Condensation of R134a and R134a-Oil Mixture in a Multiport Flat Tube

Sandra Abreu Ferreira Gomes

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisors: Prof. António Luís Nobre Moreira

Dipl.-Ing. Paul Knipper

Examination Committee

Chairperson: Prof. Edgar Caetano Fernandes

Supervisor: Prof. António Luís Nobre Moreira

Member of the Committee: Prof. Miguel Abreu de Almeida Mendes

June 2018

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Abstract With the purpose of reducing the system’s weight, while having a high heat transfer, aluminium multiport flat tubes with small dimensions are widely used in the condensers and evaporators of automotive vehicles. However, the condensation process in those tubes is not yet fully understood. To achieve the best possible design, precise computational models are needed. Therefore, the existent models for macro-channels must be further developed considering the effects of the small geometries.

This work investigates experimentally the heat transfer and the pressure drop characteristics of the pure refrigerant R134a and R134a-oil mixture during condensation in multiport flat tubes with triangular channels. The influence of the saturation pressure, mass flux and vapor quality was analysed. The obtained data was compared with previously studied geometries, as well as correlations from the literature.

The heat transfer coefficient and pressure drop measured values generally rise with increasing mass flux and vapor quality. A decrease of the pressure drop with increasing saturation pressure is also observed. Comparing with other geometries, the studied multiport flat tube presents a weaker performance. In addition, while the pressure drop is accurately predicted by some of the correlations found in the literature, the heat transfer coefficient is generally overestimated. These results will be used in the future for the development of new computational models.

The effect of the addition of the oil to the system on both pressure drop and heat transfer coefficient values was analysed. However, further research is recommended to assess the effect of higher nominal oil concentrations.

Keywords: condensation; heat transfer coefficient; pressure drop; multiport flat tubes with triangular mini-channels; R134a; R134a-lubricant mixture.

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Resumo A fim de desenvolver veículos mais eficientes, o sistema de climatização tem sido alvo de redução de peso. Apesar de tubos de alumínio com mini-canais serem de uso comum em condensadores e evaporadores, o processo de condensação nestas geometrias não é completamente conhecido. Para obter o melhor design possível, são necessários modelos computacionais precisos. Deste modo, os modelos existentes para macro-canais devem continuar a ser desenvolvidos considerando os efeitos específicos das geometrias de menor dimensão.

Neste trabalho investigou-se experimentalmente a transmissão de calor e perda de pressão do refrigerante R134a e da mistura R134a-lubrificante, num tubo de alumínio com mini-canais triangulares. A influência da pressão de saturação, do fluxo mássico e da qualidade de vapor são analisadas.

O coeficiente de transmissão de calor e a perda de pressão geralmente aumenta com o aumento do fluxo mássico e da qualidade de vapor. Verifica-se ainda uma redução da perda de pressão com o aumento da pressão de saturação. Comparativamente a geometrias anteriormente estudadas no mesmo laboratório, o tubo estudado apresenta o pior desempenho. Adicionalmente, enquanto os valores do coeficiente de transmissão de calor não foram previstos pelas correlações da literatura, os valores de perda de pressão foram parcialmente previstos. Estes resultados serão no futuro utilizados no desenvolvimento de novos modelos computacionais.

O efeito da adição de lubrificante ao sistema na perda de pressão e no coeficiente de transmissão de calor foi analisado. No entanto, o procedimento experimental deve ser repetido para superiores concentrações de lubrificante, para se poderem obter conclusões finais.

Palavras-chave: condensação; coeficiente de transmissão de calor; perda de pressão; tubos com mini-canais triangulares; R134a; mistura R134a-lubrificante.

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Acknowledgements I would like to start by expressing my gratitude to Professor António Luís Moreira, for the possibility of writing this thesis abroad, for giving me the freedom to choose a topic I have great interest in, and for the support throughout the semester.

I also want to express my thankfulness to my supervisor Dipl.-Ing. Paul Knipper, for the opportunity of developing this work at the Institute of Thermal Process Engineering of the KIT, and especially for his kind supervision. His support, patience, and knowledge were very important for writing this thesis, and for that I am incredibly thankful.

My acknowledgements are extended to my parents, my sister and my grandmother for their unconditional love, unwavering support and belief in me.

Lastly, I would like to express my sincere appreciation to my boyfriend Matthias, and to my friends Bárbara and Tiago, for their continuous encouragement and support.

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Table of Contents Abstract ......................................................................................................................iii

Resumo ........................................................................................................................ v

Acknowledgements ..................................................................................................... vii

Table of Contents ........................................................................................................ ix

List of Symbols and Acronyms .................................................................................... xi

List of Figures ............................................................................................................ xv

List of Tables ............................................................................................................. xix

1 Introduction ........................................................................................................... 1

1.1 Problem definition............................................................................................................. 1

1.2 Research methodology ....................................................................................................... 2

2 Fundamentals ......................................................................................................... 3

2.1 Channel classification ........................................................................................................ 3

2.2 Flow regimes ..................................................................................................................... 4

2.3 Void fraction ..................................................................................................................... 7

2.4 Pressure drop .................................................................................................................... 8

2.5 Heat Transfer .................................................................................................................. 13

2.6 Refrigerant-oil mixture .................................................................................................... 16

3 Experimental apparatus ....................................................................................... 19

3.1 Testing facility ................................................................................................................ 19

3.2 Determination of the experimental values ....................................................................... 23

3.3 Uncertainty analysis with GUM ...................................................................................... 25

4 Results ................................................................................................................. 27

4.1 Data analysis................................................................................................................... 27

4.2 Measurement results ....................................................................................................... 30

4.2.1 Single-phase flow ................................................................................................ 30

4.2.2 Two-phase flow ................................................................................................... 32

4.3 Reproducibility ............................................................................................................... 40

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5 Discussion ............................................................................................................ 43

5.1 Comparison with other MFT geometries ........................................................................ 43

5.1.1 Heat Transfer...................................................................................................... 43

5.1.2 Pressure Drop ..................................................................................................... 44

5.2 Comparison with correlations .......................................................................................... 45

5.2.1 Pressure Drop ..................................................................................................... 46

5.2.2 Heat Transfer...................................................................................................... 52

6 Influence of oil in flow condensation..................................................................... 61

6.1 Set-up for refrigeration-oil mixture ................................................................................. 61

6.2 Validation of the experimental set-up ............................................................................. 62

6.2.1 Single-phase results ............................................................................................. 62

6.2.2 Two-phase results ............................................................................................... 64

7 Conclusions and Future Work .............................................................................. 69

7.1 Contributions .................................................................................................................. 69

7.2 Suggestions for Future Work ........................................................................................... 71

References .................................................................................................................. 73

Appendix ................................................................................................................... 77

Part 1: Figures .......................................................................................................................... 77

Part 2: Tables ........................................................................................................................... 87

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List of Symbols and Acronyms Latin symbols

Symbol Units Interpretation

A m2 area Ac m2 cross sectional area a - variable pre-factor C - Chrisholm constant 𝑐 J kg-1 K-1 specific heat ci - sensitivity coefficient (GUM) D m diameter E - entrainment factor e m channel roughness F - function of f - friction factor Gi - weighting factor (GUM) g m s-2 gravitational acceleration h W m-2 K-1 condensation heat transfer coefficient j m s-1 superficial velocity 𝐾 - expansion factor (GUM) k W m-1 K-1 thermal conductivity L m length kg s-1 mass flow rate kg m-2 s-1 mass flux P m perimeter p bar pressure W heat flow rate 𝑞 W m-2 heat flux R - two-phase multiplier (Friedel) r - sub-cooling corrective factor RT K W-1 thermal resistance S - slip ratio T °C temperature t m thickness u m s-1 average velocity 𝑉 m3 volume 𝑉 m3 s-1 volumetric flow rate 𝑊 m width Y - measurand (GUM) y - estimation of the measurand (GUM)

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𝑥 - length parameter/measured parameter 𝑥 - vapor quality z axial coordinate oriented with the flow

Greek symbols

Symbol Units Interpretation 𝛿 m film thickness ∆ change, difference 𝜀 - void fraction 𝜇 kg m-1 s-1 dynamic viscosity 𝜈 N m-1 kinetic viscosity 𝜌 kg m-3 density 𝜎 N m-1 surface tension 𝜏 Pa shear stress 𝛸 Lockhart-Martinelli parameter 𝛹 - two-phase multiplier (Shah) 𝜔 - oil concentration 𝜙 - two-phase multiplier (Lockhart and Martinelli)

Subscripts

Symbol Interpretation a acceleration An annular flow AS adiabatic section ave average B free convection condensation term evap evaporator eq equivalent exp experimental f friction F vapor shear stress effect term g gravitational gc gas core h hydraulic hep heptane i interface liquid-vapor in inlet l liquid phase/saturated liquid

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lo liquid only Ls liquid slug (flow) M mixture of refrigerant (R134a) and oil mid middle point min minimum value MS measurement section out outlet/exit pred predicted ref refrigerant R134a (pure) sat saturation s surface S surface tension effect term SW measurement sandwich SF single-phase t total TP two-phase tr transition TS test section tt turbulent liquid-turbulent vapor tl turbulent liquid-laminar vapor lt laminar liquid-turbulent vapor ll laminar liquid-laminar vapor v vapor/saturated vapor vo vapor only Vp vapor plug (flow) W wall ∞ outside of the boundary layer

Superscripts

Symbol Interpretation b exponential factor c exponential factor + non-dimensional ′ saturated liquid ″ saturated vapor

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Acronyms and abbreviations

Acronym Interpretation a. c. after sub-cooling correction CT round single tube EB error band EF enhancement factor GUM Guide to the Expression of Uncertainty in Measurement Mix mixture of refrigerant (R134a) and oil MARD mean absolute relative deviation MFT multiport flat tubes MRD mean relative deviation OD outer diameter PF penalty factor R134a 1,1,1,2-Tetrafluoroethane Ref pure refrigerant (R134a) Rep repeated

Dimensionless numbers

Number Definition Formula and interpretation

Bo Bond number

𝐵𝑜 =𝜌 − 𝜌 𝑔𝐷

𝜎=

𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒

𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒

Co Confinement number 𝐶𝑜 =

𝜎𝑔 𝜌 − 𝜌

𝐷

Fr Froude number

𝐹𝑟 = 𝑢

𝑔𝐷=

𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑓𝑜𝑟𝑐𝑒

𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒

Ga Galileo number

𝐺𝑎 =𝑔𝜌 𝐷

𝜇=

𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒𝑠

𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑐𝑒𝑠

Nu Nusselt number

𝑁𝑢 =ℎ𝐷

𝑘=

ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑏𝑦 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛

ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑏𝑦 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑎𝑙𝑜𝑛𝑒

Pr Prandtl number

𝑃𝑟 =𝜇𝑐

𝜌𝑘=

𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚

𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 ℎ𝑒𝑎𝑡 𝑖𝑛 𝑎 𝑓𝑙𝑢𝑖𝑑

Re Reynolds number

𝑅𝑒 =𝜌𝑢𝐷

𝜇=

𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑓𝑜𝑟𝑐𝑒𝑠

𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑠ℎ𝑒𝑎𝑟 𝑓𝑜𝑟𝑐𝑒𝑠

Su Suratman number 𝑆𝑢 =

𝑅𝑒

𝑊𝑒

We Weber number

𝑊𝑒 =𝜌𝑢 𝐷

𝜎=

𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒

𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒

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List of Figures Figure 1: Extruded aluminum multiport flat tubes with various geometries (left) (Trumony Aluminium Limited 2018) and a standard automotive condenser (right) (CARiD 2018). .................. 1

Figure 2: Flow regime transition for a tube with 0.53 mm hydraulic diameter with use of the transition criteria presented by Nema et al. (2014). ........................................................................................... 6

Figure 3: Influence of flow regimes on the heat transfer coefficient during condensation (Kim and Mudawar 2014). ................................................................................................................................ 13

Figure 4: Pressure-enthalpy regime map showing the influence of the oil in the refrigerant-oil mixture (Hughes et al. 1984). ........................................................................................................................ 17

Figure 5: Schematic view of the testing facility (Knipper 2018). ...................................................... 19

Figure 6: Computer modeled view of the test section (Knipper 2018). ............................................ 22

Figure 7: Measurement section during assembly. .............................................................................. 22

Figure 8: Schematic view of the test section and the experimentally measured values. .................... 23

Figure 9: Placement of the temperature and pressure sensors in the flange (Knipper 2018). ........... 24

Figure 10: Heat transfer coefficient ratio at 15 bar before and after sub-cooling correction. ............ 28

Figure 11: Uncertainty distribution at a condensation pressure of 15 bar, a mass flux of 1000 kg/(m2s) and vapor quality of 20%, before the correction (15%). ................................................................... 29

Figure 12: Heptane mass flow rate measurement at a condensation pressure of 15 bar, a mass flux of 1000 kg/(m2s) and vapor quality of 20%, left and right, respectively. .............................................. 29

Figure 13: Comparison of the single-phase measurement results with the literature. ....................... 30

Figure 14: Single-phase flow measured pressure drop values. ........................................................... 31

Figure 15: Comparison between the calculated experimental friction factor values and Blasius and Churchill (1977) correlations. ........................................................................................................... 32

Figure 16: Experimental heat transfer coefficient values at 10 bar. .................................................. 33

Figure 17: Numerical results for a triangular channel (1 mm side size) at 500 kg/(m2s) and constant vapor and surface temperatures, 50 °C and 45 °C, respectively (Wang and Rose 2006). .................. 35

Figure 18: Overview of the measurement points over the flow regime map using the transition criteria as presented by Nema et al. (2014). ................................................................................................. 36

Figure 19: Experimental heat transfer coefficient values at 15 bar (left) and 20 bar (right). ........... 37

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Figure 20: Experimental heat transfer coefficient values measured at a constant mass flux of 1000 kg/(m2s) and respective uncertainty intervals. ......................................................................... 38

Figure 21: Experimental pressure drop values at 10 bar. .................................................................. 38

Figure 22: Experimental pressure drop values measured at 10 bar, plotted against mass flux. ........ 39

Figure 23: Experimental pressure drop values at 15 bar (left) and 20 bar (right). ........................... 40

Figure 24: Heat transfer coefficient results of the reproducibility measurements at 15 bar. ............. 41

Figure 25: Pressure drop results of the reproducibility measurements at 15 bar. ............................. 41

Figure 26: Comparison of heat transfer coefficient values between four different channel geometries at 10 bar and 400 kg/(m2s) and 600 kg/(m2s), left and right, respectively. .......................................... 43

Figure 27: Comparison of pressure drop values between four different channel geometries at 10 bar and a mass flux of 400 kg/(m2s) and 600 kg/(m2s), left and right, respectively. .............................. 44

Figure 28: Comparison of the predicted pressure drop using the Müller-Steinhagen and Heck (1986) correlation (left) and the Friedel (1979) correlation (right) with the experimental data. ................. 46

Figure 29: Comparison of the predicted pressure drop using the Cavallini (2006) correlation (left) and the Cavallini (2006) correlation modified with Blasius equation (right) with the experimental data. ......................................................................................................................................................... 47

Figure 30: Comparison of the predicted pressure drop using the Zhang and Webb (2001) correlation with the experimental data. ............................................................................................................. 49

Figure 31: Comparison of the predicted pressure drop using the Kim and Mudawar (2012) correlation (left) and the Sun and Mishima (2009) correlation (right) with the experimental data. .................. 50

Figure 32: Comparison of the predicted pressure drop using the Jige et al. (2016) correlation (left) and the Agarwal and Garimella (2009) correlation (right) with the experimental data. .................. 51

Figure 33: Comparison of the predicted heat transfer coefficient using the Akers et al. (1959) correlation (left) and the correlation Shah (1979) correlation (right) with the experimental data. .. 53

Figure 34: Comparison of the predicted heat transfer coefficient using the Webb and Ermis (2001) correlation (left) and the Webb and Ermis (2001) correlation modified (right) with the experimental data. ................................................................................................................................................. 53

Figure 35: Comparison of the predicted heat transfer coefficient using the Cavallini et al. (2006) correlation with the experimental data. ........................................................................................... 55

Figure 36: Comparison of the predicted heat transfer coefficient using the Koyama et al. (2003) correlation (left) and the Illán-Gómez et al. (2014) correlation (right) with the experimental data. 56

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Figure 37: Comparison of the predicted heat transfer coefficients using the Jige et al. (2011) correlation (left) and the Jige et al. (2016) correlation (right) with the experimental data. .............................. 57

Figure 38: Comparison of the predicted heat transfer coefficients using the Jige et al. (2016) correlation (modified) with the experimental data. ............................................................................................ 59

Figure 39: Single-flow measured pressure drop values for refrigerant-oil mixture. ............................ 63

Figure 40: Comparison of the single-phase measurement results of pure refrigerant and refrigerant-oil mixture with the literature. .............................................................................................................. 63

Figure 41: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar. ..................................................................... 64

Figure 42: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 800 kg/(m2s) and at 10 bar (left) and enhancement factor values at 10 bar (right). ......................................................................................................... 65

Figure 43: Comparison between the experimental pressure drop values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar. ....................................................................................... 66

Figure 44: Penalty factor values at 10 bar. ....................................................................................... 66

Figure 45: Heat transfer coefficient ratio at 20 bar before and after sub-cooling correction. ............ 77

Figure 46: Heptane outlet temperature measurement and refrigerant outlet temperature measurement at a condensation pressure of 15 bar, a mass flux of 1000 kg/(m2s) and vapor quality of 20%, left and right, respectively. ............................................................................................................................ 77

Figure 47: Uncertainty distribution at a condensation pressure of 15 bar, a mass flux of 1000 kg/(m2s) and vapor quality of 20%, after the correction (5%). ....................................................................... 78

Figure 48: Experimental heat transfer coefficient values at 10 bar and respective uncertainty intervals. ......................................................................................................................................................... 78

Figure 49: Experimental heat transfer coefficient values at 15 bar and respective uncertainty intervals. ......................................................................................................................................................... 79

Figure 50: Experimental heat transfer coefficient values at 20 bar and respective uncertainty intervals. ......................................................................................................................................................... 79

Figure 51: Heat transfer coefficient results of the reproducibility measurements at 10 bar. ............. 80

Figure 52: Heat transfer coefficient results of the reproducibility measurements at 20 bar. ............. 80

Figure 53: Pressure drop results of the reproducibility measurements at 10 bar .............................. 81

Figure 54: Pressure drop results of the reproducibility measurements at 20 bar. ............................. 81

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Figure 55: Comparison of heat transfer coefficient ratios between different geometries at 10 bar and 800 kg/(m2s). .................................................................................................................................... 82

