Experimental study on two-phase flow pressure drop during ethanol–water vapor mixture condensation in microchannels

International Journal of Heat and Mass Transfer 127 (2018) 160–171

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Experimental study on two-phase flow pressure drop during ethanol–water vapor mixture condensation in microchannels Rui Jiang, Zhong Lan, Tong Sun, Yi Zheng, Kai Wang, Xuehu Ma ⇑ Institute of Chemical Engineering, Dalian University of Technology, Dalian, Liaoning Province 116024, China

a r t i c l e

i n f o

Article history: Received 30 October 2017 Received in revised form 25 April 2018 Accepted 21 July 2018

a b s t r a c t Ethanol-water vapor mixtures condensation shows different flow patterns in microchannels due to the equivalent surface free energy differences. The transition point of streak flow pattern was introduced in the paper which was found closely related to the frictional pressure drop of ethanol–water vapor mixtures condensation flow in microchannels. Characteristics of two-phase pressure drop for ethanol–water vapor mixtures condensation flow in silicon microchannels of streak and smooth annular flow pattern were investigated. Four types of multi-port trapezoidal and triangular microchannels with hydraulic diameter in the range of 126–155 lm were employed. The pressure drop was determined under steam mass flux between 259.2 and 504.8 kg m
2 s
1 when the inlet ethanol weight concentration varied from 1% to 60%. The experimental pressure drop results were compared with existing correlations of flow condensation. The transition point basing on the streak flow pattern of binary vapor condensation was proposed to replace the traditional Reynolds number criterion of the laminar flow state to turbulent flow state for the frictional factor and the C parameter for Kim and Mudawar’s universal pressure drop model, which is in good agreement with the results the experiment results. Ó 2018 Published by Elsevier Ltd.

1. Introduction With advancement in modern science and technology, new frontiers have been open up for the microscale technology. Microchannel condensation has attracted more and more attention from researchers for its high heat transfer performance. Different from the traditional tube, surface tension is usually predominant in microchannels, where the flow patterns, the pressure drop and the heat transfer coefficients for condensation are obviously disparate from those observed in macrochannels [1]. The pressure drop of condensation flow has played an important role in doing more detailed studies for the condensation flow in microchannels. Extensive investigations have been conducted on two-phase pressure drop for condensing flow in microchannels for recent years. Most of the two-phase flow pressure drop models in microchannels are modified from two kinds of models in the traditional tubes: the homogeneous flow model and the separated flow model. For the former, the two phases were assumed to be well mixed and the pressure drop was calculated by regarding the two phases as one in the channel. For the separated flow model, each phase was supposed to be individual flow in channels and ⇑ Corresponding author. E-mail addresses: [email protected] (T. Sun), [email protected] (X. Ma). https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.112 0017-9310/Ó 2018 Published by Elsevier Ltd.

had interaction parameters for the vapor and liquid flow. Lockhart and Martinelli [2] and Chisholm [3] have proposed the Lockhart and Martinelli (L-M) parameter and Chisholm parameter to reflect the relationship of the two phases, which is in accordance with the experiment results. Müller-Steinhagen and Heck [4] provided a new correlation using a data bank containing 9300 measurements of frictional pressure drop for a variety of fluids and conditions, including channel diameters from 4 to 392 mm. Mishima and Hibiki [5] experimentally studied air-water two-phase flow in capillary tubes with the diameters in the range of 1 to 4 mm, and a new parameter C as a function of tube diameter was presented in the research for different shape of the tubes. Tran et al. [6] investigated the twophase flow pressure drop of R-134a, R-12, and R-113 at six different pressures ranging from 138 to 856 kPa in different minichannels, from which a new correlation for two-phase pressure drop were presented on the basis of Chisholm’s B-coefficient method. Zhang and Webb [7] studied single-phase and adiabatic phase flow pressure drop of R-134A, R22 and R404 in a multi-port extruded aluminum and copper minichannels with hydraulic diameter 2.13–6.25 mm. They modified the C parameter on the Friedel correlation with the reduced pressure, and a new correlation for two phase friction pressure drops was developed by modifying Friedel correlation, which fit experiment data well.

