Flow condensation heat transfer correlations in horizontal channels

Accepted Manuscript Title: Flow condensation heat transfer correlations in horizontal channels Author: Helei Zhang, Xiande Fang, Hui Shang, Weiwei Chen PII: DOI: Reference:

S0140-7007(15)00211-X http://dx.doi.org/doi: 10.1016/j.ijrefrig.2015.07.013 JIJR 3101

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

28-12-2014 7-7-2015 13-7-2015

Please cite this article as: Helei Zhang, Xiande Fang, Hui Shang, Weiwei Chen, Flow condensation heat transfer correlations in horizontal channels, International Journal of Refrigeration (2015), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2015.07.013. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Flow condensation heat transfer correlations in horizontal channels Helei Zhang a, Xiande Fang a,*, Hui Shang b, Weiwei Chen a a

Institute of Air Conditioning and Refrigeration, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, PR China; b

650 Research Institute, AVIC HONGDU Aviation Industry Group LTD., Nanchang, Jiangxi 330024, PR China

Highlight  Compile a database containing 2563 experimental data points of condensation heat transfer.  Analyze and evaluate 28 condensation heat transfer correlations based on the database.  Provide a guide to choosing better correlations for engineering applications.  Reveal a need for improving prediction method and better understanding mechanisms.

Abstract: Condensation heat transfer in tubes is extensively used in many industrial sectors. There were a number of investigations evaluating the correlations of condensation heat transfer in tubes. However, either the data used or correlations involved were limited, resulting in inconsistent conclusions. This paper presents a comprehensive review of correlations for flow condensation heat transfer in horizontal channels. A database containing 2563 experimental data points of condensation heat transfer in horizontal channels, including 1462 data points from conventional channels and 1101 from minichannels, is compiled from 26 published papers, with which 28 correlations are evaluated and analyzed. Twelve correlations have the mean absolute deviation (MAD) less than 30% against the database, and eight have 30%  MAD < 40%. The MADs of the best predictions for the entire database, conventional channel data, and microchannel data are 17.0%, 14.4%, and 20.6%, respectively, indicating a need to improve the prediction method for microchannels.

Key words: flow condensation; heat transfer coefficient; correlation; two-phase

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*Corresponding author. Tel: 86-25-84896381, Email: [email protected]

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Nomenclature A

tube cross-sectional area (m2)

θ

angle (rad)

Bd

Bond number

λ

thermal conductivity (W m–1 K–1)

cp

specific heat at constant pressure (kJ kg–1 K–1)

μ

dynamic viscosity (Pa s–1)

D

tube diameter (mm)

ν

kinematic viscosity(m2 s–1)

Fr

Froude number

ξ

percentage of MRD within ±30%

G

mass flux (kg m–2 s–1)

ρ

density (kg m–3)

g

gravitational acceleration (m s–2)

σ

surface tension (N m–1)

Ga

Galileo number

Φ

two-phase multiplier

Gr

Grashof number

Subscripts

H

latent heat (kJ kg–1)

an

annular flow

h

heat transfer coefficient (kW m–2 K–1)

bot

bottom

J

dimensionless superficial velocity

crit

critical

Ja

Jakob number

exp

experimental

L

length of tube (mm)

L

liquid

Nu

Nusselt number

LO

liquid-only

p

pressure (MPa)

LV

liquid convert to vapor phase

Pr

Prandtl number

k

liquid or vapor phase

q

heat flux (kW m–2)

pred

predicted

Re

Reynolds number

rd

reduced

Su

Suratman number

sat

saturation

T

temperature (K, ºC)

slug

slug flow

We

Weber number

strat

stratified flow

X

Lockhart–Martinelli parameter

trans

transition

x

vapor quality

top

top

Greek Symbols

V

vapor

α

void fraction

VO

vapor-only

Δ

increment

w

wall

δ

percentage of MRD within ±20%

wavy

wavy flow

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1 Introduction Condensation in tubes has many applications, such as refrigeration, air conditioning, electric power generation, and spacecraft thermal control systems. The determination of condensation heat transfer coefficient is important for design, development, and assessment of the systems and equipment. Condensation heat transfer coefficient is affected by various parameters, such as refrigerant properties, tube diameter, saturation temperature, heat flux, mass flux, and vapor quality [1–7]. The channel dimension has important effects on two-phase flow heat transfer, which has been proved in a number of studies. There are three influential approaches describing the channel transition of two-phase flow [5], which are the channel size method (Mehendal et al. [1]; Kandlikar and Grande [2]), the Bd-type method (Kew and Cornwell [3]; Cheng et al. [4]), and the multi-dimensionless parameter method (Li and Wu [6]; Harirchian and Garimella [7]). In this paper, the well-known Kandlikar and Grande [2] method is adopted, which defines D  3mm as conventional channels, 200 μm  D < 3mm as minichannels, and 10 μm < D < 200 μm as microchannels. For conventional channels, Dobson et al. [8–10] investigated the heat transfer coefficients of R12, R22, R134a, and near-azeotropic blends of R32/R125 in 50 percent/50 percent and 60 percent/40 percent compositions. Several correlations were suggested for gravity-dominated and shear-dominated flows, and successfully predicted data from their study and several other sources. Haraguchi et al. [11] studied experimentally the heat transfer coefficients of R22, R134a, and R123 condensing in an 8.4 mm inner diameter (ID) tube, with mass flux from 90 to 400 kg m–2 s–1 and heat flux from 3 to 33 kW m–2. An empirical equation based on the turbulent liquid film theory and Nusselts theory was proposed, which correlated the experimental data with an error of 20%. Thome et al. [12] proposed a flow pattern based model of condensation heat transfer in horizontal tubes to predict the experimental database for different flow regimes. The database contained 4621 date points from 15 fluids over the range of mass flux from 24 to 1022 kg m–2 s–1, vapor quality from 0.03 to 0.97, reduced pressure from 0.02 to 0.8 MPa, and tube ID from 3.1 to 21.4 mm. The model predicted 85% of the non-hydrocarbon data (1850 data points) and 75% of the hydrocarbon data (2771 data points) within ±20%. Cavallini et al. [13] suggested a model for condensation heat transfer coefficient in horizontal tubes, which included a criterion for the transition between two different flow categories, depending on whether the heat transfer coefficient was dependent or independent on the temperature difference ΔT. The model predicted the database containing 4471 data points from the media including HCFCs, HFCs, HCs, carbon dioxide, ammonia, and water with an MAD of 15%. As for the minichannels, Park and Hrnjak [14] investigated CO2 flow condensation heat transfer, pressure drop and flow pattern in 0.89 mm multi-port microchannels at saturation temperature of –15 and –25 ºC, mass flux from 200 to 800 kg m–2 s–1, and wall subcooling temperature from 2 to 4 ºC. The comparison of several existing correlations with the experimental data 4

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showed that the Akers and Rosson [15] correlation could predict the measurements with the main absolute deviation (MAD) less than 20%. Based on the Akers and Rosson [15] correlation and the trend of CO2 thermophysical properties, a relation was attempted, but the result was unsatisfactory. Bohdal et al. [16] investigated the heat transfer and pressure drop of the R134a and R404A condensation in minichannels with ID from 0.31 to 3.30 mm. The results were compared with calculations according to the correlations proposed by Dobson and Chato [10], Cavallini and Zecchin [17], Akers and Rosson [15], Shah [18], and Tang et al. [19]. Within the range of the examined parameters, the Akers and Rosson [15] and Shah [18] correlations predicted well within a limited range of the mass flux of the refrigerant and the mini-channel diameters. An empirical correlation was proposed on the basis of the investigations for the calculation of the local heat transfer coefficient in minichannels, within an error of ±25%. Zhang et al. [20] investigated the condensation heat transfer of R22, R410A and R407C flowing in steel tubes of 1.088 and 1.289 mm ID at saturation temperature of 30 and 40 °C, mass flux from 300 to 600 kg m–2 s–1, and vapor quality from 0.1 to 0.9. The condensation heat transfer coefficient and two-phase pressure drop increased with mass flux and vapor quality, increasing faster at high vapor quality. The comparison showed that the Wang et al. [21] and Yan and Lin [22] correlations predicted the experimental data more accurately but still had large discrepancy. Liu et al. [23] conducted measurements of heat transfer and pressure drop of R152a flow condensation in circular and square micro-channels with hydraulic diameters of 1.152 and 0.952 mm. The saturation temperatures were 40 and 50 °C, with mass flux varying from 200 to 800 kg m–2 s–1 and vapor quality from 0.1 to 0.9. The results showed that both heat transfer coefficient and pressure drop increased with mass flux and vapor quality but decreased with saturation temperature. The experimental data were compared to several existing empirical correlations, which showed that the correlations of Wang et al. [21], Koyama et al. [24], and Wang and Rose [25] exhibited good predictions for the circular tube. The brief review above shows that most evaluations of the correlations of condensation heat transfer coefficient were based on the authors own experimental data, or covered very limited number of correlations, which resulted in inconsistent results. In this paper, a database of flow condensation heat transfer in horizontal channels is complied from 26 published papers, which contains 2563 data points, including 1462 data points from conventional channels and 1101 from minichannels. Twenty-eight flow condensation heat transfer correlations are reviewed. The evaluation of the correlations with the database is carried out, and correlations with better predictions for conventional channels, minichannels, and the entire database are identified, which provides a guide to choosing a proper correlation for engineering practice.

