¼

qwater;i A  ðT sat  T w;m Þi

where A is the internal heat transfer area, Tsat and Tw,m are respectively the saturation and the mean wall temperature. The refrigerant saturation temperature along the test section is evaluated starting from the measured pressure at the inlet and outlet and considering a linear behaviour. Actually the pressure drop along the test section is not linear but, considering that the pressure gradient at low mass flux is pretty small, and the saturation-minus-wall temperature difference is pretty large, this assumption can be made without producing a significant error on the heat transfer coefficient. At G = 100 kg m2 s1, the total measured drop during a condensation test is about 20 mbar which corresponds to less than 0.1 K of saturation temperature drop. In each sub-sector the wall temperatures are measured with 6 thermocouples located at different positions. The heat transfer coefficient (Eq. (4)) can be calculated using the mean wall temperature (Tw,m) measured with the third and fourth thermocouple (Fig. 2). Alternatively, it can be evaluated with the mean logarithmic temperature difference (DTml) between the wall and the refrigerant

qwater;i A  ðDT ml Þi 

DT ml ¼

45

Water

30

   T sat;out  T w;in  T sat;in  T w;out ðT sat;out T Þ ln T T w;in ð sat;in w;out Þ

hout;i ¼ hin;i 

25 20 0,2

0,4

0,6

ð5Þ

ð6Þ

In Eq. (6) Tsat,in and Tsat,out are the refrigerant saturation temperature at the inlet and outlet of the considered sub-sector while Tw,in is the mean wall temperature between the first and second thermocouple, Tw,out the mean wall temperature between the fifth and the sixth thermocouple. The enthalpy at the outlet of each sub-sector hout,i can be determined from the heat flow rate, the mass flow rate and the inlet enthalpy (hin,i) of the condensing fluid:

40

0

ð4Þ

where the mean logarithmic temperature difference is defined as:

Refrigerant

35

ð3Þ

_ water,i is the water mass flow rate in the i-th sub-sector, where m DTwater,i the water temperature difference measured by the i-th thermopile and cwater is the water specific heat evaluated at the mean water temperature. The heat transfer coefficient in the i-th sub-sector can be then calculated as:

ai ¼

60

TEMPERATURE [°C]

in the test section at about 56.7 °C, with 16.7 K of superheating and exits from the second heat exchanger as saturated vapor. The water flows in counter-current in the two heat exchangers: in the first heat exchanger, it enters at about 26 °C, flows in three sub-sectors and exits at approximately 35 °C; in the second heat exchanger, the water enters at 27 °C and exits at 31.2 °C after crossing two sub-sectors. As it can be seen from the graph, the dominant thermal resistance is on the refrigerant side. During the heat transfer tests the heat flow rate exchanged between the refrigerant and the water in each sub-sector is evaluated as:

0,8

1

1,2

AXIAL POSITION [m] Fig. 2. Refrigerant, wall and water temperatures measured during condensation test of R134a at G = 150 kg m2 s1 and 40 °C saturation temperature.

qwater;i _ ref m

ð7Þ

In Eq. (7), the enthalpy at the inlet of the test section is evaluated from the measured temperature and pressure using REFPROP 9.1 [23] and the outlet enthalpy from one sub-sector is considered as the inlet value of the following sub-sector. The thermodynamic vapor quality at the outlet of a sub-sector (and inlet of the following one) can be calculated as:

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M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

xout;i ¼

hout;i  hL hG  hL

ð8Þ

The vapor quality x for each sub-sector is calculated as the arithmetic mean value between the inlet and outlet values. To complete the data reduction the following contributions are considered: 1. Dissipated heat flow rate. Even if the test section is well insulated there can be a heat flow rate dissipated towards the ambient. In principle, this heat flux can be reduced keeping the water temperature close to the ambient, but obviously this implies restrictions on the working conditions during tests. Some tests have been performed to evaluate the dissipated heat flow rate for each sub-sector as a function of the water-to-ambient temperature difference. Tests have been done varying the water temperature while on the refrigerant side the test section was vacuumed. As a results, the mean dissipated heat flow rate was about 1 W per sub-sector with a temperature difference of 10 K between the water and the external ambient. 2. Effect of the radial conduction. The effective wall temperature measurement is made 0.6 mm from the internal channel surface, thus the measured temperature can be corrected to account for the conduction resistance in the copper wall. Even though the temperature gradient is quite small, the effect of this conduction resistance is accounted for. 3. Effect of the axial conduction. This effect may promote heat transfer from water to the R134a between the sub-sectors. Each heat exchanger has been divided in several sub-sectors, creating an adiabatic zone (external to the test channel) between two consecutive sub-sectors. At the two edges of each sub-sector, due to the heat conduction along the copper tube, some heat can be extracted from the condensing fluid in these short adiabatic zones. The axial heat flux depends on the operating conditions and therefore numerical simulations have been performed as detailed in Appendix A.3. It was found that the average contribution of the axial heat flux at the boundaries can be as high as 13%. The experimental heat flux is corrected to account for this effect. Before starting the test campaign, some actions have been taken to check the accuracy of the measurements, including calibration of thermocouples and thermopile, control of energy balance, check of temperature and pressure under saturated conditions, single phase heat transfer coefficient test runs. The results of these calibrations and control tests are reported in Appendix A. 3.2. Uncertainty analysis The experimental uncertainty for each measured parameter during a test run is made of two contributions: the first one is the type A uncertainty that derives from repeated observations, the second one is the type B uncertainty that comes from the instruments calibration and manufacturer’s specifications. During the experiments, all the measurements have been recorded during a period of 50 s with a time step of 1 s and then the type A uncertainty can be evaluated. The type B experimental uncertainties of the measured parameters are reported in Table 1. The uncertainty on the channel diameter has been determined starting from an enlarged image of the minichannel obtained at the microscope. The uncertainty of the diameter is 0.02 mm. The uncertainty analysis has been done following the guidelines provided in [24]. The combined standard uncertainty has been calculated using the law of error propagation and an example of the procedure can be found in [1]. Table 2 reports the expanded per-

Table 1 Type B experimental uncertainty of measured parameters. Temperature Temperature difference (with thermopile) Water flow rate in measuring sector Refrigerant flow rate Absolute pressure Pressure difference (>1 kPa) Pressure difference (below 1 kPa)

