Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow

Journal of Nuclear Science and Technology ISSN: 22-3131 (Print) 1881-1248 (Online) Journal homepage: https://www.tandfonline.com/loi/tnst2 Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow Dongjin EUH, Basar OZAR, Takashi HIBIKI, Mamoru ISHII & Chul-Hwa SONG To cite this article: Dongjin EUH, Basar OZAR, Takashi HIBIKI, Mamoru ISHII & Chul-Hwa SONG (21) Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow, Journal of Nuclear Science and Technology, 47:7, 68-617 To link to this article: https://doi.org/1.18/18811248.21.972958 Published online: 5 Jan 212. Submit your article to this journal Article views: 815 Citing articles: 18 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalinformation?journalcode=tnst2

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 47, No. 7, p. 68 617 (21) ARTICLE Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow Dongjin EUH 1, Basar OZAR 2, Takashi HIBIKI 2, Mamoru ISHII 2; and Chul-Hwa SONG 1 1 Korea Atomic Energy Research Institute, Yusung, Daejeon 35-6, Republic of Korea 2 School of Nuclear Engineering, Purdue University, 4 Central Drive, West Lafayette, Indiana 4797-217, USA (Received October 29, 29 and accepted in revised form February 23, 21) In order to measure the bubble departure frequency, a flow visualization system was set up on a vertical annulus test section with a heater rod by using a high-speed camera. In this study, we developed an efficient methodology of image processing for obtaining the bubble departure frequency data. Bubble nucleation was investigated under various thermal hydraulic conditions of water, which correspond to pressures from 167 to 346 kpa, mass fluxes from 214 to 1869 kg/m 2 s, heat fluxes from 61 to 238 kw/m 2, and subcooling degrees from 7.5 to 23.4 K. The characteristics of bubble departure frequency were analyzed with the present data. The measured data was compared with models available in existing literature and a more plausible model was proposed. KEYWORDS: bubble departure frequency, subcooled boiling, nucleation, visualization, image processing I. Introduction The capability to predict two-phase flow dynamics is essential for the safety analysis of nuclear reactor transient conditions. Recently, mechanistic studies on the two-phase dynamic phenomena have been actively performed by using an interfacial area transport equation to improve the many deficiencies resulting from using a static flow regime map in the safety analysis codes. 1) The mechanistic study using an interfacial area transport equation requires a lot of phenomenological understanding and a proper model related to the source terms concerning the particle interactions and phase changes. For the subcooled boiling problem, the bubble nucleation process acts as an important mechanism in an interfacial area transport equation in the form of a boundary condition. Since the bubble nucleation terms are essential, the results of an interfacial area transport equation strongly depend on the appropriateness of the models for the phenomena. The bubble nucleation phenomena can be predicted by mechanistically dividing them into the following three parameters: active nucleation site density, bubble departure diameter, and bubble departure frequency. All these terms are currently challenging topics for boiling flows. The bubble departure frequency can be expressed using the bubble growth time and waiting time as follows: 1 f d ¼ ; ð1þ t W þ t G Corresponding author, E-mail: ishii@purdue.edu ÓAtomic Energy Society of Japan Fig. 1 Period of a nucleation cycle where t W and t G are waiting time and growth time, respectively. The growth time is the time interval between the bubble formation and departure after growing at the nucleation site. The waiting time corresponds to the period after the bubble departure to the instant when a new bubble is nucleated at the nucleation site. Figure 1 shows the conceptual definition of each time interval. Most of the studies on the bubble departure frequency can be surveyed under the pool boiling conditions. 4 1,12,15) Concerning convective flow boiling conditions, there has been very limited research. Thorncroft et al. performed an experiment on bubble departure frequency and diameter under vertical upflow and downflow boiling in a 12.7-mm- ID square duct with one side heated by a 3-cm-long nichrome strip with FC-87 as the working fluid. 14) The test conditions were 19 666 kg/m 2 s of mass fluxes, 16 963 kw/m 2 of heat fluxes, and 1. 5. C of subcooling degrees. Basu et al. measured the waiting time, bubble growth time, and bubble departure size in an upward-vertical subcooled flow boiling facility using water as the working fluid. 2,3) The experimental data were taken under atmospheric pressure condition, at mass fluxes from 235 to 68

Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow 69 Fig. 2 Layout of the test facilities 684 kg/m 2 s, and heat fluxes changing from 16 to 963 kw/m 2. The test section was almost square for its cross section with a 16.33 cm 2 flow area. The heated surface was a 3:175 3:5 cm 2 flat copper plate with a contact angle varying from 3 to 9. The waiting time was correlated against the wall superheat, while the growth time was correlated with the bulk subcooling. Podowski et al. proposed mechanistic models for both the waiting time and growth time. 11) By using a balance of the heat transfer inside the wall and fluid near the heated wall, they derived a bubble waiting time. The bubble growth time was derived using an energy equation during the bubble growth and critical bubble size. Although their model is based on the appropriate mechanistic considerations, they did not sufficiently validate the model with experimental data. Situ et al. performed a forced convective boiling experiment in a vertical upward annular channel by using water as the testing liquid. 13) The test conditions were at atmospheric pressure, inlet temperature range from 8. 98.5 C,.5.94 m/s of the inlet velocities, and 6.7 26 kw/m 2 of heat fluxes. A high-speed digital video camera was used to capture the bubble nucleation. They intensively compared data from existing literature as well as their own data with previous models, and found that there is no effective model satisfying all the data. They developed a model with a dimensionless parameter. However, their model shows a relatively large deviation from their own data and that of existing literature. In summary, few studies have been performed for experiment and modeling of bubble departure frequency under a convective flow boiling. Although many studies concerning the pool boiling conditions are available, the mechanism of the bubble departure is significantly different from the flow boiling conditions. With respect to the bubble departure frequency acting as a key variable in a two-phase analysis model based on a mechanistic approach such as using an interfacial area transport equation, the data generation and model development are important issues for a new-generation two-phase flow analysis. The purpose of this paper is to study the bubble departure frequency in a vertical upward forced-convective subcooled boiling flow. By visualization with a high-speed camera, the experimental data was obtained with the development of an efficient data processing methodology. The generated data was compared with previous models and a new correlation was proposed. II. Experiments 1. Experimental Facilities Figure 2 shows the layout of the experimental facility for the subcooled boiling phenomena in the annulus geometry with a central single heater rod. The facility is also designed so that it is capable of performing measurements of areaaveraged and local two-phase parameters. In the primary loop, water is held at the stainless steel degassing tank with an internal volume of approximately.96 m 3. This heater, with a maximum power of 6. kw, is used to heat the water and release noncondensable gases prior to each experiment. The temperature of the liquid inside the tank is monitored by using a T-type thermocouple. The flow rate measurements are performed by using a magnetic flowmeter (Honeywell, Fort Washington, PA, U.S.A.), which is located downstream of the pump. After the magnetic flow-meter, the water flows through a preheater (Orgen Manufacturing Co., Arlington Heights, IL, U.S.A.), which has a maximum power of 18 kw. Finally, before the water enters the test section, it flows through a header, which divides the flow into four separate lines. VOL. 47, NO. 7, JULY 21