Figure 56: Comparison of pressure drop for four different channel geometries at 10 bar and a mass flux of 800 kg/(m2s). ........................................................................................................................ 82

Figure 57: Calculated pressure drop using the Sakamatapan and Wongwises (2014) correlation (left) and the López-Belchí et al. (2014) correlation (right), plotted against the experimental values. ...... 83

Figure 58: Calculated heat transfer coefficients using the Wang et al. (2002) correlation (left) and the Kim and Mudawar (2013) correlation (right), plotted against the measured values. ........................ 83

Figure 59: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 400 kg/(m2s) (left); and at 600 kg/(m2s) (right). .............................................................................................................................................. 84

Figure 60: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 1000 kg/(m2s) (left), and at 1200 kg/(m2s) (right). .............................................................................................................................................. 84

Figure 61: Comparison between the experimental pressure drop values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 400 kg/(m2s) (left), and at 600 kg/(m2s) (right). 85

Figure 62: Comparison between the experimental pressure drop values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 800 kg/(m2s) (left), and at 1000 kg/(m2s) (right). ......................................................................................................................................................... 85

Figure 63: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 1200 kg/(m2s). ................................... 86

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List of Tables Table 1: Channel classification as presented by Kandlikar and Grande (2003). ................................. 3

Table 2: Two-phase flow regimes and patterns (Coleman and Garimella 2003). ................................. 4

Table 3: Transition criteria for small channels (Nema et al. 2014). .................................................... 5

Table 4: Overview of the models and constants for the determination of the void fraction. ............... 8

Table 5: Chisholm constant C as presented by Chisholm (1967). ..................................................... 11

Table 6: Operating parameters whose heat transfer coefficients were corrected regarding sub-cooling. ......................................................................................................................................................... 28

Table 7: Overview of the operating parameters. ............................................................................... 32

Table 8: Overview of the variation of the most relevant measurement parameters during the measurements. .................................................................................................................................. 33

Table 9: Variation of the thermophysical properties of R134a and values of slip ratios for different vapor qualities (Smith 1969). ........................................................................................................... 34

Table 10: Influence of the vapor quality and mass flux on the pressure drop at 10 bar. .................. 39

Table 11: Overview of the comparison of the experimental pressure drop with the correlations. ..... 46

Table 12: Effectiveness indicators for the measurements at 10 and 15 bar. ...................................... 47

Table 13: Overview of the comparison of the experimental heat transfer coefficient with the correlations considered. .................................................................................................................... 52

Table 14: Comparison of the different geometries presented in Webb and Ermis (2001). ................. 54

Table 15: Comparison between the original correlation presented by Webb and Ermis (2001) for plain rectangular geometry with the modified correlation for the triangular geometry studied................. 54

Table 16: Used substances in the experimental apparatus. ............................................................... 87

Table 17: Appliances and measurement units used in the experimental apparatus. ......................... 88

Table 18: Operating parameters at which the experimental procedure was performed. .................... 89

Table 19: Overview of the repetition points for the reproducibility analysis. ................................... 89

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Table 20: Overview of the experimental data compared between the different geometries at 10 bar. ......................................................................................................................................................... 90

Table 21: Overview of the pressure drop correlations. ...................................................................... 91

Table 22: Overview of the heat transfer correlations. ....................................................................... 92

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1 Introduction Within the automotive industry, the increasingly stricter legislation on automotive fuel consumption and carbon dioxide emissions (CO2) for combustion vehicles, as well as the great interest in increasing the mileage of the electric vehicles, require the continuous development of more efficient vehicles. One way of improving the efficiency of a vehicle is the reduction of the overall weight of the car. As one of the car’s systems, the refrigeration cycle has also been subjected to weight optimization. This system consists of four main components: evaporator, compressor, condenser and expansion valve. The refrigerant, at low pressure, absorbs energy from the air in the evaporator, which provides cooled air to the interior of the car. In the condenser, at high pressure, the refrigerant is condensed as the heat is transferred to the air flow. Compared to single-phase flow, where only the sensible heat rise of reduction could be used, using two-phase flow the combination of sensible and latent heat allows an absorption of great amounts of heat, while keeping a relatively low device temperature (Kim and Mudawar 2014).

At the department of Thermal Process Engineering of the Karlsruhe Institute for Technology, a project with the objective of experimentally studying the condensation of R134a in multiport flat tubes has been developed. These tubes are used in condensers and evaporators and consist of extruded aluminum profiles with parallel channels with reduced dimensions in which the refrigerant flows (Figure 1).

Figure 1: Extruded aluminum multiport flat tubes with various geometries (left) (Trumony

Aluminium Limited 2018) and a standard automotive condenser (right) (CARiD 2018).

1.1 Problem definition

The use of mini and micro-channels has various advantages regarding its weight and performance. The small geometry of the channels leads to a weight reduction in comparison with the macro-channels, as well as a reduction of the refrigerant charge. Additionally, these types of channels have generally a higher heat transfer when compared with conventional channels, and a reduced air side

2

pressure drop (small cross section). As a result, space, energy, and material can be saved in comparison with heat exchangers featuring conventional channels of identical capacity (Rahman et al. 2017). However, its use also comes with disadvantages, especially a higher pressure drop inside the channels. Due to the smaller hydraulic diameter, the necessary compressor power increases, in turn reducing the overall efficiency of the system (Kim and Mudawar 2012, López-Belchí et al. 2014).

To achieve the best possible design, considering both heat transfer and pressure loss, precise computational models are needed. The models which exist for macro-channels cannot be used for multiport flat tubes without further development, since the different relative influence of the gravitational force, the surface tension, and the shear forces between the phases, change the way the flow develops in the channel. Even though the multiport flat tubes are widely used, the process kinetics are not fully understood yet, as there is no precise enough model which accounts simultaneously for the flow regimes, heat transfer, and pressure loss, for different hydraulic diameters and geometries.

1.2 Research methodology

The goal of this project is to determine the two-phase heat transfer coefficient and pressure loss of R134a during condensation in multiport flat tubes with different geometries. A comparison between the different geometries' results is made possible since the same experimental apparatus is used. The profile studied experimentally in this work is a multiport flat tube with triangular channels and a hydraulic diameter of 0.529 mm. This tube consists of a rectangular tube with rounded corners, with various triangular-shaped channels. The effects of the various influencing parameters, namely mass flux, vapor quality, and condensation pressure on heat transfer coefficient and pressure drop, are investigated. The results are compared with previous geometries and against correlations found in the literature (expected to predict both heat transfer coefficient and pressure drop), to validate them for the used profile.

In addition to the experimental study of the condensation of pure refrigerant, the influence of the oil in the process is also studied. In a vapor compression refrigeration system, oil is needed to lubricate the moving parts of the compressor. The lubricant oil circulates with the refrigerant through the components of the system, including the heat exchangers. Since the oil can reach up to 10% of the weight of the circulating fluid, a strong influence in both heat transfer coefficient and pressure loss can be expected due to the change of the physical properties.

The results obtained in the context of this work, as well as the results obtained in the earlier stages of the overall project, will be used for the future development of more precise computational models for small geometries. These models will then allow an optimized design of the new generation of condensers.

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2 Fundamentals In this chapter the fundamentals of heat transfer and fluid mechanics, essential to understand the occurring phenomena during the experimental procedure, are summarized. The basis for the development of correlations for heat transfer coefficient and pressure drop in mini-channels are presented, recalling previous work done on the topic.

2.1 Channel classification

Due to the great variety of channels used in the literature, their classification became essential for thermal and flow characterizations. Out of the developed classifications, the one stated by Kandlikar and Grande (2003) has been widely used. This classification, which distinguishes the type of channels based on flow considerations, is summarized in Table 1. The hydraulic diameter (Dh) is calculated with the cross-sectional area (Ac) and the perimeter (P) with Equation 1.

Table 1: Channel classification as presented by Kandlikar and Grande (2003).

Type of channel Hydraulic Diameter (Dh)

Conventional channels > 3 mm

Mini-channels 0.2 mm – 3 mm

Micro-channels 0.01 mm – 0.2 mm

An alternative classification is presented by Kew and Cornwell (1977), which takes the effects of confinement in channels into consideration. The Confinement number (Equation 2) is calculated with the channel geometry (𝐷 ) and the fluid properties, namely the surface tension (𝜎) and the density of the two phases (𝜌 and 𝜌 ). When the confinement effects are significant, Co > 0.5, the channels

are considered mini-channels, whereas when Co ≤ 0.5, the channels are conventional channels.

𝐶𝑜 =

𝜎𝑔 · 𝜌 − 𝜌

𝐷 (2)

The channel used in this work has a hydraulic diameter of 0.529 mm and its confinement number varies between 1.08 and 1.43 mm (between 10 and 20 bar). Therefore, it is classified as mini-channel by both Kandlikar and Grande and Kew and Cornwell.

𝐷 = 4𝐴

𝑃 (1)

4

2.2 Flow regimes

In addition to what happens in the case of single-phase flow, during condensation, as the gas contacts a surface under the saturation temperature, distinguishable flow regimes can be observed along the channels. This is a consequence of the different magnitudes of the forces acting on the two phases, such as gravity, surface tension and shear stress (Nema et al. 2014). The way these forces act depends on the operating conditions of the system, namely vapor quality, mass flow density, pressure and temperature, as well as channel geometry.

In macro-channels, seven different flow regimes can be identified: bubbly flow, plug flow, stratified flow, wavy flow, slug flow, annular flow and mist flow (Steiner 2013). In channels of smaller hydraulic diameter (Dh), mini and micro-channels, a stronger influence of surface tension forces is verified. For this reason, flow regimes which are dominated by gravitational forces, such as wavy and stratified flow, become less important. As the hydraulic diameter decreases, intermittent (slug and plug) and annular flow regimes are mostly observed (Garimella 2004). The different flow regimes as defined by Coleman et al. (2003) can be observed in Table 2.

Table 2: Two-phase flow regimes and patterns (Coleman and Garimella 2003).

The different flow regimes depend on the operating conditions and are often represented in flow regime maps. There are different types of flow regime maps based on substance properties and operating conditions. The different regimes are separated using transition criteria, which are obtained from both empirical and analytical data. The transition lines are an approximation, and, in some cases, transition areas are defined.

Nema et al. (2014) presented dimensionless flow regime transition criteria for small channels. The criteria were established based on the experimental data obtained by Coleman and Garimella (2003)

5

using R134a in channels whose hydraulic diameter ranges between 1 and 4.91 mm. Additionally, due to insufficient data in the dispersed flow region, an analytical criterion from Taitel and Dukler (1976) was used. For the application of the presented transition criteria the critical Bond number is calculated. A Bond number which is equal or smaller than the critical is related to confinement effects. Bond number equation (Equation 3) is derived from the balance of forces over a liquid element, including the vapor-phase gravitational force (Nema et al. 2014).

𝐵𝑜 =1

𝜌𝜌 − 𝜌 − 𝜋

4

(3)

The transition between the flow regimes is defined based on two dimensionless numbers: vapor phase Weber number (𝑊𝑒 ) and Martinelli-Parameter (𝑋 ). The Weber number represents the ratio

between vapor inertia and surface tension forces and for the gas phase is calculated by Equation 4.

𝑊𝑒 =𝜌 · 𝑢 · 𝐷

𝜎 (4)

The Martinelli-Parameter, presented as two-phase flow parameter by Lockhart and Martinelli (1949), relates the characteristics of a two-phase and single-phase flow (see section 2.4).

𝑋 =𝜌

𝜌·

𝜇

𝜇·

1 − 𝑥

𝑥 (5)

Based on the above dimensionless parameters, Nema et al. (2014) developed the transition criteria which are presented in Table 3.

Table 3: Transition criteria for small channels (Nema et al. 2014).

Flow regime Conditions

Mist flow 𝑊𝑒 > 700 and 𝑋 < 0.175

Dispersed flow 𝑊𝑒 < 35 and 𝑋 > 0.3521 and 𝑇 ≥ ·

· ·( · )−

Annular 𝑊𝑒 ≥ 35 or 𝑊𝑒 < 35 and 𝑋 ≤ 0.3521

Intermittent/annular film 6 ≤ 𝑊𝑒 < 35 and 𝑋 > 0.3521

Intermittent flow 𝑊𝑒 < 6 and 𝑋 > 0.3521

In Figure 2, a flow regime map, based on the transition criteria presented above, for the hydraulic diameter used in this work, is shown.

6

Figure 2: Flow regime transition for a tube with 0.53 mm hydraulic diameter with use of the

transition criteria presented by Nema et al. (2014).

The annular flow has special relevance as, due to the greater influence of surface forces over gravitational, the stratified flow is oppressed. The transition to intermittent flow occurs when the minimum fluid volume fraction is reached to form a fluid bridge, represented with the vertical transition lines, as well as when there is low vapor velocity, represented with the curved transition lines. On the other hand, the transition to mist flow is verified if the fluid volume fraction is small enough and the vapor velocity high enough. The shear forces of the gaseous phase over the liquid layer leads to the formation of small drops.

The transition to dispersed flow is represented with use of the transition criteria presented by Taitel and Dukler (1976). The transition occurs when the liquid velocity is high enough for the vapor bubbles to be mixed with the fluid, overcoming the buoyancy forces.

It can also be observed that the transition lines change with the condensation pressure. The displacement of the lines determined with the Weber number is very small, whereas the displacement of the lines determined with the Martinelli-parameter is appreciable. As the pressure increases, so does the density of the gaseous phase. Therefore, the velocity of this phase decreases, thus the vapor inertia effects are smaller. Additionally, the surface tension decreases with the increasing pressure. As a result, the Weber number only changes slightly with the pressure and the position of the lines remains almost constant. As the pressure increases, vapor phase density also increases and fluid density decreases, thus the vapor volume is also reduced. Consequently, the liquid volume fraction is reached at lower liquid quantities and transition occurs at higher vapor qualities.

0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6 0.8 1

Mas

s flu

x [k

g/m

2 s]

Vapor quality [-]

10 bar15 bar20 bar

Mist Flow

Annular Flow

Dispersed Flow

Transition

Intermittent Flow

7

2.3 Void fraction

The void fraction 𝜀 is an important parameter for the characterization of the two-phase flow. The most widely used definition is the cross-sectional average void fraction, which is expressed as follows:

𝜀 =𝐴𝑔

𝐴𝑡

=𝑉𝑔𝑉𝑡

(6)

As presented in the previous sub-chapter, the two-phase flow is, partly, discontinuous. Consequently, the flow conditions can vary abruptly at a certain point. To simplify the complex and discontinuous flow behavior, different modelling approaches are used (VDI, 2010).

The homogeneous model considers that both vapor and liquid velocities have the same value. As a result, the expression for the calculation of the void fraction can be rearranged:

𝜀 =1

1 + 1 − ·

𝜌𝑔𝜌𝑙

(7)

The model has limited applicability, it can be used in case of bubbly or mist flows, where both phases flow at approximately the same velocity and at high mass fluxes and vapor qualities (Thome 2004).

The heterogeneous model considers the flow to be separated and the velocity of each phase is constant over the cross section. The ratio between the average vapor phase and liquid phase velocities is defined as slip ratio, S.

𝑆 =𝑢

𝑢=

· 𝑥𝜌 · 𝐴 · 𝜀

· (1 − 𝑥)𝜌 · 𝐴 · (1 − 𝜀)

=𝑥

1 − 𝑥·1 − 𝜀

𝜀·𝜌

𝜌 (8)

𝜀 =1

1 + 1 − ·

𝜌𝑔𝜌𝑙

· 𝑆 (9)

Various analytical and empirical correlations have been developed for the calculation of the slip ration and the determination of the void fraction. Butterworth (1975) compared six of these models and suggested an universal correlation form (Equation 10). The factors A, p, q and r of some of the compared models are presented in Table 4.

𝜀 =1

1 + 𝐴 1 −

𝑝

·𝜌𝑔𝜌𝑙

𝑞

·𝜇𝑙𝜇𝑔

𝑟 (10)

8

Table 4: Overview of the models and constants for the determination of the void fraction.

Model A p q r

homogeneous 1 1 1 0

Zivi (1964) 1 1 0.67 0

Lockhart, Martinelli (1949) 0.28 0.64 0.36 0.07

Baroczy (1963) 1 0.74 0.65 0.13

An empirical correlation which is often used in the literature was suggested by Smith (1969). He assumed a separated flow of a liquid and a vapor phase and the liquid entrained in the gas E. Based on experimental data, he considered 𝐸 = 0.4 and the expression is as follows:

𝜀 =

⎣

⎢⎡1 +

𝜌𝑔𝜌𝑙

·1 −

⎝

⎜⎜⎛𝐸+ (1 − 𝐸) ·

𝜌𝑙𝜌𝑔

+ 𝐸 · 1 −

1 + 𝐸 · 1 − ⎠

⎟⎟⎞

⎦

⎥⎤

−1

(11)

Some of the correlations have been developed specifically for refrigerants, which can also be applied to mini-channels, for example the Xu and Fang (2014) correlation. Using experimental data of different refrigerants, geometries and mass fluxes, they defined the void fraction as a function of the liquid Froude number and the homogenous void fraction.

2.4 Pressure drop

For internal flow, the pressure drop results from the decreased flow energy along the channel, caused by inner friction, wall friction and turbulence.

The Bernoulli equation can be derived taking into consideration this energy loss due to friction. The equation considers two points of a streamline in a fluid flow and is written as follows:

𝑝 +𝜌𝑢

2+ 𝜌𝑔𝑦 = 𝑝 +

𝜌𝑢

2+ 𝜌𝑔𝑦 + ∆𝑝 (12)

where p is the pressure, 𝜌 is the density, u is the mean velocity, and y is the vertical coordinate.

In this work, both dynamic and hydrostatic pressures remain constant, thus the pressure drop due to friction results in a static pressure drop.

Single-phase flow

The pressure drop is influenced by the channel’s geometry, as well as the fluid and flow properties. In a fully developed flow it can be expressed by the Darcy-Weisbach equation:

9

∆𝑝 = 𝑓𝐿

𝐷

𝜌𝑢

2 (13)

With the use of the Reynolds number equation, as well as the mean velocity of the fully developed laminar flow in a circular channel, the following expression is obtained (Hagen-Poiseuille):

𝑓 =64

𝑅𝑒

(14) 𝑅𝑒 < 2300

In laminar flow the friction factor depends on the flow conditions and not on the wall roughness. This is due to the much stronger influence of the fluid viscosity in comparison with the flow disturbance caused by the wall roughness.

