Flow boiling of carbon dioxide: Heat transfer for smooth and enhanced geometries and effect of oil. state of the art review

International Journal of Refrigeration 108 (2019) 311–335

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Flow boiling of carbon dioxide: Heat transfer for smooth and enhanced geometries and effect of oil. state of the art review R. Mastrullo, A.W. Mauro∗, L. Viscito Department of Industrial Engineering, Università degli studi di Napoli - Federico II, P.le Tecchio 80, 80125, Naples Italy

a r t i c l e

i n f o

Article history: Available online 30 August 2019 Keywords: CO2 Review Flow boiling heat transfer Enhanced tubes Heat transfer with oil Prediction methods

a b s t r a c t This paper presents a state-of-the-art review on flow boiling of carbon dioxide, including experimental studies and correlations for smooth and enhanced tubes, with pure CO2 and CO2 /lubricant mixtures. Specifically, 5223 CO2 heat transfer coefficient data in smooth tubes are collected, and the effect of the operating conditions is discussed. Additional 883 data points in microfin tubes and 1184 experimental heat transfer coefficients in smooth tubes with CO2 /oil mixture are also collected, and the influence of the microfin structure and of the oil presence on the heat transfer mechanism is analyzed. The statistical analysis has highlighted that the CO2 -based correlation of Fang et al. is very accurate (MAE = 5.1%) for the smooth tube database, whereas the heat transfer coefficients in microfin tubes are satisfactorily predicted (MAE = 30.5%) with the model of Mehendale. Among the available correlations for CO2 /oil mixture in smooth tubes, the method of Gao et al. provides the highest accuracy (MAE = 63.2%). © 2019 Elsevier Ltd and IIR. All rights reserved.

Ébullition en écoulement de dioxyde de carbone : transfert de chaleur pour géométries lisses et améliorées et effet de l’huile. Examen approfondi Mots-clés: CO2 ; Synthèse; Transfert de chaleur par écoulement en ébullition; Tubes améliorés; Transfert de chaleur avec huile; Méthodes prédictives

1. Introduction 1.1. Background and potential applications in the current scenario for the refrigerant use The use of carbon dioxide (R744 according to the ASHRAE classification) as refrigerant goes back to the earliest era of the vapor compression cycles, starting from the last decades of the 19th century. As reviewed by Kim et al. (2004), the first CO2 system was fabricated by the American Thaddeus S.C. Lowe in the late 1860s (Thevenot, 1979), even if he did not further develop his idea (Donaldson and Nagengast, 1994). Later on, in 1881, Carl Linde built the first European vapor compression cycle employing carbon dioxide (Kohlendioxid 1998). During the first decades of

∗

Corresponding author. E-mail addresses: [email protected], [email protected] (A.W. Mauro). https://doi.org/10.1016/j.ijrefrig.2019.08.028 0140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.

the 20th century, with improving technology, CO2 was widely used as working fluid in air conditioning and stationary refrigeration systems as well as in marine applications, before being suddenly phased-out with the upcoming synthetic chlorofluorocarbons (CFCs), which granted lower operating pressures and lower compressor discharge temperatures. Only in recent times, with the increasing concern for the anthropological global warming as well as the implementation of severe policies aimed at the environmental protection (Regulation (EU) No 517/2014, UNEP, 2016), carbon dioxide and other low-GWP fluids are receiving a renewed interest as alternative refrigerants in different fields. Girotto et al. (2004) presented the results of a case study related to the application of CO2 in the commercial refrigeration sector, by analyzing the performances with respect to an equivalent direct expansion R404A installation. The authors found that the solution working with carbon dioxide led only to a slight increase of the annual energy consumption (10%). As reviewed by Cavallini and Zilio (2007), carbon dioxide is one of the most interesting alternatives to R404A in commer-

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1  h pred −hexp i n hexp

Nomenclature

η

Roman AB CFC cp d Deq Dr. E Enh G GWP g h Hfin iLV J M Nfin q p PAG PAO POE PVE S T u x

Subscripts cb convective boiling cr critical exp experimental L liquid LO liquid only m related to the oil/CO2 mixture nb nucleate boiling oil lubricant pred predicted red reduced sat saturation sur surface V vapor VO vapor only wet wet portion

alkyl benzene oil chlorofluorocarbon specific heat at constant pressure [J kg−1 K−1 ] tube internal (equivalent) diameter [m] equivalent diameter (for annular flow) [m] root-to-root diameter for a microfin tube [m] convective boiling enhancement factor [-] surface enhancement ratio for microfin tubes [-] mass flux [kg m−2 s−1 ] global warming potential acceleration of gravity [m s−2 ] heat transfer coefficient [W m−2 K−1 ] fin height [m] specific latent heat [J kg−1 K−1 ] superficial velocity [m s−1 ] molecular mass [kg kmol−1 ] number of fins [-] heat flux [W m−2 ] pressure [Pa] polyalkylene glicol oil polyalphaolefin oil polyolester oil polyvinyl ether nucleate boiling suppression factor [-] temperature [°C] or [K] velocity [m s−1 ] vapor quality [-]

Greek

α β λ γ δ ε μ ηfin ρ σ θ dry ω0 ψ χ

void fraction [-] helix angle for microfin tubes [rad] thermal conductivity [W m−1 K−1 ] fin tip angle [rad] liquid film thickness [m] surface roughness [μm] viscosity [Pa s] fin efficiency [-] density [kg m−3 ] surface tension [N m−1 ] dry angle [rad] nominal oil mass fraction [-] percentage of data points falling into a ± 30% error band [%] percentage of data points falling into a ± 50% error band [%]

Non-dimensional numbers and statistical parameters Bo Boiling number G·iq LV

g(ρL −ρV )d2

Bd

Bond number

Co

Confinement number

Fa

Fang number

Fr

Froude number √u

Nu Pr

Nusselt number hd λ Prandtl number cμλ

Re We Xtt |η |

σ

1 d



σ

g(ρL −ρV )

(ρL −ρV )σ G2 d

gd

p

·d Reynolds number ρ ·u μ 2 Weber number Gρ ·σd

ρ

μ

0.9 ( V )0.5 ( L )0.1 Martinelli parameter ( 1−x x ) ρL μV  h −hexp Mean Absolute Error (MAE) 1n i | pred | h exp

Mean Relative Error (MRE)

cial refrigeration systems. From an energy performance point of view, it is known that there is a large influence of the ambient temperature and, for this reason, different plant options have been explored. In the case of supermarkets, a recent review by Gullo et al. (2018) show different configurations with a special focus on the heat recovery strategies and performance optimization. In addition, Llopis et al. (2018) highlighted the advantage of adopting a mechanical subcooling, by analyzing and reviewing several related solutions. Even if in this sector the use of CO2 as refrigerant is currently spreading, it is important to notice that there is still a large debate about the possible refrigerant alternatives and consequently about the refrigerating plant architecture. An interesting discussion was proposed by Karampour and Sawalha (2018), that presented different plant configurations working with carbon dioxide coupled with other refrigerants (ammonia, propane), with respect to a reference solution using R404A or its synthetic drop-in substitutes. Similarly, the possible uses of CO2 in cascade cycles are documented in Bansaal (2012 and Sànchez et al. (2017). As considered in the work by Mota-Babiloni et al. (2017) and Llopis et al. (2017), there are several alternatives to R404A such as R513A, R450A, R452A and R448A, which perform well especially in average climate conditions. A definitive scenario is therefore not clear yet: the evolution of this sector will be affected by the actual performance of the new refrigerants, currently under investigation based on field data (Mota-Babiloni et al., 2015). Their heat transfer efficiency might in fact be penalized depending on the temperature glide occurring during evaporation and condensation processes (Lillo et al., 2019, Mastrullo et al., 2019, Lillo et al., 2018). Similarly, the discussion is open in small/medium size commercial refrigeration units, in which CO2 , along with other synthetic fluids, is a promising option (Citarella et al., 2019, Tammaro et al., 2018). Regarding the heat pump sector, CO2 has been remarkably studied and its use has been considered for different scopes, such as hot sanitary water production (Zhang et al., 2015), combined space heating and hot sanitary water production, and residential heat pumps, as reviewed by Neksa (2002). For these applications, the discussion about the use of different refrigerants is also open, especially for warm climates. Tammaro et al. (2017) studied an innovative solution with large subcooling propane heat pump for hot sanitary water production, comparing its performance to a CO2 transcritical cycle at different ambient temperatures. For residential heat pump systems, the use of carbon dioxide is common in cold climates (Austin and Sumathy, 2011). In average

R. Mastrullo, A.W. Mauro and L. Viscito / International Journal of Refrigeration 108 (2019) 311–335

and warm climates, instead, propane (R290) and R32 can also be employed instead of R410A (Botticella et al., 2018) without significant alterations of the heat transfer performance (Lillo et al., 2019, Lillo et al., 2018, Mastrullo et al., 2017). Concerning the medium size heat pumps, the use of ejectors and the possibility to exploit space heating is increasing the interests towards CO2 , as presented in recent studies (Elbel and Lawrence, 2016, Elbel, 2011, Jim et al., 2019, Boccardi et al., 2017). Finally, other potential applications of carbon dioxide are related to industrial drying applications (Goh et al., 2011) and to on-road air conditioning units (Subei and Schmitz, 2019), in which another suitable alternative to R134a is represented by the synthetic R1234yf (Zilio et al., 2011). 1.2. CO2 properties As suggested by Lorentzen (1995), by excluding air and water, CO2 is the refrigerant coming closest to the ideal of harmlessness to the environment. As regards its safety characteristics, it is nontoxic (a maximum acceptable concentration to avoid physiological effects is about 4–5% in volume Kim et al., 2004) and incombustible. Its accidental release in the liquid form will either evaporate or become solid in the form of snow that can be easily removed or left to sublimate, being therefore easier to manage than any other halocarbon plant (Lorentzen, 1995). Having a relative low critical temperature of 31.1 °C (Lemmon et al., 2009), CO2 evaporates at much higher reduced pressures (0.43 at 0 °C (Lemmon et al., 2009) than other halogenated refrigerants (0.07 at 0 °C for R134a (Lemmon et al., 2009), thus showing peculiar thermodynamic and transport properties, for which the available boiling heat transfer prediction methods could not be sufficiently effective. Firstly, CO2 presents the highest vapor density and vapor-to-liquid density ratio when compared to halocarbons and hydrocarbons (Mastrullo et al., 2018), providing both an increased volumetric refrigeration capacity and smaller differences between the liquid and the vapor phase velocities, with less interface shear and a more homogeneous two-phase flow behavior than other fluids (Bredesen et al., 1997). Secondly, the very low liquid viscosity contributes to limited pressure drop for boiling carbon dioxide and a surface tension lower by one order of magnitude leads from one side to destabilize the liquid surface, with increased droplet formation and entrainment, possibly causing a premature onset of dryout (Bredesen et al., 1997). On the other hand, reduced surface tension tends to require lower superheat for bubble nucleation and bubble growth, thus increasing the heat transfer efficiency (Carey, 1992, Stephan, 1992). As a summary, the heat transfer coefficients of boiling CO2 are typically 2–3 times greater than those of conventional refrigerants when used at the same operating conditions, while the pressure drop is considerably smaller and can often be neglected (Thome and Ribatski, 2005). For this reason, the present review deals only with heat transfer topics and pressure drop is instead not addressed.

