**1. Introduction**

462 Mechanical Engineering

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55, 107-108, 161-162, 189-191, 245-246

It has been known that the collapse of the cavitation bubbles could cause serious destruction of pressure pipes, hydraulic machineries and turbine structures. After the cavitation bubble is generated, the variation of its surrounding velocity and pressure field could result in its collapse. If the process of the collapse of a cavitation bubble appears near the solid boundary, its impact to the boundary could generate an immense water-hammer pressure effect (Plesset and Chapman, 1971). The shock wave generated in this process of bubble collapse could possibly impact or even destroy the solid boundary of structure. The bubble collapse studies include the understanding of the shock wave, the characteristics of the resultant luminescence, and the jet related fields. If the cavitation bubble is located near the solid boundary at certain suitable distance, it is more possible for the production of counterjet in the process of bubble collapse. There has not been a firm conclusion for the exact characteristics which causes the destruction of the interface on the solid boundary.

Rayleigh (1917) studied the corrosion of high speed blade subjected to the effect of cavitation bubble. He mentioned that the bubble collapse is able to produce a high speed flow jet which damages the solid surface. Plesset (1949) further considered the influence of the physical characteristics of fluid viscosity and surface tension and derived the Rayleigh-Plesset equation. Kornfeld and Suvorov (1944) brought up the theory of bubble collapse near a solid boundary. They proposed that the bubble would be deformed to a nonspherical shape with the bubble surface tension penetrated subsequently to generate the phenomenon of flow jet. This phenomenon was proved in the experiment carried out by Naude and Ellis (1961). The numerical model in Plesset and Chapman's research (1971)also revealed this phenomenon. If the solid boundary is located on the right side of the bubble, the jet flow would be formed on the left side of the bubble and penetrates it before arriving at the right side interface of the bubble. The damage of the solid boundary might be caused by the impact of this jet flow during the bubble collapse. Benjamin and Ellis(1966)and Philipp and Lauterborn (1998) also detected the bubble collapse phenomenon and its consequent behavior of damage at the solid boundary. Recent research results reveled that the destructive power of the jet flow was not the main factor for the damage of the solid

Experimental Study on Generation

of Single Cavitation Bubble Collapse Behavior by a High Speed Camera Record 465

collapse time. If the solid boundary condition is put into consideration, a greater bubble collapse time is required. Generally the size of the cavitation bubble produced in the laboratory is about 1.5 mm in radius. Under ambient temperature, the bubble collapse time ranges from 100 s ~ 200 s . It is not easy to generate cavitation bubbles for their small volumes, short collapse time, and complicated flow fields; all of which contribute to a great difficulty of the measurement. In order to record and analyze the characteristics of the flow field of the bubble collapse, common experimental setup includes a high speed camera with framing rates ranging between several thousand to 100 million frames per second. Some researchers used the method of particle image velocimetry (PIV) to measure the velocity flow field of the process of bubble collapse (Vogel et al., 1989). However since the volume of the bubble was small and its collapse time was too short, only a rough sketch of the flow field was obtained. Lawson et al. (1999) applied the PIV method to measure the flow filed of the collapse of a 80 mm diameter rubber balloon and compared it with the numerical simulation. Although these results obtained agreement, there is great discrepancy between the flow field features of the collapse of a balloon and a bubble. Jaw et al. (2007) obtained sound experimental results using soap bubbles filled with smog particle and applied the PIV method to measure flow fields at different phases during the process of bubble collapse.

In laboratory, a single cavitation bubble could be generated in a test tube using a high energy laser beam to focus on a single point (Lauterborn, 1972). In the following years, many related studies utilized this method to generate a single cavitation bubble. Since these bubbles were generated by the high energy laser beam which causes fluid aeration, it was restricted by the strength of the energy provided by the laser. Usually the bubble created using this method has small volume with 1.5 mm in radius. In addition, the inside pressure of the bubble was not equivalent to the vapor pressure at ambient temperature. Moreover, since the bubbles were formed by fluid aeration which parted the fluid molecules, there is no re-congealable vapor inside the bubbles to repeat the experiment. Some other researchers used the method of electrolysis to generate a bubble on a platinum electrode at the bottom of a box. However, this method has a defect of disturbing the flow field during the bubble collapse. Another method for forming the bubble is through the use of a needle to inject air into the test tube before using a lithotripter to generate a shock wave up to 94 MPa to break the bubble (Philipp et al.1993). Sankin et al.(2005) also used a lithotripter to generate a 39 MPa shock wave to break the laser induced bubble in order to measure the flow field of the

