Leidenfrost temperature on porous wick surfaces: Decoupling the effects of the capillary wicking and thermal properties

International Journal of Heat and Mass Transfer 145 (2019) 118809

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

Leidenfrost temperature on porous wick surfaces: Decoupling the effects of the capillary wicking and thermal properties Gi Cheol Lee a, Seol Ha Kim b, Jun-young Kang c, Moo Hwan Kim a,d, HangJin Jo a,d,⇑ a

Division of Advanced Nuclear Engineering, POSTECH, Pohang 37673, Republic of Korea Department of Precision Mechanical Engineering, Kyungpook National University, Sangsu, 37224, Republic of Korea c Accident Mitigation Research Team, KAERI, Daejeon 34057, Republic of Korea d Department of Mechanical Engineering, POSTECH, Pohang 37673, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 8 May 2019 Received in revised form 26 August 2019 Accepted 28 September 2019 Available online 4 October 2019 Keywords: Minimum film boiling temperature Vapor permeability Surface wettability Thermal effusivity Interface temperature

a b s t r a c t The Leidenfrost temperature TLFP of falling water droplet was studied on sintered porous wick surfaces. Various surface factors were analyzed to identify those that significantly contribute to increasing the TLFP. To decouple the effects of capillary wicking on porous wick surfaces, the results obtained using ethanol as a working fluid were compared to the results obtained using water. When ethanol was used, the capillary wicking did not differ significantly between the porous wick surfaces. The evaporation time of the droplets was measured at high temperatures (100–600 °C) to evaluate the TLFP. The effect of surface permeability on the absorption of the vapor layer through a porous wick surface had a negligible influence on the TLFP. Within the range of low thermal effusivity of the heating surface, an analysis of the interface temperature shows that in liquid ethanol, the thermal properties dominate the TLFP as well as the overall boiling regime. Similarly, in water (for which the capillary wicking effect cannot be ignored), the TLFP and film boiling regime were determined by the thermal effusivity. In both liquids, the thermal effusivity was the dominant determinant of the TLFP, regardless of the capillary wicking rate. However, the capillary wicking significantly affected the boiling heat transfer in water, until it reached the transition boiling regime. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction A phase change at boiling can effectively remove heat from a surface. Therefore, this process is used in various industrial applications, including chemical processes [1], nuclear power generation systems [2], and for cooling integrated circuits [3]. Nucleate boiling has high heat transfer efficiency; therefore, it is the most suitable for use in general heat transfer systems under normal operating conditions. In contrast, film boiling has low heat transfer efficiency, because a vapor layer with low thermal conductivity forms between the hot surface and the coolant liquid [4,5]. The minimum temperature or criterion for a change from nucleate boiling to film boiling is called the Leidenfrost temperature TLFP or the minimum film boiling temperature TMFB [6]. In general, when the surface is cooled down from an extremely superheated ⇑ Corresponding author at: Division of Advanced Nuclear Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea. E-mail addresses: [email protected] (G.C. Lee), [email protected] (S.H. Kim), [email protected] (J.-y. Kang), [email protected] (M.H. Kim), [email protected] (H. Jo). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118809 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

condition, most of the cooling time elapses during the film boiling; thus, this time (tFBR) should be minimized to maximize the cooling efficiency [7]. The tFBR can be reduced by either increasing the heat transfer coefficient during film boiling, or by increasing the TLFP [8]. Recent studies have focused on increasing the TLFP to accelerate cooling. The TLFP is affected by various experimental parameters, such as the thermal properties of the liquid and surface, the subcooling effect, and the flow rate of the liquid. Either the TMFB or TLFP can be increased by using nanofluids during quenching [9–13] or by fabricating micro- and nanoscale surface structures on the heated surface [14–17]. Surface roughness [17,18] and hydrophilicity [19–22] can favor liquid–solid (L–S) contact, thereby increasing the TLFP by interfering with the formation of a vapor layer. In particular, the use of either microscale or nanoscale surface structures can increase the surface roughness and produce superhydrophilicity with a zero contact angle in water. These small surface structures are found to increase the TLFP significantly [8,15–17,23–28]. Changes in the surface morphology due to modification of the surface structure cause simultaneous changes in various surface factors, including surface roughness, wettability, thermal

