Cooling of the hot steel balls by salt –water solutions and water-based suspensions: Subcooled pool boiling experiments

International Journal of Thermal Sciences 148 (2020) 106164

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International Journal of Thermal Sciences journal homepage: http://www.elsevier.com/locate/ijts

Cooling of the hot steel balls by salt –water solutions and water-based suspensions: Subcooled pool boiling experiments Nikita Khomutov a, Alexander Oparin a, Maxim Piskunov a, *, Wei-Mon Yan b, c, ** a

National Research Tomsk Polytechnic University, 30, Lenin Avenue, Tomsk, 634050, Russia Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei, 10608, Taiwan c Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial Sectors, National Taipei University of Technology, Taipei, 10608, Taiwan b

A R T I C L E I N F O

A B S T R A C T

Keywords: Pool film boiling Cooling Brine Suspension Subcooled nucleate boiling Coolant

In this work, the subcooled pool boiling experiments are performed during the intense cooling of the heated metal balls made of carbon steel AISI 1044 and stainless steel AISI 420L by brines and water-based suspensions of graphite and clay. The heated metal balls with an initial temperature of 1000 K are cooled down with a rate up to 300–450 K/s during the initial 2–4 s. The measured results show that a change in the mass fraction of the solid admixtures in a coolant affects the cooling process insignificantly. The phenomenon of the “step” change of the vapor film thickness during the pool film boiling of the subcooled deionized water at the surface of the immersed metal ball are discussed in detail. The brines and water-based suspensions utilization as coolants enables to eliminate the film boiling of the subcooled liquid. Besides, the optical method of the planar laser-induced fluorescence is applied to measure the temperature distributions near the liquid/vapor interface emerged when the heated metal ball is cooled down in a liquid pool.

1. Introduction There is considerable tension around the problem of providing emergency cooling for the surfaces of technological equipment, in particular nuclear power plant (NPP) reactor vessels, especially after the meltdown at the infamous Fukushima Daiichi Nuclear Power Plant with the temperatures of the fuel rods in the reactor core reaching 1200–1400 K [1]. The Fukushima water cooling system appeared to be insufficiently powerful to effectively compensate for this high temper­ ature. The investigation that is known as the loss-of-coolant accident (LOCA) has shown that the reason for the ineffective (insufficient) cooling and, consequently, a physical damage to the NPP core is the decrease in the heat transfer rate due to film boiling [2] with a stable vapor film formed on a metal surface heated to the high temperature. This process later on increases the thermal resistance of the whole sys­ tem. In this case, the vapor film served as a heat insulation layer. Ac­ cording to research by Hsu et al. [2], seawater used for this purpose eliminates film boiling and improves the cooling performance. The film boiling mechanism and minimum film boiling temperature (MFBT) or

Leidenfrost point are the focus of numerous research papers, e.g. Refs. [3–5], most of them theoretical. However, the limited experimental data bank and complex numerical solutions (modeling) with many assump­ tions still remain the mechanisms and conditions of film boiling during enhanced cooling not fully understood. Scientists interested in developing the subject under study mostly focus on investigating how various nanoparticles and salts added to water affect the critical heat flux (CHF) and MFBT, when rapidly cooling small-size metal objects, e.g., Refs. [6–8]. In addition, saline solutions and suspensions are proved to have a positive effect on a number of other high-temperature heterogeneous technologies, with polydisperse fire fighting being the most interesting and promising among them. Volkov et al. [9] and Vysokomornaya et al. [10] showed the effect of adding salts and solid carbonaceous inclusions on the heterogeneous droplet evaporation enhancement in high-temperature gases. Moreover, by using a similar test bench studies [11–14] were performed to estab­ lish consistent patterns in phase transitions of the water droplets con­ taining the 3–4 mm graphite inclusions at high temperatures. When running an experiment, a new and vastly understudied phenomenon of

* Corresponding author. ** Corresponding author. Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei, 10608, Taiwan. E-mail addresses: [email protected] (M. Piskunov), [email protected] (W.-M. Yan). URL: http://hmtslab.tpu.ru (M. Piskunov). https://doi.org/10.1016/j.ijthermalsci.2019.106164 Received 17 March 2019; Received in revised form 31 October 2019; Accepted 31 October 2019 Available online 6 November 2019 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.

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International Journal of Thermal Sciences 148 (2020) 106164

