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Bubble rise characteristics after the departure from a nucleation site in vertical upflow boiling of subcooled water
Nuclear Engineering and Design 235 (2005) 1149–1161
Bubble rise characteristics after the departure from a nucleation site in vertical upflow boiling of subcooled water Tomio Okawa a,∗ , Tatsuhiro Ishida a , Isao Kataoka a , Michitsugu Mori b a
Department of Mechanophysics Engineering, Osaka University, 2-1 Yamadaoka, Suita-shi, Osaka 565-0871, Japan b Thermal-Hydraulics and Fluid-Structure Dynamics Research Group, Tokyo Electric Power Company, 4-1 Egasaki-cho, Tsurumi-ku, Yokohama-shi, Kanagawa 230-8510, Japan Received 13 January 2005; received in revised form 14 January 2005; accepted 16 February 2005
Abstract Rise characteristics of vapor bubbles after the departure from a nucleation site in forced convective subcooled flow boiling were studied visually using two synchronized high speed video cameras. The test section was a transparent glass tube of 20 mm in inside diameter, filtrated and deionized tap water was used as a working fluid, and the flow direction adopted was vertical upward. The outer surface of test section tube was electrically heated to generate vapor bubbles inside of the tube. In the present experiments, the mass flux and liquid subcooling were varied within 94–1435 kg/m2 s and 2.2–10 K, respectively. Since the observations were performed at low heat fluxes to avoid the significant increase in the number of active nucleation sites, the obtained bubble images were clear enough to carry out the detailed image analysis for the rise characteristics of individual bubbles. The following three different bubble rise paths were observed after the departure from nucleation sites: some bubbles slid upward the vertical wall for long distance, while other bubbles were detached from the wall after sliding for several millimeters and then migrated toward the bulk liquid; after the migration, some of the detached bubbles were collapsed in subcooled liquid but others remained close to the wall and were reattached to the wall. The results of detailed image analyses suggested that the variation in bubble shape from flattened to more rounded was of primary importance for the occurrence of bubble detachment from the wall. © 2005 Elsevier B.V. All rights reserved.
1. Introduction Forced convective flow boiling of water in a vertical channel is encountered in many industrial applications ∗ Corresponding author. Tel.: +81 6 6879 7257; fax: +81 6 6879 7247. E-mail address: [email protected] (T. Okawa).
0029-5493/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.02.012
including boilers, evaporators and nuclear reactors. It is known that the heat transfer rate and the cross-sectional area-averaged void fraction in this thermal hydraulic condition are significantly influenced by the rise characteristics of vapor bubbles after the departure from nucleation sites. Thorncroft and Klausner (1999) showed experimentally that the heat transfer rate from the heating wall is enhanced by the existence of vapor bubbles
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Nomenclature C db G g hb K Mo Nb P qw RA Tsub t u ut v xb yb
constant bubble size (m) mass flux (kg/m2 s) gravitational acceleration (m/s2 ) gap distance between bubble and wall (m) proportionality factor Morton number the number of bubbles analyzed pressure (N/m2 ) wall heat flux (W/m2 ) aspect ratio subcooling of bulk liquid (K) time from bubble incipience at nucleation site (s) velocity in the axial direction (m/s) terminal bubble rise velocity (m/s) velocity in the lateral direction (m/s) vertical distance from nucleation site to bubble centroid (m) distance from wall to bubble centroid (m)
Greek symbols µ viscosity (Pa s) ρ density (kg/m3 ) σ surface tension (N/m) Subscripts b bubble l liquid phase lift lift-off (detachment from a heating wall) r relative to the local liquid velocity x axial direction y radial direction z circumferential direction
sliding along the wall. Weisman and Pei (1983) reported that the critical heat flux at low vapor quality is correlated well in terms of the void fraction in near wall region. Since the bubble rise velocity is smaller in the near wall region than in the core region (Colin and Legendre, 2001; Okawa et al., 2002a), the crosssectional area-averaged void fraction should increase if
the bubbles slide along the wall. Furthermore, the vapor bubbles are rapidly condensed if they are detached from the wall and migrate toward the bulk liquid in subcooled flow boiling (Zeitoun and Shoukri, 1997); this also leads to the decrease in cross-sectional areaaveraged void fraction. Hence, the bubble rise characteristics after the departure from a nucleation site should be understood sufficiently to develop reliable mechanistic models for predicting the heat transfer rate and cross-sectional area-averaged void fraction in forced convective flow boiling. The rise characteristics of vapor bubbles in vertical upward flow boiling were observed extensively by many researchers. Some of the experiments were conducted in subcooled conditions (Gunther, 1951; Jiji and Clark, 1964; Frost and Kippenhan, 1967; Abdelmessih et al., 1972; Akiyama and Tachibana, 1974; Del Valle and Kenning, 1985; Bibeau and Salcudean, 1994; Zeitoun and Shoukri, 1996; Warrier et al., 2002; Prodanovic et al., 2002; Situ et al., 2004), and others in saturated or slightly subcooled conditions (Cooper et al., 1983; Van Helden et al., 1995; Thorncroft et al., 1998; Okawa et al., 2005). In these experiments, the important bubble parameters including the size, shape, growth and collapse rates, population, frequency and trajectory were measured in varied conditions of working fluid, system pressure, liquid subcooling, mass flux and wall heat flux. The influences of flow direction (Thorncroft et al., 1998), existence of surface-active agent (Frost and Kippenhan, 1967) and gravity level (Cooper et al., 1983) were also investigated. In general situations of forced convective flow boiling, there exist a number of active nucleation sites on a heating surface and consequently the effect of the interaction between bubbles should be taken into account. It is however expected that the sufficient knowledge on the behavior of single bubbles provides the insight into the more complicated phenomena encountered in practical situations. This type of approach has shown good success in the modeling of complicated gas–liquid two-phase flows (Ishii and Chawla, 1979). Despite the above described extensive experimental works, however, the bubble rise path after the departure from a nucleation site has not been thoroughly understood even in the low bubble number density conditions in which the interaction between bubbles may be neglected. In the experiments of refrigerant FC-87 by Thorncroft et al. (1998), typical bubbles slid along the
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heating surface after the departure from a nucleation site and were not detached from the wall in vertical upflow boiling. Several other observations may support this result (Gunther, 1951; Frost and Kippenhan, 1967). Prodanovic et al. (2002) conducted the bubble visualization study in subcooled flow boiling of water in a vertical annulus and reported that bubbles usually slid along the vertical heater with small number of exceptions when the heat flux is sufficiently low but they typically traveled into the liquid core after sliding for a couple of bubble diameters when the heat flux was increased. In the experiments by Okawa et al. (2005) for slightly subcooled water in a vertical round tube, typical bubbles were detached from the wall and migrated toward the bulk liquid after sliding for several millimeters. The bubble trajectories after the departure from an artificial cavity shown by Van Helden et al. (1995) also indicated the bubble detachment in the direction normal to the vertical wall. The above literature review revealed that the following two typical rise paths were observed for the vapor bubbles after the departure from nucleation sites in vertical upward flow boiling: (1) bubbles may slide upward the wall for long distance without detachment, or (2) bubbles may be detached from the wall after sliding for a certain distance and then migrate toward the bulk liquid. The heat transfer rate and the cross-sectional area-averaged void fraction in this flow configuration are considered to be influenced significantly by the difference in bubble rise path. Hence, in the present work, the key mechanisms to determine the bubble rise path are studied through visualization of bubble behavior after the departure from a nucleation site. In particular, the effect of the change in bubble shape on the occurrence of bubble detachment is investigated in detail through image analysis.
