Subcooling effect on boiling heat transfer of inclined downward-facing surface under low flow and pressure

International Journal of Heat and Mass Transfer 127 (2018) 182–195

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Subcooling effect on boiling heat transfer of inclined downward-facing surface under low flow and pressure Uiju Jeong a, Sung Joong Kim a,b,⇑ a b

Department of Nuclear Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Institute of Nano Science and Technology, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea

a r t i c l e

i n f o

Article history: Received 27 February 2018 Received in revised form 1 June 2018 Accepted 11 July 2018

Keywords: Critical heat flux Boiling curve Liquid subcooling Two-phase boundary layer flow Flow reversal Condensation-induced water hammer

a b s t r a c t The present study investigated the physical processes responsible for the variation in the boiling curve and critical heat flux (CHF) caused by liquid subcooling under atmospheric pressure in a rectangular flow channel; the flow channel was oriented 10° upward from the horizon. Bubble dynamics were examined using a high-speed camera and optical fiber microprobes. A solid copper block was utilized as a test heater and mounted above the flow channel to simulate the passive cooling system of an ex-vessel core catcher designed for nuclear power plants. Low mass flux and subcooling conditions ranging from 40–300 kg/m2 s and 5–25 K, respectively, were applied at the inlet of the test section. At the mass flux value of 40 kg/m2 s, large sliding bubbles were attributed to a key criterion for enhanced boiling heat transfer when the liquid subcooling was varied up to 15 K. The results showed that the CHF was weakly dependent on the degree of liquid subcooling, which deviates from the general trend reported by many researchers. A repetitive flow reversal along with a pressure shock appeared, owing to the rapid condensation at the exit, which added complexity to the analysis of the CHF. This study provides physical insights for understanding the subcooled flow boiling heat transfer mechanism (including the CHF) based on sophisticated experimental measurements, such as the visual capture of boiling dynamics using highspeed video and local void fraction. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction The vapor-liquid exchange process caused by density differences is considered one of the most central phenomena in boiling heat transfer. Desirable hydrodynamics is manifested in a boiling system where a departing bubble pumps a slug of hot liquid away from the heated wall and replaces it with a cooler liquid [1]. The vapor-liquid exchange mechanism could explain many experimental observations that the boiling curve is insensitive to degree of liquid subcooling [2–5]. Increase of subcooling brings out remarkable change in bubble dynamics via reduction of both bubble size and agitation intensity. Consequent degradation of fluid motion near the wall countervails the positive effect of subcooling on turbulent liquid convection. However, many studies showed that variation of subcooling can make a significant change in boiling heat transfer. Some studies reported that, as subcooling increases, a boiling curve was shifted toward a higher wall superheat [6,7]. On the other hand, the shift ⇑ Corresponding author at: Department of Nuclear Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea. E-mail address: [email protected] (S.J. Kim). https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.064 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

of boiling curve toward a lower wall superheat via subcooling increase was observed by other investigator, who explained the enhancement of boiling heat transfer by considering improvement of the convective heat transfer [8–13]. These conflicting reports may arise from the complex nature of the physical mechanism through which subcooled liquid affects the bubble size, nucleation frequency, and bubble dynamics related to bubble growth and collapse. Here, it should be pointed out that the significance of subcooling generally appears in the regime of partial nucleate boiling, whereas subcooling has a negligible influence on a fully developed boiling curve [8,9,11,13]. Such negligible influence can be explained by remarkable reduction of the effective area for convection owing to vigorous nucleation activity in the fully developed nucleate boiling regime. In addition, it is worth noting the heater orientation effect on subcooled boiling characteristics because the orientation would considerably affect the bubble dynamics along the heater. For the specific case of downward-facing heater, boiling curves at various subcoolings are expected to merge into a virtual asymptote even under an intermediate heat flux condition, because bubble dynamics along downward-facing heater is quite similar to that in the fully developed boiling regime. In case of downward-facing heater,

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Nomenclature Acronym BHTC CHF CIWH DAQ PID RTD SS Symbol hB kCu L m n q00 q00 CHF q00 CHF,sat

Description Boiling heat transfer coefficient critical heat flux condensation-induced water hammer data acquisition Proportional–integral–derivative resistance temperature detector stainless steel Description, Unit boiling heat transfer coefficient, W/m2-K thermal conductivity of copper, W/m-K length between the heated surface and position of Tw, m proportionality constant average slope of the P-T curve, Pa/K heat flux, W/m2 critical heat flux, W/m2 critical heat flux under saturated state, W/m2

thicker thermal boundary layer and consequent higher nucleate site density facilitate the bubble coalescence process [14], which results in formation of a large vapor mass even at low heat flux. Such large vapor mass is pushed against the heater wall by buoyancy. Only a few reports of subcooled boiling curves on downwardfacing heater are available in the literature. Haddad and Cheung reported that subcooling had little effect on the boiling curve over a wall superheat of 7 K by using a hemispherical surface as a heater [15]. In short, influence of subcooling is still unclear, and therefore a more thorough investigation should be conducted to improve the prediction capability for subcooled boiling heat transfer along the downward-facing heater. Compared to inconsistent reports on nucleate boiling characteristics, it has been consistently reported that liquid subcooling enhances critical heat flux (CHF). CHF can be presented as a linear function of liquid subcooling (DTsub), as shown in Eq. (1):

q00CHF;sub ¼ ð1 þ m  DT sub Þðq00CHF;sat Þ where DT sub ¼ T sat  T bulk

ð1Þ

where q00CHF;sub and q00CHF;sat are the CHF under subcooled and saturated boiling conditions, respectively. m is an empirically determined proportionality constant. Such a linear relationship between liquid subcooling and the CHF was observed in numerous experimental studies when various fluids were adopted, such as water, HFE7100, PF5060, FC72, FC86, R113, methanol, and isopropanol, and when several heater configurations were adopted, such as an upward-facing heater, vertical plate, and horizontal wire [11,16–29]. Positive linearity between the liquid subcooling and resulting CHF could also be confirmed in case of downward-facing heater [16,21,30–32]. Note that El-Genk and Parker [21] studied the combined effect of heater orientation and liquid subcooling and showed that the subcooling effect was rapidly diminished when the heater orientation changed from 30° to 0° (downward-facing horizontal surface). However, it should be noted that aforementioned works used either very small or curved heaters. Thus, their work might obfuscate the complex physics associated with heater size. As pointed out by Theofanous et al., Rouge, Cheung and Haddad, and Sulatskii et al., the CHF on a downward-facing surface is highly reliant on the local mass flow rate induced by natural convection, which itself is a function of geometric characteristics such as surface orientation to the gravity vector and heater geometry [33–36]. Among the aforementioned studies, only Sulatskii et al.

