Experimental research of bubble number density and bubble size in narrow rectangular channel under rolling motion

Nuclear Engineering and Design 268 (2014) 41–50

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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Experimental research of bubble number density and bubble size in narrow rectangular channel under rolling motion Shaodan Li 1 , Sichao Tan ∗ , Puzhen Gao 1 , Chao Xu 1 Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Heilongjiang 150001, PR China

h i g h l i g h t s • • • •

Bubble number density and bubble size under rolling motion are studied. Automatic processing algorithm dealing with bubble parameters is proposed. The fluctuation amplitude is mainly affected by rolling amplitude. Variation of the effective wall superheat is the main reason for the fluctuation.

a r t i c l e

i n f o

Article history: Received 27 August 2013 Received in revised form 17 November 2013 Accepted 22 November 2013 Keywords: Rolling motion Bubble size Bubble number density Narrow rectangular channel Ocean condition

a b s t r a c t Bubble number density and bubble size are two important parameters in the research of subcooled flow boiling and the channel power of water-cooled nuclear reactor are greatly affected by the two parameters through the neutron feedback caused by the variation of local void fraction. By using the high speed camera in combination with the digital image processing technology, the bubble number density and bubble mean diameter in an up-flow narrow rectangular channel under rolling motion are experimentally researched. Experimental results indicate that the bubble number density and the bubble mean diameter under rolling motion periodically fluctuated with the same period as that of the rolling motion. The camera captured bubbles consisted of sliding bubbles coming from the upstream flow and nucleation bubbles emerging in the scope of the observing window. Variations of the bubble mean diameters under rolling motion are analyzed by the distribution of the bubble diameters. Both the diameters of sliding bubbles and nucleation bubbles periodically changed under the effect of the rolling motion, and the two kinds of bubble share the same variation trend. The fluctuation amplitude of the bubble number density and the bubble mean diameter is determined by the rolling period and amplitude. The fluctuation amplitudes of the above two parameters are intensified by the rolling amplitude, whereas the effect of the rolling period is weak. At the same time, local pressure, wall temperature and local fluid velocity oscillated periodically in the rolling motion. Effect of the fluid velocity oscillation can be neglected due to its tiny fluctuation amplitude in this research. Variation of the effective wall superheat induced by the change of wall temperature and local pressure is the main reason accounting for the fluctuation of bubble parameters under rolling motion. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved.

1. Introduction Nuclear propulsion may be a worth considering option for bigger, high-speed and long period of working time commercial vessels (Khlopkin and Zotov, 1997; Vergara and McKesson, 2002).

∗ Corresponding author. Tel.: +86 451 82569655; fax: +86 451 82569655. E-mail addresses: [email protected] (S. Li), [email protected] (S. Tan). 1 Tel.: +86 451 82569655; fax: +86 451 82569655.

The safety and thermal hydraulic characteristics of reactor, as well as other boiling heat transfer equipment such as evaporator, on the nuclear vessel will be changed inevitably under the effect of ocean condition. Bubble number density and bubble mean diameter are two of the basic parameters in the study of subcooled flow boiling and determining the distribution of void fraction and interfacial area concentration. Interfacial area concentration is the key parameter in the construction of interfacial area transport equation of the two-fluid model (Ishii and Hibiki, 2005). In addition, the variation of the void fraction is not only related to the cooling capacity of

0029-5493/$ – see front matter. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.11.084

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Nomenclature A Af B C D Da De Di Dr G h Kp n N P q t T0 Tsat Tw

fitting parameter observing window area (cm2 ) fitting parameter fitting parameter bubble diameter (mm) bubble mean diameter (mm) bubble equivalent diameter (mm) pixel value of the diameter (pixel) Dx or Dy (mm) mass flux (kg/m2 s) channel height (mm) calibration of the image (␮m/pixel) bubble number density (cm−2 ) total number of the bubble pressure (kPa) heat flux (kW/m2 ) time (s) rolling period (s) saturation temperature (◦ C) wall temperature (◦ C)

