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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 372898, 10 pages
http://dx.doi.org/10.1155/2013/372898
Research Article

Two-Phase Flow and Heat Transfer during Steam Condensation in a Converging Microchannel with Different Convergence Angles

1Green Energy and Environment Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan
2Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan
3Institute of Nuclear Engineering and Science, National Tsing Hua University, Hsinchu 30013, Taiwan
4Low Carbon Energy Research Center, National Tsing Hua University, Hsinchu 30013, Taiwan

Received 15 June 2013; Revised 30 September 2013; Accepted 30 September 2013

Academic Editor: Ahmet Selim Dalkılıç

Copyright © 2013 Ben-Ran Fu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The present study experimentally investigates the effect of convergence angle of microchannel on two-phase flow and heat transfer during steam condensation. Three condensation regimes, from the inlet to the outlet, are identified: mist/annular flow, injection flow, and slug-bubbly flow. Flow pattern maps are constructed using superficial vapor and liquid velocities as the coordinates, wherein relatively distinct boundaries between the flow patterns can be identified. The experimental results show that the condensation heat flux increases with an increase in the convergence angle and/or the steam mass flux at a given coolant flow rate but decreases with an increase in the coolant flow rate at a given steam mass flux. The results further demonstrate that the local condensation heat transfer coefficient in the mist/annular flow region is much higher than that in other condensation regimes. Moreover, the local condensation heat transfer coefficient in the mist/annular flow and injection flow region decreases with an increase in the convergence angle.

1. Introduction

Condensation in microchannels is of significant fundamental interest and has diversified applications, such as in microchannel heat exchangers and micro-fuel cells. In recent years, many studies on the characteristics of two-phase flow and heat transfer during condensation in microchannels were reported. For example, Wu and Cheng [1] visualized the condensation flow patterns of steam flowing through 10 parallel microchannels with a hydraulic diameter of 82.8 μm and a trapezoidal cross-sectional area. They categorized the flow patterns observed as follows: droplet flow (mist flow), annular flow, injection flow, and slug-bubbly flow. The injection flow pattern appears periodically because of its upstream flow patterns alternate between the droplet two-phase flow and the vapor flow. Wu et al. [2] further carried out experimental studies on injection flow during steam condensation in microchannels with hydraulic diameters ranging from 53 μm to 128.5 μm. They proposed that the location of the injection flow corresponds to the Reynolds number (Re), condensation number (Co), and diameter-to-length ratio and obtained a dimensionless correlation for the location of injection flow in silicon microchannels.

Quan et al. [3] investigated the effects of the mass flux and cooling flow rate on the occurrence frequency of the injection flow in a single microchannel with hydraulic diameters of 120 and 128 μm. Their study revealed that the shape of the microchannels has a critical influence on the instability of the condensation flow mechanisms. Furthermore, Wu et al. [4] conducted an experimental study on heat transfer and flow friction during steam condensation in trapezoidal silicon microchannels with hydraulic diameters of 77.5, 93.0, and 128.5 μm. Their experimental results demonstrated that the condensation Nusselt number increases with an increase in the Re, Co, and , and the condensation two-phase frictional multiplier decreases with an increase in the Re and or a decrease in the Co.

Chen et al. [5] performed a visualization experiment to investigate the steam condensation in triangular microchannels with hydraulic diameters of 100 and 250 μm. The experimental results indicated that the droplet, annular, injection, and slug-bubbly flows are the dominant flow patterns during steam condensation in microchannels. In addition, they proposed the correlations for injection location, injection frequency, and condensation Nusselt number. Wu et al. [6] presented a visualization study on steam condensation in wide rectangular microchannels. Three typical flow patterns were identified in their study, namely, droplet-annular compound flow, injection flow, and vapor slug-bubbly flow. They demonstrated that the injection location moves to the channel outlet with an increase in the Re, and the injection frequency increases with increasing the Re and condensate Weber number. In addition, the results showed that the injection frequency is lower than that in the triangular microchannel with the same hydraulic diameter, indicating that the cross-sectional shape of the microchannel plays an important role in the instability of condensation flow.