2. Experimental description Shown in Fig. 1 is a schematic of the experimental apparatus; the same apparatus was used earlier to investigate the bubble dynamics and the dependence of vapor void fraction on wall heat flux in subcooled flow boiling (Okawa et al., 2004, 2005). In the present experiments, filtrated and deionized tap water is used as a working fluid. The water is circulated by a pump. The ultrasonic flow meter that is accurate within ± 0.08 l/min
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Fig. 1. Schematic diagram of experimental apparatus.
is used to measure the volumetric flowrate. The 15 kW plug heater is used to heat up and then keep the water temperature. After exiting the pre-heating section, the water enters the vertical tube of 20 mm in inside diameter. This section consists of the two long stainless steel tubes and the short transparent glass tube between them. The glass tube is used as a test section in the experiments. The top of these tubes is connected with the header tank open to atmosphere to separate vapor bubbles from continuous liquid phase. The fluid temperatures are measured at the inlet and outlet of
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Fig. 3. Arrangement of high speed cameras and halogen light sources (top view of test section).
Fig. 2. Schematic diagram of transparent test section.
preheating section and at the outlet of test section with type-K thermocouples that are accurate within ±1.5 K. The pressure at the test section is measured with the pressure transducer that is accurate within ±500 Pa. An analog-to-digital converter attached to a personal computer records the measurements of flowrate, temperatures and pressure every 1 s. Shown in Fig. 2 is a schematic of transparent test section. The test section is the 160.0 mm long sapphire glass tube; its inner and outer diameters are 20.0 and 23.0 mm, respectively. Sapphire glass was chosen as the material for its higher thermal conductivity (32.4 W/m K at 400 K). The region of 12.2 mm in width and 100.0 mm in length on the outer surface of glass tube is coated with the thin indium tin oxide (ITO) film. The film thickness is estimated 200 nm. Both ends of the ITO coated section are covered by nickel films that are used as electrodes. The resistance of ITO film is approximately 340 and it is electrically heated with 5 kW dc power supply to generate vapor bubbles on the inner surface of the test section tube. A digital multi
meter measures the voltage and electric current with the uncertainties of ±0.1 V and ±2.3 mA, respectively. The uncertainty in the heat supplied to the test section is less than ±0.5%. In the present experiments, however, the test section is not thermally insulated for visual observation. The heat loss to ambient air is estimated to within 2%. The successive bubble images are obtained using two high-speed digital video cameras. The arrangement of cameras and illuminating lights is schematically shown in Fig. 3. To reduce the effect of refraction on a bubble image, the glass tube is surrounded by a rectangular glass jacket and the gap between the tube and jacket is filled with silicone oil. The effect of refraction still remaining is corrected from the images of a specially designed acrylic piece inserted in the test section. Images with a spatial resolution of 512 × 128 pixels are recorded every 0.25 ms; the spatial resolution is approximately 60 m and the shutter speed is set at 0.125 ms. Prior to the boiling experiments, the radial velocity profiles of single-phase liquid flow in the test section were measured using spherical polyester particles as tracers. The diameter and specific gravity of a particle were 0.2–0.4 mm and 1.04, respectively. In the singlephase experiments, the volumetric flux and liquid tem-
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perature were varied within 0.5–2.0 m/s and 30–37 ◦ C, respectively. The measured radial distributions of axial time-averaged liquid velocity agreed with the expression by Nunner for fully developed turbulent flow (Hinze, 1959) within ±5%. The tracer particles were removed from the experimental loop using a filter for the boiling experiments. In the visualization tests of vapor bubbles, mass flux and liquid temperature are controlled by adjusting the flow control valves and the power applied to the preheater, respectively. After steady state is established, dc power is applied to the ITO film coated on the test section tube. The power to the test section is increased until vigorous boiling is observed at several nucleation sites to eliminate the effect of boiling hysteresis. The dc power is then reduced until the number of bubbles in the test section becomes sufficiently small to observe visually the rise characteristics of individual bubbles. Once successive bubble generation at several nucleation sites is confirmed, the bubble images from the two directions are recorded using the synchronized high-speed cameras.
3. Results and discussion Table 1 summarizes the 14 experimental conditions considered in this work. The test section pressure P was within 121–127 kPa and slightly higher than the Table 1 Summary of experimental conditions Exp. no.
P (kPa)
Tsub (K)
G (kg/m2 s)
qw (kW/m2 )
11 12 13 14 15 21 22 23 24 25 31 32 33 34
125 125 125 126 127 125 125 125 126 127 121 121 121 122
2.2–2.3 2.3–2.5 2.6–2.8 2.9–3.2 3.2–3.4 5.0–6.1 5.8–5.9 6.1 5.9–6.0 5.6–5.9 8.6–9.4 9.7–10 9.2–9.6 9.8
94–99 280–286 560–576 950–957 1431–1435 94–98 288–289 573–576 940–953 1420–1431 99–103 274–280 565–568 947
54–111 112–167 127–223 186–278 231–279 51–113 91–169 135–225 189–282 234–338 63–170 91–171 143–230 230
7 7 22 25 19 17 22 23 16 13 20 10 3 4
Total
121–127
2.2–10
94–1435
54–338
208
Nb
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Fig. 4. Definitions of instantaneous bubble parameters.
atmospheric pressure mainly due to the static head. The liquid subcooling Tsub was defined from the fluid temperature measured at the outlet of test section tube and varied within 2.2–10 K. The range of mass flux G was 94–1435 kg/m2 s. Bubble images were recorded at several wall heat fluxes under the similar conditions of Tsub and G. Image analysis was performed manually to deduce the bubble dimension in the three directions dbx , dby , dbz , the vertical distance from nucleation site to bubble centroid xb , the distance from the wall to bubble centroid yb and the gap distance between the bubble and wall hb . The definitions of these instantaneous bubble parameters are shown schematically in Fig. 4. 3.1. Qualitative descriptions of bubble rise characteristics In the present experiments, the three typical bubble rise paths were observed. Some bubbles slid upward the vertical wall and were not detached from the heating surface within the viewing area. The consecutive images of a typical sliding bubble are depicted in Fig. 5(a) and (b). On the other hand, other bubbles were detached from the wall after sliding upward for 1–10 mm and then migrated toward the subcooled bulk liquid. Some of the detached bubbles reversed the direction of lateral migration and then reattached to the wall but other detached bubbles were collapsed due to
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Fig. 5. Consecutive images of a typical sliding bubble (exp. no. 15; qw = 231 kW/m2 ; time interval is 2 ms). (a) Camera A, (b) camera B.
the condensation in subcooled liquid. Hereafter, these bubbles are called bouncing and collapsing bubbles, respectively. The consecutive images of typical bouncing and collapsing bubbles are depicted in Figs. 6 and 7. Even when a bubble is sliding along the wall, a bubble is expected to be separated from the wall by a thin liquid film. This implies that the occurrence of bubble detachment is slightly uncertain. In this work, bubbles were classified as detached bubbles (bouncing or collapsing bubbles) if the gap distance hb exceeded 0.1 mm. Shown in Fig. 8 are the time series of db and hb for the three bubbles depicted in Figs. 5–7; here, the bubble
Fig. 6. Consecutive images of a typical bouncing bubble (exp. no. 14; qw = 186 kW/m2 ; time interval is 2.5 ms). (a) Camera A, (b) camera B.
size db is estimated by db = 3 dbx dby dbz
(1)
All the bubbles experienced rapid growth during the short period immediately after the incipience at nucleation sites. The size of sliding bubble became fairly constant after the rapid growth. Most of the bouncing bubbles remained close to the wall but their sizes were decreased gradually after the detachment; the decreasing rate depended significantly on Tsub . The size of bouncing bubbles increased again after the reattachment to the heating wall, though several bouncing bub-
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Fig. 7. Consecutive images of a typical collapsing bubble (exp. no. 23; qw = 135 kW/m2 ; time interval is 2.5 ms but it is reduced to 1.25 ms only between the last two images). (a) Camera A, (b) camera B.