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Nomenclature A C Cp d e F g h P k K Ra r T t V v WV

area [m2] constant [-] specific heat capacity [J/(kg∙K)] diameter [m] thermal effusivity [J/(m2∙K∙s1/2)] force [N] gravitational acceleration [m/s2] water level inside tube [m] pressure [Pa] thermal conductivity [W/(m∙K)] permeability [m2] surface roughness [m] radius [m] temperature [K] time [s] volume [m2] velocity [m/s] volumetric capillary wicking rate [m2]

properties, and vapor permeability. These surface parameters are strongly coupled and affect the TLFP. However, considering such surface factors independently is difficult, because physical properties such as porosity, thermal conductivity, and permeability cannot be accurately measured on irregularly shaped structured surfaces [8,14,17,25]. This is because the morphology or thickness of the surface structures is not generally constant [14,15,17,29,30]. Therefore, previous research has described TLFP increase mechanisms that were associated with individual surface factors, such as the thermal properties of the liquid and solid [31–33], vapor permeability [29,34,35], surface roughness [17,18,28], surface wettability [20–22], and capillary wicking induced by the micro/nanoscale structures [15,17,22,25,26]. To understand the TLFP increase mechanism on a micro/nanostructured surface, a quantified and independent analysis of various coupled surface factors is needed [36] to clarify the underlying physics. Therefore, porous wick surfaces were fabricated in this study by sintering to allow the accurate measurement of various surface factors. Porous surface with small gap structure (wick) which induce high capillary pressure is called by ‘‘porous wick” or ‘‘porous wick surface” [37–39] in capillary pump loop (CPL) application. As the porosity of a surface affects its other characteristics, such as the thermal properties, capillary wicking and vapor permeability, the effects of these surface factors can be evaluated. We investigated various surface factors independently related with the TLFP results. According to the analysis, surface factors other than the thermal properties and capillary wicking have a negligible effect on the TLFP increase and boiling heat transfer results. 2. Preparation and characterization of porous wick surfaces 2.1. Fabrication procedure Porous wick surfaces were fabricated by sintering compacted powder samples. First, 3YSZ zirconia particles (TZ-3YS-E, Tosoh Corp.) containing 3% mol Y2O3 with a particle diameter of less than 0.1 lm were compacted under high pressure [40]. The sintering particles were poured into a mold having an inner diameter of ~32 mm and a height of ~80 mm. Mechanical compaction was performed at a pressure of 80 MPa in a universal testing machine (UDH-50, Shimadzu) (Fig. 1). The plugs of compacted particles were treated at a temperature of >1100 °C in a sintering furnace (Table 1). Four test specimens (S1–S4) were fabricated as circular

Greek symbols d thickness [m] l viscosity [m∙Pa∙s] q density [kg/m3] r surface tension [N/m] Subscripts cap capillary evap evaporation FBR film boiling regime i interface v vapor s surface l liquid 0 initial LFP Leidenfrost

discs with a thickness ranging from 1.05 to 1.18 mm. The porosity of each porous wick surface was calculated from the density of the test specimen and the density of the 3YSZ particles (6.088 g/cm3). After the sintering procedure, the specimens were chemically cleaned using acetone, ethanol, and distilled water. 2.2. Characterization of fabricated surface As the sintering temperature or sintering time increased, bottlenecking developed between the agglomerated particles (Fig. 2), resulting in a decrease in the porosity [40,41]. Depending on the topographic characteristics of the specimen, the wettability also changed. As a consequence of the small original particle size, all specimens had a pore size of r < 0.1 lm (Fig. 2), which can induce high capillary pressure (Pcap ¼ 2r=rÞ. The contact angle could not be measured on the specimens that quickly absorbed the liquid as it dropped onto the surface (i.e., S1 within a few seconds and S2 within 20–30 s). S3 took a few minutes to absorb all of the water, which made it possible to measure the contact angle. S4 had low porosity and thus did not absorb the water droplet. The surface roughness Ra was measured using a surface profiler at four points for each surface. All samples had 0.1  Ra  0.2 lm with no significant differences between them (Table 1). 2.2.1. Thermal properties Fig. 3 shows the relationship between the thermal conductivity and the temperature using laser flash measurements (LFA 427, Netzsch) to examine the effect of the surface temperature. As the experimental condition for the heating surface was as hot as 600 °C, this relationship was considered when interpreting the results. The test specimens had very different porosities; thus, the thermal conductivity varied by a factor of three. The measured values were similar to those reported in previous studies with similar porosity ranges and the same materials [42]. The thermal capacities were obtained from a previous study (see Supplemental Fig. 1) [43], and some of these values were interpolated. 2.2.2. Porous characteristics Porous characteristics, such as pore size distribution, mean pore diameter, and permeability, were measured using a mercury porosimeter (PoreMaster 33–15, Quantachrome Instruments). The pore size and volumetric proportion of pores decreased from S1 to S4 (Fig. 4), because the sintering condition was increasingly

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Fig. 1. Fabrication process. (1) Mechanical compaction at 80 MPa. (2) Sintering in high temperature furnace. (3) Chemical cleaning of the fabricated test specimen.