Agarwal et al. [7] reported the condensation heat transfer coefficients of R134a in six noncircular horizontal microchannels with different shapes (barrel-shaped, N-shaped, rectangular, square, and triangular tubes, and a channel with a W-shaped corrugated insert). For square, rectangular, and barrel-shaped channels, an annular-flow-based heat transfer model was developed. On the other hand, for triangular, N-shaped, and W-insert channels (i.e., those with sharp corner), a mist-flow-based heat transfer model was proposed. Ma et al. [8] investigated the two-phase flow patterns and transition characteristics during steam condensation in trapezoidal microchannels. Annular flow, droplet flow, injection flow, and bubbly flow were observed in their study. Two-phase flow pattern maps were constructed using coordinates of steam mass flux and steam quality. They also reported that the flow pattern transition from annular flow to bubbly flow occurs earlier in the smaller microchannel. In addition, criteria for transitions between flow patterns were also proposed in the form of nondimensional groups (steam quality, condensation number, Reynolds number, Weber number, Bond number, and width-to-diameter ratio).

Fang et al. [9] investigated the effect of wall hydrophobicity on the steam condensation in the rectangular microchannel. They found that the channel surface wettability has a significant impact on the condensation flow pattern, pressure drop, and heat transfer characteristics. At a given inlet vapor flux and temperature, the hydrophobic microchannel presents higher heat transfer rate and pressure drop than those in the hydrophilic one. Odaymet and Louahlia-Gualous [10] reported the local heat transfer coefficient and flow visualization during condensation in a square microchannel. They identified the following flow regimes: mist flow, churn flow, annular flow, slug flow, liquid ring flow, and annular/bubbly flow. Their results indicated that the local condensation heat transfer coefficient increases with an increase in the steam mass flux. Recently, Odaymet et al. [11] investigated the local heat transfer and flow patterns during steam condensation in a single silicon-based microchannel. They further modified condensation flow patterns as follows (from upstream to downstream): mist flow, churn flow, elongated bubbly flow followed by a bubbly sequence, and slug flow. In addition, they also found that local thermal performance of condensation flow for mist flow and upstream elongated bubbly flow is better than slug and bubbly flows.

Kim et al. [12] carried out an experimental study on condensation of FC-72 in parallel microchannels. Smooth-annular, wavy-annular, transition, slug, and bubbly flows were identified in their experimental observation. Furthermore, they discussed the condensation two-phase flow pressure drop using both two-phase homogenous and separated flow models and found that the homogenous model unexpectedly provides better predictions than the separated flow model. Furthermore, Kim and Mudawar [13] demonstrated that the local condensation heat transfer coefficient is the highest near the channel inlet and decreases along the microchannel due to an increase in the film thickness. In addition, a correlation of condensation heat transfer coefficient for annular condensation in microchannels was also proposed.

Based on the above literature reviews on microchannel condensation, it is clearly found that significant effects of microchannel cross-sectional shape on the condensation flow patterns and heat transfer are demonstrated. In our previous study [14], convective steam condensation in uniform, converging, and diverging microchannels with a mean hydraulic diameter of 117 μm was experimentally investigated. The steam flow in the microchannel was cooled by a still water bath. Flow patterns, two-phase flow pressure drop, outlet temperature, bubbly emission frequency, and bubbly velocity in the three different cross-section designs of microchannels were reported. The experimental results demonstrated that, for a given steam mass flow rate, the two-phase flow pressure drop in the diverging microchannel is considerably higher than that in the uniform and converging microchannels. The converging microchannel presents the lowest two-phase flow pressure drop, suggesting its merit for removing the two-phase fluids during steam condensation.

Furthermore, Kuo and Pan [15] investigated steam condensation in uniform and converging microchannels with a mean hydraulic diameter of 135 μm. The steam flow in the microchannels was cooled by water cross-flowing along its bottom surface, which is different from other methods reported in the literature. The flow patterns, two-phase flow pressure drop, and local condensation heat transfer coefficient were examined. The results demonstrated that although the uniform microchannel presents a higher heat transfer coefficient than those in the converging microchannel under mist/annular flow regimes, the total heat transfer rate is higher for the microchannel with the converging cross-section than that with the uniform cross-section. Moreover, empirical correlations of local condensation heat transfer for the mist and annular flow regions and a two-phase frictional multiplier in the form of the Lockhart-Martinelli correlation were developed.

This work investigates the effect of convergence angle (half of the included angle) of microchannel experimentally on two-phase flow and heat transfer during steam condensation. Flow pattern maps are constructed using coordinates of superficial vapor and liquid velocities. In addition, the effects of convergence angle on local heat transfer coefficient as well as condensation heat transfer rate are explored.

