Experimental investigation of heat transfer and pressure drop during condensation of R134a in multiport flat tubes

Accepted Manuscript

EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER AND PRESSURE DROP DURING CONDENSATION OF R134a IN MULTIPORT FLAT TUBES Paul KNIPPER , Dirk BERTSCHE , Ronald GNEITING , Thomas WETZEL PII: DOI: Reference:

S0140-7007(18)30408-0 https://doi.org/10.1016/j.ijrefrig.2018.10.019 JIJR 4145

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

11 June 2018 11 October 2018 14 October 2018

Please cite this article as: Paul KNIPPER , Dirk BERTSCHE , Ronald GNEITING , Thomas WETZEL , EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER AND PRESSURE DROP DURING CONDENSATION OF R134a IN MULTIPORT FLAT TUBES, International Journal of Refrigeration (2018), doi: https://doi.org/10.1016/j.ijrefrig.2018.10.019

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Highlights  Heat transfer and pressure drop during condensation in multiport flat tubes  Influence of an axial fin structure on heat transfer and pressure drop characteristics  Comparison with various correlations from literature  Modification of a calculation approach to confirm and match the experimental results

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EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER AND PRESSURE DROP DURING CONDENSATION OF R134a IN MULTIPORT FLAT TUBES Paul KNIPPER(*), Dirk BERTSCHE(**), Ronald GNEITING(**), Thomas WETZEL(*) (*)

Karlsruhe Institute of Technology, Kaiserstr. 12, Karlsruhe, 76131, Germany MAHLE Behr GmbH & Co. KG, Mauserstr. 3, Stuttgart, 70469, Germany [email protected]

ABSTRACT

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This paper presents the results of an experimental investigation on heat transfer and pressure drop characteristics for R134a in multiport flat tubes (MPFT). In order to perform a fundamental analysis, an experimental facility has been set up to determine both the heat transfer coefficient and the pressure drop value in the two-phase flow regime inside extruded MPFT ( ) with either rectangular channels or including an axial fin structure. The operating parameters have been varied within a broad range to ensure a high degree of reliability and comparability to heat transfer and pressure drop correlations. A very good agreement of the pressure drop data with the Friedel (1979) and Jige et al. (2016) correlations can be confirmed. The heat transfer coefficient can be predicted well for the MPFT with rectangular channels using the Jige et al. (2016) correlation, but only poor agreement can be achieved for the MPFT including the fin structure for all correlations taken into consideration. Keywords: condensation, R134a, refrigerant, multiport, microchannel

INTRODUCTION

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Refrigerant cycles are present in multiple areas of life, especially in modern AC systems. In order to achieve a high environmental compatibility, manifold investigations concerning heat transfer and pressure drop of numerous refrigerants have been performed. Gas, mostly ambient air, or a liquid coolant is usually used as secondary medium in refrigeration systems and cooled down or heated up by the refrigerant inside the cycle. The change of state and the connected two-phase transition area is located inside the condenser and evaporator. In order to achieve high heat transfer performance multiport flat tubes consisting of numerous microchannels are commonly in use inside modern condensers and evaporators (cf. Garimella (2004)). Although the application in commercial products is widely spread, the theoretical methods to determine essential values like pressure drop and heat transfer are developed to a comparatively small degree, especially concerning the application of different in-tube channel geometries. A broad database as well as reliable correlations for the pure refrigerant are needed in order to precisely determine the heat transfer coefficient and pressure drop.

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ACCEPTED MANUSCRIPT Nomenclature

Greek symbols two-phase multiplier dynamic viscosity (N s m-2) density (kg m-3) surface tension (N m-1) void fraction (-) vapour quality

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Dimensionless numbers Bond number (-) Nusselt number (-) Prandtl number (-) Reynolds number (-) Weber number (-) Lockhart-Martinelli parameter (-)

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Subscripts annular experiment forced convection dominant heptane inlet liquid literature liquid only, minimal modified outlet surface tension dominant slug two-phase vapour vapour only

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cross section area (m²) heat transfer surface (m²) average deviation (%) specific heat capacity (J kg-1 K-1) hydraulic diameter (m) friction factor heat transfer coefficient (W m-2 K-1) latent heat (J kg-1) uncertainty of the measured current (A) heat conductivity (W m-1 K-1) mass flow (kg s-1) mass flux (kg m-2 s-1) uncertainty of the mass flux (kg m-2 s-1) mean deviation (%) multiport flat tube pressure drop (bar) heat flow (W) wetted perimeter length (m) temperature (°C) refrigerant temperature (°C) wall temperature (°C) temperature difference (°C) uncertainty of a variable