the explosive breakup of a liquid was repeatedly observed. This allows us to believe that the learning of the film and nucleate boiling, as well as their effect on the surface heating or cooling is incomplete. The pro­ tection measures offered by Liang et al. [15] rest upon the proven effi­ ciency of using sea water (without specialized additives) for the emergency cooling of the NPP reactor vessel during the incidents similar to the one at the Fukushima Daiichi NPP. However, even considering the vast potential of using seawater due to many NPPs being located close to the global ocean, we should not forget about other plants located deep in the continents, in particular, in Europe and North America. The seawater using will definitely be impossible in such regions. Therefore, the problem of the efficient cooling of the NPP reactor vessel using a traditional coolant (water) is still pressing. Consequently, there are the issues related to the heat transfer deterioration due to the vapor film formation. Studies [5,16–18] consider the collapse process of the vapor film around the metal balls immersed into various coolants having a small number of nucleation centers of the vapor bubbles. Reasons for the vapor bubble collapse characterize the fundamentals of the vapor ex­ plosion phenomenon. The crucial criterion for the vapor explosion is the above mentioned MFBT. Besides, the vapor explosion intensity is esti­ mated by maximum heat flux after the collapse. As one of the criteria, the specialists distinguish the sound generated by the blast wave. The described effects are typical of the research area under examination. Further, we will discuss these processes. Kim et al. [8] claimed that the nanoparticle deposition on the surface of the heated metal spheres in­ creases CHF and the minimum heat flux temperature. Kim et al. [8] also assumed that an increase in the surface roughness and its wettability due to the nanoparticle deposition could result in the early collapse of the vapor film and consequently the cooling acceleration. In addition, study [19] mentions about the sensitivity of film boiling of the subcooled liquids to the characteristics for the heat exchange surface. However, the authors of research [8] concluded that the particle deposition and porosity accelerate the cooling process not always. Most likely, when analyzing the processes under examination it is necessary to account for the properties of a material of these particles. Moreover, during cooling of the long vertical tube manufactured from stainless steel 316 by the sea water (35‰) Lee et al. [20] established that a reason for increasing the cooling efficiency does not come from the wettability improvement resulting from the deposition of the marine salts. These experiments involve the top quenching by earlier condensation of vapor during sea salt solution reflood. Yagov et al. [21] revealed that at the high cooling rates of the heated metal balls there are significant temperature gradi­ ents not only in the radial axis but also along their surface. Hsu et al. [2] supposed that the zeta potential of the electric double layer in the ul­ trahigh temperature and the liquid/solid interfaces charged likely to decelerate the bubble coalescence in the seawater. However, as noted in Ref. [2], there are several assumptions on a decelerating effect of the bubble coalescence. Among of them are the influence of colloidal forces, solubility of gases, the Gibbs-Marangoni effect, surface rheology, etc. Nevertheless, the mechanism of this phenomenon remains unexplored [22]. The high-speed recording technology development enabled to describe in detail the boiling regimes when cooling the heated metal samples in subcooled water. For instance, study [5] distinguished boiling, at which the vapor film visually looks like a golf ball, i.e. “golf-ball” boiling period. This effect occurred during the transition from film boiling to transient one. The recent studies described in the review article [23] represent the modern concepts formulated during the last 10–15 years in terms of the nucleate boiling enhancement by adding solid particles, polymers, and surfactants. With regard to cooling of metal samples in nanofluids, it is established that cooling rates are identical or even worse than for a base fluid. However, the cooling rate increases in repeated tests due to the growth of the nanoparticle deposition layer on the surface. This layer destabilizes vapor film at rather high temperatures of surface and eliminates rapidly the film boiling. Moreover, the deposition on a

surface changes the characteristics for its wettability and improves the dynamics for bubble nucleation. Nevertheless, there are several prac­ tical issues, which do not enable suspensions to become a worthy alternative to a homogeneous coolant. Among them are sedimentation of nanoparticles, erosion to heating surface, high cost, etc. Thus, the efficiency of suspensions in terms of the nucleate boiling enhancement mainly comes from surface modification due to deposition. Generally, the cooling rate depends on surface characteristics. Li et al. [24], for instance, showed that the cooling time on the superhydrophilic surface at saturation is reduced by 50%. In this work, the peculiarities and characteristics of boiling regimes are examined in details. As a scientific novelty of the study, we state a convenient way to reach much higher cooling rates of metal spheres made of carbon steel AISI 1044 and stainless steel AISI 420L by the water-based suspensions clay and graphite as well as the water-NaCl and sea-water brines as compared to the homogeneous liquid, i.e. water. Special attention is paid to the issues of eliminating the film boiling in the case of the rapid cooling of the heated metal samples by using brines and colloid systems (e.g., the two-phase solid/liquid fluids) as coolants. The rapid and efficient cooling is required for preventing industrial di­ sasters, namely, fires and explosions, at NPPs and other power engi­ neering facilities. The purpose of this work is to explore the dynamics of the cooling process of the metal samples made of carbon steel AISI 1044 and stainless steel AISI 420L by brines and water-based suspensions. The study will perform by using seawater and water-NaCl brines because, as shown in Ref. [25], the water-NaCl brine is not able to substitute the natural seawater in the boiling process. This is conditioned by the fact that in seawater the magnesium salt may deposit on a surface and deteriorate heat transfer. Likely, the effect of these liquids on the pro­ cesses under consideration will be different. Therefore, to devote it special attention further is expedient. 2. Materials: metals and liquids To investigate the cooling dynamics of the balls heated up to high temperatures, stainless steel AISI 420L and carbon steel AISI 1044 are used. Steel AISI 420L is applied as a heat-proof material at temperatures up to 550–700� С. The application areas of steel AISI 420L are me­ chanical engineering, energy engineering, production of the furnaces and turbine blades operating at high temperatures, manufacture of fastenings. Steel AISI 1044 is also employed for general engineering purposes and in all the branches of industry. The products made of steel AISI 1044 are able to endure the frequent temperature gradients from 200� С to 600� С. Thus, with account for the properties of both steels and their application areas, they have been chosen for the test samples of the spherical shape. This shape is the most common one and is widely used in similar studies [2,5,8,16,17]. Note that within each series of experiments we used the same metal balls in contrast to the similar work, e.g., Ref. [2]. Certainly, the surface properties of metals marginally change during the high-temperature heating/rapid cooling, but in fact, such approach corresponds to actual operating conditions. We have preliminarily performed the experiments, in which the change in the surface properties of the metal balls affects insignificantly the temporal characteristics of their cooling and the phase transformations at the ball/coolant interface. As shown in Fig. 1, the ball diameter equals d � 20 mm. The heated metal balls are cooled down in the coolant with its initial temperature of Tc0�293 K. The volume of each coolant is 0.005 m3. It is poured into a reservoir. The reservoir has the following internal dimensions: height – 0.2 m, length – 0.29 m, width – 0.15 m and is made of glass to employ easily the high-speed recording. Table 1 presents the types of coolants and their characteristics. The utilization of seawater and brines comes from the demonstrated earlier possibility to eliminate the film boiling at the coolant/heated ball interface [2,22]. Accounting for findings [26] and knowledge on boiling [27–29], we also decided to employ the suspensions as coolants. 2