Fig. 8. Evolutions of bubble size and gap distance between bubble and wall.
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Fig. 9. Evolutions of bubble dimension in the three directions. (a) Sliding bubble, (b) bouncing bubble, (c) collapsing bubble.
bles showed rebounding motion after the reattachment. The behavior of a collapsing bubble was similar to that of a bouncing bubble but it disappeared before the reattachment to the wall. At low liquid subcooling, some of the detached bubbles could stay in the subcooled liquid core for long time due to the small condensation rate and did not disappear within the viewing area. These bubbles were also classified as collapsing bubbles. The time series of dbx , dby , dbz for the same bubbles are depicted in Fig. 9(a)–(c), respectively. Immediately after the incipience, dbx and dbz are fairly equal but dby
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Fig. 10. Evolutions of bubble rise velocity.
is much smaller; dby then approaches to dbx and dbz . This implies that these bubbles were flattened along the vertical wall within the initial stage but then became more rounded. It is interesting to note that the bubbles were nearly spherical at the onset of detachment in Fig. 9(b) and (c). The time series of ub and ul are depicted in Fig. 10. The bubble rise velocity ub was derived from the vertical displacement of bubble centroid and the local liquid velocity ul was estimated at the bubble centroid using the radial velocity profile of fully developed turbulent pipe flow by Nunner (Hinze, 1959). The figure indicates that upward migration of bubbles began immediately after the incipience and the bubble rise velocities became comparable with local liquid velocity within 1 ms. Since the bubbles stayed at the nucleation sites for very short period, it was difficult to detect the departure of a bubble from a nucleation site under the present experimental conditions. The figure also indicates that the rise velocity of collapsing bubble increased remarkably during the condensation period; the increase in bubble rise velocity was a common feature during the rapid condensation. 3.2. Bubble behavior during the sliding stage The variations of several bubble parameters during the sliding stage before the detachment are investigated in this section. Immediately after the incipience, all the bubbles grew rapidly and began to slide upward the vertical heating wall. For the diffusion-controlled region, Foster and Zuber (1954) and Mikic et al. (1970) expressed the growth of a vapor bubble close to a heating
Fig. 11. Evolutions of bubble size.
surface by √ db = Kt
(2)
For all the bubbles analyzed, the dependence of db /db,cal on t before the onset of detachment is depicted in Fig. 11, where db,cal denotes the bubble size calculated by Eq. (2). In order to determine the time from incipience t for the first image of each bubble and the value of proportionality factor K, Eq. (2) is assumed valid in the present experimental conditions and the least-square method is applied to the experimental data of db for the first three bubble images. Fig. 11 indicates that the growth rate is fitted with Eq. (2) fairly well within the initial stage immediately after the incipience, though it is generally overestimated when t is greater than 1 ms since bubbles are partly exposed to the subcooled liquid core. To investigate the variation of bubble shape, dby and dbz are plotted against dbx in Fig. 12(a). It is confirmed that bubbles were generally flattened along the vertical heating wall during the sliding stage in the present experiments. Since dbx and dbz were fairly equal, the aspect ratio of a bubble RA is defined by RA =
2dby dbx + dbz
(3)
The variations of RA with t are shown in Fig. 12(b). In all the experimental conditions, RA was approximately within 0.35–0.55 right after the incipience and then approached to unity. Since the bubble size in the first image of each bubble was not large enough to measure RA accurately, the value of RA measured in the second image is plotted against G in Fig. 12(c) to elucidate the influences of G and Tsub on RA within the initial stage. The figure indicates that G and Tsub have no
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significant influence on RA in the present experimental conditions. Rapidity of the change in bubble shape dRA /dt within the sliding stage is plotted against db in Fig. 12(d). It is found that dRA /dt is roughly propor−3/2 tional to db . It is known that the frequency of the shape oscillation caused by the surface tension force to the initially ellipsoidal bubble is also proportional inversely to the bubble size to the three halves power (Lamb, 1932). The results shown in Fig. 12(d) hence suggest that the change in bubble shape from flattened to more rounded observed during the sliding stage was caused primarily by the surface tension force. The instantaneous bubble rise velocities relative to the local liquid velocities estimated at the bubble centroids ur are plotted against db in Fig. 13. Okawa et al. (2003) showed experimentally that the bubble rise velocity in stagnant high temperature water is influenced by the method of bubble generation and the upper and lower boundaries of terminal rise velocity ut are approximated if the parameter n is set at 1.35 and 0.55 in the following empirical correlation by Fan and Tsuchiya (1990): −n −1/n ρ gd 2 −n 2.4σ gdb l b ut = (4) + + Kb µl ρl db 2 where Kb is the function of Morton number Mo (Kb = max(12, 14.7Mo−0.038 )). Fig. 13 depicts that the relative velocity of sliding bubbles ur in the present subcooled flow boiling experiments are much smaller than the terminal bubble rise velocity ut in infinite stagnant high temperature water. The reduction of bubble rise velocity may be attributed to the steep liquid veloc-
Fig. 12. Bubble shape within the sliding stage. (a) Bubble dimensions in the three directions, (b) evolutions of aspect ratio, (c) aspect ratio immediately after the incipience, (d) effect of bubble size on the rapidity of the variation in bubble shape. Fig. 13. Bubble rise velocity relative to the local liquid velocity during the sliding stage.
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ity profile in the proximity of the vertical wall (Okawa et al., 2002b) or the difference in bubble shape from that in infinite stagnant liquid (Tomiyama et al., 2002). Further studies are considered necessary to develop a reliable model for the interfacial force acting on these bubbles sliding along the wall. 3.3. Bubble behavior at the detachment from a vertical heating wall Experimental information on the bubble behavior at the detachment from a heating wall is of importance in the mechanistic modeling of subcooled flow boiling (Kljenak et al., 2004). In the present experimental observations, bubbles were detached from the vertical heating surface after the change in bubble shape from flattened to more rounded. If the bubble shape varies from flattened to more rounded within the sliding stage, liquid flow directing toward the bubble base is induced between the bubble and wall as illustrated in Fig. 14. It is hence probable that the bubbles were lifted from the vertical heating wall by the inertia of the liquid flow induced beneath the bubble. The test section pressure and consequently the fluid properties were fairly constant in the present experiments. It is hence considered that smaller bubbles experienced more rapid shape change and were detached from a heating wall within a shorter period since the surface tension force is inversely proportional to the radius of interface curvature. Since the bubble size is not constant within the sliding stage, the proportionality factor K defined in Eq. (2) is used as the parameter de-
Fig. 14. Supposed mechanism of the bubble detachment from a vertical heating wall.