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Nomenclature A Ca D f g G L Ma P Q Re T W We x

area, m2 capillary number hydraulic diameter, lm friction factor gravitational acceleration, m s
2 steam mass flux, kg m
2 s
1 length mm Marangoni number pressure, Pa heat transfer rate, W Reynolds number temperature, K ethanol weight concentration weber number steam quality

Greek symbols r surface tension, N m
1 l viscosity Pa s

Mikielewicz et al. [8] experimentally investigated the pressure drop of HFE7100 and HFE7000 in flow condensation which were performed in vertical (HFE7100) and horizontal (HFE7000) silver minichannels with internal diameter of 2.3 mm. The pressure drop data was compared with plenty of pressure drop models and it was found that the modified Müller-Steinhagen and Heck’s correlation exhibited a good agreement with their data. Lee and Lee [9], Hwang and Kim [10] and Quan et al. [11] reported the frictional pressure drop in minichannels or microchannels. They found that the two-phase pressure drop was closely related to hydrodynamic diameter, quality, mass flux and fluid characteristics. They proposed the modified correlation of C parameter with taking the fluid characteristics, two phase flow mass flux and the surface tension into consideration. The correlation agreed well with the pure steam condensation results. Fan et al. [12] conducted the pressure drop for condensation of pure steam in microchannels of trapezoidal cross section with different cross-sectional geometries. A modified Friedel model was presented and the effect of geometrical parameters of microchannels, the forces acting on fluid and fluid properties, which could be available to predict the two-phase flow pressure drop of pure steam condensation. Li and Wu [13] studied the published pressure drop databases in microchannels, and Bo number and Re number were introduced into the Chisholm parameter C, which was found to change with Bo and Re number. Kim and Mudawar [14] has posed a new universal approach to predict two-phase frictional pressure drop for adiabatic and condensing mini/micro-channel flows based on a consolidated database consisting of 7115 data points from 36 sources. A universal predictive model for a wide spectrum flow condition including a wide range of mass flux from laminar flow state to turbulent flow state and different fluid characteristics was presented. The different C parameters at different Re numbers were proposed by modifying the original Lockhart–Martinelli model, which fitted the results well. These aforementioned researchers have studied the flow pattern of pure steam condensation in microchannels, where the annular flow was found to be the dominate condensation flow pattern at the beginning of the condensation process. The flow patterns are at a laminar flow state in most of the researches and the liquid film keeps steady at low Re number but there was a relative

q

U

density, kg m
3 two-phase multiplier

Subscripts dec deceleration exp experiment f film g gas fri friction in inlet l liquid lo liquid only out outlet pred predict total total v vapor vo vapor only w wall

high vapor speed because of the limitation of the microchannel and the strong surface tension effect. As a high heat transfer performance condensation mode for heat transfer, dropwise condensation attracts wide interest for easier drainage of the condensate drops and lower pressure drop [15,16]. Some studies have attempted to achieve dropwise condensation in microchannels through surface modification. Fang et al. [17] and Chen et al. [18] prepared hydrophobic surfaces on silicon microchannels, where the droplet flow pattern was observed. The study indicated that droplets flow in microchannel contributed to a high heat transfer performance. However, droplets generated, grew and coalesced with each other in the microchannel until the vapor swept them to the downstream, which lead to a higher pressure drop in the microchannel. Pseudo-dropwise condensation appears in the ethanol-water vapor mixture condensation process and it shows a special droplet-film combined condensation mode [19–21]. Ethanolwater vapor mixture condensation flow in trapezoidal and triangular microchannels have been studied in previous works [22,23]. Streak annular flow [24] and churn flow happened during the ethanol-water vapor mixtures condensation in microchannels without modification. The liquid Re numbers in our experiment are all below 550 and the vapor Re numbers are all below 2000. Because of the specific characteristics of binary condensation and the restriction of the narrow space, which were totally different from the pure steam condensation flow pattern in microchannels and the mixture vapor condensation in traditional channels. Different flow patterns contribute to different pressure drop characteristics. Fluctuant flow patterns caused by the surface free energy difference which exist in the ethanol-water vapor mixture condensation at low Re number also result in special pressure drop. There are many pressure drop models for condensation flow in microchannels, focusing on the smooth annular flow at low Re number and the pure steam condensation situation, but few studies concentrate on the pressure drop characteristics of the ethanolwater vapor mixtures condensation in microchannel. In this paper, the transition point of the streak annular flow was proposed according to our experimental results. The pressure drop of ethanol-water vapor mixtures condensation in trapezoid and triangular microchannels is studied and the frictional pressure drop experiment data is compared with existing models. The flow pattern transition criterion that is highly accurate for the