Table 1 Summary of sintering conditions and resulting characteristics of the fabricated porous wick surfaces.

Sintering condition

Surface characteristics

Compaction pressure, Pc [MPa] Sintering temperature, Tsintering [°C] Heating rate, dT/dt [°C/min] Sintering time, tsintering [min] Density [g/cm3] Porosity [%] Roughness, Ra [lm] Mean pore diameter [nm] Permeability, K [1012m2] Contact angle (water) [°] WV at stage I (water) [lL/s] WV at stage I (ethanol) [lL/s]

severe from S1 to S4, which intensified the bottlenecking between particles. The mean pore diameter on all surfaces ranged from 10 to 75 nm (Fig. 4, Supplemental Fig. 2, and Table 1). This seems quite reasonable, as the range of values is still smaller than the particle size of 90 nm. This conclusion can also be indirectly confirmed from the SEM images (Fig. 1). The permeability of a surface is proportional to its porosity and pore size [44]; thus, the decreased pore size and porosity caused a decrease in the vapor permeability from S1 to S4 (Table 1). 2.2.3. Capillary wicking test and results A capillary wicking test was performed to distinguish the wettability characteristics of the samples. We used a quantitative method to measure the volumetric capillary wicking rate WV. In previous studies, two different types of measurements were reported to quantify the capillary wickability on superhydrophilic surfaces: droplet spreading [45–47] or liquid uptake [48–50]. However, the accuracy of these previous measurements was greatly influenced by the presence of empirical geometric parameters such as the surface roughness factor, the thickness of the liquid microlayer, and the isotropic nature of the surface. To avoid this problem, a novel method was proposed several years ago [51] for directly measuring the absorbed liquid volume from a superhydrophilic surface using a capillary tube. Two-dimensional spreading/wicking of the surface is transformed to a one-dimensional

S1

S2

S3

S4

80 1150 5 2 4.26 29.94 0.12 73.1 3.8 ~0 48.61 4.39

80 1100 5 90 4.87 19.90 0.21 59.5 0.9 ~0 38.64 3.02

80 1200 5 2 5.58 8.29 0.18 22.8 0.1 51.9 31.16 3.56

80 1480 5 2 6.04 0.69 0.14 11.9 0.005 84.1 0.93 3.563

liquid level drop in the small capillary tube without geometric surface parameters. Using a small tube, the wicking rate of the test specimen can be precisely calculated from the measured liquid volume [24,51–55]. A small Teflon tube (inner diameter of 1 mm) filled with deionized water (Fig. 5a) is placed on a porous surface using a micrometric screw and a movable stage; then, the distance between the tube and the surface is slowly reduced. When the liquid meniscus meets the porous surface, liquid wicking occurs and the water in the tube is absorbed by the surface. The liquid meniscus and water level in the tube are monitored using a high-speed camera at 1,000 fps with a spatial resolution of 4.762 lm/pixel. The water in the tube is rapidly absorbed into porous wick surface S1 (Fig. 5b). From the measured water level inside the tube, the water volume absorbed by the porous surface can be calculated as follows:

V absorbed ¼ V 0  prtube 2 h;

ð1Þ

Samples S1 and S2 had permeable surfaces that showed liquid wicking, whereas S3 allowed little liquid permeation, and S4 allowed no liquid wicking (Fig. 6). On permeable surfaces, the liquid absorption phenomenon is divided into two periods. Initially, the liquid wicking increases linearly with time. After ~6 ms, the rate of change gradually decreases to a rate that follows the diffusion law [56]. The absorption of liquid is governed by two forces:

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Fig. 2. SEM images and contact angles of the test specimens. Due to water wicking, the contact angles on S1 and S2 cannot be measured (almost 0°). Scale bar: 100 nm. Bottlenecking developed between agglomerated particles and the porosity decreased from S1 to S4.