noting the bubble size. The time from incipience to detachment tlift and the lift-off diameter db,lift are plotted against K in Fig. 15(a) and (b), respectively. It is confirmed that tlift and db,lift increase monotonously with the increase in K. Since tlift and db,lift are collapsed well with K, the surface tension force is expected to play important role for the bubble detachment in the present experimental conditions. Fig. 15(b) indicates that the lift-off diameter db,lift decreases slightly with the increase in Tsub . This may be because the growth rate after the rapid growth within the initial stage decreases with the increase in Tsub . The aspect ratio at the detachment RA,lift is plotted against db,lift in Fig. 15(c). It is found that RA,lift increases with db,lift but most bubbles were nearly spherical at the detachment. The lateral bubble migration velocity at the detachment vb,lift are plotted against db,lift in Fig. 15(d). Since accurate measurement of instantaneous bubble velocity in the direction normal to the wall was difficult, vb,lift was estimated from the lateral bubble displacement within 2 ms prior to the detachment. There exists significant scattering but vb,lift is roughly proportional −1/2 to db,lift as expected, since the lateral bubble migration within the sliding stage is mainly caused by the change in bubble shape from flattened to rounded and −3/2 dRA /dt is roughly proportional to db as depicted in Fig. 12(d). The bubble rise paths observed in the present experiments are plotted in the G–Tsub map in Fig. 16. The sliding bubbles were observed in high mass flux conditions. The lowest mass flux required to obtain sliding bubbles increases with the increase in Tsub . This tendency may be interpreted as follows. The inertia of liquid flow induced by the change in bubble shape lifts the bubble while the shear lift force pushes the bubble against the wall. Since the gradient of radial liquid velocity profile and consequently the shear lift force acting on a bubble increase with the increase in G, sliding bubbles are more frequently observed under high mass flux conditions. At the lowest mass flux, not only the sliding bubbles but also the bouncing bubbles were rarely observed; this may support that the bubbles were pushed against the wall by the shear lift force. The increase in Tsub leads to the retardation of bubble growth and consequently to the faster variation in bubble shape. This may be one of the main reasons why larger mass flux was needed to prevent the bubble detachment in higher subcooling experiments.
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Fig. 16. Observed bubble rise paths in G–Tsub map.
4. Conclusions The bubble visualization study was conducted in vertical upflow boiling of subcooled water to reveal the following features of bubble rise characteristics after the departure from a nucleation site in the present experimental setup:
Fig. 15. Bubble parameters at the detachment from a vertical heating wall. (a) Bubble lift-off time from the incipience, (b) bubble size, (c) bubble aspect ratio, (d) bubble migration velocity in the lateral direction.
(1) Immediately after the incipience, bubbles grew rapidly and departed from the nucleation sites by sliding upward the vertical heating wall. The growth rates in the initial stage were consistent with available theories and fitted fairly well if the bubble size was assumed proportional to the square root of the time from incipience; the growth rate then decreased gradually likely due to the partial exposure to subcooled liquid core. The bubbles were accelerated rapidly after the incipience and the rise velocity became comparable with local liquid velocity within 1 ms. (2) Bubbles were initially flattened along the vertical wall and then became more rounded while sliding on the heating surface. The variations of bubble aspect ratio with respect to time were roughly proportional to the inverse of bubble size to the
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three halves power, suggesting that the change in bubble shape was primarily caused by the surface tension force. During the sliding phase, the bubble rise velocity relative to the local liquid velocity was smaller than the terminal bubble rise velocity in infinite stagnant high temperature water. (3) After sliding for several millimeters, some bubbles kept sliding along the wall for long distance, while other bubbles were detached from the wall and then migrated toward the bulk liquid. Some of the detached bubbles reversed the direction of lateral migration and then reattached to the wall but other detached bubbles were collapsed due to the condensation in subcooled liquid. Since the bubble shape was varied from flattened to more rounded during the sliding phase prior to the detachment, surrounding liquid was expected to flow directing toward the bubble base. It was considered that the inertia of local liquid flow induced beneath the bubble was the main driving force to lift the bubble from the heating wall. The lift-off time from the incipience decreased monotonously with the decrease in bubble size; this may be because the shape change became faster due to the increase in surface tension force. The sliding bubbles were more frequently observed in high mass flux conditions; at the lowest mass flux, not only the sliding bubbles but also the bouncing bubbles were rarely observed. This may indicate that the shear induced lift force was responsible to push the bubbles against the wall and to prevent the bubble detachment. References Abdelmessih, A.H., Hooper, F.C., Nangia, S., 1972. Flow effects on bubble growth and collapse in surface boiling. Int. J. Heat Mass Transfer 15, 115–125. Akiyama, M., Tachibana, F., 1974. Motion of vapor bubbles in subcooled heated channel. Bull. JSME 17, 241–247. Bibeau, E.L., Salcudean, M., 1994. A study of bubble ebullition in forced-convective subcooled nucleate boiling at low pressure. Int. J. Heat Mass Transfer 37, 2245–2259. Colin, C., Legendre, D., 2001. Bubble distribution in turbulent shear flows: experiments and numerical simulations on single bubbles. In: Proceedings of Fourth International Conference on Multiphase Flow, Paper No. 449. Cooper, M.G., Mori, K., Stone, C.R., 1983. Behaviour of vapor bubbles growing at a wall with forced flow. Int. J. Heat Mass Transfer 26, 1489–1507.
Del Valle, V.H., Kenning, D.B.R., 1985. Subcooled flow boiling at high heat flux. Int. J. Heat Mass Transfer 28, 1907–1920. Fan, L.-S., Tsuchiya, K., 1990. Bubble Wake Dynamics in Liquids and Liquid–Solid Suspensions. Butterworth-Heinemann, Oxford (Chapter 2). Foster, H.K., Zuber, N., 1954. Growth of a vapor bubble in superheated liquid. J. Appl. Phys. 25, 474–478. Frost, W., Kippenhan, C.J., 1967. Bubble growth and heat transfer mechanisms in the forced convection boiling of water containing a surface active agent. Int. J. Heat Mass Transfer 10, 931– 949. Gunther, F.C., 1951. Photographic study of surface-boiling heat transfer to water with forced convection. Trans. ASME 73, 115–123. Hinze, J.O., 1959. Turbulence. McGraw-Hill, New York. Ishii, M., Chawla, T.C., 1979. Local drag laws in dispersed two-phase flow, NUREG/CR-1230, ANL-79–105. Jiji, L.M., Clark, L.A., 1964. Bubble boundary layer and temperature profiles for forced convection boiling channel flow. Trans. ASME J. Heat Transfer 86, 50–58. Kljenak, I., Park, G.C., Mavko, B., Lee, T., 2004. Simulation of subcooled nucleate boiling in a vertical annulus with a bubbletracking model. In: Proceedings of Fifth International Conference on Multiphase Flow, Paper No. 298. Lamb, H., 1932. Hydrodynamics, 6th ed. Cambridge University Press (Chapter 9). Mikic, B.B., Rohsenow, W.M., Griffith, P., 1970. On bubble growth rates. Int. J. Heat Mass Transfer 13, 657–665. Okawa, T., Torimoto, K., Nishiura, M., Kataoka, I., Mori, M., 2002a. Effects of turbulence and containing wall on rise velocities of single bubbles in a vertical circular pipe. In: Proceedings of 10th International Conference on Nuclear Engineering, Paper No. 22492. Okawa, T., Kataoka, I., Mori, M., 2002b. Numerical simulation of lateral phase distribution in turbulent upward bubbly two-phase flows. Nucl. Eng. Design 213, 183–197. Okawa, T., Tanaka, T., Kataoka, I., Mori, M., 2003. Temperature effect on single bubble rise characteristics in stagnant distilled water. Int. J. Heat Mass Transfer 46, 903–913. Okawa, T., Ishida, T., Kataoka, I., Mori, M., 2004. Proceedings of Japan-US Seminar on Two-Phase Flow Dynamics, vol. 1. Visual experimental study on the growth of vapor void fraction in subcooled flow boiling, 113–122. Okawa, T., Ishida, T., Kataoka, I., Mori, M., 2005. An experimental study on bubble rise path after the departure from a nucleation site in vertical upflow boiling. Exp. Thermal Fluid Sci. 29, 287– 294. Prodanovic, V., Fraser, D., Salcudean, M., 2002. Bubble behavior in subcooled flow boiling of water at low pressures and low flow rates. Int. J. Multiphase Flow 28, 1–19. Situ, R., Mi, Y., Ishii, M., Mori, M., 2004. Photographic study of bubble behaviors in forced convection subcooled boiling. Int. J. Heat Mass Transfer 47, 3659–3667. Thorncroft, G.E., Klausner, J.F., Mei, R., 1998. An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling. Int. J. Heat Mass Transfer 41, 3857– 3871.