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Section 2. The qualification of the database and a deeper analysis of the convective and boiling contributions to the heat transfer are provided in Section 3, together with the assessment of existing correlations for smooth tubes. Sections 4 and 5, respectively present the collected heat transfer coefficient data of CO2 /oil mixture in smooth tubes and of pure CO2 in microfin tubes, whereas the assessment of the available prediction methods for these two subsets is carried out in the last Section 6. 2. Experimental database for smooth tubes To the best of the authors’ knowledge, the research has highlighted 37 flow boiling studies using carbon dioxide as working fluid, from 2002 until 2019, covering a wide range of operating conditions. In this section, only pure CO2 data in smooth tubes have been isolated from those works including CO2 mixtures with other refrigerants, oils and microfinned surfaces (that will be instead the topic of the following section), by collecting a total amount of 5223 heat transfer coefficient data. The experiments have been performed for mass fluxes from 40 to 1500 kg m−2 s−1 , saturation temperatures from −40 to +25 °C, heat fluxes from 0.5 to 60 kW m−2 , tube diameters from 0.51 mm to 14 mm and different geometrical configurations (single/multi-channels, circular/rectangular pipes). All the experiments have been conducted in horizontal tubes. The roughness of the tube inner surface is provided only in the work of Ozawa et al. (2011), whereas this information is missing for the rest of the collected points. The whole database is shown in Table 1 and has been split for the readers’ convenience in macro and micro-channel studies. Some macroto-micro scale transition criteria are based on the tube diameter, as for the method of Mehendale et al. (20 0 0) and Kandlikar and Grande (2003), in which 6 mm and 3 mm are respectively set as threshold between conventional and compact tubes. In the present study, the experimental data are denominated as macro and micro scale according to the method proposed by Kew and Cornwell (Kew and Cornwell, 1997), which is an approximate physical criterion based on the confinement effect of a bubble within a channel. As stated by the authors, for Confinement numbers Co>0.5 (defined in Nomenclature), the macroscopic laws are not suitable to predicts flow pattern transitions and heat transfer coefficients. Fig. 1 shows the threshold diameter from macro to mini-scale according to the three mentioned criteria as a function of the saturation temperature, including also the experimental points from the smooth tube database. It is worth noting that, according to the method of Kew and Cornwell, the transition diameter changes with saturation temperature, passing from approximately 2.5 mm

1.3. Review objective and outline The main goal of the present work is to provide an overview of the experimental CO2 flow boiling research studies, thus updating the latest state of the art by Thome and Ribatski (2005) performed in 2005. An assessment of the available correlations specifically developed for carbon dioxide is also carried-out respectively for smooth tubes, microfin tubes and smooth tubes with the presence of oil. The indication of the most accurate prediction method for each dataset will therefore be of particular use for evaporator design purposes. The experimental database for smooth tubes and the recurrent heat transfer coefficient trends with vapor quality are presented in

Fig. 1. Transition diameter from conventional to micro-scale according to the threshold criteria of Kew and Cornwell (1997), Mehendale et al. (20 0 0) and Kandlikar and Grande (2003) implemented for CO2 , as a function of the saturation temperature. The markers represent the collected experimental data for smooth tubes in this study.

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Table 1 Experimental databank for boiling of pure CO2 in smooth tubes. Data for macro and micro-scale are split according to the criterion of Kew and Cornwell (1997). Author Macro-scale (Co<0.50) Yun et al. (2003) Yoon et al. (2004) Schael and Kind (2005) Cho and Kim (2007) and Cho et al. (2010) Zhao and Bansal (2007) Choi et al. (2007a, 2007b), Oh et al. (2011), and Chien et al. (2017) Hihara and Dang (2007) Gao et al. (2007) Park and Hrnjak (2007) Oh et al. (2008) and Oh and Son (2011) Katsuta et al. (2008) Yun and Kim (2009) Mastrullo et al. (2009, 2012) and Grauso et al. (2013, 2011) Pehlivanoglu et al. (2010) Kim et al. (2010) Ono et al. (2010) Dang et al. (2013) Zhu et al. (2015) Liang et al. (2017) Micro-scale (Co>0.50) Pettersen et al. (2000) and Pettersen (2004) Yun et al. (2005) Gasche (2006) Jeong and Park (2009) Ducoulombier et al. (2011) Ozawa et al. (2011) Wu et al. (2011) Wu et al. (2015) Linlin et al. (2017) Overall ∗

Geometry∗

Internal diameter [mm]

Tube roughness [μm]

Mass velocity [kg m−2 s−1 ]

Heat flux [kW m−2 ]

Saturation temperature [°C]

S,C,H S,C,H S,C,H S,C,H

6 7.53 14 4/7.72

NA NA NA NA

170/340 318 75/300 212/656

10/20 12.5/18.6 3/60 6/30

5/10 0/20 5 −5/20

135 53 26 200

S,C,H S,C,H

4.57 1.5/3

NA NA

139.5/231 250/600

12.6/19.3 10/40

−30 −5/10

23 446

S,C,H S,C,H S,C,H S,C,H

1/2 3 6.1 4.57/7.75

NA NA NA NA

360/1440 380 100/400 200/900

4.5/36 10 5/15 10/40

5/15 10 −30/−15 −5/20

189 13 108 209

S,C,H S,C,H S,C,H

3 0.98/2 6

NA NA NA

400 360/1500 162/526

5/15 18/40 5/20.3

0/10 0/15 −7.8/12

51 265 532

S,C,H S,C,H S,C,H S,C,H S,C,H S,C,H

6.1 11.2 3.74 2/6 2 1.5

NA NA NA NA NA NA

100/400 40/200 190/380 360/1440 200/400 300/600

2/15 0.5/10 10/30 18/36 5/15 7.5/30

−30/−15 −30/−15 10 15 0/10 −35/15

84 116 61 322 76 89

M,C,H

0.79

NA

190/570

5/20

0/25

103

M,R,H S,R,H M,C,H S,C,H S,C,H S,C,H M,C,H S,C,H

1.08/1.54 0.8 0.8 0.529 0.51/1 1.42 1.7 0.6/1.5

NA NA NA NA 8 NA NA NA

200/400 58/235 400/800 200/1400 500/900 300/600 200/600 300/600

10/20 1.8 12/18 10/30 30/40 7.5/29.8 4.17/8.33 7.5/30

0/10 23.3 0/10 −10/0 14.3 −40/0 15 −40/0

57 63 51 1185 113 445 62 146

0.51/11.2

8

40/1500

0.5/60

−40/+25

5223

Number of points

M = multi, S = single; C = circular, R = rectangular; H = horizontal, V = vertical NA = not available.

at −50 °C up to 0.35 mm in case of +30 °C. With this criterion, most of the collected data points (55%) fall within the macro-scale region. Among the macro-channel studies, Yun et al. (2003) investigated heat transfer and dryout characteristics of carbon dioxide in a horizontal tube with an inner diameter of 6.0 mm, a wall thickness of 1.0 mm and a heated length of 1.4 m. They found that dryout of CO2 is anticipated with respect to refrigerant R134a and that the correlation of Gungor and Winterton (1986) gave accurate prediction of boiling heat transfer coefficient data only for high mass fluxes. Later on, the same authors presented two new studies, the first dealing with boiling CO2 in a multi-microchannel heat exchanger with rectangular tubes (Yun et al., 2005), finding that the experimental heat transfer coefficient were accurately predicted by the typical pool boiling correlations. Their latest work (Yun and Kim, 2009) presented instead new experimental data in tubes of 0.98 and 2.0 mm, focusing on the post-dryout region and proposing a correlation. Yoon et al. (2004) measured two phase heat transfer and pressure drop of evaporating carbon dioxide in a 7.53 mm tube and a length of 5 m, in which the heat flux was provided by directly applying DC current to the test tube. It was found that the heat transfer coefficient was increasing with vapor quality and with heat flux, showing a typical nucleate boiling trend, even if a quite premature dryout was observed. Zhao and Bansal (2007) studied boiling heat transfer of CO2 at a low temperature of −30 °C in a horizontal 4.57 mm tube (at −30 °C) and observed a convective behavior, with the experimental heat transfer coefficient increasing with vapor quality up to the

onset of dryout. The authors found that none of the tested correlations (including that of Yoon et al. 2004) explicitly developed for CO2 ) were able to satisfactorily predict their experimental data. Choi et al. (2007a), Choi et al. (2007b) and Oh et al. (2011) conducted a series of experiments on boiling heat transfer of carbon dioxide in small tubes of 1.5 and 3.0 mm having a heated length of 20 0 0 and 30 0 0 mm, respectively. It was found that the heat transfer coefficient was higher for the lower diameter tube at the same conditions and that nucleate boiling contribution was predominant, especially at low vapor quality region, with a significant effect of the heat flux and a negligible influence of the mass velocity. Hihara and Dang (2007) provided experimental flow boiling data of carbon dioxide in pre- and post-dryout region in a 2 mm tube. They observed that the effects of the heat flux and saturation temperature were significant in the pre-dryout region, whereas mass flux was the dominating factor affecting both the onset of dryout and also the heat transfer coefficient in the post-dryout heat transfer region. Park and Hrnjak (2007) investigated two-phase heat transfer and pressure drop of CO2 and R410A in a 6.1 mm tube at relatively low saturation temperatures of −15 °C and −30 °C. The authors found that the heat transfer coefficients for carbon dioxide were at least 30% higher than those of R410A, especially for low vapor quality ranges, attributing this behavior to the lower molecular weight and the higher reduced pressure of CO2 that imply a higher nucleate boiling contribution. Moreover, the heat transfer coefficients of carbon dioxide showed a strong dependence only

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from the imposed heat flux, whereas in case of R410A the heat transfer efficiency was affected by the change of mass flux, heat flux and vapor quality. Oh et al. (2008) and Oh and Son (2011), in two different studies, experimentally evaluated the effect of operating conditions on the two-phase heat transfer coefficient of carbon dioxide among other fluids in smooth macro-tubes of 7.75 mm and 4.57 mm, respectively. In both cases, the authors found a strong influence of the heat flux, whereas the effect of vapor quality was dependent on the specific operating condition tested. Among the different correlations implemented, the flow pattern based methods of Thome and El Hajal (2004) and Cheng et al. (2008) developed for CO2 gave the best predictions. Mastrullo et al. (2009, 2012) and Grauso et al. (2013) presented a series of experiments on flow boiling heat transfer of carbon dioxide and R410A in a horizontal smooth tube of 6.0 mm, exploring the effect of the reduced pressure on flow pattern transition and heat transfer coefficient. The authors verified that, when working at the same reduced pressure, the two-phase flow structures and the heat transfer coefficient trends with vapor quality were similar for both fluids. However, they found strong difference in their absolute values, implying that nucleate boiling contribution was predominant for CO2 , whereas R410A was more affected by the convective boiling. Among the tested correlations, the CO2 heat transfer coefficients were quite accurately predicted by the flow pattern based method of Cheng et al. (2008). Zhu et al. (2015) presented experimental heat transfer coefficient values at different mass concentrations. By isolating the points collected with pure carbon dioxide, the authors found a significant influence of the saturation temperature and heat flux, whereas mass flux and vapor quality caused a minor effect. Concerning the micro-scale database, Pettersen et al. (20 0 0) and Pettersen (20 04) performed a comprehensive experimental campaign on flow boiling of carbon dioxide in a multiport extruded tube with circular minichannels of 0.98 mm internal diameter. The results showed that nucleate boiling contribution dominated at moderate vapor quality, in which the heat transfer coefficient was seen to increase with heat flux and temperature and was less affected by varying mass flux. Similar multi-minichannel geometries were also later on investigated by Jeong and Park (2009) and Wu et al. (2015). Gasche (2006) provided flow visualization and heat transfer data of flow boiling of CO2 in a narrow rectangular channel having an equivalent diameter of 0.8 mm. The high data scattering did not permit to identify a clear dependency of the heat transfer coefficient with the mass flux and vapor quality, even if the experimental data were quite well fitted with the pool boiling correlation of Gorenflo (1993). Ducoulombier et al. (2011) performed a comprehensive experimental campaign on flow boiling heat transfer of carbon dioxide in a single minichannel having an internal diameter of 0.529 mm. The authors observed both typical nucleate and convective boiling trends, depending on the operating conditions, and the stratification phenomenon was not explicitly detected. Similar outcomes were also found in the recent studies of Linlin et al. (2017) and Liang et al. (2017). Finally, Ozawa et al. (2009, 2011) mostly focused on the effect of the reduced pressure on the boiling CO2 flow patterns. Even if the experiments were performed in the narrowest tube of the present database (0.51 mm), the authors still observed stratification of the liquid phase and therefore a marked difference in the heat transfer coefficient at the upper and lower walls. 2.1. Recurring trends for macro and micro-channels In typical vapor compression cycle applications, carbon dioxide has a very high reduced pressure and therefore shows a peculiar