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The heat transfer strongly depends on the present flow regime and, as for now, is mostly calculated using individual correlations for different flow regimes. Early investigations, e.g. Taitel and Dukler (1976), have shown the importance of defining flow transition criteria for two-phase flows. Due to the change of vapour quality during the condensation process, a change of the flow regime can occur, which represents a major challenge regarding the setup and application of a theoretical model. Furthermore, early investigations by Garimella and Coleman (2000) and William Wang et al. (2002) have revealed that the influence of the hydraulic diameter on the flow regime becomes significant for values lower than 1-2 mm, depending on the refrigerant, which leads to a suppression of gravimetric flow patterns and prefers flow patterns controlled by surface tension and viscosity (cf. Revellin et al. (2006)). Within microchannels, the intermittent and annular flow regime can be observed for a wider range of operation parameters. The remaining flow regimes are usually subdivided into the mist, annular, slug and plug flow. All of these flow patterns result in an increase of the wetting of the wall, which again results in an increase in heat transfer. These observations and conclusions have been verified by multiple investigations, e.g. Garimella (2004) and Kim et al. (2012). Nema et al. (2014) proposed flow regime transition criteria based on the assumptions by Coleman and Garimella (2003). They relied on physical reasoning in combination with own data as well as data from literature with the aim to establish a flow pattern map based on generalized dimensionless criteria which makes it favourable for a broad application. Figure 1 shows the flow pattern map by Nema et al. (2014) as a function of the vapour-phase Weber number ( ) and the modified Lockhart-Martinelli parameter ( ). The modified Lockhart-Martinelli parameter is based on the Lockhart-Martinelli parameter and

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ACCEPTED MANUSCRIPT the slug Lockhart-Martinelli parameter (cf. equation 1) and corresponds to the minimum liquid volume fraction necessary to block the channel. (1)

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Furthermore, the experimental data of this contribution as well as the transition criteria regarding mist flow (MF) and the transition criteria from intermittent (I) to intermittent-annular flow (I-AF) and annular flow (AF) have been included. One can easily note that most of the investigations have been performed while an annular flow is present. Only a minor number of data points meet the criteria for mist flow ( and ) and several data points can be found within the transition area from annular flow ( ) to intermittent flow ( and ). The uncertainties of both values are summarized in Table 3 for the sake of clarity.

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Figure 1. Flow pattern map by Nema et al. (2014) including the data to be presented

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Therefore, the experimental heat transfer data is compared to available correlations from literature, which are applicable either for multiple flow regimes or especially for annular flow. These requirements are met regarding the correlation by Koyama et al. (2011). They considered a very detailed approach in terms of the calculation of the heat transfer coefficient for the annular flow regime in order to identify the major influences on the heat transfer coefficient. The overall Nusselt number for annular flow is given in equation 2 and is calculated based on the Nusselt number for the vapour shear stress dominant case and for the surface tension dominated case . )

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It is assumed that the heat transfer near the corners of a rectangular shaped channel can be neglected, as the liquid film is thick. For low mass fluxes as well as medium vapour qualities they state the surface tension to be the main influencing factor, while for higher vapour qualities and mass fluxes the effect of the vapour shear stress dominates. Therefore, in the surface tension dominant case, is calculated based on the relationship between the surface tension and liquid film and neglecting the shear stress (cf. equation 3). Hereby, the geometric parameters of the liquid film are considered constant in flow direction and are combined within the pre-factor, which has been fitted experimentally by Koyama et al. (2011). The void fraction is being calculated with the homogeneous model. [

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The proposed correlation was able to predict their own data with a good agreement for mass fluxes of 100 to 400 kg m-² s-1 and saturation temperatures of 40°C and 60°C using R134a and a multiport flat tube with a hydraulic diameter of 0.85 mm. The correlation was revised in 2016 by simplifying the term for the surface tension controlled case (cf. equation 5). A constant value was proposed instead of using the Bond-number to represent the influence of various geometrical parameters, e.g. the hydraulic diameter or geometrical parameters of the liquid film. ]