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ethanol-water condensation flow in microchannels is put forward to replace Kim and Mudawar’s universal pressure drop model where Reynolds number acts as the criterion for the transition of laminar flow to turbulent flow. 2. Experimental setups and data reduction 2.1. Experiment setups The experimental setup used in our previous work [22,23] is also employed in the pressure drop test, as shown in Fig. 1. The ethanol-water steam is generated from boiler, then flows through filter, pre-heater, test section, post-condenser and finally into the condensate accumulator. All the pipelines are fully insulated to ensure the vapor is at saturation state when goes through the microchannels. The condensate is collected in the condensate accumulator and weighed in the electronic balance (±0.01 g) to calculate steam mass flux. The system is vacuumed at the beginning of the experiment to remove noncondensable gas. Four microchannels are tested in the experiment, each silicon chip with the length of 70 mm, containing three zones: inlet vapor plenum, outlet vapor plenum and 14 parallel trapezoidal microchannels with the length of 50 mm, which are similar to those in the previous work [22,23] of visualization study. Detailed sections are listed in Table 1. In the experimental system, it is difficult to measure the pressure and temperature at microchannel inlet and outlet directly for the restriction of spatial scale. The temperature and pressure of binary vapor or condensate are detected by static pressure transducers (±1%) and thermocouples (±0.1 °C) fixed at the inlet mixer and outlet mixer respectively.

The total pressure drop is determined by the difference between inlet and outlet transducers. The temperature and pressure signals are collected by Agilient34970. The cooling water volume flow rate is controlled at 40 L h
1 with the inlet cooling water temperature fixed at 8 °C during testing. The steam mass flux is regulated by steam valve, 333–428 kg m
2 s
1 for No. 1 microchannels, 259–299 kg m
2 s
1 for No. 2 microchannels, 262–297 kg m
2 s
1 for No. 3 microchannels, and 413–504 kg m
2 s
1 for No. 4 microchannels. The ethanol weight concentration of the binary vapor varies from 0.01 to 0.65. The vapor quality in the microchannel during the experiment is from 0.8 to 0.1. The test flow patterns are mainly annular flow patterns, covering the smooth annular flow pattern and streak annular flow pattern under different inlet ethanol weight concentration for the binary vapor condensation in microchannels. 2.2. Data reduction The pressures of binary vapor or condensate at the entrance and exit are monitored by two absolute pressure sensors installed at the inlet mixer and outlet mixer respectively. It can be demonstrated that the total pressure drop for the test section contains the frictional pressure drop in microchannel, deceleration pressure drop in microchannel, the inlet pressure drop in the tube and the outlet pressure drop in the tube, which is shown in Fig. 2 and Eq. (1).

DPtotal ¼ DP fri þ DP dec þ DPin þ DP out

ð1Þ

The inlet pressure drop contains contraction pressure drop between inlet mixer and inlet connective tube, height pressure

Fig. 1. Schematic diagram of experimental facility.

Table 1 Geometrical parameters of the microchannels. No.

Top width WT (lm)

Height H (lm)

Bottom width WB (lm)

Hydraulic diameter Dh (lm)

Number of microchannel

1 2 3 4

440.51 607.64 244.14 299.72

85.91 82.05 172.41 211.65

318.84 491.45 0 0

134.5 138.7 126.2 155.0

14 14 14 14

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Fig. 2. Schematic diagram for local pressure drop in experimental system.

