Flow boiling in horizontal multiport tube: Development of new heat transfer model for rectangular minichannels

International Journal of Heat and Mass Transfer 144 (2019) 118668

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

Flow boiling in horizontal multiport tube: Development of new heat transfer model for rectangular minichannels Daisuke Jige ⇑, Shogo Kikuchi, Hikaru Eda, Norihiro Inoue Tokyo University of Marine Science and Technology, 2-1-6, Etchujima, Koto-ku 135-8533, Japan

a r t i c l e

i n f o

Article history: Received 4 February 2019 Received in revised form 13 July 2019 Accepted 31 August 2019 Available online 16 September 2019 Keywords: Flow boiling Heat transfer Visualization Pressure drop Multiport tube

a b s t r a c t The flow boiling characteristics of R32 and R1234ze(E) were investigated in a horizontal multiport tube with rectangular minichannels. The local heat transfer coefficient and frictional pressure drop were measured under mass fluxes of 50–400 kg m
2 s
1 at a saturation temperature of 15 °C. The heat transfer was characterized by forced convection in the region with a low heat flux, high mass flux, and high vapor quality; the heat transfer was characterized by nucleate boiling in the region with a high heat flux and a low vapor quality. Moreover, the heat transfer was characterized by the thin liquid film formed around the elongated vapor plugs with a low mass flux and low heat flux. These heat transfer mechanisms were also confirmed based on the visualization results of the flow boiling. The heat transfer deteriorated in the plug and slug-annular flows due to the occurrence of dry patches. A new heat transfer model for multiport rectangular minichannels was developed that considered forced convection, nucleate boiling, and thin liquid film evaporation. Moreover, this new heat transfer model considered flow patterns inside the multiport minichannels, heat transfer deterioration due to dry patches, and dryout inception quality. The newly model can predict the heat transfer characteristics in multiport rectangular minichannels for a mean deviation of less than approximately 15%. The frictional pressure drop of R32 was smaller than that of R1234ze(E) under the same mass flux and vapor quality conditions and compared with previous correlations. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, compact and high-performance heat exchangers employing multiport tubes have been developed for airconditioning systems to improve the heat exchanger performance and reduce the amount of refrigerant charge by downsizing the equipment. Most multiport tubes are composed of many noncircular minichannels with a hydraulic diameter of 1 mm or less. For mini- and micro-channels, the flow pattern and liquid film thickness are important factors that determine the boiling heat transfer characteristics. The influences of the surface tension and channel shape on the two-phase flow pattern and boiling heat transfer characteristics in such tubes is greater than that in conventional round tubes, and these influences become more significant with a decrease in the channel size. Several studies of the two-phase flow of refrigerants in multiport minichannels have been published. Nino et al. [1,2] visualized two-phase flows of R134a, R410A, and air–water under adiabatic conditions in a multiport tube with six minichannels with a ⇑ Corresponding author. E-mail address: [email protected] (D. Jige). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118668 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

hydraulic diameter of 1.58 mm and observed their intermittent and annular flows. Kim et al. [3] observed the condensation flow of FC-72 in parallel square minichannels with a hydraulic diameter of 1.0 mm at mass fluxes of 68–367 kg m
2 s
1, and reported smooth-annular, wavy-annular, transition, slug, and bubbly flow regimes. They proposed three transition boundaries based on the flow visualization results using the two-dimensionless parameters of the modified Weber number and Lockhart–Martinelli parameter. Jige et al. [4] visualized the adiabatic two-phase flow of R32 in two different dimensions of horizontal multiport rectangular minichannels with hydraulic diameters of 0.5 and 1.0 mm in a mass flux range of 30–400 kg m
2 s
1 and a vapor quality range of 0.1–0.9. They classified the flow into intermittent, transition, and annular regimes, and developed a prediction method for the two-phase flow regime considering the effect of the channel size on horizontal rectangular multiport minichannels. Li and Hrnjak [5] observed the condensation flow of R32 in a multiport minichannel tube with a hydraulic diameter of 0.643 mm at mass fluxes of 50–300 kg m
2 s
1 at a saturation temperature of 30 °C. They classified the observed results as plug, transition, and annular flows, and observed that a clear interface

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D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

Nomenclature Ac Ai Bo C Ca Co cp Db Dh Fdp FrVo G g h m N P q Q ReVo S T WeL WeLo WeV WeVo x

cross-sectional area, m2 inner heat transfer area, m2 boiling number, Bo ¼ q=ðGDhLV Þ, – constant, – capillary number, – pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi confinement number, Co ¼ r=fgðqL
qV Þg=Dh , –
1
1 specific heat capacity, J kg K bubble diameter, m hydraulic diameter Dh ¼ 4Ac =S , m deterioration factor of drypatch, – vapor only Froude number, Fr Vo ¼ G2 =½gDh qV ðqL
qV Þ, – mass flux, kg m
2 s
1 gravitational acceleration, m s
2 specific enthalpy, J kg
1 mass flow rate, kg s
1 data number, – pressure, Pa heat flux, W m
2 heat transfer rate, W vapor only Reynolds number, ReVo ¼ GDh =lV , – wetted perimeter, m temperature, °C liquid phase Weber number, WeL ¼ G2 ð1
xÞ2 Dh =ðqL rÞ, – liquid only Weber number, WeLo ¼ G2 Dh =ðqL rÞ, – vapor phase Weber number, WeV ¼ G2 x2 Dh =ðqV rÞ, – vapor only Weber number, WeVo ¼ G2 Dh =ðqV rÞ, – vapor quality, –