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flow boiling behavior with respect to other refrigerants, since the relative importance of the convective and nucleate boiling contributions are altered. Specifically, the nucleate boiling heat transfer is enhanced by means of a very low surface tension and a high vapor density, both of them contributing to trigger the bubble nucleation phenomenon with lower required wall superheats (Carey, 1992). As a consequence, the two-phase heat transfer coefficients of CO2 are generally higher than those of halogenated refrigerants, as testified by different comparison studies (Yun et al., 2005, Choi et al., 2007, Oh et al., 2011, Grauso et al., 2013). However, no general conclusions can be driven from the above considerations, and despite a higher magnitude of the nucleate boiling contribution, the carbon dioxide two-phase heat transfer coefficients might still present a typical convective behavior, depending on the tested operating conditions. Some recurrent trends showing the effect of the mass flux on the CO2 evaporating heat transfer coefficient are shown in Fig. 2a– d, for conventional (a-b) and small-diameter tubes (c-d). From the study of Liang et al. (2017) in Fig. 2a (borderline between the macro and micro-scale), a typical convective behavior is observed when the imposed heat flux is relative low (7.5 kW m − 2 ), with an increasing heat transfer coefficient with vapor quality and mass velocity. The slope of the curves with vapor quality also increases for higher mass fluxes. The same trends can be observed at similar conditions in other macro-channel studies (Park and Hrnjak, 2007, Chien et al., 2017, Pehlivanoglu et al., 2010, Kim et al., 2010). When a high (40 kW m−2 ) heat flux is imposed (Fig. 2b with the study of Oh and Son (2011) in a 4.57 mm tube), the effect of both mass flux and vapor quality on the local heat transfer coefficient is almost negligible. It is worth noting that a slight reduction of the dryout vapor quality is obtained with increasing mass velocity. Similar nucleate boiling-driven behaviors in macro-tubes are found in Hihara and Dang (2007), Mastrullo et al. (2009) and Dang et al. (2013). The same considerations can be made in case of minichannels, in which a typical convective behavior is observed in the work of Ducoulombier et al. (2011) in their 0.529 mm tube (Fig. 2c) as well as in Gasche (2006), Linlin et al. (2017) and Wu et al. (2011). For higher heat fluxes (40 kW m−2 ), the effect of the mass flux becomes negligible and slightly affects the dryout occurrence, as presented in the narrow tube employed by Ozawa et al. (2011) (Fig. 2d). In the multi-minichannel test section of Pettersen et al. (20 0 0) and Pettersen (20 04), the heat transfer coefficient decreases with vapor quality with almost no effect of the mass flux, as also observed in the single minitube of Jeong and Park (2009). The same decreasing trend with vapor quality is found in larger tubes (2 and 4 mm) in case of high imposed heat fluxes (>10 kW m−2 ) in Zhu et al. (2015) and Cho and Kim (2007). The typical effects of the imposed heat flux on CO2 boiling heat transfer coefficients are shown in Fig. 3 for macro- (a and b) and microchannels (c and d). In the first case, for relatively low mass velocities, the heat transfer coefficient remains substantially the same with ongoing evaporation and is strongly affected by a change of the heat flux, as observed by Grauso et al. (2013) in their 6.0 mm tubes for a saturation temperature of 7 °C and a mass flux of 200 kg m−2 s−1 (Fig. 3a). Similar behaviors in conventional channels are found in Yun et al. (2003) Yoon et al. (2004) and Oh et al. (2008), with a constant or even decreasing heat transfer coefficient trends with vapor quality, that can be caused either by an anticipated dryout or by a stratification of the flow. With increasing mass velocity (see the work of Choi et al. 2007) in Fig. 3b), the effect of the heat flux might be confined to the low vapor quality region, where the nucleate boiling contribution is still prevailing, while typical convective trends can be observed for higher vapor qualities. Similar outcomes are found also for micro-channel studies. For the data of Wu et al. (2011) in their 1.42 mm tube at G = 400 kg m−2 s−1 (Fig. 3c), the heat flux

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Fig. 2. Effect of mass flux on CO2 boiling heat transfer coefficient. (a) Convective behavior in macro-channels: data from Liang et al. (2017). (b) High imposed heat flux in macro-channels: data from Oh and Son (2011). (c) Convective behavior in micro-channels: data from Ducoulombier et al. (2011). (d) High imposed heat flux in microchannels: data from Ozawa et al. (2011).

has a significant effect for the whole investigated vapor quality region. The change from convective to nucleate boiling driven heat transfer is also clear with increasing heat flux, as also observed by Linlin et al. (2017). For the highest heat flux. Pure convective trends, with a negligible effect of the imposed heat flux, are shown for the microscale study of Ducoulombier et al. (2011) in Fig. 3d, when a high mass flux is imposed. Finally, the effect of the saturation temperature can be different according to flow pattern recorded by the original authors and hence to the relative importance of the nucleate and convective boiling contributions. In case of convective-driven heat transfer, as observed in the single 0.529 mm minichannel of Ducoulombier et al. (2011) and Linlin et al. (2017) in a 1.5 mm tube at 300 kg m−2 s−1 and 7.5 kW m−2 (Fig. 4a), an increase of the saturation temperature leads to a reduction of the heat transfer coefficient, especially for high vapor qualities. In fact, for a higher reduced pressure, the increased density leads to a reduction of the fluid mean velocity for a fixed mass flux, thus penalizing the convective contribution. For low vapor qualities, instead, a higher density benefits the nucleate boiling heat transfer by increasing the number of active sites (Lillo et al., 2019). This effect is particularly clear in case of nucleate boiling predominance throughout the evaporation, for high imposed heat fluxes, as shown in Fig. 4b for the study of Liang et al. (2017) and Wu et al. (2011) and Pettersen (2004). As already mentioned, the reduction of the surface tension with increasing reduced pressure enhances the

boiling phenomenon, but on the other hand weakens the stability of the liquid film on the heated wall, thus possibly leading to a premature dryout, as highlighted in the horizontal 4.57 mm tube of Oh and Son (2011) in Fig. 4c. An earlier dryout for carbon dioxide with increasing saturation temperature was also observed by Yoon et al. (2004) and Oh et al. (2008).

3. Assessment of predictive methods for smooth tubes 3.1. Nucleate and convective boiling contributions Fig. 5a–f presents a bar chart distribution of the smooth tube database. The experimental heat transfer coefficients from all the authors have been combined (5223 points) and segregated into different categories according to their operating conditions, in terms of tube internal diameter, mass flux, saturation temperature, heat flux, Boiling number and vapor Weber number. Most of the data are collected in tubes smaller than 2.5 mm, with the works of Ducoulombier et al. (2011) and Ozawa et al. (2011) that provide alone more than 1200 data points in minichannels of 0.5 mm. Remarkable peaks for the imposed heat flux and saturation temperature distributions are respectively found at 10, 20 and 30 kW m−2 and between −10 and +15 °C. As for the boiling and inertia contributions, 99% of the database includes Boiling numbers lower than 6·10−4 and Weber vapor numbers lower than 30 0 0.

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Fig. 3. Effect of heat flux on CO2 boiling heat transfer coefficient. (a) Low mass velocities in macro-channels: data from Grauso et al. (2013). (b) High mass velocities in macro-channels: data from Choi et al. (2007). (c) Low mass velocities in micro-channels: data from Wu et al. (2011). (d) High mass velocities in micro-channels: data from Ducoulombier et al. (2011).

The relative distribution of the liquid and vapor phases inside the tube (flow pattern) affects the heat transfer mechanism (Mastrullo et al., 2018, Charnay et al., 2015). In fact, several modeling approaches require the knowledge of the flow regime in order to evaluate the two-phase heat transfer coefficients. Unfortunately, this information is almost never provided by the original authors and only a flow pattern map can be instead used to better understand which could be the most relevant heat transfer contribution. Fig. 6a–c presents the experimental superficial liquid and vapor velocities and the indication of the flow regimes according to the models of Taitel and Dukler (1976), Cheng et al. (2008) and Mastrullo et al. (2012), respectively. The first method was developed for air-water flow, whereas models of Cheng et al. (2008) and Mastrullo et al. (2012) are explicitly conceived for high operating reduced pressures (up to 0.87). The distribution of the flow patterns for the entire smooth tube database is shown in Fig. 6d. According to the method of Taitel and Dukler (1976), approximately 85% of the data points belong to annular flow, even if this model cannot consider dryout and mist flow regimes. With respect to the map of Cheng et al. (2008), most of the collected data are expected to fall into the annular flow regime with more than 2500 experimental points, followed by the mist flow regime (961), dryout (850) and intermittent flow (450). The remaining stratified, stratified-wavy and slug flow regimes include only 450 heat transfer coefficient data. Finally, Mastrullo et al. (2012) map distinguishes between slug flow (438 points), intermittent flow (336

points), annular flow (3618 points) and dryout flow (848 points). For the present analysis, the segregation in different flow regimes is carried-out according to the flow pattern map of Mastrullo et al. (2012). Its accuracy was proven by the original authors in operating conditions similar to those of the data collected for this review. As pictured from Fig. 2 to 4, the collected heat transfer coefficients in smooth tubes showed different trends with vapor quality and a distinct influence of the mass flux, heat flux and saturation temperature, according to their operating conditions. That is to remark that both typical nucleate boiling and convective boiling behaviors are observed during flow boiling of carbon dioxide. As first analysis, the two contributions are firstly separated to evaluate their agreement to the experimental data. Particularly, the nucleate boiling Nusselt number is calculated by using the wellknown Cooper (1984) pool boiling correlation, without employing any suppression factor:

N unb =

hCooper d

λL

= N uCooper =

d

λL



.12−log ε · 55 p0red (− log ( pred ) )

−0.55

M−0.5 q0.67



(1) As regards the convective contribution, instead, the common practice is the use of a forced convection prediction method for single phase multiplied by an enhancement factor E that takes into account the flow acceleration with ongoing evaporation. Here, we assume the liquid phase distribution as a symmetric annular

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Fig. 4. Effect of saturation temperature on CO2 boiling heat transfer coefficient from different studies in micro and macro-tubes. (a) Data from Linlin et al. (2017). (b) Data from Liang et al. (2017) (c) Data from Oh and Son (2011).

flow with a constant liquid film thickness δ around the heated wall, as shown in Eq. (2).

N uconv =

hDeq

λL

=a

 ρ u D b L L eq P rLc μL

(2)

The equivalent diameter for the liquid annulus can be geometrically related to the liquid film thickness (Eq. (3)), which is in turn a simple function of the superficial void fraction α (Eq. (4)).

Deq =

δ

4 (π d δ ) ∼ = 2δ π d + π ( d − 2δ )

(3)

 d = 1 − α 0.5 2

(4)

The liquid phase actual velocity uL can be expressed as a function of the liquid-only velocity (as the liquid phase would flow alone in the whole cross section) and the vapor quality and void fraction, as shown in Eq. (5).

uL = uLO

1−x G (1 − x ) = 1−α ρL ( 1 − α )

(5)

By referring the experimental Nusselt number to the tube diameter (being the liquid film thickness unknown) and substituting Eqs. (3), (4) and (5) in Eq. (2), the convective contribution reads as Eq. (6):

N uconv,exp =

hd

λL



=

a

Gd

μL



b P rLc

·

( 1 − x )b  1−b (1 − α )b 1 − α 0.5

(6)

The first term of the third member is a typical liquid-only convection heat transfer correlation and the last term is an enhancement factor E. Given constants a, b and c as from Dittus and Boelter (1930) expression and respectively equal to 0.023, 0.8 and 0.4, the convective contribution is finally evaluated with Eq. (7):

N uconv,exp =



(1 − x )0.8 0.8 0.4  0.2 · 0.023ReLO PrL 0.8 ( 1 − α ) 1 − α 0.5

= E · N uLO,Dit t us−Boelter

(7)

in which the void fraction α is calculated with Steiner (1993) version of Rohuani and Axelsson (1970) drift flux model. The experimental Nusselt numbers are compared with both nucleate and convective Nusselt, respectively from Eqs. (1) and (7) in Fig. 7a–f, by segregating the database according to the flow regime obtained with Mastrullo et al. (2012) model. In case of slug or intermittent flow regime, the experimental Nusselt numbers are higher than the only-convection Nusselt estimated values (Fig. 7a), whereas they are surprisingly well predicted by considering only the Cooper correlation for pool boiling (Fig. 7b). As regards annular flow points, they are not fairly predicted with either only convection (Fig. 7c) or only nucleation heat transfer (Fig. 7d). For this bunch of data, a more elaborate correlation combining both contributions should instead be considered. For dryout data, the experimental Nusselt numbers are compared only to the convective heat transfer expression (Fig. 7e) and to the vapor-only Dittus-Boelter Nusselt number (Fig. 7f), since nucleation is not likely to occur for such flow regime. In both cases, the agreement is not satisfactory.