drop for inlet connective tube, bend pressure drop and frictional pressure drop in inlet connective tube, expansion pressure drop between inlet connective tube and inlet plenum, bend pressure drop in inlet plenum, contraction pressure drop between inlet plenum and microchannel inlet. The outlet pressure drop contains the expansion pressure drop between microchannel outlet and outlet plenum, bend pressure drop in outlet plenum, contraction pressure drop between outlet plenum and outlet connective tube, bend and frictional pressure drop in outlet connective tube, height pressure drop for outlet connective tube, expansion pressure drop between outlet connective tube and outlet mixer. The total pressure is gauged by the pressure sensors directly and the local pressure drops are calculated according to Ref. [12]. The inlet ethanol weight concentration is calculated by testing the condensate after the post condenser, and it is also calculated by the non-random two liquid (NRTL) method via measured inlet temperature and pressure. The two results are compared to ensure the accuracy. During the binary vapor condensation, the ethanol concentrations of the liquid and the vapor side are changing along microchannels. The microchannel is equally divided into 10 sections along the condensation direction and the physical data are calculated separately. Considering the small distance of each section, the ethanol weight concentration and the vapor temperature and the temperature of the condensation surface were used into calculate the surface free energy for the first section. The fluid properties of the first section can be calculated based on the microchannel inlet static pressure, the inlet temperature and the ethanol concentration. The surface free energy difference is calculated by Tamura method [25], and the schematic calculation diagram is shown in Fig. 3. Vapor quality, ethanol mass concentration, heat flux, temperature, phase equilibrium and fluid characteristics are calculated as described previously [23].

2.3. Uncertainty analysis All the measurement systems are calibrated before installation. Thermocouples with the accuracy of ±0.1 K are used in the experiment to measure the temperature of the microchannel and cooling water. The pressure sensors have an accuracy of ±1 kPa. The cooling water flow volume rate is controlled by a float flowmeter with the accuracy of 1%. The electronic balance weighing the condensate has a deviation within ±0.01 g. the uncertainty of the Dr and Cav are 7.35% and 9.7% respectively in the experiment. 3. Experimental results and discussion 3.1. Streak annular flow patterns and the transition criterion During the mixture vapor condensation of 10–60% inlet ethanol concentration, the streak annular flow would be the dominated flow pattern, while during the mixture vapor condensation of 1–6% and over 60% inlet ethanol concentration, the smooth annular flow would be the dominated the flow pattern. As the surface free energy difference increases, thin streak flow would occur at the entrance of the microchannel condenser [23]. With the ethanolwater vapor mixture condensation continuing, the streak annular flow disappears at the injection flow pattern area due to the lower vapor velocity and droplets appear in this part. During ethanol water vapor mixture condensation, condensate would first form droplet on the condensation surface and would be driven to form the streak flow in microchannel due to the effects of surface free energy difference and mixture vapor mass flow rate. The streak annular flow is found to be closely related to the surface free energy difference and the shearing action of the vapor side to the liquid side.

Fig. 3. The schematic diagram of the surface free energy difference calculation in Section 1.

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In our previous study [23], droplets would appear at the injection flow area when inlet surface free energy difference was more than 11 mJ m
2 in the microchannels [23]. Fig. 4 shows the photos of locations where thin streak annular flow generates under different inlet ethanol mass concentrations and mass fluxes. The surface free energy difference Dr and the Cav number are calculated. Cav number is used to present the shearing action of the vapor side to the liquid side. It has been found that with the increase of the surface free energy difference, a lower Cav number is required to form the thin streak annular flow, while a higher Cav number is needed to generate the thin streak annular flow for a lower Dr. The reason is that a higher Dr leads to a higher unstability of the liquid film and it becomes easier for the vapor to shear the liquid and form the streak annular flow. In order to obtain a better understanding of the formation of streak annular flow, the Ma number and the Cav number are calculated to represent the surface free energy difference and the shearing action in the position of streak flow occurred respectively. They are calculated based on physical data at the generation location of streak annular flow pattern for different inlet ethanol concentrations. Accordingly, a new empirical correlation for the streak annular flow in binary vapor condensation is established and expressed as follows.