Greek letters fluctuation amplitude of Da (mm) D n fluctuation amplitude of n (cm−2 ) inlet subcooling (◦ C) Tsub Tw,eff effective wall superheat (◦ C)  rolling angle (◦ ) m rolling amplitude (◦ ) Subscript effective eff i number of the bubble sat saturation subcooling sub x x direction y y direction

nuclear reactor but also affecting the reactivity of the reactor core (Jitka and Wallenius, 2011). Numerous theoretical and visible experimental researches have been conducted to study the bubble behaviors such as bubble nucleation (Hsu, 1962; Hibiki and Ishii, 2003), bubble growth (Zuber, 1961; Gerardi et al., 2010), bubble departure and lift-off (Situ et al., 2008; Wu et al., 2008; Cho et al., 2011) and bubble sliding (Donnelly et al., 2009; Li et al., 2013) in static condition with varied system pressure, subcooling and heat flux. Furthermore, flow boiling in narrow channel has been studied in recently years and it has been found that the two-phase flow regimes and the associated heat transfer differ significantly from those in conventional channels as the channel size is smaller than certain critical value (Kandlikar, 2004; Vlasie et al., 2004). However, the successful prediction of nucleate boiling has not yet been achieved due to the complex properties of flow boiling (Dhir, 2006). The flow and heat transfer characteristics of coolant under ocean conditions has been studied by many researchers before the research of bubble behavior under ocean conditions, including natural and forced circulation (Ishida et al., 1990; Murata et al., 2002; Pendyala et al., 2008). The flow rate and pressure drop in a vertical tube under heaving motion has been experimentally researched by Pendyala et al. (2008). The results indicated that the induced flow fluctuation is dependent on Reynolds number and stronger fluctuations can be found at lower Reynolds number. Tan et al.

(Si-Chao et al., 2009a,b) performed experiments to study the flow and heat transfer properties of natural circulation under rolling motion condition. The experimental results showed that the flow rate fluctuation of the single-phase natural circulation can be easily induced by the additional inertia force caused by rolling motion. The heat transfer performance of the channel is enhanced and the heat transfer coefficient increases with increasing the rolling amplitude and frequency. Besides, the flow resistance coefficient under rolling motion is larger than that in the non-rolling cases and the increase of rolling amplitude and frequency also leads to an increase of flow resistance coefficient. Xing et al. (2012, 2013) experimentally and theoretically investigated the rolling motion effects on single-phase flow with different pressure heads. They found that the fluctuation amplitude of the flow rate decreases rapidly as the increase of the pressure head and the fluctuation may vanish with extreme higher pressure head, namely the fluid flow is unaffected by rolling motion. In addition, they mentioned that the variation of rolling amplitude has more influence than that of rolling period on the amplitude of the flow oscillation under rolling motion. Bubble departure behavior in subcooled flow boiling channel under the effect of rolling motion has been theoretically researched by Qin and Gao (2008). Bubble departure under rolling motion was modeled based on the force balance combined with the effects of rolling motion. The results indicated that the bubble departure diameter under rolling motion, with the assumption that the flow rate is invariable, is almost identical to that under the static condition. While great affections may be arose by rolling motion only if the intensity of the induced flow rate fluctuation is strong enough, this may present in some natural circulation system. Similar method has been adopted by Hong et al. (2011) to analyze the bubble departure characteristics under heaving condition. By comparing the forces acted upon the bubble under different conditions, it came to a conclusion that the influence of heaving motion depends on the flow rate fluctuation for natural circulation and on the weight of buoyancy among the various bubble forces for forced circulation. A series of experimental and theoretical studies relating to bubble behaviors under heaving condition have been done by Hong et al. (2012a,b) subsequently. The experimental results shown that the fluctuation of bubble size, bubble velocity and bubble number density increases with the increase of heaving frequency. Bubble departure diameter was found to be influenced by additional heaving acceleration and the variation of flow rate caused by heaving motion. Moreover, a bubble departure model was proposed for the calculation of the bubble departure diameter under heaving motion by considering the additional acceleration and flow rate fluctuation. From the above results we can see that the most important effect of ocean conditions on bubble departure can be came down to the influence of flow rate fluctuation. However, if a time-independent flow rate under rolling condition is presented, whether the influences on bubble still exists needs further research. The above literature review indicates that the bubble behavior in subcooled flow boiling channel under static condition has been studied extensively and some works also has been done in the field of bubble behavior under ocean condition. However, most of the researches are confined to single bubble behavior and static condition. The study of bubble group characteristics such as bubble number density and bubble mean diameter in a narrow channel under rolling condition are absent at present. The aim of this study is to fill this gap considering the important role of bubble number density and bubble mean diameter in determining the flow and heat transfer performance of boiling channel. The characteristic of bubble number density and bubble mean diameter in a narrow rectangular channel under rolling condition is experimentally studied by adopting the high speed visualization technique and digital