For fully developed turbulent flow relations, empirical data is used as the friction factor depends on the Reynolds number and surface conditions. In this context, the channel relative roughness is used, and it is expressed as the ratio between the channel roughness e and the channel diameter D. The Colebrook equation results from empirical data of turbulent flow in both smooth and rough pipes and is expressed as follows:

1

√𝑓

= −2.0 𝑙𝑜𝑔

𝑒𝐷3.7

+2.51

𝑅𝑒√

𝑓

(15) 𝑅𝑒 > 4000

The expression above can only be solved implicitly with the use of numerical methods. For this reason, its practical use is limited. In the case of a hydraulic smooth pipe, the Blasius equation is widely used.

𝑓 =0.3164

𝑅𝑒

(16) 𝑅𝑒 < 𝑅𝑒 < 10

Other approximations for the Colebrook equation have been developed, although most of them are for transitional and turbulent flow. An approximation which is valid for all Reynolds numbers and channel relative roughness values was presented by Churchill (1977).

𝑓 = 88

𝑅𝑒+

1

(𝐴 + 𝐵) (17)

where 𝐴 =

⎣⎢⎡2.457 𝑙𝑛

1

7𝑅𝑒 + 0.27𝑒

𝐷 ⎦⎥⎤ (18)

𝐵 =37,530

𝑅𝑒 (19)

10

The presented equations for pressure drop in internal flow were developed for round channels. In the case of non-circular cross sections, the pressure drop should be computed considering the hydraulic diameter of the channel instead of the geometric diameter (VDI, 2010, section L1.2).

Two-phase flow

In the two-phase flow, there is an additional pressure gradient due to the momentum exchange between vapor and liquid phase. The intensity of the momentum exchange depends on the different flow regimes. The pressure during condensation along the axial coordinate z is the sum of the geodetical, acceleration and frictional pressure gradients.

d𝑝

d𝑧=

d𝑝

d𝑧+

d𝑝

d𝑧+

d𝑝

d𝑧 (20)

The gravitational pressure gradient, which is important for vertical channels, is zero in the case of horizontal channels (no change in static head).

The acceleration pressure gradient is a consequence of the different velocities of the two phases and it can be determined for condensing flows with Equation 21 (López-Belchí et al. 2014). During condensation, with a decreasing vapor quality, the velocity of the liquid phase decreases, which consequently leads to a positive pressure gradient. For this reason, the overall pressure drop during condensation is smaller than in the case of adiabatic flow.

−d𝑝

d𝑧= ·

d

d𝑧

𝑥

𝜌 · 𝜀+

(1 − 𝑥)

(1 − 𝜀)𝜌 (21)

where 𝜀 is the void fraction and it is calculated as presented by Zivi (1964).

The frictional pressure drop results from wall friction and internal friction (as in single-phase) and, additionally, friction on the interface between the two phases. In two-phase flow, the frictional pressure drop represents the greatest part of the overall pressure drop (Friedel 1978).

Correlations for Pressure drop

Due to the complexity of the two-phase flow, empirical correlations are mostly used for the prediction of two-phase pressure drop. These correlations are usually easy to use and present a good prediction of the values, frequently in the range for which the correlations were developed. The limited range of application of empirically determined correlations is a disadvantage of the method.

The simplest method of analyzing the two-phase flow is with the use of the homogeneous model. In this model it is assumed that both flow phases flow at the same velocity. The flow is expected to behave as single-phase flow and presents averaged properties of the liquid and vapor phases.

11

The separated flow model considers the two phases to flow separately and this method was first used by Lockhart and Martinelli (1949). According to their model, the flow pattern does not change along the tube length. The two-phase flow pressure drop correlations based on the two-phase multiplier for the liquid phase and the vapor phase are:

d𝑝

d𝑧= 𝜙 /

d𝑝

d𝑧 /

(22)

where and are the pressure drop per unit length if the liquid phase and the vapor phase when flowing alone in the entire cross-section of the tube.

The Martinelli parameter X is the ratio of the liquid pressure drop to the vapor pressure drop:

𝑋 =

d𝑝d𝑧

d𝑝d𝑧

(23)

For the case of turbulent liquid and gas flows (tt), the Martinelli parameter is defined as a function of densities, dynamic viscosities and vapor quality:

𝑋 =1 − 𝑥

𝑥

𝜇

𝜇

𝜌

𝜌 (24)

Chisholm (1967) developed equations to predict the friction pressure gradient for two-phase flow using the Martinelli parameter. The simplified equations, of great practical interest, are presented as follows:

𝜙 = 1 +𝐶

𝑋+

1

𝑋 (25)

𝜙 = 1 + 𝐶𝑋 + 𝐶𝑋 (26)

The Chisholm constant C values are presented in Table 5.

Table 5: Chisholm constant C as presented by Chisholm (1967).

Fluid phase Gas phase Index C

turbulent turbulent tt 20

laminar turbulent lt 12

turbulent laminar tl 10

laminar laminar l l 5

turbulent: 𝑅𝑒 > 2000

laminar: 𝑅𝑒 < 1000

12

Various correlations to predict the two-phase flow pressure drop have been derived using the two-phase frictional multipliers, 𝜙 and 𝜙 and modifying the parameter C.

Mishima and Hibiki (1966) developed a new correlation by replacing the parameter C while taking into account the influence of the small channel diameter (1-4 mm) and the geometry of the channel. The expressions for the parameter C for rectangular and circular channels are, respectively:

𝐶 = 21[1 − 𝑒𝑥𝑝(−0.319𝐷 )],𝐷 [𝑚𝑚] (27)

𝐶 = 21[1 − exp(−0.333𝐷)],𝐷 [𝑚𝑚] (28)

Most of the developed correlations for mini/micro-channels pressure drop are based on the Lockhart and Martinelli parameters. Various correlations have been developed defining the parameter C as function of relevant dimensionless groups (Kim and Mudawar 2012).

Another developed method consists in using two-phase multipliers which consider the liquid and vapor phases to flow alone in the channel with the total mass flow rate, lo and vo, respectively. The two-phase pressure drop can be computed with the liquid-only two-phase multiplier as follows:

d𝑝

d𝑧= 𝜙

d𝑝

d𝑧 (29)

Various authors have extended this model modifying 𝜙 , for example, Friedel (1979, 1978), who used a databank with 25000 measurements of frictional pressure drop, in horizontal smooth tubes with a hydraulic diameter larger than 1 mm. The two-phase multiplier was determined, and it is expressed as a function of various parameters: vapor quality, density, friction factor, dynamic viscosity, Froude number and Weber number. The two-phase multiplier presented by Friedel is mostly defined in the literature by the letter R (c.f. Equation 30).

𝜙 = 𝑅 = 𝑓 𝑥,𝜌

𝜌,𝑓

𝑓,𝜇

𝜇, 𝐹𝑟 ,𝑊𝑒 (30)

Based on measurements of frictional pressure drop for a variety of fluids and flow conditions (9300 data points), Müller-Steinhagen, Heck (1986) presented a correlation as a function of the vapor quality and the pressure drops of both single-phase flows (Equation 31).

𝑑𝑝

𝑑𝑧= 𝑓 𝑥,

𝑑𝑝

𝑑𝑧,

𝑑𝑝

𝑑𝑧 (31)

The correlations above were developed for conventional channels. However, recent authors have reported that these correlations estimate with reasonable accuracy the values of the pressure drop in small tubes (López-Belchí et al. 2016). These correlations were the basis for the development of new correlations for micro-channels.

13

2.5 Heat Transfer

Heat transfer is defined as thermal energy which is transferred if a temperature difference is present. In this work, the convective heat transfer between the fluid in motion, the refrigerant, and the MFT surface is the point of interest. During condensation, not only the sensible energy of the fluid is transferred, but also the latent heat associated with the phase change of the fluid. The rate equation which represents the convection heat transfer process is known as Newton’s law of cooling and it is shown next:

𝑞 = ℎ · (𝑇 − 𝑇 ) (32)

The heat transfer coefficient, represented by h, depends strongly on the boundary layer conditions, which are influenced by the surface geometry, the nature of fluid motion and thermodynamic and transport properties of the fluid.

The influence of the flow regimes and the velocity boundary layer on the variation of the heat transfer coefficient for condensation along a mini/micro-channel can be observed in Figure 3. At the entrance of the channel the vapor goes from superheated to saturation point (𝑥 = 1), while the sensible heat is dissipated. The fluid enters the channel as vapor and condensates gradually. As condensation begins, a very thin liquid layer is formed at the surface of the channel. The heat transfer coefficient increases rapidly due to a very small conduction resistance (thin liquid film) until it reaches the highest point shortly after the beginning of the annular regime. The increasing liquid layer results from the decreasing vapor quality. During condensation the density increases, as such the velocity decreases, which leads to reduced turbulence effects on the condensate layer and a reduced heat transfer coefficient (Kim, Mudawar 2014).

Figure 3: Influence of flow regimes on the heat transfer coefficient during condensation (Kim and

Mudawar 2014).

14

Correlations for Heat Transfer

The difficulty of obtaining the temperature profiles for various geometries of channels led to the development of correlations mostly based on empirical data to obtain the Nusselt number, Nu. The Nusselt number expresses the relation between heat transfer and heat conduction coefficients.

𝑁𝑢 =ℎ𝐿

𝑘 (33)

In the case of forced convection, the Nusselt number is influenced by various parameters, such as fluid and flow properties and geometry. It can be expressed as a function of other dimensionless numbers, like the Reynolds number (Re) and the Prandtl number (Pr).

𝑁𝑢 = 𝑓𝑅𝑒,𝑃𝑟,𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑦 (34)

The general expression for Nusselt number for single phase flow obtained with empirical data then follows:

𝑁𝑢 = 𝑎 · 𝑅𝑒 · 𝑃𝑟 (35)

In the case of fully developed turbulent flow in a smooth circular channel, the local Nusselt can be computed with the Dittus-Boelter equation (Equation 36).

𝑁𝑢 = 0.023 𝑅𝑒 𝑃𝑟 (36)

In the above equation n = 0.4 for heating (Ts > Tm) and n = 0.3 for cooling (Ts < Tm).

A widely used correlation for single phase flow in smooth channels valid through a large Reynolds number range (2300 ≤ 𝑅𝑒 ≤ 10 ) is given by Gnielinski (2013):

𝑁𝑢 =

(𝑓/8)(𝑅𝑒 − 1000)𝑃𝑟

1 + 12.7𝑓8 𝑃𝑟 − 1

(37)

where 𝑓 = (1.8 log 𝑅𝑒 − 1.5)− (38)

The heat transfer coefficient in two-phase flow is influenced by different parameters, namely fluid and flow properties, geometry and operating conditions. Due to the high complexity of the turbulent flow, the heat transfer coefficient cannot be obtained analytically, so correlations must be developed. These correlations are written as a function of various dimensionless parameters, vapor quality, geometry and pressure drop.

𝑁𝑢 = 𝑓𝑅𝑒,𝑃𝑟,𝑊𝑒,𝐹𝑟,𝐵𝑜,𝑋, 𝑥,∆𝑝,𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑦 (39)

15

For shear-controlled flow regimes, such as annular flow, several semi-empirically correlations have been developed for conventional channels. Those correlations can be divided in three main groups: correlations based on the shear force between the two-phases, correlations developed with the use of the two-phases multipliers and correlations based on the analysis of the boundary layer.

An early experimental study was held by Akers et al. (1959), who studied the condensation of propane and R12 in a horizontal tube with a hydraulic diameter of 15.8 mm. Akers based his approach on the interaction between the vapor core and the liquid film, considering that the vapor core can be replaced by a fluid which would exert the same shear force (Equation 40).

𝜏𝑔 =𝑓𝑔𝑔

2

2 · 𝑔 · 𝜌𝑔 ·𝐿=

𝑓𝑙𝑙2

2 · 𝑔 · 𝜌𝑙 · 𝐿 (40)

With 𝑓 /𝑓 = 1, which results from the assumption of turbulent vapor flow and rough surface between

the two phases, the mass flux rates can be correlated, and the equivalent liquid mass velocity is used to calculate a Reynolds number as follows:

𝑅𝑒 =𝐷 ·

𝜇 (41)

where the entire flow is considered liquid, with the equivalent mass flux computed as following:

= + ·𝜌

𝜌 (42)

Computing the Reynolds number with the equivalent mass flux, the Nusselt number can be calculated with the following expressions:

𝑁𝑢 = 5.03𝑅𝑒 𝑃𝑟 if 𝑅𝑒 < 5 × 10 (43)

𝑁𝑢 = 0.265𝑅𝑒 𝑃𝑟 𝑖𝑓 𝑅𝑒 > 5 × 10 (44)

The expressions above are only valid for annular flow, since the shear forces are considered dominant.

The two-phase multiplier concept, presented in the previous sub-chapter, is used by various authors in the development of two-phase heat transfer correlations. One of these authors is Shah (1979), who developed a correlation for condensation based on the similarity between heat transfer mechanisms of film condensation and boiling without bubble nucleation. Shah defined empirically the heat exchange coefficient with the use of a two-phase multiplier as follows:

ℎ = ℎ · 𝛹 = ℎ ·

⎣⎢⎡(1 − 𝑥) +

3.8𝑥 (1 − 𝑥)𝑝𝑝 ⎦

⎥⎤ (45)

16

Kosky and Staub (1971) created an analytical model for heat transfer coefficient in annular flow based on the analysis of the boundary layer and, thus, the thermal resistance of the condensate film. Their expression for the Nusselt number is written as function of various parameters, namely the dimensionless temperature 𝑇 +(as function of the non-dimensional film thickness 𝛿+ and the Prandtl number) and shear velocity 𝑢 .

𝑁𝑢 =𝜌 · 𝐷 · 𝑐 · 𝑢

𝑇 +(𝛿+) · 𝑘 (46)

where 𝑢 =−𝐷

4𝜌

d𝑝

d𝑧 (47)

The presented approaches represent the basis for various following models by numerous authors. The most relevant models and respective comparison with the experimental data are presented and discussed in section 5.2.2.

2.6 Refrigerant-oil mixture

The addition of oil to the system leads to a change in the thermodynamic properties of the refrigerant, in detail density, viscosity, surface tension and heat conductivity. The different physical properties are the key to understand how the oil influences the heat transfer and pressure drop characteristics and their dependence on the oil concentration. The oil concentration can be defined as nominal and local as follows:

𝜔 =𝑚

𝑚 + 𝑚 (48)

𝜔 =𝑚

𝑚 + 𝑚=

𝜔

1 − 𝑥 (49)

The vapor quality of the refrigerant-oil mixture is calculated considering that the partial pressure of oil in the vapor phase is neglected, as the saturation temperature of the oil is much higher than that of the refrigerant:

The dynamic viscosity has a significant influence on heat transfer. In various condensation heat transfer models, the two-phase heat transfer coefficient is proportional to the single-phase value, which can be expressed as a function of the Reynolds and Prandtl numbers (Equation 35). It is then suggested that the two-phase heat transfer coefficient is inversely proportional to the dynamic viscosity. The higher dynamic viscosity value of the oil would then be expected to result in a lower heat transfer coefficient value.

𝑥 =𝑚

𝑚 + 𝑚 + 𝑚 (50)

17

ℎ ∝ ℎ ∝ 𝑅𝑒 𝑃𝑟 ∝1

𝜇, 𝑎 > 𝑏 (51)

Other relevant properties for the understanding of the influence of the oil in the system are the surface tension and the thermal conductivity. Some authors reported an increase of the surface tension, which results in an increased wetted perimeter, thus higher transfer coefficient, but also increased pressure drop. The thermal conductivity of the oil is also higher, although the effect of the oil concentration on the mixture thermal conductivity is weaker. (Bandarra Filho et al. 2009)

Hughes et al. (1984) represented the influence of oil in a system in a pressure-enthalpy regime chart, as it can been seen in Figure 4. The influence of oil results in a smaller heat flow in the evaporator, thus more compressor power is needed.

Figure 4: Pressure-enthalpy regime map showing the influence of the oil in the refrigerant-oil

mixture (Hughes et al. 1984).

Two different approaches can be found for the calculation of the heat transfer coefficient. The first calculates the heat transfer enhancement factor (EF), which relates the heat transfer coefficient of the two-phase flow of the refrigerant-oil mixture to the pure refrigerant with the use of the local oil concentration and factor c as exponential factors. The value of c is then fitted to experimental data.

𝐸𝐹 =ℎ

ℎ= 𝑒 · (52)

The second approach, which was taken by Huang et al. (2010c), consists in using equations for condensation heat transfer as developed by Koyama et al. (2003) and adjusting them for the obtained experimental results with refrigerant-oil mixture. More specifically, the equation for the forced convection Nusselt number was adjusted to the experimental data with the factors a and b.

𝑁𝑢 = 0.0152(𝑎 + 𝑏𝑃𝑟 ) · 𝑅𝑒 ·𝜙

𝑋 (53)

18

Regarding the pressure drop, a clear trend between viscosity or oil quantity and pressure drop has not been found. An increase in oil quantity implies a higher viscosity, as the increasing dynamic viscosity leads to increasing shear forces and, consequently, higher pressure loss. On the other hand, an increasing oil quantity and subsequent higher viscosity leads to a decrease of the turbulent flow intensity, resulting in a lower pressure loss. (Huang et al. 2010c)

There are two different approaches to compute the pressure loss in refrigerant-oil mixtures. The first approach uses the pressure drop enhancement factor (PF) to correlate the two-phase flow pressure drop of the mixture to the pure refrigerant.

𝑃𝐹 =

d𝑝d𝑧

d𝑝d𝑧

= 𝑒 · (54)

The second approach was taken by Huang et al. (2010a). In this model, the mixture properties are used, as well as a vapor-phase multiplier. The equations used for this approach are:

∆𝑝 = 𝜙 · ∆𝑝 (55)

∆𝑝 = 2𝐿𝑓 · 𝑥

𝜌 · 𝐷 (56)

𝜙 = 1 + 1.1.457𝑋 (57)

The friction coefficient for vapor single-phase flow is calculated with vapor phase properties.

19

3 Experimental apparatus In this chapter the experimental configuration used to determine the heat transfer coefficient and pressure drop of R134a and R134a-lubricant-mixtures, in multiport flat tubes, is presented. Additionally, the measurement and calibration procedures are described. Finally, the uncertainty of the experimental data is analyzed.

3.1 Testing facility

The testing facility was developed and built with the purpose of determining the heat transfer coefficient and pressure drop of the pure refrigerant R134a and the R134a-oil mixtures in a multiport flat tube during condensation. The facility allows the determination of these parameters at different pressures, mass fluxes and vapor qualities, which can be controlled with the different cycles that constitute the system. In Figure 5 the three main cycles of the system are represented.

Figure 5: Schematic view of the testing facility (Knipper 2018).