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319

a)

b)

c)

d)

e)

f)

Fig. 5. Distribution of data points for flow boiling of CO2 in smooth tubes related to: (a) internal diameter; (b) mass flux; (c) saturation temperature; (d) imposed heat flux; (e) Boiling number; (f) vapor Weber number.

However, it is worth noting that some of these data, although classified as dryout flow according to Mastrullo et al. (2012) model, may instead belong to a different flow regime, making unsuitable the use of a vapor-only Nusselt number for comparison purposes. 3.2. Assessment of correlations for smooth tubes Several flow boiling heat transfer prediction methods explicitly developed for carbon dioxide in smooth micro and macro tubes are available in literature. In this review, 14 models are implemented to test their agreement with the experimental data. Unfortunately, missing information in the work of Mikielewicz and Jakubowska (2016) made their method not possible to implement for this assessment. The mathematical formulation and range of

validity of the chosen correlations are provided in Table 2, whereas their complete assessment is given in Table 3, in which the experimental data are segregated according to their flow pattern and in micro/macro scale. The statistical analysis is carried-out with the calculation of the Mean Absolute Error (|η|), Mean Relative Error (η), percentage of data points falling into an error range of ±30% ( ) and of ±50% (χ ). For each bunch of data, the best three working correlations are highlighted in bold and a graphical comparison is also provided in Fig. 8a–f. The methods of Fang (2013) and Fang et al. (2017) provide a very satisfactory agreement with all the experimental data in any flow regime and geometry, with an overall calculated MRE close to zero (η = 1.4% and η = −1.1%, respectively). In both cases, more than 80% of the 5223 collected heat transfer coefficients are predicted within an error band of ±30% (see Fig. 8a and b).

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Fig. 6. Experimental superficial liquid and vapor velocities and flow regimes according to the flow pattern map of: (a) Taitel and Dukler (1976); (b) Cheng et al. (2008); (c) Mastrullo et al. (2012). (d) Distribution of data points related to the occurring flow patterns for the three implemented flow pattern maps.

The first correlation (Fang, 2013) was developed based on a CO2 database of 2956 experimental flow boiling heat transfer coefficients obtained from 13 independent studies, almost all of them included in the present review. The second prediction method (Fang et al., 2017) was instead developed with a larger database of 17,778 data points from 101 sources and carbon dioxide among other 12 different fluids, still including most of the heat transfer coefficients collected for the this review. It is indeed worth noting that, although their proven accuracy, these methods require the knowledge of both the imposed heat flux and the average inner wall temperature, at which the liquid viscosity should be evaluated (see their mathematical expression in Table 2). This involves a simple reverse wall temperature calculation procedure when an assessment is carried-out, but requires instead an iterative method in case of design purposes, in which both the heat flux and the inner wall temperature could be unknown. Besides Fang (2013) and Fang et al. (2017) correlations, the previous section has shown that data belonging to slug and intermittent flow regimes were quite well predicted by only considering Cooper (1984) expression for pure pool boiling Nusselt number (Fig. 7b), having a calculated MAE of |η| = 33%. A similar agreement is here obtained by implementing the superposition method of Oh et al. (2011) (see Fig. 8c), that combines the liquid Dittus-Boelter expression to the Cooper heat transfer coefficient. The calculated MAE is |η| = 25%, with 93% of the points falling in a ± 50% error band. In case of annular flow regime, a fair agreement is found with the method of Choi et al. (2007) (see Fig. 8d),

with calculated |η| = 39%, η = −6.8%, ψ = 44% and χ = 82%, and similar results are obtained with the flow pattern based methods of Thome and El Hajal (2004). Most of the chosen correlations have a low accuracy in case of dryout flow. Besides Fang (2013) and Fang et al. (2017) correlations, with |η| = 31.5% and |η| = 9.2%, respectively, the lowest MAE (80%) is obtained with the model developed by Pettersen (2004), that uses an asymptotic approach for the pre-dryout points and Shah and Siddiqui (20 0 0) model for the post-dryout heat transfer. The onset of dryout was instead estimated using water data from Kon’kov (1965) scaled to CO2 with the dimensional analysis method of Ahmad (1973). By considering the entire database, the three best working prediction methods are those of Fang et al. (2017) (|η| = 5.1%), Fang (2013) (|η| = 19.3%), followed by Pettersen (2004) (|η| = 45.7%). Their accuracy does not significantly change when used for mini or macrochannels, being consistent to the similar behavior of small and conventional tubes when the effect of the operating parameters was analyzed in the previous section of this review. 4. Boiling of CO2 with the presence of oil in smooth tubes The presence of oil in refrigeration systems is often required for a correct lubrication of the operating devices. The choice of a suitable oil is always a demanding issue, and in case of carbon dioxide it is complicated by its higher reduced pressure and peculiar physical properties. In terms of miscibility, the following lubricants are expected (Mastrullo et al., 2018) to provide the highest solubility, in decreasing order: polyolester (POE), ester

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Fig. 7. Experimental versus predicted Nusselt numbers, separated by flow pattern. Convective (a) and nucleative (b) boiling contribution for slug and intermittent flow data. Convective (c) and nucleative (d) boiling contribution for annular flow data. (e) Convective contribution for dryout data. (f) Convective (vapor) contribution for dryout data.

oils, polyvinyl ether (PVE), polyalkylene glycol (PAG), alkyl benzene (AB), polyalphaolefin (PAO) and mineral oil (CO2 is immiscible with mineral lubricants). Nevertheless, most of the reports available do not cover wide ranges of temperature and/or concentration and the phase equilibrium and thermodynamic properties behavior are strictly associated to the operating conditions and the type of oil employed (Mastrullo et al., 2018). Seeton et al. (20 0 0) found that PAG, AB and PAO lubricants were not miscible with CO2 at high refrigerant concentrations, whereas POE oil provided complete miscibility in the range −20/+120 °C. Hauk and Weidner (20 0 0), instead, observed the coexistence of two liquid phases for three different oils (POE, PAG and PAO) over a range of 5/100 °C.

Whichever lubricant chosen, during the normal operation of a refrigeration system a non-negligible amount of oil may drift from the compressor moving parts to the heat exchangers, altering the heat transfer behavior of the working fluid because of the modification of the thermodynamic and transport properties for the mixture (Mastrullo et al., 2018). Wang et al. (2012) published a comprehensive review to summarize the general trends of the lubricant presence on the evaporating heat transfer coefficient of halogenated refrigerants and CO2 . They concluded that the influence of oil depends not only on its concentration, but also on the heat flux, mass flux and other operating parameters. As a fact, it is difficult to provide

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Table 2 Mathematical expressions of the flow boiling heat transfer prediction methods for pure carbon dioxide in smooth tubes. Author

Formulation

Hwang et al. (1997)

h = Shnb + E hcb Nucleate boiling heat transfer coefficient hnb with Forster and Zuber (1955) correlation hcb = PrL0.6 · hL , liquid heat transfer coefficient hL with Dittus and Boelter (1930) correlation E = 2 · (0.213 + 1/X )0.736 for Xtt < 10 tt E = 1 for Xtt ≥ 10 X 1−exp(−E·hL · / ) λL S= X E·h · /

Range of applicability d = 7.0 mm 200 ≤ G ≤ 400 kg m−2 s−1 3.0 ≤ q ≤ 9.0 kW m−2 −25 ≤ Tsat ≤ 5 ◦C

 λL σ

L

X = 0.05 ·

g(ρL −ρV ) 2/3

Hihara and Tanaka (2000)

h = (14700 · Bo + 0.93 · (1/X ) tt correlation.

Yoon et al. (2004)

xcr = 38.27 · (ReL )2.12 · (10 0 0Bo)1.64 · Bd−4.7 For x ≤ xcr 2 2 h = [(Shnb ) + (E hL ) ]1/2 , with nucleate boiling hnb and liquid hL heat transfer coefficients evaluated with Cooper (1984) and Dittus and Boelter (1930), respectively. E = [1 + 9.36 · 103 · PrL ( ρρVL − 1 )]0.11

) · hLO , with hLO evaluated with liquid-only Dittus and Boelter (1930)

0.7 ≤ d ≤ 2 mm q 360 ≤ G ≤ 1440 kg m−2 s−1 and Tsat ranges not available d = 7.73 mm 212 ≤ G ≤ 530 kg m−2 s−1 12.3 ≤ q ≤ 18.9 kW m−2 −4 ≤ Tsat ≤ 20 ◦C

S = (1 + 1.62 · 10−6 · E 0.69 · Re1L .11 )−1 For x > xcr θ h + ( 2 π −θ ) E h h = dry V 2π dry L , liquid and vapor heat transfer coefficients with Dittus and Boelter (1930) equation. x )0.75 ( ρρVL )0.41 E = 1 + 30 0 0Bo0.86 + 1.12( 1−x θdry 3.47 4.84 −0.27 1 = 36.23ReL Bo Bd ( /Xtt )2.6 2π Thome and El Hajal (2004)

θ

h + ( 2 π −θ

)h

h = dry V 2π dry wet , the dry angle θ dry varies from 0 in case of annular flow u to θ strat in case of fully stratified flow. The two angles expressions are available in Kattan et al. (1998a, 1998b) Gxd 0.8 ) PrV0.4 λdV , in which the void fraction is obtained with Rohuani and Axelsson (1970) model. hV = 0.023( αμ V

hwet = [(Shnb,C O2 ) + h3cb ]1/3 hnb,C O2 = 0.71hnb + 3970, with nucleate boiling heat transfer coefficient calculated with Cooper (1984) equation. 3

0.79 ≤ d ≤ 10.06 mm 85 ≤ G ≤ 1440 kg m−2 s−1 5 ≤ q ≤ 36 kW m−2 −25 ≤ Tsat ≤ 25 ◦C

0.5

(1−x ) 0.121Re0LF.225 )δ ReLF = 4(G1−(1α−x )μL = d4 1 −

S=

δ

Pettersen (2004)

Choi et al. (2007)

(

α)

hcb = 0.0133 · Re0LF.69 Pr0L .4 λδL For x ≤ xcr : h = (h3nb + h3cb )1/3 , with nucleate boiling heat transfer coefficient hnb evaluated with Cooper (1984) equation and the convective boiling heat transfer coefficient estimated with Kattan et al. (1998a, 1998b) flow pattern based model. Post-dryout region (x ≥ xcr ) heat transfer coefficient calculated with Shah and Siddiqui (2000) model. Dryout vapor quality xcr using Kon’kov (1965) expression for H2 0 and Ahmad (1973) fluid-to-fluid scaling model h = Shnb + E hL , with nucleate boiling hnb and liquid hL heat transfer coefficients evaluated with Cooper (1984) and Dittus and Boelter (1930), respectively. S = 7.2694(φ 2 )0.0094 Bo0.2814 E = 0.05 · (φ 2 ) + 0.95 φ 2 = 1 + X C + X 21 , with the Chisholm parameter C set to 20, 12, 10 and 5 in case of liquid-vapor flow t t ,Choi

Cheng et al. (2008a, 2008b)

Same expression as Choi et al. (2007), with a different evaluation of the suppression and enhancement factors: S = 469.1689(φ 2 )−0.2093 Bo0.7402 E = 0.042 · (φ 2 ) + 0.958 For any flow pattern except dryout and mist flow: h=

1.5 ≤ d ≤ 3.0 mm 400 ≤ G ≤ 500 kg m−2 s−1 30 ≤ q ≤ 40 kW m−2 −10 ≤ Tsat ≤ −5 ◦C

t t ,Choi

condition of turbulent-turbulent, laminar-turbulent, turbulent-laminar and laminar-laminar, respectively )7/8 ( ρρVL )0.5 ( μμVL )1/8 . Xt t ,Choi = ( 1−x x Choi et al. (2007)

d = 0.8 mm 190 ≤ G ≤ 570 kg m−2 s−1 5 ≤ q ≤ 20 kW m−2 0 ≤ Tsat ≤ 25 ◦C

θdry hV +(2π −θdry )hwet , vapor heat transfer coefficient hV with Dittus and Boelter (1930) equation. 2π

θdry = 0 for bubbly, slug intermittent and annular flow regimes; y −G θdry = θstrat ( GwaGwavy v−G )0.61 for stratified-wavy flow; strat Gwavy −G x θdry = θstrat xIA ( Gwavy −Gstrat )0.61 for slug/stratified-wavy flow, in case x < xIA Flow patterns, stratified angle θ strat , intermittent to annular quality transition xIA , stratified to

1.5 ≤ d ≤ 3.0 mm 200 ≤ G ≤ 600 kg m−2 s−1 10 ≤ q ≤ 40 kW m−2 Tsat = 10 ◦C f luids : C O2 , R134a, R22 0.6 ≤ d ≤ 10.06 mm 80 ≤ G ≤ 1500 kg m−2 s−1 4 ≤ q ≤ 46 kW m−2 −28 ≤ Tsat ≤ 25 ◦C

stratified-wavy flow transition Gstrat and the stratified-wavy to intermittent and annular flow transition Gwavy are obtainable in the original reference. hwet = [(Shnb ) + h3cb ]1/3 , with convective boiling heat transfer coefficient hcb as in Thome and El Hajal (2004). .0063 (−log10 ( pred ) )−0.55 M−0.5 q0.58 hnb = 131 p−0 red S = 1 for x < xIA d S = 1 − 1.14( 0.00753 )2 (1 − δδIA )2.2 for x ≥ xIA , with δ IA using the following δ expression at the intermittent to annular  flow transition. 3

δ=

d 2

−

2

( d2 ) −

π d 2 ( 1 −α ) 2(2π −θdry )

.