61 D. EUH et al. Fig. 3 Test section and flow visualization system The test section is composed of an injection port, five instrumentation ports, a cartridge heater (Watlow, St. Louis, MO, U.S.A.) and Pyrex Ò or stainless steel pipes. A schematic of the test section is given in Fig. 3. The flow channel is an annulus with an inner diameter of 19.1 mm and an outer diameter of 38.1 mm. Pyrex Ò pipes are used for pressures up to 35 kpa in order to enable flow visualization. The test section has a 2,845 mm heated section followed by a 1,632 mm unheated section. The heating of the water is achieved by using a cartridge heater, which also forms the inner wall of the annulus. The heater has a total length of 3,81 mm, which is composed of three major sections. The heater has a maximum power of 45 kw, which corresponds to a maximum heat flux of 264 kw/m 2. Once the flow goes through the test section, it enters the condenser (American Industrial Heat Transfer Inc, Zion, IL, U.S.A.) where the steam generated within the test section is condensed. The maximum capacity of the condenser is around 8 kw. A bypass section, which is between the exit of the pump and the bottom exit of the condenser, is considered in the system. The bypass carries between 5 1 times the flow rates that go through the test section during a normal operation. The reason for this is to maintain constant pressure boundary conditions across the test section. Thus, a constant flow rate is achieved through the test section. 2. Measurement Technique The flow visualization system is set up on a vertical annulus test section with a heater rod. A high-speed camera is mounted on the 3-D traverse system, which can move the camera.5 1. m above the inlet of the test section. The region for investigation is set near the onset of a boiling point. A KC microscope video lens was utilized with a speed Fig. 4 Sample of the image and control volume to measure the bubble departure of 5, frames per second (fps). Each image consists of 128 8 pixels. The real pixel size is 64 mm under the current configuration of the visualization system and test section. The corresponding image size is 8 4 mm 2 with the consideration of an image distortion due to the curvature of the glass tube that forms the outer wall of the test section. To measure the bubble departure frequency, two control volumes for each frame of the images were set for the nucleation site and upstream part of it, respectively. This is illustrated in Fig. 4. The control volume at the upstream of a nucleation site is used to discriminate the signals from the JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow 611 Fig. 5 Algorithm for an image processing in order to obtain the bubble departure frequency flowing bubbles among all the bubble signals at a nucleation site. The overall algorithm for image processing and obtaining bubble departure frequency data is shown in Fig. 5. First, the nucleation site is defined. Since it does not move on the images of the same test case, one can define and apply the exact coordinates for all the images that were obtained for the same test case. After defining the nucleation site, the average intensities at each predefined control volume were obtained along with the measurement time. Since a bubble is expressed as a dark region as shown in Fig. 4, the intensity of the control volume decreases to a low value from a higher one when a bubble appears at the nucleation site. The second graph on the right-hand side of Fig. 5 is the idealized trend of the intensity of the control volume of the upstream and nucleation site. In the graph, the rising signals indicate a bubble appearance at each control volume. Since the bubble signals at the nucleation site include those from the purely nucleated bubbles as well as from the bubbles entering from the upstream section for the flow boiling case, it is necessary to discriminate the nucleated bubble signals from among the whole bubble signals. In this figure, the bubble signals, shown in both intensity plots at control volumes including nucleation site and its upstream, are for the flowing bubbles. The nucleated bubble signals are expressed as peak signals between flowing bubble signals. It is convenient to define the time of departure by converting the continuous peak signals into a rectangular form as shown in the figure. The final process for the signal processing is to remove the peaks related to the flowing bubble signals at the nucleation site. Figure 6 shows the actual image and corresponding Fig. 6 Intensities at the control volumes intensity graph during a bubble nucleation. The rectangulartype line is the identified signal type identified for the nucleated bubbles after the above steps. The bubble departure frequency is obtained using the time interval of each nucleated bubble signal. Figure 7 presents a diagram in order to obtain the bubble departure frequency from the intensity plot. If there is a flowing bubble between the nucleated bubbles, the interval was omitted from the total problem time. In Fig. 7, the effective period including the calculation of the bubble departure frequency is expressed as solid line intervals. The final form of the bubble departure frequency is defined as the following formula: VOL. 47, NO. 7, JULY 21