2 Experimental data In the present study, a database containing 2563 data points of flow condensation heat transfer in horizontal circular tubes is complied from 26 published sources, involving 17 different working fluids, including R12, R123, R1234yf, R125, R134a, R152a, 5

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R22, R290, R32, R404A, R407C, R410A, R600, R600a, CO2, 60% R32/40% R125, and 50% R600/50% R290. The experimental parameter ranges cover hydraulic diameter from 0.493 to 20 mm, mass flux from 24 to 1532.1 kg m–2 s–1, heat flux from 2.35 to 421.14 kW m–2, saturation temperature from –25.6 to 70.7 °C, and vapor quality from 0 to 1. Tables 1 and 2 list the key information on the individual data source incorporated in the database of conventional channels (1462 data points) and minichannels (1101 data points) in chronological order, respectively, as well as the number of data points actually adopted.

Table 1 Experimental data sources of condensation heat transfer in conventional horizontal circular tubes Table 2 Experimental data sources of condensation heat transfer in horizontal minichannels

Figure 1 shows the laminar/turbulent distribution of the experimental data. The result shows that most of the data are located in turbulent liquid–turbulent vapor flow region (tt) and laminar liquid–turbulent vapor flow region (vt), accounting for 62.9% and 16.3% of the entire database, respectively. Only very small portion of data are attributed to turbulent liquid–laminar vapor flow region (tv) and the laminar liquid–laminar vapor flow region (vv), each sharing about 0.2% of the database. The distribution of heat transfer coefficient relative to the vapor quality is presented in Fig. 2. As can be seen, the vapor quality distribution is relatively uniform.

Fig. 1 Laminar/Turbulent distribution of the experimental data Fig. 2 Distribution of heat transfer coefficient relative to vapor quality

3 Existing correlations Twenty-eight correlations of flow condensation heat transfer coefficient are surveyed. According to their suitable flow regions, the correlations are divided into three categories, i.e. gravity-driven flow condensation correlations, annular flow condensation correlations, and stratified and annular flow condensation correlations. The gravity-driven flow regime includes stratified, wavy, and slug flow regions, which are lumped together primarily because the dominant heat transfer mechanism is conduction across the film at the top of the tube. Consequently, this type of condensation is commonly referred to as film condensation. Five gravity-driven flow condensation correlations are listed in Table 3, which, in chronological order, are Chato [45], Rosson and Myers [46], Jaster and Kosky [47], Dobson et al. [9], and Singh et al. [48] correlations. The annular flow regime represents the situation where the interfacial shear stress dominates the gravitational force and results in a nearly symmetric annular film with a high speed vapor core. Table 4 shows 14 annular flow condensation correlations, 6

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which, listed in chronological order, are Akers and Rosson [15], Traviss et al. [49], Cavallini and Zecchin [17], Shah [18], Chen et al. [50], Dobson et al. [51], Dobson and Chato [10], Bivens and Yokozeki [52], Moser et al. [53], Tang et al. [19], Wang et al. [21], Jung et al. [54], Park and Hrnjak [14], and Bohdal et al. [16]. In recent twenty years, several stratified and annular flow condensation correlations were supposed, which are suitable for different flow regimes or based on flow patterns. Most of them have relatively complex forms and good prediction accuracy. The correlations in this category are presented in Table 5, which are Thome et al. [12], Cavallini et al. [55], Cavallini et al. [13], Haraguchi et al. [11], Koyama et al. [24], Koyama et al. [56], Huang et al. [36], Park et al. [57], and Kim and Mudawar [58]. According to Kandlikar and Grande [2] method and the description from the literature, seven of the 28 correlations were proposed for minichannels, which are Wang et al. [21], Park and Hrnjak [14], Bohdal et al. [16], Koyama et al. [24], Koyama et al. [56], Park et al. [57], and Kim and Mudawar [58], and the rest were based on conventional channel data or mixed data from both minichannels and conventional channels. The dimensionless parameters used in the condensation heat transfer correlations in Tables 3–5 are summarized in Table 6.

Table 3 Gravity-driven flow condensation heat transfer correlations Table 4 Annular flow condensation heat transfer correlations Table 5 Stratified and annular flow condensation heat transfer correlations Table 6 Dimensionless parameters employed in condensation heat transfer correlations

4 Evaluation of previous correlations The 2563 experimental data as indicated in Tables 1 and 2 are used for the comparative study of the 28 flow condensation heat transfer correlations as described above. The criterion used for the evaluation is the mean absolute relative deviation (MAD). By the way, the mean relative deviation (MRD) is used to check whether a correlation has an over-prediction or under-prediction in general. M AD 

1 N

MRD 

1 N

N

h  i  pred  h  i  exp

i 1

h  i  exp



N

h  i  pred  h  i  exp

i 1

h  i  exp



(97)

(98)

Twelve correlations have an MAD less than 30% (Table 7), and eight correlations have 30%  MAD < 40% (Table 8).

In

Tables 7 and 8, the Greek symbols δ and ξ express the percentage of the data points having the MRD within ±20% and ±30%, respectively. The twelve correlations having an MAD less than 30% are Cavallini et al. [13], Bivens and Yokozeki [52], Haraguchi et al. 7

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[11], Cavallini et al. [55], Koyama et al. [56], Koyama et al. [24], Dobson et al. [9], Tang et al. [19], Thome et al. [12], Moser et al. [53], Huang et al. [36], and Chen et al. [50], with the MAD of 17.0%, 21.6%, 22.6%, 22.7%, 23.6%, 24.3%, 24.9%, 25%, 25.1%, 25.4%, 25.9%, and 26.3%, respectively. The Cavallini et al. [13] correlation performs best, with δ = 71.6% and ξ = 84.8%. The eight correlations having 30%  MAD < 40% are Shah [18], Park et al. [57], Jaster and Kosky [47], Dobson and Chato [10], Akers and Rosson [15], Chato [45], Cavallini and Zecchin [17], and Wang et al. [21], with the MAD of 30.0%, 31.5%, 33.5%, 33.9%, 37%, 38%, 39.3%, and 39.9%, respectively.

Table 7 Comparisons between predictions of correlations with MAD <30% and the experimental database Table 8 Comparisons between predictions of correlations with 30  MAD <40% and the experimental database

The twenty-eight correlations are also evaluated with the database of conventional channels and minichannels, respectively. With the database of conventional channels, 17 correlations have an MAD less than 30%, which are Cavallini et al. [13], Cavallini et al. [55], Bivens and Yokozeki [52], Dobson et al. [9], Koyama et al. [56], Haraguchi et al. [11], Jung et al. [54], Tang et al. [19], Moser et al. [53], Koyama et al. [24], Huang et al. [36], Shah [18], Dobson and Chato [10], Park et al. [57], Thome et al. [12], Chen et al. [50], and Cavallini and Zecchin [17], with the MAD of 14.4%, 20.5%, 20.6%, 20.6%, 21.5%, 22.1%, 22.1%, 22.7%, 23%, 23.1%, 24.5%, 25.1%, 26.8%, 26.8%, 27.5%, 28.2%, and 29.9%, respectively. For the minichannel database, 13 correlations have an MAD less than 30%, which are Cavallini et al. [13], Thome et al. [12], Bivens and Yokozeki [52], Haraguchi et al. [11], Chen et al. [50], Cavallini et al. [55], and Koyama et al. [56], Koyama et al. [24], Wang et al. [21], Huang et al. [36], Tang et al. [19], Moser et al. [53], and Akers and Rosson [15], with the MAD of 20.6%, 21.9%, 23%, 23.2%, 23.8%, 25.5%, 25.8%, 26.3%, 27%, 27.8%, 28%, 28.5%, and 28.6%, respectively. The results show that most correlations predict conventional channels better than minichannels, and only four exceptions exist which are Thome et al. [12], Chen et al. [50], Akers and Rosson [15], and Wang et al. [21]. Among the four correlations, only the Wang et al. [21] correlation was proposed specifically for minichannels. In addition, some correlations which predicted heat transfer coefficients in conventional channels well are also appropriate for minichannels, such as Cavallini et al. [13], Bivens and Yokozeki [52], Dobson et al. [9], Koyama et al. [56], and Haraguchi et al. [11]. The comparisons between the top five models and each fluid in the entire database are listed in Table 9. For different fluids, the predicted results of the top five correlations are diverse but mostly have MAD within 30%. For refrigerant R134a and R22, which own the most and the second most data points, respectively, the predictions of all the top five correlations are quite good, with the MAD around 20%. For CO2, whose data points number places third, the Koyama et al. [56] correlation predicts best, with an MAD of 16%. For R410A, the Cavallini et al. [13] and Koyama et al. [56] correlation predict best, with an MAD of 22.6% and 25%, respectively. The prediction deviations of the top five correlations against the data points of conventional channels and 8

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minichannels are illustrated in Figs. 3–7.