0.6 P 0% (Schlichting et al., 2001) P 10% (Schlichting et al., 2001) P 18.% (Schlichting et al., 2001) P 23.8% (Schlichting et al., 2001)

3.5

P 0.7% (S4) P 8.3% (S3) P 19.9% (S2) P 29.9% (S1)

S1 (P 29.9 %) S2 (P 19.9 %) S3 (P 8.3 %) S4 (P 0.7 %)

0.5

3.0 0.4

2.5

dV/d(logd)

Thermal conductivity [W/(m K)]

4.0

2.0 1.5

0.3

0.2

1.0 0.5

0.1

0.0 0

100

200

300 400 o Temperature [ C]

500

600 0.0 0.05

Fig. 3. Thermal conductivity at various temperatures and porosities in 3YSZ measured using the laser flash method. The measured data were similar to previous study results [42].

the capillary force Fcap exerted by porous structures and the frictional force Ffriction of the water flow [51] as expressed in the following Eqs. (2) and (3), respectively:

F cap ¼ C 1 DPcap A; F friction ¼ C 2 lr

  dr ; dt

ð2Þ ð3Þ

where C1 and C2 are empirical constants that are affected by the surface tension, contact angle, and geometrical curvature [57]. Initially Fcap > Ffriction, so the water moves rapidly from the tube to the

0.1

0.15

0.2

0.25 0.3

Pore diameter [ m] Fig. 4. Measured pore size distribution. The pore size and volumetric proportion of pores decreased from S1 to S4. Data for small pore diameters ranging from 0 to 0.05 lm are shown in Supplemental Fig. 2.

porous surface. As the wicking proceeds, r increases, which causes an increase in the Ffriction. Therefore, approximately 6 ms after the initial contact, WV begins to decrease as the Ffriction approaches the Fcap. In this measurement, the initial WV is important for the heat transfer phenomenon because the intermittent L–S contact during film boiling occurs within a few milliseconds [58-60]. The intermittent L–S contact was measured based on the change in the electric impedance of the heating surface [58–60]. Therefore, the relevant time scale of the Leidenfrost phenomenon is 5–10 ms because the intermittent L–S contact during the Leidenfrost state

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Fig. 5. Measurement of capillary wicking using a small tube with an inner diameter of 1 mm. (a) Experimental setup. (b) Raw results for S1 and S4 for water. Compared to S4, S1 shows high wickability. (c) Raw data for ethanol (liquid level inside a tube). Compared to water, the liquid level difference between the back and front line of the ethanol is relatively large. We set the baseline of the liquid level as the average of the front and back line. Supplementary video shows the wicking phenomenon of water and ethanol liquid on a test specimen.

0.6 S1 S2 S3 S4

0.5

The volume of absorbed liquid ethanol [ L]

The volume of absorbed liquid water [ L]

0.6

0.4

0.3

0.2

0.1

0.0 0

20

40

60

80

100

time [ms] Fig. 6. Measurement results for capillary wicking: Volume of absorbed water vs time. The capillary wicking phenomenon decreased from S1 to S4 (water data).

occurs within that short period. Therefore, the initial WV was calculated from the initial slope of the graph (Figs. 6 and 7) and used in the interpretation of the TLFP results. WV increased from 0.9 to 48.6 lL/s as the porosity increased from 0% to 30% (Table 1). The data were measured three times for each test specimen, and the standard deviation was less than 5%. Ethanol was used as an additional experimental group for WV. The overall volumetric wicking rate was smaller with ethanol than with water (Fig. 7). This phenomenon is caused by the difference in physical properties of the working fluids. For example, a decrease in the surface tension causes a decrease in the capillary dynamics, such as the penetration speed [61]. WV of the test specimens for ethanol was 3.02  WV  4.39 lL/s (Fig. 7 and Table 1); the range

S1 S2 S3 S4

0.5

0.4

0.3

0.2

0.1

0.0 0

20

40

60

80

100

time [ms] Fig. 7. Absorbed liquid volume over time (ethanol data). Supplementary video shows the wicking phenomenon of ethanol liquid on a test specimen. For ethanol liquid, the capillary wicking rate WV was almost identical for all test specimens due to the decrease in surface tension.

of values is much smaller than the range for water (0.9  WV  48.6 lL/s; Fig. 6 and Table 1). Consequently, the effect of capillary wicking on the test specimens can be ignored when ethanol is used as the fluid. The characterized surface factors are summarized in Table 1. The surface roughness was ~0.1 lm and did not differ significantly among the specimens; this roughness was miniscule compared to the thickness of the vapor layer (tens of micrometers) [62] to affect the TLFP [18,62,63]. In addition, as all test specimens were sintered from the same type of particles, the wettability of the material itself is intrinsic. As a result, the intrinsic contact angles were the