T. Okawa et al. / Nuclear Engineering and Design 235 (2005) 1149–1161 Thorncroft, G.E., Klausner, J.F., 1999. The influence of vapor bubble sliding on forced convection boiling heat transfer. Trans. ASME J. Heat Transfer 121, 73–79. Tomiyama, A., Celata, G.P., Hosokawa, S., Yoshida, S., 2002. Terminal velocity of single bubbles in surface tension force dominant regime. Int. J. Multiphase Flow 28, 1497–1519. Van Helden, W.G.J., Van Der Geld, C.W.M., Boot, P.G.M., 1995. Forces on bubbles growing and detaching in flow along a vertical wall. Int. J. Heat Mass Transfer 38, 2075–2088. Warrier, G.R., Basu, N., Dhir, V.K., 2002. Interfacial heat transfer during subcooled flow boiling. Int. J. Heat Mass Transfer 45, 3947–3959.
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Weisman, J., Pei, B.S., 1983. Prediction of critical heat flux in flow boiling at low qualities. Int. J. Heat Mass Transfer 26, 1463–1477. Zeitoun, O., Shoukri, M., 1996. Bubble behavior and mean diameter in subcooled flow boiling. Trans. ASME J. Heat Transfer 118, 110–116. Zeitoun, O., Shoukri, M., 1997. Axial void fraction profile in low pressure subcooled flow boiling. Int. J. Heat Mass Transfer 40, 869–879.
Bubble rise characteristics after the departure from a nucleation site in vertical upflow boiling of subcooled water Tomio Okawa a,∗ , Tatsuhiro Ishida a , Isao Kataoka a , Michitsugu Mori b a
Department of Mechanophysics Engineering, Osaka University, 2-1 Yamadaoka, Suita-shi, Osaka 565-0871, Japan b Thermal-Hydraulics and Fluid-Structure Dynamics Research Group, Tokyo Electric Power Company, 4-1 Egasaki-cho, Tsurumi-ku, Yokohama-shi, Kanagawa 230-8510, Japan Received 13 January 2005; received in revised form 14 January 2005; accepted 16 February 2005
Abstract Rise characteristics of vapor bubbles after the departure from a nucleation site in forced convective subcooled flow boiling were studied visually using two synchronized high speed video cameras. The test section was a transparent glass tube of 20 mm in inside diameter, filtrated and deionized tap water was used as a working fluid, and the flow direction adopted was vertical upward. The outer surface of test section tube was electrically heated to generate vapor bubbles inside of the tube. In the present experiments, the mass flux and liquid subcooling were varied within 94–1435 kg/m2 s and 2.2–10 K, respectively. Since the observations were performed at low heat fluxes to avoid the significant increase in the number of active nucleation sites, the obtained bubble images were clear enough to carry out the detailed image analysis for the rise characteristics of individual bubbles. The following three different bubble rise paths were observed after the departure from nucleation sites: some bubbles slid upward the vertical wall for long distance, while other bubbles were detached from the wall after sliding for several millimeters and then migrated toward the bulk liquid; after the migration, some of the detached bubbles were collapsed in subcooled liquid but others remained close to the wall and were reattached to the wall. The results of detailed image analyses suggested that the variation in bubble shape from flattened to more rounded was of primary importance for the occurrence of bubble detachment from the wall. © 2005 Elsevier B.V. All rights reserved.
1. Introduction Forced convective flow boiling of water in a vertical channel is encountered in many industrial applications ∗ Corresponding author. Tel.: +81 6 6879 7257; fax: +81 6 6879 7247. E-mail address: [email protected] (T. Okawa).
0029-5493/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.02.012
including boilers, evaporators and nuclear reactors. It is known that the heat transfer rate and the cross-sectional area-averaged void fraction in this thermal hydraulic condition are significantly influenced by the rise characteristics of vapor bubbles after the departure from nucleation sites. Thorncroft and Klausner (1999) showed experimentally that the heat transfer rate from the heating wall is enhanced by the existence of vapor bubbles
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Nomenclature C db G g hb K Mo Nb P qw RA Tsub t u ut v xb yb
constant bubble size (m) mass flux (kg/m2 s) gravitational acceleration (m/s2 ) gap distance between bubble and wall (m) proportionality factor Morton number the number of bubbles analyzed pressure (N/m2 ) wall heat flux (W/m2 ) aspect ratio subcooling of bulk liquid (K) time from bubble incipience at nucleation site (s) velocity in the axial direction (m/s) terminal bubble rise velocity (m/s) velocity in the lateral direction (m/s) vertical distance from nucleation site to bubble centroid (m) distance from wall to bubble centroid (m)
Greek symbols µ viscosity (Pa s) ρ density (kg/m3 ) σ surface tension (N/m) Subscripts b bubble l liquid phase lift lift-off (detachment from a heating wall) r relative to the local liquid velocity x axial direction y radial direction z circumferential direction
sliding along the wall. Weisman and Pei (1983) reported that the critical heat flux at low vapor quality is correlated well in terms of the void fraction in near wall region. Since the bubble rise velocity is smaller in the near wall region than in the core region (Colin and Legendre, 2001; Okawa et al., 2002a), the crosssectional area-averaged void fraction should increase if
the bubbles slide along the wall. Furthermore, the vapor bubbles are rapidly condensed if they are detached from the wall and migrate toward the bulk liquid in subcooled flow boiling (Zeitoun and Shoukri, 1997); this also leads to the decrease in cross-sectional areaaveraged void fraction. Hence, the bubble rise characteristics after the departure from a nucleation site should be understood sufficiently to develop reliable mechanistic models for predicting the heat transfer rate and cross-sectional area-averaged void fraction in forced convective flow boiling. The rise characteristics of vapor bubbles in vertical upward flow boiling were observed extensively by many researchers. Some of the experiments were conducted in subcooled conditions (Gunther, 1951; Jiji and Clark, 1964; Frost and Kippenhan, 1967; Abdelmessih et al., 1972; Akiyama and Tachibana, 1974; Del Valle and Kenning, 1985; Bibeau and Salcudean, 1994; Zeitoun and Shoukri, 1996; Warrier et al., 2002; Prodanovic et al., 2002; Situ et al., 2004), and others in saturated or slightly subcooled conditions (Cooper et al., 1983; Van Helden et al., 1995; Thorncroft et al., 1998; Okawa et al., 2005). In these experiments, the important bubble parameters including the size, shape, growth and collapse rates, population, frequency and trajectory were measured in varied conditions of working fluid, system pressure, liquid subcooling, mass flux and wall heat flux. The influences of flow direction (Thorncroft et al., 1998), existence of surface-active agent (Frost and Kippenhan, 1967) and gravity level (Cooper et al., 1983) were also investigated. In general situations of forced convective flow boiling, there exist a number of active nucleation sites on a heating surface and consequently the effect of the interaction between bubbles should be taken into account. It is however expected that the sufficient knowledge on the behavior of single bubbles provides the insight into the more complicated phenomena encountered in practical situations. This type of approach has shown good success in the modeling of complicated gas–liquid two-phase flows (Ishii and Chawla, 1979). Despite the above described extensive experimental works, however, the bubble rise path after the departure from a nucleation site has not been thoroughly understood even in the low bubble number density conditions in which the interaction between bubbles may be neglected. In the experiments of refrigerant FC-87 by Thorncroft et al. (1998), typical bubbles slid along the