Table 9 Comparisons between predictions of the top five correlations and the experimental database Fig. 3 Prediction deviations of the Cavallini et al. [13] correlation Fig. 4 Prediction deviations of the Bivens and Yokozeki [52] correlation Fig. 5 Prediction deviations of the Haraguchi et al. [11] correlation Fig. 6 Prediction deviations of the Cavallini et al. [55] correlation Fig. 7 Prediction deviations of the Koyama et al. [56] correlation

5 Conclusion and discussion

(1) A database containing 2563 data points of flow condensation heat transfer of 17 fluids in horizontal channels is compiled from 26 published papers, including 1462 conventional channel data points and 1101 minichannel data points. The parameters cover tube diameter from 0.493 to 20 mm, mass flux from 24 to 1532.1 kg m–2 s–1, saturation temperature from –25.6 to 70.7 °C, quality from 0 to 1, and heat mass from 2.35 to 421.1 kW m–2.

(2) For the compiled database, 28 existing correlations are evaluated. The results show that the Cavallini et al. [13] correlation performs best with an MAD of 17% and an MRD of 0.8%, predicting 71.6% of the entire database within ±20%, and 84.8% within ±30%. The rest 11 correlations having the MAD < 30% are Bivens and Yokozeki [52], Haraguchi et al. [11], Cavallini et al. [55], Koyama et al. [56], Koyama et al. [24], Dobson et al. [9], Tang et al. [19], Thome et al. [12], Moser et al. [53], Huang et al. [36], and Chen et al. [50], with the MAD of 21.6%, 22.6%, 22.7%, 23.6%, 24.3%, 24.9%, 25%, 25.1%, 25.4%, 25.9%, and 26.3%, respectively.

(3) For the 1462 conventional channels data points, 17 correlations have an MAD less than 30%, which are Cavallini et al. [13], Cavallini et al. [55], Bivens and Yokozeki [52], Dobson et al. [9], Koyama et al. [56], Haraguchi et al. [11], Jung et al. [54], Tang et al. [19], Moser et al. [53], Koyama et al. [24], Huang et al. [36], Shah [18], Dobson and Chato [10], Park et al. [57], Thome et al. [12], Chen et al. [50], and Cavallini and Zecchin [17], with the MAD of 14.4%, 20.5%, 20.6%, 20.6%, 21.5%, 22.1%, 22.1%, 22.7%, 23%, 23.1%, 24.5%, 25.1%, 26.8%, 26.8%, 27.5%, 28.2%, and 29.9%, respectively.

(4) For the 1101 minichannel data points, 13 correlations have the MAD less than 30%, which are Cavallini et al. [13], Thome et al. [12], Bivens and Yokozeki [52], Haraguchi et al. [11], Chen et al. [50], Cavallini et al. [55], and Koyama et al. [56], Koyama et al. [24], Wang et al. [21], Huang et al. [36], Tang et al. [19], Moser et al. [53], and Akers and Rosson [15], with the MAD of 20.6%, 21.9%, 23%, 23.2%, 23.8%, 25.5%, 25.8%, 26.3%, 27%, 27.8%, 28%, 28.5%, and 28.6%, respectively. The lowest MAD is 20.6%, indicating a need to develop more accurate correlations for micochannels.

(5) All of the 28 correlations, except for Thome et al. [12], Chen et al. [50], Akers and Rosson [15], and Wang et al. [21], predict 9

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conventional channels better than minichannels. Among the seven correlations developed based on minichannel data, only the Wang et al. [21] correlation performs better for minichannels than conventional channels. On the other hand, some correlations perform relatively well for both conventional channels and microchannels. For example, the Cavallini et al. [13] correlation performs best both for conventional channels and microchannels. Therefore, more efforts should be made to understand the mechanisms associated with the effects of channel size and the mechanisms of follow condensation heat transfer to develop a better correlation.

(6) A number of the correlations do not work well for the database, and the performances of correlations predictions for different fluids are often quite different, which may be because they were developed for different refrigerants or different channels. References [1] Mehendale S S, Jacobi A M, Shah R K. Fluid flow and heat transfer at micro- and meso-scales with application to heat exchanger design. Appl. Mech. Rev. 2000, 53: 175–193. [2] Kandlikar S G, Grande W J. Evolution of micro-channel flow passages – thermohydraulic performance and fabrication technology. Heat Transfer Engineering, 2003, 24(1): 3–17. [3] Kew P A, Cornwell K. Correlations for the prediction of boiling heat transfer in small-diameter channels. Applied Thermal Engineering, 1997, 17: 705–715. [4] Cheng P, Wu H Y, Hong F J. Phase-change heat transfer in microsystems. Journal of Heat Transfer, 2007, 129(2): 101–108. [5] Fang X, Zhou Z, Li D. Review of correlations of flow boiling heat transfer coefficients for carbon dioxide. Int. J. Refrigeration, 2013, 36: 2017– 2039. [6] Li, Wei, Wu, et al. A general criterion for evaporative heat transfer in micro/mini-channels. International Journal of Heat & Mass Transfer, 2010, 53(9–10): 1967– 1976. [7] Harirchian T, Garimella S V. A comprehensive flow regime map for microchannel flow boiling with quantitative transition criteria. International Journal of Heat & Mass Transfer, 2010, 53(13–14): 2694–2702. [8] Dobson M K, Chato J C, Wang S P, Hinde D K, Gaibel J A. Initial condensation comparison of R-22 with R-134a and R-32/R-125. Air Conditioning and Refrigeration Center, College of Engineering, University of Illinois at Urbana–Champaign, 1993. [9] Dobson M K. Chato J C, Wattelet J P, Wattelet J A, Ponchner M, Kenney P J, Shimon R L, Villaneuva T C, Rhines N L, Sweeney K A, Allen D G, Hershberger T T. Heat transfer and flow regimes during condensation in horizontal tubes. Air Conditioning and Refrigeration Center, College of Engineering, University of Illinois at Urbana– Champaign, 1994. [10] Dobson M K, Chato J C. Condensation in smooth horizontal tubes. Journal of Heat Transfer, 1998, 120(1): 193–213. [11] Haraguchi H, Koyama S, Fujii T. Condensation of refrigerants HCFC 22, HFC 134a and HCFC 123 in a horizontal smooth 10

