LUO Jing (罗晶), XU Wei-lin (许唯临)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China, E-mail: luojing901@sina.com

NIU Zhi-pan (牛志攀)

China Three Gorges Corporation, Beijing 100038, China

LUO Shu-jing (罗书靖), ZHENG Qiu-wen (郑秋文)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

Experimental study of the interaction between the spark-induced cavitation bubble and the air bubble*

LUO Jing (罗晶), XU Wei-lin (许唯临)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China, E-mail: luojing901@sina.com

NIU Zhi-pan (牛志攀)

China Three Gorges Corporation, Beijing 100038, China

LUO Shu-jing (罗书靖), ZHENG Qiu-wen (郑秋文)

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

(Received December 12, 2012, Revised January 30, 2013)

Experiments are carried out by using high-speed photography to investigate the interaction between the spark-generated cavitation bubble and the air bubble in its surrounding fluid. Three problems are discussed in detail: the impact of the air bubble upon the development of the cavitation bubble, the evolution of the air bubble under the influence of the cavitation bubble, and the change of the fluid pressure during the development of a micro jet of the cavitation bubble. Based on the experimental results, under the condition of no air bubble present, the lifetime of the cavitation bubble from expansion to contraction increases with the increase of the maximum radius. On the other hand, when there is an air bubble present, different sized cavitation bubbles have similarity with one another generally in terms of the lifetime from expansion to contraction, which does not depend on the maximum radius. Also, with the presence of an air bubble, the lifetime of the smaller cavitation bubble is extended while that of the bigger ones reduced. Furthermore, it is shown in the experiment that the low pressure formed in the opposite direction to the cavitation bubble micro jet makes the air bubble in the low pressure area being stretched into a steplike shape.

cavitation bubble, air bubble, high-speed photography, shock wave, aeration in cavitation-protection

Introduction

In places of the hydrodynamic cavitation or the ultrasonic cavitation, generated by the collapse of a cavitation bubble, shock waves scatter around the water and then interact with the nearby solid wall, the air bubble, and other cavitation bubbles. The interplay of the shock wave and the cavitation bubble therefore is a topic widely studied related with water conservancy and medical health. Kodama and Tomita[1]studied the interaction between the shock wave generated by the collapsing of the spherical cavitation bubble and the air bubble near the wall. It is shown that under the influence of the shock wave, a jet is generated inside of the air bubble and it further moves to the rigid wall after piercing the air bubble. Similarly but with some difference, Lindau and Lauterborn[2]analyzed the collapse and the rebound of the laser-generated cavitation bubble close to the wall through the high-speed photographical technique. Meanwhile, Zhang et al.[3], Brujan and Matsumoto[4], Shaw et al.[5,6], Brujan et al.[7]and Xu et al.[8], among others, did valuable experimental researches on the interaction between the cavitation bubble and the nearby rigid wall. Experimental studies were also conducted by such as Tomita et al.[9], focusing on the cavitation bubble near a curvy wall and Zhang and Lin[10]on the interaction between two cavitation bubbles through the ultra audible sound. Moreover, Akhatov et al.[11], Hu et al.[12]and Maigaand Buisine[13]conducted numerical simulations of the dynamical process of the cavitation bubble while Chahine[14]conducted numerical simulations of the interactions between cavitation bubbles in flow. In addition, Jamaluddin et al.[15]simulated the deformation of the air bubble under the impact of a shock wave as well as its corresponding jetting phenomenon. It is shown that the air bubble collapses when the shock wave is weak (P＜30MPa), but a jet of as high speed as 2 000 m/s will be generated inside of the air bubble when the shock wave is strong (500MPa

The present study considers the circumstances where a cavitation bubble is induced with a singlepulse high voltage discharge system, an air bubble is released at the same time, with the air bubble and the cavitation bubble present in the same medium, and uses a high-speed photography system to record the interplay of the cavitation bubble and the air bubble. The maximum radius of the cavitation bubblemaxRis selected to be the characteristic quantity, and the ratio of the air bubble radius at the initial stage to the cavitation bubble characteristic quantitymaxRis used as the dimensionless parameter for the air bubble. Section 1 deals with the experimental setup, the method, and experimental procedures. In Section 2, the impact of the air bubble upon the cavitation bubble radius is investigated. Section 3 investigates how the air bubble evolves under the impact of the cavitation bubble, and how the air bubble evolution discloses the distributive characteristics of the low-pressure region behind the micro jet.

Fig.1 Experiment arrangement

1. Experimental setup and method

To study the interaction between a flat-water cavitation bubble and an air bubble in its surrounding liquid, a single-pulsed high voltage discharge system is designed based on what is done in Ref.[17], as shown in Fig.1. A cavitation bubble is generated in a glass container (300 mm×150 mm×50 mm), with a temperature of 291 K and an atmospheric pressure of 101.5 KPa. In order to investigate how a cavitation bubble interacts with an air bubble, an air bubble releasing system is designed to produce air bubbles along with the cavitation bubble. It can yield enough air bubbles with desired size and location for the experiment.