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Jige et al. (2016) stated that the accordance with their experimental data improved compared to their previous correlation. Apart from the promising Koyama correlations, another correlation tested to mass fluxes of up to 1403 kg m-² s-1 is proposed by Kim and Mudawar (2013) and differs for annular and slug/bubbly flows. Even for different working fluids, vapour qualities, saturation pressures as well as hydraulic diameters the correlation shows a good accordance with the existing data base with 86.8 % of the data within a ±30 % error band. Cavallini et al. (2006) proposed a correlation for the annular and mist flow regime specifically adjusted for the use with minichannels and shows a promising performance in comparison to their data. Besides predicting the heat transfer coefficient, the calculation of the pressure drop is of great interest, especially regarding the comparison of different tube geometries and their efficiency. However, as the heat transfer for annular flow is strongly affected by the vapour shear stress, heat transfer correlations nowadays are often based on the considerations of the shear stress in terms of the pressure drop calculation. Jige et al. (2016) developed a calculation method for the pressure drop in microchannels calculating the frictional pressure drop for the vapour phase only and adding a two-phase multiplier. By this means, they were able to predict over 93 % of their own data points with a deviation of less than ±20 %. Most state of the art pressure drop correlation are based on the early investigations by Lockhart and Martinelli (1949), Chisholm (1967) and Friedel (1979). Cavallini et al. (2002) have been one of the first to develop a correlation particularly for the condensation of refrigerants, based on the correlation by Friedel (1979). Further investigations have been performed to adapt the known macrochannel correlations for the use of microchannels (e.g. Cavallini et al. (2006); López-Belchí et al. (2014)), as several comparisons have revealed disagreements for these correlations when used to predict the pressure drop inside microchannels. Sakamatapan and Wongwises (2014) were able to predict their pressure drop data with an accuracy of 82 % within a deviation of ±20 % using the correlation proposed by Cavallini et al. (2006). Based on the equivalent Reynolds number concept by Akers et al. (1959) Sakamatapan and Wongwises fitted the two-phase friction factor to their data and achieved an accordance of over 90 % within a deviation of ±20 %. Kim and Mudawar (2012) adapted the Lockhart and Martinelli correlation for the use with small channel diameters as well as considering the influence of the different flow regimes depending on laminar or turbulent flow in the vapour and liquid phase. The suitability of this approach is shown with a good accordance of the proposed correlation for over 7.000 data points from multiple data sources. The aim of the present investigation is to provide additional data points for a wide range of operation parameters in order to extend the available data basis for R134a. In addition, the application of an axial fin structure within two-phase flows and its impact on heat transfer and pressure drop characteristics will be discussed based on the results. Finally, existing theoretical approaches are compared to the experimental data and evaluated with respect to their prediction quality.

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EXPERIMENTAL SETUP

In order to determine both heat transfer and pressure drop in a multiport flat tube, a test facility has been set up featuring novel transition sections for the use with two-phase mixtures. The test section is based on an 5

ACCEPTED MANUSCRIPT extruded aluminium multiport flat tube with a total length of 800 mm consisting of parallel channels with a rectangular cross section with and without an axial micro-fin structure. The operation parameters have been varied within a broad range to ensure a high degree of reliability and comparability to heat transfer and pressure drop correlations as well as experimental data available in literature (cf. Table 1). Table 1. Operation parameters. test fluid mass flux [kg m-² s-1] vapour quality [% by weight] saturation temperature [°C]

R134a 200, 400, 600, 800 10 – 90 40

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Based on this wide range of different parameters representative experimental studies can be performed. As different mass fluxes and vapour qualities need to be adjusted independently in the experiment, a complex setup including the test loop and several secondary loops, e.g. cooling water loops, is needed and will be introduced in detail in the following.

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2.1. Test Loop A schematic representation of the test loop with its main components is presented in Figure 2. The mass flux is provided by the combination of a piston diaphragm pump (Verder G22) and a bypass in order to realize the wide range of mass flux specified in Table 1 using two proportional valves. Thus, the minimum mass flux of 200 kg m-² s-1 of the pump itself can be lowered further if necessary. With the help of the subsequent Coriolis mass flow meter (Rheonik RHM 03 GNT) the requested mass flow can be verified. Oscillations within the mass flux caused by the principle of the pump are supressed by using a throttling valve in combination with an upstream pulsation damper. Inside the evaporator, formed by a circular tube with an inner diameter of 10 mm and wrapped with two electrical heating cables, the subcooled liquid is heated up and partially evaporated. By adjusting the electrical heating power different vapour qualities can be set. The required electrical power can be calculated based on the thermophysical properties of the liquid and the temperature, pressure and mass flow measured prior to the evaporator. The power supply is monitored by a power meter (Yokogawa WT1030). The two-phase flow enters the test section immediately after the evaporator und leaves the test section with a reduced vapour quality. The remaining vapour is condensed inside a plate heat exchanger and can either flow into the storage tank or directly to the subcooler located in front of the sonic measurement device and the pump. In order to ensure a liquid-only flow a sight glass has been fitted at the outlet of the subcooler to provide an opportunity for visual verification. The sonic measurement device (Anton-Paar SPRn 4214) is used to determine the density of the refrigerant as well as the oil content of the refrigerant-lubricant-mixture in subsequent investigations.

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Test Section

Post-Condenser

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Figure 2. Schematic representation of the test loop. After the setup of the test loop, a static pressure test with a pressure 25 % higher than the maximum operation pressure using pure nitrogen is performed. Hereby, only a pressure loss below 1 mbar every 3 hours is acceptable. Subsequently, the test loop is being evacuated using a Lebyold Trivac 2.5E vacuum pump until the pressure sensors display a pressure below 1 mbar. This pressure is held constant for 30 min to

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2.2. Test Section The test section consists of the multiport flat tube including the required measuring devices as well as the secondary cooling loop. Two multiport flat tubes with rectangular channels and a hydraulic diameter of 0.91 mm and 0.77 mm and one multiport flat tube with a hydraulic diameter of 0.82 mm incl. an axial fin structure have been investigated. The hydraulic diameter has been determined according to the definition given in Jige et al. (2016) in all cases. The multiport flat tube is divided into two areas, an adiabatic section and the condensation section. The condensation heat from the refrigerant is transferred to the cooling loop using the cross-current-flow principle (cf. Figure 3). N-heptane is used as coolant as its thermophysical properties have a favourable effect on the measuring accuracy. The specific heat capacity of n-heptane is only about 50% of the amount of pure water, which leads to a higher rise of the temperature between inlet and outlet of the coolant. As the obtained temperature difference is being adjusted to , the uncertainty of measurement of the temperature sensors can be reduced significantly. Still the temperature difference within the coolant is low enough as a mean heat capacity can be assumed. The condensation section is reducible to a length of 190 mm in the range of the cross-flow of the n-heptane.