612 D. EUH et al. Intensity 2 15 Upstream of N.S. Nucleation Site Signal Conversion Included in Problem Excluded in Problem Numbers 1 8 6 4 5 2 Fig. 7 τ i τ i+1 1 2 3 4 5 6 Time (ms) Plot of typical intensity and signal conversion Table 1 5 1 15 2 25 Time Interval Between Nucleating Bubbles (ms) Fig. 8 A typical distribution of time interval between bubble nucleation Test matrix Present study (Pressure 1) Present study (Pressure 2) Situ et al. Basu et al. (28) 13) (23, 25) 2,3) Fluid Water Water Water Water Flow channel geometry Annulus Annulus Annulus Square No. of points 36 4 58 11 Pressure, kpa 167 214 328 346 13 13 G, kg/m 2 s 221 1465 214 1869 466 9 235 684 Re number 1.75e4 1.23e6 2.2e4 1.78e6 3.2e4 6.1e4 2.9e4 8.5e4 Subcooling, K 7.9 16.7 7.5 23.4 8 98.5 (Inlet temperature) 7.7 46.7 Heat flux, kw/m 2 61.3 237.9 79.3 238 6.7 26 16 963 Comments Definite pressure effect f d ¼ X X i i i : Figure 8 shows a typical distribution of time interval between each nucleated bubble at the same nucleation site. From the time distribution and Eq. (2), the standard deviation and uncertainty with 95% confidence level for the bubble departure frequency can be obtained as follows: 2 ð2þ f d ¼ 1 ; ð3þ ðf d Þ 95% ¼ r tf ffiffiffiffiffiffiffi X : ð4þ III. Results and Discussion i 1. Test Matrix The visualization was performed at three different nucleation sites under various thermal hydraulic boundary conditions for each site. One second of data with 5, fps speed was utilized based on the camera s capabilities. Since the pressure effect on the bubble departure frequency is found to be significant for investigation, the pressure was set as one of the major boundary conditions. The experimental test range is summarized in Table 1 with a comparison of those shown in the literature. The present experimental data have a wider range with respect to the mass flux as well as the pressure conditions. 2. Data Analysis The data shows a definite trend such that the bubble departure frequency is increasing as the pressure and heat flux are increased; meanwhile, it is decreasing as the mass flux and subcooling are increasing. To investigate the effect of the variables more clearly, a parametric study was performed. Figures 9(a) and 9(b) show the bubble departure frequency data according to the heat flux for 18 and 33 kpa, respectively. The increasing trend of bubble departure frequency as the heat flux increases is well presented under both pressure conditions. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow 613 5 4 3 2 1 8 6 4 2 ~13K v f ~.5m/s P~175kPa ~11K v f ~.5m/s P~175kPa ~11K v f ~1.m/s P~185kPa 5 1 15 2 25 Heat Flux (kw/m 2 ) Figures 1(a) and 1(b) show the effect of the subcooling on the bubble departure frequency under the two pressure conditions, respectively. Under 18 kpa condition, the reducing trend as a result of increased subcooling is shown at a liquid velocity of.5 m/s. However, for a liquid velocity of 1. m/s, the effect of subcooling on the bubble departure frequency is not definite. Under 33 kpa condition, the subcooling effect is definite at.5 m/s; in the meantime, it is not sensitive at a liquid velocity of.24 m/s. Therefore, the effect of the subcooling degree is not clear for all thermal hydraulic conditions. Figure 11 shows that the bubble departure frequency is reduced as liquid flow is increased. The definite effect of liquid velocity indicated that the pool boiling model is hard to apply to the convective flow boiling conditions. The present data have two pressure conditions, which are unique features when compared with the data available in the literature. The pressure effect on the bubble departure frequency under similar subcooling, heat flux, and liquid velocity conditions is clearly shown in Fig. 12. The results show a very definite pressure effect such that the bubble nucleation becomes more active under higher pressure conditions. The effect of the four parameters on the bubble departure frequency can be explained on the basis of the mechanistic (a) ~14.5K v f ~.5m/s P~33kPa ~23K v f ~.24m/s P~33kPa ~18K v f ~.24m/s P~33kPa 6 8 1 12 14 16 18 2 Heat Flux (kw/m 2 ) (b) Fig. 9 Heat flux effect on bubble departure frequency (a) Trend for lower pressure conditions (b) Trend for elevated pressure conditions 6 4 2 5 q"=79.3kw/m 2 v f ~.5m/s P~175kPa q"=15.7kw/m 2 v f ~.5m/s P~175kPa q"=149.1kw/m 2 v f ~1.m/s P~185kPa q"=196.9kw/m 2 v f ~1.m/s P~185kPa 6 8 1 12 14 Subcooling (K) study on the bubble nucleation mechanism. As Podowski et al. considered, the bubble nucleation is closely related to the periodic wall temperature variation. 