**3.2 Flow field measurement of bubble collapse atγ≈ 2**

As described in the introduction, the counter jet would be generated when the distance between the center of the bubble and the solid boundary is within one to three times the bubble's radius (1 < γ ≈ 3). The experiments conducted with γ≈ 2 falls within this range.

The distance from the right side of the bubble surface to the solid boundary is only one radius long. The Kelvin-Helmholtz vortex was generated after the bubble surface is broken and the jet flow is formed. This vortex would touch the solid boundary and subsequently form the stagnation ring on the solid boundary shown in the left front view diagram in Figure 5. After the stagnation ring touched the solid boundary, it was divided into two fluid flows. One of them was outside the stagnation ring splashing outwardly along the radial direction. The other fluid flow inside the stagnation ring was squeezed inwardly along the central direction to form a counter jet shown in the lower right side of the diagram in Figure 5. The preexistence of fluid between the bubble surface and the solid boundary allowed the fluid inside the stagnation ring to be squeezed towards the center

during the bubble surface was pressured to touch the solid boundary, the pressure is uniformly distributed across the tube area, the bubble deformation was approximate a symmetrical development condition. Under this condition, using a high speed camera and 2D PIV method could be obtained flow field. Figure 4 show the velocity flow field of the Kelvin-Helmholtz vortex formation process that used the PIV method to obtain flow field variation during the liquid jet to form vortex formation. The jet flow instantaneously spouted into the static fluid that cause between the jet flow and static fluid shear force difference increased, then the Kelvin-Helmholtz vortex formation is generated, as shown in Figure 4. From these series of images, the features of the cavitation bubble collapse without

Fig. 4. Exhibit the PIV measurement results at 7 . (The velocity flow field of the Kelvin-Helmholtz vortex formation process) The peak strength of the pressure wave is 155 kPa. Image interval time is 1/4000 second. The size of each individual frame is 11.0 mm 3.1 mm.

As described in the introduction, the counter jet would be generated when the distance between the center of the bubble and the solid boundary is within one to three times the bubble's radius (1 < γ ≈ 3). The experiments conducted with γ≈ 2 falls within this range.

The distance from the right side of the bubble surface to the solid boundary is only one radius long. The Kelvin-Helmholtz vortex was generated after the bubble surface is broken and the jet flow is formed. This vortex would touch the solid boundary and subsequently form the stagnation ring on the solid boundary shown in the left front view diagram in Figure 5. After the stagnation ring touched the solid boundary, it was divided into two fluid flows. One of them was outside the stagnation ring splashing outwardly along the radial direction. The other fluid flow inside the stagnation ring was squeezed inwardly along the central direction to form a counter jet shown in the lower right side of the diagram in Figure 5. The preexistence of fluid between the bubble surface and the solid boundary allowed the fluid inside the stagnation ring to be squeezed towards the center

solid boundary effect are clearly manifested.

The bubble Rmax is 2. 3 mm.

**3.2 Flow field measurement of bubble collapse atγ≈ 2** 

Fig. 5. Upper Part: The process of bubble collapse at γ≈ 2 (the Kelvin-Helmholtz vortex is indicated by a dotted line with an arrow, the counter jet indicated by a solid line with an arrow). The peak strength of the pressure wave is 250kPa. The image time interval is 1/4000 second. The size of each individual frame is 9.4mm 3.1 mm. Rmax is 2.5mm. (Lower Part: sketch of Kelvin-Helmholtz vortex forming the counter jet.

Experimental Study on Generation

The bubble Rmax is 2. 3 mm.

of Single Cavitation Bubble Collapse Behavior by a High Speed Camera Record 473

Figure 7 show image and the velocity flow field from the Kelvin-Helmholtz vortex touch to the solid boundary and transfer to form the counter jet formation which used the PIV method to obtain velocity flow field variation. After the Kelvin-Helmholtz vortex touch solid boundary, the vortex is formed a planiform shape bubble along the solid boundary, and meantime the vortex formed a radial direction outward splashed out motion, as shown in upper left image and calculation result of Figure 7. Following by the bubble on the forward stretched effect and between the bubble and solid boundary space restriction conditions, the Kelvin-Helmholtz vortex at center part splash out are restricted and caused the velocity gradually decreased to stagnation at near the solid boundary center, as shown in upper right image and calculation result of Figure 7. Finally, the stagnation ring and counter jet are formed as shown in lower image and calculation results of Figure 7. They can be clear revealed that the stagnation ring location and counter jet motion that shown in Figure 8. The stagnation ring formation is located at a turning point of the velocity vectors

Fig. 7. Exhibit the PIV measurement results at 2 . (The velocity flow field of the Kelvin-Helmholtz vortex formation process) The peak strength of the pressure wave is 260 kPa. Image interval time is 1/4000 second. The size of each individual frame is 11.0 mm 3.1 mm.

Fig. 8. The velocity flow field is the Figure 7 lower left diagram near solid boundary enlarged result that can reveal the stagnation ring location, splashing and the counter jet formation.

resulting in a counter jet. Therefore in order to generate a counter jet, the bubble should be located at γ> 1 so that there would be enough space between the bubble surface and the solid boundary.

On the other hand, after the bubble surface was penetrated to form the Kelvin-Helmholtz vortex, a zone with high velocity and low pressure was formed at the root of the central axis of the vortex where the bubble was stretched and deformed towards its right side shown in images from the first to the third rows of Figure 5. In the first image at the fifth row of Figure 5, a counter jet located at the central axis of the bubble could be clearly seen.

