Visualization study of critical heat flux mechanism on a small and horizontal copper heater

International Journal of Multiphase Flow 41 (2012) 1–12

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International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w

Visualization study of critical heat flux mechanism on a small and horizontal copper heater Ho Seon Ahn, Moo Hwan Kim ⇑ Division of Advanced Nuclear Engineering, POSTECH, Pohang 790-784, Republic of Korea

a r t i c l e

i n f o

Article history: Received 17 August 2011 Received in revised form 8 December 2011 Accepted 15 December 2011 Available online 27 December 2011 Keywords: Pool boiling Critical heat flux Visualization

a b s t r a c t We examined the influence of the macrolayer under a large vapor mushroom on critical heat flux (CHF) during pool boiling with a small plate heater. Evidence of a macrolayer was provided, and its measured thickness was compared and well agreed with values reported in the literature. The classical CHF models of pool boiling do not consider the effect of the heater size. For a small and horizontal heater, a hydrodynamic liquid inflow increases the CHF beyond the predictions of most models, which are based on an infinite and horizontal heater. Using high speed visualization of CHF, we proposed a new CHF triggering mechanism for a small heater. Because the hydrodynamic liquid inflow supplies liquid to the edge of the heater, nucleate boiling is maintained in this region, even when a large dry patch beneath the large mushroom is generated at the center of the heater. The CHF occurs when the macrolayer at the edge of the heater dries out (i.e., becomes coated with a vapor film) and meets the large dry patch at the center of the heater. Finally, we proposed the shape of macrolayer beneath the large mushroom in order to explain the CHF triggering mechanism on the small heater. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Critical heat flux (CHF) is the maximum heat flux at which nucleate boiling heat transfer sustains high cooling efficiency. After the surface heat flux reaches the CHF value, the surface becomes coated with a vapor film that interferes with the contact between the surface and the ambient liquid, with decreasing the heat transfer efficiency. The system temperature rises, and a system failure occurs if the temperature exceeds the limits of the materials in the system. For this reason, systems incorporate a safety margin by operating at a heat flux much lower than the CHF, even though this reduces their efficiency. This compromise between safety and efficiency is an important issue in thermal systems such as nuclear power plants. A number of models for CHF in pool boiling have been proposed. However, the ones that have been most widely accepted were developed by Kutateladze (1950) and Zuber (1959) for boiling on an infinite, upward-facing, horizontal, flat plate. Kutateladze (1950) described CHF as a hydrodynamic phenomenon. At high heat flux, if the vapor velocity reaches a critical velocity, CHF occurs due to a breakdown in the stability between the two-phase flows. He proposed the following correlation based on a dimensional analysis:

q00CHF hlg q

rgðql  qg Þ1=4

0:5 ½ g

¼K

⇑ Corresponding author. Tel.: +82 54 279 2165; fax: +82 54 279 3199. E-mail address: [email protected] (M.H. Kim). 0301-9322/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2011.12.006

ð1Þ

where q00CHF , hlg, r, g, ql, and qg are the critical heat flux, the latent heat, the surface tension, the gravity, the density of the liquid, the density of the vapor, respectively, and used 0.16 as the value of constant K. Zuber (1959) postulated that the vapor generated on a flat plate accumulates to form a continuous column of escape flow with a diameter of k2c at intervals of Taylor’s critical wavelength kc and that CHF occurs when the vapor–liquid interface of the escape passage becomes unstable due to Helmholtz instability. However, the magnitude of the Helmholtz critical wavelength kH is indefinite, so it is set to kH ¼ p2kc from the Rayleigh stability limit of a circular gas jet on a liquid (Rayleigh, 1878), and a few approximations are made to give the following formula for CHF: 1=4 q00CHF ¼ 0:131hlg q0:5 g ½rgðql  qg Þ

ð2Þ

Zuber’s correlation does not consider the size, geometry, or surface condition of a finite plate because it was derived using an infinite-plate assumption. Lienhard and Dhir (1973) evaluated Zuber’s (1959) theory and modified it to consider size and geometry effects. The characteristics dimension that were a radius, a length, a height and a perimeter was related with the ratio between the Rayleigh and Taylor’s wave length and the heater’s dimension. They reexamined the Zuber’s (1959) theory in the light of up-to-date experimental evidence and have concluded that constant K given by Zuber should be increased by a factor 1.14, i.e. K should be 0.149. The Zuber’s (1959) analysis is strictly valid only for boiling of pure fluids on large thick well-wetted horizontal surfaces facing upward. Lienhard et al. (1973) have showed both