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same [64]. Therefore, in this study, only three surface factors can affect the TLFP: vapor permeability, thermal properties, and capillary wicking. Furthermore, capillary wicking can be excluded when ethanol is used. 3. Experiment This study used the classic definition of TLFP as the surface temperature Ts at which the evaporation time tevap is longest, where tevap is defined as the time from when the droplet contacts the heated surface until the droplet has evaporated completely [4,17,20,29,31,63,65,66]. The experimental setup (Fig. 8) was designed to generate drops of uniform size. Deionized water was transferred from a syringe to a needle (31G) by using a syringe pump, and then a water droplet with a diameter of 2 mm or an ethanol droplet with a diameter of 1.5 mm was dropped onto the test specimen from a height of 2

14 mm; the corresponding Weber number We ¼ qdv =r was 7.6 for water and 14.5 for ethanol. Droplet diameters were consistently within 5%. To minimize the inertia of a falling droplet, a small falling height is desirable. In this experiment, the temperature of the heated surface increased to 600 °C; to minimize the radiation heat transfer of the heated surface, a moderate falling height is set. At approximately the TLFP, the droplet levitated on the heated surface. To prevent the droplet from escaping the heated surface, an openended cylinder slightly smaller than the size of the specimen was placed on the test specimen. The interior cylinder wall was hydrophobic (coated with Teflon) to minimize the droplet–wall contact time. The levitating droplet did not attach itself to the cylinder wall or frequently contact the wall. During the levitating time (10–20 s), the contact number and time was less than 2–5 times and 1 s, respectively. During the contact, there was no significant change in the size or behavior of the droplet. The temperature of the test specimen was maintained by a heater, and the heat was transferred to the test specimen by thermal conduction. The heater (SU-200-HH-TH, MeiVac, Inc.) is made of Haynes metal, which has good resistance to thermal oxidation at high temperature, ensuring the surface temperature can be heated to 600 °C. A connection jig was used to press the test specimen to reduce the thermal contact resistance between the test specimen and the heater. The tevap of the droplet on each surface was measured at least three times in repeated tests; the uncertainty was ~0.5 s. The uncertainty of the temperature measurement was 1 °C. To visualize the dynamics of the water droplet, a high-speed camera (Phantom Miro, Vision Research) and LED light source were used.

4. Results and discussion 4.1. Evaporation time and definition of TLFP The relationship between the evaporation time tevap and the surface temperature Ts was measured on each test specimen (Figs. 9 and 10). At the early stages, the Ts increased and the tevap of the water droplet gradually decreased. After the transition temperature Ttran at which the minimum tevap of the droplet occurred, the tevap began to increase. Then it reached a local peak tevap, which is defined as the TLFP. The tevap differed greatly between the test specimens. The tevap decreased as the porosity of the surface increased; i.e. the cooling efficiency increased as the porosity increased. The TLFP for ethanol was 243.5 °C  TLFP  274 °C, which is much lower than that for water (422 °C  TLFP  550 °C). This difference is a result of the different physical properties of ethanol and water (Supplemental Table 1). Ethanol has a lower latent heat of vaporization compared to that of water, which means that the superheating required to generate the same amount of vapor is lower for ethanol than for water. Therefore, the Leidenfrost state occurs at a lower temperature with ethanol than with water. In the following sections, we infer how the TLFP is affected by the surface factors. In the previous section, we confirmed that only three surface factors can affect the TLFP: vapor permeability, thermal properties, and capillary wicking. The effects of these surface factors on the TLFP results are introduced in following sections. 4.2. Vapor permeability effect The vapor generated from the Leidenfrost droplet can flow into a porous surface (Fig. 11; this phenomenon decreases the effective thickness of the vapor layer). Therefore, the required superheat of the heating surface increases on a porous surface because the thickness of the vapor layer that forms in the Leidenfrost state is insufficient [34]. A previous study used a 1D calculation to analyze the vapor absorption into a porous substrate and verified the results by measuring the TLFP, but the particle material, diameter, and thickness of the porous layer were not uniform [34]. Subsequently, an accurate boundary condition and 2D calculation for a Leidenfrost droplet on a porous surface were developed [35], which we applied to the present data (Fig. 12). The normalized thickness of the vapor layer is plotted as a function of K/a2, where K is the permeability of the surface and a is the boundary condition as a function of the porosity [67]. In the porosity range shown in Fig. 12, a was set from 1 to 6.8 depending on the porosity [67]. The effective thickness of the vapor layer decreases as K/a2

Fig. 8. Experimental setup for the Leidenfrost experiment.

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1 Fatehi and Kaviany (1990) S1 S2 S3

/R0 [-]

0.1

0.01

1E-3 1E-15 Fig. 9. Evaporation time of an ethanol droplet as a function of the surface temperature. The temperature in the legend indicates the TLFP for each porous wick surface (ethanol data).