q00 CHF,sub critical heat flux under subcooled state, W/m2 rc cavity mouth radius, m temperature in the heating block at distance of 4.7 mm Tw from the heater surface, °C Tm temperature in the heating block at distance of 14.7 mm from the heater surface, °C Td temperature in the heating block at distance of 24.7 mm from the heater surface, °C Tsat saturation temperature, °C Ts temperature at the heater surface, °C temperature of liquid in bulk region, °C Tbulk DTsub liquid subcooled degree, °C Um (arbitrary) absolute uncertainty of the subscripted parameter (m) Dx distance between the vertically aligned thermocouples, m Greek Symbol Description, Unit rl Surface tension, N/m

thoroughly investigated the effect of subcooling on the CHF at various subcooling degrees on a large downward-facing flat heater with a slight inclination [36]. Interestingly, a nonlinear characteristic between subcooling and the CHF was observed in their work. They discovered a regime in which subcooling negatively affected the CHF. This unusual instance of CHF dependence on subcooling was simulated in their CHF model by incorporating the negative influence of subcooling on local mass flow rate along the heater surface. Specifically, a term representing single-phase heat transfer to the subcooled liquid was added in calculation of the vapor mass flow rate. Their CHF model could successfully predict the anomalous dependence of subcooling on the CHF observed in their experiments. Note that the anomalous dependence can be interpreted as a weak contribution of the additional sensible energy needed to heat the subcooled liquid to a saturated state. Another interpretation may be thought of as a strong contribution of vapor layer motion on the CHF. It is apparent that a strong vapor layer motion contribution comes from the large geometry of the heater surface. The literature review described thus far revealed that there exists a lack of knowledge for the accurate prediction of subcooling effect on the CHF, accordingly motivated us to establish the experimental basis for large-scale cooling systems. The cooling systems of interest include ex-vessel core catcher cooling systems designed for nuclear power plants, such as ABWR, VVER-1000, ESBWR, and EU-APR1400 [37–40]. These systems have a common feature, which utilizes boiling heat transfer to remove residual heat after a core meltdown. Particularly for EU-APR1400, the heat transfer surface was designed to be inclined at 10° from the horizontal plane to facilitate vapor venting. In this study, beyond a specific liquid subcooling and heat flux level, we faced two-phase instability, which is quite similar to the geysering phenomenon explained by Ruspini et al. [41]. This instability can be characterized by the repetitive pressure shocks and momentary flow reversal. Physically, the instability can be regarded as repetitive occurrence of the condensation-induced water hammer (CIWH), but its pressure amplitude was confirmed to be far insufficient to break a pipeline in the present study. Owing to safety concerns regarding the water hammer, it has been investigated in various industrial fields for the last few decades [42–44]. Note that the observed instability may cause a significant disturbance in the bubble behavior along the heater surface through a physical coupling between the induced pressure shock and the bubble ebullition cycle. This may affect the boiling crisis phenomenon significantly.

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Therefore, the purpose of this work is to present experimental data for the nucleate boiling curve and CHF on a flat, downwardfacing surface at various subcooling conditions and flow rates to investigate the influence of subcooling on boiling heat transfer, especially in two-phase boundary layer flow along the heater surface. An effort was made to examine the two-phase instability including the CIWH observed in the present study, and also to investigate their influence on the CHF. A high-speed video system was used to capture instantaneous bubble behavior to understand the physical phenomenon related to the boiling crisis. In addition, an optical fiber microprobe was employed to measure the local void fraction near the heater surface. The information on void fraction was mainly utilized to quantify the boiling crisis characteristics.

2. Experimental apparatus 2.1. Test section assembly To consider a potential application for large-scale passive cooling systems, two-phase boundary layer flow was chosen as a key similarity criterion when designing a test section. This is because the existence of a two-phase boundary layer influences flow velocities and phase distributions near the heater surface, and may affect the liquid supply to heater surface. To successfully mimic the thermal-hydraulic phenomena that appear in large-scale cooling systems, the dimensions of the test section were carefully determined. The dimensions of the heated area were selected to provide sufficient space to form a stable two-phase boundary layer flow. The sufficient space enables the bubbles to actively coalesce

in the lateral and bulk flow directions into a large one. Inspiration for this design process was taken from the work conducted by Sulatskii et al. in which they observed that the CHF always occurred over a length of 50–120 mm from the lead of the heated region, regardless of total heater length [36]. Thus, it is reasonably determined that two-phase boundary layer flow can be developed over approximately 120 mm of the heated length under the heat flux close to the CHF. This judgement can be valid if the twophase boundary layer flow obstructs the liquid supply to the heater surface. Also, we could infer that immediately after the formation of the two-phase boundary layer, the flow within the layer experiences sufficient acceleration so that the CHF can be increased. Accordingly, heater length and width were set as 216 mm and 108.5 mm, respectively. A channel height was also set to 30 mm to sufficiently minimize the direct interaction between bubbles and the unheated wall. However, it should be noted that the small dimensions of the lab-scale test section could make a different situation compared to real core catcher cooling channel, which has a very long width of 16 m. Particularly, existence of the side walls in the lab-scale test section restrict the bubble motion by forcing the bubble to proceed only in the axial direction, and also by eliminating the lateral flow. Such restriction on bubble behavior may cause significant reduction of turbulence in the channel. As turbulent behavior is a key process in destabilization and breakup of a large bubble, the bubble coalescence process can proceed more actively in the lab-scale test section. Consequently, it is expected that the more active coalescence process would limit the liquid supply process to the heater surface by restricting the liquid inflow path. Accordingly, the lower CHF might result in the lab-scale test section.

Fig. 1. Illustration of the test section assembly. (a) expanded view; (b) transversal cross-sectional view; (c) longitudinal cross-sectional view.