Many researchers who studied the counter jet have mentioned the existence of the stagnation ring. However, in these studies, the time for the collapse of the bubble was too short for the appearance of the Kelvin-Helmholtz vortex. The relationship between the stagnation ring and the Kelvin-Helmholtz vortex was still not clear. In this study, the process for the formation of the Kelvin-Helmholtz vortex and the counter jet was clearly revealed for a shock wave of lower pressure was utilized to impact the cavitaiton bubble. If the strength of the pressure wave is increased, the resultant counter jet could penetrate the cavitation bubble and subsequently separated the bubble into a number of small bubbles as shown in Figure 6. In the second image at the fourth row of Figure 6 a counter jet located at the central axis of the bubble could be clearly seen.

Fig. 6. Images of the process of bubble collapse at γ≈ 2 with image time interval of 1/4000 second. The peak strength of the pressure wave is 405 kPa. The size of each individual frame is 9.8 mm 3.1 mm (the Kelvin-Helmholtz vortex is indicated by a dotted line with an arrow; the counter jet indicated by a solid line with an arrow). Rmax is 2.5 mm.

resulting in a counter jet. Therefore in order to generate a counter jet, the bubble should be located at γ> 1 so that there would be enough space between the bubble surface and the

On the other hand, after the bubble surface was penetrated to form the Kelvin-Helmholtz vortex, a zone with high velocity and low pressure was formed at the root of the central axis of the vortex where the bubble was stretched and deformed towards its right side shown in images from the first to the third rows of Figure 5. In the first image at the fifth row of Figure 5, a counter jet located at the central axis of the bubble could be clearly seen.

Many researchers who studied the counter jet have mentioned the existence of the stagnation ring. However, in these studies, the time for the collapse of the bubble was too short for the appearance of the Kelvin-Helmholtz vortex. The relationship between the stagnation ring and the Kelvin-Helmholtz vortex was still not clear. In this study, the process for the formation of the Kelvin-Helmholtz vortex and the counter jet was clearly revealed for a shock wave of lower pressure was utilized to impact the cavitaiton bubble. If the strength of the pressure wave is increased, the resultant counter jet could penetrate the cavitation bubble and subsequently separated the bubble into a number of small bubbles as shown in Figure 6. In the second image at the fourth row of Figure 6 a counter jet located at

Fig. 6. Images of the process of bubble collapse at γ≈ 2 with image time interval of 1/4000 second. The peak strength of the pressure wave is 405 kPa. The size of each individual frame is 9.8 mm 3.1 mm (the Kelvin-Helmholtz vortex is indicated by a dotted line with an

arrow; the counter jet indicated by a solid line with an arrow). Rmax is 2.5 mm.

the central axis of the bubble could be clearly seen.

solid boundary.

Figure 7 show image and the velocity flow field from the Kelvin-Helmholtz vortex touch to the solid boundary and transfer to form the counter jet formation which used the PIV method to obtain velocity flow field variation. After the Kelvin-Helmholtz vortex touch solid boundary, the vortex is formed a planiform shape bubble along the solid boundary, and meantime the vortex formed a radial direction outward splashed out motion, as shown in upper left image and calculation result of Figure 7. Following by the bubble on the forward stretched effect and between the bubble and solid boundary space restriction conditions, the Kelvin-Helmholtz vortex at center part splash out are restricted and caused the velocity gradually decreased to stagnation at near the solid boundary center, as shown in upper right image and calculation result of Figure 7. Finally, the stagnation ring and counter jet are formed as shown in lower image and calculation results of Figure 7. They can be clear revealed that the stagnation ring location and counter jet motion that shown in Figure 8. The stagnation ring formation is located at a turning point of the velocity vectors

Fig. 7. Exhibit the PIV measurement results at 2 . (The velocity flow field of the Kelvin-Helmholtz vortex formation process) The peak strength of the pressure wave is 260 kPa. Image interval time is 1/4000 second. The size of each individual frame is 11.0 mm 3.1 mm. The bubble Rmax is 2. 3 mm.

Fig. 8. The velocity flow field is the Figure 7 lower left diagram near solid boundary enlarged result that can reveal the stagnation ring location, splashing and the counter jet formation.

Experimental Study on Generation

dotted line with an arrow).

Figure 10.

Figure 11.

of Single Cavitation Bubble Collapse Behavior by a High Speed Camera Record 475

Fig. 10. Images of the process of bubble collapse at γ ≈ 3. The peak strength of the pressure wave is 300kPa. The size of each individual frame is 9.6 mm 3.1 mm. Rmax : 2.35 mm. The image time interval is 1/4000 second. (The Kelvin -Helmholtz vortex is indicated by a

moving towards the right side until it touched the solid boundary and generated a subsequent shock wave which rebounded to produce the phenomenon of Richtmyer-Meshkov instability shown near the solid boundary in every image from the second to the third rows of Figure 10. Although the Kelvin-Helmholtz vortex could be generated under this strength of pressure wave, the vortex had already splashed and touched the surrounding solid boundary, disabling the vortex from forming the stagnation ring and the counter jet. At the end of this process, the bubble was divided by the liquid jet and the root of the vortex into two smaller bubbles shown in the images from the fifth to seventh rows in

If the strength of the pressure wave is increased to a peak value of 365 kPa, the Kelvin-Helmholtz vortex would touch the solid boundary before the formation of the stagnation ring and the counter jet. This process is shown in the image listed at the 5th and 6th rows of

near the solid boundary. The counter jet formation is located at between two stagnation rings. The above-mentioned of the PIV calculation results reveal that the stagnation ring and the counter jet formation identically with Figure 5 lower part schematic diagram.