Greek symbols a heat transfer coefficient, W m
2 K
1 b volumetric flow rate, –

between the liquid slug and vapor plug existed in the plug flow regime. Tanaka et al. [6] observed flow boiling patterns for the vertical upward annular flow inside the rectangular minichannels and semicircular minichannels with a hydraulic diameter of around 0.9 mm using R1234yf at mass fluxes of 60 and 120 kg m
2 s
1 and a heat flux range of 4–16 kW m
2. The liquid refrigerant attracted at the channel corners, and a thin liquid film was formed on the channel surfaces owing to the surface tension inside the rectangular channels. Several experimental studies of boiling heat transfer inside multiport tubes have also been published. Mortada et al. [7] investigated the boiling heat transfer of R134a and R1234yf in rectangular minichannels with a hydraulic diameter of 1.1 mm for a mass flux range of 20–100 kg m
2 s
1. The heat transfer coefficient was independent of the heat flux but highly dependent on the mass flux and vapor quality, and forced convective heat transfer was the dominant heat transfer mechanism. Tanaka et al. [6] measured the local heat transfer coefficients using R1234yf inside multiport tubes with rectangular and circular minichannels at mass fluxes of 60 and 120 kg m
2 s
1. They reported that the heat transfer coefficients of the rectangular minichannels were 2–3 times greater than those of the circular minichannels, and that the difference in the heat transfer coefficient caused by the channel shape was greater under conditions with a lower mass flux and heat flux. Kudo et al. [8] studied the heat transfer of R134a inside two multiport tubes with rectangular minichannels for a mass flux

de Xtt

DhLV DP DZ k

q l r

effective liquid film thickness, m 0:9 qV 0:5 lL 0:1 Lockhart-Martinelli parameter, X tt ¼ ð1
x ð q Þ ðl Þ , x Þ L V –
1 vaporization latent heat, J kg pressure drop, Pa length, m thermal conductivity, W m
1 K
1 density, kg m
3 viscosity, Pa s surface tension, N m
1

Subscripts cal calculated cb convective boiling crit critical de dryout completion di dryout inception e abrupt contraction and expansion E electric heater exp experimental F frictional fc forced convection in inlet L liquid phase lf liquid film mes measurement nb nucleate boiling s saturation TS test section V vapor phase w tube wall

range of 50–200 kg m
2 s
1 and a heat flux range of 2–10 kW m
2, and reported that the boiling heat transfer characteristics are different from those in conventional diameter tubes. Jige et al. [9] investigated the boiling heat transfer and pressure drop of R32 in a horizontal multiport tube consisting of rectangular minichannels with straight microfins for a mass flux range of 50– 400 kg m
2 s
1 and a heat flux range of 5–20 kW m
2. The heat transfer coefficient increased with the increasing vapor quality owing to an increase in the forced convection, but the effect of the heat flux on the heat transfer was minimal. The enhancement in the heat transfer due to the inner microfins could be observed only under specific conditions such as in high vapor quality regions for a mass flux of 200 kg m
2 s
1 and in low vapor quality regions for a mass flux of 400 kg m
2 s
1. Li et al. [10] performed experiments on the upward flow boiling heat transfer of R1234yf in two multiport tubes with crosssectional dimensions of 0.91 mm  0.21 mm and 0.34 mm  0.21 mm under a mass flux range of 60–240 kg m
2 s
1 and a heat flux range of 3–16 kW m
2. They reported that the heat transfer coefficient decreased almost linearly as the vapor quality increased in both multiport tubes because the dry patch areas increased as the vapor quality increased. For smaller channels, the heat transfer was characterized by a thin liquid film, but as the vapor quality increased, the dry patch area increased, and the heat transfer decreased significantly. To design evaporators using multiport tubes, it is necessary to accurately determine the boiling heat transfer coefficient and pressure drop inside a multiport tube with rectangular minichannels.

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D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

In particular, it is important to clarify the flow boiling characteristics of low-GWP refrigerants in order to decrease their environmental effects. However, very few studies have been conducted on multiport tubes under various conditions for air-conditioning system design. This study experimentally investigated the flow boiling heat transfer and pressure drop of R32 and R1234ze(E) inside a horizontal multiport extruded tube under a range of operating conditions including lower mass flux and heat flux conditions. Moreover, the two-phase flow under various heating conditions was visualized using a high-speed video camera, and the mechanism leading to heat transfer deterioration in multiport rectangular minichannels was clarified. The influences of mass flux, heat flux, and vapor quality on the local heat transfer characteristics were clarified. A new heat transfer model was developed considering the contributions of forced convection, nucleate boiling, and liquid film evaporation heat transfer for horizontal multiport rectangular minichannels. Moreover, the model considered the flow regimes inside a multiport tube, the heat transfer deterioration owing to dry patches in plug and slug-annular flows, and the dryout inception quality.

Abs. pressure transducer

P

ΔP

Refrigerant

Insulator Heater

Fig. 1. Experimental setup.