Flow

20

For the description of the system, it is considered that the cycle starts in a piston diaphragm pump, which is used to regulate the mass flow. Due to the discontinuous nature of the pump, there are mass flow oscillations. To minimize these oscillations, specially at low mass flow rates, two proportional valves are used which are placed around the pump. One of the proportional valves is located parallelly to the pump, which can create a bypass of the pump. Additionally, a pulsation attenuator, placed after the pump, is used to minimize the mass flow oscillations. The mass flux is measured in a Coriolis flowmeter.

For two-phase flow, there is the additional need of adjusting the vapor quality. To achieve the desired vapor quality, an evaporator prior to the entrance of the test section is used. With the entrance temperature of the fluid at the evaporator and the desired vapor quality value, the necessary power to achieve that state is computed. This value can be seen in the Labview interface for the measured mass flow of refrigerant at any moment. The power of the evaporator is then controlled manually based on the value read. The evaporator power is computed as follows:

= · 𝑐 𝑇 − 𝑇 + 𝑥(ℎ − ℎ ) (58)

where is the refrigerant mass flow rate, 𝑐 is the specific heat of the refrigerant, 𝑇 is the

saturation temperature, 𝑇 is the temperature of the refrigerant at the entrance of the

evaporator, 𝑥 is the vapor quality, ℎ and ℎ are the enthalpies of the saturated liquid and saturated vapor, respectively, at the desired condensation pressure.

The two-phase flow enters the multiport flat tube where flow is partially condensed, and the heat transfer coefficient and pressure drop are measured. The vapor quality is reduced between 5-20% and is then further condensed in the condenser to all-liquid.

The different pressures at the test section are achieved with the regulation of the thermostat connected to the condenser. The heat transfer to the condenser can be computed with Equation 59, where is the mass flow rate of the water, 𝑐 is the specific heat of the water and ∆𝑇 is the

temperature difference between inlet and outlet. An increase in the temperature of the thermostat leads to a smaller temperature difference, ΔT, which means that less energy is taken from the system, in turn resulting in a higher pressure inside the refrigeration cycle. The mass flow of the condenser can also be changed resulting in the same effect, and it can be regulated with both hand valve and proportional valve.

= · 𝑐 · ∆𝑇 (59)

The reservoir is placed in front of the condenser and it assures the circuit always has enough fluid in all operating conditions. The fluid leaves the reservoir at saturation temperature and is then sub-cooled in the subsequent sub-cooler, to avoid pump damages with the usage. The absence of bubbles in the flow can be observed through a sightglass in the circuit, behind the sub cooler. Both condenser

21

and sub-cooler cycles are represented with the colour blue in the lower part of the system diagram. Before passing again through the pump, the flow density is measured at the density measurement unit located before the pump. This measurement is particularly important when the mixture refrigerant-oil is flowing, as it also measures the oil quantity.

The heptane cycle, represented in blue in the upper part of the diagram, is responsible for removing the condensation heat from the measurement section. The cycle consists mainly of a gear pump to control the mass flow of heptane and a thermostat to control the temperature. The inlet and outlet temperatures of the heptane are measured, as well as the absolute pressure, which is necessary for the determination of the physical properties. A Coriolis mass flowmeter is situated after the outlet of the test section.

The oil cycle is represented in purple, black and green. This cycle has the purpose of introducing, increasing or reducing the oil quantity in the system.

The components of the system, including tubing, are thermally isolated with foam to minimize the heat losses to the surroundings. The test section is additionally covered with a Plexiglas structure, which is a security measure, as the system is operated at very high pressures.

The tables with the used substances and components can be found in Appendix, Part 2 (Table 16 and Table 17).

Test section

The test section is delimited by two transition parts, whose aim is to provide a smooth transition from and to the circular tube. A measurement flange is attached to each of the transition parts. There is a third flange, which divides the test section into two parts. The test section has a total length of 800 mm. The first section, which is 415mm long between flanges, is the adiabatic section, which aims to assure a fully developed state of the two-phase flow regime before it enters the second section, the measurement section, which is 315mm long. In each of the three flanges the temperature of the flow is measured. The relative pressures of both adiabatic and measurement sections are measured between the flanges. The absolute pressure is measured at the outlet of the flat tube. A representation of the test section can be seen in Figure 6.

The multiport flat tube used in the context of this work has a hydraulic diameter of 0.529 mm and it is made of extruded aluminium. With the use of the channels classification presented in section 2.1, these channels can be classified as mini-channel.

22

During the condensation of the two-phase flow in the measurement section (cross-flow), the heat is removed by the heptane cycle. The heptane flows perpendicularly to the measurement section, which approximates the boundary conditions for the real application of such heat exchangers. Furthermore, the low heat capacity of the heptane, in comparison with water, leads to a bigger temperature difference between inlet and outlet temperatures of the heptane, thus, more precise determination of heat transferred from the measurement section can be made. In Figure 7 can be observed the section where the heat exchange between the heptane flow and the measurement section takes place.

Figure 7: Measurement section during assembly.

measurement flanges

Figure 6: Computer modeled view of the test section (Knipper 2018).

23

3.2 Determination of the experimental values

The aim of this work is the determination of the heat transfer coefficient and pressure loss in a multiport flat tube during condensation. However, unlike the pressure drop, the heat transfer coefficient cannot be measured directly. For its computation different quantities are needed, namely the dissipated condensation heat, , fluid and wall average temperatures, 𝑇 and 𝑇 (c.f.

Equation 60). The heat transfer surface on the inside of the flat tube is determined with a CT-analysis. The different measured experimental values are represented in Figure 8.

ℎ =

𝐴 · 𝑇 − 𝑇 (60)

Figure 8: Schematic view of the test section and the experimentally measured values.

During condensation the temperature remains constant and is equal to the saturation temperature of pure refrigerant. However, due to pressure loss in the section, the temperature of the refrigerant decreases. The refrigerant temperature is then computed as an average of the inlet and outlet temperatures, 𝑇 and 𝑇 , respectively.

𝑇 =𝑇 + 𝑇

2 (61)

The temperatures and the relative and absolute pressures are measured in the flanges. The flanges are made of two parts which are assembled to the multiport flat tube with epoxy glue. Inside the flanges a small reservoir is connected through perforated holes to the channels of the multiport flat tube. The temperature sensors placed in the flanges measure an average flow temperature. In addition, the pressure is compared between flanges which indicates the pressure drop and, at the end of test section, the absolute pressure is also measured. In Figure 9 a representation of a measurement flange can be observed and the location of both temperature and pressure sensors are indicated.

𝑇𝑇

𝑇

Δ𝑝 Δ𝑝

𝑇 𝑇

adiabatic section

measurement section

𝑇𝑇

, 𝑇 ,

𝑇 ,

24

Figure 9: Placement of the temperature and pressure sensors in the flange (Knipper 2018).

According to Equation 60 the wall temperature is essential for the computation of the heat transfer coefficient, although its measurement is especially difficult due to the low thickness of the walls. The best-found configuration in the previous work consists in four resistance temperature sensors (Pt100) placed into four holes, which are inserted in an aluminum plate soldered to the multiport flat tube. This connection provides a very good thermal conduction between the multiport flat tube and the temperature sensors, thus making the temperature measured very close to the actual temperatures of the wall. Two of the sensors are placed in the upper part of the tube and two are placed in the lower part. The temperature value then used is an average of the four measured temperatures (Equation 62). Additionally, a rounded plastic component is glued perpendicularly to the heptane flow, with the purpose of having the most homogenous possible flow around the measurement section. This section with all its constituents is named measurement sandwich (MS).

𝑇 = 𝑇 =𝑇 + 𝑇 + 𝑇 + 𝑇

4 (62)

The condensation heat received within the measurement section is computed with Equation 63. The section of the tube where the condensation takes place is 200 mm long. The heat removed by the heptane flow is computed with the heptane inlet and outlet temperatures, 𝑇 and 𝑇 , respectively, the mass flow, , and the heat capacity, 𝑐 , thus the absolute pressure, as follows:

= · 𝑐 · 𝑇 − 𝑇 (63)

For a valid measurement, the stationarity of the system is essential. When a stationary state is reached, the measurement starts, and all the parameters to be measured are recorded for 900 seconds. The pressure at which the measurement starts should be at a range of ±0.05 bar of the desired value. During the measurement this value should stay in a ±0.02 bar interval of the initial value. The oscillations of the pressure are not problematic, if they keep a constant behaviour and do not show a clear increase or decrease of the pressure during the measurement time, as it represents a not stationarity of the system. The temperatures of the heptane (entrance and exit) must also be constant,

25

as well as the temperature of the refrigerant at the entrance of the evaporator, this assures then a constant value of the vapor quality.

Calibration

The temperatures of the system are measured with platin resistance thermometers (Pt-100). The temperature is measured based on the electrical resistance. In the case of this temperature sensors, the electrical resistance is directly proportional to the temperature and at 0 °C the measured resistance is 100 Ω. The difference between the temperature measured at the measurement sandwich and the average temperature of the refrigerant is sometimes smaller than 1 °C, so, even though the temperature sensors supplied come with a small deviation, a further calibration should be made. A high precision temperature sensor is used for the calibration. Both Pt-100 and high precision temperature sensor are inserted in a bath with controlled temperature. The temperature calibration range is 10-85 °C and the measurements take place with steps of 5 °C. During the calibration it is waited until the temperature measured by the high precision temperature sensor is stable, around the desired value (±0.001 °C), and it is then taken a measurement for 30 seconds. The mean value of this measurement is used to create a calibration curve. This curve is a polynomial function of third degree and it is then implemented in both data acquisition software and uncertainty analysis procedure.

3.3 Uncertainty analysis with GUM

The experimentally measured values are associated to an uncertainty, which defines a probability interval for the measured value. The uncertainty value of a certain parameter is dependent on the uncertainty of the respective measurement equipment. The norm ISO/IEC Guide 98-2:2008 is used in this work for its determination. This norm is presented by JCGM (2008) as the Guide to the Expression of Uncertainty in Measurement, also known as GUM.

The value of 𝑦, which is an estimate of the measurand Y, is dependent on the measured parameters, 𝑥 . This dependency can be expressed using process equations.

𝑦 = 𝑓(𝑥 ,… , 𝑥 ) (64)

The standard combined uncertainty of y, u(x), is computed combining the standard uncertainties of the estimates of the input parameters with the sensivity factor, ci as follows:

𝑢 (𝑦) = (𝑢(𝑥 ) · 𝑐 )=

(65)

The sensitivity factor is computed with the derivation of the value to be measured in function of the measured parameter (a partial derivative). For the case of the heat removed by the heptane, the sensivity factor related to the mass flux of the heptane is computed as follows:

26

𝑐 =𝜕𝑦

𝜕𝑥=

𝜕

𝜕 (66)

Each of the parameters on which the experimental value depends has its uncertainty, which must be considered in the computation of the uncertainty of the obtained experimental value. The standard uncertainty of each of the input parameters is computed with the uncertainty interval, ∆𝑢 , and the weighting factor, 𝐺 . The weighting factor depends on the type of distribution chosen.

𝑢(𝑥 ) = 𝐺 · ∆𝑢 (67)

The term expanded uncertainty, denoted by UK, is then used to establish the limits of the interval which is expected to contain a large fraction of the distribution of values which are attributed to Y. For a level of confidence of 95%, a factor K=2 is used, assuming a normal distribution (Annex G, JCGM 2008).

𝑈 = 𝐾 · (𝑢(𝑥 ) · 𝑐 )=

(68)

27

4 Results In this chapter it is described how the data is edited, considering the limitations of the testing facility and data recording, and the obtained results are presented. The reproducibility of the results is verified with the repetition of the measurements at various points.

The experimental values of both heat transfer coefficient and pressure drop are presented in dimensionless form. The values are nondimensionalized by heat transfer coefficient and pressure drop of liquid-only flow in rectangular shaped channels with a hydraulic diameter of 0.91 mm, which is the geometry with greater dimensions used in the context of this project.

4.1 Data analysis

With decreasing mass flux and vapor quality, the heat transfer coefficient is expected to reduce. However, at low mass fluxes and vapor qualities, an abnormal rise of the heat transfer coefficient is verified. Another anomaly is identified in the uncertainty values at various points, as the value is higher than the values around this point. These two anomalies are further analyzed, and the conclusions are presented in the following sections.

Sub-cooling

Along the measurement section, the temperature decreases due to the pressure losses. The measurement section, which is proceeded by the adiabatic section, is expected to have a smaller temperature reduction, as it is shorter. However, at five of the measured points, the temperature difference measured at the second section is greater than the one measured at the first section. This occurs at low mass fluxes and low vapor qualities. The lower temperature measured at the outlet of the measurement section results from the sub-cooling of the liquid phase of the flow. The slight sub-cooling of the fluid is essential for the occurrence of condensation. However, at low vapor qualities, the thickness of the liquid layer leads to a temperature measurement strongly influenced by this sub-cooling. To overcome the influence of the sub-cooling in the measured temperature, a correction is used.

The correction of 𝑇 at the points affected with sub-cooling is made with the premise that the temperature decrease in the measurement section should be proportional to the one measured in the adiabatic section with a factor r (see Equation 69). The factor r used for the correction is computed with the measurements in which the effects of sub-cooling were negligible at the same mass flux.

∆𝑀𝑆

∆𝐴𝑆

= 𝑟 (69)

28

In addition to the sub-cooling effect in 𝑇 , a considerable decrease of the temperature along the measurement sandwich was also measured. This difference is particularly relevant at 20 bar, 400 kg/m2s and 40%, where it was measured to be approximately 5 °C. As no correction can be developed for 𝑇 , the experimental heat transfer coefficient measured at this point has no validity and it is not further considered in the following analysis.

The data points whose heat transfer coefficient values were corrected are presented in Table 6. The application of the correction on the measurement results at a condensation pressure of 15 bar can be observed in Figure 10. The application of the correction at a condensation pressure of 20 bar is represented in Appendix, Part 1 (cf. Figure 45).

Table 6: Operating parameters whose heat transfer coefficients were corrected regarding sub-cooling.

Pressure Mass flux Vapor quality

15 bar 400 kg/(m2s) 20%

15 bar 600 kg/(m2s) 20%

20 bar 600 kg/(m2s) 20%

20 bar 800 kg/(m2s) 20%

Figure 10: Heat transfer coefficient ratio at 15 bar before and after sub-cooling correction.

In the following chapters the values are always presented in their corrected form.

Heptane mass flux anomalies

At certain measurement points, an abnormally high experimental uncertainty value of the heat transfer coefficient has been calculated. A further analysis showed that this increase results from the computation of the heat transferred to the heptane flow in the measurement section. With the analysis

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)400 kg/(m²s) a. c.600 kg/(m²s)600 kg/(m²s) a. c.

29

of the parameters which are used for this computation, the measurement of the heptane mass flow rate was identified as the cause (cf. Figure 11). This occurs due to electronic disturbances on the mass flow rate measurement which results in some erratic values to be recorded at certain time points. These values are either considerably higher or lower than the average of the measured value (cf. Figure 12).

Figure 11: Uncertainty distribution at a condensation pressure of 15 bar, a mass flux of

1000 kg/(m2s) and vapor quality of 20%, before the correction (15%).

Figure 12: Heptane mass flow rate measurement at a condensation pressure of 15 bar, a mass flux of

1000 kg/(m2s) and vapor quality of 20%, left and right, respectively.

No other sudden increase or decrease of the measurement values was verified in the heptane and refrigerant temperatures in the measurement section outlet, which supports the theory of electronic disturbance in the measured values of the heptane mass flow rate (Appendix, Part 1, Figure 46).

The uncertainty distribution at a condensation pressure of 15 bar, a mass flux of 1000 kg/(m2s) and vapor quality of 20%, after the correction is also represented in Appendix, Part 1, in Figure 47.

1

2

3

4

5

𝑐 , : < 1%

:78%

Δ𝑇 :14%

𝐴: < 1%

Δ𝑇 :8%

0.012

0.013

0.014

0.015

0.016

0 150 300 450 600 750 900

Hep

tan

mas

s flu

x [k

g/s]

Time [s]

30

4.2 Measurement results

In this sub-chapter the measurement points and the respective measured heat transfer coefficients and pressure drops are presented. Firstly, the data obtained for single-phase flow is presented. Then, the analysis of the obtained data for two-phase flow is performed, considering the influence of the operating conditions, namely condensation pressure, mass flux and vapor quality.

4.2.1 Single-phase flow

To validate the experimental set-up and procedure after the implementation of a new test section, the determination of the single-phase pressure drop and heat transfer is performed at approximately 8 bar.

Heat transfer

The obtained Nusselt number results are compared with some well-known correlations and are presented in Figure 13. A change of slope can be observed between a Reynolds number of 1000 and 2000.

Figure 13: Comparison of the single-phase measurement results with the literature.

For lower Reynolds numbers, the Shah correlation was used as comparison. In the context of this work, neither , nor 𝑇 have constant values along the tube. However, the measurement uncertainty of these values is greater than their variation along the tube. The boundary condition 𝑇 = 𝑐𝑜𝑛𝑠𝑡. is then used as an approximation. At the lowest Reynolds number, the measured value is very closed to its predicted value. As the Reynolds number gets closer to the transition zone, a poorer prediction of Shah correlation can be stated. An explanation for the poorer prediction of Shah correlation is the transition to turbulent flow occurring at lower Reynolds number than in conventional channels.

0

1

2

3

4

5

6

7

8

9

0 1000 2000 3000 4000 5000 6000

Nu/

Nu m

in[-]

Reynolds number [-]

Experimental resultsShah (constant Tw)Dittus-BoelterGnielinski

31

At higher Reynolds numbers (𝑅𝑒 > 3000), the measured values are compared with both Dittus-Boelter correlation and Gnielinski. A good prediction from Gnielinski correlation can be observed.

Pressure drop

The measured pressure drop values for single-phase flow are represented in Figure 14. As expected the pressure drop value increases with increasing Reynolds number value. The increasing velocity of fluid results in higher values of the friction forces.

Figure 14: Single-phase flow measured pressure drop values.

At low Reynolds number the pressure drop is expected to increase linearly with Reynolds number, however, it starts increasing not linearly before a Reynolds number of 2000. One can then conclude that the transition to turbulent flow occurs before this Reynolds number value. Identical results were obtained by Hwang and Kim (2006) for circular tubes with identical hydraulic diameter with R134a.

The experimental friction factor was deduced rearranging Equation 7 as follows:

𝑓 =∆𝑝 · 𝜌12

·𝑑

𝐿 (70)

where ∆𝑝 is the pressure drop between the two measurement flanges of the test section and L is the distance between the respective flanges.