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Figure 3. Schematic representation of the test section.

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As the vapour quality is adjusted by setting the heating power of the evaporator, the calculation of the actual value of the vapour quality uses the measured power and the heat losses determined in advance. Furthermore, a redundant approach to determine the vapour quality and heat flow has been included in the layout of the test loop. By skipping the storage tank and leading the flow directly from the post-condenser into the subcooler, an energy balance from the inlet of the evaporator up to the outlet of the subcooler calculates the heat transferred in the condensation section. Data thus obtained cannot provide a similar accuracy as the data obtained using the method first described, but can be used to verify the data and detect any malfunction of the used measurement devices. Immediately after the partial evaporation, the two-phase flow enters a nozzle connecting the circular tube of the evaporator with the multiport flat tube. An integrated sight glass provides visual information about the distribution of the vapour and the liquid phase prior to the entry into the multiport flat tube. At that point, a separation into the numerous micro channels has not been realized, but the geometry has been changed from the circular shaped pipe to the flat tube. The nozzle is required to ensure a smooth transition of the flow cross section in order to achieve a homogeneous distribution of vapour and liquid into all channels of the flat tube. At three positions of the flat tube, i.e. at the inlet of the flat tube and just prior and after the condensation section (cf. Figure 3), temperature and pressure inside the flat tube are determined by using so called “measurement flanges”. By this, no further calculation to include the inlet or outlet of the flat tube is needed as the pressure drop is measured in the flat tube only. However, only an average temperature, pressure or pressure drop can be determined for all channels in one “measurement flange”. The temperatures measured correspond to the condensation temperature as a two-phase flow is present. Furthermore the pressure drop can be determined, firstly for the adiabatic section and secondly for the condensation section. The adiabatic section between the first and second measurement flange is designed to provide nearly adiabatic conditions, 7

ACCEPTED MANUSCRIPT as a change of the vapour quality has to be avoided. In addition, a fully developed flow can be ensured within the condensation section, as influences of the transition section will be absorbed. Nevertheless, a decrease of temperature and pressure can be recorded corresponding to the pressure drop inside the microchannels. After leaving the test section the two-phase flow passes through a diffusor to provide the change of the cross section back to circular shape as shown in Figure 3.

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EVALUATION PROCEDURE

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Each measurement is evaluated regarding heat transfer and pressure drop as well as the associated uncertainty of measurement and its impact on the target values. The selected evaluation methods will be detailed in the following. The required thermophysical properties have been derived from the NIST Standard Reference Database 23 (April 2013, Version 9.1). 3.1. Heat Transfer And Pressure Drop The heat transfer coefficient inside the multiport flat tube is calculated using equation 6. ̇

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[m²] represents the heat transfer surface, ΔT [K] corresponds to the difference between the average condensation temperature measured inside the measuring flanges and the wall temperature of the flat tube and ̇ [W] represents the heat flow transferred to the cooling fluid (n-heptane). The heat flow is determined by a steady-state enthalpy balance of the test section (cf. eq. 7). The specific heat capacity is being averaged using mean values from the inlet and outlet temperatures of the n-heptane flow. This approach seems justified, as the maximum temperature difference between inlet and outlet does not exceed 5 K, which only leads to minor deviations of the averaged specific heat capacity in comparison to the actual value. The mass flow of the heptane is represented by ̇ . )

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The temperature difference ΔT, as mentioned in equation 6, results from the average condensation temperature measured inside the measuring flanges at the beginning and the end of the condensation section. The average wall temperature is determined by four temperature sensors. These wall temperatures are determined by using a so-called “sandwich”, which surrounds the multiport flat tube along the condensation section (cf. Figure 4).

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(a) (b) Figure 4. Illustration of the flat tube cross sections (a) and the sandwich setup incl. two of the four temperature sensors (b).