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a temperature range of 233–1273 K and a thermal lag of not more than 1 s. The measuring temperature error in a range from 607 K to 1273 K can be estimated as �0.0075|T–273|. This thermocouple is inserted in the hole of 1.5 mm in diameter and ~10 mm in depth. The space be­ tween the thermocouple and the walls of the hole was filled with the thermal sealant to prevent the direct contact between the coolant and the thermocouple junction. The thermocouple measures the tempera­ ture in the center of the ball. A choice of this thermocouple relies on the required experimental conditions, such as low thermal lag, wide tem­ perature range, and design peculiarities of fixing the ball. The location distance for the metal ball being heated and cooled is kept to be 0.25 m (as depicted in Fig. 2b). Heating is accomplished by a portable butane burner with a controllable heating intensity. The flame cross-section exceeds the metal ball diameter. Furthermore, the heating of the ball is performed from different sides to maintain the uniform heating. The ball is heated to the temperatures Tb of 700 K and 1000 K, which are from the operating temperatures of power engineering facil­ ities. A temperature Tb � 1000 K characterizes a transition of these fa­ cilities to emergency mode, e.g., in the case of breakdown of the regular cooling system [1]. The heating up to Tb � 700 K typifies the permissible operating temperature of many power facilities and their protective structures, primarily in nuclear power engineering [31]. High-speed recording is accomplished together with a LED spotlight. The readings of the type-K thermocouple inserted in the ball are trans­ ferred into the data acquisition device National Instruments 9219 con­ nected to PC. The sampling rate of the thermocouple readings equals 0.5 s. The cooling process of the heated ball is considered as completed when its temperature reaches the coolant temperature in the pool, i.e. 293–298 K. The coolant temperature Tc in the reservoir is controlled by four type-L thermocouples with a temperature range of 223–873 K and a measurement error of 2.5 K. The initial coolant temperature is T0 � 293 K. The thermocouples measure the coolant temperatures at different depths throughout the reservoir to provide for reliable tem­ perature monitoring. After each test, Tc increases insignificantly with less than 0.5 K. We do not record the readings of the thermocouples, but only control Tc by using a temperature recorder to achieve the identical conditions for each test run. When Tc values increase by more than 4 K relative to the initial one, we stabilize Tc up to 293–298 K. The prepa­ ration of the coolants requires an applying of the analytical balance VIBRA AF 225DRCE with an accuracy to five decimal places (when the mass is up to 92 g) to weight the admixtures being added into water, namely graphite and clay powders, and salts.

Fig. 1. Photo of the ball made of stainless steel AISI 420L with an indication of its diameter and holder.

Researches [9,11–14,26] demonstrated the heat transfer enhancement due to the carbonaceous admixtures. In the case of the graphite particles, this effect results from the rapid phase transitions, namely, the explosive fragmentation of the heterogeneous liquid due to the local overheating at the solid/water interface. Because the purpose of the study involves determining conditions for the short-duration efficient cooling, a utili­ zation of such liquids can surely affect the cooling dynamics. Moreover, the suspension utilization efficiency in the processes of heat sup­ ply/extraction are examined in the open literature. As a rule, such an efficiency comes from the improved thermal and physical properties of the two-phase fluids as compared to water [30]. The shape and the size (diameter) of the metal balls, as well as the mass concentrations of admixtures in the brines and suspensions, are chosen based on existing data [2,5,8,16,17]. The film boiling is better to learn by using the objects with almost uniform temperature distribution along the surface during heating. Moreover, such a shape reduces the effect of the convective heat transfer enhancement through edges. The volume of the coolants depends on the dimensions of the glass reservoir. In all the experiments with various coolants, the volume is constant to provide for the appropriate repeatability of results. 3. Experimental Fig. 1 is the schematic of the experimental setup, which is typical one used in the related works [2,5,8]. The major components of the exper­ imental setup consist mainly of the high-speed camera, the heater of the metal balls, thermocouples, and the linear module to move a ball into the liquid pool. The high-speed monochrome Phantom Miro M310 camera (Fig. 2) with a sample rate of 3268 frames per second at a maximum resolution of 1280 � 800 pixels is employed. As for the lens of this camera, the Macro Lens Nikon AF MICRO-NIKKOR 200 MM F/4D IF-ED with a focal distance of 200 mm is used. Due to the high value of the depth of focus, there is a possibility to observe and analyze the phase transitions as at the front of the metal ball, as at the ball/coolant inter­ face. The video recording of the processes is carried out through the vertical glass wall of the pool. The recording axis is perpendicular to this wall. The wall thickness is 0.004 m. The distance between the reservoir wall and the closest point of the ball equals 0.02 m. The distance be­ tween the lens and the vertical wall of the reservoir is about 0.2 m. The depth of immersion of the ball is 0.02 m. By using the Phantom Camera Control software, we determine a scale factor when analyzing the test video demonstrating the object with known dimensions. These mea­ surements have been done previously for the tests without heating of the ball. The linear module immerses the heated ball in a coolant. The time of the ball movement tm toward the recording area (as shown in Fig. 2) is about 1 s. As a holder of the ball, we apply the type-K thermocouple with