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tube(2nd report, proposals of empirical expressions for the local heat transfer coefficient). NII-Electronic Library Service, 1994, 60(574): 2117–2124. [12] Thome J R, Haja J E, Cavallini A. Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes. International Journal of Heat and Mass Transfer, 2003, 46(18): 3365–3387. [13] Cavallini A, Del Col D, Doretti L, Matkovic M, Rossetto L, Zilio C, Censi G. Condensation in horizontal smooth tubes: a new heat transfer model for heat exchanger design. Heat Transfer Engineering, 2006, 27(8): 31–38. [14] Park C Y, Hrnjak P. CO2 flow condensation heat transfer and pressure drop in multi-port microchannels at low temperatures. International Journal of Refrigeration, 2009, 32(6): 1129–1139. [15] Akers W W, Rosson H F. Condensation inside a horizontal tube. Chemical Engineering Progress Symposium Series, 1960, 56: 145–149. [16] Bohdal T, Charun H, Sikora M. Comparative investigations of the condensation of R134a and R404A refrigerants in pipe minichannels. Int. J. Heat Mass Transfer, 2011, 54(9): 1963–1974. [17] Cavallini A, Zecchin R. A dimensionless correlation for heat transfer in force convection condensation. In 5th Int. Heat Transfer Conference, 1974, 2: 309–313. [18] Shah M M. A general correlation for heat transfer during film condensation inside tube. International Journal of Heat and Mass Transfer, 1979, 22: 547–556. [19] Tang L, Ohadi M M, Johnson A T. Flow condensation in smooth and microfin tubes with HCFC-22, HFC-134a, and HFC-410 Refrigerants. part II: Design equations. Journal of Enhanced Heat Transfer, 2000, 7(5): 311–325. [20] Zhang H Y, Li J M, Liu N, Wang B X. Experimental investigation of condensation heat transfer and pressure drop of R22, R410A and R407C in mini-tubes. International Journal of Heat and Mass Transfer, 2012, 55(13): 3522–3532. [21] Wang W W, Radcliff T D, Christensen R N. A condensation heat transfer correlation for millimeter-scale tubing with flow regime transition. Experimental Thermal Fluid Science, 2002, 26(3): 473–485. [22] Yan Y Y, Lin T F. Condensation heat transfer and pressure drop of refrigerant R-134a in a small pipe. International Journal of Heat and Mass Transfer, 1999, 42(4): 697–708. [23] Liu N, Li J M, Sun J, Wang H S. Heat transfer and pressure drop during condensation of R152a in circular and square microchannels. Experimental Thermal and Fluid Science, 2013, 47: 60–67. [24] Koyama S, Kuwahara K, Nakashita K, Yamamoto K. An experimental study on condensation of refrigerant R134a in a multi-port extruded tube. International Journal of Refrigeration, 2003, 24(4): 425–432. [25] Wang H S, Rose J W. Theory of heat transfer during condensation in microchannels. International Journal of Heat and Mass Transfer, 2011, 54(11): 2525–2534. [26] Traviss D P, Baron A G, Rohsenow W M. Forced-convection condensation inside tubes. Cambridge, Mass: MIT Heat 11

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Transfer Laboratory, 1971. [27] Hinde D K. Condensation of refrigerants 12 and 134a in horizontal tubes with and without oil. Air Conditioning and Refrigeration Center, College of Engineering, University of Illinois at Urbana-Champaign, 1992 [28] Zhang M. A new equivalent Reynolds number model for vapor shear-controlled condensation inside smooth and micro-fin tubes. Department of Mechanical Engineering, Pennsylvania State University, 1998. [29] Cavallini A, Censi G, Del Col D, Diretti L, Longo G A, Rossetto L. Experimental investigation on condensation heat transfer and pressure drop of new HFC refrigerants (R134a, R125, R32, R410A, R236ea) in a horizontal smooth tube. International Journal of Refrigeration, 2001, 24(1): 73–87. [30] Zilly J, Jang J, Hrnjak P S. Condensation of CO2 at low temperature inside horizontal microfinned tubes. Air Conditioning and Refrigeration Center, College of Engineering, University of Illinois at Urbana–Champaign, 2003. [31] Aprea C, Greco A, Vanoli G P. Condensation heat transfer coefficients for R22 and R407C in gravity driven flow regime within a smooth horizontal tube. International Journal of Refrigeration, 2003, 26(4): 393–401. [32] Jang J, Hrnjak P S. Condensation of CO2 at low temperatures. Air Conditioning and Refrigeration Center, College of Engineering, University of Illinois at Urbana-Champaign, 2004. [33] Kim M H, Shin J S. Condensation heat transfer of R22 and R410A in horizontal smooth and microfin tubes. International Journal of refrigeration, 2005, 28(6): 949–957. [34] Agra O, Teke I. Experimental investigation of condensation of hydrocarbon refrigerants (R600a) in a horizontal smooth tube. International Communications in Heat and Mass Transfer, 2008, 35(9): 1165–1171. [35] Kim Y J, Jang J, Hrnjak P S, Kim M S. Condensation heat transfer of carbon dioxide inside horizontal smooth and microfin tubes at low temperatures. Journal of Heat Transfer, 2009, 131(2): 021501. [36] Huang X, Ding G, Hu H, Zhu Y, Peng H, Gao Y F, Deng B. Influence of oil on flow condensation heat transfer of R410A inside 4.18 mm and 1.6 mm inner diameter horizontal smooth tubes. International Journal of Refrigeration, 2010, 33(1): 158–169. [37] Wang L, Dang C, Hihara E. Experimental study on condensation heat transfer and pressure drop of low GWP refrigerant HFO1234yf in a horizontal tube. International Journal of Refrigeration, 2012, 35(5): 1418–1429. [38] Baird J R, Fletcher D F, Haynes B S. Local condensation heat transfer rates in fine passages. International Journal of Heat and Mass Transfer, 2003, 46(23): 4453–4466. [39] Shin J S, Kim M H. An experimental study of condensation heat transfer inside a mini-channel with a new measurement technique. International Journal of Multiphase Flow, 2004, 30(3): 311–325. [40] Shin J S, Kim M H. An experimental study of flow condensation heat transfer inside circular and rectangular mini-channels. Heat transfer engineering, 2005, 26(3): 36–44. 12

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[41] Wen M Y, Ho C Y, Hsieh J M. Condensation heat transfer and pressure drop characteristics of R-290 (propane), R-600 (butane), and a mixture of R-290/R-600 in the serpentine small-tube bank. Applied thermal engineering, 2006, 26(16): 2045–2053. [42] Matkovic M, Cavallini A, Del Col D, Rossetto L. Experimental study on condensation heat transfer inside a single circular minichannel. International Journal of Heat and Mass Transfer, 2009, 52(9): 2311–2323. [43] Del Col D, Torresin D, Cavallini A. Heat transfer and pressure drop during condensation of the low GWP refrigerant R1234yf. International Journal of Refrigeration, 2010, 33(7): 1307–1318. [44] Oh H K, Son C H. Condensation heat transfer characteristics of R-22, R-134a and R-410A in a single circular microtube. Experimental Thermal and Fluid Science, 2011, 35(4): 706–716. [45] Chato J C. Laminar condensation inside horizontal and inclined tubes. ASHRAE J 1962, 4: 52–60. [46] Rosson, H F, Meyers J A. Point values of condensing film coefficients inside a horizontal tube. Chemical Engineering Progress Symposium Series, 1965, 61(59): 190–199. [47] Jaster H, Kosky P G. Condensation in a mixed flow regime. International Journal of Heat and Mass Transfer, 1976, 19(1): 95–99. [48] Singh A, Ohadi M M, Dessiatoun S V. Empirical modeling of stratified-wavy flow condensation heat transfer in smooth horizontal tubes. ASHRAE Transactions, 1996, 102(2): 596–603. [49] Traviss D P, Rohsenow W M, Baron A B. Forced convective condensation in tubes: a heat transfer correlation for condenser design. ASHRAE Transactions, 1973, 79(1): 157–165. [50] Chen S L, Gerner F M, Tien C L. General film condensation correlations. Experimental Heat Transfer, 1987, 1(2): 93-107. [51] Dobson M K, Chato J C, Hinde D K, et al. Experimental evaluation of internal condensation of refrigerants R-134a and R-12. Air Conditioning and Refrigeration Center. College of Engineering. University of Illinois at Urbana-Champaign, 1993. [52] Bivens D B, Yokozeki A. Heat transfer coefficient and transport properties for alternative refrigerants. Purdue, Indiana: International Refrigeration and Air Conditioning Conference, 1994: 299–304. [53] Moser K W, Webb R L, Na B. A new equivalent Reynolds number model for condensation in smooth tubes. ASME J. Heat Transfer, 1998, 120(2): 410–417. [54] Jung D, Song K, Cho Y, Kim S J. Flow condensation heat transfer coefficients of pure refrigerants. Int. J. Refrigeration, 2003. 26(1): 4–11. [55] Cavallini A, Censi G, Del Col D, Doretti L, Longo G A, Rossetto L. In-tube condensation of halogenated refrigerants. ASHRAE Transactions, 2002, 108(1): 146–161. [56] Koyama S, Kuwahara K, Nakashita K. Condensation of refrigerant in a multi-port channel. New York: International Conference on Microchannels and Minichannels, 2003: 193–205. 13

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[57] Park J E, Vakili-Farahani F, Consolini L, Thome J R. Experimental study on condensation heat transfer in vertical minichannels for new refrigerant R1234ze (E) versus R134a and R236fa. Experimental Thermal and Fluid Science, 2011, 35(3): 442–454. [58] Kim S M, Mudawar I. Universal approach to predicting heat transfer coefficient for condensing mini/micro-channel flow. Int. J. Heat Mass Transfer, 2013, 56(1): 238–250.