Ma 1 ¼ Mamax 174:77Cav Ma ¼

ðDr
11Þl

la

ð2Þ ð3Þ

Mamax ¼

Cav ¼

Drmax l

ð4Þ

la

Gin  x  lv qv  r

ð5Þ

0 6 Ma=Mamax 6 1;

0:01 6 Cav 6 0:35

Ma is the Marangoni number, and Dr is the difference in the surface free energy difference between the liquid film and the droplet in the position of streak flow occurred, which is calculated as described previously [23]. The number 11 is the minimum value of Dr for the droplet formation during the binary vapor condensation in the microchannels. Mamax is the maximum Marangoni number in the process of the ethanol-water vapor mixture consideration. L, l and a could be cross out in Eq. (2), so the Ma/Mamax means the value of surface free energy difference between droplets and film in the position of streak flow occurred. It represents the interactions of the surface free energy difference to the liquid film. r is the surface tension of the liquid and x represents the vapor quality. Fig. 5 shows the significant effects of the Ma/Mamax and the Cav number on the two-phase flow patterns. Obvious streak annular flow, point A in Fig. 5, generates at the position above the correlation curve for the surface energy difference and the shearing action both keep at a high level at this position. Obvious smooth annular flow, point B in Fig. 5, occurs at the position under the correlation curve for the surface free energy difference is too low to form the fluctuation of the liquid film.

3.2. Total pressure drop and local pressure drop Total pressure drops, deceleration pressure drop and frictional pressure drop are calculated as described in chapter 2. Fig. 6 shows the total pressure drop in microchannels under different mass fluxes and inlet ethanol concentrations of No. 1 trapezoidal microchannels and No. 3 triangular microchannels. The local pressure drops including the deceleration pressure drop (DPdec), the frictional pressure drop (DPfri), the inlet pressure drop (DPin) and the outlet pressure drop (DPout) of No. 3 microchannel are presented in Fig. 7. It could be found that the total pressure drop goes up with the increase of the mass flux for the same inlet ethanol concentration because the deceleration pressure drop and the

0.6

A

0.5

Ma/Ma max

0.4 0.3 0.2 0.1 0.0 -0.1

B

-0.2 0.0

0.2

0.4

Cav Fig. 4. Surface free energy differences and Cav under different inlet ethanol concentration and mass flux when streak annular flow generated.

Fig. 5. Streak annular flow pattern transition maps.

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300

Win=0.65

Win=0.65

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steam mass flux (kg·m -2·s-1)

(a)No.1 microchannels

(b) No.3 microchannels

-2

-1

500

Fig. 6. Total pressure drop in No. 1 and No. 3 microchannels.

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0.3

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(d) the outlet pressure drop

Fig. 7. The local pressure drop of the No. 3 microchannel.

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frictional resistance both grow. The total pressure drop decreases at the same mass flux as the inlet ethanol concentration increases. As illustrated in Fig. 7, the deceleration pressure drop decreases with the increase of inlet ethanol mass concentration, while the frictional pressure drops don’t change a lot with the change of inlet ethanol mass concentration. The density of binary vapor increases with the increase of inlet ethanol concentration, which leads to a smaller density difference between vapor-liquid phase and a higher frictional resistance. Deceleration pressure drop increases with the increase of the density difference. The inlet pressure drop (DPin) and the outlet pressure drop (DPout) also slightly increase with the mass flux, but they do not show significant difference under different inlet ethanol concentrations. Compared with the four parts of the local pressure drops, the inlet pressure drop (DPin) and the outlet pressure drop (DPout) only represent a small part of the total pressure drop. To determine the two-phase frictional pressure drop, both homogeneous equilibrium and separated flow models are considered. The accuracy of each model is judged by mean absolute error, which is defined as