4. Experimental procedures and analysis Fig. 2b shows the measured temporal characteristics, namely the cooling time of the ball t and the time tm of movement from the point of heating to the recording area. The heating time of the ball th is longterm. Above, we have mentioned that tm is about 1 s for the heated ball being moved from the heating point to the recording area. Highspeed recording is activated simultaneously with the movement pro­ cess of the heated ball toward the recording area, i.e. about in the second before emerging the ball within the recording area. While Tb is contin­ uously controlled during all the stages, namely, heating of the ball, its transportation and cooling in the subcooled liquid. The moment, when the bottom of the ball appears in the recording area, corresponds to time t0 and temperature Tb0. At this moment, the ball is already cooling down in the coolant, because the distance from the coolant/air interface to the top of the recording area is about 0.02 m (Fig. 2b). The latter is in line with the ball diameter, i.e. it is fully immersed. The main parameter characterizing the cooling dynamics of the ball and the efficiency of the coolant used is ΔTb. This parameter is calcu­ lated by Eq. (1): ΔTb ¼ TbðnÞ

3

Tbðn

1Þ ;

(1)

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International Journal of Thermal Sciences 148 (2020) 106164

Table 1 Coolants and their characteristics. Coolant

Characteristics

Deionized water (DI water)

Without inorganic ions, particulates, gases, etc.

Coolant appearance

Tap water (hard water)

Increased concentration of calcium and magnesium cations

Sea water

Sodium and magnesium salt content is approx. 18 g/l; the Black Sea coastline near Gelendzhik, Russia

Water-salt solution (brine)

NaCl salt content is approx. 27 g/l; NaCl is dissolved in distilled water

Aqueous slurry of clay

o Clay concentrations are 0.1 wt% and 0.5 wt%; o Particle size is lower than 50 μm

Aqueous slurry of graphite

o Graphite concentrations are 0.05–1 wt.% o Particle size is lower than 100 μm

where Tb(n) is the ball temperature at a time of n, and Tb(n-1) is the ball temperature at a time of (n–1). A difference in time Δt is a sampling rate of thermocouple 10, i.e. 0.5 s. Actually, the parameter ΔTb shows how the ball temperature changes during the minimum time step. When analyzing the film boiling regime, namely, the instability of the vapor film around the ball, the Fourier number (Fo) is employed, see Eq. (2): Fo ¼

αt ; δ2

where α stands for thermal diffusivity of the water vapor at a tempera­ ture of 373 K and a pressure of 105 Pa. The t time is the cooling one of the ball, and δ indicates the vapor film thickness. The thickness δ is deter­ mined according to the following equation, Eq. (3) � δ ¼ Rf R b ; (3) In Eq. (3), Rf is vapor film radius, i.e. a distance between the center of the ball and the water vapor/coolant interface, and Rb indicates the ball radius. To examine heat transfer from the heated ball to the coolant through

(2)

4

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International Journal of Thermal Sciences 148 (2020) 106164

Fig. 2. Schematic of the experimental set-up (a) and the measuring area (b).

the stable vapor film, we estimate conductive (qc) and radiative (qr) heat flux densities by using the Fourier’s law of heat conduction and the Ste­ fan–Boltzmann law, respectively. The study of the cooling dynamics of the heated ball involves 7–10 tests per each coolant. The experimental uncertainty analysis shows that under the identical system parameters, the maximum root-mean-square deviation within a series of the ther­ mocouple temperature measurements inside the ball is less than 4 K.

subcooled DI water (Tc0�293 K). It is clearly observed that there are three boiling regimes, namely, film, transient, and nucleate ones. When the ball temperature Tb drops below 500 K, the cooling is mainly caused by natural convection without the intensive vaporization at the interface (Fig. 3g). The film boiling begins when the ball is immersed into the coolant. The formed stable vapor film (Fig. 3a and b) prevents the ball surface from the coolant. During the film boiling, the pulsating oscilla­ tions (“wave” motion) take place at the vapor/coolant interface. These oscillations, as a rule, move from bottom to top. Such a behavior of the vapor film lasts during its lifetime. Fig. 3c demonstrates the shot of the cooling process, at which the vapor film collapse occurs. Importantly, the collapse front, as the pulsating oscillations (Fig. 3a and b), moves from the bottom, i.e. the collapse initiates at the bottom of the ball. The same outcome is discussed in research [8]. It is important to note that the collapse front curvature visually corresponds to the wave fronts during the pulsating oscillations (Fig. 3a–c). The rapid collapse of the

5. Results and discussion 5.1. Modes of cooling processes The cooling evolutions of the heated balls with an initial temperature of Tb � 1000 K in various coolants allowed us to find out the conditions for different boiling regimes (as shown in Figs. 3 and 4). Fig. 3 presents the cooling processes of the ball made of stainless steel AISI 420L by the

Fig. 3. Cooling process photos of the ball made of stainless steel AISI 420L by the DI water with a frame rate of 5000 fps. 5

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International Journal of Thermal Sciences 148 (2020) 106164