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Note that the aforementioned core catcher cooling system inevitably adopts a thick wall of very large thermal inertia. Implementing such a large thermal inertia is very important for avoiding a boiling crisis, because thermal and structural integrity can be maintained even when a local dry patch appears permanently. Considering that a considerable number of dry patches are likely to more frequently appear in the horizontal channel compared to the vertical channel, even under a moderate heat flux level, there is a strong likelihood that the downward-facing CHF will occur at a significantly lower heat flux level when using a thin-plate heater. Thus, an indirect heating method that utilizes a large copper block was chosen for the heat transfer. Fig. 1 shows a detailed view of the test section assembly, which mainly consists of a test section body, transparent windows, a cover plate, and a heating block. The materials used for the test section body, windows, and heating block are stainless steel grade 316, quartz, and oxygen-free copper, respectively. Fifteen 19 mm diameter holes were machined in the heating block, and 15 cartridge heaters (4 kW per heater) were inserted in these holes to serve as the heating elements. The heating block was mounted on the upper wall of the test section body. Thus, the heating block serves as the ceiling of the rectangular channel and the heat source for one-sided heating.

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Three vertically-aligned K-type thermocouples (0.5 mm diameter) spaced 10 mm apart were inserted into the heating block to measure the temperature gradient near the heating surface. Based on this value, the heat flux applied to the test section could be estimated. Six thermocouple sets were positioned at specific locations in the heating block, as presented in Fig. 2b. An additional four thermocouples were inserted at the locations close to the heater surface in order to detect a spatial and temporal temperature excursion right before and after the CHF is reached. These locations are marked as empty circles in Fig. 2b.The heat flux and the temperature gradient were calculated using a three-point, backwardspace Taylor series approximation, which is defined as follows:

q00 ¼ kCu

dT ; dx

dT 3T w  4T m þ T d ¼ ; dx 2 Dx

ð2Þ

ð3Þ

where Tw (nearest to the surface), Tm, and Td are temperatures in the heating block in the order of nearest to farthest from the heater surface.

Fig. 2. (a) Schematic of the water boiling loop, (b) Spatial distribution of the thermocouples installed in the copper heating block.

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2.2. Flow boiling loop Fig. 2a shows a schematic of the water boiling loop. It was built to investigate subcooled flow boiling heat transfer, in addition to the CHF under low pressure and low mass flux conditions. In the loop, subcooled water is circulated through a centrifugal pump that is controlled with a variable-frequency drive and a valve located upstream of the test section. The fluid bulk temperatures were measured by 4-wire RTD (Pt100) sensors and controlled by a PID-controlled preheater, which are located upstream of the test section. The analog electrical signals from the K-type thermocouples inserted in the copper heating block, RTD sensors, turbine flowmeter, pressure transducers, and voltage/current/power meters were collected and converted to digital data through a data acquisition system, National Instrument (NI) SCXI and cDAQ series. The digitized data were collected using NI LabVIEW software and stored in the computer. The signals were recorded at a 0.5 s interval. A high-speed video camera (Phantom V7.3) was used to visualize the boiling phenomena at a photographing rate of 2000 frames per second. Furthermore, an optical fiber microprobe with diameter of 125 lm was used to measure the void fraction at the tip of the probe. Except for about 5 mm from the tip, the optical fiber part was enveloped by a stainless steel sheath with outer diameter of 0.75 mm. Due to very small diameter of the sheath, the flow field distortion induced by the probe was considered to be negligible. The collected data are expected to provide information about the two-phase flow structure in the vicinity of the heater surface that is optically blocked by stratified bubbles near the heating surface. The overall system measuring the void fraction was supplied by R.B.I Instrumentations et Mesures.

2.3. Experimental procedure, operating conditions, and measurement uncertainty In the first step of the boiling experiment, hydrochloric acid (35 wt.%) was used to remove the contaminant deposited on the heater surface during the previous boiling experiment. Then, the heater surface was cleaned with acetone and subsequently polished using 400-grit silicon carbide sandpaper. Next, the boiling loop was filled with ultrapure water and circulated by a centrifugal pump while being heated by a preheater to degas for 1 h. The boiling experiment proceeded by heating the cartridge heaters in the copper heating block through a silicon-controlled rectifier. To obtain reliable experimental data, electrical power was delivered to the cartridge heaters at an increase rate less than 5 kW/m2 per minute. Meanwhile, pressure, mass flux, and inlet subcooling were maintained at steady conditions until either the boiling crisis occurred, or severe flow instability was observed. The absolute pressure in the test section and the orientation angle of the heater surface were fixed at 1.07 bars and 10°, respectively. Low mass flux conditions ranging from 40 to 300 kg/m2-s were applied at the test section inlet by considering the characteristics of natural circulation at the interest of the core catcher cooling system. At a mass flux of 40 kg/m2-s, the inertia force of the flow exerted on the vapor was insignificant compared to the buoyancy force. Thus, the corresponding bubble dynamics could be regarded as similar to that observed in pool boiling. The maximum mass flux was determined based on the experimental results obtained using the natural circulation flow rate [45]. The liquid subcooling varied from 5 K (near saturated) to 25 K in increments of 5 K. However, the CHF data at a mass flux of 40 kg/m2-s could be measured under limited subcooling up to 20 K, because under high subcooling, the condensation induced water hammer violently appeared and endangered the boiling loop, even at heat flux levels below the CHF.

The measurement uncertainties in the present experiment were estimated to be ±1% for the water flow rate, ±0.08 °C for the fluid temperature, ±0.2% for the gauge pressure, and ±0.01 for the local void fraction in the range of over 0.7, respectively. The high accuracy in the void fraction measurement was achieved through the high-qualified hardware system, which provides very short signal settling time less than 1 ls and also very high sampling rate of 1 MHz. In addition, appearance of large elongated bubbles in slug flow helps achieve low uncertainty of void fraction because it greatly increases the vapor residence time, which is inversely proportional to the uncertainty. Furthermore, the longer residence time reduced a contribution of the piercing phenomenon, which is one of the major uncertainty sources. The most notable measurement uncertainties were generated from the calculation of the local heat flux, surface temperature, and boiling heat transfer coefficient (BHTC). Because the local heat flux was calculated from the three thermocouples aligned in order, its uncertainty was expected to be significant. The uncertainty may originate from three categories of parameters: calibration accuracy of the thermocouples, variation in the thermal conductivity of the copper block where the temperature changes, and uncertainty of the length measurements and spacing between the thermocouples. The geometric uncertainties were determined by the engineering tolerance applied when fabricating the thermocouple holes. Because the most influential parameter is the calibration accuracy of the thermocouples, all the thermocouples used in the experiments were calibrated precisely using FLUKE-9173. Propagation of the aforementioned uncertainties was investigated by a general uncertainty analysis based on the partial sum method [46]. Finally, the relative uncertainty of the local heat flux could be expressed as shown in Eq. (4).