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analytically and experimentally that, in general, CHF would decrease with increasing heater size up to a point and then become relatively constant. They related this behavior to the number of ‘‘vapor jets’’ that could be supported by the surface area. Similarly, Saylor and Simon (1989) have found that CHF was relatively constant for large surfaces and increased for decreasing heater size past a certain transition point. For nucleate boiling at high heat fluxes, Gaertner and Westwater (1960, 1963) reported that a thin liquid layer exists immediately adjacent to the heated surface. This liquid layer is generally referred to as the macrolayer to distinguish it from the microlayer that exists under the base of individual nucleating bubbles. Their results were based on extensive photography of the heated surface and the near-surface regions during pool boiling on a flat heater. They noted that the macrolayer contains numerous columns or stems of vapor. At short distances from the heater, they found that vapor stems from several adjacent active nucleation sites merged into a large vapor mushroom. The occurrence of CHF has been linked closely to the behavior of the macrolayer. Gaertner (1965) proposed that CHF occurred as a result of the collapse of the vapor stems because of hydrodynamic instabilities on their walls. He conjectured that such a collapse of the stems causes the formation of dry patches on the heated surface. In his opinion, classical Kelvin–Helmholtz instabilities may not be applicable in this situation because the predicted values were orders of magnitude higher than the thickness of the liquid layer observed by Kirby and Westwater (1965). Additionally, Sadasivan et al. (1992) postulated that Kelvin–Helmholtz instabilities do not appear to be the main factor in determining the macrolayer thickness. The macrolayer formation mechanism has been examined based on available detailed experimental measurements of vapor and liquid flow patterns close to the heated surface. Katto and Yokoya (1968) proposed that CHF was the result of consumption of the macrolayer due to evaporation. They noted that the supply of liquid to the heater surface occurs only when the vapor mushroom detaches from the macrolayer. Immediately after the mushroom departs, fresh liquid is supplied to the heated surface, the macrolayer is reestablished, and a new vapor mushroom begins to grow above it. The time period between the inception and departure of the mushroom is termed the hovering period of the mushroom. Thus, they postulated that the heater surface becomes completely dry when the time required to evaporate the entire macrolayer is less than the hovering period of the vapor mushroom. Ouwerkerk (1972) visualized bubble generation and coalescence in a thin liquid layer under the vapor mass. He observed a dry spot at the base of these bubbles. As the liquid film evaporated, the dry spot grew and combined with nearby dry spots, making a large dry area. These dry areas were rewetted after the vapor mushroom departure; however, if heat flux was large enough, some dry areas reached the burnout stage without full rewetting. This was a local phenomenon: some parts of the heater surface had local dry areas, while others did not. Both nucleate boiling and film boiling coexisted near the same area, and drying and rewetting were repeated simultaneously. Ouwerkerk (1972) reported that the dry patch did not change the size and lift time of the mushrooms at 80% of CHF, but their frequency of occurrence increased with heat flux. CHF occurred when one of the dry patches grew abruptly. Unal et al. (1992) postulated that the generation of dry patches was the result of local liquid macrolayer evaporation and that the thickness of the liquid macrolayer was non-uniformly distributed. However, they did not consider the radial growth of a dry patch. If the temperature in the center of a dry patch reached the critical point, it became harder to make a good liquid–solid contact. Thus, a hot spot began to grow, the dry patch covered the heating surface completely, and film boiling began. For this reason, they believed that a hot spot causes CHF. Therefore, the

temperature in center of a dry patch is an important parameter and is closely related to the surface rewetting behavior. Finally, Haramura and Katto (1983) insisted heat transfer related with macrolayer formation and evaporation. They said that if heat flux is high enough to evaporate all of macrolayer before the departure of vapor mushroom bubble, the liquid film on the heating surface cannot be fed with bulk liquid, CHF occurs. It is come from the Helmholtz instability induced lateral coalescence among the small vapor jets in macrolayer. Following equations are the main heat balance equation and CHF correlation on a horizontal, infinite flat plate.

sd q00 Aw ¼ ql dc ðAw  Av Þhlg

ð3Þ

where sd, Aw, dc, and Av are the hovering period of the large mushroom, the area of water stems, the thickness of the macrolayer, and the area of the vapor stems, respectively. 1=4 q00CHF ¼ hlg q1:2 g ½rgðql  qg Þ



1=16 

p4 11

2

Av Aw

5=8

2 3 !,  5=16 " 3=5 #5=16 Av ql 11 ql  1 þ1 þ1 16 qv Aw qg

ð4Þ

In addition, they postulated that if CHF occurs on a small (finite) heater, its value will be higher than that on an infinite heater due to the hydrodynamic liquid inflow, as shown in Fig. 1. They indicated that an inflow factor of k = 0.83 matched the experimental CHF value on a 10-mm-diameter copper disk heater at atmospheric pressure. The meaning of the adding factor k is the thicker macrolayer due to the hydrodynamic liquid inflow. In addition, the effect of heater’s diameter on CHF was neglected on the Haramura and Katto’s (1983) model.

sd qAw ¼ ql dc ðAw  Av Þð1 þ kÞhlg 1=4 ð1 q00CHF ¼ hlg q1=2 g ½rgðql  qg Þ    5=8  5=16 1=16 p4 Av Av 1 þ kÞ5=16 11 2 Aw Aw 2 3 !, " 3=5 #5=16 ql 11 ql  þ1 þ1 qg 16 qv

ð5Þ

ð6Þ

In this paper, we describe a macrolayer model that includes the concept of a layer of liquid and vapor stems beneath a large vapor mushroom. Through high-speed visualization of nucleate boiling in

Fig. 1. Pool boiling at high heat fluxes on a small horizontal disk and macrolayer’s concept (Haramura and Katto, 1983).