± 0.05 °C ± 0.03 °C ± 0.14% at 10 kg h1 ± 0.2% at 2 kg h1 ± 5 kPa (level of confidence: 99.7%) ± 0.12 kPa (level of confidence: 99.7%) ± 0.1% (level con confidence 99.7%)

Table 2 Minimum, maximum and mean combined experimental uncertainty of the experimental heat transfer coefficient. G (kg m2 s1)

Orientation

U(a) min. (%)

U(a) max. (%)

U(a) mean (%)

50 100 150 200 50 75 100 110 120 150 200

Horizontal Horizontal Horizontal Horizontal Vertical Vertical Vertical Vertical Vertical Vertical Vertical

2.7 2.6 2.8 2.5 3.8 3.8 3.3 3.6 3.1 2.8 2.9

7.1 4.7 5.8 6.4 7.3 5.3 5.0 5.1 4.3 4.7 5.0

4.4 3.7 3.5 3.3 5.4 4.3 4.2 4.3 3.6 3.3 3.5

centage uncertainty (considering a coverage factor equal to 2, level of confidence of approximately 95%) for the condensation heat transfer coefficient measured during horizontal and vertical flow. On average the percentage uncertainty is 4.1% with a maximum of 7.3% at G = 50 kg m2 s1. Regarding vapor quality, the maximum expanded uncertainty (coverage factor equal to 2) is about ± 0.015. 4. Condensation heat transfer results Because a main objective of the paper is to investigate the effect of channel orientation at low mass flux, the tests have been done at mass flux equal or below 200 kg m2 s1 in horizontal and vertical configuration. 4.1. Horizontal tube Condensation tests in the 3.4 mm test section in horizontal configuration have been performed with R134a at 40 °C saturation temperature and mass velocity of 50, 100, 150, 200 kg m2 s1. The heat transfer coefficient was measured in the five subsectors with the exception of the first one where the working fluid enters the test section as superheated vapor and thus part of the first sub-sector serves to desuperheat the fluid and achieve the thermodynamic conditions at the inlet of the following subsector. Between the 3rd and the 4th sub-sector the visualization window allows to record the flow pattern using a Photron FASTCAM Mini UX100 high speed camera. The high speed camera has been coupled with a 100 mm Tokina macro lens and a LED illumination system used as light source. Images have been recorded at 2000 fps except for the visualization at 200 kg m2 s1 mass flux, that have been recorded at 3200 or 4000 fps depending on the vapor quality. The flow pattern observed in this study, following the classification adopted in [25] are: annular, stratified-wavy, stratified smooth and intermittent. The experimental heat transfer coefficients measured in the sub-sectors are plotted versus the mean vapor quality x, in Fig. 3.

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M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

HEAT TRANSFER COEFFICIENT [W m -2 K-1]

a)

6000

5000

4000

G200 6.7
G200 10.3
G200 13.1
G200 19.8
G150 7.4
G150 9.7
G150 12.1
G150 15.3
3000

2000

1000

0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\]

c)

5000

G200

G100 4.8
G100 9.5
G100 12.2
HEAT TRANSFER COEFFICIENT [W m-2 K -1]

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

b) 6000

G100 15.3
3000

2000

1000

0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\]

6000

5000

G200

G50 5.3
G50 7.9
G50 12.9
4000

3000

2000

1000

0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\]

Fig. 3. Experimental heat transfer coefficients versus vapor quality during condensation of R134a in a horizontal 3.4 mm diameter tube: (a) G = 200 and 150 kg m2 s1, (b) G = 200 and 100 kg m2 s1, (c) G = 200 and 50 kg m2 s1. DT is the temperature difference between the fluid and the wall.

As expected for forced convective condensation inside pipes, the heat transfer coefficient decreases as the condensation process is moving forward and the vapor quality decreases in the channel. Beside, the heat transfer coefficient increases when the mass velocity is increased, due to the effect of the shear stress. At G = 200 kg m2 s1 and 150 kg m2 s1, the effect of the saturation-to-wall temperature difference is negligible. The measured heat transfer coefficients at 100 and 50 kg m2 s1 are reported in Fig. 3b and 3c. For comparison, in these graphs the results obtained at G = 200 kg m2 s1 are also depicted. At 50 and 100 kg m2 s1, the heat transfer coefficient is affected by the saturation-to-wall temperature difference and in particular it decreases when the saturation-to-wall temperature difference is increased. The effect of the temperature difference is more evident at G = 50 kg m2 s1. The visualized flow patterns are the following (Fig. 4):

1. at G = 200 kg m2 s1 and quality 0.79 < x < 0.88 the flow is annular and in the quality range 0.44 < x < 0.7 the flow pattern is in transition between annular and stratified-wavy. The thickness at the bottom of the tube becomes gradually thicker due to the gravity force; 2. at G = 150 kg m2 s1 the annular flow and stratified-wavy flow are still the two predominant flow regimes. When decreasing the vapor quality from 0.81 to 0.58 the film thickness at the bottom of the tube progressively increases and the flow pattern moves from annular to stratified-wavy flow. At vapor quality x = 0.52 and x = 0.41, stratified-wavy flow regime has been visualized; 3. at G = 100 kg m2 s1 the stratified-wavy flow pattern can be recognized in a wide range of vapor qualities, from x = 0.81 to x = 0.37. The wave intensity and amplitude varies but the liquid-vapor interface is always clearly distinguishable. At

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M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

x = 0.44

x = 0.52

x = 0.60

x = 0.69

x = 0.79

x = 0.88 G=200 kg m-2 s-1 FLOW

Transition annular / stratified-wavy x = 0.41

x = 0.52

x = 0.58

x = 0.69

Annular

Annular

x = 0.77

x = 0.81

GRAVITY

G=150 kg m-2 s-1 FLOW

Stratified-wavy x = 0.21

Transition annular / stratified-wavy x = 0.27

x = 0.37

x = 0.41

Annular x = 0.59

GRAVITY

x = 0.81 G=100 kg m-2 s-1 FLOW

Transition stratified-wavy / smooth-stratify x = 0.26

x = 0.37

GRAVITY

Stratified-wavy x = 0.45

x = 0.58

x = 0.81 G=50 kg m-2 s-1 FLOW

Intermittent

Stratified-wavy

GRAVITY

Fig. 4. Flow pattern, at various vapor qualities (x), during horizontal flow condensation of R134a at 40 °C saturation temperature; mass velocity equal to (from top) 200, 150, 100 and 50 kg m2 s1.