U q00 ¼ q00

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2  2  2 kU T d Uk U Dx 3kU T w 2kU T m þ þ þ þ ; k Dx 2Dxq00 Dxq00 2Dxq00

ð4Þ 00

where q is the heat flux, Dx is the length between the adjacent thermocouples, and U and k denote the uncertainty of the subscripted parameter and the thermal conductivity of copper, respectively. The heater surface temperature, Ts, can be calculated using the local heat flux and the temperature, Tw, using the following expression:

L T s ¼ T w  q00 ; k

ð5Þ

where L is the length between the heated surface and the position of Tw. The uncertainty of the surface temperature can be calculated in the same manner based on the partial sum method. The final expression for the uncertainty can be expressed as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2 !2 !2 u UT s u UTw LU q00 q00 LU k q00 U L t ¼ þ þ 2 þ Ts T w  q00 kL kðT w  q00 kLÞ kðT w  q00 kLÞ k ðT w  q00 LÞ k

ð6Þ

BHTC, hB and its uncertainty can be calculated by Eqs. (7) and (8), respectively.

hB ¼

q00 T s  T sat

U hB ¼ hB

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 U q00 UTs þ q00 T s  T sat

ð7Þ

ð8Þ

The relative uncertainty of the local heat flux and the BHTC, which are functions of the heat flux and the corresponding wall temperature, continuously and rapidly decrease from 32% to 5%

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and from 33% to 5.4% as the heat flux varies from 50 to 400 kW/m2, respectively. In other words, the relative uncertainty of the CHF is calculated to be less than 5% because the CHF values were mostly higher than 400 kW/m2 in this study. The absolute uncertainty of the surface temperature was calculated as ±0.6 K.

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defined as an average of the local heat flux data collected 1 min before the CHF occurred, in order to eliminate subjective judgments in determining the CHF. In addition, the BHTC was defined as an averaged value over 1 min. 3.2. Nucleate boiling heat transfer

3. Results and discussion 3.1. Characterization of BHTC and CHF In this study, the BHTC and the CHF were defined based on local parameters such as the local heat flux and the local surface temperature measured at a specific location. The BHTCs were measured downstream of the heater surface where the two-phase boundary layer appeared in a stable condition in the location marked Q5C in Fig. 2b. The CHF was defined as the local heat flux level where a sudden and continuous rise in the surface temperature beyond 200 °C first appears simultaneously with an abrupt decrease in the local heat flux, following an incremental increase in the heater power. However, owing to the frequent appearance of reversible dry patches at high heat flux levels, it was difficult to measure the definitive CHF and BHTC values because the local heat flux was instantaneously dropped with the transitory appearance of the local dry patch. Therefore, in this study, the CHF was

Fig. 3. Reproducibility of the boiling curves of subcooled water on the slightly inclined downward-facing heater surface.

To ensure reproducibility of the experimental results, boiling experiments were conducted separately three times at every thermal-hydraulic condition tested. Fig. 3 presents the boiling curves for water on a Cu surface with mass flux of 300 kg/m2-s and inlet subcooling of 5 K. The reproducibility of the experimental results was confirmed even though each boiling curve was obtained on different dates. In the present study, nucleated bubbles were observed to slide along the heater surface by buoyancy, which pushed the bubbles up to the surface and allowed them to grow by merging with neighboring small bubbles. As reported by Nishikawa and Fujita, Rouge, and Qiu and Dhir [34,47,48], a thin liquid layer evaporating on the surface exists between the large bubble and the heater surface. It is apparent that if the mass flux is reduced, large bubbles would appear to form more frequently because of the increased heat transfer from the heater surface. Accordingly, the contribution of evaporative heat transfer would increase. Because of effective phase change heat transfer, even though a decrease in bulk flow velocity deteriorates the convective heat transfer by several degrees, a reduction in the mass flux may only slightly affect the boiling heat transfer. The expected weak influence of mass flux on the boiling heat transfer was confirmed in this study as shown in Fig. 4. The nucleate boiling curves and hB curves are presented as functions of the mass flux under fixed liquid subcooling at the inlet of the test section. From Fig. 4, an interesting feature was observed; the boiling curves at different mass fluxes ranging from 40 to 300 kg/m2-s are merged together into a virtual asymptote even at heat fluxes below 75 kW/m2. This implies that, at least for low flow conditions less than 300 kg/m2-s, mass flux may not be a dominant parameter affecting the boiling heat transfer on the inclined downward-facing surface at atmospheric pressure. The observed trend is similar to the results from the experiments carried out by Song, as plotted in Fig. 4 [49]. The trend can be explained by considering the crucial role of the sliding bubble in convective heat transfer at the downward-facing inclined surface along with the evaporative heat transfer at the thin liquid layer. As shown in Fig. 5, even at heat flux conditions below 75 kW/m2, a bubble grows rapidly after its departure by merging with small

Fig. 4. Boiling curves (a) and hB curves (b) under several mass flux conditions at fixed liquid subcooling.

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Fig. 5. Captured bubble behavior showing its sliding motion along the heater surface and growth process at different mass fluxes under a low heat flux regime (flow direction: from bottom to top).

neighboring bubbles along its path. Then, the enlarged bubble moves up along the heater surface. It was clearly observed that the liquid flowing near the heater surface was significantly disturbed by the bubble-sweeping process, which generated considerable turbulence around and behind the sliding bubble. According to previous works conducted by Bayazit et al. and Donnelly et al., it is expected that the turbulent motion induced by the sliding bubble would enhance the convective heat transfer to a level approximately three times that of the natural convection level [50,51]. Such