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a small heater immediately before, at, and immediately after CHF, a new triggering mechanism is proposed that includes the liquid inflow effect.

2. Experiments 2.1. Pool boiling experimental facility Fig. 2 shows a schematic diagram of the pool-boiling experimental facility. It consisted of an actual boiling pool, a test sample, and a heating section. The boiling pool had a test pool, immersion heaters, visualization windows, and a reflux condenser.

The aluminum test pool was a rectangular vessel with a height of 600 mm. Three immersion heaters with a maximum heating power of 1 kW were embedded in the pool to preheat the working fluid. Polycarbonate windows, 10-mm thick and with a maximum allowable temperature of 140 °C, were placed in the front and back walls of the pool to visualize the boiling phenomenon on the test heater. The reflux condenser was located at the top of the pool to condense the phase-changed vapor into liquid. Three T thermocouples were immersed in the pool to measure the average bulk temperature. During the experiment, the bulk temperature was maintained at 100 °C using feedback control based on the thermocouples and cartridge pool heaters. The test sample was located at the bottom of the pool, as shown in Fig. 2. For the boiling experiments, the

Reflux Condenser

Pool temperature T-Type Thermo Couple

Window

Pool Cartridge Heater

Test Sample & Boiling Surface

Insulation material

Thermo Couple 0 Thermo Couple 1 Thermo Couple 2 Thermo Couple 3

Conduction copper block

Aluminum Vessel Copper Block

Thermo Couple 4

Cartridge Heater (Heating Zone) 500W * 10 EA Air Insulated Wool

Aligner Disk

Aligner Bolt Cartridge Heater (Non heating zone)

Insulated Disk (Alumina) Spring Base

Z-Aligner (Support Jack)

Fig. 2. Schematic diagram of pool boiling experimental facility.

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sample was heated by conduction from the heating section, which consisted of conductive copper blocks and ten cartridge heaters, each with an individual maximum heating power of 500 W. The cartridge heaters, which had a total capacity of 5 kW, heated the copper block, and the generated thermal energy was transferred to the test sample via conduction. All parts of the heating section contained uniformly spaced mechanical springs on a supporting jack, and thus a small and uniform thermal contact resistance was guaranteed at the interface between the copper block and the test sample. When CHF was reached on the heating surface, the heated copper block was immediately lowered using the supporting jack so that direct contact with the heating surface was removed. This mechanism helped protect the test samples from thermal damage caused by the tremendous temperature increase right after CHF. 2.2. Test heater and data acquisition Fig. 3 shows a schematic diagram of the test heater used in the present work. The test heater was underneath a 10-mm-diameter cylindrical high-grade (99.999%) copper block whose sidewall was insulated by polyether ether ketone (PEEK). Heat was transferred through the copper block from the test heater by means of thermal conduction, which led to boiling of the cooling liquid on the top surface of the block. The test heater was detachable to allow investigation of the boiling surface at the end of the experiment. Holes were drilled in the side of the copper block through the PEEK insulator to install three 0.5-mm-diameter K thermocouples along the centerline at 7-mm intervals. The heating system consisted of ten cartridge heaters, a separate conductive copper block to transfer and concentrate the heat generated from the cartridge heaters, and the high-grade cylindrical copper block described above. The heat flux transferred to the test section was measured inside the high-grade copper block using the three thermocouples. Since the high-grade copper block was insulated with PEEK, which has a very small thermal conductivity of 0.1 W/m/K, the heat transfer through it could be simplified to a one-dimensional steady-state conduction heat transfer problem as follows: 0

q00 ¼ k 

DT T2  T1 0 ¼k  Dx Dx

ð7Þ

where T1 and T2 are the temperatures recorded in the conductive copper block, q00 is the measured heat flux (kW/m2), k0 is the thermal conductivity (W/m K), and Dx is the distance between the temperature-measurement points in the conduction copper block

(m). The linear relationship among the three temperature measurements in the cylindrical copper block was examined using a numerical simulation for steady-state heat conduction in the actual heater geometry using the commercial software FLUENT 6.0 (Ahn et al., 2010). The numerical simulation results confirmed that Eq. (7) provides a good heat flux estimate. The wall superheat was calculated by extrapolating the temperature T0 measured inside the test heater using the heat flux obtained in Eq. (7):

  q00 DT wall ¼ T wall  T sat ¼ T 0  0 d  T sat k

where DTwall is the wall superheat, Twall is the surface wall temperature, Tsat is the saturated temperature of the bulk fluid, and d is the distance between the point (where T0 was measured) and the surface. All temperature data were gathered by a 34970A data acquisition system (HP-Agilent) over a 300-ms duration. The wall temperature and heat flux were measured using the thermocouples, which were calibrated using a reference resistance temperature detector (RTD) sensor with a maximum measurement error of ±0.1 K. Therefore, we assumed that the measurement error of the thermocouples was ±0.1 K. The surface heat flux was calculated by Eq. (7). We applied the following equations to determine the uncertainty of the heat flux measurements (Kline and McClintock, 1953):