x = 0.27 and x = 0.21 the interface is smooth with some waves appearing from time to time. These waves are large enough to wash the upper part of the tube; 4. at G = 50 kg m2 s1 the flow pattern is smooth stratified for vapor quality x > 0.45. When decreasing the vapor quality from 0.81 to 0.45 the thickness of the liquid film increases gradually. For vapor qualities equal to 0.37 and 0.26, intermittent flow can be recognized. Large amplitude waves intermittently wash the top of the tube creating liquid plugs that separate the elongated bubbles. With the exception of the waves, the interface is smooth. For smooth-stratified or stratified-wavy flow, the saturation-to-wall temperature difference starts to clearly affect the heat transfer coefficient. The different flow regimes are the results of the balance between inertia, gravity and surface tension forces. The annular flow regime is present when the vapor velocity is high and it is characterized by a liquid film layer around the perimeter of the tube and a vapor core in the middle. Stratified-wavy and smooth-stratified flows are present when the shear stress is decreased and the effect of gravity becomes important. In the present case, the tube has an internal diameter equal to 3.4 mm, and the effect of gravity is clearly visible: even at the higher mass velocity, it promotes the liquid stratification and the liquid film is thinner at the top of the tube. In addition to the shear stress and gravity forces, there may be an effect of the surface tension but, in a 3.4 mm diameter tube, the contribution of the surface tension on the liquid film distribution is negligible, as it was shown with VOF (volume of fluid) numerical simulations in [11].

4.2. Vertical tube In vertical downflow, the condensation heat transfer coefficient of R134a at 40 °C saturation temperature has been measured at mass flux between 50 and 200 kg m2 s1. At these mass velocities, in vertical configuration, the flow pattern is annular for the whole range of vapor qualities (Fig. 5). During vertical annular flow, the liquid forms a uniform continuous film around the internal perimeter of the tube and the heat transfer coefficient depends on the interfacial shear stress, the liquid film thickness and turbulence. The liquid-vapor interface, depending on the vapor quality, is disturbed by waves with different amplitude. In vertical downflow, the effect of the saturation-to-wall temperature difference is less important, as can be seen in Fig. 6a at G = 50 kg m2 s1. On the contrary, in horizontal configuration at the same mass velocity, the heat transfer coefficient is dependent on the saturation-to-wall temperature (Fig. 3c). As depicted in Fig. 6b, when varying G between 120 and 200 kg m2 s1 the heat transfer coefficient displays a clear effect of the mass velocity. At mass velocities between 100 and 110 kg m2 s1 there is a sudden change of the heat transfer coefficient. Below 100 kg m2 s1 the dependence on the mass velocity is reduced. Table 3 reports the ratio of the heat transfer coefficient measured at G = 110 kg m2 s1 and G = 100 kg m2 s1 to the one at G = 50 kg m2 s1 and the ratio of the heat transfer coefficient at G = 110 kg m2 s1 to the one at G = 100 kg m2 s1 at vapor quality from 0.5 to 0.8. In the first and second column of Table 3, the values are always higher than 1 and the ratio increases when the

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x = 0.38

x = 0.47

x = 0.57

x = 0.62

x = 0.67

x = 0.79

x = 0.89 G=200 kg m-2 s-1 FLOW GRAVITY

x = 0.30

x = 0.40

x = 0.59

x = 0.66

x = 0.73

x = 0.79

x = 0.88 G=150 kg m-2 s-1 FLOW GRAVITY

x = 0.29

x = 0.34

x = 0.40

x = 0.58

x = 0.68

x = 0.76

x = 0.85 G=100 kg m-2 s-1 FLOW GRAVITY

x = 0.11

x = 0.19

x = 0.50

x = 0.59

x = 0.68

x = 0.76 G=50 kg m-2 s-1 FLOW GRAVITY

Fig. 5. Flow pattern, at various vapor qualities (x), during vertical downflow condensation of R134a at 40 °C saturation temperature.

a)

b) 4500

4500

G200 4000

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

HEAT TRANSFER COEFFICIENT [W m-2 K -1]

15.4 °C < DT < 17.9 °C 4000 11.3 °C < DT < 13.6 °C 3500

3.1 °C < DT < 4.3 °C 5.9 °C < DT < 9.7 °C

3000 2500

G=50 kg m-2 s-1

2000 1500 1000

500 0

G150 3500

G120 G110

3000

G100 2500

G75 G50

2000 1500 1000

d=3.4 mm R134a Tsat=40°C Vertical

500 0

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\]

VAPOR QUALITY [\]

Fig. 6. Experimental heat transfer coefficients versus vapor quality during vertical downflow condensation of R134a at 40 °C saturation temperature: (a) mass velocity equal to 50 kg m2 s1, DT is the temperature difference between refrigerant and wall; (b) mass velocity ranges between 50 and 200 kg m2 s1.

Table 3 Ratio of the measured heat transfer coefficient at G = 110 kg m2 s1 to the one at G = 50 kg m2 s1, at G = 110 kg m2 s1 to the one at G = 100 kg m2 s1 and at G = 100 kg m2 s1 to the one at G = 50 kg m2 s1. x

HTCG110/HTCG50 [/]

HTCG110/HTCG100 [/]

HTCG100/HTCG50 [/]

0.5 0.6 0.7 0.8

1.50 1.45 1.36 1.24

1.59 1.51 1.33 1.14

0.94 0.96 1.02 1.09

vapor quality decreases (the heat transfer coefficient ratio is between 1.59 and 1.14). This means that, for a given vapor quality, the heat transfer coefficient measured at G = 110 kg m2 s1, is higher than the heat transfer coefficient measured at G = 50 kg m2 s1 and G = 100 kg m2 s1. Looking at the third column of Table 3, the heat transfer coefficient ratio is around 1 and it displays a small increase with vapor quality. This means that, at vapor quality between 0.5 and 0.8, the heat transfer coefficients at G = 50 kg m2 s1 and G = 100 kg m2 s1 display similar values. The flow pattern recorded at G = 50 kg m2 s1 and 100 kg m2 s1 is annular for both the mass velocities but the

9

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

For R134a at 40 °C saturation temperature, the transition Reynolds number according to McNaught and Butterworth [26] is equal to 1357. Cioncolini et al. [27] developed a method to identify the laminar to turbulent flow transition in liquid films. This criterion considers vertical upflow conditions and it is based on the liquid film Reynolds number:

G=110 kg m-2 s-1 x=0.49 ReLF=1172

a)

FLOW GRAVITY

G=100 kg m-2 s-1 x=0.51 ReLF=1023 FLOW GRAVITY

b)

ReLF ¼ G dð1  xÞð1  eÞ=lL

where d is the diameter, lL is the liquid viscosity and e is the entrained liquid fraction, which can be calculated according to Cioncolini and Thome [28] for values of the core Weber number (Wec) between 101 and 105 (Eq. (11)). In the present case, the entrained liquid fraction is always below 0.08 and thus the liquid film Reynolds number ReLF corresponds to the liquid Reynolds number ReL (Eq. (12)).