11) If a bubble is nucleated, the wall superheat temporarily contributes to the vaporization of a liquid film between a heated wall and vapor. During the process, the wall temperature is reduced to the saturation temperature. After the nucleated bubble grows and departs from the nucleation site, the wall temperature starts to increase since a single-phase convective heat transfer is insufficient to transfer the supplied heat from a wall inside. When the wall temperature reaches a required (a) q"=15.7kw/m 2 v f ~.5m/s P~33kPa q"=15.7kw/m 2 v f ~.24m/s P~33kPa q"=79.3kw/m 2 v f ~.24m/s P~33kPa 8 1 12 14 16 18 2 22 24 Subcooling (K) Fig. 1 Subcooling effect on bubble departure frequency (a) Trend for lower pressure conditions (b) Trend for elevated pressure conditions Fig. 11 8 6 4 2 (b) ~12K, q"=145.7kw/m 2, P~18kPa ~15K, q"=15.7kw/m 2, P~33kPa ~18K, q"=15.7kw/m 2, P~33kPa..2.4.6.8 1. 1.2 Velocity (m/s) Liquid velocity effect on bubble departure frequency VOL. 47, NO. 7, JULY 21

614 D. EUH et al. Fig. 12 8 6 4 2 ~12K, q"=15.7kw/m 2, v f ~.5m/s ~11K, q"=15.7kw/m 2, v f ~.5m/s ~14.5K, q"=15.7kw/m 2, v f ~.5m/s ~8K, q"=15.7kw/m 2, v f ~.5m/s 15 2 25 3 35 Pressure (kpa) Pressure effect on bubble departure frequency superheat to initiate nucleation, a bubble nucleates and the wall temperature is reduced again. Therefore, a periodic temperature variation of the wall surface is expected during a nucleation process. The rate of the wall temperature increase and the highest allowable wall temperature are the key variables for characterizing the bubble waiting time. In the meantime, the parameters that affect the bubble growth time are the bubble size and heat transfer rate. Heat flux acts as a driving force for the increase in wall surface temperature during a waiting period. Although the average heat flux is balanced by a single-phase heat transfer, evaporating heat transfer, and pumping works, a periodic unbalance can be considered during a cycle of a nucleation. Since just a single-phase heat transfer is active during a waiting period, the wall heat transfer is unbalanced by the amount related to the boiling heat transfer. As the applied heat flux is increased, the unbalance of the heat transfer at the wall surface becomes larger during a single-phase heat transfer process of a waiting time period. Therefore, the speed of the temperature increase would be proportional to the applied heat flux, which results in a higher bubble departure frequency. The pressure effect shown in the present bubble departure frequency data can be considered as two parts: bubble waiting time and bubble growth time. For the bubble waiting time, the effect can be explained on the basis of the required wall superheat for nucleation. The initial formation of vapor is related to an unstable equilibrium state started from the equation defining the mechanical equilibrium of a spherical vapor nucleus in a liquid at constant temperature T g and pressure p f as follows: p g p f ¼ 2 ; ð5þ r c where r c is cavity radius. The pressure and temperature near the saturation state are related by the Clausius-Clapeyron equation: dp dt ¼ i fg : ð6þ Tv fg By using the above two equations and ideal gas law, the wall superheat requirement to initiate nucleate boiling could be simply expressed: T sat ¼ T w T sat ¼ 2T sat : ð7þ r c g i fg The density of the vapor is increased as pressure is increased. Although the saturation temperature and latent heat are also varied according to the pressure change, the effect of density variation is dominant compared with those factors. According to Eq. (7), the increased vapor density at the elevated pressure condition induces a reduced required wall superheat. The waiting time for bubble nucleation would be shorter due to the reduced required wall superheat under other similar thermal hydraulic conditions. The pressure effect on the bubble growth time is reflected by the bubble s departure size. According to the force balance developed by Situ et al. 13) and Klausner et al., 16) the forces acting on a departing