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Fig. 1. Schematic diagram of the experimental setup.

image processing method. And the effects of rolling motion on these two parameters are also analyzed. 2. Experimental apparatus 2.1. Experimental loop and test section The schematic diagram of the experimental setup is shown in Fig. 1, which is composed of a main circulation loop and a cooling loop. The main circulation loop consisted of a test section, a centrifugal pump, a condenser, a pre-heater, a pressurizer, a flow meter and a storage tank. The centrifugal pump forced the distilled water to circulate through the experimental loop. The mass flow rate of the system was adjusted by a ball valve. Based on the characteristic of centrifugal pump, a lower flow rate corresponds to a higher pressure head. After passed through the flow meter, the distilled water entered an electrical heating preheater. A volumetric flow meter (OPTIFLUX4300) was chosen here to eliminate the effects of rolling motion on the measure of the flow rate and the measurement error was ±0.002 m3 /h. The fluid was preheated to an arranged temperature firstly in the preheater, and then pumped into the test section directly for subcooled flow boiling experiment. The degassing process was conducted through boiling the water in the preheater into saturation state, and the non-condensable gas was removed from the tube which connected the outlet of test section vents to atmosphere. The fluid which flew out of the test section was liquid–vapor two-phase flow, thus the fluid was condensed by a shell-tube condenser before entered the centrifugal pump. The system pressure of the experimental loop was maintained and adjusted by a pressurizer through changing the pressure of the upper nitrogen gas space. The storage tank provided the distilled water for the loop and the water was boiled in the tank at least two hours before injected into the loop in order to accomplish the primary degassing process. Then the non-condensable gas was removed by the preheater as mentioned before. In addition, the cooling loop provided cooling water (with room temperature) for the condenser. A narrow rectangular test section with a single-side heated surface which can be observed form both front and side was used in this experiment, as shown in Fig. 2. The flow channel of the test section consisted of a stainless steel plate and a quartz glass

with an etched groove of 2 mm in height and 40 mm in width on the surface, thereby constituting the vertical narrow rectangular channel of 550 mm in length and with a cross-sectional area of 2 mm × 40 mm. The stainless steel plate served as the heating source of the test section and its surface was polished by #3000 sandpaper. For the purpose of eliminating the heat losses to the environment, the test section was covered by thermal insulation materials. A wide range of heat fluxes was supplied to the rectangular channel with a DC power though two copper electrodes welding on the heater plate. The heated surface temperature was detected by ten N type shielded thermocouples with 1 mm outer diameter which were embedded in the outer surface of the heater plate. The fluid temperature was measured at the inlet and outlet of the test section with two N type shielded thermocouples with 1.5 mm outer diameter. All of the thermocouples were calibrated by a standard mercury thermometers prior to installation and have an accuracy of ±0.5 ◦ C after calibration. The heat flux of the channel was measured by the ratio of the heat power (obtained through the product of the voltage and current across the heater plate) and the area of active heating surface. The voltage was measured by a voltmeter with the precision of ±0.015 V and the current was measured using a hook-on galvanometer with the precision of ±4 A. The outlet and inlet pressure of the test section was measured by two pressure transducers and both of the corresponding measurement accuracy was ±7.8 kPa. 2.2. High speed visualization system The high speed visualization system in this experiment included high speed digital camera, camera lens, fiber light and personal computer with Gigabit Ethernet, as shown in Fig. 2. The maximum frame rate of the FASTCAM SA5 high speed camera was 1 Megaframes per second (Mfps) and the frame rate was set as 5000 fps in this work. A Sigma 105 mm 1:2.8 lens was mounted in front of the camera in order to get enough magnification. The camera and two power-adjustable fiber lights (0–150 W) were placed on a 2-D traverse rail parallel on the test section in order to move horizontally and vertically. The resolution of the obtained image was set as 512 × 360 pixels and the corresponding viewing area was about 7.5 mm × 10.5 mm. The captured bubble video was firstly stored at

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Fig. 2. Configuration of the test channel and visualization system.