As the tube wall thickness is very small (≈0.3 mm), temperature sensors cannot be fitted inside the wall in order to determine the actual wall temperature (cf. Figure 4 (a)). If mounted on the flat tube, the geometry of the sensor would influence the surrounding flow of the coolant and would most likely lead to the determination of non-representative temperatures. Therefore, the wall is being enlarged by soldering two aluminium plates above and underneath the flat tube alongside the condensation section (cf. Figure 4 (b)). Within these aluminium plates, the temperature sensors can be fitted inside drilled holes. Due to the high thermal conductivity of the aluminium and the solder the temperature gradient inside the “sandwich” is very small und offers a reliable approach for the determination of wall temperatures of thin-walled tubes. Furthermore, high precision resistance temperature sensors can be used, which further reduces the 8

ACCEPTED MANUSCRIPT measurement uncertainty (cf. Bertsche et al. (2016)). A correction of the measured value is not required as the deviation from the calculated wall temperature is within the measurement uncertainty and therefore is included in the calculation. The determination of the pressure drop is done directly by differential pressure sensors (ABB 265DS) calibrated on the spot. The geometrical properties of the three multiport flat tubes are summarized in Table 2 and are displayed at the ratio of the data for the MPFT with a hydraulic diameter of 0.91 mm and rectangular channels.

width of the MPFT 16 mm 16 mm 16 mm

heat transfer area 100 % 74 % 100 %

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Table 2. Geometric Properties of the Multiport Flat Tubes cross section and number of height of the hydraulic diameter channels MPFT rectangular 0.91 mm 18 1.8 mm rectangular 0.77 mm 18 1.3 mm fin structure 0.82 mm 13 1.8 mm

The height of the fin structure covers nearly 70 % of the channel height.

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3.2. Uncertainty In Measurement The accuracy of each measured value and its impact on the target values heat transfer coefficient and pressure drop is determined following the “Guide to the Expression of Uncertainty in Measurement” (GUM / ISO/IEC Guide 98-3) (Evaluation of measurement data — Guide to the expression of uncertainty in measurement). This provision requires the investigation of input and output quantities of each parameter prior to the actual evaluation. Errors which influence these parameters result for example from inaccuracies in recording the measured current and electrical resistance values or those from using averaged temperatures for the calculation of the thermophysical properties. Based on the Gaussian error propagation the GUMmethod assigns every influencing parameter a specific sensitivity coefficient, which rates the impact on the uncertainty of the determined parameter value on the target quantity. This is shown exemplary in equation 8, which is used to calculate the combined uncertainty of the heat transfer coefficient . (8)

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The sensitivity coefficient for each input parameter, for example the temperature difference ΔT, is determined by equation 9.

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The determination of the uncertainty in measurement for the mass flow, as another example, results from the uncertainty of the measured current value (cf. eq. 10).

ΔI includes the inaccuracies of the data loggers as well as discrepancies within repeatability, reversing and analogous measurements. Furthermore, the accuracy of the calibration curve is taken into account. This approach is being included in the evaluation procedure for each data point. Regarding the experimental data shown in this paper, the calculated values of the combined uncertainty in measurement for the results of heat transfer, pressure drop, vapour-phase Weber number and the Lockhart-Martinelli parameter presented within this contribution are shown in Table 3. Table 3. Uncertainty of the Target Values 200 mass flux [kg m-² s-1] heat transfer coefficient ±5–8% pressure drop ±2–3%

400 ± 5 – 11 % ±1–6%

600 ± 5 – 10 % ±1–4%

800 ± 4 – 10 % ±1–6% 9

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±4–8% ±1–3%

±3–6% ±1–3%

±2–6% ±1–3%

A summary of the uncertainties of the used measurement devices as well as the evaluation variable ̇ , which represents the transferred condensation heat, is given in Table 4. The uncertainty range is shown as a maximum range for all used devices of one kind and therefore does not necessarily reflect the uncertainty of each individual temperature sensor for instance.

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Table 4. Uncertainty of the Process Parameters Pt100 temperature sensors uncertainty range ± 0.02 – 0.05 °C

RESULTS AND DISCUSSION

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For each heat transfer and pressure drop data point the measurement data is recorded for 15 minutes after steady-state has been reached to ensure an adequate amount of data to eliminate possible errors in measurement. Prior to the two-phase investigations, a validation of the test facility has been performed using the MPFT with rectangular channels and a hydraulic diameter of 0.91 mm. Hereby, a single-phase flow has been adjusted and the liquid refrigerant inside the MPFT is cooled using the identical setup as described in section 3. Figure 5 shows the experimental Nusselt number in comparison to the correlation by Gnielinski (2013). One can note a very good accordance of the data with the correlation for laminar as well as turbulent flow conditions. Due to the low hydraulic diameter, the transition region has been adjusted to 1900 < Re < 3000 for the calculation of the correlation. This can be verified well by the present data. Although an operating pressure of 8 bar has been chosen, the uncertainty in measurement does increase significantly for higher Reynolds number in the turbulent region as the temperature difference between the liquid and the wall temperature decreases to very low values. Nevertheless, the data does not scatter but reasonably follows the trend of the correlation. The transition region can be further verified by the pressure drop data as well as in comparison with single-phase investigation in the literature by Agostini et al. (2004). Agostini et al. investigated two multiport flat tubes with square channels and hydraulic diameters of 1.17 mm and 0.77 mm. The presented data of the MPFT with rectangular channels and a hydraulic diameter of 0.91 mm is located between the results of Agostini et al. as expected, although a higher Nusselt number can be stated for lower Reynolds numbers. However, this is in good accordance with the correlation by Gnielinski.