2. Experimental Details

2.1. Experimental Setup

Figure 1 shows the experimental setup, which is similar to that employed in our previous study [15], that consists of a water tank, a high-performance liquid chromatography (HPLC) pump (P680: Dionex), a heating module, a test section, a cooling water circulation system, a condensate collecting container, an electronic balance (XS625 M: Precisa Gravimetrics), a flow visualization system, and related control and measurement systems. Before conducting experiments, the deionized water in the water tank was boiled to evacuate dissolved gas. Then, water was driven by the HPLC pump through the helical tube immersed in the silicone oil bath and heated and stirred by a heating module to vaporize the water to steam. The steam subsequently flowed into the test section. Three K-type thermocouples were placed in the bath to measure the oil temperature. A cooling water circulation system combined with a metering pump (FEM03KT: KNF) drove water with a constant inlet temperature of 22°C at a specific flow rate in the cross-flow direction along the backside surface of the test section. The condensate was collected by a container at atmosphere pressure and condensate was weighed using an electronic balance to verify the steam mass flow rates (). The steam mass flow rates in the present study ranged from  kg/s to  kg/s.

372898.fig.001
Figure 1: Experimental setup: (1) CCD, (2) microscope, and (3) and (4)   mechanism.

The test section with a converging microchannel was a silicon strip with dimensions of 10 mm × 48 mm. Three convergence angles (, 1.0°, and 1.5°) of the microchannel with the same mean hydraulic diameter () of 135 μm were employed to study the effect of convergence angle. Here, the mean hydraulic diameter of the converging microchannel was calculated based on the following definition [16]:

Figures 2 and 3 depict schematics of the test section and cooling chamber, respectively. The detailed dimensions of the microchannels with different convergence angles are summarized in Table 1. Two T-type thermocouples and a differential pressure transducer (692: Huba) were employed to measure the inlet and outlet temperatures and the pressure drop between the inlet and outlet chambers. Three T-type thermocouples were embedded in the backside surface of the test section (facing the coolant) to measure the local wall temperature (), which is then used to evaluate the local heat transfer coefficient. These three thermocouples were located at , 17.5, and 25.5 mm, respectively, in reference to the channel inlet. The data of the thermocouples and the differential pressure transducer were recorded by a data acquisition system (MX100: Yokogawa) with a sampling rate of 2 Hz.

tab1
Table 1: Detailed dimensions of the microchannels with different convergence angles.
fig2
Figure 2: Schematic of the test section: (a) side view and (b) top view.
372898.fig.003
Figure 3: Schematic of the test section combined with a cooling chamber. Locations “a” to “d” are points for temperature measurement and “e” and “f” are pressure tap locations in the microchannel.

The flow visualization system included a high-speed digital camera (XS-4: IDT) mounted with a microlens (zoom 125C: OPTEM) and a computer. In addition, an mechanism was installed to hold the CCD and microlens with an accurate position on the test plane ( plane) and focus in the -direction. The typical frame rate employed in the study was 4000 frames/s. A 250 W fiber optic illuminator (FOI-250: TechniQuip) was used as the light source.

2.2. Fabrication of the Test Section

To prepare the microchannel with a uniform depth, the test section was made of P-type (100) orientation silicon on insulator (SOI) wafer, which consisted of three layers (from bottom to top): (1) handle layer (P-type (100) bare wafer, thickness: μm); (2) box layer (SiO2, thickness: 0.5 μm); and (3) device layer (P-type (100) silicon wafer, thickness: μm). The converging microchannels with inlet and outlet chambers were etched on the surface of the device layer. The fabrication processes of the test section employed deep reactive ion etching (DRIE) with photolithography, laser-cutting technology, and anodic bonding processes. The etching stop mechanism on the box layer for the DRIE process ensured a uniform depth for the microchannels and chambers. Subsequently, an excimer laser micromachining technology was applied to make through holes, which were used as the inlet and outlet chambers for the working fluid to flow through the microchannel. Finally, to enable flow visualization the test section was covered with the Pyrex no. 7740 glass through anodic bonding.