shown in Fig. 5. As in study [2], when using the subcooled (room tem­ perature) seawater as a coolant, the film boiling disappears. The main boiling regime providing for the intensive and rapid heat removal is the nucleate one in the subcooled liquid. In the tests with cooling of the balls with an initial temperature of Tb0�700 K by various coolants, only the subcooled nucleate boiling is accomplished. 5.2. Cooling time As mentioned above, the measured results show when using the DI water as a coolant, the vapor film emerges in each test. Utilizing the tap water, the film boiling is unstable, i.e. it is impossible to predict how the cooling process will occur. We compare the curves of the cooling by brines and suspensions with those of the tap water because the DI water used is an idealized case to demonstrate the maximum effect of the subcooled pool film boiling on the cooling time delay. Fig. 6 illustrates the cooling curves of the balls made of stainless steel AISI 420L and carbon steel AISI 1044. The cooling process of the ball made of carbon steel AISI 1044 is accomplished in all the cases without emerging the vapor film in contrast to cooling of the ball made of stainless steel AISI 420L. Besides, Fig. 6d–f clearly demonstrate that the utilization of the water-based suspensions and brines promotes to considerable temper­ ature drop inside the ball as compared to that with cooling by the tap water. However, the increment in the mass concentration γ of clay and graphite as well as salts does not affect significantly the temporal characteristics of cooling. Fig. 6a–c allow us to believe that using the brines and suspensions affects the cooling of the ball made of carbon steel AISI 1044. In this case, the duration of the transition and nucleate boiling regimes is quite close. These regimes are characterized by a sharp heat removal and the rapid decrease in the ball temperature. In particular, the cooling of the ball made of steel AISI 1044 by seawater from ~1000 K (the ball center) to the conditions for cooling by the natural convection lasts about 6–8 s (Fig. 6a). Unfortunately, the cooling times decrease insignificantly. It is found that at the identical experi­ mental conditions and with using two different steel types, the sub­ cooled pool film boiling is noticed in different ways. This implies the vapor film emergence depends on the ball surface structure and treat­ ment as well as metal properties [8,19]. From the physical viewpoint, the results in Fig. 6 characterize the positive effect of solid and dissoluble admixtures on decreasing on the cooling times of the metal balls. The presence of the admixtures con­ tributes to a local intensive warming-up of a liquid due to their heat accumulation supplied from the heated surface of the ball [6,8]. Based on the studies [13,36], the admixtures in liquids are considered to be additional nucleate points. Nevertheless, from the experimental results as well as the tests of the water-based nanofluids with alumina nano­ particles as coolants [8], the increase in the admixture concentration does not guarantee an increase in the heat removal and the corre­ sponding decrease of the cooling time. However, with certainty, it is possible to conclude the heterogeneity of liquids enables to eliminate the subcooled pool film boiling. Kim et al. [8] finds out that the vapor film break-up due to the nanoparticle deposition on the surface is a physical mechanism that accelerates the film boiling ending. In this case, the authors state that the particles in a liquid in different concentrations do not have a meaningful effect on the cooling process in terms of decreasing the complete cooling time. The question is about decreasing the film boiling time only. Here, the authors concluded that the signif­ icant differences between times of the film boiling ending under iden­ tical experimental conditions come from increasing the nanoparticle deposition on a surface. Ciloglu and Bolukbasi [6] reported that during the subcooled pool boiling the main reason for increasing CHF in the two-phase liquids (nanofluids) is a change of the surface characteristics due to the formation of the porous layer consisting of particles. The results presented in Fig. 6 for the water-based suspensions of clay and graphite with different concentrations enable to draw similar conclu­ sions concerning the physical model of the cooling process. In addition,

Fig. 4. Vapor film collapse time points during the cooling of the ball made of stainless steel AISI 420L by the DI water; the tests* are carried out under the identical conditions. Note: *we illustrate maximum and minimum time points as well as several intermediate ones; the total number of tests is not less than 10.

vapor film is accompanied by low clap. After collapsing the vapor film at the metal ball/coolant interface, the vapor bubbles formation begins instantly. In the beginning, they are quite small. Therefore, on the video frames, the ball envelope visually becomes white, like a foam. The fuel reverse emulsions with the water droplets of 1–10 μm in size as a dispersed phase have a similar color [32–35]. Let us assume that during the transition boiling (Fig. 3d), the size of the water vapor bubbles varies in the same range. In addition, note that at this stage (Fig. 3d) the vapor bubbles are released in the form of clusters away from the ball surface. We regard boiling as a transition one until the water vapor bubbles begin to enlarge (Fig. 3e and f). When the enlarged bubbles become noticeable, the nucleate boiling is likely fulfilled. The further growth of bubbles is followed by decreasing their number and, consequently, by “decoloring” the regions around the ball/coolant interface (Fig. 3e and f). Many small bubbles in the form of clusters (groups) move away from the ball. During the nucleate boiling, the departure diameter of the vapor bubbles can reach tenths of a millimeter. The reaching of such size is possible due to both the phase transition and the coalescence of the smaller bubbles. It is expected that bubbles expand due to filling them with the water vapors supplied from the three-phase coolant-vapors-wall boundary during vaporization. Moreover, coalescence and the corresponding growth of the vapor bubbles happen during their expanding on the wall surface as well as after their departure. Then, the vapor bubbles intensively collapse. The stable vapor film collapse lasts during the pronounced time in­ terval. However, the duration of the vapor film existence is absolutely unpredictable (Fig. 4). Hsu et al. [2] discussed the similar findings in terms of the vapor film existence. In particular, during the cooling of the balls made of stainless steel 304 and zircaloy 702 by the DI water, the stable vapor film lifetime varies in a wide range. Using the seawater as a coolant, the film boiling is eliminated similar to this experimental research. The comparison of the cooling curves presented in Hsu et al. [2] and Fig. 4 allows us to make a conclusion of the similarity of the results. It is clearly noted in Fig. 4 that the vapor film exists from ~6 s to ~13 s. To find out the reasons explaining the instability of the vapor film, it is necessary to carry out the supplementary research. Such a research is critically important for the water-cooling technologies because the efficiency of the heat removal strongly depends on this boiling regime and its duration. The cooling processes of the ball made of stainless steel AISI 420L by seawater under the heating conditions identical to those in Fig. 3 are 6

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International Journal of Thermal Sciences 148 (2020) 106164

Fig. 5. Cooling process photos of the ball made of stainless steel AISI 420L by seawater with transition and nucleate boiling regimes as well as the free convection (the frame rate is 5000 fps).