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heating surface after the departure from a nucleation site and were not detached from the wall in vertical upflow boiling. Several other observations may support this result (Gunther, 1951; Frost and Kippenhan, 1967). Prodanovic et al. (2002) conducted the bubble visualization study in subcooled flow boiling of water in a vertical annulus and reported that bubbles usually slid along the vertical heater with small number of exceptions when the heat flux is sufficiently low but they typically traveled into the liquid core after sliding for a couple of bubble diameters when the heat flux was increased. In the experiments by Okawa et al. (2005) for slightly subcooled water in a vertical round tube, typical bubbles were detached from the wall and migrated toward the bulk liquid after sliding for several millimeters. The bubble trajectories after the departure from an artificial cavity shown by Van Helden et al. (1995) also indicated the bubble detachment in the direction normal to the vertical wall. The above literature review revealed that the following two typical rise paths were observed for the vapor bubbles after the departure from nucleation sites in vertical upward flow boiling: (1) bubbles may slide upward the wall for long distance without detachment, or (2) bubbles may be detached from the wall after sliding for a certain distance and then migrate toward the bulk liquid. The heat transfer rate and the cross-sectional area-averaged void fraction in this flow configuration are considered to be influenced significantly by the difference in bubble rise path. Hence, in the present work, the key mechanisms to determine the bubble rise path are studied through visualization of bubble behavior after the departure from a nucleation site. In particular, the effect of the change in bubble shape on the occurrence of bubble detachment is investigated in detail through image analysis.
2. Experimental description Shown in Fig. 1 is a schematic of the experimental apparatus; the same apparatus was used earlier to investigate the bubble dynamics and the dependence of vapor void fraction on wall heat flux in subcooled flow boiling (Okawa et al., 2004, 2005). In the present experiments, filtrated and deionized tap water is used as a working fluid. The water is circulated by a pump. The ultrasonic flow meter that is accurate within ± 0.08 l/min
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Fig. 1. Schematic diagram of experimental apparatus.
is used to measure the volumetric flowrate. The 15 kW plug heater is used to heat up and then keep the water temperature. After exiting the pre-heating section, the water enters the vertical tube of 20 mm in inside diameter. This section consists of the two long stainless steel tubes and the short transparent glass tube between them. The glass tube is used as a test section in the experiments. The top of these tubes is connected with the header tank open to atmosphere to separate vapor bubbles from continuous liquid phase. The fluid temperatures are measured at the inlet and outlet of
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Fig. 3. Arrangement of high speed cameras and halogen light sources (top view of test section).
Fig. 2. Schematic diagram of transparent test section.
preheating section and at the outlet of test section with type-K thermocouples that are accurate within ±1.5 K. The pressure at the test section is measured with the pressure transducer that is accurate within ±500 Pa. An analog-to-digital converter attached to a personal computer records the measurements of flowrate, temperatures and pressure every 1 s. Shown in Fig. 2 is a schematic of transparent test section. The test section is the 160.0 mm long sapphire glass tube; its inner and outer diameters are 20.0 and 23.0 mm, respectively. Sapphire glass was chosen as the material for its higher thermal conductivity (32.4 W/m K at 400 K). The region of 12.2 mm in width and 100.0 mm in length on the outer surface of glass tube is coated with the thin indium tin oxide (ITO) film. The film thickness is estimated 200 nm. Both ends of the ITO coated section are covered by nickel films that are used as electrodes. The resistance of ITO film is approximately 340 and it is electrically heated with 5 kW dc power supply to generate vapor bubbles on the inner surface of the test section tube. A digital multi
meter measures the voltage and electric current with the uncertainties of ±0.1 V and ±2.3 mA, respectively. The uncertainty in the heat supplied to the test section is less than ±0.5%. In the present experiments, however, the test section is not thermally insulated for visual observation. The heat loss to ambient air is estimated to within 2%. The successive bubble images are obtained using two high-speed digital video cameras. The arrangement of cameras and illuminating lights is schematically shown in Fig. 3. To reduce the effect of refraction on a bubble image, the glass tube is surrounded by a rectangular glass jacket and the gap between the tube and jacket is filled with silicone oil. The effect of refraction still remaining is corrected from the images of a specially designed acrylic piece inserted in the test section. Images with a spatial resolution of 512 × 128 pixels are recorded every 0.25 ms; the spatial resolution is approximately 60 m and the shutter speed is set at 0.125 ms. Prior to the boiling experiments, the radial velocity profiles of single-phase liquid flow in the test section were measured using spherical polyester particles as tracers. The diameter and specific gravity of a particle were 0.2–0.4 mm and 1.04, respectively. In the singlephase experiments, the volumetric flux and liquid tem-
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perature were varied within 0.5–2.0 m/s and 30–37 ◦ C, respectively. The measured radial distributions of axial time-averaged liquid velocity agreed with the expression by Nunner for fully developed turbulent flow (Hinze, 1959) within ±5%. The tracer particles were removed from the experimental loop using a filter for the boiling experiments. In the visualization tests of vapor bubbles, mass flux and liquid temperature are controlled by adjusting the flow control valves and the power applied to the preheater, respectively. After steady state is established, dc power is applied to the ITO film coated on the test section tube. The power to the test section is increased until vigorous boiling is observed at several nucleation sites to eliminate the effect of boiling hysteresis. The dc power is then reduced until the number of bubbles in the test section becomes sufficiently small to observe visually the rise characteristics of individual bubbles. Once successive bubble generation at several nucleation sites is confirmed, the bubble images from the two directions are recorded using the synchronized high-speed cameras.
3. Results and discussion Table 1 summarizes the 14 experimental conditions considered in this work. The test section pressure P was within 121–127 kPa and slightly higher than the Table 1 Summary of experimental conditions Exp. no.