In case of mist flow regime: hmist = 2 · 10−8 Re1H.97 PrV1.06 Y −1.83 λdV

Gd [x + ρρVL (1 − x )] ReH = μ V Y = 1 − 0.1[ ( ρρVL − 1 )(1 − x )]0.4

(continued on next page)

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323

Table 2 (continued) Author

Formulation

Range of applicability

In case of dryout flow regime: di [h (xdi ) − hmist (xde )] hdryout = h (xdi ) − xx−x −x de

di

0.17

xdi = 0.58 exp[0.52 − 0.236( ρGV σd ) 2

0.16

xde = 0.61 exp[0.57 − 0.502( ρGV σd ) 2

qcr = 0.131ρV0.5 iLV [gσ (ρL − ρV )]0.25 Yun and Kim (2009)

0.17

( gρV (ρGL −ρV )d ) 2

( ρρVL )

0.15

( gρV (ρGL −ρV )d ) 2

0.25

0.27

( qqcr )

( ρρVL )

−0.09

]

0.72

( qqcr )

]

.88 h = 16.26 · q0.72 · p0red , for δ ≥ δ cr h = 1.09 · 10−3 λdV [ReV O (x + ρρVL (1 − x ))]0.989 PrV1.41 Y −1.15 , for δ < δ cr

Y = 1 − 0.1[ ( ρρVL − 1 )(1 − x )]0.4

δ = d2 (1 − α 0.5 ) δcr = ( 34 ( μρLL )2 1g ReL )1/3

Oh et al. (2011)

h = Shnb + E hL , with nucleate boiling heat transfer coefficient hnb evaluated with Cooper (Cooper, 1984) expression. S = 0.279(φ 2 )−0.029 Bo−0.098 E = max[(0.023φ 2.2 + 0.76), 1] φ 2 = 1 + XC + X12 , with the Chisholm parameter C set to 20, 12, 10 and 5 in case of liquid-vapor flow condition of turbulent-turbulent, laminar-turbulent, turbulent-laminar and laminar-laminar, respectively. )( ρρVL )0.5 , with f = 16/Re for laminar flows and f = 0.049Re−0.25 for turbulent flows. X = ( ffL )0.5 ( 1−x x

0.98 ≤ d ≤ 2.0 mm 360 ≤ G ≤ 1500 kg m−2 s−1 18 ≤ q ≤ 40 kW m−2 0 ≤ Tsat ≤ 15 ◦C

0.5 ≤ d ≤ 3.0 mm 200 ≤ G ≤ 600 kg m−2 s−1 5 ≤ q ≤ 40 kW m−2 0 ≤ Tsat ≤ 20 ◦C f luids : C O2 , R134a, R22, R410A, R290

V

hL = 4.36 λdL for ReL < 230

hL = hL =

fL 2

)(

λL

1+12.7(Pr2L /3 −1 ) (

fL 2

)

(ReL −10 0 0)PrL (

hL =

ReL PrL (

fL 2

)(

λL d

)

d 0.5

for 30 0 0 ≤ ReL ≤ 104

0.5

for 104 ≤ ReL ≤ 5 · 106

) f

1+12.7(Pr2L /3 −1 ) ( 2L ) 0.023Re0L .8 Pr0L .4 λdL

(

) for ReL ≥ 5 · 106

Pamitran et al. (2011)

Same model as Oh et al. (2011), with a different evaluation of the enhancement and suppression factors: S = 0.25(φ 2 )−0.2093 Bo0.7402 E = max[(0.009φ 2.2 + 0.76), 1]

1.5 ≤ d ≤ 3.0 mm 50 ≤ G ≤ 600 kg m−2 s−1 5 ≤ q ≤ 70 kW m−2 0 ≤ Tsat ≤ 10 ◦C

Ducoulombier et al. (2011)

h = max([hnb , hcb ] ), with nucleate boiling heat transfer coefficient evaluated with the model of Cheng et al. (2008) and Kim et al. (2004); 2/3 hcb = hLO (1.47 · 104 Bo + 0.93(1/X ) ), for Bo > 1.1 · 10−4 tt 0.986 ), for Bo < 1.1 · 10−4 hcb = hL (1 + 1.80(1/X ) tt The liquid hL and liquid-only hLO heat transfer coefficients evaluated with Dittus and Boelter (1930) equation.

d = 0.529 mm 200 ≤ G ≤ 1200 kg m−2 s−1 10 ≤ q ≤ 30 kW m−2 −10 ≤ Tsat ≤ 0 ◦C

h = 0.0 0 061(S + E )ReL F a0.11 PrL0.4 [log( 1μ.024μL )]−1 ( λdL )

0.529 ≤ d ≤ 7.75 mm 97.5 ≤ G ≤ 1400 kg m−2 s−1 3.93 ≤ q ≤ 40 kW m−2 −40 ≤ Tsat ≤ 26.8 ◦C

Fang (2013)

L,wall

where μL, wall is the liquid viscosity at the inner wall temperature and Fa is the Fang number, defined in Nomenclature. S = 410 0 0Bo1.13 − 0.275 x )a ( ρρVL )0.4 E = ( 1−x a = 0.48 + 0.00524(ReL F a0.11 )0.85 − 5.9 · 10−6 (ReL F a0.11 )1.85 , for (ReL Fa0.11 ) < 600 a = 0.87, for 600 ≤ (ReL Fa0.11 ) ≤ 6000 a = 160.8 · (ReL F a0.11 )−0.6 , for (ReL Fa0.11 ) > 6000

Fang et al. (2017)

h = Ff M−0.18 Bo0.98 F rL0.48 Bd0.72 ( ρρVL )0.29 [log( μμL )]−1Y ( λdL )

Y = 1, for pred ≤ 0.43 .15 Y = 1.38 − p1red , for pred > 0.43 F rL =

L,wall

G2 gdρL2

0.207 ≤ d ≤ 32 mm 20 ≤ G ≤ 1500 kg m−2 s−1 1.99 ≤ q ≤ 140 kW m−2 0.043 ≤ pred ≤ 0.61 ◦C

Ff = 2260 for CO2

general indications due to the large difference of properties in the available commercial lubricants, and different studies may therefore provide inconsistencies. Table 4 summarizes the flow boiling heat transfer coefficient data for CO2 /oil mixtures in smooth tubes collected for this review. PAG and POE type lubricants have been used for nominal mass concentrations ω0 from 0.1% to 5% in tubes of diameters from 2 to 11.2 mm in different operating conditions in terms of mass flux (from 100 to 1400 kg m−2 s−1 ), saturation temperature (from −30 to 15 °C) and heat flux (from 0.5 to 36 kW m−2 ), for a total amount of 1184 data points. All the experiments refer to single, circular and horizontal tubes. In the study of Gao et al. (2007), performed with PAG oil in a 3.0 mm tube, the CO2 local heat transfer coefficients were seen to decrease with vapor quality and they were considerably lower for oil concentrations higher than 0.11%. The authors also found PAG oil to be immiscible or only partially miscible with carbon dioxide for their operating conditions.

Pehlivanoglu et al. (2010) pointed out that the presence of lubricant strongly reduced the nucleative boiling contribution, as shown in their experimental data in Fig. 9a at moderate heat and mass fluxes, in which the heat transfer coefficient passes from approximately 9 kW m−2 K−1 up to 7.5 kW m−2 K−1 (−18%) when a small nominal oil mass fraction of 2% is considered. This behavior can be explained with the simultaneous significant increase of the saturation temperature and of the liquid surface tension for the refrigerant/oil mixture, both penalizing the bubble nucleation with a higher superheat required with respect to the pure fluid at the same operating conditions. Similar trends and strong penalizations of the nucleate boiling heat transfer coefficient with increasing oil concentration are also found in most of the data collected (Katsuta et al., 2008, Ono et al., 2010, Dang et al., 2013). It is important to remark that the increase of the saturation temperature for the oil/CO2 mixture leads to an intrinsic error in the data reduction procedure. For all the experimental studies reviewed, in fact, the flow boiling heat transfer coefficient is obtained according to

324

Author

Hwang et al. Hihara and (1997) Tanaka (20 0 0)

Yoon et al. (2004)

Thome and El Hajal (2004)

Pettersen (2004)

Choi et al. (2007a)

Choi et al. (2007b)

Cheng et al. Yun and Kim (20 08a, 20 08b) (2009)

Oh et al. (2011)

Pamitran Ducoulombier Fang (2013) et al. (2011) et al. (2011)

Fang et al. (2017)

Slug+ Intermittent flow regimes

|η | = 182 η = 181 ψ = 10.4 χ = 19.0

|η | = 31.2 η = −21.7 ψ = 50.6 χ = 85.8

|η | = 31.3 η = −1.1 ψ = 66.3 χ = 85.0

|η | = 38.8 η = 20.5 ψ = 59.6 χ = 79.8

|η | = 28.0 η = 12.9 ψ = 68.3 χ = 86.0

|η | = 27.9 η = 11.1 ψ = 67.8 χ = 85.5

|η | = 31.2 η = −8.3 ψ = 55.7 χ = 86.0

|η | = 43.1 η = 24.4 ψ = 61.8 χ = 79.4

|η | = 28.1 η = 1.3 ψ = 62.3 χ = 83.7

|η| = 25.0 η = −10.0 ψ = 65.8 χ = 93.5

|η | = 81.6 η = –81.6 ψ =0 χ = 0.8

|η | = 34.4 η = 26.4 ψ = 60.5 χ = 78.0

|η| = 14.4 η = 4.9 ψ = 90.3 χ = 96.6

|η| = 3.7 η = −3.5 ψ = 100 χ = 100

Annular flow regime |η | = 114 η = 109 ψ = 35.5 χ = 48.2

|η | = 42.5 η = 22.5 ψ = 62.2 χ = 79.6

|η | = 41.8 η = 5.3 ψ = 47.9 χ = 74.7

|η | = 40.9 η = −8.0 ψ = 44.6 χ = 76.9

|η | = 41.3 η = −3.9 ψ = 48.6 χ = 75.5

|η | = 44.6 η = 26.3 ψ = 58.2 χ = 76.1

|η| = 39.4 η = −6.8 ψ = 44.3 χ = 82.4

|η | = 46.5 η = −7.1 ψ = 46.7 χ = 67.7

|η | = 81.5 η = −67.2 ψ = 11.4 χ = 16.9

|η | = 42.9 η = −12.0 ψ = 37.4 χ = 67.9

|η | = 76.6 η = −75.4 ψ = 1.9 χ = 5.1

|η | = 44.6 η = 32.4 ψ = 62.8 χ = 76.7

|η| = 17.5 η = −1.3 ψ = 85.4 χ = 96.1

|η| = 4.5 η = 0.8 ψ = 99.9 χ = 100

Dryout flow regime |η | = 317 η = 315 ψ = 12.7 χ = 16.0

|η | = 284 η = 283 ψ = 15.3 χ = 22.5

|η | = 199 η = 168 ψ = 14.9 χ = 25

|η | = 148 η = 118 ψ = 26.4 χ = 44.7

|η| = 80.4 η = 10.5 ψ = 11.6 χ = 27.0

|η | = 273 η = 269 ψ = 13.3 χ = 19.6

|η | = 227 η = 217 ψ = 22.6 χ = 36.7

|η | = 80.5 η = −9.6 ψ = 15.9 χ = 26.3

|η | = 68.9 η = −31.2 ψ = 14.4 χ = 26.3

|η | = 234 η = 220 ψ = 14.4 χ = 24.3

|η | = 93.5 η = 18.2 ψ = 12.7 χ = 27.0

|η | = 270 η = 268 ψ = 14.4 χ = 21.5

|η| = 31.5 η = 9.5 ψ = 65.6 χ = 79.7

|η| = 9.2 η = −7.0 ψ = 94.1 χ = 100

Macro-channels (Co<0.5)

