Dynamics of the bubble near a triangular prism array

Dynamics of the bubble near a triangular prism array 1,2 Yuning Zhang*; 1,2 Shida Li; 1,2 Yongxue Zhang; 3 Yuning Zhang 1 College of Mechanical and Transportation Engineering, China University of Petroleum-Beijing, Beijing 102249, China 2 Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum-Beijing, Beijing 102249, China 3 School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China 1. Introduction Abstract The behaviors of cavitation bubbles are significantly influenced by the nearby objects. In practice, the bubble usually oscillates and collapses near complex structures. In this study, the dynamics of a laserinduced single bubble near a triangular prism array are investigated experimentally. The behaviors of the bubble, such as the collapse, the resound, and the jet formation, are revealed, which are strongly influenced by several parameters, e.g., the relative position of the bubble and the prisms, the size of the bubble and the distance between the bubble and the array. Keywords: bubble dynamics; unconventional boundaries; triangular prism array Due to its significant mechanical effects, cavitation has been applied widely in the fields of ultrasound cleaning, sonochemistry, biomedicine, and so on. Cavitation has also contributed to the damage of the materials of various fluid machineries [1]. For understanding the underlying mechanisms of these processes, the interaction between cavitation bubbles and the nearby structures is an essential issue to study. In the literature, the bubble behaviors near flat boundary [2], curved boundary [3], cylinder [4] or sphere particles [5] have been studied intensively. However, in practice, cavitation usually occurs near more complex structures, the dynamics of which have not been fully revealed yet. In present study, the dynamics of a single cavitation bubble near a triangular prism array are investigated experimentally. 2. Experimental Methods Figure 1(a) demonstrates the experimental system employed in this study. The triangular prism array was prepared by employing 3D printing technique with polylactic acid. As shown in figure 1(b), the array consisted of ten triangular prisms, of which the triangular faces are equilateral triangle with height of 2 mm, and the length of the prism is 25mm. The array was placed in a tank filled with deionized water. The single bubble was induced by a pulsed Nd:YAG laser through a focusing lens and was generated above the array. Cases with two kinds of the bubble position were investigated. As shown in figure 1(c), the center of the bubble was located right above the top vertex of the equilateral triangular. In the other condition, the center of the bubble was located right above the bottom vertex of the equilateral triangular, as shown in figure 1(d). The behaviors of the bubble was recorded by a high speed camera (Phantom V1212) operated at 200,000 frames per second. L represents the distance between the horizontal line crossing the bubble center and the top vertex of the triangular. The size of the bubble was controlled by adjusting the energy of the laser beam. In this study, L varied between 0.20 mm and 3.26 mm. For each value of L, the maximum bubble radius (R max) varied within five grades, such as 0.89±0.05 mm, 1.04±0.05 mm, 1.23±0.05 mm, 1.38±0.05 mm, and 1.53±0.05 mm. 3. Results 3.1 The bubble above the top vertex of the triangular The dynamics of the bubble right above the top vertex of the equilateral triangular is shown in figure 2. Figure 2(a) shows the case with R max=1.48 mm and L=0.20 mm, i.e., the bubble is quite near the prism. During the collapse of the bubble, there is an indentation forming at the top of the bubble, as shown in frame 12. With continued shrinking, the bubble is separated into two parts by the prism, as shown in frame 13. Then, the two parts of the bubble begin rebounding. Meanwhile, jets are produced paralleling with the lateral faces of the prism, towards the adjacent prisms, as shown in frame 15 to 28. Figure 2(b) illustrates the case with L=1.43 mm and R max=1.23 mm. Compared with figure 2(a), due to larger L, during the first collapse of the bubble, the bubble is elongated (frames 4-6) and a jet is produced vertically towards the top vertex of the prism (frames 9-12). Meanwhile, a counterjet formation away from the vertex of the triangle is observed, as shown in frames 8-18. This phenomenon is similar with the bubble collapse near