a wide scatter of the data presented in Fig. 4 and an instability of the vapor film emergence when using the tap water (Fig. 6d–f) are likely explained by similar reasons. In particular, among of them is a change of the surface structure due to the porous layer consisting of the salt de­ positions and the particles used, as well as due to the gradual burning-out of the surface layer of the balls. Fig. 7 presents cooling curves of the balls with an initial temperature of Tb0�700 K. It is noted that the effects of the admixtures on the cooling times are not considerable, i.e. when using the brines and suspensions t decreases only by 1–2 s. The subcooled pool film boiling is not accom­ plished. The transition boiling is clearly observed when using the tap water. Applying the brines and suspensions at an initial temperature of Tc0�293 K, we can distinguish the nucleate boiling only. In this case, the cooling curves demonstrate a sharp drop of Tb from the beginning of the cooling process in contrast to the cooling curve Tb(t) for the tap water. The film boiling elimination in the case of the tap water at the lower temperature Tb0 (Fig. 7) is likely explained by the following reasons: (1) temperature Tb0 becomes lower MFBT; (2) at a higher temperature Tb0, i. e. 1000 K, the vapor film already arises unsteadily (Fig. 6d–f). The latter is probably caused by the boundary condition, i.e. Tb reaches or is close to MFBT during the ball cooling by the tap water. Basically, a decreasing of the effect of solid and dissoluble admixtures on the cooling times significantly results from the above discussed reasons.

beginning of cooling. While the cooling dynamics of the ball by the tap water show a maximum about at 5 s (Fig. 8a–b), or as in the case in Fig. 9a–b the cooling dynamics look like the sinusoidal function. In the latter case, the maximum temperature drop rate exceeds 50 K/s. While the maximum temperature drop rate, ΔTb/Δt(t), is about 200 K/s when using the suspensions (Fig. 9a–b). In Fig. 8a–b, the maximum tempera­ ture drop rate, ΔTb/Δt(t), for the suspensions attains 300–450 K/s. The latter result is one of the main fundamental findings of this research. In the case of cooling the ball made of stainless steel AISI 420L with an initial temperature of Tb0�700 K (Fig. 9c–d), the better cooling per­ formance by suspensions, i.e. a higher temperature drop rate, is not observed. Moreover, a comparison of the peak values of the function ΔTb/Δt(t) for the tap water and suspensions also does not allow us to reveal a better cooling performance. However, the ball made of carbon steel AISI 1044 and heated up to Tb0�700 K (Fig. 8c–d) is cooled fastly down with suspensions by 1–1.5 s relative to that using the tap water. The cooling rate ΔTb/Δt can reach 350 K/s using the suspensions. While the cooling rate for the tap water is also not low, up to 250 K/s. The suspensions as coolants show the high efficiency of cooling of the balls with an initial temperature of Tb0�1000 K. Generally, the maximum heat removal from the heated balls to the two-phase liquids occurs at the initial transients, 2–4 s, after the beginning of cooling. Certainly, this outcome is a desirable one for the emergency cooling technologies of the thermally-loaded equipment.

5.3. Cooling dynamics

5.4. Film boiling mode

Figs. 8 and 9 illustrate the dynamics of the cooling process of the balls. The parameter ΔTb/Δt characterizes a rate of the Tb temperature change during the shortest time interval corresponding to the minimum sample rate of the thermocouple inside the ball. Obviously, for the cases with an initial ball temperature of Tb0�1000 K (Fig. 8a–b and 9a-9b) and using the coolants with the solid admixtures, the sharp temperature drop occurs during 2–4 s from the

During the cooling process of the balls by the DI water, some features of the subcooled pool film boiling are observed (Fig. 10). The vapor film thickness and the Fourier number lowers step by step with time (Fig. 10a). When the vapor film reaches the critical thickness corre­ sponding to the film collapse, i.e. Rf/Rb � 1.32, the Fourier number Fo equals to zero. It is assumed that the stepped type in Fig. 10a results from 7

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International Journal of Thermal Sciences 148 (2020) 106164

Fig. 6. Cooling curves of the metal balls with an illustration of the transition and nucleate boiling regimes (Tb0�1000 K): a-c – carbon steel AISI 1044, d-f – stainless steel AISI 420L.

the pulsating oscillations of the vapor film/coolant interface, see Fig. 3a–c and the corresponding discussion. When the heat exchange surface has a high roughness, the vapor/liquid interface is always wave-shaped during the subcooled pool film boiling [8]. This is due to the short-term mul­ tiple contact between coolant and surface. Fig. 10b provides for the heat flux densities typical of the vapor film during its lifetime. The radiative heat flux density is reduced almost by half to the moment of the vapor film collapse. The conductive heat flux density grows gradually. In the case presented in Fig. 10b, the lifetime of the vapor film is approx. 8.5 s.

5.5. Optical temperature measurements near the liquid/vapor boundary To understand how the coolant temperature changes near the liquid/ vapor interface during the subcooled pool film boiling, we have per­ formed the optical measurements. To carry out the corresponding tests, the experimental set-up has improved. Fig. 11 provides for the scheme of the measuring area by an optical method as well as the experimental calibration curve T ¼ f(α), where α – fluorescent dye luminosity expressed in units of brightness. We employ the optical method of the planar laser-induced fluorescence (PLIF), the methodology of which is described in detail in the related studies [13,37,38]. Using this method, we measure the temperature at the liquid/vapor interface (T2) and the 8

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International Journal of Thermal Sciences 148 (2020) 106164

Fig. 7. Cooling curves of the balls with an illustration of the transition and nucleate boiling regimes only (Tb0�700 K): a-c – carbon steel AISI 1044, d-f – stainless steel AISI 420L.