14

Page 14 of 30

Fig. 1 Laminar/Turbulent distribution of the experimental data Fig. 2 Distribution of heat transfer coefficient relative to vapor quality Fig. 3 Prediction deviations of the Cavallini et al. [13] correlation Fig. 4 Prediction deviations of the Bivens and Yokozeki [52] correlation Fig. 5 Prediction deviations of the Haraguchi et al. [11] correlation Fig. 6 Prediction deviations of the Cavallini et al. [55] correlation Fig. 7 Prediction deviations of the Koyama et al. [56] correlation

15

Page 15 of 30

6

10

5

10

4

10

3

10

2

10

1

vt

tt

vv

tv

ReV

10

10

1

10

2

10 ReL

3

10

4

10

5

Fig. 1 Laminar/Turbulent distribution of the experimental data

20

-2

-1

h (kW m K )

30

10

0 0.0

0.2

0.4

x

0.6

0.8

1.0

Fig. 2 Distribution of heat transfer coefficient relative to vapor quality

16

Page 16 of 30

(b) 100

(a) 100 30%

30%

hpred (kW m K )

-30%

10

-2

-1

10

-2

-1

hpred (kW m K )

-30%

1

1

D > 3 mm MAD = 14.4% = 77.6%  = 92.7% 1

10 -2 -1 hexp (kW m K )

100

D < 3 mm MAD = 20.6% = 63.7%  = 74.3% 1

10 -2 -1 hexp (kW m K )

100

Fig. 3 Prediction deviations of the Cavallini et al. [13] correlation

(b) 100

(a) 100

30%

30%

-30%

hpred (kW m K )

10

-2

-1

10

-2

-1

hpred (kW m K )

-30%

1

1

D > 3 mm MAD = 20.6% = 60.2%  = 81.6% 1

10 -2 -1 hexp (kW m K )

100

D < 3 mm MAD = 23% = 59.3%  = 74.8% 1

10 -2 -1 hexp (kW m K )

100

Fig. 4 Prediction deviations of the Bivens and Yokozeki [52] correlation

17

Page 17 of 30

(a) 100

(b) 100 30%

30% -30%

-1

hpred (kW m K )

10

10

-2

-2

-1

hpred (kW m K )

-30%

1

1

D > 3 mm MAD = 22.1% = 54%  = 73.2% 1

10 -2 -1 hexp (kW m K )

100

D < 3 mm MAD = 23.2% = 47.1%  = 71.4% 1

10 -2 -1 hexp (kW m K )

100

Fig. 5 Prediction deviations of the Haraguchi et al. [11] correlation

(a) 100

(b) 100 30%

30%

hpred (kW m K )

-30%

10

-2

-1

10

-2

-1

hpred (kW m K )

-30%

1

1

D > 3 mm MAD = 20.5% = 52.5%  = 78% 1

10 -2 -1 hexp (kW m K )

100

D < 3 mm MAD = 25.5% = 54.2%  = 68.5% 1

10 -2 -1 hexp (kW m K )

100

Fig. 6 Prediction deviations of the Cavallini et al. [55] correlation

18

Page 18 of 30

(a) 100

(b) 100 30%

30%

hpred (kW m K )

-30%

10

-2

-1

10

-2

-1

hpred (kW m K )

-30%

1

1

D > 3 mm MAD = 21.5% = 52.1%  = 73.2% 1

10 -2 -1 hexp (kW m K )

100

D < 3 mm MAD = 26.3% = 42.2%  = 61.6% 1

10 -2 -1 hexp (kW m K )

100

Fig. 7 Prediction deviations of the Koyama et al. [56] correlation

19

Page 19 of 30

Table 1 Experimental data sources of condensation heat transfer in conventional horizontal circular tubes Table 2 Experimental data sources of condensation heat transfer in conventional horizontal circular minichannels Table 3 Gravity-driven flow condensation heat transfer correlations Table 4 Annular flow condensation heat transfer correlations Table 5 Stratified and annular flow condensation heat transfer correlations Table 6 Dimensionless parameters employed in condensation heat transfer correlations Table 7 Comparisons between predictions of correlations with MAD <30% and the experimental database Table 8 Comparisons between predictions of correlations with 30  MAD <40% and the experimental database Table 9 Comparisons between predictions of the top five correlations and the experimental database

20

Page 20 of 30

Table 1 Experimental data sources of condensation heat transfer in conventional horizontal circular tubes D(mm)/L(mm)/ Author(s) Refrigerant(s) Tsat(C)/psat(Mpa)/G(kg m–2 s–1)/q(kW m–2)/x material Traviss et al. [26] R12, R22 8.001/5029/copper 21.4–59/0.59–1.83/161.1–59/7.86–85.43/0.02–0.96 Hinde et al. [27] R12, R134a 4.57/2950/copper 35–60/0.85–1.68/75–300/2.35–15.52/0.1–0.83 Dobson et al. [8] R22, R134a, 4.572/#/copper 35–45/0.89–2.76/69–512/3.12–16.08/0.08–0.96 60%R32/40%R125 Dobson et al. [9] R22, R134a, R410A, 3.14, 7.04/#/copper 33.5–46.4/0.85–2.85/24–812/2.98–54.95/0.02–0.95 60%R32/40%R125 Haraguchi et al. [11] R22, R123, R134a 8.4/6000/copper 47.91–70.67/0.38–1.85/300/14.42–27.3/0.03–0.95 Zhang [28] R22, R134a, R404A 3.25, 6.2/914/copper 25–65/0.99–1.94/200–1403/8–12/0.19–0.83 Cavallini et al. [29] R125, R134a 8/1600/copper 40/1.02–2.01/65–200/4.4–9.7/0.22–0.78 Zilly et al. [30] R22, CO2 6.1/150/copper (–25)–10/1.67–2.29/200–400/7.07–43.5/0.1–0.81 Aprea et al. [31] R22 20/6600/copper 37.1–39.6/1.43–1.5/45.5–120/8.69–42.76/0.08–0.88 Jang and Hrnjak R22, CO2 6.1/150/copper (–25.58)–20/0.25–2.25/197.1–406.2/8–36.4/0.1–0.9 [32] Kim and Shin [33] R22, R410A 8.7/920/copper 45/1.73–2.73/280.36/11/0.15–0.82 Agra and Teke [34] R600a 4/#/copper 43/0.57/92/7.57–25.71/0.45–0.9 Kim et al. [35] CO2 3.48/1000/copper (–25)/1.68/200–800/8.77–85.12/0.09–0.9 Huang et al. [36] R410A 4.18/1720/copper 40/2.43/200–600/4.23–19.07/0.19–0.82 Wang et al. [37] R32, R134a, 4/3400/copper 40–50/1.02–2.48/100–401/5.5–31.7/0.11–0.92 R1234yf # the value is not found.

Table 2 Experimental data sources of condensation heat transfer in horizontal circular minichannels D(mm)/L(mm)/ Author(s) Refrigerant(s) Tsat(C)/psat(Mpa)/G(kg m–2 s–1)/q(kW m–2)/x material Zhang [28] R134a 0.96–2.13/508 25–65/0.99–1.94/200–1403/8–12/0.19–0.83 /aluminum Yan and Lin [22] R134a 2/200/# 25–50/0.67–1.32/100–200/10–20/0.08–0.96 Baird et al. [38] R123 1.95/30/# 20.9–55.31/0.29–0.3/170/14.13–68.71/0.11–0.97 Shin and Kim [39] R134a 0.691/171/copper 40/1.02/100–600/5–20/0.1–0.92 Shin and Kim [40] R134a 0.493/171/copper 40/1.02/200/6–20/0.25–0.85 Wen et al. [41] R134a, R290, R600, 2.46/3850/copper 40/0.38–1.37/205–320/5.2/0.12–0.84 50%R600/50%R290 Park and Hrnjak [14] CO2 0.89/150/aluminum (–25)–(–15)/1.67–2.29/200–800/6.13–28.7/0.09–0.9 Matkovic et al. [42] R32, R134a 0.96/225/copper 40–40.4/1.02–2.5/100–1200/12.4–325.46/0.01–0.99 Del Col et al. [43] R1234yf 0.96/230/copper 39.83–40.58/1.01–1.03/800/54.98–140.86/0.2–0.85 Huang et al. [37] R410A 1.6/1720/copper 40/2.43/200–600/4.23–19.07/0.19–0.82 Oh and Son [44] R22, R134a, R410A 1.77/1220/copper 40/1.02–2.43/450–1050/29.65–421.14/0.22–0.87 Zhang et al. [20] R22, R407C, R410A 1.088, 40/1.53–2.43/300–600/12.09–146.17/0.01–0.88 1.289/200/steel Liu et al. [23] R152a 1.152/336/steel 40–50/0.91–1.18/200–800/20.31–136.75/0.11–0.9