3500 Turbulent liquid film Cioncolini et al.

3000

2500

ReL G200

ReLF G200

ReL G110

ReLF G110

ReL G100

ReLF G100

ReL G75

ReLF G75

ReL G50

ReLF G50

ReL , ReLF [/]

WeG=120

WeC ¼ qC J 2G d =r

2000 McNaught and Butterworth transition

ReL ¼ G d ð1  xÞ=lL

1000 ReL=240

500

Laminar liquid film - Cioncolini et al.

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\] Fig. 7. (a) Flow pattern during vertical downflow condensation of R134a at x = 0.5 and 40 °C saturation temperature, at G = 110 kg m2 s1 and G = 100 kg m2 s1. (b) Liquid Reynolds number (ReL Eq. 12) and liquid film Reynolds number (ReLF Eq. 10) versus vapor quality. ReLF is calculated as proposed by Cioncolini et al. [27]. In figure (b) the red lines correspond to the transitions proposed by Cioncolini et al. [27], the blue line corresponds to the McNaught and Butterworth [26] transition and the black line is the transition criterion proposed in the present paper. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

waviness is different (Fig. 5). Moreover, Fig. 7a shows a sequence of images of the flow pattern taken at 100 and 110 kg m2 s1 at 0.5 vapor quality. The intensity and the frequency of the waves at G = 110 kg m2 s1 are much higher compared to the tests at G = 100 kg m2 s1 (waves are still present at G = 100 kg m2 s1 while they diminish considerably at G = 50 kg m2 s1, as showed in Fig. 5). Toninelli et al. [11] performed volume of fluid simulations in a tube with 3.4 mm internal diameter, showing that waves can enhance the heat transfer compared to the case of smooth interface but the heat transfer coefficient increase is limited to 10–20%. However, in the present case, the heat transfer coefficient increases by 30 to 50% when moving from 100 to 110 kg m2 s1. Thus the difference in the heat transfer coefficient between G = 100 kg m2 s1 and G = 110 kg m2 s1 cannot be explained only with a different waviness; instead this can be the signal of a change of the turbulence in the liquid film. McNaught and Butterworth [26] proposed a predicting method starting from the Nusselt theory by adding the effects of waves and turbulence to the heat transfer coefficient. They suggested that the transition from laminar-wavy to turbulent flow takes place at a transitional Reynolds number equal to:

ReTR ¼ 4658 Pr 1:05 L where PrL is the liquid Prandtl number.

qC ¼

x þ eð1  xÞ x

qG

1500

0

ð10Þ

ð9Þ

þ eð1xÞ q

ð11Þ

L

ð12Þ

In Eq. (11), qc is the vapor core density as defined in [27], Jg is the superficial velocity of vapor and r is the surface tension. The aforementioned criteria have been applied to the present case (R134a, 40 °C saturation temperature, 3.4 mm inner diameter) and the results are reported in Fig. 7b1. For the present case (downflow configuration), the Cioncolini criterion predicts the liquid film in the transition between laminar to turbulent flow for all the experimental points except those at G = 200 kg m2 s1 and x  0.3, that are predicted in the turbulent region, and those at G  75 kg m2 s1 and x  0.9, that are predicted in the laminar region. When considering the present experimental database, a clear difference in the heat transfer coefficient is measured at mass flux between 100 kg m2 s1 and 110 kg m2 s1 and vapor quality values below 0.7. When the two aforementioned criteria are compared to the present data, they seem not so accurate in predicting the influence of turbulence effect on the heat transfer coefficient: the Cioncolini et al. [27] criterion (red lines in Fig. 7b) identifies a large transition region and the McNaught and Butterworth [26] (blue line in Fig. 7b) provides a value of the transitional Reynolds number which is constant with the vapor quality. However, the present results are significant and suggest that during condensation the effect of turbulence on the heat transfer coefficient starts at lower Reynolds number. In past studies, Carpenter and Colburn [29] and Kutateladze [30] highlighted that the condensate layer tends to be laminar in the absence of vapor velocity at Reynolds number below 2000 while, in presence of high vapor friction, the turbulence in the liquid layer starts at lower Reynolds number. In particular, Carpenter and Colburn [29] proposed that, in presence of high frictional forces due the vapor, the condensate layer can become turbulent at Reynolds number around 240 (the database of Carpenter and Colburn included data of pure vapor of steam, methanol, ethanol, toluene and trichloroethylene condensing in a 11.6 mm inner diameter tube). From the present database it can be inferred that there is a change in the turbulence which clearly and suddenly enhances the heat transfer at G = 110 kg m2 s1 and x = 0.7; it corresponds to a liquid Reynolds number around 700. Thus, the vapor friction seems to affect the turbulence in the liquid film and the Weber number (Eq. (13)) can be used as parameter to determine the beginning of this turbulence effect on the heat transfer coefficient. 1 For interpretation of color in Figs. 7 and 10, the reader is referred to the web version of this article.

10

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

b)

6000

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

5000

4000 G200 HORIZ. G200 VERT. G150 HORIZ. G150 VERT. 2000

1000

x=0.81 HORIZ. x=0.85 VERT.

x=0.88 HORIZ. x=0.89 VERT.

G200

3000

6000 x=0.54 HORIZ. x=0.58 VERT.

x=0.60 HORIZ. x=0.57 VERT.

x=0.81 HORIZ. x=0.88 VERT.

x=0.41 HORIZ. x=0.40 VERT.