the internal memory of the camera and then transferred into the hard disk of the computer for further analysis. Bubble images were obtained from the front view of the narrow rectangular channel for the purpose of studying the variation of bubble number density and bubble size under the effects of rolling motion. 2.3. Rolling platform Most of the equipment in main circulation loop described in the previous sections were fixed on a rolling platform to simulate the rolling motion of ocean condition. The rolling platform was driven by two fluid drive shaft which could perform reciprocating motion. The control signal from the computer determined the movement of the rolling platform through an electromagnetic regulating valve. Fig. 3 shows the configuration of the rolling platform as well as the location of the test section. The angle between the rolling platform and the horizontal plane was measured by an angular transducer located at the axis of the platform. The rolling motion of ship was approximated by sinusoidal motion, thus the angle variation of the rolling platform with time can be denoted as the following expression (t) = −m sin

 2  T0

t

(1)

where  m is the rolling amplitude, namely the maximum angle of the rolling platform can be reached, and T0 is the rolling period. The time-dependent angle of the rolling platform and the relation between the rolling angle of the platform and the inclination of the heating surface are shown in Fig. 4. The rolling amplitude and period of the rolling platform were adjusted by the control signal produced by a computer. Three rolling periods of 8 s, 12 s and 16 s and two rolling amplitudes of 10◦ and 15◦ were included in this experiment. The ranges of the parameters chosen above for the rolling platform are in accordance with the practical operation condition of ships while sailing in the ocean. 3. Image data processing Auto-processing of the high speed image obtained from the experiments was necessary for the reason that some of the statistical bubble information such as bubble number density and bubble mean diameter were involved in this study. A series of preprocessing process was needed before the identification of bubble in order to eliminate the influence of the background noises and the deflection of the light. Medium filter, erode filter and dilate filter were included in these process. The grayscale image was converted into a binary image by setting threshold after the pre-processing. Bubble centroid, diameter and number could be obtained from this binary image. Because of the complicated deformation of the observed bubble in this experiment, further consideration on the evaluation of bubble diameter was needed. The calculation of the bubble equivalent diameter in a narrow rectangular channel was same as reference (Li et al., 2013), namely

⎧  Dx + Dy Dx + Dy ⎪ ⎪ ≤h ⎨ 3 Dx Dy 2 2 De =  ⎪ ⎪ ⎩ 3 3 (Dx + Dy − 2h)2 h + h3 Dx + Dy > h 8

(2)

2

where h is the height of the rectangular channel, Dx and Dy are the real diameter of the bubble measured from different direction. The mean diameter of the bubble can be calculated by averaging all of the bubble equivalent diameters in the observing window, i.e.

N Da =

Fig. 3. Rolling platform and the location of test section.

i=1

N

Dei

(3)

where N is the total number of the bubble in the observing window. The image of a 7 mm long scaleplate was captured after each case

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Fig. 4. Definition of rolling curve and corresponding surface orientation.

by fixing the focus length of the lens in order to determine the calibration of the bubble image. If the calibration of the bubble image was Kp , the measured bubble diameter could be expressed as Dr = Kp Di

(4)

where Dr denotes Dx or Dy of the previous section and Di is the pixel value of the bubble diameter in the image. The identification error was 1 pixel when determining the calibration and the maximum Kp was 21.7 ␮m/pixel. Thus the maximum error of the calibration was ±0.0602 ␮m/pixel. The identification error was also 1 pixel when measuring the bubble diameter in the image and the measured bubble diameter would not exceed 3 mm. Therefore, the maximum measurement error of the bubble diameter was ±30 ␮m. Bubble number density was defined by the bubble number per area, viz. n=

N Af

(5)

where Af denote the area of the observing window. The size of Af was related to Kp and the maximum error of Af was ±0.512 mm2 , thus the measurement accuracy of n could be determined as ±1.43 cm−2 . 4. Results and discussion This experiment includes 14 thermal-hydraulic conditions, and all the parameters are shown in Table 1. Each thermal-hydraulic condition is corresponding to one static condition and six rolling conditions as described above and thus 98 cases were conducted in this study. An auto-processing program based on the previous algorithm was programmed to deal with the huge amount of image data. Then the transient variation of local bubble number density and bubble mean diameter under rolling motion could be obtained. Table 1 Summary of thermal-hydraulic parameters. Test no.