U q00 ¼ q00

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2 1 1 1 U Dx þ U DT þ 0 U k0 T2  T1 Dx k

U T wall ¼ T wall

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2  2 U T measure 1 q00 1 q00 Dx 1 Dx þ þ U k0 þ 0 U Dx 0 U q00 2 T wall k T wall k T wall k T wall

ð9Þ

ð10Þ

where the parameters U q00 ; U T 2 T 1 , Uk and UDx are the uncertainties of the heat flux q00 , T2  T1, k0 and Dx, respectively. All the thermocouples were calibrated using a reference resistance temperature detector sensor with a measurement accuracy of ±0.1 K certificated by the Korea Testing Laboratory. The maximum uncertainties in the heat flux measurements were 0.75% at 2000 kW/m2 and 10.2% at 100 kW/m2. 2.3. Visualization method Obtaining photographs of the boiling phenomenon was complicated by the small bubbles, water, and bubble coalescence. Large camera magnifications were required with a well-adjusted depth of field to allow both the heating surface and the tails of the bubble Boiling surface

10 mm K-Type Thermo Couple (Wall temperature)

Insulated PEEK

O-ring seal

ð8Þ

T1

Epoxy seal and insulation T2

Embedded K-Type Thermo Couple

T3

Fig. 3. Schematic of a conductive test heater (10 mm dia. copper heater).

H.S. Ahn, M.H. Kim / International Journal of Multiphase Flow 41 (2012) 1–12

coalescences to be in focus, as the commercial lens used in these tests had a long focal length. Additionally, the high-speed camera required intense lighting to capture and freeze the motion of the boiling phenomenon. A high-speed camera with a unique pre-trigger ability was used to take pictures of the CHF phenomenon. CHF could be predicted roughly through many repeated experimental trials; however, an accurate prediction of CHF was difficult to obtain. Instead, photographs were taken immediately before (CHF) or immediately after (CHF+) CHF using the pre-trigger ability of the high-speed camera. Fig. 4 shows the concept of the visualization method. Optical access was available through the two transparent polycarbonate windows, enabling photographs to be taken with the high-speed camera using reflected light from the lighting source on the opposite (back) side of the heating surface. A Redlake MotionXtra HG-100K high-speed digital camera, capable of up to 100,000 frames per second, was used to visualize the pool boiling. A 1000-W incandescent light source was used for the backlighting. Video imaging at a rate of 1000 frames per second was required. Bang et al. (2005) conducted a CHF visualization study on a strip heater under pool boiling and found evidence of a liquid layer beneath the large vapor mushroom. We used a similar technique to visualize the boiling phenomena. Fig. 4 shows the concept of the visualization and the boiling structures obtained from actual photographs. When a large dry patch of vapor was generated under the large vapor mushroom, which contained many vapor and liquid stems, the vapor layer reflected the light from the backlight. This allowed us to detect the existence of the vapor layer during vigorous boiling, as illustrated in the figure.

3. Results and discussion Haramura and Katto (1983) reported that CHF occurred when the macrolayer beneath a single mushroom dried out. They showed that the macrolayer consisted of liquid and vapor stems

5

and that its thickness (dc) was dependent upon the unstable wavelength, somewhere between dc = 0 and dc ¼ k2H . kH can be determined theoretically. They tentatively assumed a mid-value for dc, dc ¼ k4H . On a horizontal infinite flat plate, they took the most dangerous wavelength from the Rayleigh and Taylor instabilities instead of the critical wavelength to determine the interval between bubble columns. Thus, their model considered the most dangerous wavelength of intervals between bubbles columns for large scales and the critical wavelength for the macrolayer thickness for small scales. On a small horizontal plate heater, they considered the effect of liquid inflow on CHF; this liquid is supplied hydro-dynamically from the bulk flow to edge of the heater. However, they included its effect only through an empirical factor and superimposed this onto the solution.

3.1. Boiling phenomenon on a small heater A set of pool-boiling tests was performed using distilled water on a small heated copper surface to verify the test procedure and its repeatability. As shown in Fig. 5, the experimental data for pure (deionized) water showed good repeatability for nucleate boiling heat transfer and CHF, with a scatter within ±7% and ±5%, respectively. The CHF values (1504 kW/m2) were considerably higher than the predictions (1109 kW/m2) obtained from the Zuber correlation for an infinite flat surface, but close to the predictions (1540 kW/m2) obtained from the Haramura and Katto (1983) correlation, which included the effect of liquid inflow to the heater surface from the surroundings for a small horizontal disk. Accordingly, the repeatability and reproducibility of the pool boiling facility appeared sufficient to systemically investigate the CHF and the boiling phenomena. Values of the heat flux at which photographs were taken to capture the pool boiling phenomena are also indicated in Fig. 5 (points A–F). The onset of nucleate boiling on the small copper heater was near a wall superheat of 4–6 °C.

Fig. 4. The concept and boiling structures of visualization method.