distribution of T2 near this interface (T2 … n). The temperature in the center of the ball made of carbon steel AISI 1044 (T1) is measured by the thermocouple described in Section 3. By using the type-K thermocouple with a temperature range of 233–1023 K, an error in measuring tem­ peratures up to 650 K of �1.5 K, and a junction thickness of 0.25 mm, we can determine the temperature of the ball surface (T3) (Fig. 11a). The optical method relies on the natural fluorescence of fluorophore molecules after inducing by laser [39–41]. Preliminarily, the Rhoda­ mine B powder is dissolved into the DI water at a concentration of 1 mg/l

within several minutes. The method requires a fluorescent dye, a cross-correlation digital camera equipped with a macro lens with a 200-mm focal length and a filter blocking excessive laser light, a dual pulsed laser, a lens for generating a light sheet with an opening angle of 8� , and PC with Actual Flow and PLIF Kit software packages. During the experiments, the DI water/Rhodamine B solution in the pool is cut by the dual pulsed laser along the symmetry axis. After immersing, the 100 μm-vertical light sheet is incident on the ball axis of symmetry. The CCD images of the coolant/ball system are produced with the 9

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Fig. 8. Comparisons of the cooling dynamics of the balls (carbon steel AISI 1044) when using the water-based suspensions of clay and graphite as well as the tap water as coolants: (a, b) – Tb0�1000 K and (c, d) – Tb0�700 K.

cross-correlation camera and processed by Actual Flow. More details on how to implement the PLIF method in similar conditions can be found in studies [13,37,38], including the calibration stage. The calibration curve presented in Fig. 11b demonstrates what a temperature corre­ sponds to a certain luminosity of the fluorescence dye induced by laser light. It is necessary to single out several conditions dealing with the effect of fluorophore and laser power on temperature measurements per­ formed by the PLIF method. Strizhak et al. [42] discusses the effect of the Rhodamine B powder on the evaporation times of droplets inserted into the flow of hot air. These experiments did not reveal any noticeable differences in the evaporation times as compared to the droplets of distilled water. The maximum differences did not exceed 1.5%. This value is less than an error of these measurements. Note that the Rhodamine B concentration was quite low and similar to the concen­ tration in research [42]. The Rhodamine B concentration was too low to affect the droplet heating-up. We have carried out pilot experiments earlier, which showed that if the Rhodamine B concentration would be 2 mg/l, then in the case of the single droplets of less than 3 mm in size the heating-up and evaporation characteristics would differ by 20–30% in the tests with and without dye. In addition, during the tests the pulse energy was minimum, about 35 MJ, to eliminate the vapor bubble nucleation and pool boiling. Antonov et al. [43] found out that even the power of a pulse laser applied for PLIF and PIV measurements is suffi­ cient to affect the temperature field, deformation, and break up of a droplet. In this study, the liquid volume is massively more, and therefore

the effect of a laser should not be as strong. Such minimum pulse energy is the mean one at the distance from the pool wall to the ball. Fig. 12 illustrates the coolant temperature profiles near the liquid/ vapor interface while the ball heated up to 1000 K is cooled down. Notice that with time the temperature near the liquid/vapor interface or de­ creases, or increases. We suppose that these weak fluctuations in tem­ perature come from the described earlier phenomenon of the “step” change of the vapor film thickness due to the pulsating oscillations resulting from the short-term multiple contacts between the coolant and solid surface [8]. During these contacts, the heat transfer between the ball surface and coolant is enhanced, and the coolant temperature locally rises. After recovering the stable vapor film in the local region, the heat transfer becomes noticeably difficult, and the temperature near the liquid/vapor interface reduces again due to the convective mixing with deeper cold layers of a coolant. In addition, if moving away from the interface, the temperature gradually decreases with time. Note that the coolant temperature near the interface is quite low while the center temperature of the ball is very high (Fig. 13). Due to the low thermal conductivity of the water vapor, heat is transferred slowly from the heated ball to the coolant. While the vapor film exists, the latter is confirmed by the moderate increase in temperature T2 with the cooling time (Fig. 13). The slope of the linear fitted curve is as little as 16� . The findings indicate that the thermal energy accumulated by the ball is used during the cooling process for phase transition of the coolant sur­ rounding this ball, i.e. for maintaining the existence of the stable vapor film. Only the limited part of this energy is transferred to the coolant 10

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Fig. 9. Comparisons of the cooling dynamics of the balls (stainless steel AISI 420L) when using the water-based suspensions of clay and graphite as well as the tap water as coolants: (a, b) – Tb0�1000 K and (c, d) – Tb0�700 K.

Fig. 10. The Fourier number versus the ratio between the radii of the vapor film Rf and the ball Rb (a); conductive and radiative heat flux densities in the vapor film (b); stainless steel AISI 420L, coolant – DI water, Tb0�1000 K; the figure presents the example of a single test.

separated from the ball by the vapor film. This is evident from the fact that temperature T1 during the existence of this film lowers about by 200 K, but temperature T2 during the same time grows insignificantly, by as little as several Kelvins (Fig. 13). The experimental uncertainty analysis shows that a data spread within a series of PLIF temperature measurements for T2 equals to about

15 K, and the maximum root-mean-square deviation within a series of the thermocouple measurements for T3 is maximum 5 K. The optical measurement results of the temperature at the liquid/ vapor interface can be utilized during developing and improving math­ ematical cooling models (e.g., Ref. [44]) taking into account emerging the stable vapor film separating the heat-exchange surface from a 11

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International Journal of Thermal Sciences 148 (2020) 106164

Fig. 11. Schematic of the optical measurement area (a) and experimental calibration curve for the PLIF method (b).