P (kPa)

q (kW/m2 )

Tsub (◦ C)

G (kg/m2 s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

208 410 396 406 405 409 408 397 406 407 565 547 554 558

164.1 92.4 114.2 114.2 138.1 164.1 164.1 192.2 92.4 138.1 92.4 114.2 192.2 255.3

14.7 11.6 5.7 17.0 14.3 19.7 9.9 24.8 15.6 10.8 13.1 18.9 17.0 20.9

457.0 313.2 304.4 307.8 306.7 318.3 304.3 457.9 456.5 456.4 300.2 307.0 453.3 457.8

Local pressure was needed in the analysis of the results. Considering only inlet and outlet pressure of the test section was measured, it was assumed that the distribution of the pressure drop in the test section was linear. Thus we could obtain the local pressure at the observing window. The error brought by this assumption in the calculation of the local pressure could be accepted due to the small pressure drop of the experiments.

4.1. Visual observation and statistical analysis Bubble image sequence under rolling motion is depicted in Fig. 5. It can be seen from the figure that the diameter, number and location of bubbles varied at different time instant while the effects of rolling motion on bubble behavior is not clear. Further analysis on the image data and gathering more information are necessary in order to identify the affection of rolling motion on bubble behaviors. Two kinds of bubbles can be observed in the image shown in Fig. 5. One is generated from the nucleation site in the observing window, noted as nucleation bubble. And the other one is sliding from upstream, noted as sliding bubble. There were few bubbles disappeared because of condensation in the subcooled channel and most bubbles were sliding near the heating surface. Most of subcooled boiling experiments in this study can be categorized into isolated bubble region. Consequently, the interaction between bubbles seldom occurs and then the bubble coalescence phenomenon is unfamiliar. Furthermore, bubble rupture is also an occasional phenomenon in this experiment for the lower bubble Reynolds number. The distributions of bubble number density and bubble diameter under the effect of rolling motion are shown in Figs. 6 and 7, respectively. There are 400 frames of bubble image in each count and the corresponding time is 80 ms which is much less than the period of the rolling motion. Therefore, the instantaneous distribution in these figures can represent the dynamic characteristic of the bubble behavior under rolling motion. It should be noted here that the bubble diameter in Fig. 7 is the diameter of each recorded bubble rather than the mean diameter of bubble image. It can be seen from Fig. 6 that the probability of bubble images with less bubbles increased from t = t0 to t = t0 + 2 T0 /8, and thus the bubble number density decreased. Subsequently, the probability of images with different bubble number in t = t0 + 4 T0 /8 is close to that of t = t0 . From t = t0 + 4 T0 /8 to t = t0 + 6 T0 /8 the probability of bubble images with more bubbles increased and the bubble number density also increased. As described above, the observed bubbles in the observing window consisted of nucleation bubbles and sliding bubbles. In addition, the quantity of these two types of bubbles will influence the variation of the bubble number density. The quantity of the nucleation bubbles is determined by nucleation frequency

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Fig. 5. Bubble image sequence under rolling condition (Test No.2,  m = 15◦ , T0 = 16 s).

and nucleation site number density. While the quantity of the sliding bubbles is related to the nucleation frequency and nucleation site number of the upstream, the condensation and the coalescence of bubbles. It can be observed from Fig. 5 that the nucleation site number was unchanged during the rolling process while the nucleation bubble number varied with the same trend as bubble number density. The effect of rolling motion on bubble nucleation will be discussed in detail in the later section of the paper. The distribution of bubble diameter in Fig. 7 indicates that the bubbles can be classified into two categories by diameter. One has smaller diameters (0–0.6 mm), corresponding to the nucleation bubbles in Fig. 5. And the other has larger diameters (0.6–2 mm), corresponding to the sliding bubbles from the upstream. It should be noted that the proportion of the smaller bubbles (nucleation bubbles) dropped from t = t0 to t = t0 + 2 T0 /8, while the diameter of the larger bubbles (sliding form the upstream) has a little increase. Therefore, the bubble mean diameter increased from t = t0 to t = t0 + 2T0 /8. The distribution of bubble diameter in t = t0 + 4T0 /8 was close to t = t0 later. Then the proportion of the smaller bubbles