a strong positive influence of the sliding bubble on the heat transfer would be enhanced if the mass flux diminishes, because larger bubbles would appear more frequently with similar or larger velocity due to the linearity between bubble volume and its velocity, as clearly shown in Fig. 5. Also, as mentioned above, the evaporative heat transfer would be increased via reduction of mass flux. The resulting heat transfer enhancement can compensate for the deterioration of the convective heat transfer owing to the decrease in mass flux. In this way, the apparent independence of the boiling heat transfer and the mass flux can be explained. Fig. 6 presents the obtained subcooled boiling curves in the experiments with water at different mass fluxes. Many boiling curves obtained under pool boiling conditions were plotted in Fig. 6a and compared with the experimental data from previous works [15,52–55]. In addition, the boiling curves obtained at various degrees of liquid subcooling under the flow condition were plotted in Fig. 6b. Compared to the flow boiling condition, the subcooled pool boiling curves show that the rate of heat transfer is significantly dependent on the degree of liquid subcooling. Note that such dependence is contrary to the expectation of the author, as described in the introduction section. Under pool boiling conditions, the trend observed in the present study appears to be very similar to the experimental results reported by El-Genk and Glebov [52]; their results qualitatively agree with our data. The consistent trend revealed from the subcooled pool boiling experiments is that the boiling curves shift upward from the saturated state with liquid subcooling to 15 K. In other words, the BHTC increases with liquid subcooling up to approximately 15 K. This linear relation between the BHTC and subcooling manifested in the experiments of El-Genk and Bostanci [12]. However, they used HFE-7100 dielectric liquid as a working fluid instead of water [12]. As emphasized in the introduction section, especially in the low heat flux condition, the boiling curves generally shift upward when liquid subcooling is applied. This means that the rate of convective heat transfer increases with subcooling. At this point, it should be noted that the convective heat transfer is considerably enhanced by the sliding characteristics of the bubbles observed in this study, even under a low heat flux condition. Thus, a dominant heat transport mode in this study is convective heat transfer. Therefore, the clear linear relation between the BHTC and liquid subcooling can be explained by considering the sliding bubbles and the corresponding dominant heat transport mode. However, it is noteworthy that beyond 15 K subcooling, the boiling curves experience an abrupt and large downward shift with an increase of the subcooling when the subcooling is below 5 K.

Fig. 6. Boiling curves with several liquid subcooling conditions obtained from the downward-facing heater; (a) pool boiling condition with experimental data from previous studies, (b) flow boiling condition.

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Also, negligible difference between the boiling curves was observed at the subcooling of 20 K and 25 K. This result is the opposite of what was expected based on the results obtained by El-Genk and Bostanci [12]. There are only a few investigations involving pool boiling of subcooled water beyond 20 K liquid subcooling using a downward-facing plate heater. The abrupt deterioration of the heat transfer rate beyond 15 K subcooling was caused by the change in the characteristics of bubble behavior and a corresponding change in the enhancement of the convective heat transfer due to sliding bubble motion. The change in bubble behavior was visually examined by comparing the videos recorded at different degrees of subcooling (15 K and 20 K) under same heat flux of 165 kW/m2. A difference in bubble behavior was clearly observed. While most of the heater surface was covered by small isolated bubbles and infrequent appearances of large bubbles at 20 K subcooling, larger bubbles appeared along the heater surface consistently and frequently at 15 K subcooling. This visual observation provides reasonable evidence for the abrupt and large downward shift. This is because the evaporative heat transfer may be considerably degraded and also the observed change in bubble behavior with the subcooling would considerably enfeeble the turbulent motions created by bubble growth, condensation, and movement along the surface. This would proportionally deteriorate the convective heat transfer. In summary, a non-linear relation between subcooling and the boiling heat transfer was revealed under the pool boiling condition in the present study, which shows the best performance at 15 K subcooling. However, under the flow boiling condition, it was observed that the subcooling hardly affected the heat transfer. While the pool boiling curve of Nishikawa et al. [53], obtained at inclination angle of 5°, nearly overlaps the present boiling curve, the boiling curves of other investigators were confirmed to be quite different from the present result. This discrepancy can be explained by considering weak bubble coalescence process on the heater and corresponding low rate of evaporative heat transfer in the liquid sublayer in experiments of Haddad and Cheung [15], Guo and El-Genk [54], and Kim et al. [55]. This is because, their heaters were so short that the bubbles couldn’t grow up to a large one, which can contains large amounts of the liquid sublayer underneath the bubble. As a result, the rates of evaporative heat transfer in their experiments were significantly lower than that of the present study and Nishikawa et al. This is the most probable cause for the discrepancy. The boiling curve developed by Kim et al. was shifted toward a higher wall superheat most severely compared to the others [55]. This discrepancy may arise from an inherent feature of their experimental apparatus. That feature utilizes a mirrorpolished silicon wafer plate as a main heater, and therefore the cavity mouth radius and corresponding roughness on the heater surface were very small. According to Webb and Kim [56], the required conditions for boiling nucleation on a surface was defined as shown in Eq. (9).

Tw  Ts ¼

q00 r c 2rl þ ; kl nrc

189

3.3. Critical heat flux 3.3.1. Influence of mass flux on the CHF under near saturated condition As a first step in the investigation of the boiling crisis phenomenon, a relation between the mass flux and corresponding CHF was examined to obtain a better understanding of the CHF triggering mechanism on a downward-facing plate-type heater surface. Note that the heater surface of interest is large enough to manifest a remarkable contribution of convective heat transfer, which is achievable by the sliding characteristics of large bubbles. Fig. 7 [58] shows a linear dependence between the CHF and mass flux under the near-saturated condition, and also provides CHF values predicted from the existing pool boiling CHF models. The data points marked by hollow circles in the figure were produced at the experimental facility used in the present study. From Fig. 7, it is observed that a transitional mass flux exists, beyond which the proportionality between the mass flux and CHF almost doubles. According to Jeong et al. [58], the enhanced proportionality may be attributed to the delayed flow pattern transition over the specific liquid mass flow rate, and, correspondingly, the delayed restriction of the liquid supply path to the surface. This is because the flow pattern obviously determines the phase distribution near the surface, along with the corresponding size and occurrence frequency of the path through which bulk liquid is supplied to the heater surface. Their results motivate us to take an approach based on the liquid supply process, which is highly dependent on two-phase macroscopic hydrodynamics towards the boiling crisis at the downward-facing heater surface. The importance of the phase distribution near a heater surface for the liquid supply was more noticeable in the observed large discrepancy of the CHF value between the present data and Brusstar and Merte [59], as shown in Fig. 7. Note that they obtained CHF data, which are utilized to develop their CHF model by using a small copper plate heater measuring 19.1 (length)  38.1 (width) mm2. In such a small heater, the departed bubbles could quickly escape from the surface to the surrounding bulk liquid region, and thus liquid access to the heater surface was easier compared to the current observation. In addition, the small dimensions of their heater restrict the coalescence process between neighboring bubbles along the heater surface by limiting the bubble size. The weak coalescence phenomenon could be responsible for the enhanced liquid supply process. As a result, a significantly higher CHF value could be obtained. This analysis provides crucial evidence for the necessity of the consideration of the two-phase

ð9Þ

where rc is the cavity mouth radius and n is the slope of the vapor pressure curve. The first term of right hand side in Eq. (9) is not significantly affected by rc because q00 is very large. Therefore, the decrease in rc would increase the wall superheat. In this way, the shift toward the higher superheat observed in the boiling curve of Kim et al. [55] can be explained mathematically. Furthermore, the experimental study of Jabardo et al. clearly showed that the BHTC deteriorated with a decrease in the surface roughness measured by the arithmetical mean deviation of the profile [57].