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1800 1600 Haramura and Katto[13]'s prediction 2

Heat Flux (kW/m )

1400

F E

D

1200 1000 800 C

600 B

400

Test 1 Test 2 Test 3

A

200

the visualization and measurement errors. The literature reports of Gaertner and Westwater (1960, 1965), Gaertner (1963), and Kirby and Westwater (1965) that the thickness of the macrolayer is about 11–300 lm. For example, Haramura and Katto’s (1983) theoretical predictions give a macrolayer thickness of 56 lm, while Gaertner’s (1965) measurements indicate a macrolayer thickness of 120 lm. These previous results are in agreement with the present data. In addition, there is a large twinkling view in a large mushroom just before CHF as shown in Fig. 7b. It means that the macrolayer beneath a large mushroom is partially dried out at the center of the heater. However, the macrolayer is still observed beneath the large mushroom. Therefore we have a question about the macrolayer shape and formation as described in Section 3.3.

0 0

5

10

15

20

25

Twall -Tsat (K) Fig. 5. Boiling curves of test heater and visualization points; (A) 100 kW/m2, (B) 400 kW/m2, (C) 600 kW/m2, (D) 1200 kW/m2, (E) 1400 kW/m2 and (F) 1504 kW/m2 [CHF(), CHF and CHF(+)].

Fig. 6 shows the boiling phenomenon visualized on the horizontal 10-mm-diameter copper heater for pure water. The flow pattern depended on a massive vapor clot (mushroom) formed by the coalescence of bubbles with increasing heat flux. At the lowheat-flux regions of A (100 kW/m2) and B (400 kW/m2), small and single vapor bubbles were generated on the heated surface. As the bubbles grew and departed from the surface, they coalesced, creating an upward-flowing vapor stream due to their buoyancy; this is known as a vapor column. At the heat flux of C (600 kW/ m2), there were many nucleate boiling sites on the heated surface. Many small nucleate sites coalesced into a single vapor mushroom near the heated surface. In addition, many vapor stems were observed continuously beneath a single vapor mushroom during its generation and departure. As the heat flux increased to D (1200 kW/m2) and E (1400 kW/m2), the single vapor mushroom became larger. When one mushroom departed from the heated surface, a second mushroom was immediately generated with cutting off the upward-flowing vapor stream. The second mushroom was smaller than the first, but its size increased with the heat flux. Nucleate boiling still occurred entirely on the heated surface during the departure period of the mushrooms. The formation and behavior of the bubbles and mushrooms at different heat fluxes were also reported by Kumada and Sakashita (1995). Fig. 7 provides evidence of macrolayer existence in our experiment based on the visualization results. The macrolayer consisted of many vapor and liquid stems beneath a large mushroom, indicating that nucleate boiling occurred throughout it (Kumada and Sakashita, 1995). Within the macrolayer, there was a microlayer beneath the vapor stem. As described in the literature (Zhanxiong et al., 1994; Dwyer and Hsu, 1976), the main mechanism of heat transfer in the microlayer consists of direct evaporation from the superheated and thin liquid layer to the vapor stem. However, we decided to concentrate only on the macrolayer, as our visualization could not capture the microlayer, which were only a few microns thick. To estimate the effect of the hydrodynamic liquid inflow on CHF, we considered a new CHF mechanism based on the theory of Haramura and Katto (1983) without using the concept of a microlayer. Fig. 7 shows evidence of a macrolayer beneath a large single mushroom. The thickness of the macrolayer was estimated to be 230 lm through image processing which had the resolution to indicate the 10 lm per the 1 pixel; this was averaged from three measurements in each of twenty photographs. The thickness of the macrolayer had an accuracy of ±10.8%, considering

3.2. CHF visualization Fig. 8 shows photographs of nucleate boiling well before (1400 kW/m2) and just before (1504 kW/m2) CHF. At a heat flux of 1400 kW/m2, single and large mushrooms that covered the heated surface entirely were generated and then departed from the surface periodically. As previously mentioned in Section 3.1, vigorous nucleate boiling (see 30 ms at 1400 kW/m2 in Fig. 8) occurred after the first mushroom departed from the heated surface. The vapor stems in the macrolayer grew into the second mushroom during the interval after the first mushroom departed. The departure periods of the first and second vapor mushrooms were about 40–50 ms and 10–20 ms, respectively. Just before the CHF of 1504 kW/m2 was reached, a large dry patch in the mushroom was observed firstly (Nishio and Tanaka, 2004). The large dry patch at the center in the large mushroom indicated that the macrolayer beneath the large mushroom was partially dried out. The large dry patch in the mushroom is covered by a vapor film in Figs. 4 and 8, and reflected the backlight differently than the liquid did. Therefore, in the visualization, the vapor film on the dry patch in the mushroom appeared as an illuminated image of the heater surface or as a twinkling image. (Ahn et al., 2011). Even though a large dry patch was generated just before CHF, the nucleate boiling was still maintained at the edge of the heater, as shown in Fig. 8. This provides evidence that the large dry patch alone cannot trigger CHF because of the hydrodynamic liquid inflow at the edge of the heater. Fig. 9 shows photographs taken at the instant of the CHF phenomena. A dry patch in the large mushroom also can be observed in Fig. 9. In the photograph at 15 ms, the evaporation at the edge of heater started with maintaining the dry patch at the center of mushroom, and finally the vapor film was formed at the edge of the heater. As time elapsed, the vapor film penetrated into the center of the heater and finally coalesced with the dry patch. Just before CHF, the vigorous nucleate boiling at the edge of the heater immediately changed to film boiling, which is known as ‘‘dryout’’. Before CHF, the vigorous nucleate boiling at the edge of the heater maintained its own boiling regime due to the hydrodynamic liquid flow into the macrolayer from the bulk liquid. The nucleate boiling at the edge of the heater transited to the film boiling, and after the coalescence between the penetrated vapor film from the edge of the heater and the dry patch under the mushroom, finally CHF occurred. In previous literature related to the macrolayer, CHF was reported to trigger the drying out of the macrolayer on a horizontal infinite heater. However, a small finite horizontal heater has not previously been investigated. Fig. 10 shows film boiling just after CHF. The large mushroom had disappeared, and the vapor film covered the entire heater. At this point, the wall temperature of the heater increased significantly. The new findings of this study on triggering CHF for a small, horizontal heater are as follows.