increased while the diameter of larger bubbles decreased comparing the distributions in t = t0 + 4T0 /8 and t = t0 + 6T0 /8. Thus the bubble mean diameter was expected to fall when the rolling angle decreased. Nucleation frequency (the nucleation site marked in Fig. 5) under the effect of rolling motion is given in Fig. 8 in order to manifest the effects of bubble nucleation on bubble number density and bubble mean diameter. The data in Fig. 8 indicates that the nucleation frequency increases with the rolling angle. This trend is same with the variation of bubble number density in Fig. 6 and the proportion of nucleation bubbles in Fig. 7. Higher nucleation frequency means more bubbles with smaller diameter are produced in the flow channel and the bubble number in the observing window performs an increasing trend. Thus the bubble number density increases with the increase of the probability of bubble images with more bubbles. But the increasing of nucleation frequency gives a rising of the probability of bubble images with smaller bubbles. Therefore the bubble mean diameter decreases with the nucleation frequency increase under rolling motion.

Fig. 6. Cumulative distribution of bubble number density (Test No.2,  m = 15◦ , T0 = 16 s).

Fig. 7. Cumulative distribution of bubble diameter (Test No.2,  m = 15◦ , T0 = 16 s).

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level. The stochastic characteristic of the subcooled boiling is the main reason of this feature. Besides, the limited observing window is also an important reason for this phenomenon. The other fluctuation is the periodical oscillation with the same period as rolling motion. In the following, attention will be mainly paid be to this periodical oscillations caused by rolling motion. In order to eliminate the affection of the random fluctuations on the analysis of the obtained data and to stress the impact of the rolling motion, the data in Fig. 9 are fitted by a sin function. It can be seen from the figure that the fitting line fits the data very well. The function adopt here can be expressed as f (t) = A + B sin

Fig. 8. Nucleation frequency under rolling motion (Test No.2,  m = 15◦ , T0 = 16 s).

4.2. The fluctuation of bubble number density and bubble mean diameter under rolling motion The variations of bubble number density under different rolling conditions are shown in Fig. 9. The calculation method of bubble number density is indicated in Eq. (5). The error bars is not included in the figure for the reason that the trend of the parametric effects can be better illustrated without the cover of the error bars. For clear illustrations, the corresponding angle of the platform is also shown on the top of the figure as reference. The time axis in Fig. 9 was scaled by relative time and the period of the rolling motion was used as the scale factor. The total recording time of the bubble images under rolling motion was 1.25 times of rolling period. Two kinds of fluctuations of bubble number density can be observed from Fig. 9. One is the random fluctuations, namely all of the experimental data fluctuate randomly around a specified

 2 T0

t+C



(6)

where f(t) denotes the variation of the bubble number density, A, B and C denote the fitting parameters. From the physical significance, A, B and C represent the average value of bubble number density, the amplitude of the fluctuation and the oscillation phase lag between bubble number density and rolling angle, respectively. Some of the details will be lost during this fitting process, such as the strong oscillations in Fig. 9(a) while the bubble number density reached its maximum value. But this method will be used for each case to study the effect of rolling motion on bubble number density for the purpose of simplifying the analysis procedure. Fig. 9 indicates that the variation of bubble number density was nearly same with that of rolling angle although some phase lag did exist. Comparing with the rolling curve, we can see that the maximum bubble number density could be obtained when the angular orientation of the heater surface reached its maximum during rolling process. And the minimum bubble number density could be reached for the smallest rolling angle. Furthermore, the amplitude of the bubble number density fluctuations increased with the rolling amplitude, and vice versa. While the effect of rolling period on the fluctuation amplitude of bubble number density was much weak. The instantaneous variation of bubble mean diameter is shown in Fig. 10. The rolling amplitudes are 15◦ and 10◦ , respectively, and the rolling period increases from 8 s to 16 s. It can be seen from the

Fig. 9. Variations of bubble number density under rolling condition (Test No.2).