Fig. 7. Dependence of the critical heat flux on the mass flux under low flow conditions [58].

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distribution near a heater surface when analyzing the downwardfacing CHF mechanism. 3.3.2. Influence of liquid subcooling on CHF An apparent increase in liquid subcooling would facilitate the liquid supply process because additional sensible energy is required to heat the liquid from the subcooled to the saturated state. Furthermore, higher subcooling would reduce the net rate of vapor generation because of the introduction of sensible energy and the increased amount of condensate at the vapor/liquid interfaces. As a result, the thickness of the two-phase boundary layer in this study can be reduced. A decrease in the boundary layer thickness may exert positive influence on the liquid supply process by lowering the resistance to liquid entrainment from a bulk region to the heater surface. In this way, higher liquid subcooling would lead to considerable enhancement in CHF, as reported in almost all subcooled boiling experiments. However, for downward-facing heaters, increased subcooling can generate an adverse effect on the liquid supply process, according to following physical process. An increase in liquid subcooling reduces the net rate of vapor generation along the heater surface. Subsequently, reduced vapor generation would lead to a decrease in the velocity of the two-phase boundary layer, because a lower amount of vapor in the test section decreases the buoyancy force exerted on the vapor layer. Furthermore, at the unheated channel right behind the heated section, higher subcooling accelerates the condensation-induced collapse of a bubble exiting from the test section. The resulting reduction in bubble lifetime downstream of the test section also would decrease the velocity of the two-phase boundary layer by lowering the buoyancy force. The deteriorated flow characteristics in the two-phase boundary layer would degrade an entrainment process behind the sliding bubble, through which the bulk liquid is pumped into the heater surface. In addition, the decrease in the velocity of the two-phase boundary layer may increase the resistance to the liquid supply by increasing the thickness of the boundary layer and stabilizing the vapor-liquid interface. In this way, the negative aspects caused by the increase in liquid subcooling can appear in the liquid supply process for the large downward-facing heaters. The physical connection between the vapor layer velocity along the heater surface and the CHF has already been investigated and modeled in the downward-facing CHF models [35,36,59]. Note that the influence of liquid subcooling on the vapor layer velocity would be stronger if the heater size becomes larger, especially in length. The present subcooled boiling data under the pool boiling condition (G = 40 kg/m2-s) are compared to the CHF models of Brusstar and Merte, Sulatskii et al., and He et al. in Fig. 9 [36,59,60]. Subcoolings of 5, 10, 15, and 20 K were applied to investigate the effect of subcooling on the CHF under the pool boiling condition. The subcooling effect appeared in two types of trends. One is a rather linear relationship between the subcooling degree and the CHF, which was also observed in the CHF models of Brusstar and Merte [59] and He et al. [60]. The other is a weak dependence of subcooling on the CHF, which appeared in the present study and the CHF model of Sulatskii et al. [36]. The non-linear dependence of CHF on subcooling was observed in work conducted by Sulatskii et al., which shows the existence of a minimum CHF under a subcooling of approximately 20 K. Their CHF model predicted a decrease in CHF with subcooling up to approximately 20 K. For up to 15 K subcooling, the present subcooled CHF data are comparable with the trend observed in the CHF model developed by Sulatskii et al., and is also consistent with the adverse effect of subcooling on velocity of two-phase boundary layer flow, as stated in the previous paragraph. The large discrepancy in the trends can be explained by examining the heater configuration used in the CHF experiments. As

mentioned earlier, Brusstar and Merte [59] used a small heater, and thus the departing bubbles could quickly escape from the heater surface to the surrounding bulk liquid region in an isolated form; this was possible because of the weak bubble coalescence phenomenon along the heater surface, even at a high heat flux condition. As a result, the liquid access to the heater surface was easier compared to that of the present study. This indicates that the subcooled liquid could effectively cool the heater surface, and the CHF increases proportional to the subcooling degree. It is also noteworthy that their CHF model is inherently anticipated to bear less accuracy for large heaters. This is because the bubble terminal velocity along the heater surface is highly dependent on the size of the sliding bubble, and the size heavily relies on the geometric dimensions of heater surface and the liquid subcooling. However, their CHF model does not consider the effect of subcooling on the bubble size, and therefore also does not consider the buoyancy force determined by the length of the bubble. He et al. [60] used the SBLB CHF data obtained on a curved surface, such as a nuclear reactor vessel, for the validation of their CHF model. On such a curved surface, the two-phase boundary layer experiences continuous flow direction changes, and the buoyancy force induced by a bubble strengthens as the surface orientation angle increases from 0° (downward) to 90° (vertical). This implies that bubbles in the layer are in a rather unstable state compared to that of flat-plate-type heater, thus such an unstable state may hinder the formation of large bubbles and affect the flow pattern. As analyzed above, the weak bubble coalescence phenomenon would enlarge the liquid supply paths, and correspondingly result in an enhanced contribution of the subcooled liquid on the liquid supply process. In this way, the proportional relation between the CHF and degree of liquid subcooling can be explained. A notable feature was observed in Fig. 8; an abrupt increase in the CHF value occurred when the liquid subcooling changed from 15 to 20 K. Such an abrupt change is similar to the downward shift observed in the boiling curves of the present study, which are shown in Fig. 6. While the rate of heat transfer was deteriorated beyond 15 K subcooling, the boiling crisis was delayed considerably as the subcooling changed from 15 to 20 K. Similar to the case of the nucleate boiling, the abrupt increase in CHF can be explained based on the characteristics of bubble behavior described in Section 3.2. When the liquid subcooling increases from 15 to 20 K, the sliding bubble motions prevalent in the two-phase boundary layer were observed to decrease substantially, and thus the bubble coalescence process was weakened. The resulting phase

Fig. 8. Dependence of the critical heat flux on degree of liquid subcooling under the pool boiling condition (G = 40 kg/m2-s) in comparison to the existing CHF models.