Data point 161 60 130 647 30 64 15 42 66 90 11 15 20 21 90

Data point 42 76 18 74 14 64 113 359 11 14 108 160 48

21

Page 21 of 30

Author(s) Chato [45]

Table 3 Gravity-driven flow condensation heat transfer correlations Remarks 0.25 Based on Nusselts theory and test on (1)  0.555  G rPrL / Ja   R113 in 27.94 mm tube. (2)   Nu top  1    Nu bot

Equation Nu

Nu

 G rPrL

N u top  0.31 ReV

0.12

N u bot  0.2  L  8 Re L 

/ Ja ' 

0.25

0.1  R eV

Rosson and Myers [46]

(4)

if R eV R e L / G r  6.4  10 0.6

 

1.74  10 G r /  R eV R e L  5

1

0.5

0.6 V

if R e

0.5

Re

0.5 L

5

/ G r  6.4  10

(5)

5

2

 L  1  X vt  12 X vt 2

X vt 

 fL

/ fV



0.5

(6)

 1  x  / x    V /  L 

16 R e k  1   0.25 f k   0.079 R e k  0.046 R e  0.2 k 

Jaster and Kosky [47]

(3)

/ 1  ln 1  5 PrL  / PrL 

0.5

N u  0.728 

0.75

  1    V /  L  

(7)

for R e k  2000 for 2000  R e k  20000

(8)

for R e k  20000

 G rPrL 2/3

0.5

/ Ja ' 

0.25

1  x  / x 

(9)

(  1)

(Zivi void fraction)

(10)

Nu  Nu top  1   /   Nu bot

(11)

    arccos  2   1 

(12)

where α is calculated with Eq. (10) Dobson et al. [9]

N u top  0.23 R eV O

0.12

 G rP rL

N u bot  0.0195 Re L PrL 0.8

0.4

/ Ja ' 

0.25

/ 1  1.11 / X tt

1.376  C

0.58

C

1

/ X tt 2





(13)

0.5

(14)

 for 0  F rL  0.7 C 1  4.172  5.48 F rL  1.564 F r , C 2  1.773  0.169 F rL  C 1  7.242, C 2  1.655  for F rL  0.7 2 L

Nu   Nu bot   2     Nu top 1

N u bot  0.023 Re

0.8 L

0.4 L

Pr

1  0.2332 / X

Based on their own experiments of R12, R22, R134a, R410A, 60%R32/ 40%R125 in 7.04 mm and 3.14 mm ID tubes. Experimental range: Tsat = 33.5–46.4 °C, G = 25–800 kg m–2 s–1, x = 0.02–0.95.

(15)

 2   1 where α is calculated with Eq. (10) 0.25 N u top  0.09253  G rPrL / Ja '    2 cos

Singh et al. [48]

Based on Chatos model and experiment of water in12.5 mm tube, with G = 12.6–145 kg m–2 s–1.

1.402 tt

(16) (17)



Based on their own experiments of R134a in 11 mm tubes. Experimental range: G = 20–500 kg m–2 s–1, q = 10–30 kW m–2, ReL = 1200–24000.

(18)

22

Page 22 of 30

Author(s) Akers and Rosson [15] Traviss et al. [49]

Table 4 Annular flow condensation heat transfer correlations Equation Remarks 0.8 0.5 Based on data of R12 and propane in 19.05 0.8 0.333 (19) N u  0.026 Re L PrL   x / 1  x     L /  V   1 mm tube. 0.9 Based on R12 and R22 data. Experimental (20) N u  R e L P rL F1 / F2 range: D = 8 mm, Tsat = 25–58.3 °C, G = a  0.476 (21) F1  0.15 1 / X tt  2.85 X tt  161.4–1532 kg m2 s–1, PrL > 3. for X tt  0.155 , a  1 ; for X tt  0.155 , a  1.15  0.7 07 P r R e 0.5 if R e L  50 L L   0.585 F2   5 P rL  5 ln 1  P rL  0.0964 R e L  1  if 50  R e L  1125    0.812 5 P rL  5 ln  1  5 P rL   2.5 ln  0.00313 R e L  if R e L  1125  

Cavallini and Zecchin [17] Shah [18]

N u  0.05 Re L PrL 0.8

0.33

  x / 1  x    

N u  0.023 R e LO P rL 0.8

0.4

1  3.8  x / 1  x  

Chen et al. [50]

N u  0.018   L /  V

Dobson et al. [51]

Nu  0.023 Re L PrL

 2.61 / X

Dobson and Chato [10]

N u  0.023 Re L PrL

1  2.22 / X

Bivens and Yokozeki [52] Moser et al. [53]

N u  N u shah  0.78738  6187.89 / G

0.8



0.3

0.8

 V /  L 

0.39

0.4

C

Nu 

0.078

where

C 1  0.126 P r

H    L / V



 Re LO

0.035

  L /  V   fVO

2

0.91

 V /  L 

0.19

2

 cm   x /  V   1  x  /  L 

f kO

1 16 R e kO   0.25   0.079 R e kO  0.046 R e  0.2 kO 

 19.1 



(30)

/ f LO 

,

F  x

1   V /  L 

0.78

1  x 

0.24

0.7

,

1

if R e kO  2000 if 2000  R e kO  20000 if R e kO  20000 0.4

0.6792

x

0.22 08

0.836

 V / X tt

(31)

(32)

1.665 tt

(33)

Jung et al. [54]

N u  0.5152 R e L P rL

Park and Hmjak [14]

N u  D  c p,L / L 

0.8

Based on 1197 data points of R11, R12, R125, R22, R134a and R410A in D = 3.14–20 mm.

8/7

N u  0.0274 PrL Re L  1.376  8 X

(25)

Based on R12, R22, R113 data. 7000 ≤ ReLO ≤ 53000. Based on a database of 474 data points of 10 fluids condensing in horizontal, vertical, and inclined pipes Based on analytical and empirical results with experimental data of condensation inside vertical tubes from the literature. Experiment on R134a, R12 in 4.57 mm tube. Experimental range: G = 75–500 kg m–2 s–1, Tsat = 35 and 60°C, q = 4–15 kW m–2, x = 0.1–0.9. Experiment on R12, R22, R134a, R410A, 60%R32/40%R125 in 7.04mm and 3.14mm tube. Experimental range: G = 75–800 kg m–2 s–1, Tsat = 35–45 °C, q = 5–15 kW m–2, x = 0.1–0.9. Modified Shah’s correlation.

Reeq   LO Re LO

,

Wang et al. [21]



0.65

PrL

(29)

N u  0.023 R e L P rL (1  4.863   ln  p rd  x / 1  x  

2 V

(24)

0.815

P rL

Tang et al. [19]

0.8

0.7

0.8

(28)

2

2

 Re L 



Frcm  G /  gD  cm  , W ecm  G D /   cm 2

1  x 

(27)

C 2   0.113 Pr

0.045

2

0.2

Re L





0.89 tt

 LO  E  3.24 FH /  Frcm W e cm 2

(23)

0.38

 0.563 L

,

0.8

/ p rd

 3.28   2.58 lnR e eq  13.7 P r  0.448 L



1

0.76

2/3 L

eq

E  1  x   x

0.5

(26)

1  0.875 C1

C





0.805 tt

0.0994 1 R e L 2 R e eq

1.58 lnR e

/ V

L

(22)

0.4

0.333

1  2 /

 7 /15

L

X tt 

0.81

 q /  G H L V  

  x / 1  x    

L

/ V



0.33

0.5

(34)



1

(35)

Based on data of R22, R134a, and R410A in 8.81 mm tube; Tsat = 35–45°C, G = 250–810 kg m–2 s–1, q = 5.5–37 kW m–2. R134a in a horizontal rectangular multi-port aluminum tube of 1.46 mm hydraulic diameter. Based on data of R12, R22, R32, R123, R125, R134a, R142b in 9.52 mm tube. Experimental range: Tsat = 40 °C, G = 100–300 kg m–2 s–1, q = 7.3–7.7 kW m–2. Based on data of CO2 in 0.89 mm tube. Experimental range: Tsat = –15 and –25 °C, G = 200–800 kg m–2 s–1.

23

Page 23 of 30

Bohdal et al. [16]

N u  25.084 R e L

0.258

 0.495

P rL

 0.288

p rd

 x / 1  x  

0.266

(36)

Based on data of R134a and R404A in pipes with D = 0.31–3.30 mm, Tsat = 30–40 °C, x = 0–1, G = 100–1300 kg m–2 s–1.