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Fig. 6. Boiling phenomena on a small heater as increasing heat flux.

Fig. 7. The evidence of macrolayer during vigorous boiling: (a) the concept of macro and microlayer and (b): the evidence of macrolayer.

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Fig. 8. The photographs of 1400 kW/m2 and CHF(): just before CHF.

Fig. 9. The photographs of CHF (1504 kW/m2) trigger.

1. A large dry patch in the mushroom was immediately generated at a high heat flux that was less than CHF. CHF did not occur at this point due to the hydrodynamic liquid inflow into the macrolayer at the edge of the heater. Therefore, the nucleate boiling at the edge of the heater was maintained, despite the presence of the large dry patch at the center of the heater and in the large mushroom. 2. Large dry patches in the mushroom were frequently generated near CHF. Once a vapor film was generated by the evaporation at the edge of the heater, the vapor film started to penetrate into the center of the heater, eventually coalescing with the already generated large dry patch. CHF occurred when the vapor film covered the entire heater. The new finding of triggering CHF is that the penetrated vapor film from the edge of the heater to the center of heater was collapsed with the large dry patch at the center of heater and in the large mushroom. It was revealed by the high speed visualization; actually, its mechanism seemed to have a strong relationship with the hydrodynamic liquid inflow on the small and horizontal heater, to be different from classical CHF models of Zuber (1959), or Haramura

and Katto (1983). However, the more detailed discussion about the effect of hydrodynamic liquid inflow on the mechanism of triggering CHF would be conducted in the next section. 3.3. Discussion about the effect of the hydrodynamic liquid inflow on the mechanism of triggering CHF We re-examined representative CHF theories for infinite and horizontal heaters to determine why they are not applicable to the present study. These theories included the hydrodynamic instability CHF model of Zuber and the macrolayer dryout model of Haramura and Katto. From Taylor instability analysis (Carey, 1992) and Zuber’s model, the critical wavelength (kC) is k = 2pR, where R is the radius of the vapor column. From the mathematics of Rayleigh–Taylor, the critical wavelength can be expanded as follows:

kC ¼ 2p



r

gðql  qv Þ

1=2 ð11Þ

When an upward vapor jet disturbs a liquid column, the most dangerous wavelength with the maximum wavenumber is

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9

Fig. 10. The photographs of CHF(+): just after CHF.

 kD ¼ 2p

3r gðql  qv Þ

1=2 ð12Þ

Eq. (12) was derived from an instability analysis at the transition between film boiling and nucleate boiling. The hydrodynamic CHF model of Zuber was developed for an infinite heater. The normal wavelength during the vigorous boiling is located between the critical wavelength (kC) and the most dangerous wavelength (kD). The value of the wavelength of water representing the radius of one vapor column is always larger than the heater size (10 mm diameter) used in the present study. Therefore, Zuber’s approach cannot be applied to explain the CHF triggering mechanism in the present study. The macrolayer dryout model of Haramura and Katto focuses on the liquid sublayer (macrolayer) with a number of nucleation sites beneath the large mushroom. As previously mentioned, the key element of the macrolayer dryout model is that the thickness of macrolayer beneath the large mushroom (dc) must always be smaller than the Helmholtz unstable wavelength (kH) for the vapor columns to ensure that they are not Helmholtz unstable, as shown in Fig. 11. The equation obtained based on this assumption (Eq. (4)) is in good agreement with Zuber’s predictions and the experimental data for an infinite heater. Haramura and Katto postulated that the large mushrooms (vapor columns) formed at spacings equal to the most dangerous wavelength (kD), similar to Zuber’s model. When the macrolayer dries out completely during the hovering period1 of the large mushroom, CHF occurs. By adding the concept of a macrolayer to Zuber’s hydrodynamic CHF model, Haramura and Katto developed a macrolayer dryout CHF model for an infinite heater. Zuber’s hydrodynamic CHF model and Haramura and Katto’s upgraded macrolayer dryout CHF model both contain a number

1 The hovering period is defined by Haramura and Katto as the period of time when the massive mushroom hovers on the liquid film, mainly due to the hydrodynamic action, because the surface tension of the vapor stems is generally much weaker than the buoyancy force.