A high-speed photography system, consisting of a high-speed camera, lens, illuminating device, and computer components, is used to record the whole interaction process. This includes a long-distance microscope (Zoom 6000 Navitar, USA) and a high-speed camera of Motion Xtra HG-LE (Redlake MASD Inc, USA). In view of the tiny size and the transient lifetime of cavitation bubbles and air bubbles, a Halogen cold light illuminator and the optical fiber are used to illuminate the filmed area for pronounced images.

2. Impact of air bubble upon cavitation bubble

In the early stage of a cavitation bubble, generated by putting a high-voltage pulse into water, it emits a main shock wave to the liquid, followed by its expansion stage. As soon as its radius reaches the maximum size, the contraction begins, right after which,the water promptly fills the vacancy. When a cavitation bubble collapses and reduces to its minimum size, a second shock wave is emitted, which, due to its large amount of energy, is one of the main causes for the cavitation corrosion. Thus, the first cycle of expansion and contraction is completed and the second expansion of an irregular spatial form develops.

Fig.2 Evolution of cavitation bubbles without air bubble present (photo-frequency, 10 000 fps, exposure time: 80 μs, frame size: 3.743 mm

If there is no air bubble present in the water, the medium density around the cavitation bubble is uniformly distributed. In the first cycle of expansion and contraction, the cavitation bubble remains spherical[11]. Based on a series of selected experiments, Fig.2 shows the evolution of different sized cavitation bubbles under the circumstance of no air bubble present. The cavitation bubbles a, b, c and d are in order of their maximum radii. The radius of the cavitation bubble a is smallest. Correspondingly, it takes the shortest time to expand and contract. As the radius increases, the time for expanding and contracting increases. At the moment a4of, the cavitation bubble a has completed its first cycle of expansion and contraction, while the cavitation bubbles b, c and d complete their first cycles of expansion and contraction at b5, b6and b7, respectively. Note that the rebound bubble for each cavitation bubble occurs right after its expansionand-contraction process is completed, but in a different manner, with the spatial form of these rebound bubbles being non-spherical.

Figure 3 illustrates how different sized cavitation bubbles, which are selected from a series of experiments, evolve under the circumstance of an air bubble present. For each picture, the bubble on the left is the air bubble, and on the right is the cavitation bubble, andmaxRincreases in order from the bubble a to the bubble b. It can be seen that the process of expansion and contraction is similar, and a rebound bubble is also generated. Note that during the expansion, the water travels outwards. As a result of the distributive nature of the medium density around the cavitation bubble, the expansion becomes somehow irregular. As is seen in Fig.3, before the 4th column is the expansion stage, and after that is the contraction stage, the collapse happens in the 5th column, and the rebound bubbles of various size occur from the bubbles b to e in the 6th column. Even though they are similar in the spatial evolution to the cases when no air bubble is present, here we see differences in many ways.

Figure 4 and Fig.5 show how the radius changes over time without and with an air bubble present, respectively, as determined from Fig.2 and Fig.3. As is shown, the cavitation bubbles appear to be non-spherical when there is an air bubble present, and their radii are measured from where the bubble center line and the cavitation bubble boundary intersect to the centerof the cavitation bubble. As is clearly shown in the figures, it takes more time for bigger cavitation bubbles to expand and contract when no air bubble exists, less time for smaller ones. Before the time of 200 μs, the cavitation bubbles are similar between one another in the expanding velocity, which decreases as the cavitation bubbles evolve. On the other hand, when there is an air bubble present, the bigger cavitation bubbles expand faster than the smaller ones, and before the time of 200 μs, the expansion velocities see notable differences. Then before reaching their maximum radii, the cavitation bubbles in the presence of air bubbles hardly change in the expansion velocity, which is different from the case with no air bubbles present, where the velocity is decreasing . When there is an air bubble present, all cavitation bubbles, bigger or smaller, take roughly the same time to contract to its minimum radius, with the bigger bubbles in faster speed, the smaller ones in slower speed.