|η | = 212 η = 210 ψ = 12.0 χ = 19.5

|η | = 82.6 η = 58.1 ψ = 43.6 χ = 65.7

|η | = 67.9 η = 40.9 ψ = 46.8 χ = 69.9

|η | = 55.6 η = 19.2 ψ = 47.2 χ = 74.2

|η| = 47.5 η = 8.69 ψ = 41.7 χ = 61.6

|η | = 86.6 η = 75.8 ψ = 40.6 χ = 57.8

|η | = 65.0 η = 36.2 ψ = 48.9 χ = 73.7

|η | = 52.4 η = 21.5 ψ = 44.4 χ = 66.0

|η | = 57.6 η = −26.5 ψ = 31.3 χ = 44.4

|η | = 65.1 η = 38.5 ψ = 50.9 χ = 72.9

|η | = 80.4 η = −61.9 ψ = 2.71 χ = 7.80

|η | = 88.3 η = 80.4 ψ = 40.2 χ = 58.2

|η| = 20.5 η = 0.133 ψ = 79.6 χ = 93.3

|η| = 4.95 η = −3.63 ψ = 98.7 χ = 100

Micro-channels (Co>0.5)

|η | = 87.7 η = 82.2 ψ = 48.3 χ = 62.7

|η | = 76.9 η = 58.3 ψ = 64.4 χ = 78.3

|η | = 63.0 η = 18.1 ψ = 43.3 χ = 66.0

|η | = 60.9 η = 13.5 ψ = 39.6 χ = 69.5

|η| = 43.4 η = −8.82 ψ = 53.3 χ = 78.7

|η | = 70.0 η = 47.8 ψ = 67.2 χ = 81.6

|η | = 73.0 η = 20.7 ψ = 34.4 χ = 77.9

|η | = 50.5 η = −33.0 ψ = 43.4 χ = 58.8

|η | = 89.1 η = −82.1 ψ = 4.51 χ = 8.12

|η | = 78.7 η = 10.1 ψ = 21.5 χ = 54.3

|η | = 79.6 η = −60.3 ψ = 4.12 χ = 8.25

|η | = 68.6 η = 56.5 ψ = 72.7 χ = 80.2

|η| = 17.8 η = 2.98 ψ = 87.1 χ = 93.8

|η| = 5.32 η = 2.06 ψ = 99.5 χ = 100

Overall database

|η | = 157 η = 153 ψ = 28.1 χ = 38.7

|η | = 80.0 η = 58.2 ψ = 52.9 χ = 71.3

|η | = 65.7 η = 30.8 ψ = 45.3 χ = 68.2

|η | = 58.0 η = 16.7 ψ = 43.8 χ = 72.1

|η| = 45.7 η = 0.91 ψ = 45.5 χ = 69.2

|η | = 79.1 η = 63.4 ψ = 52.4 χ = 68.4

|η | = 68.6 η = 29.3 ψ = 42.5 χ = 75.6

|η | = 51.6 η = −2.87 ψ = 44.0 χ = 62.8

|η | = 71.6 η = −51.2 ψ = 19.4 χ = 28.3

|η | = 71.1 η = 25.9 ψ = 37.8 χ = 64.6

|η | = 80.0 η = −61.2 ψ = 3.34 χ = 8.00

|η | = 79.5 η = 69.7 ψ = 54.6 χ = 68.0

|η| = 19.3 η = 1.40 ψ = 82.9 χ = 93.5

|η| = 5.12 η = −1.10 ψ = 99.0 χ = 100

R. Mastrullo, A.W. Mauro and L. Viscito / International Journal of Refrigeration 108 (2019) 311–335

Table 3 Assessment of the CO2 flow boiling heat transfer coefficient prediction methods for smooth tubes (along the columns), compared to the experimental database separated by the operative conditions (along the rows). The flow regimes are recognized using Mastrullo et al. (2012) flow pattern map.

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325

Table 4 Experimental databank for boiling of CO2 in smooth tubes with the presence of oil. Author

Geometry∗

Internal diameter [mm]

Mass velocity [kg m − 2 s − 1 ]

Heat flux [kW m − 2 ]

Saturation temperature [°C]

Oil mass fraction [%]

Oil type

Gao et al. (2007) Katsuta et al. (2008) Pehlivanoglu et al. (2010) Kim et al. (2010) and Kim and Hrnjak (2012) Ono et al. (2010) Dang et al. (2013) Overall

S,C,H S,C,H S,C,H S,C,H

3 3 6.1 11.2

193/1094 400 100/400 100/200

10/20 5/15 2/15 0.5/10

10 0/10 −30/−15 −15

0.11/0.57 0.3/3.5 0.5/2 0.5/2

PAG PAG VG100 POE C85 POE RENSIO C85

45 164 179 117

S,C,H S,C,H

3.76 2/6 2/11.2

100/380 360/1440 100/1440

10/30 4.5/36 0.5/36

10/10 15 −30/15

0.1/1 0.5/5 0.1/5

PAG PAG 100

151 528 1184

∗

Number of points

M = multi, S = single; C = circular, R = rectangular; H = horizontal, V = vertical.

Fig. 8. Experimental versus predicted heat transfer coefficients for smooth tubes according to different correlations, implemented for the entire database and separated by flow pattern.

326

R. Mastrullo, A.W. Mauro and L. Viscito / International Journal of Refrigeration 108 (2019) 311–335

Fig. 9. Effect of lubricating oil on flow boiling heat transfer of CO2 . (a) Reduction of the nucleative boiling contribution. Data from Pehlivanoglu et al. (2010). (b) Slight enhancement of convection. Data from Kim et al. (2010).

Eq. (8), thus incorrectly using the saturation temperature of the pure carbon dioxide.

h=

q Twall − Tsat

(8)

As suggested by Thome (1995), Bandarra Filho et al. (2009), one should use instead the mixture saturation temperature Tsat,m as shown in Eq. (9), which could significantly increase with proceeding evaporation, as a function of the local oil mass concentration, defined in Eq. (10).

h=

q Twall − Tsat,m

ωoil,x =

ω0 1−x

(9) (10)

However, as experimented by Yokozeki (2007) and Marcelino Neto and Barbosa Jr (2009), the saturation temperature remains almost unchanged with both POE and PAG lubricants up to local oil mass concentrations of 50–70%, that are reached, for the present database (ω0 ≤ 5%), only at very high vapor qualities (x > 0.90). In some cases, a positive effect of the presence of oil for high vapor qualities has been observed, as shown in Fig. 9c for the data of Kim et al. (2010) with POE lubricant in a 11.2 mm tube. In case of pure CO2 , the low mass flux of 100 kg m−2 s−1 leads to a decreasing heat transfer coefficient trend with vapor quality for pure CO2 , due to the growth of the dryout region on the top of the tube in a stratified flow. When oil is added, the higher liquid surface tension of the mixture tends to increase the wetted fraction of the tube wall, thus shaping an annular flow and a convective heat transfer behavior. 5. Boiling of pure CO2 in enhanced surfaces To the best of the authors’ knowledge, the research has highlighted 10 flow boiling studies in microfinned surfaces using pure carbon dioxide as working fluid, from 2005 until 2015, by collecting a total amount of 883 heat transfer coefficient data. The whole database is shown in Table 5: tests have been performed with different kinds of geometrical characteristics, covering mass fluxes from 75 to 800 kg m − 2 s−1 , saturation temperatures from −30 to +20 °C, heat fluxes from 1.67 to 61 kW m − 2 , with and single/multi tube diameters from 0.8 mm to 11.2 mm. All the experiments have been conducted in circular and horizontal channels. Schael and Kind (2005) performed CO2 flow boiling experiments with a microfin 8.62 mm tube made up of 60 fins with a 18° helix angle. The authors observed that convection was promoted by the helical grooves, with increasing heat transfer coefficients with mass flux. On the other hand, the bubble formation was seen to be suppressed. Microfin tubes with similar geometrical

characteristics were investigated by Cho and Kim (2007) and Cho et al. (2010), together with smooth pipes having the same internal diameters. The heat transfer coefficients in the microfin channels were found 150–210% higher than those in the smooth tubes at the same test conditions. The authors attributed this behavior to a larger heated surface and a promoted annular flow regime by means of the fin structure. Gao et al. (2007) performed a comprehensive investigation on flow boiling of carbon dioxide in smooth and enhanced tubes of 3 mm ID, with and without the presence of oil. In case of pure CO2 , the heat transfer coefficients showed a strong dependency on heat flux and a negligible influence of the mass velocity for both smooth and microfin tube. Indeed, dryout vapor quality was seen to decrease with mass flux in the smooth channel, whereas no changes were observed in the enhanced tube. A peculiar grooved multi-port test section was tested by Jeong and Park (2009), made up of 8 minichannels with an internal diameter of 0.8 mm, together with a similar structure having 6 smooth narrow circular tubes for comparison purposes. Some details of this test section are shown in Fig. 10a. It was found that at lower vapor qualities (x<0.3), the heat transfer was considerably enhanced by the micro-grooves (+320%), especially in case of high saturation temperatures. At higher qualities, however, the grooves showed a negative effect on the heat transfer coefficient. A multimicrofin tube test section with zero helix angle was also used by Wu et al. (2015) in their investigation on flow boiling heat transfer and pressure drop with pure CO2 . The authors reported a significant influence of the heat flux and of the saturation temperature, which increased the heat transfer coefficient but also tended to anticipate the onset of dryout. Dang et al. (2010) studied the effect of the operating parameters in a with a 2 mm microfin tube, whose picture is shown in Fig. 10b. The heat transfer coefficients were also compared to the values obtained in a smooth tube at the same operating conditions, as presented in Fig. 11a. It was found that the use of fins was able to enhance the turbulence of the liquid phase, conveyed further in the tube and thus delaying the dryout occurrence with respect to the smooth tube. A similar behavior was found by Zhao and Bansal (2012), that performed flow boiling experiments in a 7.31 mm microfin tube at a single low saturation temperature of −30 °C, thus working with a reduced pressure similar to that of halogenated refrigerants at higher temperatures. Finally, for a 11.2 mm microfin tube, Kim and Hrnjak (2012) found that the carbon dioxide heat transfer coefficient trend with vapor quality was altered by the presence of fins, as shown in Fig. 11b. The authors stated that the internal tube peculiar structure was able to drive the liquid phase in the grooves, thus anticipating the appearance of the annular flow regime and providing a convective behavior. This was also corroborated by the flow patterns observations carried out in their work.

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327

Table 5 Experimental databank for boiling of CO2 in enhanced tubes. Author

Geometry∗

Internal diameter [mm]

Mass velocity [kg m − 2 s − 1 ]

Heat flux [kWm−2 ]

Saturation temperature [°C]

Schael and Kind (2005)

S,C,H microfinned: Hfin = 0.25 mm β = 18° Nfin = 60 γ = 30° S,C,H microfinned: Hfin = 0.15 mm β = 18° Nfin = 60 S,C,H microfinned: Hfin = 0.11 mm β = 12° Nfin = 40 γ = 40.5° M,C,H grooved: Hfin = 0.1 mm width = 0.2 S,C,H microfinned: Hfin = 0.12 mm β = 6.3° Nfin = 40 γ = 34.8° S,C,H microfinned: Hfin = 0.11 mm β = 12° Nfin = 50 γ = 40° S,C,H microfinned: Hfin = 0.20 mm β = 18° Nfin = 50 γ = 52° S,C,H microfinned: β = 30° Nfin = 68 M,C,H microfinned: Hfin = 0.16 mm β = 0° Nfin = 13 γ = 30

8.62

75/500

3.9/61

5

30

4.4/8.92

212/656

6/30

−5/20

200

3.04

190/770

10/30

10

71

0.8

400/800

12/18

0/10

51

2

360/720

4.5/18

15

185

3.75

190/380

10/30

10

58

7.31

100/250

9.9/30

−30

82

11.2

100/200

10

−15

11

1.7

100/600

1.67/8.33

1/15

195

0.8/11.2

75/800

1.67/61

−30/20

883

Cho and Kim (2007) and Cho et al. (2010)

Gao et al. (2007)

Jeong and Park (2009)

Dang et al. (2010)

Ono et al. (2010)

Zhao and Bansal (2012)

Kim and Hrnjak (2012)

Wu et al. (2015)

Overall ∗

Number of points

M = multi, S = single; C = circular, R = rectangular; H = horizontal, V = vertical.

a)

b)

Fig. 10. Examples of enhanced surfaces for flow boiling of CO2 . (a) Grooved multi-port test section of Jeong and Park (2009) and reference smooth multi-port mini-tubes. Measurements are in mm. (b) Single microfin tube of Dang et al. (2010).