The experimental friction factor values are compared with Blasius and Churchill (1977) correlations in Figure 15. Blasius correlation presents a good prediction of the measured values even at lower Reynolds numbers, which can be explained with the earlier transition to turbulent flow.

0

20

40

60

80

100

120

0 1000 2000 3000 4000 5000 6000

Δp/

Δp m

in[-]

Reynolds number [-]

Experimental resultsTransition

32

Figure 15: Comparison between the calculated experimental friction factor values and Blasius and

Churchill (1977) correlations.

The positive results of the single-phase flow allowed the validation of the testing facility, which was then used for the measurements of two-phase flow.

4.2.2 Two-phase flow

Measurement points

The heat transfer coefficient and pressure loss of the refrigerant R134a in the triangular shaped multiport flat tube were measured at various operating conditions. An overview of the operating parameters ranges is given in Table 7. The detailed list of the operating parameters at which the experimental procedure was performed is given in Appendix, Part 2.

Table 7: Overview of the operating parameters.

Parameter Variation range

Condensation pressure [bar] 10 − 20

Vapor quality [%] 10 − 90

Mass flux [kg/(m2s)] 400 − 1200

The use of different mass fluxes for each of the condensation pressures aims to cover a wide range of the Reynolds number. The variation of both mass fluxes and vapor quality leads to a good coverage of the different flow regimes. In addition to the points presented in the table, in some cases 10% and 90% vapor qualities were also measured with the purpose of analysing the behaviour at more extreme points. At 20 bar and 400 kg/(m2s), the 20% point was not measured due to limitations of the experimental apparatus. In addition, even though the 40% point was measured it has no validity in the context of this work (see section 4.1).

0

0.02

0.04

0.06

0.08

0.1

0 1000 2000 3000 4000 5000 6000

Fric

tion

fact

or [-

]

Reynolds number [-]

Experimental friction factorBlasiusChurchill (1977)

33

Each measurement corresponds to 15 minutes long data recording with the system in a stationary state. The stationarity is verified when the condensation pressure, mass flux and heptane entrance temperature remain approximately constant. An overview of the variation limits of these values during the measurements is presented in Table 8 and the list of all the measured points is in Appendix, Part 1.

Table 8: Overview of the variation of the most relevant measurement parameters during the measurements.

Parameter Relative variation Absolute variation

Condensation pressure 0.008 – 0.2 % 0.0015 – 0.02 bar

Refrigerant mass flow 2.6 – 20 % 0.0002 – 0.0006 kg/s

Heptane inlet temperature 1.9 - 2.8 % 0.04 – 0.07 °C

4.2.2.1 Heat Transfer

In Figure 16 the experimental results obtained at a condensation pressure of 10 bar for mass fluxes and vapor qualities are presented. A general tendency of an increase of the heat transfer coefficient for increasing vapor quality and mass flux can be observed.

Figure 16: Experimental heat transfer coefficient values at 10 bar.

4

5

6

7

8

9

10

11

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

34

Effect of vapor quality and mass flux

The increasing vapor quality, and transition from dispersed or intermittent flow to annular flow, leads to a consistent wetting of the wall and, therefore, a higher heat transfer. As the vapor quality further increases, the thickness of the condensate layer reduces. The thermal resistance of the condensate layer is the main resistance for the heat transfer, thus, a decrease of the liquid film thickness has a favorable effect on the heat transfer. In addition, the higher vapor quality leads to a higher ratio between vapor and liquid velocities (see Table 9), hence, stronger shear forces between the vapor and liquid phase. The velocity gradient rises and, as a result, the turbulence in the condensate film influences positively the heat transfer.

Table 9: Variation of the thermophysical properties of R134a and values of slip ratios for different vapor qualities (Smith 1969).

Pressure 𝝆

𝝆 𝝁

𝝁

𝑺 =𝒖

𝒖

20% 40% 60% 80% 90%

10 23.35 13.18 2.26 2.72 2.99 3.17 3.24

15 14.06 9.97 1.87 2.21 2.42 2.55 2.61

20 9.40 7.79 1.63 1.90 2.06 2.16 2.20

The heat transfer is also enhanced with the increase of the mass flux. The velocity increase of both phases has a positive influence on the heat transfer. The momentum exchange promotes a better heat transfer from the gas phase to the liquid phase. Moreover, the increase of the velocity leads to a reduction of the thickness of both thermal and velocity layers.

At a vapor quality of 20%, the measured heat transfer coefficient does not increase with the increasing mass flux. In contrast to the effects of higher mass fluxes, for lower mass fluxes the condensation is not dominated by shear stress but by surface tension forces (Matkovic et al. 2009, Jige et al. 2011).

The phenomenon previously described at 20% vapor quality and lower mass fluxes, is verified within the results obtained at 400 kg/(m2s). The variation of the heat transfer coefficient, as the vapor quality decreases, is not as one would expect, as the values measured remain approximately constant with the change of vapor quality. Identical results were obtained by Jige et al. (2016) with a rectangular channel with a hydraulic diameter of 0.85 mm and R134a as refrigerant at 100 kg/(m2s). Due to the extrusion of the aluminum in manufacture of the multiport flat tube, the isosceles triangles have rounded vertices, and the edges are slightly curved. The condensate accumulates in the sharper corner of the triangle due to capillarity and, as a result, the condensate thickness increases considerably in this area and it decreases in the remaining channel’s perimeter, improving the heat transfer even at lower vapor qualities.

35

The accumulation of the condensate in the vertices of the triangle was studied numerically by Wang and Rose (2006). At lower Reynolds numbers, due to the surface tensions, the condensate remains at the corners of the channel. As a result, the liquid layer is kept thin between the corners at lower vapor qualities, which positively influences the heat transfer. This occurs in non-circular channels due to the viscosity in transverse flow. The numerical results obtained Wang and Rose (2006) for a triangular channel with a side size of 1 mm by are presented in Figure 17. The refrigerant (R134a) enters the considered section as saturated vapor and each of the figures represent the cut view at a certain distance (z) from the inlet. It can be observed that the accumulation of the condensate in the corners occurs even at lower relative vapor qualities.

Figure 17: Numerical results for a triangular channel (1 mm side size) at 500 kg/(m2s) and constant

vapor and surface temperatures, 50 °C and 45 °C, respectively (Wang and Rose 2006).

Effect of the flow regimes

All the data points are represented in Figure 18 in the flow regime map as defined by Nema et al., 2014. As it can be observed in the figure, most of the points are in the annular flow regime. Nonetheless, mist flow, dispersed flow and transition to intermittent flow are likely to be observed within the experimental results as well. The use of the transition criteria of the flow leads to a better comprehension of the variation of the heat transfer coefficient.

36

Figure 18: Overview of the measurement points over the flow regime map using the transition

criteria as presented by Nema et al. (2014).

At high mass fluxes (1000 and 1200 kg/(m2s)) and between 20% and 60% vapor qualities, it can be observed a similar increasing tendency, as all the points are in the annular flow area. The same can be observed at 400, 600 and 800 kg/(m2s), between 40% and 80%.

At higher mass fluxes and vapor qualities, it is expected a lower increase of the heat transfer as the flow transits to mist, however, the measurements at a vapor quality of 80% show otherwise. Due to the uncertainty interval for these points, no final conclusions can be made.

At the mass fluxes of 600 and 800 kg/(m2s), the increase of the heat transfer between 80% and 90% is similar between one another, though at 800 kg/(m2s) these points are expected to be in the mist flow area. As referred above, the transition lines are approximations and, as the vapor quality decreases along the tube, those points may be in fact in the annular flow area, which would justify the similar behavior.

At low vapor qualities, a higher drop of the measured values is observed at 600, 800 and 1000 kg/(m2s). While the first two are in the transition area, the third is still located in the annular flow, despite being very close to the line which should be taken as an approximation. Furthermore, as the vapor quality decreases along the tube, the transition of regime probably occurs during the condensation. Between 60% and 80% at the higher mass fluxes, the inclination is similar which supports the assumption that those values refer to mist flow.

0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6 0.8 1

Mas

s flu

x [k

g/m

2 s]

Vapor quality [-]

10 bar 10 bar15 bar 15 bar20 bar 20 bar

Mist Flow

Annular Flow

Dispersed Flow

Transition

Intermittent Flow

37

Effect of condensation pressure

The general tendency of increasing heat transfer coefficient with increasing vapor quality and mass flux is also observed at condensation pressure of 15 bar and 20 bar. The measurement results at these condensation pressures is presented in Figure 19.

Figure 19: Experimental heat transfer coefficient values at 15 bar (left) and 20 bar (right).

At 15 bar and 20 bar, the weaker increase of the heat transfer coefficient, when the flow is considered mist, is noticeable. At low mass fluxes, the drop of the measured values between 20% and 40% supports the assumption that at those points the flow is the transition to intermittent. At this regime, the flow is in part completely liquid, which has a negative influence on the heat transfer.

In Figure 20 it can be observed that the increasing condensation pressure between 10 bar and 15/20 bar leads to a decreasing heat transfer coefficient. This behavior can be explained by the change of the thermophysical properties of both liquid and gaseous phases as the saturation temperature changes. With increasing saturation temperature, the liquid-gas density ratio decreases, thus the velocity difference also decreases (cf. Table 9), which means reduced interfacial shear forces. As a result, the condensate layer is thicker, consequently, higher thermal resistance (Ding and Jia, 2017). However, between 15 and 20 bar, the influence of the saturation pressure is not clear. A possible explanation is the smaller difference of the fluid properties between 15 and 20 bar. The unclarity of the influence of the saturation pressure in the heat transfer coefficient during condensation was also concluded by López-Belchí et al. (2016) with propane (R290).

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

38

Figure 20: Experimental heat transfer coefficient values measured at a constant mass flux of

1000 kg/(m2s) and respective uncertainty intervals.

The measured data are represented with respective uncertainty intervals in Appendix, Part 1.

4.2.2.2 Pressure drop

In Figure 21 are represented the measured values of pressure loss of five different mass fluxes at different vapor quality values, measured at 10 bar.

Figure 21: Experimental pressure drop values at 10 bar.

5

6

7

8

9

10

11

12

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

10 bar15 bar20 bar

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

39

Effect of the vapor quality and mass flux

It can be observed that the pressure drop increases with increasing mass flux and vapor quality. The increasing vapor quality leads to an increase of mean specific volume which means higher average flow velocity, hence, higher inner friction. As shown in Table 10, the ratio of vapor to liquid velocity increases with vapor quality, therefore, there is an augmentation of interfacial shear. Identical results were obtained by Hwang and Kim (2006) and Sakamatapan and Wongwises (2014).

In Figure 22 it can be observed how the pressure drop value increases at constant mass fluxes, with the increase of the vapor quality. The variation of mass flux at constant vapor quality has a much stronger effect on the pressure drop than the variation of vapor quality at constant mass flux. The relative variation of the pressure drop with constant mass flux and constant vapor quality, with increasing vapor quality and mass flux, respectively, is shown in Table 10.

Figure 22: Experimental pressure drop values measured at 10 bar, plotted against mass flux.

Table 10: Influence of the vapor quality and mass flux on the pressure drop at 10 bar.

= 𝑐𝑜𝑛𝑠𝑡. ∆𝑝

(𝑥 = 20 → 80 %) 𝑥 = 𝑐𝑜𝑛𝑠𝑡. ∆𝑝

= 400 → 1200kg

𝑚 s

400 kg/(m2s) 341 % 20% 1001 %

600 kg/(m2s) 207 % 40% 738 %

800 kg/(m2s) 284 % 60% 634 %

1000 kg/(m2s) 236 % 80% 644 %

1200 kg/(m2s) 219 %

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400

Δp T

P/Δ

p lo[-]

Mass flux [kg/(m²s)]

20%40%60%80%

40

Effect of the condensation pressure

The tendency of increasing pressure drop with the increasing vapor quality or mass flux was also verified at 15 bar and 20 bar (cf. Figure 23).

Figure 23: Experimental pressure drop values at 15 bar (left) and 20 bar (right).

At the same mass flux and vapor quality values, the pressure drop value is generally lower when the condensation pressure is higher. Table 9 shows the decrease of ratio between the gas and liquid velocities with increasing condensation pressure. The smaller shear forces between the two phases and the lower viscosity of the liquid phase, thus lower inner friction, are the explanation for the smaller pressure drop with increasing condensation pressure. It can be concluded that the mass flux, vapor quality and condensation pressure play an important role in the pressure drop values. Identical conclusion has been reached recently by Rahman et al. (2017).

4.3 Reproducibility

To validate the experimental results, 26 repetition measurements were made, which represents approximately one third of the measurement points (cf. Table 19 in Appendix, Part 2).

The heat transfer coefficients obtained with the repeated measurements at 15 bar are represented over the original results with the respective uncertainty intervals in Figure 24. All the results obtained are inside the uncertainty interval, which for the heat transfer coefficient at 15 bar is in average 5.4%. It can be then concluded that the measurements feature a good reproducibility.

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1Δ

p TP/Δ

p lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

41

Figure 24: Heat transfer coefficient results of the reproducibility measurements at 15 bar.

The pressure drop results of the repeated measurements at 15 bar are represented in Figure 25. The first measurements have an average uncertainty of 1.6% and the respective repeated results are located inside the uncertainty intervals. As a result, it can be concluded that the pressure drop results also present a very good reproducibility.

Figure 25: Pressure drop results of the reproducibility measurements at 15 bar.

The results of the repeated measurements at 10 bar and 20 bar are presented in Appendix A, Part 1. At 10 bar and higher mass fluxes, the heat transfer coefficient obtained values were relatively lower. However, at these points, the uncertainty is considerably higher, as well as, the heat transfer coefficient values, which results in wider uncertainty intervals. Moreover, the respective uncertainty intervals of the first and repeated measurements overlap. Thus, it can be concluded those values also present a satisfying reproducibility.

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s) 400 kg/(m²s) Rep600 kg/(m²s) 600 kg/(m²s) Rep800 kg/(m²s) 800 kg/(m²s) Rep1000 kg/(m²s) 1000 kg/(m²s) Rep

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

400 kg/(m²s) 400 kg/(m²s) Rep600 kg/(m²s) 600 kg/(m²s) Rep800 kg/(m²s) 800 kg/(m²s) Rep1000 kg/(m²s) 1000 kg/(m²s) Rep

42

43

5 Discussion In this chapter, the experimental results presented in the previous chapter are further analyzed. To evaluate the geometry of the used measurement section relatively to its thermal and hydraulic characteristics, the experimental results are compared with the previously obtained results for other geometries. Finally, the results are compared with correlations found in the related literature for the use of R134a and with correlations which showed good agreement with other experimental studies.

5.1 Comparison with other MFT geometries

In the context of this project, three other geometries have been analyzed previously. Hereby, two MFT consist of rectangular shaped channels, with hydraulic diameters of 0.77 mm and 0.91 mm. A third MFT featured rectangular shaped channels, including an axial fin in the upper and lower surfaces. Due to its resemblance with a H, it is then considered H-shaped, with a hydraulic diameter of 0.83 mm. With the use of previously obtained data, the different geometries can be compared at a saturation pressure of 10 bar and three different mass fluxes.

5.1.1 Heat Transfer

In Figure 26 the experimental values obtained with each of the four different geometries of the channels are presented.

Figure 26: Comparison of heat transfer coefficient values between four different channel geometries

at 10 bar and 400 kg/(m2s) and 600 kg/(m2s), left and right, respectively.

The measurement data presented in the figure above show the general tendency of increasing heat transfer with the increasing vapor quality and mass flux. At 400 kg/(m2s), the heat transfer coefficients of both H-shaped and triangular sections are relatively constant with the increasing vapor quality. As

4

8

12

16

20

24

28

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

0.77 mm0.91 mm0.82 mm (H-shaped)0.53 mm (triangular)

4

8

12

16

20

24

28

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

0.77 mm0.91 mm0.82 mm (H-shaped)0.53 mm (triangular)

44

discussed previously for the triangular geometry, this can be explained with the accumulation of condensate in the fins of the H-shaped channels and the corners of the triangular channels.

At higher mass fluxes, for both H-shaped and triangular channels, higher heat transfer coefficients were measured with the rise of vapor quality. It can also be observed a parallel shift of the rectangular channels data points, and the heat transfer coefficients are higher for the channel with smaller hydraulic diameter. As it can be demonstrated, considering 𝑥 = 𝜀, the thickness of the condensate layer for the same operating point is proportional to the hydraulic diameter. As a result, a larger hydraulic diameter leads to a thicker condensate layer, hence, higher thermal resistance. Therefore, considering channels with identical geometry and at the same saturation temperature, mass flux and vapor quality, the increase of hydraulic diameter results in a lower heat transfer coefficient. However, neither the H-shaped channels, nor the triangular channels, present the expected performance considering the respective diameters. It can be also explained with the accumulation of condensate around the fins in the H-shaped channels, and in the triangle vertices. This accumulation reduces the perimeter of the channels where the heat transfer coefficient would have a higher value, which results in lower overall heat transfer. In addition, the increasing vapor quality does not have such a strong influence in the heat transfer as it is verified in rectangular geometries, which can be explained with the two-phase distribution as well. Consequently, the overall heat transfer in such geometries presents a weaker performance in comparison with rectangular geometries.

5.1.2 Pressure Drop

In Figure 27 the pressure drop values measured at 10 bar, 400 kg/(m2s) and 600 kg/(m2s) are represented for each of the four geometries.

Figure 27: Comparison of pressure drop values between four different channel geometries at 10 bar

and a mass flux of 400 kg/(m2s) and 600 kg/(m2s), left and right, respectively.

0

40

80

120

160

200

240

280

320

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

0.53 mm (triangular)0.77 mm0.82 mm (H-shaped)0.91 mm

0

40

80

120

160

200

240

280

320

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

0.53 mm (triangular)0.77 mm0.82 mm (H-shaped)0.91 mm

45

Figure 27 reveals the general tendency of an increasing pressure drop as the vapor quality increases. The rise of pressure drop decreases with an increase of vapor quality. Furthermore, the pressure drop increases inversely to the hydraulic diameter. The same behaviour was registered by Sakamatapan and Wongwises (2014), Jige et al. (2016) and Rahman et al. (2017). In the case of single-phase flow, the pressure drop due to friction is inversely proportional to the hydraulic diameter to the power of 1.2 and the effect of the hydraulic diameter on the pressure drop can be considered comparable between single-phase and two-phase flow (Jige et al. 2016).