Copper plate Multiport tube

Thermocouples

(a) Heat transfer and pressure drop

2. Experimental setup and method A schematic of the experimental setup is shown in Fig. 1. The test refrigerant flowed into a water preheater, electric preheater, and then the test section. The refrigerant temperature at the outlet of the water preheater was adjusted to a predetermined subcooling temperature. The refrigerant was heated by an electric preheater to control the vapor quality of the refrigerant at the inlet of the test section. The refrigerant was cooled using a condenser, receiver, and subcooler, and the subcooled refrigerant was returned to the pump. The refrigerant flow rate was measured using a Coriolis mass flow meter with an accuracy of ±0.5%. The refrigerant temperatures were measured using K-type sheathed thermocouples with an accuracy of ±0.1 K. The refrigerant pressure at the inlet to the electric preheater was measured using an absolute pressure transducer with an accuracy of ±3.0 kPa. Fig. 2 shows the test section used for measuring the heat transfer and pressure drop. The test multiport tube was heated using electric sheet heaters attached to the upper and lower surfaces of the tube. A copper plate was inserted between the electric sheet heater and test tube to improve the non-uniform heating of the metal heating element. The tube wall temperatures were measured using K-type thermocouples with an accuracy of ±0.1 K attached on the tube wall at prescribed positions at 25 mm interval

Thermocouple

Diff. pressure transducer

Gravity direction High-speed camera Observation Refrigerant

Insulator

Heater

Glass

SUS cover

Aluminum visualization channels

(b) Flow visualization Fig. 2. Test sections for heat transfer, pressure drop, and flow visualization.

lengths. The refrigerant pressures at the tube inlet were measured using an absolute pressure transducer with an accuracy of ±3.0 kPa. The pressure drop between the inlet and outlet of the test tube was measured using two differential pressure transducers with accuracies of ±40 Pa and ±14 Pa, respectively. The flow boiling inside the horizontal multiport rectangular minichannels was visualized using a test facility for flow visualization. The details of the facility for flow visualization are described in the literature [4]. The visualization flow channels are square minichannels with dimensions of 1.0 mm  1.0 mm and a hydraulic diameter of 1.0 mm. Both the flow path length and heating length are 200 mm. The temperature and vapor quality of the test refrigerant were adjusted using the electric preheater provided upstream of the observation section, and the visualization minichannels, made of aluminum alloy, were heated from below using an electric sheet heater. The two-phase flow was observed from above, using a high-speed camera. Fig. 3 shows a photograph of the cross-section of the test multiport tube. The test tube was made of aluminum and had 12 rectangular minichannels measuring 0.82 mm  0.82 mm. The hydraulic diameter was calculated to be 0.82 mm using the total

Fig. 3. Cross-sectional view of test multiport tube.

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D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

cross-sectional area and a wetted perimeter. The tube width, tube thickness, and cross-sectional area were 16.0 mm, 1.51 mm, and 8.0 mm2, respectively. The effective heat transfer length of the test tube was 300 mm.

where hE,in is the specific enthalpy of the subcool refrigerant at the inlet to the electric preheater obtained using the measured temperature and pressure of the refrigerant, QE is the heating rate in the electric heater, and m is the refrigerant mass flow rate. The distribution of the vapor quality x in the test section is calculated using:

3. Data reduction methods and experimental conditions

x¼ The local heat transfer coefficient a was calculated as follows:

a¼

q Tw
Ts

ð1Þ

where q is the heat flux based on the actual inner surface area, Tw is the inner wall temperature, and Ts is the refrigerant saturation temperature. The inner wall temperature was calculated using the measured outer wall temperature, based on the one-dimensional heat conduction equation; the estimated temperature difference between the inner and outer walls was 0.004–0.06 K. The heat flux was assumed to be uniform in the flow direction, and was calculated using the following equation.

q ¼ Q TS =Ai

ð2Þ

where QTS is the supplied electric power calculated from the voltage and current of the electric sheet heater, and Ai is the actual inner heat transfer area. The uncertainty of the boiling heat transfer coefficient was evaluated based on the calculation procedure given by Jige et al. [9]. The uncertainties were estimated to be ±8–44% for R32 and ±6– 28% for R1234ze(E). The uncertainty was a maximum under conditions such as the lowest heat flux, higher mass flux, and higher quality region. The frictional pressure drop DPF was measured between the inlet and outlet of the test tube and was calculated using the following equation:

DPF ¼ DP mes
DPe

ð3Þ

where DPmes is the measured pressure drop, and DP e is the pressure loss due to the abrupt contraction and expansion at the inlet and outlet of the test tube estimated via equations established by Collier and Thome [11]. In this study, the DPe =DPmes ratio was 10% or less. The specific enthalpy at the inlet of the test section hTS,in was calculated using the following equation:

hTS; in ¼ hE; in þ Q E =m

ð4Þ

h
hL hV
hL

ð5Þ

where hV and hL are saturated vapor and liquid specific enthalpies, respectively, calculated using the refrigerant pressure. The distribution of the refrigerant pressure is calculated using a combination of the energy and momentum equations. The refrigerant pressure distribution in the test tube was calculated by the interpolation method using the measured pressure at the inlet and outlet of the test section. The refrigerant mass flux was calculated using the mass flow rate and total cross-sectional area of the test multiport tube. The local heat transfer coefficients for R32, and R1234ze(E) as test refrigerants were measured in a mass flux range of 50– 400 kg m–2 s
1, a heat flux range of 5–40 kW m
2, and a vapor quality range of 0.05–1 at a saturation temperature of 15 °C. The experiments were conducted while changing the inlet vapor quality at the test section inlet to obtain data for a range of vapor quality conditions. The flow boiling was visualized using a high-speed video camera, and the mechanism of heat transfer deterioration due to the presence of dry patches was clarified. The refrigerant thermodynamic and transport properties were calculated using REFPROP version 10 (Lemmon et al. [12]). 4. Two-phase flow characteristics The two-phase flow regimes in the horizontal multiport minichannels were categorized into intermittent flow, transition flow, and annular flow according to the results of the visualization [4,5]. In this study, two-phase flow was visualized under various heating conditions using the experimental facility used in previous research [4] for horizontal rectangular multiport minichannels. The flow channels were heated using an electric sheet heater on the lower surface of the test section, and the boiling flow in the multiport tube was simulated. Fig. 4(a)–(c) show the boiling flow patterns of the visualization channels at a mass flux of 100 kg m
2 s
1, heat fluxes of 0 kW m
2 (adiabatic condition), 5 kW m
2, and 20 kW m
2, and vapor quali-

Flow

(a) Adiabatic condition

(b) q = 5 kWm-2

Fig. 4. Boiling flow patterns at G = 100 kg m
2 s
1 and x = 0.2.

(c) q = 20 kWm-2

D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

Flow Original images

Subtracted images

0 ms Front of the vapor plug

Drypatch 23 ms

Drypatch

27 ms

Drypatch

5

ties of 0.2 at the center of the angle of view. The flow regime under these conditions was a plug flow. Many bubbles, which were not observed under adiabatic conditions, were observed in the liquid slug flow under the same conditions, with the number of bubbles increasing with the heat flux. It is assumed that the nucleate boiling heat transfer is enhanced with an increase in the heat flux. Fig. 5 shows close-up views of the flow patterns in one of the channels at a mass flux of 30 kg m
2 s
1, a heat flux of 5 kW m
2, and a vapor quality of 0.5. Dry patches were observed on the channel wall in the vapor plug after liquid slug flow. The image processing was performed by subtracting the image before the occurrence of dry patch from the original images in order to show clearly the occurrence of dry patch. The subtracted images in Fig. 5 clearly show the difference before and after the occurrence of the dry patches. The occurrence of dry patches was observed for mass fluxes of 30–100 kg m
2 s
1 such as in the low-mass flux range and for plug and slug-annular flows. The flow patterns changed for slug and slug-annular flows under a range of heating conditions. However, there is no significant difference in the churn flow or in the annular flow regimes as shown in Fig. 6(a)–(d).

31 ms

5. Flow boiling heat transfer Drypatch

37 ms

Fig. 5. Evaporation of liquid film at G = 30 kg m
2 s
1, q = 5 kW m
2, and x = 0.5.

Churn flow G = 400 kgm-2s-1, x = 0.2

Flow

(b) q = 20 kWm-2

(c) Adiabatic condition

(d) q = 20 kWm-2

Annular flow G = 200 kgm-2s-1, x = 0.8

(a) Adiabatic condition

Fig. 6. Effect of heat flux on flow boiling for churn and annular flows.

Fig. 7 shows the measured heat transfer coefficient of R32 in the horizontal multiport tube with a hydraulic diameter of 0.82 mm for mass fluxes of 50, 100, 200, and 400 kg m
2 s
1. Under each condition, the heat transfer coefficients were obtained by applying the non-linear least squares method to data measured for a vapor quality range of 0.05–0.95 in increments of 0.05, as shown in the figure. For mass fluxes of 50 and 100 kg m
2 s
1, the heat transfer coefficients in the lower heat flux condition were higher than those in the higher heat flux condition. Jige et al. [4] reported that intermittent flow was observed under low vapor velocity conditions inside the multiport rectangular minichannels. In the intermittent flow regime, elongated vapor plugs and liquid slugs alternately flowed in each channel. The liquid film thickness around the elongated vapor plugs is extremely thin. For the rectangular minichannel, the liquid refrigerant was attracted to the corners of the crosssection of the rectangular minichannel and a thick liquid film was formed, while a thin liquid film was formed at the side of rectangular minichannel. A high heat transfer coefficient was obtained when the thin liquid film with a small thermal resistance was formed at the sides of the rectangular minichannels. However, at a lower mass flux, the heat transfer coefficient decreased as the heat flux increased, and it gradually decreased at lower vapor quality. As shown in Fig. 5, the liquid film on the sides of the channels quickly disappeared despite the low vapor quality. The occurrence of a dry patch resulted in decreased heat transfer. The area ratio and frequency of the occurrence of dry patches increased as the heat flux increased, and the flow rate of the refrigerant liquid decreased. The heat transfer coefficient for under a varying heat flux at a mass flux of 400 kg m
2 s
1 is shown in Fig. 7(d). According to the visualization results inside the rectangular multiport minichannels, the flow patterns change from an intermittent to an annular flow via transition flow with an increasing vapor quality [4]. The heat transfer coefficient at heat fluxes of 5 and 10 kW m
2 increased with increasing vapor quality owing to the enhanced forced convection. However, there was no increase in the heat transfer coefficient with increasing heat flux, and nucleate boiling had only a small effect on the heat transfer coefficient at a mass flux of 400 kg m
2 s
1. In the low vapor quality region, the heat transfer coefficient decreased as the heat flux increased. Moreover, in the higher vapor quality region, the heat transfer

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D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

Fig. 8. Effect of mass flux on heat transfer coefficient at heat fluxes of 5 and 20 kW m
2.