6. Assessment of prediction methods for enhanced surfaces and oil effect 6.1. Nucleate and convective boiling contributions Fig. 12a–e presents a bar chart distribution for both databases including microfin tubes and smooth tubes with the presence of

oil. 883 data points in enhanced surfaces and 1184 heat transfer coefficient values for CO2 /oil mixtures are segregated into different categories according to their operating conditions, in terms of tube internal diameter, mass flux, saturation temperature, heat flux and nominal oil mass fraction ω0 . For the microfin tube database, a consistent amount of experimental points are collected with diameters of 1.7 and 2.0 mm (43% of the entire databank) and for the

328

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Fig. 11. Effect of the microfin structure on flow boiling heat transfer of CO2 . (a) Heat transfer enhancement and delayed dryout. Data from Dang et al. (2010). (b) Improved convection. Data from Kim and Hrnjak (2012).

saturation temperatures of 15 °C (35% of the databank), all belonging to the studies of Wu et al. (2015) and Dang et al. (2010). As for the CO2 /oil heat transfer coefficient data, remarkable peaks are found for saturation temperatures of −15 °C, 10 °C and 15 °C and for imposed heat fluxes of 10, 18 and 36 kW m−2 , due to the comprehensive experimental investigation of Dang et al. (2013) that represents alone the 45% of the entire CO2 /oil collected database. Finally, more than 550 points are taken at a nominal oil mass fraction of 1.0%, including both synthetic PAG and POE lubricants. The experimental Nusselt numbers of the two databases are compared with both nucleate and convective Nusselt, respectively from Eqs. (1) to (7) in Fig. 13a and b, as previously presented for conventional geometries and pure carbon dioxide. As already pointed out, the heat transfer coefficients in microfin tubes can be considerably higher than those obtained in an equivalent smooth geometry, mainly due to the increased heat transfer surface and also to a higher turbulence of the liquid in the tube with a subsequent enhancement of the heat transfer convection efficiency (Thome, 1990, Mastrullo et al., 2018). As a consequence, the experimental Nusselts calculated in enhanced tubes (black circular markers) are significantly underestimated by considering either only convection or only nucleation, and therefore specific heat transfer prediction methods should instead be employed. In case of CO2 /oil mixtures, the experimental Nusselt numbers (red diamond markers in Fig. 13) are lower than the corresponding values calculated for only convective and only nucleative Nusselt values, implying a non-negligible penalization with respect to the flow boiling in smooth tubes with pure carbon dioxide. In fact, the two-phase heat transfer coefficient is altered by the presence of lubricant that affects both convective and nucleate boiling contributions, as also shown in Fig. 9. From one side, bubble nucleation and growth tend to be suppressed due to the simultaneous increase of the saturation temperature and the surface tension of the liquid mixture. However, as suggested by Thome (1996), this effect can be partially compensated with foaming, that increases the nucleation phenomenon. As regards the convective contribution, although the increase of the surface tension might delay the onset of dryout (which occurs at low vapor qualities in case of CO2 ) through an increased wettability, the higher viscosity of the mixture liquid phase greatly penalizes the flow velocity and thus convective heat transfer. 6.2. Assessment of methods: oil effect Four different flow boiling heat transfer coefficient correlations developed for CO2 /PAG oil mixtures in smooth tubes are

considered for this review. Most of the methods use a typical flow boiling structure, such as either a superposition or an asymptotic model, with an adjustment of the nucleate boiling suppression factor by considering the oil properties and/or its concentration in the evaporating flow. A summary of the mathematical expressions of the four prediction methods is given in Table 6. Aiyoshizawa et al. (2006) proposed a typical superposition model in which the convection enhancement and the boiling suppression factors were calibrated on the experimental data of Dang et al. (2013) for carbon dioxide and PAG oil. The simplicity of this method consists in the use of the pure CO2 physical properties, whereas the presence of lubricant is taken into account only with the normal oil normal boiling point temperature Tb, oil . Gao et al. (2008) developed a flow boiling heat transfer coefficient prediction method for oil/CO2 mixures based on their own experimental data for carbon dioxide and PAG oil. The same equations of Cheng et al. (20 08, 20 08) were employed for their asymptotic model, except for the additional suppression factor related to the vapor quality. Katsuta et al. (2008) employed a superposition model in which the nucleate boiling contribution was additionally penalized by the factor  depending on the nominal oil mass fraction. Finally, Li et al. (2014) developed an asymptotic method for flow boiling of carbon dioxide with entrained PAG oil for smooth horizontal tubes in the pre-dryout region. The thermodynamic properties labeled with the subscript m refer to the oil/refrigerant mixture. For their evaluation, a comprehensive set of equations can be found in the original references (Li et al., 2014). The assessment of the CO2 /oil flow boiling prediction methods with the individual works and for the entire collected database is provided in Table 7. The calculated errors are quite high in any case, but the correlations of Aiyoshizawa et al. (2006) and Gao et al. (2008) provide a discrete agreement with almost all the single databases, with overall calculated MAE of 73.7% and 63.2%, respectively. The graphical comparison of these two prediction methods is shown in Fig. 14a and b, in which it is clear the large scatter for a considerable amount of points, especially those obtained for nominal oil mass fractions higher than 2.5% (defined by the color bar). The correlation of Katsuta et al. (2008) works particularly well with the data collected from Pehlivanoglu et al. (2010) and Kim et al. (2010) and Kim and Hrnjak (2012), together with the authors’ own database, but largely fails in the other cases. The remaining prediction method of Li et al. (2014) greatly overestimates all the experimental heat transfer coefficients, providing an overall relative error of +165%.

R. Mastrullo, A.W. Mauro and L. Viscito / International Journal of Refrigeration 108 (2019) 311–335

329

Fig. 12. Distribution of data points for flow boiling of CO2 in enhanced tubes and in smooth tubes with the presence of lubricating oil, related to: (a) internal diameter; (b) mass flux; (c) saturation temperature; (d) imposed heat flux; (e) nominal oil mass fraction.

Fig. 13. Experimental versus predicted Nusselt numbers, for enhanced tubes and CO2 /oil mixtures. Comparison with convective (a) and nucleate (b) boiling contribution.

330

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Table 6 Mathematical expressions of the flow boiling heat transfer prediction methods for carbon dioxide and lubricants mixtures in smooth tubes. Author

Equations

Aiyoshizawa et al. (2006)

h = E hL + Shnb , liquid heat transfer coefficient with Dittus-Boelter equation hnb = 207( λqDTb )0.745 ( ρρVL )0.581 Pr0L .533 DλL

Range of validity

L b

Db = 0.51[ g(ρ2−σρ ) ]0.5 L V E = 0.8 + 0.5(1/X )1.2 tt 1 S= −4 3 6+ (Ret p ·10

2 ≤ d ≤ 6 mm 360 ≤ G ≤ 1440 kg m−2 s−1 4.5 ≤ q ≤ 36 kW m−2 Tsat = 15 ◦C PAG oil; ω0 ≤ 5.0%

b

)

Ret p = ReL · E Gao et al. (2008)

Same equations of Cheng et al. (2008a, 2008b) model, with an additional suppression factor 3 h = [(S hnb ) + h3cb ]1/3 S = S · (−0.5x + 0.35) for x ≤ 0.7 S = 0 for x ≤ 0.7.

d = 3 mm 190 ≤ G ≤ 1100 kg m−2 s−1 10 ≤ q ≤ 20 kW m−2 Tsat = 10 ◦C PAG oil; ω0 ≤ 0.57%

Katsuta et al. (2008)

h = E hL + Shnb  E = 1 + 0.258(1/X )0.886 + 92.32( ρρVL )3 (1/X )0.9

d = 3 mm G = 400 kg m−2 s−1 5 ≤ q ≤ 15 kW m−2 0 ≤ Tsat ≤ 10 ◦C PAG oil; ω0 ≤ 3.5%

S = ln(2.332 ·

= Li et al. (2014)

tt

0.518

1.27

Bo Bd Fr Ret0p.834 1 0.698 Bo0.207 Bd 0.912 1+ωoil

0.964

tt

), with Retp taken from Aiyoshizawa et al. (2006)

h = [(Shnb ) + Eh3m ]1/3 , nucleate boiling heat transfer coefficient from Forster and Zuber (1955) and hm from Dittus-Boelter equation. Both of them must be calculated with the properties of the CO2 /oil mixture, as recommended in Li et al. (2014) E = 1 for Xtt ≥ 10 E = 2.55 · (0.413 + 1/X )1.05 for Xtt < 10 3

S = Soil ·

1

0.9+

ω

0.3 0.4 ( (E 1.25 ·Rem )·10−3 ) 0.23 (Bo·103 )

oil,x Soil = − 2 ln(1− ω

ωoil,x = Rem =

ω0

oil,x

)

, local oil concentration

1−x G(1−x )d

μm

tt

2 ≤ d ≤ 6 mm 360 ≤ G ≤ 1440 kg m−2 s−1 4.5 ≤ q ≤ 36 kW m−2 Tsat = 15 ◦C PAG oil; ω0 ≤ 5.0%

, with Rem as the oil/CO2 mixture Reynolds number.

Table 7 Assessment of the CO2 flow boiling heat transfer coefficient prediction methods for smooth tubes in the presence of oil (along the columns), compared to the individual experimental database (along the rows). Author

Aiyoshizawa et al. (2006)

Gao et al. (2008)

Katsuta et al. (2008)

Gao et al. (2007)

|η | = 108 η = 94.5 ψ = 71 χ = 71

|η | = 45.4 η = 32.2 ψ = 73 χ = 82

|η | = 300 η = 300 ψ = 4.4 χ = 4.4

Katsuta et al. (2008)

|η | = 48.2 η = 15.7 ψ = 54 χ = 79 |η | = 54.2 η = −50.5 ψ = 17 χ = 34 |η | = 54.6 η = −50 ψ = 9.4 χ = 26 |η | = 76.1 η = 58.7 ψ = 68 χ = 78 |η | = 89 η = 85.6 ψ = 68 χ = 70 |η| = 73.7 η = 38.8 ψ = 52.4 χ = 62.4

|η | = 130 η = 130 ψ =0 χ = 8.5 |η | = 54.4 η = −52.2 ψ = 21 χ = 33 |η | = 56.9 η = −55.8 ψ =6 χ = 33 |η | = 43.6 η = 11.9 ψ = 62 χ = 80 |η | = 82 η = 75.7 ψ = 43 χ = 55 |η| = 63.2 η = 24.2 ψ = 42.2 χ = 56.9

|η | = 39.8 η = 8.2 ψ = 62 χ = 77 |η | = 31.1 η = −30.4 ψ = 34 χ = 99 |η | = 24.1 η = −24.1 ψ = 65.8 χ = 97 |η | = 226 η = 226 ψ =0 χ =0 |η | = 312 η = 312 ψ =0 χ =0 |η| = 204 η = 190 ψ = 11.9 χ = 26.1

Pehlivanoglu et al. (2010)

Kim et al. (2010) and Kim and Hrnjak (2012)

Ono et al. (2010)

Dang et al. (2013)

Overall database with oil

6.3. Assessment of methods: enhanced tubes To the best of our knowledge, the only flow boiling heat transfer prediction method explicitly developed for microfin tubes (with 0° helix angle) and carbon dioxide as working fluid is that of Wu et al. (2015). Before the dryout region, the heat transfer coefficient was calculated using the same expression of Yoon et al. (2004), by introducing the fin height Hfin as supplementary

Li et al. (2014) |η | = 202 η = 191 ψ =0 χ = 8.9 |η | = 162 η = 160 ψ = 17 χ = 26 |η | = 70 η = 36.8 ψ = 34 χ = 53 |η | = 61 η = 34.1 ψ = 39.3 χ = 62 |η | = 170 η = 155 ψ = 4.6 χ =8 |η | = 242 η = 242 ψ = 0.4 χ = 2.3 |η| = 176 η = 165 ψ = 12.2 χ = 20.1

geometrical parameter, as shown in Eq. (11):

 hW u,x
C2

C1 Bo

psat d

+ C4

σ

· ReCLO7 P rCL 8

C3

δ H f in



1/ Xtt

C5 GH

C6  f in

μL

C9 · hL

(11)

R. Mastrullo, A.W. Mauro and L. Viscito / International Journal of Refrigeration 108 (2019) 311–335

331

Fig. 14. Experimental versus predicted heat transfer coefficients with the presence of oil for the entire database presented in Table 4. The color bar refers to the initial oil mass fraction. (a) Correlation of Gao et al. (2008). (b) Correlation of Aiyoshizawa et al. (2006).