Regarding the effect of the geometry, one could conclude that the shape of the channel does not have a great influence in the pressure drop. Agarwal and Garimella (2009) studied various geometries with identical hydraulic diameters. They concluded that the channel which would present higher pressure drop is the rectangular channel (aspect ratio of 2), followed by the triangular, N-shaped (identical to H-shaped) and the square. The considerable differences between the hydraulic diameters of the channels studied surpass the effect of the shape, therefore no direct comparison with the results obtained by Agarwal and Garimella can be made.

At a mass flux of 800 kg/(m2s), the results obtained for the four different geometries are identical to the ones obtained at 600 kg/(m2s), for both pressure drop and heat transfer coefficient. The data relative to a mass flux of 800 kg/(m2s) are represented in Appendix A, Part 1.

5.2 Comparison with correlations

In this sub-chapter the data are compared with existing correlations from the related literature. The correlations presented were developed for macro and mini-channels; single tubes and multiport; circular and non-circular channels and different fluids. It should be addressed that none of the correlations was developed specifically for a triangular geometry. The overviews of the pressure drop and heat transfer correlations are given in Appendix, Part 2.

To study the effectiveness of the correlations, two important relations are used, the mean relative deviation (MRD) and the mean absolute relative deviation (MARD). The equations to compute these are the following:

𝑀𝑅𝐷 =1

𝑁

𝑌 − 𝑌

𝑌=

(71)

𝑀𝐴𝑅𝐷 =

1

𝑁

𝑌 − 𝑌

𝑌=

(72)

where 𝑌 is the experimentally determined value, 𝑌 is the predicted value with the correlation and N is the number of data points in each set. The percentage of points within ±20% error band (EB-20%) was also determined and it is presented together with the mean deviation and average deviation, as an indicator of the effectiveness of the correlation.

46

5.2.1 Pressure Drop

The 96 data points are compared with the correlations from the literature and an overview, as well as the correlation effectiveness indicators, is presented in Table 11.

Table 11: Overview of the comparison of the experimental pressure drop with the correlations.

Correlation MRD (%) MARD (%) EB-20% (%)

Cavallini et al. (2006) -7 12 94

Kim and Mudawar (2012) 7 14 80

Müller-Steinhagen and Heck (1986) 13 17 67

Agarwal and Garimella (2009) 6 23 56

Jige et al. (2016) 22 23 55

Sun and Mishima (2009) -13 21 52

Friedel (1979) 23 24 46

Sakamatapan and Wongwises (2014) 20 34 41

López-Belchí et al. (2014) -25 25 29

Zhang and Webb (2001) -29 30 19

The correlations developed for conventional channels presented in section 2.4, such as Friedel (1979) and Müller-Steinhagen and Heck (1986), show relatively good accuracy with the measured data (cf. Figure 28).

Figure 28: Comparison of the predicted pressure drop using the Müller-Steinhagen and Heck (1986)

correlation (left) and the Friedel (1979) correlation (right) with the experimental data.

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

47

Both correlations have been developed based on large data banks containing frictional pressure drop measurements for various fluids and operating conditions. In the case of the Friedel correlation, the good prediction of the measured data even in small geometries can be explained with the use of the Weber number in the correlation, which accounts for the surface tension effects, highly relevant in micro channels.

The values obtained with the correlations generally overpredicted the data, with a mean relative deviation of 13% and 23% (cf. Figure 28). However, the overprediction of the data increases in terms of higher saturation pressure. Once we only consider the lower saturation pressures of 10 and 15 bar, the accordance improves (cf. Table 12).

Table 12: Effectiveness indicators for the measurements at 10 and 15 bar.

Correlation MRD (%) MARD (%) EB-20% (%)

Müller-Steinhagen and Heck (1986) 8 13 82

Friedel (1979) 16 18 62

The most satisfactory prediction of the measured data, based on the effectiveness indicators, is obtained with the Cavallini et al. (2006) correlation, with 94% of the measured values located within the 20% error band (cf. Figure 29). The correlation generally under predicts the experimental values (MRD = -7%). The good prediction of the data with this correlation can be explained by most of the data points being within the annular and mist flow regime, which is the range of validity of the correlation.

Figure 29: Comparison of the predicted pressure drop using the Cavallini (2006) correlation (left) and the Cavallini (2006) correlation modified with Blasius equation (right) with the experimental

data.

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

48

Cavallini et al. (2006) compared the experimental data relative to adiabatic flow of various fluids, including R134a, in rectangular multiport mini-channel with a hydraulic diameter of 1.4 mm with different correlations. The Friedel correlation predicted the data satisfactorily, except at low mass fluxes. A new pressure drop correlation based on Friedel correlation was developed for shear-dominated regime (annular and mist flows), with the use of the entrainment factor, which adds the effect of the entrainment rate of droplets from the liquid film to the model. The used entrainment factor equation was presented by Paleev and Filippovich (1966) and it is used for the computation of the two-phase multiplier 𝜙 .

𝐸 = 0.015 + 0.44 · 𝑙𝑜𝑔𝜌

𝜌·

𝜇 𝑢

𝜎· 10 (73)

𝜌 = 𝜌 1 + (1 − 𝑥)𝐸

𝑥 (74)

The two-phase multiplier was then obtained with the modification of the constants and exponents of Friedel’s correlation to fit their experimental data. The single-phase pressure drop is calculated with the friction factor correlation presented in Equation 75, for the entire range of liquid-only Reynolds number.

𝑓 = 0.184𝑅𝑒− (75)

However, this correlation is recommended for 𝑅𝑒 ≥ 2 × 10 and the 𝑅𝑒 of the data is within 1300-8300. The Cavallini correlation was computed with the use of Blasius friction (Equation 16), which showed good agreement with the single-phase experimental friction factor (section 4.2.1), and the results are represented in Figure 29. The effectiveness indicators do not show a general improvement with a MRD of 8%, a MARD of 11% and 85% of the points in the EB-20%, however, at higher mass fluxes and vapor qualities, the correlation presents better prediction of the data (lower MARD). At low mass fluxes and vapor qualities, the prediction of the data is considerably poorer.

The Zhang and Webb (2001) generally under predicts the measured values (Figure 30), however, at low vapor qualities, the mean relative error is smaller, showing satisfactory prediction of the experimental data. Their correlation is based on the Friedel equations as well, but the approach differs from the one used by Cavallini. Zhang and Webb do not consider the entrainment of droplets from the liquid film and the term (𝜌 /𝜌 ) (𝜇 /𝜇 ) is replaced by the reduced pressure (𝑃/𝑃 ), based on the work of previous authors with different fluids. Additionally, the Weber and Froude numbers are not used in the correlation. The correlation obtained for the two-phase multiplier is then written as function of the vapor quality and the reduced pressure.

49

Figure 30: Comparison of the predicted pressure drop using the Zhang and Webb (2001) correlation

with the experimental data.

Based on the comparison of the two previous models with the measured data, one could conclude that the two are complementary. While the reduced pressure seems to have a great influence on the pressure drop at lower vapor qualities, the entrainment of the liquid droplets has a stronger influence at higher mass fluxes and vapor qualities.

Different correlations, developed based on a large data banks, were presented by Sun and Mishima (2009) and Kim and Mudawar (2012). The databases consisted of various working fluids, wide range of hydraulic diameters, mass fluxes, and flow qualities. Both correlations were based on the Lockhart and Martinelli-Chrisholm equations and the Chrisholm constants were fitted to their experimental data, considering the effect of the flow conditions. The comparison of the measured data with these correlations is presented in Figure 31. The first generally underpredicts the data (MRD=-13%), specially at a saturation pressure of 10 bar. At higher saturation pressure, it presents a satisfactory prediction of the data. The latter presents a very good accuracy with a MRD of 7%, a MARD of 14% and 80% of the points within the EB-20%. A slight scatter of the data, dependent on the saturation pressure, can also be observed.

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

50

Figure 31: Comparison of the predicted pressure drop using the Kim and Mudawar (2012)

correlation (left) and the Sun and Mishima (2009) correlation (right) with the experimental data.

Sun and Mishima verified a strong dependency of C with Reynolds number and of C/X with the ratio 𝑅𝑒 /𝑅𝑒 . A new correlation for the two-phase multiplier based on statistical analysis was obtained:

𝜙 = 1 +

𝐶𝑅𝑒𝑅𝑒 , 1 − 𝑥

𝑥

𝑋+

1

𝑋 (76)

Kim and Mudawar aimed to achieve a universal model which, by means of the appropriate dimensionless relations, would include the effects of both small channels and different combinations liquid and vapor states. They used their wide database to study the dependency of C of various combinations of dimensionless groups, which were already used for the prediction of two-phase pressure gradient. This analysis led to a new correlation for mini/micro-channels for each of the four combinations of flow regimes (tt, tv, vt and vv). The value C is written for each of the combinations as a function of liquid-only Reynolds number, 𝑅𝑒 , vapor-only Suratman number, 𝑆𝑢 , and density ratio, 𝜌 /𝜌 .

Jige et al. (2016) and Agarwal and Garimella (2009) developed models which take the effect of the channel shape into account. The predicted values, considering an approximation of the used geometry, are shown in Figure 32. The first correlation generally overpredicts the data (MAD=22%) and this overprediction increases as the saturation pressure rises. The second correlation presents a wide scatter of the data, with a MRD of 6% and a MARD of 23%. For saturation pressure of 20 bar, the model overpredicts the data and, on the contrary, at 10 bar, it underpredicts the data. The model originally showed a good accuracy for the authors’ measured data, with 80% of the data points within an error band of 25%. For the data obtained in this work, this value drops to 60% of the experimental data within the same error band.

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

51

Figure 32: Comparison of the predicted pressure drop using the Jige et al. (2016) correlation (left)

and the Agarwal and Garimella (2009) correlation (right) with the experimental data.

Jige et al. (2011, 2016) developed a correction with their experimental data using the two-phase multiplier 𝜙 and the pressure drop for the vapor phase with total flow .

𝜙 = 𝑥 + (1 − 𝑥)𝜌 𝑓

𝜌 𝑓+ 0.65𝑥 (1 − 𝑥)

𝜇

𝜇

𝜌

𝜌 (77)

In their model, the friction factors of both liquid and vapor phase (lo and vo), for Reynolds numbers inferior to 1500, are computed with a constant Cl determined by the channel geometry. The value of this constant was given for different geometries by Shah and London (1978). The used channels are approximated to equilateral triangle with three rounded three rounded corners constant as given, which is identical to the constant for circular channels. As a result, the correlation used is identical to the one originally developed for circular geometries. Due to reduced number of points, which have Reynolds number of liquid and vapor phases in the laminar region, the results obtained are identical to the ones obtained for a rectangular geometry.

Agarwal and Garimella (2009) studied the condensation of R134a in circular and non-circular channels with hydraulic diameters between 0.42 – 0.8 mm. They calculate the pressure drop with Equation 13, considering the density and velocity of the vapor phase, and the friction factor is replaced by the interfacial friction factor. This factor is computed with the liquid-phase Churchill friction factor (Equation 17), the Martinelli parameter, the liquid phase Reynolds number, the superficial velocity, the liquid phase viscosity, the surface tension and a pre-factor (Equation 78). The pre-factor A was determined, for each of the used geometries, while keeping the exponent factors constant. The predicted values represented in Figure 32 were obtained with the pre-factor obtained for the triangular geometry with a hydraulic diameter of 0.829 mm.

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

52

𝑓

𝑓= 𝐴 · 𝑋 𝑅𝑒

𝑗 𝜇

𝜎 (78)

The correlation obtained for rectangular geometries presents considerably poorer results: MRD = -30%, MARD = 32% and 25% points within the EB-20%. The authors concluded in their study that the effect of the channel shape has a stronger effect on the pressure drop than the hydraulic diameter.

5.2.2 Heat Transfer

A summary of the comparison of the heat transfer coefficients predicted with correlations from the literature and the experimentally determined data is presented in Table 13. In general, the correlations show an unsatisfactory prediction of the experimental data, presenting high relative deviations and few or no data points within the EB-20%.

Table 13: Overview of the comparison of the experimental heat transfer coefficient with the correlations considered.

Correlation MRD (%) MARD (%) EB-20% (%)

Webb and Ermis (2001) 48 50 18

Illán-Gómez et al. (2014) 92 102 4

Akers et al. (1959) 103 103 2

Koyama et al. (2003) 106 106 1

Jige et al. (2011) 128 128 1

Jige et al. (2016) 135 135 0

Wang et al. (2002) 150 150 1

Kim and Mudawar (2013) 164 164 1

Cavallini et al. (2006) 213 213 0

Shah (1979) 243 243 0

The prediction of the correlations developed for conventional channels presented in section 2.5 are presented in Figure 33. Akers et al. (1959) developed his model based on the shear force between the two phases, while Shah (1979) used the two-phase multiplier. Both correlations were neither developed for R134a, nor for mini-channels and clearly overpredict the data. However, the prediction effectiveness is identical to the correlations developed for more similar operating conditions and geometries.

53

Figure 33: Comparison of the predicted heat transfer coefficient using the Akers et al. (1959)

correlation (left) and the correlation Shah (1979) correlation (right) with the experimental data.

The correlation which presents lower relative deviation was developed by Webb and Ermis (2001). For the overall experimental data, it presents a MRD of 48%, a MARD of 50% and 18% of the predicted values are in the EB-20%. The Webb and Ermis (2001) correlation was modified to fit the experimental data. Both correlations are represented in Figure 34. The modified correlation slightly underpredicts the data at a condensation pressure of 10 bar and it slightly overpredicts the data at a condensation pressure of 20 bar.

Figure 34: Comparison of the predicted heat transfer coefficient using the Webb and Ermis (2001)

correlation (left) and the Webb and Ermis (2001) correlation modified (right) with the experimental data.

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Webb and Ermis (2001) studied the effect of the hydraulic diameter on the condensation of R134a in aluminium extruded tubes. They used four different geometries (with and without fins) with hydraulic diameters between 0.44 and 1.56 mm, a mass flux range of 300-1000 kg/(m2s), a vapor quality range of 15-90% and a saturation temperature of 65 °C (approximately 19 bar). They presented a mathematically simple correlation which resulted from the multiple regression correlations made to fit their data (Equation 79). The factor b and exponents p and q were determined for each of the used geometries.

ℎ = 𝑏 · · 𝑥 (79)

The experimental data was predicted considering the different geometries and the results are shown in Table 14. The correlation which gives a better prediction of the data is the one obtained for the rectangular plain tube. Additionally, even though the correlation was developed for 19 bar, at lower saturation pressure, namely 10 bar, it provides better prediction of the data: a MRD of 35%, a MARD of 39% and 39% of the predicted values are in the EB-20%.

Table 14: Comparison of the different geometries presented in Webb and Ermis (2001).

Geometry MRD (%) MARD (%) EB-20% (%)

Plain tube, 𝐷 = 1.33 mm 48 50 18

Micro-fins, 𝐷 = 0.61 mm 79 79 5

Micro-fins, 𝐷 = 0.44 mm 65 66 10

The pre-factor and the exponents were fitted to the experimental data as shown in Table 15. One can observe the stronger dependency on the mass flux than on the vapor quality, as 𝑝 > 𝑞. The original equation expresses a stronger dependency on both vapor quality and mass flux than the modified expression, with higher exponential factors. The weaker dependency of the heat transfer coefficient on both vapor quality and mass flux verified for triangular, in comparison with rectangular geometries, has already been discussed in section 5.1.1.

Table 15: Comparison between the original correlation presented by Webb and Ermis (2001) for plain rectangular geometry with the modified correlation for the triangular geometry studied.

Constants

MRD (%) MARD (%) EB-20% (%) b p q

Original corr. 52.02 0.729 0.456 48 50 18

Modified corr. 296.14 0.386 0.200 0 9 98

These expressions have limited applicability, as they are obtained empirically based on a single geometry, hydraulic diameter and saturation pressure, as well as a relatively small database. The modified correlation has a limited validity as well, however, the expression was obtained for a wider saturation pressure range (10-20 bar).

55

In Figure 35, the predicted values determined with Cavallini et al. (2006) are displayed. The correlation presented the best results for the pressure drop prediction. The prediction of the heat transfer coefficient is, however, unsatisfactory, which can be concluded with the absence of points within the EB-20% and both MRD and MARD have a value of 214%.

Figure 35: Comparison of the predicted heat transfer coefficient using the Cavallini et al. (2006)

correlation with the experimental data.

Cavallini et al. (2006) used experimental data with R410A, R134a and R236ea in mini-channels of different geometries and hydraulic diameters between 0.4 and 3 mm to develop their model. The entrainment rate of droplets from the liquid film E and the empirically determined pressure drop correlation discussed in section 5.2.1 were introduced in the Kosky and Staub (1971) model. The model is based on the boundary layer analysis and the entrainment factor is used for the calculation of 𝑅𝑒 . However, this correlation does not consider the effects of the surface tensions. Even though they used hydraulic diameters is identical to the one used experimentally, the effectiveness of the prediction of the heat transfer coefficient in the smallest channels is not presented. Nonetheless, the model showed a good agreement with their data for R134a, R410A and R236a in a mini-channel with a hydraulic diameter of 1.4 mm. For R134a, 100% of the points were within the EB-20%. However, no results are presented for smaller diameters.

Koyama’s research group has presented two correlations for the calculation of the heat transfer coefficient. The first correlation (Koyama et al. 2003) resulted from the experimental study of the condensation of R134a in four different multiport tubes with hydraulic diameters around 1 mm. Due to the inexistence of a correlation to predict condensation heat transfer in tubes whose diameter are smaller than 1 mm, a new correlation was developed. The Mishima and Hibiki (1966) correlation (Equation 27 and Equation 28) was modified with the addition of the surface tension effects, considering the kinematic viscosities of both phases and the Bond number (Equation 82). The new heat transfer equation was developed from the correlation of Haraguchi et al. (1994) with the

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modification of the effect of the diameter (with the two-phase multiplier). The Nusselt number is computed with the forced convection term, 𝑁𝑢 , and the free convection condensation term, 𝑁𝑢 .

𝑁𝑢 = (𝑁𝑢 + 𝑁𝑢 ) (80)

𝑁𝑢 = 0.0112𝑃𝑟𝜙

𝑋𝑅𝑒 (81)

where 𝜙 = 1 + 13.17𝜈

𝜈1 − 𝑒−

√

𝑋 + 𝑋 (82)

Illán-Gómez et al. (2014) modified the constants of the forced convection Nusselt number from the Koyama et al. (2003) correlation. These constants were determined with an adjustment to their experimental data, obtained with R134a and R1234yf in a multiport flat tube with rectangular channels and a hydraulic diameter of 1.16 mm. The results obtained with both correlations is shown in Figure 36. The Illán-Gómez et al. (2014) correlation presented a better prediction of the measured data, although only 4% of the data points are in the EB-20%. Despite that, both correlations present a poor prediction of the data.