Fig. 7. Boiling heat transfer coefficients of R32 for a mass flux range of 50– 400 kg m
2 s
1.

coefficient significantly decreased with increasing heat flux when the heat flux was greater than 10 kW m
2. Fig. 8 shows the heat transfer coefficient for heat fluxes of 5 and 20 kW m
2 under a varying mass flux. For a heat flux of 5 kW m
2, the mass flux does not affect the heat transfer coefficient when the vapor quality is less than 0.1. There is a tendency for the dryout inception quality to decrease as the mass flux decreases and the heat flux increases. Except for the post-dryout region, the heat transfer coefficient was almost constant at a mass flux of less than 200 kg m
2 s
1, while it decreased for a mass flux of 400 kg m
2 s
1. It is well-known that the heat transfer coefficient increases with

increasing mass flux owing to the increased forced convection in the case of conventional-diameter circular tubes. This result suggests that the heat transfer mechanism is different for non-circular minichannels. For rectangular minichannels, the heat transfer through the thin liquid film formed on the sides of the channels was the dominant heat transfer mechanism at a low heat flux; this thin liquid film also indicated a high heat transfer coefficient. However, the thickness of the liquid film in the circumferential direction became uniform as the vapor shear stress increased; the surface tension effect decreased relative to the shear stress effect, such that forced convection heat transfer became dominant. However, the heat transfer coefficient at a heat flux of 20 kW m
2 increased with the increasing mass flux, unlike in the condition with low heat flux. The thin liquid film on the sides of the channels, which is formed due to surface tension effect, disappears quickly at a high heat flux. The liquid film becomes thicker as the mass flux increases. Hence, the deterioration of the heat transfer caused by the occurrence of dry patches was suppressed at a high mass flux. Fig. 9(a)–(d) compares the heat transfer coefficients of R32 and R1234ze(E) at a heat flux of 5 kW m
2 under a varying mass flux. The heat transfer coefficients of the two refrigerants exhibited similar overall tendencies, while the value of R32 was highest under the same mass flux, heat flux, and vapor quality conditions, with the largest difference being at the lowest mass flux. This difference is due to the refrigerant thermodynamic and transport properties; R32 has a higher liquid thermal conductivity than R1234ze(E), as shown in Table 1. Therefore, R32 has the highest heat transfer coefficient in the dominant regions where forced convection heat transfer and evaporation heat transfer occur through the thin liquid film. For a higher heat flux, as shown in Fig. 7(e), R32 has a higher heat transfer coefficient that is strongly affected by the nucleate boiling heat transfer.

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D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

mass flux and heat flux. In the present study, an empirical correlation that can be used to predict the local heat transfer coefficient of the annular flow from the plug flow was developed for rectangular multiport minichannels. For multiport tubes composed of rectangular minichannels, the liquid film is attracted to the corners by surface tension, whereas its distribution is different in a circular minichannel where the liquid film thickness at the center of each side decreases and the liquid film evaporation heat transfer increases. Furthermore, for multiport minichannels, intermittent flow, with alternate elongated vapor plug and liquid slug flows, occurs under a lower mass flux and a lower vapor quality [4,5]. Kattan–Thome–Favrat [13] proposed a heat transfer model based on a two-phase flow pattern for horizontal boiling flow; however, the flow pattern inside the multiport minichannels differs from that in horizontal conventional-diameter tubes. Jige et al. [4] classified intermittent (plug), transition (churn/slugannular), and annular flow regimes, and proposed transition boundaries calculated using the following equations:

40 -2 -1

[kWm K ]

-2 -1

(a) G = 50 kgm s -2 q = 5 kW m

30

Rec0.82 Ts = 15 °C

20 10 0 40

-2 -1

[kWm K ]

-2 -1

(b) G = 100 kgm s -2 q = 5 kW m

30 20 10 0 40

-2 -1

[kWm K ]

-2 -1

(c) G = 200 kgm s -2 q = 5 kW m

30 20 10 0 40

-2 -1

[kWm K ]

ð6Þ

3:7  WeL WeV ¼ 2:3  10
4 Co Co

ð7Þ

20 10 0 40

-2 -1

[kWm K ]

-2 -1

(e) G = 200 kgm s -2 q = 20 kW m

30

intermittent to transition flow

Moreover, the transition flow regime is classified as intermittent flow at WeLo < 4 based on the results of the visualization of the horizontal rectangular minichannel [4] for convenience. The modified flow regime map under experimental conditions in this study is shown in Fig. 10. The transition flow regime was subdivided into a churn flow at WeLo  4 and slug-annular flow at WeLo < 4.

-2 -1

(d) G = 400 kgm s -2 q = 5 kW m

30

WeV ¼ 75 transition to annular flow Co

1000

R32 R1234ze(E)

Annular

500

20

Churn

0 0

0.2

0.4

0.6

0.8

1

x [-] Fig. 9. Comparison of heat transfer coefficients of R32 and R1234ze(E).