Fig. 12. Coolant temperature profiles near the liquid/vapor interface during the vapor film existence: h – length of the vertical cross-section from the liquid/ vapor interface into the depth of coolant.

Fig. 13. Mean temperatures T1, T2, and T3 versus cooling time (while the vapor film exists); the inner diagram presents the T2 values at the liquid/ vapor interface.

coolant. Moreover, knowing the T2 values near the liquid/vapor inter­ face, minimum heat flux (MHF) at the film boiling characterizing the transition from the film boiling to the transient one can be estimated by formula (4) [45,46]:

Under the experimental conditions, the CHF value is around 1.18 MW/m2.

� q’’min ¼ 0:09ρw rw

�1 ρv Þ 4

σgðρl ðρl þ ρv Þ2

5.6. Research results using

(4)

;

The approach discussed in this work develops the line of research presented in Ref. [50]. Legros and Piskunov [50] provided for the theo­ retical foundations of the emergency cooling technology of the thermally-loaded equipment based on a coolant with high thermal conductivity, which flows over the heated surface. Using the example of the interaction between a single particle (as an element of the two-phase coolant) and water volume, heat transfer is learnt with due account for phase transitions at interfaces. The studies within metal quenching are carried out by the same approach [51–53]. The coolants containing solid and insoluble admixtures can help to reach the rapid and efficient heat removal in the emergency cooling systems of power engineering

where 0.09 – constant from Ref. [47], ρl and ρv – densities of liquid and vapor, respectively, kg/m3, rw – latent heat of evaporation, J/kg, σ – surface tension of water, N/m, g – acceleration of gravity, m/s2. The MHF value equals about 19.46 kW/m2. In addition, by Kutateladze formula (5) [48,49], we determine the critical heat flux characterizing the transition from transient boiling to the nucleate one: 1

qcrit ¼ 0:14rw ðρv Þ2 ðσgðρl

1

ρv ÞÞ4 ;

(5) 12

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equipment. The heterogeneous coolants can be applied during the elimination of emergency similar to Fukushima Daiichi nuclear disaster by their spraying on the heated surfaces. Moreover, for power engineering equipment, it is possible to create cooling loops circulating such cool­ ants. The performed study contributes to the research area of the cooling process of the metal samples of different geometry by two-phase cool­ ants during their pool boiling and spraying. Among the studies repre­ senting this research area are experimental [2,5,6,8] and theoretical [4, 17] ones. A need to determine the factors affecting the lifetime of the stable vapor film during the subcooled pool film boiling can be distinguished as a logical extension of the findings. Furthermore, it is necessary to carry out the study of the spray cooling by the coolants containing the solid and dissoluble admixtures used.

(2) The pool film boiling is extremely unpredictable when using the subcooled tap water. This restricts the utilization of this liquid as a coolant even under laboratory conditions. The phenomenon of the “step” change of the vapor film thickness during the pool film boiling of the subcooled deionized water is observed. (3) By using the optical method of the planar laser-induced fluores­ cence, the temperature distributions are measured near the liquid/vapor interface during the pool film boiling of the sub­ cooled deionized water/Rhodamine B solution that results from the immersion of the heated ball made of steel AISI 1044. Declaration of competing interest The authors declare no conflicts of interest.

6. Conclusions

Acknowledgments

(1) The most rapid and efficient cooling of the heated metal balls with initial temperatures of 700 K and 1000 K occurs at the initial transient (2–4 s) when using the graphite and clay suspensions. The maximum cooling rate of the metal balls reaches 300–450 K/ s. During the cooling process of the heated up to 700 K balls made of carbon steel AISI 1044 and stainless steel AISI 420L, the effi­ ciency of the brines and water-based suspensions of clay and graphite as coolants is less noticeable. If using the brines and water-based suspensions as coolants of the heated balls made of stainless steel AISI 420L and carbon steel AISI 1044, the vapor film does not emerge in the pool boiling process.

The research was supported by the Foundation of President of Russian Federation (SP-1049.2016.1). The optical measurements were carried out within the framework of the development program of the National Research Tomsk Polytechnic University. Professor W.M. Yan acknowledges the financial support by the “Research Center of Energy Conservation for New Generation of Residential, Commercial, and In­ dustrial Sectors” from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.

Nomenclature cp d Fo K qc qcrit q’’min qrad Rb Rf T tf th tm t0 T Tb Tb0 Tc Tc0 T1 T2 T2 … T3

n

specific heat capacity of the water vapor at constant pressure, J/kg∙K diameter of the metal ball, mm the Fourier number thermal conductivity of the water vapor, W/(m∙K) conductive heat flux density in the vapor film, W/m2 critical heat flux, W/m2 minimum heat flux, W/m2 radiative heat flux density, W/m2 radius of the ball, mm radius of the vapor film, mm cooling time, s; cooling time during the vapor film lifetime, s; heating time of the ball, s; time of the metal ball movement toward the recording area, s; initial cooling time of the ball, s; temperature, K; ball temperature, K; initial cooling temperature of the ball, K; coolant temperature, K; initial coolant temperature, K; temperature in the center of the ball, K; temperature at the liquid/vapor interface, K; temperature distribution from the liquid/vapor interface into the depth of a coolant, K; surface temperature of the ball, K.

Greek symbols А thermal diffusivity of the water vapor at a temperature of 373 K and a pressure of 105 Pa, m2/s Γ mass concentration of admixtures in a coolant, wt.% Δ thickness of the vapor film, mm Δt sampling rate of a thermocouple, s; ΔTb parameter characterizing the cooling dynamics of the ball and the efficiency of the coolant used, K; Р density of the water vapor, kg/m3

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