Figure 36: Comparison of the predicted heat transfer coefficient using the Koyama et al. (2003)

correlation (left) and the Illán-Gómez et al. (2014) correlation (right) with the experimental data.

The second correlation developed by Koyama’s research group was presented in Jige et al. (2011). In their work, a multiport tube with rectangular channels with a hydraulic diameter of 0.85 mm was investigated. At higher mass fluxes they measured a decrease in the heat transfer value with decreasing vapor quality, as expected. However, at low mass fluxes, the heat transfer coefficient was almost constant within the vapor quality range, because of the dominance of surface tension effect.

The new correlation was developed considering both vapor shear stress and surface tension effects, which outweigh the effect of gravity in small geometries. The free convection term presented in

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Koyama et al. (2003) is suppressed. The Haraguchi et al. (1994) form is used with a vapor shear stress effect term and a surface tension effect term as follows:

𝑁𝑢 = (𝑁𝑢 + 𝑁𝑢 ) / (83)

For the calculation of the term 𝑁𝑢 , the effect of the surface tension is neglected and the liquid film between the corners is assumed to be laminar and thin with constant thickness along the channel. The two-phase multiplier 𝜙 is calculated with Equation 82. Additionally, a correction function was used to account for the turbulence effect and it was determined based on the experimental results.

𝑁𝑢 =𝜙

1 − 𝑋· 𝑓 ·

𝜌

𝜌· 𝑅𝑒 · 𝐹(𝑅𝑒 ,𝑃𝑟 ) (84)

For the calculation of the term 𝑁𝑢 , 𝑟 and 𝑡 are assumed to be constant along the channel.

𝑁𝑢 =𝜌 ∆ℎ 𝜎𝐷

𝑘 𝜇 (𝑇 − 𝑇· 𝑆(𝑑, 𝑟 , 𝑡) (85)

They presented an expression for 𝑆(𝑑, 𝑟 , 𝑡) as a function of the Bond number and the void fraction, obtained with their experimental data. The correlation gave a “fairly good” prediction of their experimental data, however, it generally overpredicted it. The data obtained in the context of this work is being overpredicted as well, as can be observed in Figure 37.

Figure 37: Comparison of the predicted heat transfer coefficients using the Jige et al. (2011) correlation (left) and the Jige et al. (2016) correlation (right) with the experimental data.

Jige et al. (2016) expanded their previous correlation, which considers the effects of the vapor shear stress and surface tension on condensation heat transfer, as well as the different flow regimes, the annular flow and the intermittent flow.

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The transition from annular to intermittent flow can be approximated as an alternation between vapor plug flow and liquid slug flow. Vapor plug flow Nusselt number can be expressed as for annular flow, 𝑁𝑢 = 𝑁𝑢 . The liquid slug Nusselt number is calculated using the correlations of forced

single-phase liquid flow (section 2.5). The intermittent Nusselt number can then be calculated as following:

𝑁𝑢 =𝑁𝑢 𝐿 + 𝑁𝑢 𝐿

𝐿 + 𝐿 (86)

where 𝐿 and 𝐿 are the and it can be expressed as function of void fraction (calculated by the

homogeneous model):

𝑁𝑢 = 𝜀𝑁𝑢 + (1 − 𝜀)𝑁𝑢 (87)

The model to calculate 𝑁𝑢 is identical to the one presented by Jige et al. (2011). A relevant difference is the replacement of the parameter 𝑆(𝑑, 𝑟 , 𝑡) in Equation 85 by a constant obtained with their experimental data. The influence of the hydraulic diameter and densities is then suppressed with the elimination of Bond number in the calculation of the parameter S. This is a possible explanation for the slightly worse prediction of this correlation in comparison to the Jige et al. (2011) correlation, nonetheless, the difference is minimal.

The parameter S was fitted to the obtained experimental, however, the best result was obtained for 𝑆 = 0, which results in a MARD = 117%. Since the surface tension effects have a strong influence in the used channels, this result highlights the necessity of not only correcting the parameter S, but also the parameter F. The best results, considering the correlation effectiveness indicators, where achieved considering 𝑆 = 0.30 and a pre-factor for the parameter F with a value of 0.31. These values reflect the dominance of the surface tension over the shear forces effects. The results obtained are represented in Figure 38, which correspond to a MRD of -6%, a MARD of 12% and 83% of the points within the EB-20%.

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Figure 38: Comparison of the predicted heat transfer coefficients using the Jige et al. (2016)

correlation (modified) with the experimental data.

Despite the fact these parameters resulted from a small amount of experimental data, it confirms the importance of the surface tension term inclusion in the heat transfer coefficients prediction in small geometries.

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6 Influence of oil in flow condensation The introduction of oil in a vapor compression refrigerant system is unavoidable, due to the necessity of lubricating the compressor. The influence of the oil introduction has been studied in the literature, although the conclusions on how it affects both heat transfer and pressure drop vary.

Due to the scarce literature on the effects of the oil in flow condensation of R134a in small geometries, its experimental study is of great interest. To address the situation, the oil cycle was used to introduce oil in the system and the software was adapted for refrigerant-oil mixture properties.

6.1 Set-up for refrigeration-oil mixture

Introduction of oil into the system

As presented in section 3.1, in addition to the main cycle, there is an oil cycle, which is used for both introduction and removal of oil in the system.

The system is vacuum drawn, due to the hydrophilicity of the oil, and the oil reservoir is filled up. The connection between the main and oil cycles is opened to increase the pressure inside the oil cycle. A pump promotes the flow in the oil cycle. To facilitate the introduction of the oil, the pressure of the main cycle is reduced. The proportional valve is then opened, and the oil is injected into the main cycle.

The quantity of oil in the system is determined by the density oscillator placed before the pump. Additionally, the gravimetric analysis is used on a removed sample of the mixture. The nominal oil concentration is determined as follows:

𝜔 =𝑊 − 𝑊

𝑊 − 𝑊 (88)

where 𝑊 is the weight of the empty measurement capsule, 𝑊 is the weight of the measurement capsule filled with the mixture sample, and 𝑊 is the weight of the capsule after the refrigerant was removed.

Software adaptation The properties of the refrigerant-oil mixture and of the pure oil were introduced in the data acquisition software LabView. The properties of these are recorded after the sub-cooler, before the evaporator and at the outlet of the measurement section. These properties are then used in the MATLAB code for the determination of the experimental data and calculations of the correlation’s predicted values.

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In the MATLAB code, the computation of four new quantities is introduced: vapor quality including the mass of oil (Equation 50), at the inlet and outlet of the measurement section; the Nusselt number including the mixture properties; and the local oil quantity (Equation 49).

During the measurements, the vapor quality used as reference is based on pure refrigerant flow for simplification. The vapor quality including the mass of oil is calculated with the refrigerant-oil mixture properties:

𝑥 =

− 𝑐 𝑇 − 𝑇

(ℎ − ℎ ) (89)

6.2 Validation of the experimental set-up

For the study of the influence of the introduction of oil in the cycle, the operating conditions used for the two-phase flow measurements of the pure refrigerant are reproduced for different oil concentrations. These measurements are planned for different nominal oil concentrations up to 10%. In this work, the measurements were performed with a nominal oil concentration of 1%. These results should be then compared with future results obtained for higher oil concentrations to analyse its influence on the variation of heat transfer coefficient and pressure drop values.

6.2.1 Single-phase results

The first measurements aimed to quantify the influence of the oil in the single-phase flow at approximately 8 bar, comparing these values with the data obtained for pure refrigerant (section 4.2.1). Even though the measurements were performed for the same mass flux, due to the higher viscosity of the refrigerant-oil mixture, the Reynolds numbers are inferior than the ones obtained for pure refrigerant. As a result, there is a displacement of the data points to the left.

Pressure drop

The results obtained for the pressure drop are represented in Figure 39. For the same Reynolds number, the measured data shows a rise of the pressure drop with the introduction of the oil in the cycle. This effect is stronger for higher values of Reynolds number (turbulent flow). The higher viscosity of the refrigerant-oil mixture results in a higher inner friction, which is reflected in the increasing pressure drop.

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Figure 39: Single-flow measured pressure drop values for refrigerant-oil mixture.

Heat transfer coefficient

As stated in Equation 51, the higher viscosity of the mixture in comparison to the pure refrigerant is expected to be reflected in a reduction of the heat transfer coefficient of the single-phase flow. In Figure 40 the measured values for both pure refrigerant and refrigerant-oil mixture are given for comparison.

For identical flow conditions, thus the same Reynolds number, the heat transfer coefficient measured for the refrigerant-oil mixture does not show a considerable influence when compared with the results for pure refrigerant. Hence, a stronger influence of the addition of oil in the heat transfer is expected with the increase of the oil concentration.

Figure 40: Comparison of the single-phase measurement results of pure refrigerant and refrigerant-

oil mixture with the literature.

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6.2.2 Two-phase results

The two-phase measurements were performed at a condensation pressure of 10 bar, for a mass flux range of 400-1200 kg/(m2s) and for a vapor range of 20-80%. Additionally, the saturation temperature corresponds to the refrigerant-oil mixture, since it is the average of the temperatures directly measured at the inlet and outlet of the measurement section (see section 3.2). In the literature, the results are presented in some cases with either pure refrigerant or mixture saturation temperatures, when the temperature is not directly measured but calculated from the pressure measurement. The results obtained for each of these cases are considerably different, especially at higher vapor qualities (Shao and Granryd 1995). As a result, one should confirm how the data reduction is made before proceeding to the comparison of the experimental results.

Heat transfer coefficient

The experimental results obtained for heat transfer coefficient are given in Figure 41. The rise of the heat transfer coefficient with an increase of both vapor quality and mass fluxes is also observed for the refrigerant-oil mixture.

Figure 41: Comparison between the experimental heat transfer coefficient values measured with

pure refrigerant and with refrigerant-oil mixture at 10 bar.

For better a visualization of the experimental data, the measured values and respective uncertainty intervals are represented for each of the mass fluxes individually. The data correspondent to a mass flux of 800 kg/(m2s) are represented in Figure 42, and the remaining data can be consulted in the Appendix, Part 1. For each of the mass fluxes, an overlap between the uncertainty levels can be observed.

The effect of the oil can be quantified with the enhancement factor EF (Equation 52), and the corresponding values for each of the mass fluxes are presented in Figure 42. Most of the EF values

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are greater than 1, which shows a positive influence of the oil in the heat transfer coefficient, especially at lower mass fluxes and at higher vapor qualities, when the percentage of the oil in the liquid phase is higher.

Figure 42: Comparison between the experimental heat transfer coefficient values measured with

pure refrigerant and with refrigerant-oil mixture at 800 kg/(m2s) and at 10 bar (left) and enhancement factor values at 10 bar (right).

A possible explanation for the enhanced heat transfer at lower mass fluxes is the higher surface tension of the refrigerant-oil mixture, which promotes the accumulation of the condensate in the vertices of the channels, improving the heat transfer in the remaining perimeter. At higher mass fluxes the influence of the increased viscosity of the flow has a prevalent effect, thus the enhancement factor is mostly inferior to 1. Hence, due to the proximity of the EF values to 1 and the uncertainty intervals, no final conclusions can be reached.

Most of the literature reported a decrease of the heat transfer coefficient with the addition of oil. However, its influence varies with the type of refrigerant and oil used. Moreover, some authors have measured a negligible influence of the oil when the mass concentration was inferior to 3% (Wang et al. 2012). The influence of the oil in the heat transfer coefficient for this geometry should be further analyzed for higher oil concentrations.

Pressure drop

The experimental pressure drop measurements are presented in Figure 43. The pressure drop of the refrigerant-oil mixture increases with the rise of both mass fluxes and vapor qualities as previously measured for pure refrigerant. The data obtained for each of the mass fluxes can be consulted in the Appendix, Part 1. The uncertainty of the measurements is between 0.95 and 4.38%, thus there is no overlap of the uncertainty intervals.

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Based on the measured values, one can conclude that the oil has a negative effect on the pressure drop as the values measured for the mixture are generally higher than the ones measured for pure refrigerant. The effect is stronger with increasing vapor quality, since both the absolute and the relative pressure drop differences increase with the rise of vapor quality. The calculated penalty factors (Equation 54) are given in Figure 44.

Figure 43: Comparison between the experimental pressure drop values measured with pure

refrigerant and with refrigerant-oil mixture at 10 bar.

Figure 44: Penalty factor values at 10 bar.

There are two opposite effects which can explain the measured results. Firstly, the oil addition leads to an increase of the liquid viscosity, thus in a lower Reynolds number of the liquid phase and, as a result, a weaker turbulent flow intensity. This effect makes the flow regime change from turbulent to laminar, resulting in a lower frictional pressure loss than the measured for pure refrigerant. The second effect is related with the rise of vapor quality and subsequent increasing vapor velocity, which promote

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the turbulent flow, increasing the PF. These effects were reported by (Huang et al. 2010b), who studied the two-phase frictional pressure drop of R410a-oil mixture flow in smooth tubes with hydraulic diameters of 1.6 and 4.18 mm. He obtained a PF inferior than 1 at lower vapor qualities and superior at higher vapor qualities. The transition vapor quality was defined as the value at which the PF equals 1. Furthermore, oil concentration amplified the two effects previously described, since a higher concentration led to a lower PF for values inferior than the transition vapor quality, and a higher PF for the remaining. Additionally, the vapor quality transition value reduces as smaller channels are used.

Regarding the influence of the mass flux in the penalty factor, Huang et al. (2010b) reported a small rise with increasing mass flux due to the enhanced turbulence effects. The present data shows otherwise, since the PF is higher than the remaining values for a mass flux of 400 kg/(m2s). Identical results have been obtained by Eckels et al. (1994), who experimentally studied the heat transfer and pressure drop of R134a and ester lubricant mixtures in a smooth tube with a hydraulic diameter of approximately 8.92 mm. When the lubricant concentration is inferior than 1.5%, the measurements obtained with the two different used lubricants show an increase of the PF at the lower mass flux. This phenomenon was then explained by Wang et al. (2012) with the increasing lubricant entrainment as the vapor shear increases as a consequence of the increasing mass flux.

As the data is expected to vary considerably with the oil concentration, more data is needed to make a further analysis.

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7 Conclusions and Future Work The purpose of this work is to study the condensation of R134a in a multiport flat tube with triangular channels and a hydraulic diameter of 0.529 mm. The aim of the experimental characterization regarding the thermohydraulic properties of the tube is the determination of both heat transfer coefficient and pressure drop. The measurements were performed within a mass flux range of 400-1200 kg/(m2s), a saturation pressure of 10-20 bar and an inlet vapor quality between 10 and 90%.

To validate the experimental set-up and procedure after the implementation of a new test section, the determination of the single-phase pressure drop and heat transfer was performed. This was concluded with positive results, since both heat transfer coefficient and pressure drop were similar to the values predicted by well-known single-phase correlations.

7.1 Contributions

The variation of the vapor quality and mass flux showed a strong influence on the heat transfer coefficient. With the increase of the vapor quality the condensate layer thickness reduces, which results in a lower thermal resistance, hence higher heat transfer. Along with this effect, the ratio between the vapor and liquid phases velocities also increases, thus stronger shear forces. Likewise, a higher mass flux promotes a higher heat transfer, as along with the rise of both phases velocities, there is an improvement of the momentum exchange. At lower mass fluxes, an approximately constant heat transfer coefficient value was measured, with increasing mass flux and vapor quality. This insensibility to the variation of these operating conditions can be explained by the dominance of the surface tension over the shear forces on the condensation flow in small geometries. In the studied geometry, the condensate accumulates in the sharpest corner. Consequently, the liquid layer is thin in the remaining perimeter, promoting a better heat transfer even at low mass fluxes and vapor qualities.

The pressure drop rises with increasing vapor quality and mass flux. It can be explained with the higher flow velocity and resultant increased inner friction and interfacial shear. Moreover, the effect on the measured values was detected to be higher for the mass flux than for the vapor quality. The influence of the saturation pressure on the pressure drop was also considered. One could observe a decrease of the pressure drop with increasing saturation pressure. This is a consequence of the variation of the thermophysical properties of the refrigerant with the saturation pressure. A higher saturation pressure means a lower slip ratio, which results in lower shear forces between the two phases, as well as lower fluid inner friction.

The experimental results were compared with the previously obtained data with different MFT geometries. Two MFT consist of rectangular shaped channels, and a third MFT is H-shaped. The channels have different hydraulic diameters, are however all larger than the channel used in this work. The triangular geometry presents a worse performance than the previously tested ones, considering

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both the heat transfer coefficient and the pressure drop. Its performance in regard of the heat transfer is identical to the H-shaped tube, since both show insensibility to the vapor quality increase at lower mass fluxes. At higher mass fluxes the heat transfer coefficient increases with increasing vapor quality and mass flux as expected. Despite lower heat transfer coefficients being expected for larger hydraulic diameters, that was not confirmed for both triangular and H-shaped channels. This result can be explained by the accumulation of the condensate in the corners, which reduces the perimeter of the channel with higher heat transfer coefficient. Along with the heat transfer, the pressure drop results were also compared with the ones obtained with other geometries. The values increase with the rise of both the vapor quality and mass flux. Moreover, the value of the pressure drop decreases for larger hydraulic diameters, as it was expected. Regarding the effect of channels’ geometry on the pressure drop, based on the data one could conclude that this effect is not very influential.

The experimental data were also compared with the values predicted by various correlations found in the literature. While the pressure drop has a satisfactory accordance with the correlations, the heat transfer correlations could not predict the measured data.. Both types of correlations presented partly good predictions. Regarding the heat transfer coefficient, the predicted values are considerably higher than the ones measured. A possible reason is the relatively stronger influence of surface tensions in the smaller geometries. Some of the correlations were fitted to the experimental data, hence the validity of this modification is very limited, due to the small databank used.

Lastly, the influence of adding oil in the cycle was studied. The oil was introduced with the activation of the oil cycle and the software used for the data analysis was adapted. The performed experimental measurements for pure refrigerant were partly repeated for a refrigerant-oil mixture with approximately 1% nominal oil concentration, at a condensation pressure of 10 bar. The data obtained with the single-phase measurements showed, for the same Reynolds number, a rise of the pressure drop with the addition of oil in the cycle. These results can be explained with the effect of the higher viscosity of the refrigerant-oil mixture in comparison to the pure refrigerant. In addition, the heat transfer coefficients measured do not show a considerable influence of the oil addition. This effect is expected to be more noticeable for higher oil concentrations. Regarding the two-phase measurements, the influence of the oil in the cycle was noticed. Considering the heat transfer, the measured values showed a slightly positive influence of the addition of oil at lower mass fluxes and vapor qualities. A possible explanation for these results is the effect of the higher surface tension of the mixture when compared with the pure refrigerant, which influences the condensate distribution around the channel. Additionally, the pressure drop was generally higher than the previously measured results, and it is considerably influenced by the rise of the vapor quality. A relevant effect at lower vapor qualities is the reduced turbulence effect due to the higher viscosity of the mixture. Furthermore, the lowest mass flux presented the highest value of PF, which possibly results from the reduced lubricant entrainment.