1E-13

1E-11 2

1E-9

1E-7

2

K/ [m ] 2

Fig. 12. Effects of K/a on the normalized vapor film thickness [35]. On the most permeable surface, S1, the vapor layer decreased by approximately 6.8% (0.3% at S2, 0% at S3 and S4).

effect on the results. Similarly, the negligible effect of the vapor permeation into the porous medium, which is reported elsewhere [68], is consistent with the results presented herein. The permeability is proportional to the square of the pore size [69–72]. In our test specimens, the mean pore diameter dpore ranged from 10 to 75 nm, and the resulting permeability was too low to affect the TLFP. The pore size should be >100 lm (i.e., porosity ~40%) to cause a decrease in the vapor layer thickness of >20% from the calculated data. Therefore, in a recent study on micro/nanostructured surfaces, the effects of permeability and vapor absorption on the TLFP should be ignored, but they should be considered in debris beds, which are porous media composed of millimeterscale particles [73]. Finally, in our experiment, only the thermal properties and capillary wicking can significantly affect the TLFP results.

Fig. 10. Evaporation time of a water droplet as a function of the surface temperature. Legend: TLFP for each porous wick surface (water data).

increases. On the most permeable surface (S1), the thickness of the vapor layer decreased by approximately 6.8% compared to the impermeable surface, which can be treated as having a negligible

4.3. Effect of thermal properties: analysis of the interface temperature 4.3.1. Interpretation of ethanol results: governed only by thermal properties When ethanol is used as the working liquid, the differences in the capillary wicking rates Wv among the test specimens are negligibly small (3.02  WV  4.39 lL/s; Fig. 7 and Table 1). Therefore,

Fig. 11. Absorption of vapor inside the porous layer. (a) Schematic illustration of a Leidenfrost droplet on a porous wick surface. (b) Radial velocity profile in the vapor layer and porous layer. d is the distance between the solid and liquid, which indicates the effective vapor layer thickness.

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we assume that only the thermal properties are the dominant factor for the TLFP in the case of ethanol. Several researchers have reported that the TLFP increased on poorly conducting materials. This is because the poor thermal conduction of solids reduces the L–S interface temperature and enables L–S contact, even at highly elevated surface temperatures [31,33,68]. From a thermodynamics perspective, the interface temperature Ti represents the real temperature at the solid–liquid interface of a droplet colliding with a heated surface. The measured surface temperature Ts can be converted to Ti as a function of the liquid temperature Tl, Ts, and thermal effusivity e = (k∙q∙Cp)1/2 of the liquid and solid. Ti is defined as follows [32]:

T i ¼ ðes T s þ el T l Þ=ðes þ el Þ:

ð4Þ

Tl is assumed as the saturation temperature. The cooling curve of Fig. 9, plotted as a function of Ts, was converted to Ti (Fig. 13). In Fig. 13, the resulting Ti, LFP values as a criterion for film boiling were approximately 221.7 °C. Although all data do not exactly converge to 221.7 °C, the differences are not large (4.3 °C standard deviation). The differences in the resulting Ti, LFP value are likely due to experimental error and because the interface temperature is a rough estimation rather than an exact solution for the TLFP. Nevertheless, experimental results in Fig. 13 are quite close, for most boiling regimes including the TLFP. The study shows that es is the dominant factor for the TLFP and the overall boiling heat transfer of a droplet on the tested porous wick surfaces when ethanol is used as the working fluid except for film boiling regime. In the film boiling state, during most of the evaporation time, the droplet does not contact the heated surface. Matching the evaporation time results with interface temperature is not applicable in the film boiling state. 4.3.2. Interpretation of water results: governed by thermal properties and capillary wicking. In the case of water, the differences between the capillary wicking rates Wv among the test specimens are not negligible (0.9  WV  48.6 lL/s; Fig. 6 and Table 1). Therefore, the effect of the capillary wicking as well as the thermal properties should be considered. The heat transfer results for water were also converted

Fig. 13. Cooling curve conversion from surface temperature to interface temperature. Differences in the data for various test specimens were negligible throughout the investigated temperature range except for film boiling regime. i.e. in film boiling state, the droplet does not contact the heated surface during most of time. Matching the evaporation time results with interface temperature is not applicable in the film boiling state. The temperature in the legend indicates the Ti, LFP of each porous wick surface (ethanol data). The Ti, LFP in figure and dashed line next to Ti, LFP is average value (221 °C).