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(b) Figure 5. Comparison of the experimental Nusselt number for single phase flow with the correlation by Gnielinski (2013) (a) and the corresponding pressure loss (b). 10

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The results of the subsequent two-phase investigations are given in relation to the results of the single-phase investigations for the rectangular tube with (cf. Figure 5). Figure 6 shows the ratio of the twophase heat transfer coefficient to the liquid-only heat transfer coefficient as presented in Figure 5. This normalization is used for all presented heat transfer values in order to ease comparison. Regarding the heat transfer coefficient as a function of vapour quality (cf. Figure 5), one can observe an increase in heat transfer with an increase of the vapour quality as well as for an increasing mass flux. This can be noted independently for each flat tube and is in accordance with the data published in literature (e.g. Jige et al. (2016); Sakamatapan et al. (2013)).

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Figure 6. Heat transfer coefficient as a function of the vapour quality for a mass flux of 200 kg m-² s-1 (a), 400 kg m-² s-1 (b), 600 kg m-² s-1 (c), 800 kg m-² s-1 (d)

Although the higher heat transfer coefficient for the rectangular channel with a hydraulic diameter of 0.77 mm compared to the channel with a hydraulic diameter of 0.91 mm appears as expected, an unexpected low heat transfer performance of the flat tube with the axial fin structure and a hydraulic diameter of 0.82 mm can be determined. For liquid only investigations Zhang et al. (2015); Zhang et al. (2014) observed an increase of heat transfer using multiport flat tubes with a fin structure compared to a smooth tube with an identical hydraulic diameter. According to Figure 6 this cannot be confirmed for condensation conditions for any of the chosen operation parameters, which might be explained by the specific two-phase distribution in 11

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the channel. Relying on the prevailing opinion in literature, the liquid phase is likely to accumulate at the corners of the channel due to surface tension effects (cf. Wang and Rose (2006)). By comparing the cross section of the flat tubes with rectangular microchannels with the cross section of those with fins, one can assume a high accumulation of liquid between the channel wall and the fin structure (cf. Figure 4). The gaps between fin and walls are likely to fill mostly with liquid, which decreases the heat transfer coefficient due to an increase of the liquid film thickness for a large part of the heat transfer surface. In addition, the shear stress gradient inside the liquid phase will be lowered which again results in a decrease of the lateral mixing of the liquid. According to assumptions made by Thome (2004) and Jige et al. (2016) concerning two-phase flow regimes, one can expect laminar flow within the liquid phase for a wide range of the present operation conditions. If the influence of the shear stress on the liquid is lowered, a stratified flow regime appears and therefore a rise of the thermal boundary layers. Thus, the increase of the heat transfer surface cannot compensate the negative effect of the increasing heat transfer resistance within the liquid phase. Therefore, a more promising approach in order to increase the heat transfer performance of MPFT could be the application of micro-fin structures. Rahman et al. (2018) recently presented promising results regarding the application of axial micro-fins, which underline the present results. The comparison of the present data with various models in literature shows different results for the deviation depending on the channel shape, which again confirms the proposed explanation. Especially for small hydraulic diameters a very good accordance of the experimental data with the Jige et al. (2016) correlation can be observed. Although the experimental data for the flat tube with a hydraulic diameter of 0.91 mm can be predicted with some limitations as well, a poor accordance is given for the flat tube with fins (cf. Figure 7). The correlation clearly overestimates the heat transfer performance of the flat tube with the fin structure. For the flat tube with a hydraulic diameter of 0.91 mm, an underestimation of the experimental data for low heat transfer coefficients can be observed as well as an overestimation for higher values of the heat transfer coefficient. As the correlation assumes a very thin and homogeneous condensate film, one could claim, that the upright rectangular shaped channels with a hydraulic diameter of 0.91 mm are likely to show a higher influence of gravitation than the microchannels with a hydraulic diameter of only 0.77 mm. Based on the previous considerations regarding the distribution of the liquid within the flat tube including an axial finstructure, it is clear that the requirements of the theoretical model cannot be met. Thus, a higher accordance of the data for a hydraulic diameter of 0.77 mm comes as expected and can be verified by comparing the average and mean deviation (cf. equation 6 and 7) of only 9 % and 11 % with the values for all three flat tubes shown in Table 5.