P (kPa)
Tsub (K)
G (kg/m2 s)
qw (kW/m2 )
11 12 13 14 15 21 22 23 24 25 31 32 33 34
125 125 125 126 127 125 125 125 126 127 121 121 121 122
2.2–2.3 2.3–2.5 2.6–2.8 2.9–3.2 3.2–3.4 5.0–6.1 5.8–5.9 6.1 5.9–6.0 5.6–5.9 8.6–9.4 9.7–10 9.2–9.6 9.8
94–99 280–286 560–576 950–957 1431–1435 94–98 288–289 573–576 940–953 1420–1431 99–103 274–280 565–568 947
54–111 112–167 127–223 186–278 231–279 51–113 91–169 135–225 189–282 234–338 63–170 91–171 143–230 230
7 7 22 25 19 17 22 23 16 13 20 10 3 4
Total
121–127
2.2–10
94–1435
54–338
208
Nb
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Fig. 4. Definitions of instantaneous bubble parameters.
atmospheric pressure mainly due to the static head. The liquid subcooling Tsub was defined from the fluid temperature measured at the outlet of test section tube and varied within 2.2–10 K. The range of mass flux G was 94–1435 kg/m2 s. Bubble images were recorded at several wall heat fluxes under the similar conditions of Tsub and G. Image analysis was performed manually to deduce the bubble dimension in the three directions dbx , dby , dbz , the vertical distance from nucleation site to bubble centroid xb , the distance from the wall to bubble centroid yb and the gap distance between the bubble and wall hb . The definitions of these instantaneous bubble parameters are shown schematically in Fig. 4. 3.1. Qualitative descriptions of bubble rise characteristics In the present experiments, the three typical bubble rise paths were observed. Some bubbles slid upward the vertical wall and were not detached from the heating surface within the viewing area. The consecutive images of a typical sliding bubble are depicted in Fig. 5(a) and (b). On the other hand, other bubbles were detached from the wall after sliding upward for 1–10 mm and then migrated toward the subcooled bulk liquid. Some of the detached bubbles reversed the direction of lateral migration and then reattached to the wall but other detached bubbles were collapsed due to
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Fig. 5. Consecutive images of a typical sliding bubble (exp. no. 15; qw = 231 kW/m2 ; time interval is 2 ms). (a) Camera A, (b) camera B.
the condensation in subcooled liquid. Hereafter, these bubbles are called bouncing and collapsing bubbles, respectively. The consecutive images of typical bouncing and collapsing bubbles are depicted in Figs. 6 and 7. Even when a bubble is sliding along the wall, a bubble is expected to be separated from the wall by a thin liquid film. This implies that the occurrence of bubble detachment is slightly uncertain. In this work, bubbles were classified as detached bubbles (bouncing or collapsing bubbles) if the gap distance hb exceeded 0.1 mm. Shown in Fig. 8 are the time series of db and hb for the three bubbles depicted in Figs. 5–7; here, the bubble
Fig. 6. Consecutive images of a typical bouncing bubble (exp. no. 14; qw = 186 kW/m2 ; time interval is 2.5 ms). (a) Camera A, (b) camera B.
size db is estimated by db = 3 dbx dby dbz
(1)
All the bubbles experienced rapid growth during the short period immediately after the incipience at nucleation sites. The size of sliding bubble became fairly constant after the rapid growth. Most of the bouncing bubbles remained close to the wall but their sizes were decreased gradually after the detachment; the decreasing rate depended significantly on Tsub . The size of bouncing bubbles increased again after the reattachment to the heating wall, though several bouncing bub-
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Fig. 7. Consecutive images of a typical collapsing bubble (exp. no. 23; qw = 135 kW/m2 ; time interval is 2.5 ms but it is reduced to 1.25 ms only between the last two images). (a) Camera A, (b) camera B.
Fig. 8. Evolutions of bubble size and gap distance between bubble and wall.
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Fig. 9. Evolutions of bubble dimension in the three directions. (a) Sliding bubble, (b) bouncing bubble, (c) collapsing bubble.
bles showed rebounding motion after the reattachment. The behavior of a collapsing bubble was similar to that of a bouncing bubble but it disappeared before the reattachment to the wall. At low liquid subcooling, some of the detached bubbles could stay in the subcooled liquid core for long time due to the small condensation rate and did not disappear within the viewing area. These bubbles were also classified as collapsing bubbles. The time series of dbx , dby , dbz for the same bubbles are depicted in Fig. 9(a)–(c), respectively. Immediately after the incipience, dbx and dbz are fairly equal but dby
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Fig. 10. Evolutions of bubble rise velocity.
is much smaller; dby then approaches to dbx and dbz . This implies that these bubbles were flattened along the vertical wall within the initial stage but then became more rounded. It is interesting to note that the bubbles were nearly spherical at the onset of detachment in Fig. 9(b) and (c). The time series of ub and ul are depicted in Fig. 10. The bubble rise velocity ub was derived from the vertical displacement of bubble centroid and the local liquid velocity ul was estimated at the bubble centroid using the radial velocity profile of fully developed turbulent pipe flow by Nunner (Hinze, 1959). The figure indicates that upward migration of bubbles began immediately after the incipience and the bubble rise velocities became comparable with local liquid velocity within 1 ms. Since the bubbles stayed at the nucleation sites for very short period, it was difficult to detect the departure of a bubble from a nucleation site under the present experimental conditions. The figure also indicates that the rise velocity of collapsing bubble increased remarkably during the condensation period; the increase in bubble rise velocity was a common feature during the rapid condensation. 3.2. Bubble behavior during the sliding stage The variations of several bubble parameters during the sliding stage before the detachment are investigated in this section. Immediately after the incipience, all the bubbles grew rapidly and began to slide upward the vertical heating wall. For the diffusion-controlled region, Foster and Zuber (1954) and Mikic et al. (1970) expressed the growth of a vapor bubble close to a heating
Fig. 11. Evolutions of bubble size.
surface by √ db = Kt
(2)
For all the bubbles analyzed, the dependence of db /db,cal on t before the onset of detachment is depicted in Fig. 11, where db,cal denotes the bubble size calculated by Eq. (2). In order to determine the time from incipience t for the first image of each bubble and the value of proportionality factor K, Eq. (2) is assumed valid in the present experimental conditions and the least-square method is applied to the experimental data of db for the first three bubble images. Fig. 11 indicates that the growth rate is fitted with Eq. (2) fairly well within the initial stage immediately after the incipience, though it is generally overestimated when t is greater than 1 ms since bubbles are partly exposed to the subcooled liquid core. To investigate the variation of bubble shape, dby and dbz are plotted against dbx in Fig. 12(a). It is confirmed that bubbles were generally flattened along the vertical heating wall during the sliding stage in the present experiments. Since dbx and dbz were fairly equal, the aspect ratio of a bubble RA is defined by RA =
2dby dbx + dbz
(3)
The variations of RA with t are shown in Fig. 12(b). In all the experimental conditions, RA was approximately within 0.35–0.55 right after the incipience and then approached to unity. Since the bubble size in the first image of each bubble was not large enough to measure RA accurately, the value of RA measured in the second image is plotted against G in Fig. 12(c) to elucidate the influences of G and Tsub on RA within the initial stage. The figure indicates that G and Tsub have no
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significant influence on RA in the present experimental conditions. Rapidity of the change in bubble shape dRA /dt within the sliding stage is plotted against db in Fig. 12(d). It is found that dRA /dt is roughly propor−3/2 tional to db . It is known that the frequency of the shape oscillation caused by the surface tension force to the initially ellipsoidal bubble is also proportional inversely to the bubble size to the three halves power (Lamb, 1932). The results shown in Fig. 12(d) hence suggest that the change in bubble shape from flattened to more rounded observed during the sliding stage was caused primarily by the surface tension force. The instantaneous bubble rise velocities relative to the local liquid velocities estimated at the bubble centroids ur are plotted against db in Fig. 13. Okawa et al. (2003) showed experimentally that the bubble rise velocity in stagnant high temperature water is influenced by the method of bubble generation and the upper and lower boundaries of terminal rise velocity ut are approximated if the parameter n is set at 1.35 and 0.55 in the following empirical correlation by Fan and Tsuchiya (1990): −n −1/n ρ gd 2 −n 2.4σ gdb l b ut = (4) + + Kb µl ρl db 2 where Kb is the function of Morton number Mo (Kb = max(12, 14.7Mo−0.038 )). Fig. 13 depicts that the relative velocity of sliding bubbles ur in the present subcooled flow boiling experiments are much smaller than the terminal bubble rise velocity ut in infinite stagnant high temperature water. The reduction of bubble rise velocity may be attributed to the steep liquid veloc-
Fig. 12. Bubble shape within the sliding stage. (a) Bubble dimensions in the three directions, (b) evolutions of aspect ratio, (c) aspect ratio immediately after the incipience, (d) effect of bubble size on the rapidity of the variation in bubble shape. Fig. 13. Bubble rise velocity relative to the local liquid velocity during the sliding stage.