of idealized assumptions that are, at best, weakly justifiable. For example, there is no clear justification for why the radius of the vapor columns in Zuber’s model should have a constant value of kD independent of the heat flux. Furthermore, the assumption that the vapor column spacing for film boiling persists throughout the transition boiling regime is plausible but difficult to justify. Haramura and Katto postulated the existence of a thin liquid sublayer (macrolayer) adjacent to the surface that is replenished only after the large mushroom covering it departs. This feature of their model has been questioned because large vapor mushrooms in boiling systems have been visually observed as separated from the sublayer by long, larger vapor columns, suggesting that the macrolayer beneath the large mushroom could be continuously replenished. This visual evidence contradicting the postulated morphology of the system leaves serious doubts about the correctness of the CHF mechanism embodied in this model. The good agreement of the resulting correlation with data could simply be a consequence of the fact that it is dimensionally consistent with the correlation obtained from Zuber’s model (Carey, 1992). In addition, Haramura and Katto considered the effect of hydrodynamic liquid inflow on a small horizontal heater using the simple concept of an added meaningless term (k), as in Eq. (5). Because Haramura and Katto compared the experimental CHF values of only a 10-mm-diameter copper heater with the calculated values from Eq. (6) using k = 0.83, the effect of hydrodynamic liquid inflow strongly depends on having a heater size less than kD. For example, in our study, the average CHF value on a 10-mm-diameter copper heater was 1540 kW/m2, but Zuber and Haramura and Katto estimated the CHF to be 1109 kW/m2 on an infinite heater. The CHF value becomes constant with increasing heater size after a certain point, as described in the Introduction. In this study, CHF tests and visualizations were also only conducted on a 10-mm-diameter copper heater and were sufficient to justify the small horizontal heater used. However, it is impossible to verify modeling of the parameter k based on the effects of the hydrodynamic liquid inflow without additional data. Instead, we used a simple and conceptual model

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Fig. 11. Vapor column spacing in the Zuber’s (1959) hydrodynamic CHF model, Haramura and Katto’s (1983) macrolayer CHF model (Carey, 1992).

to help understand the effect of hydrodynamic liquid inflow on triggering the CHF for a small horizontal heater. We re-examined the macrodryout model of Haramura and Katto on an infinite heater to investigate the mechanism of replenishing the liquid layer. It is reasonable that the liquid layer on an infinite heater is replenished through liquid columns with opposite jets compared to the vapor columns. However, on the small heater, Haramura and Katto postulated that the liquid could be replenished from the side of the heater, which is surrounded by the bulk liquid. If there is an additional liquid supply, the CHF will increase. Katto and Kikuchi (1972) showed that the temperature of the CHF in pool boiling can be increased by artificially adding liquid to a small horizontal plate heater through a very thin tube in order to validate the effect of liquid inflow on CHF. However, it is unclear how the liquid forming the thin liquid layer penetrates between the heater surface and the large mushroom. When the liquid is replenished from the edge of a small heater, it is reasonable that the friction between the replenished liquid and the heater surface disrupts the movement of liquid into the center of the heater; instead, one expects that the liquid will be replenished at the edge of the heater rather than at the center. This suggests that the replenishing hydrodynamic liquid inflow has a smaller effect on

a larger heater. If friction plays a dominant role in liquid replenishment, we conjecture that the macrolayer beneath the large mushroom will be as shown in Fig. 12. Due to this friction, the macrolayer at the edge of the heater is thicker than it is at the center of the heater, producing a concave shape. Non-uniform macrolayer formation beneath the large mushroom has been studied by Sakashita et al. (2010). They directly measured the macrolayer thickness of water and 2-propanol/water mixtures at CHF using a conductance meter. According to their results, the radial macrolayer thickness of 2-propanol/water mixtures varied, while that of water did not. However, because their heater (12-mm-diameter copper) consisted of an extended area of stainless steel, the effective heating area was larger than a small 10-mm-diameter heater, which would affect hydrodynamic liquid inflow. Results of the Sakashita group (Ono and Sakashita, 2007) indicate that the macrolayer thickness could have a strong influence on the CHF phenomenon and value. Fig. 7 shows that even though there is a large dry patch beneath the large mushroom at the center of the heater, a macrolayer is still present at the edge of the heater. It is reasonable that the replenishing liquid moving from the edge to the center of the heater will be superheated and evaporate. The macrolayer on the small heater

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11

Fig. 12. The proposed formation of the macrolayer on the small, horizontal heater.