Fig.3 Evolutions of cavitation bubbles with air bubble present (photo-frequency:10 000 fps, exposure time: 80 μs, frame size: 3.743 mm

When there is no air bubble around the cavitation bubble, the medium density is uniformly distributed and there is little difference in water’s impact on its outward development. The cavitation bubble therefore expands and contracts spherically. But when there is an air bubble, the medium around the cavitation is not uniform: the side with the air bubble is less dense thanthe side without the air bubble. Also, the applied forces from the medium differ in different directions, which accounts for the non-spherical expansion. Since the contraction force in the interior of the air bubble is stronger than that of the water outside, the air bubble is passively contracted when the water travels outward during the cavitation bubble expansion. Then, the interior force is changed which therefore buffers the expanding velocity of the cavitation bubble, which does not change notably. On the other hand, the cavitation bubble expands intensely instead of slightly with a large velocity. When the maximum radius is reached, it begins to contract along with the water which is moving towards its center. Meanwhile, the volume of the air bubble is notably changed, which thereupon buffers the liquid moving towards the bubble center. Because some cavitation bubbles are small, they have less energy, less impact upon the medium around them, and are less influenced by the air bubbles, which is exactly the opposite of what happens for the bigger cavitation bubbles. In the expanding phase, the air bubble is prone to be contracted and, correspondingly, it takes less time for the cavitation bubble to reach its maximum radius. In the contraction phase, however, because the air bubble is prone to be elongated, bigger cavitation bubbles contract to their minimum radius earlier than smaller ones, and the contraction would take notably shortened time as compared to the case when there is no air bubble. The longer the radius a cavitation bubble has, the bigger the impact an air bubble has upon the cavitation bubble. And, an air bubble will make different sized cavitation bubbles behave similarly in the expanding and contracting phases.

Fig.4 Radius changing along with time without air bubble present (the data determined from Fig.2)

Fig.5 Radius changing along with time with air bubble present (the data determined from Fig.3)

3. The impact of cavitation bubble upon air bubble

3.1Evolution of air bubble under the influence of cavitation bubble

When a cavitation bubble is near an air bubble, the main shock wave emitted at the early expanding stage acts upon the air bubble, which is then compressed. We will see a liquid jet scenario, a micro jet develops gradually at the final stage of the cavitation bubble collapse. During this evolution, the air bubble is elongated and a side view of the detailed flow field behind the micro jet is shown. Therefore, during the interplay of the sparks-induced cavitation bubbles and the air bubbles, the evolution and the movement of the air bubbles are of great significance to the study of air entrainment to alleviate the cavitation.

In order to study the evolution of the air bubbles under the impact of the cavitation bubbles, three typical cases are selected according to a series of experimental results, as shown in Fig.6. The air bubbles, which are correspondingly under the influence of the cavitation bubbles a, b and c, change in shape. A shock wave is emitted at the early stage of the cavitation bubble, and then it acts upon the air bubble which thereafter is compressed, as is indicated in the second column of Fig.6. Compared to the first column, the air bubbles near the cavitation bubbles are compressed to become flat. Consider the bubble c in particular, not only is the air bubble compressed under the influence of the shock wave, but also one sees the liquid jet scenario. It is the first bubble collapse before the 3rd column of Fig.6. Column 3 shows the shape of the air bubble after the cavitation bubble reaches its maximum radius. Against column 2, the air bubbles of column 3 are constantly compressed, decreasing in volume, all due to the liquid compression from the surrounding liquid’s outward motion, which is impelled by the expansion of the cavitation bubble. Columns 5 and 6 show the evolution of the air bubbles in the collapse stage, and Column 4 in the contraction stage. As compared to column 3, the air bubbles from columns 4 to 6 grow in volume, and those nearest to the cavitation bubble appear to be flat, which remains so even when the cavitation bubble develops to column 5.

From Fig.3 it can be seen that the some cavitation bubbles rebound after the first cycle of expansion and collapse. Then in Fig.6, the evolution of the airbubble affected by the rebound bubble is shown in the sixth and following columns. The cavitation bubbles rebound as well as expand between the 5th and 6th columns. For the three given bubbles a, b and c, the bubbles in the 6th column all are smaller than those in the 5th column. Also, a spherical frustum varied in height appears on the surface of all air bubbles near to the cavitation bubbles. Visible rebound bubbles are found at the base of the cavitation bubbles b and c of the 6th column. Then, it can be safely concluded that the spherical frustum on the surface of the air bubble develops between the 5th column and the 6th column also in the expanding phase of the rebound bubble. With the development of the cavitation bubble, the air bubbles of the 7th column in Fig.6 are all bigger than those of the 6th column. Even the height of the spherical frustum develops increasingly. Similarly, the air bubble of the 8th column grows bigger than that of the 7th column, so does the spherical frustum height.