24

Page 24 of 30

Table 5 Stratified and annular flow condensation heat transfer correlations Author(s) Thome et al. [12]

Equation N u   r N u F   2     rN u C  /  2  r 

Nu C  0.003 Re L ,Thome PrL f i D /  0.74

0.5

N u F  0.728  G rPrL / Ja 

,

R e L , T hom e  4 G 1  x   /  1     L 

 h  1    V /  L  1  x  / x 

 ra

, 

0.25

(38)

   h   ra  / ln   h /  ra 

(  1)

(39)

(40)

0.25   x   x 1  x  1.18 1  x   g    L   V         1  0.12 1  x      0.5 V L  GL  V      

  1      3  / 2 1 / 3 1  2 1     1    

 strat  2   2 

  0.05  1    1  2 1     1  4 1   

AL   1    A

ALd  1    A / D

,

PL d  sin   2    strat  / 2 

x  2

AV d   A / D

,

2

 W e

2

/ h Ld

/ F rL 

L

1   2 H Ld  1 

2

2

1/ 3





(41)

(42)



 1 

2

2 2 2 3 G strat  226.3 A L d AV d  V   L   V   L g /  x 1  x   

    

(  1)

H L d  0.5 1  cos   2    strat  / 2 

,

 1.023

1/ 3

2   

2



3 16 AVd gD  L  V   0.04  

G w avy 

2





 1.138  2 log   / 1.5 ALd  

, 



1/ 3





2    0 .5 D   D  8 A L /  2     

0.5

if    r ,     if    r ,   r Cavallini et al. Dimensionless vapor velocity: [55] (a) for JV ≥ 2.5, annular flow

T



0.5

2   x 2  0.97   50  75 exp    x 1  x  

 20 x





J V  xG /  gD  V   L   V  

 D / L 

2

E  1  x   x 2



2

/ 30   if  

(44)

2

0.1458

 V /  L 

1  16  G D /  k  f ko    0.2   0.046  G D /  k 

f LO 

 1.181

,

2

/  

0.25

0.5

Based on 600 data points of R22, R134a, R125, R32, R236ea, R407C, and R410A in an 8 mm tube, at saturation temperature of 30 and 50°C, mass velocities from 100 to 750 kg m–2 s–1.

(46)

 5





 30

(48)

 30

(49)

 LO  E  1.262 FH / W eV

  L f VO  /   V

0.3278



if R e L  1145

,



if 5  

if R e L  1145

2

H    L / V

if 



  0.5  LO f LO G /  L

(43)

(47)



  R e / 2  L  7 /8  0.0504 R e L

   

(45)

   P rL       T  5 P rL  ln 1  P rL   / 5  1        T  5  P rL  ln  1  5 P rL   0.495 ln   0.5



/T





2

0.25 0.5 2  for G  G ,   0, f i  1    V /  L     L   V  g  /   w avy  0.5 0.5   for G strat  G  G w avy ,    strat   G w avy  G  /  G w avy  G strat   , f i  1    V /  L     L   V  g   0.25 0.5 2  G / G strat   for G  G strat ,    strat , f i  1    V /  L     L   V  g  /   

N u an    L c p , L    /  L 

Remarks Proposed a new simplified flow structures of the flow regimes, and compared to test data for 15 fluids with: D = 3.1–21.4 mm, G = 24–1022 kg m–2 s–1, x = 0.03–0.97, prd = 0.02–0.8.

(37)

F  x

0.6978

1   V /  L 

(50)

,

3.477

for R e kO  2000 for R e kO  2000

(b) for JV < 2.5 and Xtt < 1.6, annular-stratified flow transition and stratified flow Nu trans   Nu an  Nu strat  J V / 2.5   Nu strat (51)



N u strat  0.725 1  0.82  1  x  / x 

0.268



1

 G rP rL

/ Ja 

0.25

 N u LO 1  x 

N u LO  0.023 Re LO PrL

(53)

    arcos  2   1 

(54)

0.8

0.4

0.8

1   /  

(52)

where α is calculate by Eq. (10) (c) for JV < 2.5 and Xtt > 1.6, stratified–slug transition and slug flow 25

Page 25 of 30

N u slug  N u LO  x ( N u an , x 1.6  N u LO ) / x1.6

x1.6    L /  V

Cavallini et al. [13]

  V /  L 

5/9

T 1.111 J V   7.5 /  4.3 X tt  1   

3

1/ 9



(55)

/ 1.686    L /  V  3

 CT



  V /  L  1/ 9

5/9

 

(56)

1/ 3

(57)

for hydrocarbons, CT = 1.6; other refrigerants, CT = 2.6 JV is calculated by Eq. (46) (a) for JV > JVT, ∆T independent flow regime 0.817 N u an  N u L O 1  1.128 x   L / V 



0.3685

  L / V 

0.2363

1   V /  L 

2 .144

 0.1

P rL

 

(58)

where NuLO is calculated by Eq. (53). (b) for JV ≤ JVT, ∆T dependent flow regime T N u   N u an  J V / J V 



0.8

 N u strat   J V / J V 

T



N u strat  0.725 1  0.741  1  x  / x 

Haraguchi et al. [11]

Nu 

NuF  NuB 2

N u F  0.0152 Re L

0.77



1  0.6 Pr   0.8 L

1

 G rP rL

/ Ja 

0.25

 N u LO 1  x



0.1

V

0.087



(60) Test on R22, R134a, R123 condensating in 8mm horizontal tube. PrL = 2.5–4.5, ReL = 200–20000, ReLO = 3000–30000, Xtt = 0–1300, GaLPrL/HLV = 4.8×109–9.5×1010.

(63)



0.75 0.35

 V   1  x      0.4  0.6   L   x  

(64)

X tt

 1   1.7  10 

  1  

(62)

/ X tt

0.25

gD V   L  V



 



(59)

strat

(61)

H       10  1     

0.3321

2

N u B  0.725 H     G a L PrL / Ja   V  1  0 .5 G /

  Nu

4



R e LO 

0.5

1    0.5

 L /  V  0.4 1  x  / x  

(65)

1

   

1  0.4 1  x  / x

(66)

Koyama et al. [24]

They modified Haraguchi et al. [11] method by replacing Eq. (64) with 2 2  V  1  21 1  exp   0.319 D   X tt  X tt (67)

Koyama et al. [56]

They used Haraguchi et al. [11] equation (61), where NuF and NuB are calculated by 0.7 1.37 N u F  0.0112 R e L P rL  V / X tt (68) N u B  0.725 1  exp   0.85 B d   V  1  13.17  L /  V



0.17

H       10 1   



0.1

2

Huang et al. [36]

0.5

  H     G a

L

P rL / Ja 

0.25

1  exp   0.6 B d 0.5   X tt  X tt2  

 8.9   

0.5

1    0.5

(69) (70) (71)

where the void fraction α is calculated with Eq. (66). They modified Haraguchi et al. [11] corelation by replacing Eq. (62) with 0.77 0.8 (72) N u F  0.0152 Re L   0.33  0.83 PrL   V / X tt

 V  1  13.17  L /  V 2



0.17

0.5

  H     G a

L

P rL / Ja 

0.25

1  exp   0.6 B d 0.5   X tt  X tt2  

(74) (75)

where H(α) is calculated by Eq. (71) and α is determined by Eq. (66).

Kim and Mudawar [58]

 2.4 5 R e 0.64 /  S u 0.3 1  1.0 9 X 0.039 0.4  if R e L  1 2 50   V tt  V O   ' We   0.084 0.4 0.79 0.157 0.3 0.039    /   2  /     0 .8 5 R eV X tt /  S u V O 1  1.0 9 X tt   if R e L  1 2 50 L V L   V  

 0.048 Re L0.69 PrL0.34  V / X tt  Nu   2 2 0.69 0.34 7  0.38 1.39   0.048 Re L PrL  V / X tt    3.2  10 Re L Su VO  V  1  CX  X 2

X

2

2

 f L L  1  x  / 2

(78)

f V

V

x

2



(79)

for W e  7 X tt '

0.2

for W e  7 X tt '

0.2

Expreiment on R134a in 1.11 mm and 0.8 mm rectangular tubes. Based their own experimental data on R134a in four multi-port extruded aluminum tubes, with D ≈ 1 mm, G = 100–700 kg m–2 s–1, Tsat = –8–17 °C. Test on R410A in 4.18 mm and 1.6 mm tubes.