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Fig. 9. A simplified schematic of the mechanism responsible for the flow reversal, and an accompanying pressure oscillation with a sporadic pressure shock.

distribution near the surface with less vapor fraction is obviously favorable for the liquid supply process because of the enlarged cooling path through which liquid is supplied to the heater surface from the bulk region. In this way, the considerable increase in CHF value can be explained by examining the transition of the flow pattern. However, it should be noted that the repetitive flow reversal phenomenon with pressure oscillation appeared in the subcooled boiling experiments, as mentioned in the introduction. Such a transient phenomenon in two-phase flow should be considered when analyzing the observed abrupt increase in the CHF value with increase in subcooling from 15 to 20 K. This will be covered in the next section. 3.3.3. Transient two-phase flow and its influence on the CHF A violent boiling process was observed in the present experiment beyond a specific subcooling and heat flux. The violent boiling phenomenon is characterized by the repetition of rapid growth of a large bubble, and its condensation at the unheated downstream channel. The rapid condensation of a large bubble causes flow reversal and pressure oscillation with sporadic pressure shocks. This violent boiling phenomenon appears similar to geysering, as explained by Ruspini et al. [41]. In the present study, the observed sporadic pressure shocks can be regarded as the condensation induced water hammer, even though its amplitude was confirmed to be insufficient to break the pipeline. This is because the experimental facility in the present study experiences substantial mechanical loadings, such as vibration of the entire boiling loop when sporadic pressure shocks appear. Thus, the experiment should be stopped for the integrity of the facility. In fact, the flow reversal and accompanying pressure oscillation are physically correlated with each other because the pressure change is caused by a rapid change in the fluid velocity. The physical correlation is schematically presented in Fig. 9, which shows the mechanism responsible for the flow reversal and pressure oscillation. A large sliding bubble along the heater surface experiences rapid condensation at the unheated section near the test section outlet. Such rapid condensation may appear when a large vapor mass is brought into contact with subcooled water through a sufficiently large interface as a form of entrapment. According to a report by Griffith [61], during the condensation process, the vapor pressure in the bubble drops to a value that is close to the saturation pressure associated with the temperature of the subcooled liquid. Fairly low saturation pressure helps the liquid adjacent to the right of the bubble to accelerate to a high velocity toward the left side of the bubble, as shown in Fig. 9. The fast-moving liquid creates a significant pressure shock through

the conversion of the kinetic energy of the moving liquid into pressure energy. In this way, beyond a specific liquid subcooling and heat flux, a pressure shock and flow reversal can occur. The pressure shock and reversed liquid would increase if the bubble grows into a larger one. In other words, the transient behavior of velocity and pressure would be intensified with heat flux. The simultaneous occurrence of the flow reversal and pressure shock is regarded as a notable transient behavior that is responsible for the abrupt change in the CHF with the increased subcooling. Note that the flow reversal is concentrated near the heater surface. Thus, the bubbles hovering right above the heater surface can be effectively mixed with the reversed subcooled liquid and condensed therein. Furthermore, the sporadic pressure shocks with rather large amplitudes were observed to contribute to condensing the bubbles and suppressing bubble growth by significantly increasing the saturation temperature. In this way, the bubbles covering most of the heater surface can be eliminated instantaneously, which in turn facilitates the liquid supply to the heater surface. As a result, the heater surface can be effectively cooled down and a higher CHF can be achieved. Pressure and high-speed camera records represented in Figs. 10 and 11 provide direct evidence for the flow reversal and the pressure shock phenomena that occurred in the present study. They appeared beyond a specific subcooling and heat flux. Fig. 10 presents the transient behavior of pressure measured at the test section as a function of the inlet subcooling and heat flux. The pressure data were recorded at time interval of 1 ms to capture the fast-transient pressure shocks. As clearly shown in Fig. 10, the pressure shocks exceeding 0.4 bar were frequently observed only in case of the 20 K subcooling beyond a heat flux of 340 kW/m2. However, a pressure shock was not observed in the pressure data obtained at a 15 K subcooling. Using a high-speed camera, the flow reversal that occurred at the time of the pressure shock is shown in Fig. 11. The video was recorded at a heat flux of 360 kW/m2, at which the pressure shocks appeared frequently. Fig. 11 presents the representative high-speed images with a time interval of 70 ms, where the large bubble obstructing the liquid supply process was removed quickly. The physical process observed over time can be summarized as follows: (1) formation of a large bubble covering most of the heated area; (2) simultaneous occurrence of the flow reversal and the pressure shock due to rapid condensation of bubbles at the unheated downstream channel, as shown in Fig. 9; (3) condensation of the large bubble hovering above the heater surface caused by the mixing process between the subcooled liquid and the bubble, and also due to the substantial increase in the saturation temperature; (4) suppression of bubble nucleation due to the pressure buildup; (5) simultaneous bubble nucleation and

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Fig. 10. Transient behavior of pressure measured at the test section channel as a function of the subcooling and heat flux.

growth throughout the entire heater surface after alleviation of the pressure buildup; (6) re-formation of large bubbles. In short, the flow reversal and the pressure shock were observed in the subcooled boiling experiments at a mass flux of 40 kg/m2-s with inlet subcooling fixed at 20 K. Based on these experimental observations, it is confirmed that a large bubble covering most of the area of the heater surface is removed quickly when flow reversal and pressure shocks appear. This type of vapor removal process is efficiently continued and thus is regarded as a highly favorable phenomenon for CHF enhancement. Therefore, it can be concluded that the abrupt increase in CHF with the change in inlet subcooling from 15 to 20 K may be attributed to the fast-transient phenomenon in two-phase flow, as well as the substantial reduction in the bubble coalescence process. It is noteworthy that, in subcooled boiling experiments, there is a possibility of the wall temperature oscillation as a result of the violent flow reversal and pressure buildup during the CIWH phenomenon. The oscillatory temperature may interfere the steady state condition of experiments. However, amplitude of the oscillation was confirmed to be very low, ±1 K. This is because the high thermal inertia of thick copper heating block minimized the temperature variation induced by the water hammer. Furthermore, the CHF data and boiling curve data were obtained by averaging the raw data collected in 1 min, which is far longer the time scale of the water hammer phenomenon. As a result, the oscillation of temperature during the subcooled boiling experiments is not