G150

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

a)

G100

5000

x=0.81 HORIZ. x=0.76 VERT.

x=0.58 HORIZ. x=0.59 VERT.

4000 G50

3000

2000

1000 G100 HORIZ.

G50 HORIZ.

G100 VERT.

G50 VERT.

0

0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\]

VAPOR QUALITY [\]

Fig. 8. Experimental heat transfer coefficients versus vapor quality during condensation of R134a at (a) G = 200 and 150 kg m2 s1 and (b) G = 100 and 50 kg m2 s1. Data points in horizontal and vertical downflow are depicted. At G = 100 and 50 kg m2 s1 and horizontal configuration the saturation-to-wall temperature difference is 7.9 °C < DT < 13.9 °C.

WeG ¼

G2 d

ð13Þ

qG r

According to the present data, the effect of the turbulence on the heat transfer coefficient is evident at low liquid Reynolds number in presence of high frictional forces, in particular when WeG > 120. This threshold value of the Weber number can be used to calculate the mass velocity and then the liquid Reynolds number that sets a transition for the sudden change of the heat transfer coefficient due to turbulence in the liquid film. Fig. 7b reports the transition line (black line) corresponding to WeG = 120. However, according to the present experimental data, this wavyturbulence transition line can be drawn for vapor quality values between 0.2 and 0.7. When the vapor quality is higher than 0.7, data do not show a clear trend. Here, as a first attempt, this transition line is extended until it reaches ReL = 240, as suggested by Carpenter and Colburn [29]. McNaught and Butterworth [26] guessed that the transitional liquid Reynolds number was lower than 2000 but they gave a criterion that fixed a constant value of the liquid Reynolds number. The present wavy-turbulence transition goes beyond the fixed value of the liquid Reynolds number and accounts for the vapor quality: it provides ReL = 1746 at x = 0.2 and ReL = 240 at x = 1. To summarize, the present wavy-turbulence transition is obtained from the analysis of the heat transfer coefficients and can be determined as follow: 

1. calculate the value of mass flux G [kg m2 s1] at which WeG = 120; 

2. calculate the liquid Reynolds number using the mass velocity G; 3. the minimum transition value of the liquid Reynolds number is fixed equal to 240. This wavy-turbulence transition defines the region where some turbulence in the liquid film significantly increases the heat transfer coefficient (the operative liquid Reynolds number is higher than the transition value) and the region with mostly laminar liquid film flow (the operative liquid Reynolds number is lower than the transition value).

4.3. Comparison between horizontal and vertical configurations Fig. 8 compares the heat transfer coefficient for the two orientations. At mass velocity equal to 200 kg m2 s1 and 150 kg m2 s1 (Fig. 8a), vapor quality between 0.9 and 0.65, the heat transfer coefficient presents similar value for both orientations. At vapor quality around 0.8, the flow pattern is annular at G = 200 kg m2 s1 and in transition between annular and stratified-wavy in the case of G = 150 kg m2 s1. Decreasing the vapor quality, the heat transfer coefficient, at the same mass velocities, tends to diverge and the flow pattern, which in the vertical orientation is annular, in the horizontal configuration moves from annular to stratified-wavy. The difference in the flow pattern between the vertical and the horizontal configuration produces a decrease of the heat transfer coefficient during vertical downflow, which can reach 5% at G = 150 kg m2 s1 and x = 0.7, and 17% at x = 0.5 (Fig. 9). In horizontal configuration, due to gravity, the liquid film thickness is thinned at the top and in the middle of the tube while it becomes thicker at the bottom. This leads to a cross sectional average heat transfer coefficient which is higher compared to the vertical configuration in which the flow is annular. Fig. 8b shows the heat transfer coefficient for horizontal and vertical configuration at mass velocity equal to 100 kg m2 s1 and 50 kg m2 s1. For these mass velocities, the flow pattern is annular in the vertical configuration and stratified-wavy (G = 100 kg m2 s1) or smooth stratified (G = 50 kg m2 s1) in the horizontal configuration. As observed for the higher mass velocity, the heat transfer coefficient increases in horizontal channel compared to the vertical one due to the different flow pattern and to drainage of the condensed liquid from the top of the tube to the bottom. Toninelli et al. [11] have shown, with numerical simulations by means of the VOF method, that 85% of the heat transfer is exchanged in the upper part of the tube where the liquid film thickness is thinner. The ratio of the heat transfer coefficient in horizontal to that in vertical configuration can reach 0.44 at x = 0.5 and 0.58 at x = 0.7 for G = 100 kg m2 s1 (Fig. 9). These results on the effect of the channel orientation can be used to assess the criterion in [17] which predicts when gravity starts to play a role in the condensation process. The orientation

11

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

3500

b)

3000

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

HEAT TRANSFER COEFFICIENT [W m -2 K-1]

a)

2500

2000

1500 Horiz. x=0.7 1000

Vert. x=0.7 500

3500

3000

2500

2000

1500

Horiz. x=0.5 1000 Vert. x=0.5 500

0

0 0

50

100

150

MASS VELOCITY [kg

200

m-2

0

250

50

100

150

200

250

MASS VELOCITY [kg m-2 s-1]

s-1]

Fig. 9. Experimental heat transfer coefficients versus mass velocity in horizontal and vertical configuration at (a) x = 0.7 and (b) x = 0.5.

b) 25000

a) 1000 Transition region

Gravity independent region

G200 HTC oriz/HTCvert oriz/HTCv ert < 1 G150

20000

G100

Reeq=14700

G50

17500 100 15000 Reeq [/]

Dimensionless inclination parameter Y [/]

G200 HTC oriz/HTCvert oriz/HTCv ert = 1

22500

Gravity dependent region

Y=Y*

12500 Y=Y*

10000

10 7500 G100 5000

G150 G200 HTC oriz/HTCvert vert/HTC horiz < 1

2500

d=3.4 mm

G200 HTC oriz/HTCvert vert/HTC horiz = 1 1

Gravity dependent region

0 0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0,0

0,1

0,2

0,3

VAPOR QUALITY[\]

0,4

0,5

0,6

0,7

0,8

0,9

1,0

VAPOR QUALITY [\]

Fig. 10. Map of gravity dependent region for condensation of R134a in a 3.4 mm inner diameter tube. (a) Dimensionless inclination parameter versus vapor quality, according to [11]. (b) Equivalent Reynolds number versus vapor quality.