1 X jDPpred
DPexp j  100% M DPexp

ð6Þ

800 1400

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700 1200 1000

+800%

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MAE ¼

Fig. 8 is a comparison of the experimental data with four homogenous flow models of the two phase pressure drop prediction given by Cicchitti et al. [26], Dulker et al. [27] and Mcadams [28], where MAE are 77.3%, 58.2%, 68.1% respectively. For the homogeneous equilibrium model, the void fraction and the fluid characteristics are relevant to thermodynamic equilibrium quality. It could be found that the homogeneous equilibrium model provides inaccurate predictions of the experimental data. The reason is that the large velocity difference of the two phases in microchannels during condensation leads to the velocity-slip between the liquid and the wall, which is also deemed as an significant impact on pressure drop. Fig. 9 is a comparison of two-phase pressure drop predictions of the three separated flow correlations given by Chisholm [3], Friedel [29] and L-M [2] model, where MAE are 41.2%, 66.0%, 78.2% respectively. Müller-Steinhagen and Heck [4] also posed a model for the prediction of frictional pressure drop for two-phase flow in conventional pipes, which is shown in Fig. 8d with the MAE of 95.6%. These models exhibit a low prediction precision as well. Different from the flow in the conventional tubes, surface tension and shear force instead of body force are predominate influencing factors on pressure drop in microchannels. The fluid characteristics in

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Experimental pressure drop (kPa)

(c) Mcadams Fig. 8. Experimental data versus predicted pressure drop by homogeneous models of Cicchitti, Dukler and Mcadams.

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Fig. 9. Experimental data versus predicted pressure drop by separated models of Chisholm, Friedel Lockhart-Martinelli and Müller-Heck.

our experiments are different from those in the models, which also contributes to the deviations. Many researchers studied frictional pressure drop of two-phase flow in microchannels for different material condensation because the traditional homogenous flow models and separated flow models show an evident deviation for the data prediction in microchannels. Fig. 10 shows a comparison of two-phase pressure drop predictions of the four frictional pressure condensation flow models given by Quan et al. [11], Li and Wu [13], Kim and Mudawar [14] and Mishima and Hibiki [5]. Compared with the pressure drop models in traditional tubes, models in mini or microchannels succeed to offer better predictions of the experimental data. It is found that Kim and Mudawar’s correlation predict the present experimental data with the MAE of 22.5%, which presents a better fit than the other two correlations because it is developed for wide working fluids in microchannels and the properties are appropriate for binary vapor condensation in this experiment. Although the studies for comparison are also carried out for steam condensation in microchannels, the predicted values are all slightly higher than our experimental data, making it imperative to modify the existing models.

3.3. Pressure drop model for streak annular flow pattern and smooth annular flow pattern Usually during condensation flow in microchannels, Re number plays important an role in characterizing different flow patterns, which also impact significantly on the pressure drop. Most of the condensation flow states in these models are regarded as smooth laminar states when the liquid and vapor Re number is below 2000. However, although the liquid and vapor Re numbers are all below 2000 during the ethanol water vapor mixture condensation flow in our experiment, the flow state is different from the pure steam condensation flow in microchannels. The schematic photos of smooth annular flow and streak annular flow is shown in Fig. 11. During the pure steam condensation in microchannel, the condensation liquid was pulled into the corner of the noncircular microchannels due to the effect of surface tension, and it would form the smooth annular flow shown in the Fig. 11a. However, for the streak annular flow, the droplets appear and are driven to form the streak annular flow by the vapor on the condensation surface by the effect of surface free energy difference, as shown in Fig. 11b.

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Fig. 10. Experimental data versus predicted pressure drop by microchannel models of Quan, Li, Kim and Mudawar and Mishima and Hibiki.

a smooth annular flow

b streak annular flow

Fig. 11. The schematic photos of smooth annular flow and streak annular flow.

The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, which is defined in pipes as:

Re ¼

duq

l

¼

4A uq L l

ð7Þ

where A is the cross-sectional area, and L is the wetted perimeter. It could be seen in Fig. 11 that the wetted perimeter between liquid and the wall could be reduced at the streak characteristic flow pattern. The practical ReL numbers for the streak flow pattern are

higher than the ReL numbers calculated by the normal method. It shows that the ReL numbers for the transition of the pure vapor condensation flow in microchannels are not suitable for the streak flow pattern during ethanol water vapor mixture condensation in microchannels. It is reported that when the inlet ethanol concentration is below 10% or over 60%, the flow pattern of ethanol-water vapor mixture condensation, where the smooth annular flow dominates, is similar to that of the pure steam condensation. There is a more fluctuant flow pattern under 10–60% inlet ethanol concentration,

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250

200

+30%

150

-20%

100

50

0

350 300 250

+90%

200 150

+10%

100 50 0

0

50

100

150

200

250

Experimental pressure drop (kPa)

(a4) Mishima and Hibiki

300

0

50

100

150

200

250

300

Experimental pressure drop (kPa)

(b4) Mishima and Hibiki

Fig. 12. Experimental data versus predicted pressure drop by Quan, Li, Kim and Mudawar and Mishima and Hibiki models under different inlet ethanol concentrations (a1–a4) 1–6% and over 60% inlet ethanol concentration where smooth annular flow dominated (b1–b4) 10–40% inlet ethanol concentration where streak annular flow dominated.