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ity profile in the proximity of the vertical wall (Okawa et al., 2002b) or the difference in bubble shape from that in infinite stagnant liquid (Tomiyama et al., 2002). Further studies are considered necessary to develop a reliable model for the interfacial force acting on these bubbles sliding along the wall. 3.3. Bubble behavior at the detachment from a vertical heating wall Experimental information on the bubble behavior at the detachment from a heating wall is of importance in the mechanistic modeling of subcooled flow boiling (Kljenak et al., 2004). In the present experimental observations, bubbles were detached from the vertical heating surface after the change in bubble shape from flattened to more rounded. If the bubble shape varies from flattened to more rounded within the sliding stage, liquid flow directing toward the bubble base is induced between the bubble and wall as illustrated in Fig. 14. It is hence probable that the bubbles were lifted from the vertical heating wall by the inertia of the liquid flow induced beneath the bubble. The test section pressure and consequently the fluid properties were fairly constant in the present experiments. It is hence considered that smaller bubbles experienced more rapid shape change and were detached from a heating wall within a shorter period since the surface tension force is inversely proportional to the radius of interface curvature. Since the bubble size is not constant within the sliding stage, the proportionality factor K defined in Eq. (2) is used as the parameter de-
Fig. 14. Supposed mechanism of the bubble detachment from a vertical heating wall.
noting the bubble size. The time from incipience to detachment tlift and the lift-off diameter db,lift are plotted against K in Fig. 15(a) and (b), respectively. It is confirmed that tlift and db,lift increase monotonously with the increase in K. Since tlift and db,lift are collapsed well with K, the surface tension force is expected to play important role for the bubble detachment in the present experimental conditions. Fig. 15(b) indicates that the lift-off diameter db,lift decreases slightly with the increase in Tsub . This may be because the growth rate after the rapid growth within the initial stage decreases with the increase in Tsub . The aspect ratio at the detachment RA,lift is plotted against db,lift in Fig. 15(c). It is found that RA,lift increases with db,lift but most bubbles were nearly spherical at the detachment. The lateral bubble migration velocity at the detachment vb,lift are plotted against db,lift in Fig. 15(d). Since accurate measurement of instantaneous bubble velocity in the direction normal to the wall was difficult, vb,lift was estimated from the lateral bubble displacement within 2 ms prior to the detachment. There exists significant scattering but vb,lift is roughly proportional −1/2 to db,lift as expected, since the lateral bubble migration within the sliding stage is mainly caused by the change in bubble shape from flattened to rounded and −3/2 dRA /dt is roughly proportional to db as depicted in Fig. 12(d). The bubble rise paths observed in the present experiments are plotted in the G–Tsub map in Fig. 16. The sliding bubbles were observed in high mass flux conditions. The lowest mass flux required to obtain sliding bubbles increases with the increase in Tsub . This tendency may be interpreted as follows. The inertia of liquid flow induced by the change in bubble shape lifts the bubble while the shear lift force pushes the bubble against the wall. Since the gradient of radial liquid velocity profile and consequently the shear lift force acting on a bubble increase with the increase in G, sliding bubbles are more frequently observed under high mass flux conditions. At the lowest mass flux, not only the sliding bubbles but also the bouncing bubbles were rarely observed; this may support that the bubbles were pushed against the wall by the shear lift force. The increase in Tsub leads to the retardation of bubble growth and consequently to the faster variation in bubble shape. This may be one of the main reasons why larger mass flux was needed to prevent the bubble detachment in higher subcooling experiments.
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Fig. 16. Observed bubble rise paths in G–Tsub map.
4. Conclusions The bubble visualization study was conducted in vertical upflow boiling of subcooled water to reveal the following features of bubble rise characteristics after the departure from a nucleation site in the present experimental setup:
Fig. 15. Bubble parameters at the detachment from a vertical heating wall. (a) Bubble lift-off time from the incipience, (b) bubble size, (c) bubble aspect ratio, (d) bubble migration velocity in the lateral direction.
(1) Immediately after the incipience, bubbles grew rapidly and departed from the nucleation sites by sliding upward the vertical heating wall. The growth rates in the initial stage were consistent with available theories and fitted fairly well if the bubble size was assumed proportional to the square root of the time from incipience; the growth rate then decreased gradually likely due to the partial exposure to subcooled liquid core. The bubbles were accelerated rapidly after the incipience and the rise velocity became comparable with local liquid velocity within 1 ms. (2) Bubbles were initially flattened along the vertical wall and then became more rounded while sliding on the heating surface. The variations of bubble aspect ratio with respect to time were roughly proportional to the inverse of bubble size to the
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three halves power, suggesting that the change in bubble shape was primarily caused by the surface tension force. During the sliding phase, the bubble rise velocity relative to the local liquid velocity was smaller than the terminal bubble rise velocity in infinite stagnant high temperature water. (3) After sliding for several millimeters, some bubbles kept sliding along the wall for long distance, while other bubbles were detached from the wall and then migrated toward the bulk liquid. Some of the detached bubbles reversed the direction of lateral migration and then reattached to the wall but other detached bubbles were collapsed due to the condensation in subcooled liquid. Since the bubble shape was varied from flattened to more rounded during the sliding phase prior to the detachment, surrounding liquid was expected to flow directing toward the bubble base. It was considered that the inertia of local liquid flow induced beneath the bubble was the main driving force to lift the bubble from the heating wall. The lift-off time from the incipience decreased monotonously with the decrease in bubble size; this may be because the shape change became faster due to the increase in surface tension force. The sliding bubbles were more frequently observed in high mass flux conditions; at the lowest mass flux, not only the sliding bubbles but also the bouncing bubbles were rarely observed. This may indicate that the shear induced lift force was responsible to push the bubbles against the wall and to prevent the bubble detachment. References Abdelmessih, A.H., Hooper, F.C., Nangia, S., 1972. Flow effects on bubble growth and collapse in surface boiling. Int. J. Heat Mass Transfer 15, 115–125. Akiyama, M., Tachibana, F., 1974. Motion of vapor bubbles in subcooled heated channel. Bull. JSME 17, 241–247. Bibeau, E.L., Salcudean, M., 1994. A study of bubble ebullition in forced-convective subcooled nucleate boiling at low pressure. Int. J. Heat Mass Transfer 37, 2245–2259. Colin, C., Legendre, D., 2001. Bubble distribution in turbulent shear flows: experiments and numerical simulations on single bubbles. In: Proceedings of Fourth International Conference on Multiphase Flow, Paper No. 449. Cooper, M.G., Mori, K., Stone, C.R., 1983. Behaviour of vapor bubbles growing at a wall with forced flow. Int. J. Heat Mass Transfer 26, 1489–1507.
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