bubble from the nucleation site are surface tension, unsteady drag, quasi-steady force, and buoyancy force. Among them, unsteady drag, named as bubble growth force, is drastically reduced as the pressure increases due to an increased steam density. The following equation is a form of unsteady drag force developed by Situ et al., 13) where F duy ¼ C 2 f fja 4 e sin i; Ja e fc pf ðt w T s Þ S; g i fg C: constant, and i : contact angle: To achieve a balance of the forces, buoyancy and quasisteady forces should also be reduced, which induces a small bubble departure size. The reduced bubble departure size results in a shorter bubble growth time since the departure bubble size is a boundary condition of the energy equation related to the bubble growth. Therefore, an increased pressure induces a shorter bubble waiting time and also bubble growth time, which results in a high bubble departure frequency. The subcooling degree is related to the lower wall surface temperature during a nucleation process. Since it can be expected that a large subcooling induces a lower wall surface temperature after a bubble departure, the duration for the wall temperature to recover to the required wall surface temperature would be longer, which results in a lower bubble departure frequency. For convective flow boiling, a temperature gradient is formed near a heated wall. The thickness of the thermal boundary layer is inversely proportional to the magnitude of the velocity. Under higher liquid velocity condition, the temperature gradient is steeper within a thin thermal boundary layer. When a bubble departs from a nucleation site, the surrounding liquid that has a lower temperature outside the thin thermal boundary layer would directly be in contact with the heated wall and thereby reduce the wall temperature. Under higher liquid velocity conditions, the wall temperature reduction becomes more significant, which results in a longer period for the wall temperature to recover to the required superheat for successive nucleation. The mechanism can explain the reciprocal relationship of bubble de- ð8þ JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow 615 Fig. 13 1 P=~.2MPa P=~.33MPa 1 5 1 15 2 25 Ja w Dependency of Ja w on bubble departure frequency Model : N fd =1.7N qnb.634 Fig. 15 1 4 P= ~.2MPa 1 3 1 2 1 1 1 1-1 +1% -1% P= ~.33MPa 1-2 1-2 1-1 1 1 1 1 2 1 3 1 4 Exp : N fd =f d D 2 d /α f Comparison of current data and Situ et al. 13) model Model for Fig. 14 1 3 P=~.2MPa 1 2 1 1 1 P=~.33MPa +1% -1% 1 1 1 1 2 1 3 Exp. Data for Comparison of current data and Basu et al. 3) model parture frequency to the liquid velocity, which is shown in Fig. 11. Therefore, the effects of four major parameters on the bubble departure frequency that is shown in the present experimental data can be explained by analyzing the mechanisms of bubble nucleation. In the following section, the models that are available in existing literature are analyzed by using the present experimental data and a new correlation is proposed based on the analysis. 3. Data Comparison with Existing Models This study shows the data in the form of comparisons with the models that are available in existing literature and developed under the convective flow boiling conditions. Figure 13 shows a trend of the data according to the dimensionless parameter, Ja w, which is considered as an important parameter in many studies and is defined as Ja w fc pf ðt w T s Þ : ð9þ g i fg Since the wall temperature was not measured, it was calculated with a modified Chen correlation, which extends its applicability to the subcooled boiling conditions. Although the results show an increasing trend according to an increase in Ja w, the degree of the data scatter is large. Model for f d (1/s) Model for f d (1/s) 1 4 Present Data P=~.2MPa 1 3 1 2 1 1 +1% -1% 1 1 1 1 1 2 1 3 1 4 Exp. Data for f d (1/s) 1 3 1 2 1 1 Present Data P=~.33MPa +1% -1% Furthermore, the data for different pressure conditions form a separate group. It means that Ja w is not a unique parameter for characterizing the bubble departure frequency. Figures 14 to 16 show the trends of the models in existing literature. In this study, the models of Basu et al., 3) Situ et al., 13) and Podowski et al. 11) were validated with the current data. The Basu et al. model was developed with two Ja numbers based on the wall temperature and liquid (a) 1 1 1 1 1 2 1 3 Exp. Data for f d (1/s) Fig. 16 Comparison of current data and Podowski et al. 11) model (a) For lower pressure conditions (b) For elevated pressure conditions (b) VOL. 47, NO. 7, JULY 21