G [kgm-2s-1]

10

Slug–annular

100 Plug (Intermittent)

50

6. Heat transfer correlation for rectangular multiport channels

R32, Ts = 15 °C Dh = 0.82 mm

6.1. New heat transfer model 6.1.1. Flow pattern For flow boiling heat transfer in conventional circular tubes, it is known that the heat transfer mechanism is affected by forced convection and nucleate boiling. Moreover, for minichannels, the surface tension strongly influences the heat transfer under a lower

Jige et al. WeLo = 4

10 0

0.2

0.4

0.6

0.8

1

x [-] Fig. 10. Modified flow regime map for horizontal multiport tube.

Table 1 Thermodynamic and transport properties of R32 and R1234ze(E) at a saturation temperature of 15 °C. Refrigerant R32 R1234ze(E)

P [kPa]

qL

qV

[kg m
3]

kL [mW m
1 K
1]

lL [lPa s]

cpL [kJ kg
1 K
1]

DhLV [kJ kg
1]

r

1281 364

1001 1195

35 19

134 78

127 216

1.84 1.36

290 174

8.4 10.3

[kg m
3]

[m N m
1]

8

D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

6.1.2. Heat transfer correlation for pre-dryout region The heat transfer coefficient is obtained from an asymptotic expression with the exponent n = 5, considering the contributions of convective boiling acb and nucleate boiling heat transfer anb .

a ¼ ða5cb þ a5nb Þ

1=5

ð8Þ

The convective boiling acb is obtained by

acb ¼ maxðafc ; alf Þ

ð9Þ

where afc is the forced convection and alf is the thin liquid film evaporation heat transfer coefficient. The contribution of the nucleate boiling is calculated using the correlation proposed by Jung et al. [14], wherein the measurement results of the pool boiling heat transfer coefficients of low-, medium-, and high-pressure refrigerants are utilized, as follows:

anb ¼ 10

kL Db



q Db k LTs

C 

Ps Pcrit

0:1  
1:4   Ts lL cpL
0:25 1
T crit kL

ð10Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r Db ¼ 0:511 gðqL
qV Þ

ð11Þ


0:437  0:309  qV Ps C ¼ 0:855 qL P crit

ð12Þ

(a) Annular and churn flows The effective liquid film thickness for annular or churn flows is different for that of the plug and slug-annular flows. For liquid film evaporation, as determined by experimental data obtained under the lowest heat flux, the effective liquid film thickness is correlated using the hydraulic diameter Dh and capillary number Ca (Eq. (17)).

de =Dh ¼ 0:014Ca0:1

ð18Þ

The thin liquid film heat transfer coefficient alf for the annular and churn flows is calculated by Eqs. (15)–(18). (b) Plug and slug-annular flows For plug and slug-annular flows, the contribution of the forced convection afc is small and the liquid film heat transfer is dominant. The thin liquid film formed around the vapor plugs promotes heat transfer, while it decreases by dry patches under higher heat flux conditions for plug and slug-annular flows. Therefore, it is necessary to consider deterioration due to dry patches to predict the heat transfer. Considering this, the thin liquid film heat transfer alf for the plug and slug-annular flows is calculated by multiplying Eq. (15) and Fdp.



alf ¼ F dp b

kL de



ð19Þ

The contribution of the forced convection afc in Eq. (9) is calculated using the liquid single-phase heat transfer coefficient.

Based on experimental data, the effective liquid film thickness de and Fdp are obtained as follows:

afc ¼ ð1 þ 1:3Xtt
1 ÞaL

de =Dh ¼ 0:005Ca0:05 ðqL =qV Þ0:2

ð13Þ

The liquid single-phase heat transfer coefficient aL is obtained by

 0:8   k Gð1
xÞDh lL cpL 0:4 aL ¼ 0:023 L Dh lL kL

b¼

kL de


0:3 

qV qL

0:2 

GDh


0:16

lL

 ; 1 ð21Þ

where Ca is the capillary number obtained by Eq. (17), and Co is confinement number. 6.1.3. Heat transfer correlation for dryout region The heat transfer coefficient under those conditions with the highest mass flux significantly decreased with an increase in the

ð15Þ

x x þ ð1
xÞqV =qL

q  104 GDhLV

ð14Þ

In Eq. (9), the contribution of the thin liquid film evaporation heat transfer, alf , is calculated as described in Miyata et al. [15], who expressed the liquid film evaporation heat transfer using the equivalent liquid film thickness de and time-averaged volume flow rate of the vapor phase b in the intermittent flow region, as follows:

alf ¼ b

  F dp ¼ min 7:8Co
1:0

ð20Þ

1

ð16Þ

0.8

R0.05 = 71% R0.1 = 100%



Ca ¼

lL G x 1
x þ r qV qL

 ð17Þ

For non-circular minichannels, the liquid film thickness varies along the channel perimeter owing to surface tension, and the liquid film at the center of the channel is thinner compared with that in the circular minichannel. Correlations of the liquid film thickness around the vapor plug are suggested to be a function of capillary number Ca (e.g. [17,18]). However, the liquid film thickness differs not only between square and circular minichannels [19], but also between adiabatic and boiling flows. Based on experimental data obtained under the lowest heat flux, the effective liquid film thickness is correlated for two types of flow patterns; (a) annular and churn flows, and (b) plug and slug-annular flows.

xdi, cal [-]

The liquid film thickness in the plug flow is predicted using the capillary number Ca [15,16], which is given by

0.6 0.4 +0.1

0.2 0 0

–0.1

0.2

R32 R1234ze(E)

0.4 0.6 xdi, exp [-]

0.8

1

Fig. 11. Comparison of the measured and predicted dryout inception qualities.