Fig. 15. Experimental versus predicted heat transfer coefficients for enhanced surfaces. (a) Correlation of Wu et al. (2015); (b) Modified correlation of Cheng et al. (2008); (c) Correlation of Rollmann and Spindler (2016); (d) Correlation of Mehendale (2018).

where ReLO is the Reynolds number evaluated for liquid-only flow, hL is the liquid Dittus-Boelter heat transfer coefficient and δ is the liquid film thickness that must be calculated in the hypothesis of symmetric annular flow (Eq. (4)), by employing the void fraction from Rohuani and Axelsson (1970) expression. The nine coefficients from C1 to C9 were fitted by the experimental data, obtaining, respectively: 0.0077, 2.1, 1.1, 25, 0.41, −1.3, 0.82, 0.45 and −0.11. In the post-dryout region the heat transfer coefficient was instead correlated to the dry angle and the wet and vapor heat transfer

coefficients values, as shown in the following Eq. (12):

hW u,x>xcr

  θdry hV + 2π − θdry hwet = 2π

(12)

where hV is the Dittus-Boelter vapor heat transfer coefficient and the dry angle is a function of the vapor Reynolds, Boiling and Bond numbers:

θdry = D1 ReDL 2 BoD3 BdD4 2π

(13)

332

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Table 8 Assessment of the heat transfer coefficient prediction methods for microfin tubes (along the columns), compared to the individual experimental database (along the rows). Author

Wu et al. (2015)

Modified Cheng et al. (2008)

Rollmann and Spindler (2016)∗

Schael and Kind (2005)

|η | = 290 η = 290 ψ = 6.7 χ = 6.7

|η | = 24.7 η = −1.5 ψ = 76.7 χ = 93.3

|η | = 90.2 η = −90.2 ψ =0 χ =0

|η | = 29.9 η = −29.2 ψ = 56.7 χ = 90.0

Cho and Kim (2007) and Cho et al. (2010)

|η | = 295 η = 286 ψ = 1.0 χ = 2.0

|η | = 49.2 η = 20.3 ψ = 47.0 χ = 65.5

|η | = 82.8 η = −74.8 ψ = 5.5 χ = 10.5

|η | = 36.4 η = −0.7 ψ = 49.5 χ = 79.0

Gao et al. (2007)

|η | = 133 η = 131 ψ = 5.6 χ = 11.3

|η | = 33.3 η = −4.8 ψ = 73.2 χ = 91.5

|η | = 54.3 η = −40.6 ψ = 4.2 χ = 47.9

|η | = 21.9 η = −12.1 ψ = 76.1 χ = 97.2

Jeong and Park (2009)

|η | = 98.5 η = 96.5 ψ = 25.5 χ = 39.2

|η | = 64.6 η = 57.0 ψ = 37.2 χ = 54.9

|η | = 44.2 η = −34.4 ψ = 35.3 χ = 62.7

|η | = 77.4 η = 63.6 ψ = 39.2 χ = 60.8

Dang et al. (2010)

|η | = 94.3 η = 90.2 ψ = 16.8 χ = 35.1

|η | = 38.1 η = 36.6 ψ = 53.0 χ = 73.0

|η | = 32.3 η = 13.1 ψ = 62.2 χ = 92.4

|η | = 29.8 η = 12.8 ψ = 64.9 χ = 93.5

Ono et al. (2010)

|η | = 202 η = 202 ψ =0 χ =0

|η | = 24.8 η = −4.1 ψ = 82.8 χ = 89.7

|η | = 51.8 η = −51.6 ψ = 10.3 χ = 32.8

|η | = 20.0 η = −9.3 ψ = 82.8 χ = 94.8

Zhao and Bansal (2012)

|η | = 320 η = 320 ψ = 2.4 χ = 3.7

|η | = 59.9 η = 59.7 ψ = 34.1 χ = 54.9

|η | = 86.3 η = −86.3 ψ =0 χ =0

|η | = 59.4 η = 56.5 ψ = 23.2 χ = 40.2

Kim and Hrnjak (2012)

|η | = 500 η = 500 ψ =0 χ =0

|η | = 92.0 η = 92.0 ψ = 2.1 χ = 9.5

|η | = 119 η = −119 ψ =0 χ =0

|η | = 13.5 η = 11.3 ψ = 90.9 χ = 100

Wu et al. (2015)

|η | = 23.8 η = 8.3 ψ = 71.3 χ = 91.8

|η | = 33.0 η = −33.0 ψ = 47.2 χ = 82.1

|η | = 47.4 η = −45.4 ψ = 37.4 χ = 59.0

|η | = 25.5 η = −23.6 ψ = 53.8 χ = 95.9

Overall enhanced tubes database

|η| = 163 η = 156 ψ = 22.1 χ = 32.2

|η| = 41.4 η = 13.3 ψ = 52.1 χ = 73.8

|η| = 58.9 η = −45.4 ψ = 25.6 χ = 44.4

|η| = 30.5 η = 0.2 ψ = 58.4 χ = 87.6

∗

Not specifically developed for carbon dioxide.

The recommended values for the four coefficients from D1 to D4 are 0.37, 0.29, 0.23 and −0.46. The heat transfer coefficient of the wet portion must be evaluated with Eq. (11), in which the liquid film thickness δ is calculated with the following expression:



δ

Mehendale (2018)∗

d = 1− 2



1−

1−α



(14)

θ

1 − 2dry π

hCheng,enh = hCheng · Enh

Finally, the dryout vapor quality was correlated to the liquid Reynolds, Boiling and Bond numbers and to the ratios of liquid and vapor density and viscosity as follows:

xcr = E1 ReEL 2 BoE3 BdE4

 ρ E5  μ E6 V

ρL

heat transfer coefficient is multiplied by the surface enhancement ratio Enh with respect to an equivalent smooth tube, by following a similar approach of Cavallini et al. (1999) and Mastrullo et al. (2019). In Eq. (17), β is the helix angle, Hfin is the fin height, Nfin is the number of fins, ηfin is the fin efficiency, Dr is the root-to-root tube diameter and γ is the fin tip angle.

L

μV

(15)

The fitted coefficients from E1 to E6 were, respectively: 1.3, −0.24, −0.11, 0.0 0 095, 1.1 and 1.1. This correlation was entirely calibrated on the multi-minichannel microfin tube tested by Wu et al. (2015) and was intended to cover mass fluxes from 100 to 600 kg m−2 s−1 , heat fluxes from 1.67 to 8.33 kW m−2 and saturation temperatures from 1 to 15 °C. Besides Wu et al. (2015) prediction method, the experimental data are compared with the flow pattern based prediction method of Cheng et al. (2008) for smooth tubes, by including the effect of an increased heat transfer surface. Particularly, the calculated

 2H f in N f in 1 Enh = · 1+ cos (β ) π Dr

(16)



γ  η f in  γ  − tan

cos

2

2

 (17)

Finally, the assessment is carried out by considering also the correlations of Rollmann and Spindler (2016) and Mehendale (2018). The first does not consider the fin main features and was developed by using the authors’ own experimental 1614 heat transfer coefficient data with R407C and R410A. Mehendale (2018) model was calibrated with a large database of 2622 points within horizontal microfin tubes, including 9 fluids from 25 sources. For the sake of briefness, the mathematical expressions of these non-CO2 related methods is not provided here and the reader is referred to the references mentioned. The agreement between the chosen methods and the entire database for enhanced tubes is shown in Figure 15a-d and the

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summary of the calculated statistical parameters for each author is given in Table 8. Although Wu et al. (2015) correlation includes the effect of the enhanced channel characteristics through the fin height, it largely fails to capture the experimental data (with a calculated MAE of 163%) and works quite well only for the authors’ own database, as shown in Fig. 15a, in which 92% of the data are predicted within an error band of ±50%. The method of Rollmann and Spindler (2016) provides a MAE of 58.9%, underpredicting (MRE = −45.4%) most of the experimental CO2 heat transfer coefficients. The Mehendale model (Mehendale, 2018), developed with a larger database including also carbon dioxide points, gives the best agreement with the collected heat transfer coefficients in enhanced tubes, with an overall calculated MAE of 30.5% and almost 90% of the data that are predicted within an error range of ±50%. A slightly lower accuracy (MAE = 41.4%) is obtained with the modified Cheng et al. (2008) flow pattern based model. 7. Conclusions A comprehensive review of flow boiling heat transfer of carbon dioxide has been presented in this paper. The review addresses flow boiling experimental studies in smooth and enhanced tubes with pure CO2 and CO2 /lubricant mixtures, collecting more than 70 0 0 heat transfer coefficient data points and analyzing the main trends with operating conditions. The experimental Nusselt numbers are compared to the nucleate and convective contribution for each data set and the assessment of existing prediction methods explicitly developed for carbon dioxide is finally carried out. The main outcomes of this review are summarized as follows: •

•

•

•

•

By considering the macro-to-micro scale transition criterion of Kew and Cornwell (1997), there are no significant differences in the flow boiling behavior of pure CO2 in smooth tubes. Pure convective (h increasing only with vapor quality and mass flux) and pure nucleative (h increasing only with saturation temperature and heat flux) trends can in fact be both found either for small and conventional channels, depending on the operating conditions explored. Data from smooth tubes and pure CO2 are segregated into different flow patterns according to the flow pattern map of Mastrullo et al. (2012). Points belonging to intermittent and slug flow are fairly fitted by considering a pure nucleate boiling contribution (MAE = 33%), expressed by Cooper (1984) correlation for pool boiling heat transfer. Annular flow data are instead not fairly predicted with either only convection or only nucleation heat transfer Among the fourteen CO2 -related heat transfer coefficient prediction methods available in literature for smooth tubes, the model of Fang et al. (2017) best fit the entire database, with a calculated MAE of 5.1%. Generally, with respect to smooth tubes at the same operating conditions, the two-phase heat transfer coefficients in microfin tubes are considerably higher (up to +500%). It was observed that the increased turbulence generated by the microfin structure is able to drive the liquid phase in the grooves, thus anticipating the appearance of the annular flow regime, providing at the same time a more convective behavior and a delayed dryout occurrence. The only available CO2 -related prediction method of Wu et al. (2015) strongly overestimates the collected database for enhanced tubes, with an overall MAE of 163%. A better agreement is found with the correlation of Mehendale (2018), developed for various fluids, having a calculated MAE of 30.5%. The presence of lubricant negatively affects both the convective and nucleate boiling heat transfer contributions of carbon dioxide, with a significant suppression of the bubble nucleation and an increased flow viscosity. On the other hand, it was observed

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that the higher surface tension of the mixture increases the stability of the liquid film and may delay the onset of dryout. The correlations of Aiyoshizawa et al. (2006) and Gao et al. (2008) provide the best agreement, even if the deviations are quite high (MAE of 73.7% and 63.2%, respectively). Generally, the available methods tend to poorly predict the present database. This could be related to the fact that these models are conceived with a restricted amount of data and by using a different type of lubricant. On this regard, more experiments and research is still recommended in order to develop more generalized correlations including the oil-type characteristics and their effect on CO2 properties, with a possible significant increase of the prediction accuracy. 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