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Fig. 10. Variations of bubble diameter under rolling condition (Test No.2).

figure that two kinds of fluctuation perform together in the above data, including the stochastic oscillation and the periodic oscillation induced by rolling motion, as same as bubble number density. Same fitting method is adopted to process the data of bubble mean diameter under rolling motion for the same purpose. The fitting curve can represent the variation of bubble mean diameter well as the case in bubble number density. The results manifest that significant temporal oscillations in bubble mean diameter occurred and an opposite variation trend to that for the rolling angle could be observed. Besides, it should be noted that the bubble mean diameter oscillations were also periodical and with the same period as the rolling motion. The maximum bubble mean diameter could be achieved when the angular orientation of the heater surface reached to its minimum during the rolling motion. Furthermore, when comparing with the oscillations of bubble number density in Fig. 9, an opposite trend could be observed in bubble mean diameter. As the bubble number density raised gradually, the bubble mean diameter decreased correspondingly. In fact, both the increase of bubble number density and bubble mean diameter during the rolling motion need more heat to be injected to the flow boiling channel for the increase of latent heat for vaporization. While the heat flux to the channel was invariable with time because of the constant current through the heater plate. Thus the opposite trend taken place under this certain constraint. Moreover, it is worth to note that with the raising of the rolling amplitude, a strong increase could be observed in the fluctuation amplitude of the bubble mean diameter. But the bubble mean diameter was negligibly affected by the period of the rolling motion, similar to bubble number density. 4.3. Effects of rolling parameters Bubble number density and bubble size of a subcooled flow boiling channel depends on the nucleation frequency, the nucleation site density, the growth and condensation rate and the interaction between neighbor bubbles. Because most of the working conditions located in isolated bubble region the interaction between bubbles

was a minor phenomenon in this study. Therefore, the oscillations of bubble number density and bubble mean diameter are related to the first three factors. Corresponding changes of nucleation frequency, nucleation site density and growth and condensation rate of bubbles would occur when mass flux, local pressure, inlet temperature and heat flux of the test channel varied under the effect of rolling motion. The factor which was mainly responsible for the oscillation of bubble number density and bubble mean diameter will be identified in the following. Resistive heating was adopted for the power source of the subcooled flow boiling. The heat flux of the channel will be maintained in a constant level during the rolling motion because the current and voltage of the heater plate is time independent. Furthermore, it is noticed that the variation of inlet temperature was smaller than 0.5 ◦ C and behaved no correlation with the rolling of the platform. Then we can conclude that the inlet temperature would not influence the variation of bubble number density and bubble mean diameter under rolling motion. Under the effects of rolling motion, the corresponding variation of mass flux, local pressure of the observing window and wall temperature could be observed in the experiment, as shown in Fig. 11. The data in the figure reveal that the mass flux, the local pressure and the wall temperature oscillated periodically and significantly with time. Moreover, it can be seen that the period of the oscillations in Fig. 11 was identical with that of rolling motion. In the following, we will illustrate in detail how the time periodic bubble characteristics were affected by the variation of these parameters. The oscillation of mass flux under rolling motion was determined by the relation of driving force of the loop, friction pressure drop and additional pressure drop caused by rolling motion. The driving force consisted of two parts, one was the pressure head provided by the pump and the other one was caused by the temperature difference of the loop, namely the natural circulation pressure head. In general, the fluctuation of the system flow rate will be intensified by the rising of the additional drop induced by rolling motion and the dropping of the driving force. Large flow rate fluctuation was observed in the experiment of Tan et al. (Si-Chao et al., 2009a) for the reason that the driving force was

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Fig. 12. Fluctuation amplitude of bubble number density versus effective wall superheat.

Fig. 11. The fluctuation of mass flux, inlet pressure and wall temperature (Test No.2).

small comparing with the additional pressure drop and the natural circulation pressure head was also influenced by rolling motion. Similar phenomenon was observed in the experiments of Pendyala et al. (2008) and Hong et al. (2012a,b) due to the reason described above. The fluctuation of the flow rate in this experiment was not influenced by the decrease of Reynolds number and the fluctuation was very weak (less than 3%). This indicates that the flow rate oscillation was inhibited by the large driving head of the pump. In a word, the flow rate oscillation was very small in this study and such small oscillation would not induce a notable variation of bubble number density and bubble mean diameter. The variation of the wall temperature under rolling motion will change the wall superheat of the flow channel and more bubbles will generate in higher wall superheat if other parameters remain constant. It can be seen from Fig. 11 that the wall temperature fluctuation is about 0.5 ◦ C while the thermocouples used in this experiment have an uncertainty of ±0.5 ◦ C. This indicates that the wall temperature fluctuation is so small that cannot be detected accurately in this experiment. Thus the effect of rolling motion on heat transfer is very limited in this work. But the fluctuation of the bubble number density and bubble size caused by rolling motion should not be neglected due to the void effect on neutron feedback in a nuclear reactor. It is worth to note that the parameters which change the wall superheat not only include the wall temperature but also the saturation temperature of water which is dependent on the local pressure. Meanwhile, some of the other physical properties, such as surface tension and latent heat of vaporization, in relation with bubble dynamics vary with local pressure. But only the variation of saturation temperature will be considered to analyze the oscillations of bubble number density and bubble mean diameter caused by rolling motion. Based on this consideration, the factors affected the bubble behaviors can be attributed to the effective wall superheat, namely Tw,eff = Tw − Tsat (Plocal )