Park et al. [57] They used Haraguchi et al. [11] equation (61), where NuF and NuB are calculated by 0.7 1.37 N u F  0.0055 R e L P rL  V / X tt (73) N u B  0.746 1  exp   0.85 B d 

Developed from an extensive analysis of 425 experimental heat transfer data points, compared against a total number of 4471 data points. D > 3 mm.

(77)

(76)

Experiment on R1234ze, R134a and R236fa in 1.45 mm multi-port extruded rectangular aluminum tubes. Tsat = 25–70 °C, G = 50–260 kg m–2 s–1, q = 1–62 kW m–2, x = 0–1. Based on 4045 data points from 28 sources, consisting of 17 different working fluids. Test condition: D = 0.424 –6.22 mm, G = 53–1403 kg m–2 s–1, ReLO = 276– 89798, x = 0–1, prd = 0.04–0.91.

26

Page 26 of 30

16 R e k 1   0.25 f k   0.079 R e k  0.046 R e  0.2 k 

if R e k  2000 if 2000  R e k  20000

(80)

if R e k  20000

 0.39 R e 0.03 Su 0.1   /   0.35 LO VO L V  0.14 4 0.17 0.5  8.7  10 R e L O Su V O   L /  V  C  0.36 0.59 0.19  0.0015 R e L O Su V O   L /  V  0.48 5 0.44 0.5   3.5  10 R e L O Su V O   L /  V 

for R e L  2000 and R eV  2000 for R e L  2000 and R eV  2000 for R e L  2000 and R eV  2000

(81)

for R e L  2000 and R eV  2000

27

Page 27 of 30

Table 6 Dimensionless parameters employed in condensation heat transfer correlations Parameter Definition 2 Bond number (82) Bd  g   L   V  D /  Froude number

Frk  G /  gD  k

Galieo number

G a L   L gD /  L

Grashof number

Gr   L g   L   V  D / 

Jakob number

Ja  c p , L  Tsat  Tw  / H LV

(86)

Modified Jakob number

Ja '  c p , L  Tsat  Tw  / H LV '

(87)

2

2

2

3

(83)

2

(84) 3

where

2 L

(85)

  H LV  0.68 c p , L  Tsat  Tw  H LV

Nu k  hD /  k

Nusselt number Prandtl number

P rk   k c p , k /  k

Reynolds number

ReV  GxD /  V

Liquid- or vapor-only Reynolds number Liquid- or vapor-only Suratman number Weber number

RekO  GD /  k

Reduced pressure Lockhart-Martinelli parameter



(89) (90) ,

Re L  G 1  x  D /  L

(93)

W ek  G D / (  k )

(94) (95)

2

2

p rd  p sat / p crit



0.1

(91)

(92)

Su kO   k  D /  k

X tt    L /  V

(88)

 1  x  / x 

0.9

 V /  L 

0.5

(96)

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Table 7 Comparisons between predictions of correlations with MAD <30% and the experimental database Conventional channels Minichannels All Data Correlation MAD MRD δ a ξb MAD MRD δ ξ MAD MRD δ ξ (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) Cavallini et al. [13] 14.4 –6.1 77.6 92.7 20.6 10 63.7 74.3 17.0 0.8 71.6 84.8 Bivens and Yokozeki [52] 20.6 –4 60.2 81.6 23 12.2 59.3 74.8 21.6 3 59.8 78.6 Haraguchi et al. [11] 22.1 3.5 54 73.2 23.2 –0.1 47.1 71.4 22.6 2 51 72.4 Cavallini et al. [55] 20.5 –13.5 52.5 78 25.5 18.5 54.2 68.5 22.7 0.3 53.3 73.9 Koyama et al. [56] 21.5 –0.6 52.1 73.2 26.3 –9.7 42.2 61.6 23.6 –4.5 47.9 68.2 Koyama et al. [24] 23.1 3.2 50.3 70.6 25.8 –3.7 37.9 63.7 24.3 0.3 45 67.6 Dobson et al. [9] 20.6 –1.7 57.7 73.7 30.4 –5.8 36.6 53.5 24.9 –3.5 48.6 65 Tang et al. [19] 22.7 –9.2 55.5 68.4 28 22.2 55 68.8 25.0 4.3 55.3 68.6 Thome et al. [12] 27.5 –24.4 32.8 50.3 21.9 –13.2 49.5 75.3 25.1 –19.6 40 61.1 Moser et al. [53] 23 –11.1 52.8 68.4 28.5 18.2 50.7 67 25.4 1.5 51.9 67.8 Huang et al. [36] 24.5 –3 47.5 65.7 27.8 –14.3 39.1 52.7 25.9 –7.9 43.9 60.2 Chen et al. [50] 28.2 –22.1 45.6 61.1 23.8 –5.3 53 69.6 26.3 –14.9 48.7 64.8 a δ denotes the percentage of the data points having the MRD within ±20%. b ξ stands for the percentage of the data points having the MRD within ±30%.

Table 8 Comparisons between predictions of correlations with 30  MAD <40% and the experimental database Conventional channels Minichannels All Data MAD MRD δ ξ MAD MRD δ ξ MAD MRD δ ξ Correlation (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) Shah [18] 25.1 –3.4 47.2 63.1 36.5 31 39 57 30 11.4 43.7 60.5 Park et al. [57] 26.8 –11.2 43.4 60 37.8 –32.4 26.8 39.2 31.5 –20.3 36.3 51.7 Jaster and Kosky [47] 30.3 –14.3 38.9 53.4 37.9 –18.8 27.7 41.2 33.5 –16.2 34.1 48.1 Dobson and Chato [10] 26.8 3.2 45.1 62 43.4 40.6 30.2 44.9 33.9 19.3 38.7 54.7 Akers and Rosson [15] 43.4 –43.1 11.7 22.5 28.6 –22 31.2 53.3 37 –34 20.1 35.7 Chato [45] 33.6 –20.6 33.8 49.6 43.8 –21.6 23.3 35.6 38 –21 29.3 43.6 Cavallini and Zecchin [17] 29.9 9.2 41.7 57.9 51.7 49.6 26.5 36.6 39.3 26.5 35.2 48.7 Wang et al. [21] 49.5 –49.4 4.4 10.4 27 –21.3 34.2 56.2 39.9 –37.3 17.2 30.1

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Table 9 Comparisons between predictions of the top five correlations and the experimental database Cavallini et al. Bivens and Haraguchi et al. Cavallini et al. Koyama et al. Data [13] Yokozeki [52] [11] [55] [56] Refrigerant points MAD MRD MAD MRD MAD MRD MAD MRD MAD MRD (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) R12 132 19.1 –16.9 27.3 –26.2 33.1 –19.3 23.6 –22.2 38.1 –22.7 R123 27 22.2 19.6 24.6 10 24.7 14.3 51.3 47.3 41.2 41 R1234yf 71 22.5 –20.8 19.2 –18.2 21.8 –21.2 27.1 –25.7 16.4 –11.4 R125 10 5.1 –0.9 9.3 –0.1 9.6 9.2 27.6 –27.6 13.7 13.7 R134a 748 13.7 –2.6 17.1 –4.6 19.6 –1.8 18.9 3 22.3 1.5 R152a 48 18.6 18 14 11.9 12.9 –6.2 27 27 22.2 –18 R22 577 15.9 –2 23.3 –1.6 19.2 –2.1 23 –7.2 21.5 –7.5 R290 16 21.2 –21.2 13.7 –11.8 15.8 –15.1 19.9 –19.9 20.6 –18.6 R32 212 7.5 –0.6 16.1 12.2 14.9 –10.5 8.9 –2.3 34 –33.8 R404A 16 9.7 –9.7 10.8 –2.7 17.6 –17.6 16 –16 12.3 –10.5 R407C 43 48.5 48.2 50.6 50.1 24.7 18.8 52.5 52.1 20.6 20.2 R410A 221 22.6 4 30.4 18.5 31 13.4 29.4 –7.7 25 –2.7 R600 16 21.2 –21.2 24.2 –24.2 20.3 –18.3 16.2 –13.8 24.7 –22.3 R600a 15 14.5 –14 40.1 40.1 6.3 –2.7 6.1 –1.1 9.1 8.5 60%R32/ 149 11.9 1.6 15.2 13.1 27.9 19.7 15.7 –9.7 25.8 7.6 40%R125 50%R600/ 16 28.7 –28.7 26.5 –25.5 22.4 –22.4 23.2 –23.2 27.2 –27.2 50%R290 CO2 246 26.8 24.1 25.9 22.3 33.5 33.2 34.1 31 16 8.2 Total 2563 17 0.8 21.6 3 22.6 2 22.7 0.3 23.6 –4.5

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