D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

9

inception and completion qualities for three regimes, i.e., S1, S2, and S3. The best agreements in the trends in this study were obtained for the S1 and S3 regimes; the dryout inception quality increased with an increase in the mass flux and a decrease in the heat flux. However, the correlation proposed by Mori et al. overestimated xdi in the S3 regime. Hence, the dryout inception and completion qualities were obtained using a modified correlation, which was optimized for multiport rectangular minichannels, based on the approach proposed by Mori et al.

xdi ¼ minðxdi1 ; xdi3a ; xdi3b Þ

ð22Þ

where

xdi1 ¼ 0:94
1:75  10
6 ðReVo BoÞ1:75 ðqV =qL Þ
0:86

ð23Þ

0:16 Bo
0:12 We0:48 xdi3a ¼ 0:253Fr
0:32 Vo Vo ðqV =qL Þ

ð24Þ


1:00 xdi3b ¼ FrVo Bo
0:21 We0:70 Vo

ð25Þ

In this study, xde = 1.0, assuming that the liquid refrigerant flows as a liquid film and that no liquid droplets are entrained in the vapor flow. Fig. 11 compares the measured and predicted dryout inception quality, as calculated using Eqs. (22)–(25). The dryout inception qualities can be predicted almost within ±0.1. For the dryout region, the heat transfer coefficient can be obtained using the linear interpolating equation

Fig. 12. Comparison of measured heat transfer coefficient of R32 and proposed heat transfer correlation.

vapor quality in the dryout region, which is generally the case for conventional-diameter tubes (e.g., Wojtan et al. [20]). For lower mass fluxes, the heat transfer coefficient gradually decreases as the vapor quality increases because of the increasing area of the dry patches. From a practical viewpoint, the decrease in the heat transfer coefficient inside the minichannels can be calculated using the prediction method for conventional-diameter tubes [15,16]. Mori et al. [21] defined the dryout inception quality xdi and completion quality xde for conventional-diameter tubes, which are obtained from three straight lines tracing change in the heat transfer coefficient. In this study, xdi and xde were obtained using the approach proposed by Mori et al.[21]. Moreover, for conventional-diameter tubes, Mori et al. classified the dryout

Fig. 13. Components of developed heat transfer correlation.

10

D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

a ¼ axdi


x
xdi ðaxdi
axde Þ xde
xdi

ð26Þ

where axdi is the heat transfer coefficient calculated at x = xdi using Eqs. (8)–(21), and axde is the heat transfer coefficient of the vapor single-phase flow, calculated as follows:

Fig. 15. Comparison between the present correlation and heat transfer data of R32, R410A, R1234yf inside a single rectangular minichannel.

axde ¼ 0:023

kV Dh



GDh

lV

0:8 

lV cpV

0:4

kV

ð27Þ

6.2. Comparison of previous and present correlations

Fig. 14. Comparison of measured values for previous and proposed heat transfer correlations.

Table 2 Deviation between the measured and predicted heat transfer coefficients. Correlation

MD [%]

MAD [%]

R30 [%]

Gungor and Winterton [22] Saitoh et al. [23] Kim and Mudawar [24] Present


17.1
67.3
34.5
0.3

48.5 67.3 53.3 10.7

34.6 3.3 22.0 91.1

Fig. 12 compares the measured heat transfer coefficients of R32 and the proposed heat transfer correlation for mass fluxes of 50, 100, 200, and 400 kg m
2 s
1. The proposed correlation was found to be in good agreement with the measured heat transfer coefficient of R32 at all tested mass fluxes and heat fluxes containing the dryout region. Fig. 13 shows the components of the developed heat transfer correlation, namely, the convective boiling heat transfer acb and nucleate boiling heat transfer anb . The components of the convective boiling heat transfer acb are forced convection afc dominated by shear stress and thin liquid film evaporation alf dominated by the surface tension effect. The classification of flow patterns by the modified flow regime map [4] is also shown in Fig. 13. It can be confirmed that the proposed heat transfer model faithfully reproduces the boiling heat transfer characteristics of a multiport rectangular tube: that is, under lower heat flux conditions, the thin liquid film evaporation was dominant, as shown Fig. 13(a) and (b), while the nucleate boiling heat transfer was dominant in those regions with a high heat flux and a low vapor quality region, as shown in Fig. 13(c). At a lower heat flux and higher mass flux, the forced convection significantly increased with an increase in the increasing vapor quality: the heat transfer was characterized by forced convection heat transfer in a higher vapor quality region (Fig. 13(b)). In the case of rectangular-shaped and smaller channels, for the plug flow region observed under the lower vapor velocity conditions, the influence of forced convection is small and did not affect the prediction of the heat transfer coefficient. However, it is necessary to consider the thin liquid film evaporation heat transfer except for the high vapor quality region even for annular and churn flows. Fig. 14 compares the measured and predicted heat transfer coefficients calculated from the correlations proposed by Gungor

11

D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

Fig. 16. Frictional pressure drops of R32 and R1234ze(E) at a saturation temperature of 15 °C.

and Winterton [22], Saitoh et al.[23], Kim and Mudawar [24], and that developed in the present study. Table 2 lists the deviations between the measured and predicted heat transfer coefficients. The mean deviation MD and mean absolute deviation MAD are calculated as follows:

MD ¼

  1 X acal
aexp N N aexp

ð28Þ

  1 X  acal
aexp  N N  aexp 

ð29Þ

MAD ¼

R30 is the ratio of the number of data points within a deviation of ±30% to the total number of measured data points. The proposed model was in good agreement with the measured heat transfer coefficients, and the values of MD and MAD were
0.3% and

Fig. 17. Comparison of previous correlations and measured frictional pressure drops.