616 D. EUH et al. Model : N fd =1.6N qnb 1.3 1 4 1 3 Present Data P=~.2MPa 1 2 1 1 1 1-1 +1% 1-2 -1% 1-3 Present Data P=~.33MPa 1-3 1-2 1-1 1 1 1 1 2 1 3 1 4 Exp : N fd =f d D 2 d /α f Model : N fd =1.6N qnb 1.3 1 6 1 5 1 4 1 3 1 2 1 1 1 1-1 1-2 1-3 Present Data P=~.2MPa +1% -1% Basu's Data Situ's Data Present Data P=~.33MPa 1-3 1-2 1-1 1 1 1 1 2 1 3 1 4 1 5 1 6 Exp : N fd =f d D 2 d /α f Fig. 17 Comparison of current data and proposed correlation Fig. 18 Comparison of proposed correlation and data of current study and literatures temperature, respectively. 3) Since Ja w is not a unique parameter as discussed above, the model underestimates the data. Under higher pressure conditions, the degree of underestimation is more significant, as shown in Fig. 14. Figure 15 shows that the Situ et al. 13) model also has a large discrepancy with the current data. However, the comparison shows a considerably reduced scattering degree. Therefore, the model approach can correlate the current data with modified experimental constants. Figure 16 shows separately the evaluation results for the Podowski et al. 11) model for around the 2 and 33 kpa pressure conditions. Although it shows results that underestimate the data under the 33 kpa condition, the data under the 2 kpa condition are scattered within a relatively similar band of the model prediction values. Considering that the Podowski et al. 11) model is based on a mechanistic approach, this model could be a good reference for model development. 4. Improvement of Existing Model Although all the literature models do not predict the current data well, the Situ et al. 13) model shows a small scattering degree for the present experimental data. Therefore, a modified Situ et al. 13) model with constants different from the original ones is proposed in this study, f d D 2 d ¼ 1:6NqNB 1:3 ; ð1þ l where N qnb q qnb D d : ð11þ f g i fg The results of the comparison with the proposed correlation are shown in Fig. 17. The model predicts the current data well within a 76% deviation. In order to examine the applicability of the proposed correlation, Situ et al. s 13) and Basu et al. s 3) data were also assessed. As shown in Fig. 18, the proposed correlation also agrees well with Situ et al. s 13) data, whereas it overestimates Basu et al. s 3) data. It is remarkable that the test geometry of Situ et al. s 13) data is similar to the current ones, and Basu et al. s 3) data covers a higher heat flux under mass flux conditions lower than the current ones. Therefore, the proposed correlation has a limit when applied to a wide range of thermal hydraulic conditions, especially the higher heat flux conditions. IV. Conclusions A visualization test was performed under subcooled boiling conditions in an annulus with a central heater rod in order to investigate the bubble departure frequency. The test conditions were set under various thermal hydraulic conditions in order to investigate the effects of several parameters that affect the nucleation phenomena. The mass flux, heat flux, subcooling, and pressure were the major parameters controlling the bubble departure frequency. The parametric investigation shows a definite trend that the bubble departure frequency is increasing with the heat flux and pressure; meanwhile, it is decreasing with the mass flux and subcooling degree. Among these, it is remarkable that a significant dependence of the bubble departure frequency on the pressure was shown. In this study, we developed an efficient methodology to obtain bubble departure frequency data by using a variation of the intensity at a predefined control volume, including the nucleation site in each of the highspeed images as time passes. The data were compared with the literature models for the convective flow boiling conditions. All the referred models do not entirely agree with the present experimental data. Among the models, the Situ et al. 13) model shows a lower scattering degree in the comparison plot, although it also shows a large discrepancy with the current data. In this study, a new correlation was proposed based on Situ et al. s 13) dimensionless parameter with different experimental constants. The proposed correlation predicts Situ et al. s 13) data as well as data from this research. However, it overestimates Basu et al. s 3) data. Since Basu et al. s 3) data corresponds to lower mass flux and higher heat flux conditions when compared with the current and Situ et al. s 13) data, an intensive modeling effort for these regions should be performed in the future. Meanwhile, although the Podowski et al. 11) model does not predict the current data well, it can also be a good reference point in the sense that it is based on a mechanistic approach. It is remarkable that the Podowski et al. 11) model predicts the lower pressure conditions of the current data well. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow 617 Since there is currently no universal model to predict the bubble departure frequency, it is necessary to develop a new model that is applicable to an interfacial area transport equation as a key constitutive relation for a wall nucleation. The current data that were generated in this study could be utilized as a good database for the development of a future model. Nomenclature C p : specific heat at constant pressure D d : bubble departure diameter f d : bubble departure frequency i fg : heat of vaporization (latent heat) Ja e : effective Jacob number Ja sub : Jacob number of liquid subcooling Ja w : Jacob number of wall superheat N qnb : dimensionless nucleate boiling heat flux p: pressure q qnb: nucleate boiling heat flux r c : cavity radius S: suppression factor t: Student-t T: temperature t G : growth time t W : waiting time v fg : difference in liquid and steam specific volumes Greek symbols : thermal diffusivity i : inclination angle : density : surface tension : time interval between bubble nucleation Subscripts f: liquid phase g: vapor phase s, sat: saturation w: wall Acknowledgements One of the coauthors, D. J. Euh was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) and would like to thank the School of Nuclear Engineering, Purdue University. This work was sponsored by the United States Nuclear Regulatory Commission (USNRC) under contract no. NRC 4-7-94. The authors would like to extend their appreciation to the USNRC staff for their support. References 1) M. Ishii, S. Kim, J. Kelly, Development of interfacial area transport equation, Nucl. Eng. Technol., 37, 6 (25). 2) N. Basu, Modeling and Experiments for Wall Heat Flux Partitioning during Subcooled Flow Boiling of Water at Low Pressures, Ph.D. Thesis, University of California, Los Angeles, USA (23). 3) N. Basu, G. R. Warrier, V. K. Dhir, Wall heat flux partitioning during subcooled flow boiling: Part 1 model development, J. Heat Transfer, 127, 131 139 (25). 4) R. Cole, A photographic study of pool boiling in the region of the critical heat flux, AIChE J., 6, 533 542 (196). 5) C. Y. Han, P. Griffith, The mechanism of heat transfer in nuclear pool boiling Part I. bubble initiation, growth and departure, Int. J. Heat Mass Transfer, 8, 887 94 (1965). 6) A. P. Hatton, I. S. Hall, Photographic study of boiling on prepared surfaces, Proc. Third Int. Heat Transfer Conf., Chicago, Illinois, USA, Aug. 7 12, 1966, Vol. 4, 24 37 (1966). 7) H. J. Ivey, Relationship between bubble frequency, departure diameter and rise velocity in nucleate boiling, Int. J. Heat Mass Transfer, 1, 123 14 (1967). 8) M. Jakob, Heat Transfer, Vol. 1, Wiley, New York, Chapter 29 (1949). 9) I. G. Malenkov, Detachment frequency as a function of size of vapor bubbles, J. Eng. Phys., 2, 74 78 (1971). 1) B. B. Mikic, W. M. Rohsenow, A new correlation of poolboiling data including the effect of heating surface characteristics, J. Heat Transfer, 91, 245 25 (1969). 11) R. M. Podowski, D. A. Drew, R. T. Lahey, Jr., M. Z. Podowski, A mechanistic model of the ebullition cycle in forced convection subcooled boiling, Proc. Eight Int. Top. Mtg. on Nuclear Reactor Thermal-Hydraulics, Vol. 3, 1535 1542 (1997). 12) M. Shoukri, R. L. Judd, A theoretical model for the bubble frequency in nucleate pool boiling including surface effects, Proc. Sixth Int. Heat Transfer Conf., Toronto, Aug. (1978). 13) R. Situ, M. Ishii, T. Hibiki, J. Y. Tu, G. H. Yeoh, M. Morid, Bubble departure frequency in forced convective subcooled boiling flow, Int. J. Heat Mass Transfer, 51, 6268 6282 (28). 14) G. E. Thorncroft, J. F. Klausner, R. Mei, An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling, Int. J. Heat Mass Transfer, 41, 3857 3871 (1998). 15) N. Zuber, Nucleate boiling. The region of isolated bubbles and the similarity with natural convection, Int. J. Heat Mass Transfer, 6, 53 78 (1963). 16) J. F. Klausner, R. Mei, D. M. Bernhard, L. Z. Zeng, Vapor bubble departure in forced convection boiling, Int. J. Heat Mass Transfer, 36, 651 662 (1993). VOL. 47, NO. 7, JULY 21