2.3. Uncertainty Analysis

The measurement uncertainty for the liquid volumetric flow rate through the HPLC pump in the microchannels after calibration was estimated to be ±0.2%. The accuracy of the metering pump was ±2%. The measurement uncertainty of the pressure transducer was 0.5% over the full scale, resulting in an actual uncertainty of ±1.25 kPa. The uncertainties in the temperature measurements were ±0.2°C and ±0.5°C for T-type and K-type thermocouples, respectively. The ambient temperature was controlled at about 25°C by an air conditioner during experiments. The uncertainties for the temperature of the cooling water, ambient condition, and steam were estimated to be ±0.5°C. The uncertainty analysis methodology developed by Moffat [17] was used to estimate the uncertainty for the total condensation heat transfer rate and the local condensation heat transfer coefficient, which were 1.9% and 6.6%, respectively. In addition, the uncertainty of the void fraction of 0.52 is about 9.6%, estimated from our previous study [18], which is due to the image analysis tool. As shown in Fu et al. [18], the uncertainty of the void fraction decreases with an increase in the void fraction. Consequently, the uncertainty for the void fraction of 0.8, which is corresponding to transition location between mist/annular flow and injection flow, will be smaller than 9.6%. And the highest uncertainty of the condensation heat transfer rate for a particular flow region is 9.8%, which is higher than that of total condensation heat transfer rate.

3. Data Reduction

In the present study, the heat released by the steam is mainly carried away by the forced convection to the cooling water flowing underneath the test section, defined as , and a small fraction may be lost by natural convection via the top glass surface of the test section to the ambient air. In the present study, the estimated heat transfer by natural convection is less than 0.1% of the measured heat dissipation. Thus, the total heat () released by the steam can be reasonably considered to be absorbed totally by the coolant (); that is, . Thermal radiation to the ambient is considered to be negligible. Here, is estimated by the following equations:

Following a methodology developed by Kuo and Pan [15], the total condensation heat transfer rate along the microchannel is divided into three parts, that is, , , and , corresponding to three distinct two-phase flow regimes: (1) the mist/annular flow, (2) injection flow, and (3) slug/bubbly flow regions, respectively, as depicted in Figure 4. These three regions can be distinguished clearly by flow visualization. Consider

fig4
Figure 4: Typical condensation flow patterns in the microchannel.

The distributions of the condensation heat transfer rate in regions (1) and (3) are assumed to be uniform. For region (1), mist/annular flow prevails and the void fraction is close to unity. Therefore, it is reasonable to assume a uniform condensation heat transfer rate there. On the other hand, for region (3) bubbly flow appears, and thus the condensation heat transfer rate is low and is also uniformly distributed. The condensation heat transfer rates in regions (1) and (3) can be evaluated by the following equations based on the energy balance with a vapor quality () determined from the void fraction () data: where vapor quality at any axial location, , can be estimated from the following equations: proposed by Kawahara et al. [19]. Consider

For the present study, the void fraction for a particular region is determined by the mean value of the projected area of vapor bubbles on the bottom wall of 100 frames, randomly selected from the flow visualization of different conditions, divided by the bottom surface area of the region [18]. The present results demonstrate that the void fraction decreases sharply during the injection flow and keeps nearly constant toward the channel outlet, as reported in our previous study [15]. The persistence of such a nearly constant void fraction near the channel outlet reflects the poor condensation heat transfer therein, which will be demonstrated later. Given local void fraction determined, the corresponding vapor quality and local condensation heat flux in each region may then be determined.

After the condensation heat transfer rates in different regions are obtained, the local condensation heat transfer coefficient can be estimated on the basis of the temperature difference between the saturation temperature () of the fluid flowing through the microchannel and the local wall temperature () as follows: where is extrapolated from the wall temperature measured on the backside, , by considering the total thermal resistances () of the silicon layer and the thin layer of silicon dioxide: The above equation neglects heat conduction in the axial and lateral directions, as the wall thickness (450 μm) is much smaller than the channel length (35 mm) and the width of the test section (10 mm).

4. Results and Discussion

4.1. Condensation Two-Phase Flow Pattern

Condensation two-phase flow patterns in microchannels have been investigated in many studies. In the literature, five distinct flow regimes have been reported, namely, mist flow, annular flow, injection flow, slug/plug flow, and bubbly flow. In the present study, three flow regimes, from the inlet to the outlet, can be identified: mist/annular flow (Figure 4(a)), injection flow (Figure 4(b)), and slug/bubbly flow (Figure 4(c)) regions. More detailed discussions on the characteristics of condensation two-phase flow pattern in rectangular microchannels with different cross-section designs have been presented in our previous study [14].