From the paper reviews presented above, it is perceived that the cavitation bubble collapse flow is very difficult to measure due to the facts that the bubble size is small, the collapse time is very short, and the flow induced is very complicate. In addition, as mentioned before, the bubble generated by the optical breakdown is different from a true cavitation bubble. A cavitation bubble containing re-condensable vapor, when collapsed, will produce greater energy than the ones without re-condensable vapor (Zhu and Zhong, 1999). To resolve these problems, a simpler method for the generation of a true cavitation bubble is proposed in this study. By rotating a L tube filled with tap water, a single cavitation bubble is generated and stayed at the center of the rotational axis due to the effect of centrifugal force. The cinematographic analysis of bubble collapse flows induced by pressure waves of different strengths can thus be performed easily. By lowering the strength of the pressure wave, the bubble collapsed in a longer period of time, the characteristics of the true

interaction between the bubble collapse and the shock wave.

boundary. However, the jet flow influence which causes the collapse of the bubble is still an important element for the research of the hydrodynamics of the flow field.

Rayleigh (1917) first analyzed the theoretical pressure variation of the flow field of the bubble collapse. The bubble collapse results in a very high pressure, forming a shock wave which is sent towards the outside of the bubble. Harrison (1952) in his experimental results proved the existence of a noise generated by the collapse of bubble at its surrounding rigid boundary. Vogel and Lauterborn (1988) found a close relationship between the strength of the wave pulse and the distance between the position of the bubble and the rigid boundary. This wave pulse could then generate a series of shock waves. This phenomenon was studied and revealed in the experiments carried out by Tomita and Shima (1986); Ward and Emmony (1991) ; Ohl et al.; Shaw et al. (1995); Lindau and Lauterborn (2003).

Light could be emitted in the process of the bubble collapse when the volume of the bubble is compressed to its minimum radius during which the gas inside is heated in a heatinsulated process. For bubbles under low viscosity and high pressure, it is easier for the emission of light. This is because at high viscosity, the time for bubble collapse is increased and the gas inside is not heated to the sufficient temperature to emit light. Ohl et al. (1998) also found the emission of light near the solid boundary under specific conditions in the process of bubble collapse. This phenomenon is called the "Single Cavitation Bubble Luminescence (SCBL)". Buzukov and Teslenko (1971) and Akmanov et al. (1974) also had similar research reports.

Counter jet could be generated when the bubble is located near the solid boundary. The initial formation and increment of the size of the counter jet is very rapid and it could exist for a while. Experiments related to the counter jet are found in Harrison (1952) and Kling and Hammitt's (1972) researches but it is until Lauterborn (1974) who first described the counter jet phenomenon. There has not been a final conclusion for the cause of the generation of the counter jet. Counter jet did not appear in the numerical simulations carried out by Best (1993); Zhang et al. (1993); Blake et al. (1997). However, it appeared in the experiments carried out by Tomita and Shima (1986); Vogel et al. (1989); Ward and Emmony (1991); Philipp and Lauterborn (1998); Kodama and Tomita (2000). The discrepancy between the numerical simulations and the experimental results leads to the assumption that the counter jet flow field is not part of the bubble collapse process. Its formation might be generated by a complicated mechanism in the fluid during the bubble collapse. For example, if the bubble is in contact with the solid boundary, the counter jet would not be generated. The shock wave generated appears at the final stage of the process of bubble collapse. Since the counter jets also appear at the final stage of the bubble collapse, there are speculations for their possible formation due to the shock wave structure.