to the interface temperature Ti (Fig. 14). As with the ethanol results, the Ti, LFP and tevap during film boiling were similar for all test specimens. In Fig. 14, the calculated Ti, LFP values were approximately 329.6 °C with a standard deviation of 13.6 °C. Except for S4, the Ti, LFP ranged from 340 to 335 °C with a standard deviation of 3.6 °C. In contrast, S4 showed Ti, LFP values as low as 310 °C. On the S4 substrate, the capillary wicking rate Wv was almost zero. The low Ti, LFP is likely due to the absence of capillary wicking. Although S1, S2, and S3 showed different capillary wicking ability, their calculated Ti, LFP values converged with a standard deviation of 3.6 °C, similar to the ethanol data. This means that if the capillary wicking is above a certain level, additional capillary wicking cannot meaningfully increase the TLFP. At the TLFP, the substrate temperature is much higher than the boiling point, and the liquid–solid contact between the heated substrate and the liquid droplet is limited to a local point with intermittent period [58,60]. For this limited liquid–solid contact situation, the additional increase in capillary wicking does not affect the TLFP. Unlike the TLFP and film boiling regime, the Ti conversion results before TLFP on the test specimens (S1–S4) were not collected but showed significant variation (Fig. 14). Even if the surface temperature differs by only a few degrees Celsius, the results among the test specimens for the cooling curve change completely based on the TLFP (Fig. 14). This trend implies that the capillary wicking effect is not limited but in fact is dominant until the transition boiling regime when there is consistent liquid–solid contact. Finally, the thermal effusivity es of the surface is the dominant factor affecting the Ti, LFP and film boiling. From the acquired average of the Ti, LFP, TLFP can be calculated using Eq. (4), where Ti = 329.6 °C for water and 221.7 °C for ethanol. The thermodynamic critical temperature of water and ethanol is approximately 647 K (374 °C) and 514 K (241 °C), respectively. Therefore, the interface temperature should be lower than the critical temperature of liquid. We found that the liquid cannot exist on the surface over a certain L–S interface temperature (Ti, LFP). The predicted TLFP and measured TLFP are plotted in Fig. 15. The predicted TLFP is consistent with the measured TLFP in the tested es range. In other words, in the porosity range of 0 to 30%, the TLFP of porous zirconia can be predicted using the Ti, LFP value for water and ethanol liquid.

Fig. 14. Cooling curve conversion from surface temperature to interface temperature (water data). Differences in the data for various test specimens were negligible only at Ti, LFP. The Ti, LFP in figure and dashed line next to Ti, LFP is average value (329.6 °C). Matching the evaporation time results with interface temperature is not applicable in the film boiling state. i.e. in film boiling state, the droplet does not contact the heated surface during most of time.

G.C. Lee et al. / International Journal of Heat and Mass Transfer 145 (2019) 118809

700 Measured TLFP (Water)

Predicted TLFP (Water)

Measured TLFP (Ethanol)

Predicted TLFP (Ethanol)

600

o

TLFP [ C]

500

400

300

200

100 1000

2000

Effusivity, (k Cp)

3000 1/2

2

4000 1/2

[J/(m Ks )]

Fig. 15. Measured and predicted TLFP as a function of the thermal effusivity of the surface.

According to Eq. (4), as the thermal effusivity es of the surface decreases, the Ti decreases. To produce enough vapor to levitate the droplet, a sufficiently high Ti is required. Therefore, on a low es surface, the TLFP increases due to the lowered Ti. This trend, a subcooling effect of poorly conducting material on TLFP, is consistent with previous studies [30,32,68,74]. However, it was not possible to use the previous study results for comparison, as various surface characteristics such as capillary wicking, thermal conductivity, density, and heat capacity should be known. Due to the irregular shape and lower thickness, the thermal properties of the capillary structures in previous studies [8,14,15,17,26, 29,55,75,76] cannot be quantified. Furthermore, the conclusions of the relevant studies have limited assumptions for the test specimen such as a specific fin shape [68] or finite thin oxide layer thickness [76]. In the present study, only a limited, low range of thermal effusivity was tested. Recent studies reporting high wicking surface structures often have pores [14,15,17,26,55,75] or oxide layers [8,14,17,29,76], so the range of thermal effusivity is low. Therefore, the present study, which evaluates and decouples both the thermal effusivity and capillary wicking, has important relevance to recent work. For practical predictions of the TLFP, results for a broad range of thermal effusivity with decoupling and various surface parameters are needed.