Compared to the 8th column, the air bubbles of the 9th column all decrease in size, which is more noticeable in the cavitation bubbles b and c, with the cavitation bubble c having the most reduction. While the air bubble decreases in size, the second spherical frustum occurs on the surface of those air bubbles nearest to the cavitation bubble. Unlike the spherical frustum and the air bubble of the 8th column, the first-layer spherical frustum of the cavitation bubble b decreases in the 9th column. However, for the cavitation bubble c, not only the spherical frustum decreases in height, but also the air bubble decreases in size, and an inward dent is seen at the bottom of the first layer spherical frustum. In column 10, the first-layer spherical frustums of the cavitation bubbles a and b increase constantly in height while the parent air bubble remains flat. However, the first-layer spherical frustum of the cavitation bubble c has already broken way from its parent air bubble. The cavitation bubbles a and b in columns 11 and 12 decrease further in size, but there is no visible change of the parent air bubbles.

Fig.6 Air bubble motion under the impact of the cavitation bubble (photo-frequency:10 000f ps, exposure time: 80 μs, frame size: 3.743 mm, cavitation bubble lower side, air bubble upper side

Fig.7 Schematic diagram of the low pressure range changing with time (the 1st column shows the relative locations of cavitation bubbles at the initial moment, the 2nd column shows the expansion stage after the rebound bubble occurs, from the 3rd to 8th columns, the process of the evolution of the cavitation bubble)

3.2Discussion of the low pressure region behind the micro jet

Under the impact of a cavitation bubble, an air bubble is not only compressed by the shock wave emitted by a cavitation bubble but also is prolonged bythe micro jet generated in the contraction phase. Also, under the impact of rebound and contraction, the spherical frustum, the multilayer spherical frustum, and the separation bubble make their appearance. A conclusion can be drawn that the evolution of an air bubble can to some extent reflect the characteristics of the micro jet flow field formed at the later collapse stage of a cavitation bubble.

Figure 7 shows an auxiliary analysis drawn according to the shapes of the two typical air bubbles. The cavitation bubble reduces in volume rapidly when it develops to the contraction phase and the water quickly rushes into the vacancy. Then, a complicated micro jet flow field is formed. While the cavitation bubble is expanding, the surrounding water travels outward, which in turn pushes the air bubble, on whose surface a spherical frustum is generated. From the analysis of the air bubble shape, it is found that the low pressure region expands from the lineation of the bubble centers to the normal lines, and that the spherical frustum is gradually developed. Moreover, at the later stage of contraction, the cavitation bubbles near the air bubbles contract more intensely than others and gradually an inward dent is developed. As is shown in the 3rd column of Fig.7, the spherical frustum comes out on the surface of the air bubbles, wider than the inward dent of the cavitation bubble. By connecting the edge of the spherical frustum and the pits of the cavitation bubble dent, a higher water flow speed is obtained; the vertical low pressure range near the surface of the cavitation bubble becomes denser. With the cavitation bubble contracting further, the spherical frustum grows higher, the second layer grows wider while the first layer keeps in compression, the low presser range near the cavitation bubble contracts constantly, decreasing in height and increasing in taper angle. However, with the cavitation bubble collapsing, a rebound low pressure range develops towards the cylinder.

Fig.8 Schematic diagram of spatial transition of the low pressure region

Figure 8 shows how the low pressure range of the air bubble distributes at a certain moment of the contraction phase, which is drawn according to the shape of the two typical air bubbles. Vertically, it can be observed that the low presser range is getting denser along with the development of the micro jet, and is expanding along the central line of the air bubble. Meanwhile, horizontally, the outer flank of the pyramid becomes higher as is the range 1 in Fig.8, and the interior pressure range decreases gradually and to the lowest at the lineation of the bubble center as is the range 3 in Fig.8.

4. Conclusion

Experiments are carried out with high-speed photography to investigate the interaction between the cavitation bubble generated through a single-pulsed and high-pressured discharge system with an individual air bubble in their surrounding fluid. Focus is on the influence of the air bubble on the development of the cavitation bubble; the impacts of a cavitation bubble upon the evolution of an air bubble, and the change of the fluid pressure during the development of the micro jet. It is shown that under the condition of no air bubble present, the lifetime of the cavitation bubble from expansion to contraction increases with the increase of the maximum radius. On the other hand, when there is an air bubble present, the different sized cavitation bubbles have similarity with one another generally in terms of the lifetime from expansion to contraction, notwithstanding the different maximum radii. Also, with the presence of an air bubble, the lifetime of the smaller cavitation bubble is extended while that of the bigger ones reduced. Through analyzing the form of the air bubble in the contraction phase of the cavitation bubble, it is found that the low pressure formed in the opposite direction to the cavitation bubble micro jet makes the air bubble in the low pressure area being stretched into a steplike shape.

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10.1016/S1001-6058(13)60438-2

* Project supported by the National Key Basic Research Development Program of China (973 Program, Grant No. 2013CB035905), the National Natural Science Foundation of China (Grant No. 51179114).

Biography: LUO Jing (1983-), Male, Ph. D. Candidate

XU Wei-lin,

E-mail: xuwl@scu.edu.cn