According to Rayleigh's equation, when the effect of the surrounding solid boundary is excluded, the relationship between the time of bubble collapse and its radius is:

$$\mathbf{R}\_{\text{max}} = 1.09 \sqrt{\frac{\mathbf{p} - \mathbf{p}\_{\text{v}}}{\rho}} \,\mathrm{t}\_{\text{c}} \tag{1}$$

where Rmax is the maximum radius, p and ρ are the pressure of the flow field and the fluid density at ambient temperature respectively, pv is the vapor pressure, ct is the bubble

boundary. However, the jet flow influence which causes the collapse of the bubble is still an

Rayleigh (1917) first analyzed the theoretical pressure variation of the flow field of the bubble collapse. The bubble collapse results in a very high pressure, forming a shock wave which is sent towards the outside of the bubble. Harrison (1952) in his experimental results proved the existence of a noise generated by the collapse of bubble at its surrounding rigid boundary. Vogel and Lauterborn (1988) found a close relationship between the strength of the wave pulse and the distance between the position of the bubble and the rigid boundary. This wave pulse could then generate a series of shock waves. This phenomenon was studied and revealed in the experiments carried out by Tomita and Shima (1986); Ward and

Light could be emitted in the process of the bubble collapse when the volume of the bubble is compressed to its minimum radius during which the gas inside is heated in a heatinsulated process. For bubbles under low viscosity and high pressure, it is easier for the emission of light. This is because at high viscosity, the time for bubble collapse is increased and the gas inside is not heated to the sufficient temperature to emit light. Ohl et al. (1998) also found the emission of light near the solid boundary under specific conditions in the process of bubble collapse. This phenomenon is called the "Single Cavitation Bubble Luminescence (SCBL)". Buzukov and Teslenko (1971) and Akmanov et al. (1974) also had

Counter jet could be generated when the bubble is located near the solid boundary. The initial formation and increment of the size of the counter jet is very rapid and it could exist for a while. Experiments related to the counter jet are found in Harrison (1952) and Kling and Hammitt's (1972) researches but it is until Lauterborn (1974) who first described the counter jet phenomenon. There has not been a final conclusion for the cause of the generation of the counter jet. Counter jet did not appear in the numerical simulations carried out by Best (1993); Zhang et al. (1993); Blake et al. (1997). However, it appeared in the experiments carried out by Tomita and Shima (1986); Vogel et al. (1989); Ward and Emmony (1991); Philipp and Lauterborn (1998); Kodama and Tomita (2000). The discrepancy between the numerical simulations and the experimental results leads to the assumption that the counter jet flow field is not part of the bubble collapse process. Its formation might be generated by a complicated mechanism in the fluid during the bubble collapse. For example, if the bubble is in contact with the solid boundary, the counter jet would not be generated. The shock wave generated appears at the final stage of the process of bubble collapse. Since the counter jets also appear at the final stage of the bubble collapse, there are speculations

According to Rayleigh's equation, when the effect of the surrounding solid boundary is

<sup>v</sup> max <sup>c</sup>

where Rmax is the maximum radius, p and ρ are the pressure of the flow field and the fluid density at ambient temperature respectively, pv is the vapor pressure, ct is the bubble

p p R 1.09 t (1)

excluded, the relationship between the time of bubble collapse and its radius is:

important element for the research of the hydrodynamics of the flow field.

Emmony (1991) ; Ohl et al.; Shaw et al. (1995); Lindau and Lauterborn (2003).

for their possible formation due to the shock wave structure.

similar research reports.

collapse time. If the solid boundary condition is put into consideration, a greater bubble collapse time is required. Generally the size of the cavitation bubble produced in the laboratory is about 1.5 mm in radius. Under ambient temperature, the bubble collapse time ranges from 100 s ~ 200 s . It is not easy to generate cavitation bubbles for their small volumes, short collapse time, and complicated flow fields; all of which contribute to a great difficulty of the measurement. In order to record and analyze the characteristics of the flow field of the bubble collapse, common experimental setup includes a high speed camera with framing rates ranging between several thousand to 100 million frames per second. Some researchers used the method of particle image velocimetry (PIV) to measure the velocity flow field of the process of bubble collapse (Vogel et al., 1989). However since the volume of the bubble was small and its collapse time was too short, only a rough sketch of the flow field was obtained. Lawson et al. (1999) applied the PIV method to measure the flow filed of the collapse of a 80 mm diameter rubber balloon and compared it with the numerical simulation. Although these results obtained agreement, there is great discrepancy between the flow field features of the collapse of a balloon and a bubble. Jaw et al. (2007) obtained sound experimental results using soap bubbles filled with smog particle and applied the PIV method to measure flow fields at different phases during the process of bubble collapse.