R. Jiang et al. / International Journal of Heat and Mass Transfer 127 (2018) 160–171

where the streak annular flow and churn flow are primary. Fig. 12 illustrates the comparison of two-phase pressure drop predictions of different researchers’ mini or microchannel pressure drop models with our experiment data under different inlet ethanol concentrations. It could be found that all the frictional pressure drop models show good agreement with the experimental data when the inlet ethanol concentration is below 10% and over 60%, which is similar to the pure steam or pure ethanol flow. The MAE of the four models are 8.4%, 11.2%, 11.3% and 12.2% respectively. However, all frictional pressure drop models provide relative higher predictions with the experiment data under 10–60% inlet ethanol concentration, which shows completely different pressure drop characteristics under streak dominating flow patterns. The MAE of the four models are 36.9%, 44.9%, 30.1% and 41.3% respectively, which shows a poorer agreement with the comparison of the smooth annular flow. Consider the ethanol-water vapor mixture condensation flow pattern under different inlet ethanol concentration. Although the liquid and vapor Re numbers in the experiment are below 2000, the flow patterns under 10–40% inlet ethanol concentration is similar to the transition state or the turbulent state, which are totally different from the annual flow in microchannels. The surface free energy difference and the shearing action for the vapor side to the liquid side have a much stronger influence on the flow state than the Re number. In other words, the Re number criterion for transition of laminar flow state to turbulent flow state fails to reflect the flow state of ethanol-water vapor mixture condensation flow in microchannels. The friction factors and C parameters in Kim and Mudawar’s model change with the Re number for different flow states. The transition criterion for the streak annular flow was proposed on Section 3.1. Under the streak annular flow pattern, transitional frictional factor and C parameter of liquid turbulent and vapor laminar were used to calculate the frictional pressure drop of ethanolwater vapor mixture condensation flow in microchannels. Kim and Mudawar’s model with the new transition criterion can be expressed as follows:

    dP dP ¼ U2f  dZ TP dZ L

U2f ¼ 1 þ

ð8Þ

C 1 þ X X2

ð9Þ

dZ l  X2 ¼ dP

ð10Þ

dZ v

  2f f G2 ð1
xÞ2 dP ¼
dZ l ql Dh

ð11Þ

  dP 2f G2 x2 ¼ v
dZ v qv Dh

ð12Þ

For Smooth annular flow pattern

Ma Mamax

1 6 174:77Ca . v

16Re
1 k

ð13Þ

For Smooth annular flow pattern 0:50 C ¼ 3:5  10
5 Re0:44 lo Suvo



ql qv

Ma Mamax

1 6 174:77Ca . v

0:48

For Streak annular flow pattern

f k ¼ 0:079Re
0:25 k

250

200

+20% 150

-20% 100

50

0 0

50

100

150

200

250

300

Experimental pressure drop (kPa) Fig. 13. Experimental data versus predicted pressure drop by Kim and Mudawar’s model with new transition point.

For Streak annular flow pattern 0:50 C ¼ 8:7  10
4 Re0:17 lo Suvo



ql qv

Ma Mamax

0:14

1 > 174:77Ca . v

ð16Þ

where subscript k denotes f or g for liquid and vapor phases, respectively.