(7)

in which Tw is the wall temperature and Tsat (P) is the local saturation temperature. The effect of the oscillation intensity of effective wall superheat on the fluctuation amplitude of bubble number density and bubble mean diameter are shown in Figs. 12 and 13, respectively.

Fig. 13. Fluctuation amplitude of bubble mean diameter versus effective wall superheat.

Although the data are scattered, an increasing trend with the oscillation intensity of effective wall superheat can also be observed. Therefore, it can be inferred that higher oscillation intensity will occur in the process of bubble nucleation for larger fluctuation of effective wall superheat. Thus the quantity of the nucleation bubbles will vary intensively with the rolling motion as described in the previous section, and cause larger fluctuation of bubble number density and bubble size. This result reveals that the bubble behavior under rolling motion can also be influenced by the variation of effective wall superheat even the flow rate of the system was relative steady. 5. Conclusions Bubble number density and bubble mean diameter in a narrow rectangular channel under rolling motion are experimentally researched by adopting high speed visualization system and digital image processing technology in this paper. Auto-processing program is proposed to deal with the huge amount of bubble image data. The major results for this study are outlined below. 1. The distribution characteristic of the bubble diameter in rolling motion reveals that the bubbles in the observing window consist of nucleation bubbles and sliding bubbles. Both of them are responsible for the variation of the bubble mean diameter. Moreover, the nucleation frequency periodically oscillates with the

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rolling motion and induces the fluctuation of bubble number density. 2. Bubble number density and bubble mean diameter periodically fluctuates under the effect of rolling motion and the period of the fluctuation is identical with that of rolling motion. Opposition variation trend can be observed between bubble number density and bubble mean diameter. 3. The fluctuation amplitude of bubble number density and bubble mean diameter increases as the rolling amplitude increases, while the effect of rolling period is much weaker although most of the cases show an increasing trend with the decrease of rolling period. 4. Periodical oscillations of mass flux, wall temperature and local pressure in the channel are observed during rolling motion. The variation of the mass flux is very small due to the large driving force supplied by the pump and imposes very limited influence on the fluctuation of bubble characteristics. The main reason for bubble behavior fluctuations could be concluded to the fluctuation of the effective wall superheat induced by the variation of wall temperature and local pressure. Acknowledgements The experimental facilities and numerical software were supported by the Fundamental Research Funds for the Central Universities (no. HEUCFZ1008), Foundation of Fundamental Science on Nuclear Safety and Simulation Technology Laboratory of Harbin Engineering University (HEUFN1305), Foundation for Returnees of Heilongjiang Province (no. LC2011C18) and China Government (no. 2012-1707), the Heilongjiang Province Postdoctor Scientific Research Fund (LBH-Q10131). References Cho, Y., Yum, S., Lee, J., Park, G., 2011. Development of bubble departure and lift-off diameter models in low heat flux and low flow velocity conditions. Int. J. Heat Mass Transfer 54, 3234–3244. Dhir, V.K., 2006. Mechanistic prediction of nucleate boiling heat transfer-achievable or a hopeless task? J. Heat Transfer 128, 1–12. Donnelly, B., Donovan, T.S.O., Murray, D.B., 2009. Surface heat transfer due to sliding bubble motion. Appl. Therm. Eng. 29, 1319–1326. Gerardi, C., Buongiorno, J., Hu, L., McKrell, T., 2010. Study of bubble growth in water pool boiling through synchronized, infrared thermometry and high-speed video. Int. J. Heat Mass Transfer 53, 4185–4192.

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