Figure 7. Comparison of the experimental data with the correlation by Jige et al. (2016). Based on the considerations made regarding the poor heat transfer performance of the flat tube with an axial fin structure, a modification of the Jige correlation in terms of calculating the overall Nusselt number for annular flow (cf. equation 2) has been made. is now determined using only the Nusselt number for the surface tension dominant case (cf. equation 5)

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Hereby, the differing flow conditions from a rectangular channel can be represented in an easy and effective manner in a first step. As shown in Figure 8 this modification clearly leads to an improvement of the accordance with the experimental data for the flat tube with a fin structure. In comparison to the original correlation (green), the calculated data of the modified calculation (red) focusses on a small area just as the experimental data. This is in accordance with the suggestions made, as the influence of the vapour quality as well as the mass flux is significantly lower if the flow conditions within the tube remain the same. In this case, a thick liquid film is likely to be present within the grooves of the channel of the flat tube with an axial fin structure for nearly all operation conditions, which has an inhibitory effect on the heat transfer performance. The influence of the vapour shear stress on the heat transfer can be neglected for these conditions, which is reasonable first approach for a theoretical model as Figure 8 displays.

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Figure 8. Comparison of the experimental data for the flat tube with an axial fin structure (hydraulic diameter of 0.82 mm) with the original correlation by Jige et al. (2016) and a modified version.

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The split up of the data for each flat tube can be observed for the Cavallini et al. (2006) (cf. Figure 9) and Kim and Mudawar (2013) (cf. Figure 10) correlation as well. However, even more than with the Jige correlation, one can observe a stronger segregation of the heat transfer values for the flat tubes without fins. Furthermore, a very high overestimation of the experimental data is given for nearly all data points and the results are in a poor accordance with only 26 % of the data within ±20 % and 63 % of the data within ±50 % deviation for the Cavallini correlation. The numbers improve if one only considers the flat tube with a hydraulic diameter of 0.77 mm but do not reach the level of the Jige correlation. Again, the phase distribution might explain the poor results for the fin-structured flat tube, but, in comparison with the Jige correlation, both correlations tend to overestimate most of the experimental data for the smooth rectangular shaped channels as well. Regarding the proposed scope of application of the theoretical model by Cavallini et al., an annular or annular-mist flow is required. This cannot be fully ensured regarding the flat tube with a hydraulic diameter of 0.91 mm as well as the flat tube with the fin-structure. Although the correlation by Kim and Mudawar includes an approach for slug and bubbly flow regimes as well, it can be assumed that the flat tube with a fin-structure does not reflect the common phase distribution inside rectangular channels. Liquid and gas phase are likely not to mix as expected due to the partial separation of the channel and the resulting higher influence of the surface tension within these areas.

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Figure 9. Comparison of the experimental data with the correlation by Cavallini et al. (2006).

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Figure 10. Comparison of the experimental data with the correlation by Kim and Mudawar (2013).

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In Table 5, a summary of the comparison with various correlations from literature is given. Depending on the channel shape, a higher accordance of various correlations, such as the Koyama or Kim and Mudawar correlation, can be achieved, especially concerning those with a rectangular cross section. This can be verified by considering the split up of the shown data for the different cross sections shown in Figure 8 to Figure 10. Furthermore, the average deviation (ad) as well as the mean deviation (md) are given. Table 5. Comparison of the experimental data for the heat transfer coefficient with selected correlations ± 20 % ± 50 % ad md Akers et al. (1959) 41 % 83 % -5 % 28 % Cavallini et al. (2006) 26 % 63 % 60 % 66 % Kim and Mudawar (2013) 40 % 72 % 31 % 41 % Jige et al. (2016) 50 % 79 % 35 % 35 % López-Belchí et al. (2014) 26 % 64 % -15 % 42 % Shah (2016) 31 % 66 % 44 % 52 % Webb et al. (1998) 23 % 83 % -28 % 33 %

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Although the correlation by Akers et al. (1959) shows a good overall accordance for the present data as well as a small average and mean deviation compared to the other correlations, one has to take into account that the data for the rectangular channels is being underpredicted and the data for the channels including a finstructure is being overpredicted by the correlation. Furthermore, the calculated data using the Akers correlation shows a similar scatter as the other correlations. While a good overall performance can be stated for the present data, significant discrepancies have to be named for the individual channels.

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Compared to the results for the heat transfer, the pressure drop characteristics appear as expected (cf. Figure 11). An increase of the pressure drop can be observed for an increase of the vapour quality and mass flux. Furthermore, the pressure drop of the three different flat tubes differs as expected regarding their hydraulic diameter. One could assume a slightly higher pressure drop for the flat tube including the fin structure due to the increase of the frictional pressure loss between the liquid and the fins. However, this cannot be verified as the expected impact of the fins on the pressure drop is within the measurement uncertainty.