Rel ¼

Gð1
xÞDh

ll

;

Rev ¼

GxDh

lv

;

Refo ¼

GDh

ll

;

q rD h Suvo ¼ v 2

lv

0  Ma/Mamax  1, 0.01  Cav  0.35, 100  Rev  1500, 30  Rel  400, 170  Relo  500, 1000  Suvo  40,000. The predicted pressure drop determined from the Kim and Mudawar’s model of the new transition criterion according to different flow patterns are compared with the experimental data in our experiments, as shown in Fig. 13. It can be seen that 92.5% of the predicted values fit within ±20% of the experimental data with the MAE of 9.8%, showing good agreement with the whole experimental data including the streak annular flow pattern and the smooth annular flow pattern. 4. Conclusion

dP

fk ¼

300

Predictive pressure drop (kPa)

170

ð14Þ Ma Mamax

1 > 174:77Ca . v

ð15Þ

In the present study, the characteristics of two-phase flow pressure drop have been investigated experimentally for ethanol-water vapor mixture condensation in microchannels. According to the flow pattern, the transition criterion of streak annular flow pattern is presented, which is also found closely related to the pressure drop. New transition criterion is proposed basing on the flow patterns and replaces the Re number used in Kim and Mudawar’s model. Conclusions can be drawn from the experimental results: 1. The transition point of streak annular flow pattern is presented by considering of the surface free energy difference and the shearing action of vapor side to the liquid side, which is consistent with the experiment phenomena. 2. The total pressure drop goes up with the increasing mass flux under the same inlet ethanol concentration, while the deceleration pressure drop decreases with the increase of inlet ethanol concentration. 3. Re number criterion for the pressure drop is not applicable for the ethanol-water vapor mixture condensation flow in microchannels. Considering the flow patterns of the ethanol-

R. Jiang et al. / International Journal of Heat and Mass Transfer 127 (2018) 160–171

water vapor mixture condensation, the transition criterion of the thin streak annular flow is proposed to substitute the Re number of laminar flow state to turbulent flow state for the frictional factor and C parameter in the Kim and Mudawar’s model, showing good agreement with the experimental data. Conflict of interest The authors declared that there is no conflict of interest. Acknowledgments This work was supported by the State Key Program of National Natural Science of China (No. 51236002). References [1] Y. Chen, M. Shi, P. Cheng, et al., Condensation in microchannels[J], Nanoscale Microscale Thermophys. Eng. 12 (2) (2008) 117–143. [2] R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal twophase, two-component flow in pipes[J], Chem. Eng. Prog 45 (1) (1949) 39–48. [3] D. Chisholm, A theoretical basis for the Lockhart-Martinelli correlation for twophase flow[J], Int. J. Heat Mass Transf. 10 (12) (1967) 1767–1778. [4] H. Müller-Steinhagen, K. Heck, A simple friction pressure drop correlation for two-phase flow in pipes[J], Chem. Eng. Process. Process Intensif. 20 (6) (1986) 297–308. [5] K. Mishima, T. Hibiki, Some characteristics of air-water two-phase flow in small diameter vertical tubes[J], Int. J. Multiph. Flow 22 (4) (1996) 703–712. [6] T.N. Tran, M.C. Chyu, M.W.E.A. Wambsganss, Two-phase pressure drop of refrigerants during flow boiling in small channels: an experimental investigation and correlation development[J], Int. J. Multiph. Flow 26 (11) (2000) 1739–1754. [7] M. Zhang, R.L. Webb, Correlation of two-phase friction for refrigerants in small-diameter tubes.[J], Exp. Therm Fluid Sci. 25 (3–4) (2001) 131–139. [8] D. Mikielewicz, J. Wajs, R. Andrzejczyk, et al., Pressure drop of HFE7000 and HFE7100 during flow condensation in minichannels[J], Int. J. Refrig. 68 (2016) 226–241. [9] H.J. Lee, S.Y. Lee, Pressure drop correlations for two-phase flow within horizontal rectangular channels with small heights[J], Int. J. Multiph. Flow 27 (5) (2001) 783–796. [10] Y.W. Hwang, M.S. Kim, The pressure drop in microtubes and the correlation development[J], Int. J. Heat Mass Transf. 49 (11–12) (2006) 1804–1812. [11] X. Quan, P. Cheng, H. Wu, An experimental investigation on pressure drop of steam condensing in silicon microchannels[J], Int. J. Heat Mass Transf. 51 (21– 22) (2008) 5454–5458.

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