considered to interfere the steady state condition significantly in terms of the CHF and the boiling curve. 3.3.4. Local void fraction near the heater surface The departed bubbles moved along the downward-facing heater surface in the form of the two-phase boundary layer. Owing to the bubbles concentrated near the heater surface, the bubble coalescence proceeded very actively. Thus, the bubbles generally grew into a large one through bubble coalescence with neighboring bubbles, and then the liquid-vapor structure in the vicinity of the heater surface was optically blocked by stratified thick bubbles. Therefore, the optical fiber microprobe was utilized to obtain information about the two-phase structure near the heater surface. The microprobe was held at the Q5C position indicated in Fig. 2b with a distance of 3 mm from the heater surface to measure the local void fraction in the bubble-detached region. Based on the local void fraction data, we could obtain a better understanding of the influence of the mass flux and the subcooling on the nucleate boiling and CHF. Fig. 12 presents the timeaveraged local void fraction data with an acquisition time of 50 s as a function of the heat flux, mass flux, and subcooling. It is noteworthy that the void fraction curve appeared to be affected differently than the operating parameters, such as the mass flux and the subcooling. At the same 5 K subcooling, the void fraction curve at the mass flux of 40 kg/m2-s was thoroughly overlapped with that of the mass flux of 210 kg/m2-s. This result indicates that the mass

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Fig. 11. Bubble behavior when the flow reversal and the accompanying pressure shock occur.

Fig. 12. Variation of local void fraction near the heater surface with respect to the wall heat flux as a function of the mass flux and the subcooling at the inlet.

flux only slightly affects the vapor fraction near the heater surface. However, the void fraction near the surface was observed to heavily depend on the subcooling, showing that increased subcooling caused a substantial decrease in the void fraction at the same mass flux of 40 kg/m2-s. The trends observed in the relation between the void fraction curve and operating parameters appear similar to the relation between the parameters and boiling curve, as presented in Figs. 4 and 6. While the independence between the boiling curve and the mass flux is shown in Fig. 4, Fig. 6 showed that the boiling curve has a considerable level of dependence on the liquid subcooling. It could be inferred from the experimental results that heat

transfer characteristics in the nucleate boiling regime for the downward-facing heaters are highly interrelated with the phase distribution, quantified as a void fraction in the present study, near the heater surface. A notable feature in Fig. 12 is the existence of a critical void fraction of around 0.95, beyond which CHF occurs regardless of the mass flux and the subcooling. This result seems to agree well with the assumption used in the CHF models developed by Weisman and Pei, Cheung and Haddad [35,62]. Weisman and Pei [62] suggested a constant value of 0.82 as the critical void fraction in the bubble layer along a vertical channel, at which an array of ellipsoidal bubbles could be maintained without significant contact between the bubbles. Cheung and Haddad [35] experimentally obtained a constant value very close to 0.915 as the critical void fraction in the two-phase boundary layer along a curved surface using a high-speed camera. The quantitative difference in the critical void fraction between the two studies, including the present study, implies that the heater configuration could be an influential factor in determining the critical void fraction. The fact that the critical void fraction has a constant value of approximately 0.95 in the present experiments can be utilized to develop a CHF model that is applicable to the downward-facing heater configuration. Fig. 13 presents two typical traces of local void fraction of binary data form variation of the mass flux at the subcooling of 5 K. The binary data consist of ‘‘0” and ‘‘1”. When the tip of the optical fiber microprobe is occupied by vapor, the binary data indicates ‘‘1”. Therefore, the ratio of the number ‘‘1” to the total number of the binary data increases as the heat flux increases. An interesting feature could be captured from Fig. 13: the residence time of a bubble was significantly reduced when the mass flux was varied from 40 to 210 kg/m2-s, even under the same conditions, such as wall heat flux and time-averaged void fraction. Here, the residence time is defined as the length of each width of the vapor phase in the void fraction

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Fig. 13. Void fraction traces of binary data form measured by an optical fiber microprobe at a specific subcooling of 5 K and different inlet mass flux conditions; (a) G = 40 kg/ m2-s, (b) G = 210 kg/m2-s.

traces. It should be noted that the CHF increases substantially from 360 to 440 kW/m2 as the mass flux increases. From these results, it can be seen that the wetting frequency is a more influential factor than the wetting period in the boiling crisis phenomenon, at least for downward-facing heaters. This implies that a larger wetting frequency enables better liquid supply to a thin liquid sublayer beneath large vapor bubbles confined near the heater surface. 4. Summary and conclusions The present study investigated bubble dynamics with the help of a high-speed camera and optical fiber microprobe to determine the influence of subcooling on the nucleate boiling and CHF with a 10° inclined downward-facing heater. The major outcomes from this study can be summarized as follows: (1) A non-linear relation between the subcooling and the boiling heat transfer was revealed under the pool boiling condition (G = 40 kg/m2-s), showing the best performance at a subcooling of 15 K. Enhancement in the boiling heat transfer may be attributed to appearance of the large sliding bubbles. However, under the flow boiling condition, it was observed that the subcooling hardly affected the rate of heat transfer. (2) Up to subcooling of 15 K, a weak dependence of CHF on the subcooling was observed. This result is consistent with the experimental results from Sulatskii et al. [36], where a non-linear dependence of CHF on the subcooling was observed. The subcooling provides an adverse effect on velocity of the two-phase boundary layer flow and correspondingly degrades an entrainment process behind the sliding bubble, through which the bulk liquid is pumped into the heater surface.

(3) The repetitive flow reversal phenomenon with the pressure shock appeared in the subcooled boiling experiments owing to rapid condensation at the unheated section right after the test section. Such a transient phenomenon in two-phase flow is considered to be responsible for the observed abrupt increase in the CHF with an increase in subcooling from 15 to 20 K. This is because the flow reversal and pressure shock effectively eliminated the large amount of vapor hovering right above the heater surface. (4) Regardless of the mass flux and subcooling, the local void fraction near the heater surface was measured as a constant value of 0.95 in the two-phase boundary layer along the downward-facing heater surface as the CHF limit is approached. This result seems to agree well with the assumption used in the CHF models developed by Weisman and Pei [62], Cheung, and Haddad [35]. Acknowledgement The authors gratefully acknowledge the late Dr. In-Cheol Chu for his technical support in setting the void fraction measurement system, and also for his invaluable advice in undertaking this work. This research was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Nos. NRF-2017M2B2A9A02049735 and NRF-2016R1A 5A1013919).

Conflict of interest We declare that the submitted work has no conflict of interest with any relevant research institutes, academics, or industries.

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Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.07.064.

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