In laboratory, a single cavitation bubble could be generated in a test tube using a high energy laser beam to focus on a single point (Lauterborn, 1972). In the following years, many related studies utilized this method to generate a single cavitation bubble. Since these bubbles were generated by the high energy laser beam which causes fluid aeration, it was restricted by the strength of the energy provided by the laser. Usually the bubble created using this method has small volume with 1.5 mm in radius. In addition, the inside pressure of the bubble was not equivalent to the vapor pressure at ambient temperature. Moreover, since the bubbles were formed by fluid aeration which parted the fluid molecules, there is no re-congealable vapor inside the bubbles to repeat the experiment. Some other researchers used the method of electrolysis to generate a bubble on a platinum electrode at the bottom of a box. However, this method has a defect of disturbing the flow field during the bubble collapse. Another method for forming the bubble is through the use of a needle to inject air into the test tube before using a lithotripter to generate a shock wave up to 94 MPa to break the bubble (Philipp et al.1993). Sankin et al.(2005) also used a lithotripter to generate a 39 MPa shock wave to break the laser induced bubble in order to measure the flow field of the interaction between the bubble collapse and the shock wave.

From the paper reviews presented above, it is perceived that the cavitation bubble collapse flow is very difficult to measure due to the facts that the bubble size is small, the collapse time is very short, and the flow induced is very complicate. In addition, as mentioned before, the bubble generated by the optical breakdown is different from a true cavitation bubble. A cavitation bubble containing re-condensable vapor, when collapsed, will produce greater energy than the ones without re-condensable vapor (Zhu and Zhong, 1999). To resolve these problems, a simpler method for the generation of a true cavitation bubble is proposed in this study. By rotating a L tube filled with tap water, a single cavitation bubble is generated and stayed at the center of the rotational axis due to the effect of centrifugal force. The cinematographic analysis of bubble collapse flows induced by pressure waves of different strengths can thus be performed easily. By lowering the strength of the pressure wave, the bubble collapsed in a longer period of time, the characteristics of the true

Experimental Study on Generation

bubble generation.

depth difference.

of Single Cavitation Bubble Collapse Behavior by a High Speed Camera Record 467

the highly sensitive pressure sensor that measures the shock wave pressure at different strengths during the process of the single bubble collapse (shown at the upper part of Figure 1). On the other hand, the cavitation bubble generation takes place at the site on the platform of the rotational axis where the pressure is at the lowest. Therefore, the transparent cylindrical tube must be located across the center of the rotational axis for easier cavitation

During the experiment of generating a single cavitation bubble, the transparent cylindrical tube on the U-shape platform is filled with tap water shown in Figure 2. The surface of the fluid at the part of the vertical forearm tube is in touch with air with one atmosphere pressure. Therefore, the center location of the L tube at initial condition has a hydrostatic pressure of p0

 p0=patm+ρgΔh, (2) where patm is the atmosphere pressure, g is the acceleration of gravity, and h is the water

When the U-shape platform is rotated by the motor, the fluid is subjected to a centrifugal force resulting in a parabolic fluid pressure distribution shown as the solid line in Figure 2 at different radius. At the vertical forearm, although the h is slightly increased, the hydrostatic water pressure is still kept at one atmospheric pressure because the surface interface is still in touch with the air. Therefore, the pressure difference between the free

 Pc=ρgΔh -1/2ρr2ω2, (3) where r is the rotational radius and is the rotational velocity. When is gradually increased, the pressure at the center of the rotation in the transparent cylindrical tube is gradually decreased to a saturated vapor pressure at local present water temperature. At this condition, a single cavitation bubble at the rotational center can be generated. The

Fig. 2. The pressure distribution for a rotating U-shape platform.

surface atmospheric pressure and the pressure at the center of rotation is pc

cavitation bubble collapse flow are clearly manifested. Improvement in the further used the PIV method that can be clear revealed velocity flow field feature during the bubble collapse. The present study focuses on the investigation of the formation of the liquid jet and the counter jet, at different stand-off distances to the boundary, and their consequent influences on the bubble collapse flow.