effect can be seen from the ratio of the heat transfer coefficient in horizontal to the one in vertical. In Fig. 10: 1. filled dots correspond to experimental data with a ratio HTCvert/ HTChoriz equal to 1, when orientation does not affect the heat transfer coefficient; 2. empty dots correspond to experimental data with a ratio HTCvert/HTChoriz lower than 1. Fig. 10a displays a comparison between the experimental data and the criterion reported in [17] when applied to the present tube (inner diameter equal to 3.4 mm) and fluid R134a. The criterion shows that the test runs at mass velocity equal to 150 kg m2 s1 fall in the gravity dependent region while at G = 200 kg m2 s1 the dimensionless inclination parameter Y is borderline the gravity dependent region. The curve of Y* bounds the gravity-dependent region and determines at which G* the inclination starts to affect

the condensation heat transfer coefficient, taking the horizontal configuration as the reference case. According to the present data, Y = Y* at G = 214 kg m2 s1. The ratio HTCvert/HTChoriz < 1 at G = 200 kg m2 s1 and x < 0.7; this ratio is lower than 1 for whole the vapor quality range at 150 kg m2 s1 mass velocity. Therefore this criterion is able to predict at which mass velocity and vapor quality the heat transfer coefficient is affected by gravity. Another parameter that can be used to map a gravity dependent zone is the equivalent Reynolds number:

"



q Reeq ¼ ð1  xÞ þ x L qG

1=2 #

Gd

lL

ð14Þ

This parameter is reported versus vapor quality for the mass velocities investigated in this study in Fig. 10b. In this figure, the same legend is used for the data: when the ratio of the heat transfer coefficient in horizontal to the one in vertical is equal to 1, the

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

symbols are filled otherwise they are empty. A transition between the gravity independent zone and the gravity dependent zone occurs at an equivalent Reynolds number around 14,700 (red dotted line in Fig. 10b). In Fig. 10b, the blue continuous line sets the equivalent Reynolds number calculated using the mass velocity (G = 214 kg m2 s1) corresponding to Y* (Eq. (1)); thus the blue line represents the equivalent Reynolds number that predicts the transition between gravity dependent and gravity independent regions using the criterion in [17]. In conclusion the criterion in [17] to detect the gravity dependent region is confirmed by the present data, up to Reeq = 14700, as reported in Fig. 10b. This result completes the criterion reported in [17] for the mapping of a gravity dependent region.

5. Predictions of the heat transfer coefficient While in the literature there are various correlations to predict the condensation heat transfer coefficient inside horizontal tubes, very few are available for vertical flow. As shown in Fig.s 8 and 9, under certain conditions, the heat transfer coefficient is influenced by the channel orientation and the heat transfer correlations should account for this. In the present case, the experimental data are compared against the predictions by the Cavallini et al. correlation [31] developed for convective condensation inside horizontal tubes and against the Shah [32] correlation (comprehensive correlation 1) which was developed for both horizontal and vertical flow. When only data in horizontal configuration are considered, the mean absolute deviation obtained with the Cavallini et al. [31] correlation is 6.1% and for the Shah [32] correlation is 8.9% (Fig. 11). When the database in vertical configuration is considered, the Shah [32] correlation provides much higher deviations: average absolute deviation equal to 30.1% and standard deviation equal to 31.3%. The experimental database in vertical configuration can be divided in two sets according to the wavy-turbulence criterion proposed in Section 4.2. The liquid Reynolds number and the wavyturbulence transition for the data in vertical orientation are reported in Fig. 12a: black dots are used for data with liquid Reynolds number higher than the transition and empty dots for ReL lower than the transition. When the experimental data points marked with black symbols are compared with the Shah [32] correlation, the heat transfer coefficient is predicted with a mean absolute deviation equal to 8.1% (in Fig. 12b); for data points marked with empty symbols the values predicted by the Shah [32] correlation highly deviate from the experiments and the dataset is overestimated with a mean absolute deviation equal to 58.0% (in Fig. 12b). Therefore, in vertical downflow configuration, the Shah [32] model well predicts the heat transfer coefficient only for ReL higher than the transitional value in Section 4.2, when the heat transfer coefficient is affected by some turbulence in the liquid film. This result shows a direction for further improvement of this correlation.

CALC. HEAT TRANSFER COEFFICIENT [W m-2 K -1]

6000 G200 Cavallini et al. G150 Cavallini et al. G100 Cavallini et al. G50 Cavallini et al. G200 Shah G150 Shah G100 Shah G50 Shah

5000

4000

+20%

-20%

3000

2000

Horizontal 1000

0 0

1000

2000

3000

4000

5000

EXP. HEAT TRANSFER COEFFICIENT [W

m-2

6000

K-1]

Fig. 11. Predictions of the condensation heat transfer coefficient in horizontal orientation with the Cavallini et al. [31] and the Shah [32] model for R134a in a 3.4 mm inner diameter channel. G is the mass velocity in [kg m2 s1].

a)

2500

b)

G200

G150 G120

WeG=120

2000

G110 G100 G75 G50

1500 ReL [/]

Transition

1000 ReL=240

500

6000

CALC. HEAT TRANSFER COEFFICIENT [W m-2 K-1]

12

G200 Shah +20%

G150 Shah G120 Shah

5000

G110 Shah -20%

G100 Shah

4000

G75 Shah G50 Shah

3000

2000

Vertical 1000

0

0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

VAPOR QUALITY [\]

0,7

0,8

0,9

1,0

0

1000

2000

3000

4000

5000

6000

EXP. HEAT TRANSFER COEFFICIENT [W m-2 K-1]

Fig. 12. Condensation in vertical downflow in the 3.4 mm diameter channel. (a) Values of the liquid Reynolds number (Eq. (12)) for the present experimental database, and wavy-turbulence transition calculated as reported in Section 4.2. (b) Predictions with the Shah [32] model. Black dots refer to ReL higher than the transition, empty dots refer to data with ReL lower than the transition. G is mass velocity in [kg m2 s1].