Figure 5 presents the occurrence location for the injection flow as a function of steam mass flow rate in the converging microchannel with . This figure indicates that the location of the injection flow retreats toward the channel inlet with increasing the coolant flow rate () at a given steam mass flow rate or decreasing the steam mass flow rate at a given coolant flow rate. Moreover, the occurrence of injection flow moves to downstream with an increase in the convergence angle at a given coolant flow rate. Such movement of the location of injection flow with mass flow rate and/or convergence angle has a significant effect on the characteristics of condensation heat transfer, which will be discussed in the following sections.

372898.fig.005
Figure 5: Occurrence location of the injection flow as a function of steam mass flow rate in the microchannel with .

Flow pattern maps are used to determine the flow pattern prevailing under a particular operating condition. Figures 6, 7, and 8 further show the flow pattern maps, constructed in the coordinates of superficial vapor and liquid velocities, that is, and , respectively, observed during experiments in microchannels with different convergence angles. In the present study, flow patterns were observed in four different locations, that is, channel inlet, channel outlet, and locations for void fraction of 0.52 and 0.8 corresponding to the transition boundaries between injection flow and slug/bubbly flow and between mist/annular flow and injection flow, respectively. In the channel inlet region, as shown in the figures, the superficial vapor velocity is the highest and greater than 10 m/s. With a decrease in the void fraction, the superficial vapor velocity decreases while the superficial liquid velocity increases. The transition boundaries that separate the mist/annular flow from the injection flow () and the injection flow from the slug/bubbly flow () are also identified in the figure. Figures 6, 7, and 8 demonstrate that the transition boundaries between mist/annular flow and injection flow and between injection flow and slug/bubbly flow become more instinct as the convergence angle is increased. For these two transition boundaries, the superficial liquid velocity increases very rapidly with an increase in the superficial vapor velocity.

372898.fig.006
Figure 6: Flow pattern map for the microchannel with .
372898.fig.007
Figure 7: Flow pattern map for the microchannel with .
372898.fig.008
Figure 8: Flow pattern map for the microchannel with .
4.2. Condensation Heat Transfer

Figure 9 shows the condensation heat transfer rate as a function of steam mass flow rate in the converging microchannel with . This figure clearly demonstrates that the condensation heat transfer rate increases with an increase in the steam mass flow rate at a given coolant flow rate, as reported earlier by Odaymet and Louahlia-Gualous [10], but decreases with an increase in the coolant flow rate at a given steam mass flow rate. The decrease of condensation heat transfer rate with increasing coolant flow rate results primarily from the occurrence location of injection flow moves upstream, as shown previously in Figure 5. This shortens the length of mist/annular flow region and decreases the total condensation heat transfer rate, as the mist/annular flow presents the highest heat transfer compatibility among the three possible flow regimes [15].

372898.fig.009
Figure 9: Condensation heat transfer rate as a function of steam mass flow rate in the microchannel with .

To further understand the heat transfer characteristics among microchannels with different convergence angles, the condensation heat fluxes () are also examined, as shown in Figure 10(a). Note that in this figure the experimental data of the uniform microchannel () are from our previous study [15]. This figure shows that at a given coolant flow rate and steam mass flux the condensation heat flux increases with an increase in the convergence angle. This is mainly due to the occurrence of injection flow moves to downstream with an increase in the convergence angle, as shown in Figure 10(b). The occurrence of injection flow taking place in a further downstream location indicates that the region of mist/annular flow prevails larger, and, therefore, a much higher bottom heat transfer area for the mist/annular region can be obtained. As the condensation heat transfer rate from the channel is the sum of heat transfer rate from mist/annular flow, injection flow, and bubbly flow regions, that is, where , , and are the condensation heat flux from the mist/annular flow, injection flow, and bubbly flow regions, respectively, , , and are the corresponding heat transfer area for the mist/annular flow, injection flow, and bubbly flow regions, respectively. The heat flux in the mist/annular flow region is much higher than that in the injection flow and bubbly flow regions due to its much thinner liquid film between the vapor and the cooling wall [15]. Consequently, a much higher heat transfer area for the mist/annular flow region will result in a higher total condensation heat transfer rate, as suggested by [10]. Therefore, the mean condensation heat transfer rate is higher for the microchannel with a larger convergence angle.