a flat boundary [2]. Then in the rebound process of the bubble, it touches the edge of the prism and the lower side of the bubble is split by the prism (frames 12-21). Until the second collapse, the bubble split into two parts, and jets are generated towards adjacent prisms (frames 22-28). In figure 2(c), the bubble is located much further from the prism with L=3.26 mm and R max=1.58 mm. The bubble is elongated during the first collapse (frames 5-10). When the bubble rebounds, two jets penetrate the bubble simultaneously, of which the directions parallel with the lateral faces of the prism (frames 12-15). Then in the second collapse, another jet is produced vertically downwards (frames 21-24). Several cases with different L and R max were analyzed. The patterns of bubble behaviors can be classified into three kinds by the value of the stand-off distance, i.e., γ = L/R max. When γ<0.7, the bubble will behave as figure 2(a) demonstrating. When 0.7<γ<1.6, the bubble will behave like the case shown in figure 2(b). When γ>1.6, the bubble will behave like the case shown in figure 2(c). 3.2 The bubble above the bottom vertex of the triangular The dynamics of the bubble right above the bottom vertex of the equilateral triangular is shown in figure 3. In the case shown in figure 3(a), L=0.49 mm and R max=1.53 mm. As shown in frame 1, because of the adjacent prisms, the growth of the lower side of the bubble is obstructed. During the collapse, the upper side of the bubble shrinks faster than the lower side (frames 2-14). Then two jets, which perpendicular to the lateral faces of the adjacent prisms respectively, are produced (frames 15-19). From frame 19, the bubble splits into two parts. The upper part is like a torus and the lower part consists of the jets towards the faces of the prisms. Then all the parts rebound (frames 21-28). In the case shown in figure 3(b), L=1.13 mm and R max=1.38 mm. During the first collapse of the bubble, the upper side shrinks faster than the lower side (frames 4-11) and two jets perpendicular to the faces of the adjacent prisms at first (frames 12-13), which is similar with the case shown in figure 3(a). In addition, a counterjet forms, as shown in frame 13. However, the two jets towards to the faces of the adjacent prisms are covered by a vertical downward jet to the bottom vertex of the triangular very soon. This new jet develops fully, as shown in frames 15-28. In the case shown in figure 3(c), L=1.87 mm and R max=1.53 mm. During the first collapse of the bubble, the bubble is elongated (frames 4-9). Then a jet is generated vertically downwards, while a counterjet is produced upwards (frames 10-23). During the rebound process, the bubble moves towards the bottom of the array, which splits into two parts (the upper one and the lower one) when it collapses again (frames 24-26). Several cases with different L and R max were analyzed. Both of these two parameters will affect the bubble behaviors. The variation of the bubble dynamics with L and R max is summarized in Figure 4. The square, the circle and the star indicate the bubble behaviors similar with the cases shown in figure 3(a), 3(b) and 3(c), respectively. 4. Conclusion In this study, the bubble dynamics near a triangular prism array are investigated experimentally. In the cases with the bubble right above the top vertex of the triangular, the bubble may be separated into two parts by the prism and generate jets in several different directions. The patterns of the bubble behaviors can be classified into three kinds by the stand-off distance. In the cases with the bubble right above the bottom vertex of the triangular, the bubble may also produce jets in several different directions. The bubble behaviors are affected by the size of the bubble and the distance between the bubble and the array. Acknowledgements The authors would like to acknowledge the National Natural Science Foundation of China (Project No. 51606221) and Science Foundation of China University of Petroleum, Beijing (No. 2462016YJRC003). References [1] Zhang, Y., Zhang, Y., Qian, Z., Ji, B., & Wu, Y. (2016). A review of microscopic interactions between cavitation bubbles and particles in silt-laden flow. Renewable and Sustainable Energy Reviews, 56, 303-318. [2] Lauterborn, W., Bolle, H. (1975). Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary. Journal of Fluid Mechanics, 72(2), 391-399. [3] Tomita, Y., Robinson, P. B., Tong, R. P., Blake, J. R. (2002). Growth and collapse of cavitation bubbles near a curved rigid boundary. Journal of Fluid Mechanics, 466, 259-283.

[4] Zhang, A. M., Xiao, W., Wang, S. P. (2013). Experimental investigation of the interaction between a pulsating bubble and a rigid cylinder. Acta Mechanica Sinica, 29(4), 503-512. [5] Poulain, S., Guenoun, G., Gart, S., Crowe, W., Jung, S. (2015). Particle motion induced by bubble cavitation. Physical review letters, 114(21), 214501. Figures: (a) (b) b (c) (d) Figure 1 The experimental setup employed in this study. (a) The experimental system. (b) The triangular prism array. (c) & (d) Demonstrations of two kinds of the positions of the bubble. (a) L=0.20 mm and Rmax=1.48 mm. From frames 1 to 15, the time interval between frames is 10 μs. From frames 15 to 28, the time interval between frames is 5 μs.

(b) L=1.43 mm and R max=1.23 mm. From frames 1 to 7, the time interval between frames is 20 μs. From frames 7 to 28, the time interval between frames is 10 μs. (c) L=3.26 mm and Rmax=1.58 mm. From frames 1 to 9, the time interval between frames is 15 μs. From frames 9 to 28, the time interval between frames is 10 μs. Because of the limitation of the vision of the camera, the main body of the prisms are outside the frames, and the black points at the bottom of each frame are the top vertices of the triangulars. Figure 2 The dynamics of the bubble right above the top vertex of the equilateral triangular (the positions of the bubble and the array are demonstrated in figure 1(c)). The frame size is 6.31mm 6.31mm.

(a) L=0.49 mm and Rmax=1.53 mm. From frames 1 to 13, the time interval between frames is 10 μs. From frames 13 to 28, the time interval between frames is 5 μs. (b) L=1.13 mm and Rmax=1.38 mm. From frames 1 to 11, the time interval between frames is 10 μs. From frames 11 to 28, the time interval between frames is 5 μs.

(c) L=1.87 mm and Rmax=1.53 mm. The time interval between frames is 15 μs. Figure 3 The dynamics of the bubble right above the bottom vertex of the equilateral triangular, (the positions of the bubble and the array are demonstrated in figure 1(c)). The frame size is 6.31mm 6.31mm. Figure 4 Variation of the dynamics of the bubble right above the bottom vertex of the equilateral triangular with the size of the bubble and the value of L. The labels of the x axis represent the grades of the maximum bubble radius: R max is 0.89±0.05 mm for column 1; R max is 1.04±0.05 mm for column 2; R max is 1.23±0.05 mm for column 3; R max is 1.38±0.05 mm for column 4; R max is 1.53±0.05 mm for column 5. The square, the circle and the star indicate the bubble behaviors similar with the cases shown in figure 3(a), 3(b) and 3(c), respectively.