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Figure 11. Pressure drop as a function of the vapour quality for a mass flux of 200 kg m-² s-1 (a), 400 kg m-² s-1 (b), 600 kg m-² s-1 (c), 800 kg m-² s-1 (d)

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For low mass fluxes, such as 200 kg m-² s-1 (cf. Figure 11 (a)), a low dependency on the hydraulic diameter can be noted. However, with an increase of the mass flux a higher influence of the hydraulic diameter as well as of the vapour quality appears. On one hand, the shear stress at both interfaces, i.e. the gas-liquid and the liquid-solid interface, increases as the velocity of each phase is being raised. On the other hand the velocity gradient inside the condensate film increases, which leads to a higher lateral mixing and turbulences inside the liquid phase. By comparing Figure 11 (a) to (d), one can observe a higher impact of the mass flux on the pressure drop compared to the impact of the vapour quality. Although quadruplicating the vapour quality leads to a fourfold increase of the pressure drop as well, a quadruplicating of the mass flux raises the pressure drop by a factor of up to nine for high vapour qualities. This can be stated independently for all three flat tubes. Comparing with literature, a very good accordance of the Friedel (1979) correlation for the three multiport flat tubes can be observed (cf. Figure 12). Although the trend shows a slight underestimation of the experimental data regarding higher values of the pressure drop, 94 % of the experimental data can be predicted within a deviation of ±20 % and 99 % of the data within ±50 %. For low mass velocities in combination with low vapour qualities, which again results in low values for the pressure drop, a slightly higher deviation can be observed. In this case, the correlation seams to under predict the experimental data 16

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but the reason might also to be found within the measurement accuracy of the pressure drop sensor for very low pressure drops. Slightly lower accordance can be achieved by using the Jige et al. (2016) correlation with 76 % of the data within a deviation of ±20 % and 99 % of the data within ±50 % (cf. Figure 13).

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Figure 12. Comparison of the experimental data with the correlation by Friedel (1979).

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Figure 13. Comparison of the experimental data with the correlation by Jige et al. (2016).

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Figure 14. Comparison of the experimental data with the correlation by Cavallini et al. (2006).

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Although adapted to the use with microchannels and based on the Paleev and Filippovich (1966) equation, the correlation of Cavallini et al. (2006) does not provide reasonable agreement with the present data. The comparison clearly shows an underestimation of the experimental data for nearly all operation parameters. However, the accordance increases with decreasing hydraulic diameter and the data is located within a narrow band. As stated by Cavallini et al. (2009) an application for flat tubes with a fin-structure is possible. As shown in Figure 14 this can be confirmed with a similar accordance as for rectangular shaped channels. Further comparisons with selected correlations from literature are given in Table 6. The average deviation (ad) and mean deviation (md) have been calculated using eq. 12 and 13 and the data for the pressure drop. One can easily note that all correlations tend to underpredict the present pressure drop data.

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Table 6. Comparison of the experimental data for the pressure drop with selected correlations ± 20 % ± 50 % ad Cavallini et al. (2006) 38 % 99 % -24 % Friedel (1979) 94 % 99 % -10 % Kim and Mudawar (2013) 30 % 99 % -23 % Jige et al. (2016) 76 % 99 % -11 % López-Belchí et al. (2014) 2% 75 % -45 % Müller-Steinhagen and Heck 45 % 82 % -34 % (1986) Sakamatapan and Wongwises 14 % 81 % -40 % (2014) Zhang and Webb (2001) 6% 73 % -40 %

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md 24 % 12 % 23 % 15 % 45 % 34 % 40% 40%

CONCLUSIONS

Heat transfer and pressure drop characteristics for pure R134a have been investigated, with special emphasis on the effect of the channel shape in comparison to the effect of the hydraulic diameter. The presented results lead to the following conclusions: 1. Heat transfer and pressure drop increase with increasing vapour fraction and mass flux. For rectangular channels, both values increase with a decrease of the hydraulic diameter regarding rectangular shaped microchannels. 2. The use of a fin structure for condensation channels does not resemble the positive results of singlephase investigations concerning the heat transfer performance of such channel shapes. Although a slightly higher pressure drop can be noted, the heat transfer performance decreases in comparison to the rectangular channels. This can be explained by considering the two-phase flow distribution within the channel, which most likely leads to an accumulation of the liquid at the numerous grooves 18

ACCEPTED MANUSCRIPT of the fin structure. This again increases the heat transfer resistance due to the increase of the liquid film thickness and suppression of internal mixing within the film. 3. As the experimental data for the pressure drop strongly depends on the hydraulic diameter, the presented data can be predicted well by using the Jige et al. (2016) or Friedel (1979) correlation. For the heat transfer, a satisfying accordance of the Jige et al. (2016) correlation with the data can be stated. As for the Cavallini et al. (2006) correlation only a poor accordance is given, especially for the flat tube with a hydraulic diameter of 0.91 mm and the fin structured tube. A reasonable explanatory approach is the consideration of the phase distribution as the correlation assumes an annular or annular-mist flow, which is most likely to be present for the flat tube with a hydraulic diameter of 0.77 mm. For both the other flat tubes an influence of either the fin structure or the gravitational force on the flow regime cannot be fully neglected.

ACKKNOLEDGEMENTS

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The authors would like to thank MAHLE Behr GmbH & Co. KG and BMWi for their funding of this research project. The project has been funded according to a decision by the Bundestag under the contract number 03ET1106A.

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