372898.fig.0010
Figure 10: (a) Condensation heat flux and (b) injection flow location as a function of steam mass flux for the microchannels with different convergence angles. Data of are from Kuo and Pan [15].

Figure 11 shows the effect of convergence angle on the local condensation heat transfer coefficient. This figure indicates that, for the microchannel with a given convergence angle, the mist/annular flow region is much higher than that in other condensation regimes, as reported by Kuo and Pan [15]. Moreover, for mist/annular flow and injection flow regimes the local condensation heat transfer coefficient decreases generally with an increase in the convergence angle. Interestingly, the uniform microchannel presents a higher heat transfer coefficient in both mist/annular flow and injection flow regions than those in the converging microchannels with convergence angles from 0.5° to 1.5°. As indicated earlier, the injection flow takes place in a much downstream location as the convergence angle increases; much more steam has been condensed in the mist/annular flow region and the liquid film formed may be thicker. Consequently, the local heat transfer coefficient in the mist/annular flow region decreases with an increase in the convergence angle. However, the mean condensation heat flux in the converging microchannel increases with an increase in the convergence angle. This can be understood by rewriting (9) as

372898.fig.0011
Figure 11: Local condensation heat transfer coefficient as a function of convergence angle for different flow regimes. Data of are from Kuo and Pan [15].

The condensation heat transfer rate is primarily influenced by the product of heat transfer coefficient and area in the mist/annular flow region. Although the heat transfer coefficient decreases with an increase in the convergence angle, the heat transfer area increases more significantly with an increase in the convergence angle. This explains why the condensation heat transfer rate and, therefore, the mean condensation heat flux increase with an increase in the convergence angle.

5. Conclusions

This work experimentally investigates the effect of convergence angle of microchannel on two-phase flow and heat transfer during steam condensation. Three convergence angles (0.5°, 1.0°, and 1.5°) of microchannel with the same mean hydraulic diameter of 135 μm are studied. Flow visualization is conducted using a high-speed digital camera. Three condensation regimes, namely, mist/annular flow, injection flow, and slug-bubbly flow can be identified. Flow pattern maps are constructed using coordinates of superficial vapor and liquid velocities, wherein relatively distinct boundaries between the flow patterns are identified. The experimental results show that the condensation heat flux increases with an increase in the convergence angle and/or the steam mass flux at a given coolant flow rate but decreases with an increase in the coolant flow rate at a given steam mass flux. The results further demonstrate that the local condensation heat transfer coefficient in the mist/annular flow region is much higher than that in other condensation regimes. Moreover, the local condensation heat transfer coefficient in the microchannel with a convergence angle of 0.5° is larger than that in the microchannel with a bigger convergence angle under the condition of the same condensation regime.

Nomenclature

: Condensation heat transfer area (m2)
Co: Condensation number (—)
: Specific heat (kJ/kg K)
: Mean hydraulic diameter of a channel (m)
: Channel depth (m)
: Heat transfer coefficient (kW/m2 K)
: Latent heat of vaporization (kJ/kg)
: Superficial velocity (m/s)
: Channel length (m)
: Mass flow rate of coolant (kg/s)
: Mass flow rate of steam (kg/s)
: Condensation heat transfer rate (W)
: Condensation heat flux (kW/m2)
: Coolant flow rate (mL/min)
: Total thermal resistances for conduction through the silicon and silicon dioxide (m2 K/W)
Re: Reynolds number (—)
: Temperature (K or °C)
: Channel width (m)
: Quality (—)
: Axial distance from the channel inlet (m).
Greek Symbols
: Void fraction (—)
: Convergence angle of a channel (°)
: Density (kg/m3).
Subscripts
1: Mist/annular flow region
2: Injection flow region
3: Slug/bubbly flow region
: Coolant or forced convection
ch: Channel
: Homogeneous
in: Inlet
: Liquid
out: Outlet
sat: Saturation
: Total
: Vapor
: Wall
: Distance from channel inlet in the axial direction.

Acknowledgments

This work was supported by the National Science Council of Taiwan under the contract no. NSC 100-2221-E-007-112-MY3, and Ben-Ran Fu would like to express gratitude to Geothermal Technology Department at Industrial Technology Research Institute. This work is reconstructed based on a proceeding paper presented at the 8th International Symposium on Heat Transfer, October 21–24, 2012, Beijing, China.

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