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

6. Conclusions Convective condensation of R134a at low mass flux in a 3.4 mm diameter channel is investigated in this paper. The main conclusions are reported hereafter. 1. In horizontal configuration, annular flow, stratified-wavy flow and smooth-stratified flow have been visualized; at G = 50 kg m2 s1 and G = 100 kg m2 s1 the heat transfer coefficient results to increase when the saturation-to-wall temperature difference is decreased. In vertical configuration, no effect of the saturation-to-wall temperature difference is detected. 2. In vertical downflow, when the mass velocity changes from 100 kg m2 s1 to 110 kg m2 s1 there is a sudden increase in the heat transfer coefficient which can be due to the effect of waves and increased turbulence in the liquid film. 3. On the basis of the heat transfer data in vertical downflow, a transition criterion to set the effect of turbulence in the liquid film can be derived. This transition corresponds to the liquid Reynolds number calculated for WeG = 120. When ReL < 240, this transition is set at ReL = 240. 4. By comparing the heat transfer coefficient in horizontal tube to the one in vertical flow, it is possible to define the gravity dependent region and assess the criterion by Del Col et al. [17]. 5. In horizontal configuration, the gravity force drains the condensed liquid to the lower part of the tube thinning the liquid film on the top and leading to higher heat transfer coefficient in horizontal configuration. The ratio of heat transfer coefficient in vertical downflow to that in horizontal can be as low as 0.45 at G = 100 kg m2 s1 and x = 0.5. 6. The Cavallini et al. [31] and Shah [32] correlations are able to satisfactory predict the condensation heat transfer coefficient during horizontal flow. 7. During vertical downflow, the Shah [32] correlation provides accurate predictions only for the data at WeG > 120, in agreement with the transition liquid Reynolds number criterion. More work needs to be done to improve correlations below this transition.

Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors acknowledge the financial support of the MIUR through the program PRIN 2015 (Grant Number 2015M8S2PA) and of the Department of Industrial Engineering of the University of Padova through the project BIRD160582/16. Part of the research activity has been possible also through the financial support of the European Space Agency through the MAP Condensation program ENCOM-3 (AO-2004-096). Appendix A A.1. Calibration tests A.1.1. Calibration of thermopile and thermocouples The calibration of water thermopiles has been done using as reference thermometers two calibrated thermistors coupled with an Hart Scientific Super-Thermometer II 1590; this configuration achieves an uncertainty of 0.002 K on the measured temperatures. Once the temperature sensors on the water side were calibrated they have been installed in the sub-sectors and used to calibrate

13

the thermocouples in the wall. Water was circulated in the subsectors and the test channel was vacuumed. From the readings of the thermocouples and thermopiles installed in each sub-sector it was possible to get the mean temperature and to calibrate each wall thermocouple. A.1.2. Energy balance The energy balance has been checked comparing the water side heat flow rate to the one calculated on the refrigerant side. The total water side heat flow rate is calculated as the sum of the heat flow rate for each sub-sector, while on the refrigerant side the heat flow rate is evaluated as:

_ ref Dhref qref ¼ m where Dhref is the refrigerant enthalpy difference at the inlet and outlet of the test section where the pressure and temperature sensors are installed. The thermal balance has been performed in two conditions: heating or cooling the refrigerant as liquid, or condensing the refrigerant from the superheat vapor state to subcooled liquid. Considering single phase heat balance tests the difference between the heat flow rate measured on the water side and the heat flow rate measured on the refrigerant side is below 4 W for all the mass fluxes. During two-phase heat balance tests the maximum percentage difference between the heat flow rate measured on the water side and the one evaluated on the refrigerant side is below ±3% for mass velocities greater than 100 kg m2 s1; at G = 50 kg m2 s1 the heat balance is within ±5%, corresponding to a difference of approximately 4 W. A.1.3. Check of temperature and pressure under saturated conditions The refrigerant temperature at the outlet of the test section has been measured during two-phase flow and compared with the saturation temperature obtained from the pressure measurement. The agreement is typically in the order of 0.2 K, which is within the uncertainty range of the two instruments. A.1.4. Single phase heat transfer coefficient During single phase heat transfer tests, the refrigerant enters the test section as subcooled liquid and then is heated up or cooled down with the secondary fluid that flows in counter-flow, with Reynolds number from 2400 and 4600. The measured heat transfer coefficients have been compared with the Gnielinski correlation, from VDI [34], for the transition region between laminar and fully developed turbulent flow and the Dittus and Boelter correlation. Both the correlations well predicts the database with an agreement of 12%. During single phase tests, the heat transfer coefficient in the first and second sub-sector has been determined in two ways: using the mean wall temperature and the mean logarithmic temperature difference. The disagreement between the two methods is about 0.8% for the first sub-sector and about 0.3% for the second. A.2. Control tests during condensation A.2.1. Sensitivity to coolant conditions during condensation tests As can be seen from the data reduction (Section 3), the technique for the evaluation of the heat transfer coefficient is highly dependent on the measurement of the water conditions, especially on the water temperature; for this reason on the water side there is a double check of the temperature in each sub-sector, using a triple-junctions thermopile and two thermocouples. After checking the thermal balance, as an indirect validation of the technique and to assure its goodness, it was checked that the coolant operating conditions do not affect the internal heat transfer coefficient at fixed refrigerant conditions. Fig. A1 reports the experimental heat transfer coefficient for R134a at 200 kg m2 s1 and 40 °C saturation temperature.

14

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

b)

6000

5000

WMF = 9.5 kg/h

WMF = 11 kg/h

WMF = 14 kg/h

WMF = 18.5 kg/h

5000 T_in water 13.4°C 4500

HEAT TRANSFER COEFFICIENT [W m -2 K-1]

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

a)

4000

3000

2000

1000

T_in water 18.8°C T_in water 23.4°C

4000

T_in water 26.9°C 3500

T_in water 31.4°C T_in water 34.8°C

3000 2500 2000

1500 1000 500 0

0 0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0,0

1

0,1

0,2

0,3

VAPOR QUALITY [\]

c)

5000

d) Sub-sector 2

0,6

0,7

0,8

0,9

1,0

0,7

0,8

0,9

1,0

Δx = 0.21 4500

Sub-sector 5

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

HEAT TRANSFER COEFFICIENT [W m-2 K-1]

0,5

5000

Sub-sector 3

4500 Sub-sector 4

0,4

VAPOR QUALITY [\]

4000 3500 3000

2500 2000 1500 1000 500

Δx = 0.15 Δx = 0.1

4000

Δx = 0.07

3500 3000

2500 2000 1500 1000

500 0

0 0,0

0,1

0,2

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Fig. A1. Experimental heat transfer coefficient versus vapor quality for R134a at G = 200 kg m2 s1 during horizontal configuration: (a) varying water mass flow (WMF) rate, (b) varying the inlet water temperature, (c) measurements in different sub-sectors at the same mean vapor quality, (d) measurements when varying the quality change.