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7.2 Suggestions for Future Work

Even though the MFT with triangular channels presented the worst overall performance, no conclusion should be made, since it was not compared yet with rectangular channels with identical hydraulic diameter. For future research, it is suggested that other geometries with similar dimension are studied. This will allow to conclude if the weaker performance observed is caused by the geometry itself or by the smaller dimension and consequent effects.

Regarding the experimental study of the refrigerant R134a-oil mixture, as the data is expected to vary considerably with the saturation pressure and the oil concentration, more data is needed to make a further analysis. The measurements should additionally be done for 15 and 20 bar to allow a complete comparison with the values measured for pure refrigerant. Other nominal oil concentrations should also be studied, namely 3, 5 and 10%, which is the typically maximum value used in an automotive AC system. This will allow a better understanding of the oil influence in the heat transfer and pressure drop.

The pressure drop values obtained with the correlations for macro-channels are identical to the ones measured for the studied geometry. As a result, one can expect that the existent computational models are adequate for the estimation of the pressure drop in triangular-shaped mini-channels. However, the heat transfer coefficient tends to be overestimated by the correlations for macro-channels, thus a condenser developed with models based on these would be under-dimensioned.

It is recommended that the results presented in this document are added to a broader databank, which could be used for the development of the desired universal model for the prediction of the heat transfer coefficient and pressure drop in MFT. This addition is of high interest since the available data is very limited, especially for smaller hydraulic diameters and for refrigerant R134a-oil mixture, and almost inexistent for triangular geometries. A computational model which includes correlations developed based on a more complete databank will facilitate an optimized design of the new generation of condensers. This can result in a lower weight of the final component used in a vehicle, reducing then its overall weight.

72

73

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77

Appendix Part 1: Figures

Figure 45: Heat transfer coefficient ratio at 20 bar before and after sub-cooling correction.

Figure 46: Heptane outlet temperature measurement and refrigerant outlet temperature

measurement at a condensation pressure of 15 bar, a mass flux of 1000 kg/(m2s) and vapor quality of 20%, left and right, respectively.

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

600 kg/(m²s)600 kg/(m²s) a. c.800 kg/(m²s)800 kg/(m²s) a. c.

21.6

21.7

21.8

0 150 300 450 600 750 900

Hep

tane

outle

t tem

pera

ture

[°C

]

Time [s]

38.9

39

39.1

0 150 300 450 600 750 900

Ref

riger

ant o

utle

t tem

pera

ture

[°C

]

Time [s]

78

Figure 47: Uncertainty distribution at a condensation pressure of 15 bar, a mass flux of

1000 kg/(m2s) and vapor quality of 20%, after the correction (5%).

Figure 48: Experimental heat transfer coefficient values at 10 bar and respective uncertainty

intervals.

1

2

3

4

5

𝑐 , : < 1%

:2%

Δ𝑇 :35%

𝐴: < 1%

Δ𝑇 :16%

3

4

5

6

7

8

9

10

11

12

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

79

Figure 49: Experimental heat transfer coefficient values at 15 bar and respective uncertainty

intervals.

Figure 50: Experimental heat transfer coefficient values at 20 bar and respective uncertainty

intervals.

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

400 kg/(m²s)600 kg/(m²s)800 kg/(m²s)1000 kg/(m²s)1200 kg/(m²s)

80

Figure 51: Heat transfer coefficient results of the reproducibility measurements at 10 bar.

Figure 52: Heat transfer coefficient results of the reproducibility measurements at 20 bar.

23456789

101112

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

600 kg/(m²s) 600 kg/(m²s) Rep800 kg/(m²s) 800 kg/(m²s) Rep1000 kg/(m²s) 1000 kg/(m²s) Rep1200 kg/(m²s) 1200 kg/(m²s) Rep

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

600 kg/(m²s) 600 kg/(m²s) Rep1000 kg/(m²s) 1000 kg/(m²s) Rep

81

Figure 53: Pressure drop results of the reproducibility measurements at 10 bar

Figure 54: Pressure drop results of the reproducibility measurements at 20 bar.

0

200

400

600

800

1000

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

600 kg/(m²s) 600 kg/(m²s) Rep800 kg/(m²s) 800 kg/(m²s) Rep1000 kg/(m²s) 1000 kg/(m²s) Rep1200 kg/(m²s) 1200 kg/(m²s) Rep

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

600 kg/(m²s) 600 kg/(m²s) Rep1000 kg/(m²s) 1000 kg/(m²s) Rep

82

Figure 55: Comparison of heat transfer coefficient ratios between different geometries at 10 bar and

800 kg/(m2s).

Figure 56: Comparison of pressure drop for four different channel geometries at 10 bar and a mass

flux of 800 kg/(m2s).

468

1012141618202224

0 0.2 0.4 0.6 0.8 1

h TP/h

lo[-]

Vapor quality [-]

0.77 mm0.91 mm0.82 mm (H-shaped)0.53 mm (triangular)

0

50

100

150

200

250

300

350

400

450

0 0.2 0.4 0.6 0.8 1

Δp T

P/Δ

p lo[-]

Vapor quality [-]

0.53 mm (triangular)0.77 mm0.82 mm (H-shaped)0.91 mm

83

Figure 57: Calculated pressure drop using the Sakamatapan and Wongwises (2014) correlation (left)

and the López-Belchí et al. (2014) correlation (right), plotted against the experimental values.

Figure 58: Calculated heat transfer coefficients using the Wang et al. (2002) correlation (left) and

the Kim and Mudawar (2013) correlation (right), plotted against the measured values.

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20% 0

200

400

600

800

0 200 400 600 800

Δp p

red/

Δp l

o[-]

ΔpTP/Δplo [-]

10 bar15 bar20 barCorrelation+-20%

0

10

20

30

40

50

0 10 20 30 40 50

h pre

d/h l

o[-]

hTP/hlo [-]

10 bar15 bar20 barCorrelation+-20%

0

10

20

30

40

50

0 10 20 30 40 50

h pre

d/h l

o[-]

hTP/hlo [-]

10 bar15 bar20 barCorrelation+-20%

84

Figure 59: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 400 kg/(m2s) (left), and at

600 kg/(m2s) (right).

Figure 60: Comparison between the experimental heat transfer coefficient values measured with pure refrigerant and with refrigerant-oil mixture at 10 bar and at 1000 kg/(m2s) (left); and at

1200 kg/(m2s) (right).

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

h M/h

Ref

[-]

Vapor quality[-]

Pure refrigerantRefrigerant-oil mixture

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

h M/h

Ref

[-]

Vapor quality[-]

Pure refrigerantRefrigerant-oil mixture

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

h M/h

Ref

[-]

Vapor quality[-]

Pure refrigerantRefrigerant-oil mixture

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

h M/h

Ref

[-]

Vapor quality[-]

Pure refrigerantRefrigerant-oil mixture

85

Figure 61: Comparison between the experimental pressure drop values measured with pure

refrigerant and with refrigerant-oil mixture at 10 bar and at 400 kg/(m2s) (left), and at 600 kg/(m2s) (right).

Figure 62: Comparison between the experimental pressure drop values measured with pure

refrigerant and with refrigerant-oil mixture at 10 bar and at 800 kg/(m2s) (left); and at 1000 kg/(m2s) (right).

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1

Δp M

/Δp R

ef[-]

Vapor quality [-]

Pure refrigerantRefrigerant-oil mixture

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1

Δp M

/Δp R

ef[-]

Vapor quality

Pure refrigerantRefrigerant-oil mixture

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Δp M

/Δp R

ef[-]

Vapor quality [-]

Pure refrigerantRefrigerant-oil mixture

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Δp M

/Δp R

ef[-]

Vapor quality [-]

Pure refrigerantRefrigerant-oil mixture

86

Figure 63: Comparison between the experimental heat transfer coefficient values measured with

pure refrigerant and with refrigerant-oil mixture at 10 bar and at 1200 kg/(m2s).

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Δp M

/Δp R

ef[-]

Vapor quality [-]

Pure refrigerantRefrigerant-oil mixture

87

Part 2: Tables Table 16: Used substances in the experimental apparatus.

Substance designation Supplier Use

1,1,1,2 - Tetrafluoroethane Schick GmbH & Co. KG refrigerant

n-Heptane Carl Roth GmbH & Co. KG coolant for the measurement

section

Demineralized water provided by KIT cooling

Original oil for Denso compressors type ND8

Dometic WAECO International GmbH

oil

88

Ta

ble

17: A

pplia

nces

and

mea

sure

men

t un

its u

sed

in t

he e

xper

imen

tal a

ppar

atus

.

Inst

rum

ent

Mod

el

Fabr

ican

t U

se

Con

trol

cab

inet

with

Sip

lus

touc

h pa

nel

vario

us

Siem

ens

AG

co

ntro

l of t

he p

ump,

val

ves

and

evap

orat

or p

ower

Cor

iolis

flow

met

er

RH

M 0

3 R

heon

ik M

essg

erät

e G

mbH

m

easu

rem

ent

of t

he m

ass

flow

rat

e

Pres

sure

diff

eren

ce s

enso

r 26

5 D

S A

BB

Gro

up

mea

sure

men

t of

the

pre

ssur

e di

ffere

nce

Abs

olut

e pr

essu

re s

enso

r 26

5 A

S A

BB

Gro

up

mea

sure

men

t of

the

abs

olut

e pr

essu

re

Pres

s sw

itch

PSA

06

PKP

Proz

essm

esst

echn

ik

emer

genc

y sw

itch

for

the

hept

ane

pum

p

The

rmos

tat

Uni

chill

er U

S055

Tw

Pete

r H

uber

Käl

tem

achi

nenb

au

Gm

bH

tem

pera

ture

con

trol

of t

he c

oolin

g wa

ter

cycl

e fo

r th

e he

ptan

e

The

rmos

tat

Laud

a Va

rioco

ol V

C 3

000

Laud

a D

r. R

. Wob

ser

Gm

bH &

C

o. K

G

tem

pera

ture

con

trol

of t

he c

oolin

g wa

ter

cycl

e of

the

con

dens

er

The

rmos

tat

Laud

a Va

rioco

ol V

C 2

000

Laud

a D

r. R

. Wob

ser

Gm

bH &

C

o. K

G

tem

pera

ture

con

trol

of t

he c

oolin

g wa

ter

cycl

e of

the

sub

cool

er

Gea

r pu

mp

Powe

r un

it B

VP-

Z w

ith p

ump

head

ID

EX H

ealth

& S

cien

ce G

mbH

he

ptan

e su

pply

ing

Pist

on d

iaph

ragm

pum

p H

ydra

Cal

l G20

Ve

rder

Gm

bH &

Co.

KG

re

frige

rant

sup

plyi

ng

Mag

netic

val

ve

6240

B

ürke

rt F

luid

Con

trol

Sys

tem

s G

mbH

& C

o. K

G

cont

rol o

f the

flow

ing

fluid

Prop

ortio

nal v

alve

86

50

Bür

kert

Flu

id C

ontr

ol S

yste

ms

Gm

bH &

Co.

KG

co

ntro

l of t

he fl

owin

g flu

id

Dig

ital p

ower

met

er

WT

1030

Yo

koga

wa E

lect

ric C

orpo

. po

wer

mea

sure

men

t of

the

ev

apor

ator

Pl

atin

um r

esist

ance

the

rmom

eter

(P

t-10

0)

Pt 1

00 A

20/

050/

NB

/4 C

u T

T17

/5m

El

ectr

onic

Sen

sor

Gm

bH

tem

pera

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mea

sure

men

t

89

Table 18: Operating parameters at which the experimental procedure was performed.

Pressure [bar] Mass flux [kg/(m2s)] Vapor quality [%]

10

400 20, 40, 60, 80

600 20, 40, 60, 80, 90

800 20, 40, 60, 80, 90

1000 10, 20, 40, 60, 80, 90

1200 20, 40, 60, 80, 90

15

400 20, 40, 60, 80, 90

600 20, 40, 60, 80, 90

800 20, 40, 60, 80, 90

1000 20, 40, 60, 80, 90

1200 20, 40, 60, 80

20

400 40, 60, 80

600 20, 40, 60, 80, 90

800 20, 40, 60, 80, 90

1000 20, 40, 60, 80, 90

1200 20, 40, 60, 80, 90

Table 19: Overview of the repetition points for the reproducibility analysis.

Pressure [bar] Mass flux [kg/(m2s)] Vapor quality [%]

10

600 40, 80

800 40, 60, 90

1000 20, 40, 60 (2), 80

1200 20, 40, 60 (2), 80

15

400 60, 80

600 60, 80

800 60, 80

1000 60, 80

20 600 40

1000 60, 80

90

Table 20: Overview of the experimental data compared between the different geometries at 10 bar.

MFT Mass flux [kg/(m2s)] Vapor quality [%]

Rectangular, 𝐷 = 0.77 mm

400 20, 40, 60, 80, 90

600 20, 40, 60, 80, 90

800 20, 40, 60, 80

Rectangular, 𝐷 = 0.91 mm

400 20, 40, 60, 80, 90

600 10, 20, 40, 60, 80, 90

800 20, 40, 60, 80, 90

H-shape, 𝐷 = 0.96 mm

400 20, 40, 60, 80, 90

600 10, 20, 40, 60, 80, 90

800 20, 40, 60, 80, 90

91

Ta

ble

21: O

verv

iew

of t

he p

ress

ure

drop

cor

rela

tions

.

Aut

hors

Flu

id(s

) C

hann

el

geom

etry

* 𝑫

[𝐦

𝐦]

𝒎

[𝐤𝐠/(

𝐦𝐬)

] P

ress

ure

[b

ar]

MR

D

[%]

MA

RD

[%

] EB

-20%

[%

] A

garw

al,

Gar

imel

la (

2009

) R

134a

M

-C, M

-R,

M-T

, M-F

, etc

. 0.

42−

0.80

15

0−

750

13.9

6 6

23

54

Cav

allin

i et

al.

(200

6)

R13

4a, R

410A

, R

236e

a M

-R

1.4

200

−14

00

10.2

-7

12

94

Frie

del (

1979

) wa

ter,

R12

, air-

wate

r, ai

r-oi

l, et

c.

S-C

, S-R

1

−15

4 2

−10

330

1−

64

23

24

46

Jige

et

al. (

2016

) R

134a

, R32

, R

1234

ze(E

), R

410A

M

-R

0.85

10

0−

400

10.

2−

16.8

22

23

55

Kim

, Mud

awar

(2

012)

R13

4a, R

12, C

O2,

air-

wat

er, R

410A

, et

c.

M-C

, M-R

, S-

C, S

-R

0.0

695

−6.2

2 4

−85

28

−

7 14

80

Lópe

z-B

elch

í et

al.

(201

4)

R13

4a, R

1234

yf, R

32

M-R

1.

16

350

−94

0 5.

7−

14.9

-2

5 25

29

Mül

ler-

Stei

nhag

en,

Hec

k (1

986)

air-

wate

r, ai

r-oi

l, hy

droc

arbo

ns, s

team

-wa

ter

R11

, etc

. S-

C

7−

392

50−

1038

−

13

17

67

Saka

mat

apan

, W

ongw

ises

(201

4)

R13

4a

M-R

1.

1−

1.2

345

−68

5 8.9

−11

.6

20

34

41

Sun,

Mish

ima

(200

9)

R13

4a, R

410A

, CO

2, wa

ter,

air,

etc.

M

-C, M

-R,

S-C

, S-R

0.

506

−12

50

−10

80

−

-13

21

52

Zhan

g, W

ebb

(200

1)

R13

4a, R

22, R

410A

M

-C, S

-C

2.13

−6.

25

200

−10

00

5.7

−18

.9

-29

30

19

*M: m

ultip

ort,

S: s

ingl

e, C

: circ

ular

, R: r

ecta

ngul

ar, T

: tria

ngul

ar, F

: rec

tang

ular

with

mic

rofin

s.

92

Tabl

e 22

: Ove

rvie

w o

f the

hea

t tr

ansf

er c

orre

latio

ns.

Aut

hors

Flu

id(s

) C

hann

el

geom

etry

* 𝑫

[𝐦

𝐦]

𝒎

[𝐤𝐠/(𝐦

𝐬)]

Pre

ssur

e

[bar

] M

RD

[%

] M

AR

D

[%]

EB

-20%

[%

]

Ake

rs e

t al

. (19

59)

prop

ane,

R12

S-

C

15.8

−

−

10

3 10

3 2

Cav

allin

i et

al.

(200

6)

R13

4a, R

410A

, R23

6ea

M-R

1.

4 20

0−

1400

10

.2

213

213

0

Illán

-Góm

ez e

t al

. (2

014)

R

134a

, R12

34yf

M

-R

1.16

275

−94

0 6.7

−14

.9

92

102

4

Jige

et

al. (

2011

) R

134a

, R32

M

-R

0.85

100

−40

0 10

.2−

16.8

12

8 12

8 1

Jige

et

al. (

2016

) R

134a

, R32

, R

1234

ze(E

), R

410A

M

-R

0.85

100

−40

0 10

.2−

16.8

13

5 13

5 0

Kim

, Mud

awar

(2

013)

R

134a

, R12

, CO

2, ai

r- w

ater

, R41

0A, e

tc.

M-C

, M-R

, S-

C, S

-R

0.19

−6.5

19

−16

08

−

164

164

1

Koy

ama

et a

l. (2

003)

R

134a

M

-R

0.8

−1.

1 100

−70

0 17

106

106

1

Shah

(19

79)

wate

r, R

11, R

12,

met

hano

l, et

c.

S-C

7

−40

−

−

24

3 24

3 0

Wan

g et

al.

(200

2)

R13

4a

M-R

1.

46

75−

750

18

−19.

3 15

0 15

0 1

Web

b, E

rmis

(200

1)

R13

4a

M-R

, M-F

0.

44−

1.57

30

0−

1000

18.9

48

50

18

*M: m

ultip

ort,

S: s

ingl

e, C

: circ

ular

, R: r

ecta

ngul

ar, T

: tria

ngul

ar, F

: rec

tang

ular

with

mic

rofin

s.