5. Conclusion Porous wick surfaces were fabricated using a high-pressure and high-temperature sintering process. Various surface factors that can affect TLFP were measured, such as surface roughness, vapor permeability, thermal properties, and capillary wicking, and their effects were analyzed individually. The results of this study show that the vapor permeability effect is negligible for a porous wick structure composed of submicron particles. According to the analysis at successively thinner vapor layers, the effect of vapor absorption on the TLFP can be negligible on most surfaces with micron- or submicron-scale structures because the permeability is proportional to the square of the mean pore diameter [44]. The capillary wicking effect and the effect of other surface factors can be ignored with ethanol, and we hypothesize that only the thermal properties affect the results. This hypothesis was verified by converting the

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surface temperature to an interface temperature. The heat transfer results for the overall boiling regimes (including the TLFP) were governed by the es when ethanol was used as the working fluid. When water was used, the results were affected by both the capillary wicking and the thermal properties: capillary wicking is dominant before the onset of film boiling, and the thermal effusivity of the surface es is dominant for the TLFP and during film boiling. Finally, the TLFP herein was predicted by calculating the interface temperature within the range of the thermal effusivity values tested. Therefore, within the tested low ranges of es, the final determinant of the TLFP is the thermal effusivity es, which represents the ability to transfer the heat to an interface. Until now, various surface factors have been reported and found to affect the TLFP on structured surfaces. Here, we show that the most important surface factor is es within a range of low values. Although the thickness of the porous layer was not considered, and only a specific range of es values was examined, the results of this study will be useful for certain ranges of thickness or low es values, such as with ceramic materials or oxide layers. In particular, the results may be useful for structured oxide surfaces formed via chemical or electrochemical etching processes. The results of this study are expected to contribute to the design of the operating ranges of various thermal systems. Declaration of Competing Interest The authors declared that there is no Conflict of Interest. Acknowledgment This research was supported by National Research Foundation of South Korea (NRF) grants funded by Korean government (MSIP) (NRF-2017M1A7A1A03072748). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118809. References [1] J.R. Thome, Enhanced Boiling Heat Transfer, Hemisphere Pub Corp.(Taylor & Francis), 1990. [2] J. Buongiorno, Can corrosion and CRUD actually improve safety margins in LWRs?, Ann Nucl. Energy. 63 (2014) 9–21. [3] I. Mudawar, Assessment of high-heat-flux thermal management schemes, IEEE Trans. Components Packag. Technol. 24 (2001) 122–141. [4] J.D. Bernardin, I. Mudawar, The leidenfrost point: experimental study and assessment of existing models, J. Heat Transf. 121 (1999) 894, https://doi.org/ 10.1115/1.2826080. [5] G.C. Lee, H. Noh, H. Yeom, H.J. Jo, T. Kyun Kim, M. Kim, K. Sridharan, H. Sun Park, Zirconium-silicide coating on zircaloy-4 substrate for accident tolerance: Effects on oxidation resistance and boiling, Ann. Nucl. Energy. 126 (2019) 350– 358, https://doi.org/10.1016/j.anucene.2018.11.019. [6] F.L. Curzon, The leidenfrost phenomenon, Am. J. Phys. 46 (1978) 825–828. [7] J.-Y. Kang, T.K. Kim, G.C. Lee, M.H. Kim, H.S. Park, Quenching of candidate materials for accident tolerant fuel-cladding in LWRs, Ann. Nucl. Energy. 112 (2018), https://doi.org/10.1016/j.anucene.2017.11.007. [8] J.Y. Kang, S.H. Kim, H.J. Jo, G. Park, H.S. Ahn, K. Moriyama, M.H. Kim, H.S. Park, Film boiling heat transfer on a completely wettable surface with atmospheric saturated distilled water quenching, Int. J. Heat Mass Transf. 93 (2016) 67–74, https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.049. [9] H. Kim, G. DeWitt, T. McKrell, J. Buongiorno, L. Hu, On the quenching of steel and zircaloy spheres in water-based nanofluids with alumina, silica and diamond nanoparticles, Int. J. Multiph. Flow. 35 (2009) 427–438. [10] H.H. Khoshmehr, A. Saboonchi, M.B. Shafii, The quenching of silver rod in boiling carbon nano tube–water nanofluid, Int. J. Therm. Sci. 75 (2014) 95–104. [11] D. Ciloglu, A. Bolukbasi, The quenching behavior of aqueous nanofluids around rods with high temperature, Nucl. Eng. Des. 241 (2011) 2519–2527. [12] K. Babu, T.S.P. Kumar, Effect of CNT concentration and agitation on surface heat flux during quenching in CNT nanofluids, Int. J. Heat Mass Transf. 54 (2011) 106–117.

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