In Fig. A1a, the water mass flow rate was varied between 18.5 kg h1 and 9.5 kg h1 and no effect on the internal heat transfer coefficient was detected. Fig. A1b shows the experimental heat transfer coefficient of R134a at the same refrigerant conditions, G = 200 kg m2 s1 and Tsat = 40 °C, when the inlet water temperature changes between 13.4 °C and 34.8 °C. This inlet water temperature variation affects the saturation-to-wall temperature difference. At a mass velocity equal to 200 kg m2 s1 no effect of the saturation-to-wall temperature difference on the heat transfer coefficient is detected. Anyway, the effect of the saturation-to-wall temperature difference at lower mass velocities deserves a detailed discussion and it is presented Section 4. Since a single value of the heat transfer coefficient is measured in each sub-sector, varying the water temperature and the water mass flow rate, it is possible to measure the heat transfer coefficient at the same vapor quality but in different sub-sectors, thus at different axial positions. Fig. A1c presents the measured heat transfer for each sub-sector for R134a at G = 200 kg m2 s1. It can be seen that at x = 0.75 the heat transfer coefficient has been measured in the second, third, fourth and fifth sub-sector or at x = 0.6 the same heat transfer

coefficient has been measured in the third, fourth and fifth sector. It is clear that the heat transfer coefficient is independent from the axial position in which it is measured. In the same way, in Fig. A1d, the experimental heat transfer coefficients have been plotted reporting the condensation rate of each experimental point; here it accounts for the condensing heat flow rate exchanged in each sub-sector or, in other words, for the vapor quality change in a sub-sector. As one can see the heat transfer coefficient is independent from the variation of vapor quality. A.3. Model for axial conduction The effect of the axial conduction may promote heat transfer from the refrigerant to water in between the sub-sectors of the test section. As showed in Fig. 1, the two heat exchangers are divided in five sub-sectors, and the length of the copper tube on the refrigerant side is higher than the total length of the external water annulus. Therefore, before and after each sub-sector, there is a short zone without water flow. Due to heat conduction along the copper tube, some heat can be subtracted from the condensing refrigerant

M. Azzolin et al. / International Journal of Heat and Mass Transfer 144 (2019) 118646

in this zone and then rejected to the water. To evaluate the contribution of the axial conduction, numerical simulations have been performed, imposing as boundary conditions: – water inlet temperature and water mass flow rate; – refrigerant saturation temperature and internal heat transfer coefficient. Several simulations have been done with various combinations of water and refrigerant boundary conditions to include all the possible operative conditions. Moreover some simulations have been done varying the number of elements in the mesh domain to seek for a possible effect of the mesh size. As results of the simulations, the temperature in the copper tube is obtained; then, with the temperature profile the axial heat conduction at the two edges of the sub-sector can be evaluated. Using the results of the simulations, a function to correlate each operative condition to the corresponding estimated heat flux has been determined. With this procedure, the contribution of the axial heat flux can be evaluated starting from the experimental operative condition. This procedure has been validated using the single phase heat transfer tests. Appendix B. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118646. References [1] D. Del Col, M. Bortolato, M. Azzolin, S. Bortolin, Condensation heat transfer and two-phase frictional pressure drop in a single minichannel with R1234ze(E) and other refrigerants, Int. J. Refrig. 50 (2015) 87–103, https://doi.org/10.1016/ j.ijrefrig.2014.10.022. [2] D. Del Col, M. Azzolin, S. Bortolin, A. Berto, Experimental results and design procedures for minichannel condensers and evaporators using propylene, Int. J. Refrig. 83 (2017) 23–38, https://doi.org/10.1016/j.ijrefrig.2017.07.012. [3] M.K. Bashar, K. Nakamura, K. Kariya, A. Miyara, Experimental study of condensation heat transfer and pressure drop inside a small diameter microfin and smooth tube at low mass flux condition, Appl. Sci. 8 (2018) 2146, https://doi.org/10.3390/app8112146. [4] B.-X. Wang, X.-Z. Du, Study on laminar film-wise condensation for vapor flow in an inclined small/mini-diameter tube, Int. J. Heat Mass Transf. 43 (2000) 1859–1868, https://doi.org/10.1016/S0017-9310(99)00256-2. [5] P. Toninelli, S. Bortolin, M. Azzolin, D. Del Col, Effects of geometry and fluid properties during condensation in minichannels: experiments and simulations, Heat Mass Transf. Und Stoffuebertragung. 55 (2019) 41–57, https://doi.org/10.1007/s00231-017-2180-7. [6] J. Xiao, P. Hrnjak, Flow regimes during condensation from superheated vapor, Int. J. Heat Mass Transf. 132 (2019) 301–308, https://doi.org/10.1016/J. IJHEATMASSTRANSFER.2018.12.016. [7] G. Nema, S. Garimella, B.M. Fronk, Flow regime transitions during condensation in microchannels, Int. J. Refrig. 40 (2014) 227–240, https://doi. org/10.1016/J.IJREFRIG.2013.11.018. [8] N. Liu, J.M. Li, J. Sun, H.S. Wang, Heat transfer and pressure drop during condensation of R152a in circular and square microchannels, Exp. Therm Fluid Sci. 47 (2013) 60–67, https://doi.org/10.1016/j.expthermflusci.2013.01.002. [9] B. Mederic, P. Lavieille, M. Miscevic, Heat transfer analysis according to condensation flow structures in a minichannel, Exp. Therm Fluid Sci. 30 (2006) 785–793, https://doi.org/10.1016/j.expthermflusci.2006.03.008. [10] B. Mederic, M. Miscevic, V. Platel, P. Lavieille, J.-L. Joly, Experimental study of flow characteristics during condensation in narrow channels: the influence of the diameter channel on structure patterns, in: Eurotherm 75 Microscale Heat Transf, Academic Press, 2004, pp. 573–586, https://doi.org/10.1016/j. spmi.2003.11.008.

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