Table 3 Deviation of frictional pressure drops determined using various correlations. Correlation

MD [%]

MAD [%]

R30 [%]

Friedel [28] McAdams et al. [29] Muller–Steinhagen and Heck [30] Mishima and Hibiki [31] Kim et al. [3] Jige et al. [32]

166.3 58.3 31.3 13.6 2.7 15.0

167.2 80.2 35.1 25.9 11.5 21.2

22.3 31.5 45.4 68.5 96.2 69.2

10.7%, respectively. The present correlation was in good agreement with the measured heat transfer coefficients of R32 and R1234ze (E). Although it is known that the heat transfer coefficient for a plug flow changes cyclically with time within the mini/microchannels, as explained by the three-zone model (Magnini and Thome [25]), the proposed correlation can be used to easily predict the

12

D. Jige et al. / International Journal of Heat and Mass Transfer 144 (2019) 118668

time-averaged heat transfer coefficient. A more detailed approach will be needed to obtain the local heat transfer coefficient considering the void fraction, liquid film thickness, bubble frequency, and vapor-plug length for a plug flow. Fig. 15(a) and (b) show the comparison between the present correlation and boiling heat transfer data of R410A, R32 and R1234yf inside a single rectangular minichannel with hydraulic diameter of 1.0–2.0 mm, mass flux range of 30–400 kg m
2 s
1, and heat flux range of 2–40 kW m
2 [26,27]. The present correlation was in good agreement with previously reported data; however, it underpredicted a few results classified under post-dryout region. Results classified under post-dryout region are expressed by closed plots. Eq. (22), as proposed for results of the multiport tube, tends to underestimate the dryout inception quality for a single rectangular minichannel. This result suggests that the dryout inception quality inside multiport tubes is less than that of a single rectangular minichannel. 7. Frictional pressure drop Fig. 16 shows the frictional pressure drops for R32 and R1234ze (E) under adiabatic conditions inside a horizontal multiport tube at a saturation temperature of 15 °C. The pressure drop increased with increasing mass flux and vapor quality due to an increase in the vapor shear stress. For the same mass flux and vapor quality, the pressure drops for R32 were smaller than those of R1234ze (E). This is due to the difference in the refrigerant transport properties, because R32 has higher vapor density and a lower liquid viscosity, resulting in a smaller wall-shear stress. Fig. 17 compares the measured frictional pressure drops with the predicted values, while Table 3 shows the deviations between the measured and predicted values. The correlation proposed by Kim et al. [3] was found to be in good agreement with the measured data. 8. Conclusions The flow boiling heat transfer and frictional pressure drop of R32 and R1234ze(E) inside a horizontal rectangular multiport tube were experimentally investigated under various operating conditions including low mass flux and heat flux conditions. Moreover, the flow boiling was visualized using a high-speed video camera and the mechanism of heat transfer deterioration in the horizontal rectangular minichannels was clarified. Dry patches were observed for mass fluxes of 30–100 kg m
2 s
1 such as in the low mass flux range for plug and slug-annular flows. The influences of the mass flux, heat flux, and vapor quality on the local heat transfer characteristics were investigated. In regions with a low heat flux, high mass flux, and high vapor quality, the heat transfer was characterized by forced convection heat transfer, while nucleate boiling heat transfer was dominant in those regions with a high heat flux and low vapor quality. Moreover, the heat transfer was characterized by the thin liquid film formed around the elongated vapor plugs with a low mass flux and low heat flux. These heat transfer mechanisms were confirmed based on observations of the flow boiling. The heat transfer deteriorated in the intermittent (plug) flow regime due to the disappearance of the liquid film around the vapor plug, as well as the occurrence of dry patches. A new heat transfer model was developed that considers the contributions of nucleate boiling, forced convection, and thin liquid film evaporation for horizontal multiport rectangular minichannels. Moreover, the model considered the flow regimes inside a multiport tube, the heat transfer deterioration owing to dry patches in plug and slug-annular flows, and the dryout inception

quality. The newly developed correlation produced better prediction results for R32 and R1234ze(E) than the previous correlations for mean absolute deviations of less than 11%. The frictional pressure drop increased with the mass flux and vapor quality. The frictional pressure drop of R32 was smaller than that of R1234ze(E) under the same mass flux and vapor quality conditions. The previous correlations proposed for minichannels produced accurate predictions.

Declaration of Competing Interest The authors declare that there are no conflicts of interest.

Acknowledgments The study was financially supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan. The test multiport tube was provided by the UACJ Corporation. The authors wish to express their gratitude to their supporters.

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