should form in a concave shape due to both the friction and the superheated evaporation of the macrolayer, as shown in Fig. 12. Just before the CHF phenomenon (Figs. 12b, 7b, and 8), nucleate boiling was maintained at the edge of the heater, even though a large dry patch was observed in the center of the large mushroom. As previously mentioned in Section 3.2, to trigger CHF, the vapor film at the edge of the heater must penetrate into the center of the heater and coalesce with the large dry patch that formed prior to CHF. This means that the vapor film at the edge of the heater is formed by the dryout of the thicker macrolayer, and the bulk liquid cannot replenish the liquid on the heater. This conjecture supports our new findings about the mechanism that triggers CHF. Further parametric studies of heater sizes under kD with visualization to measure the thickness of the macrolayer beneath the large mushroom are recommended to expand on the present study. Finally, we compared our proposed macrolayer findings with the hot/dry spot theory (Theofanous et al., 2002) to explain the triggering of CHF on a small heater. If the heat flux is high, hot/ dry spots develop within the bases of the bubbles growing at certain nucleation sites. The hot/dry spots can be reversible or irreversible, according to the occurrence of rewetting upon bubble departure. Rewetting of those spots is strongly related to the liquid replenishment in the macro/microlayer beneath the large mushroom. As previously mentioned, we focused on rewetting in the macrolayer without a microlayer. If there is a hydrodynamic liquid inflow at the edge of the small heater from the bulk fluid, rewetting will be effective due to the hydrodynamic liquid replenishment. This also supports the idea that liquid replenishment along the macrolayer promotes hotspot rewetting when there is hydrodynamic liquid inflow at the edge of a small heater, thus delaying CHF.

4. Conclusion and recommendation In this study, we first confirmed the behavior of the boiling regime with increasing heat flux on a small plate heater through high-speed flow visualization. Second, we established the macrolayer concept based on previous literature and provided experimental evidence of a macrolayer beneath a single mushroom of vapor stems near CHF. The thickness of the macrolayer was estimated using our visualization results. Third, a new mechanism triggering CHF was postulated that included the effect of the hydrodynamic liquid inflow found on a small horizontal heater. The hydrodynamic liquid inflow enhanced CHF compared with the predictions of Zuber and Haramura and Katto, which were based on the hydrodynamic instabilities found on an infinite heater. Based on our CHF observations, our proposed CHF mechanism

for a small horizontal heater represents the effect of the hydrodynamic liquid inflow. CHF occurs when the macrolayer at the edge of the heater dries out (i.e., becomes coated with a vapor film) and meets a large dry patch beneath the large vapor mushroom. Finally, our proposed CHF mechanism was further explained by the concave shape of the macrolayer. For future research, we recommend bottom- and side-view visualization of the synchronized boiling structure to confirm our observations and measurement of the macrolayer thickness using a conductance meter, as described by Sakashita et al. (2010). Acknowledgments This research was supported by WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (R31-30005). References Ahn, H.S., Kim, H., Jo, H.J., Kang, S.H., Chang, W.P., Kim, M.H., 2010. Experimental study of critical heat flux enhancement during force convective flow boiling of nanofluid on a short heated surface. Int. J. Multiph. Flow 36, 375–384. Ahn, H.S., Kang, S.H., Jo, H.J., Kim, H., Kim, M.H., 2011. Visualization study of the effects of nanoparticles surface deposition on convective flow boiling CHF from a short heated wall. Int. J. Multiph. Flow 37, 215–228. Bang, I.C., Chang, S.H., Baek, W.P., 2005. Visualization of a principle mechanism of critical heat flux in pool boiling. Int. J. Heat Mass Transfer 48, 5371–5385. Carey, Van P., 1992. Liquid–Vapor Phase Change Phenomenon. Taylor and Francis, pp. 246–258. Dwyer, O.E., Hsu, C.J., 1976. Evaporation of the microlayer in hemispherical bubble growth in nucleate boiling of liquid metals. Int. J. Heat Mass Transfer 19, 185– 192. Gaertner, R.F., 1963. Distribution of active sites in the nucleate boiling of liquids. Chem. Eng. Prog. Symp. Ser. 59, 52. Gaertner, R.F., 1965. Photographic study of nucleate pool boiling on a horizontal surface. J. Heat Transfer 87, 17. Gaertner, R.F., Westwater, J.W., 1960. Population of active sites in nucleate boiling heat transfer. Chem. Eng. Prog. Symp. Ser. 56, 39. Haramura, Y., Katto, Y., 1983. A new hydrodynamic model of critical heat flux, applicable widely to both pool and forced convective boiling on submerged bodies in saturated liquids. Int. J. Heat Mass Transfer 26, 389. Katto, Y., Kikuchi, M., 1972. Study of forces acting on a heated surface in nucleate boiling at high heat fluxes. Heat Transfer – Jpn., Res. 1, 34–46. Katto, Y., Yokoya, S., 1968. Principal mechanism of boiling crisis in pool boiling. Int. J. Heat Mass Transfer 11, 993. Kirby, D.B., Westwater, J.W., 1965. Bubble and vapor behavior on a heated horizontal plate during pool boiling near burnout. Chem. Eng. Prog. Symp. Ser. 61, 238. Kline, S.J., McClintock, F., 1953. Describing uncertainties in single-sample experiments. Mech. Eng.. Kumada, T., Sakashita, H., 1995. Pool boiling heat transfer – II. Thickness of liquid macrolayer formed beneath vapor masses. Int. J. Heat Mass Transfer 38, 979– 987. Kutateladze, S.S., 1950. A hydrodynamic model of the critical heat transfer in boiling liquids with free convection. Zhurn. Tekhc. Fiz. 20, 1389–1392.

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