Research on the dynamic characteristics of the cavitation bubble collapsing between multiple particles

Abstract

The combined action of multiple particles and cavitation bubbles can severely damage hydraulic machinery. Combining the Kelvin impulse theory and the results of high-speed photography experiments, this paper researches the dynamic behaviors of a single bubble located between three equal-sized spherical particles. Non-spherical morphological evolution characteristics in the collapse stage of the bubble are described. The influence of the arrangement of the three particles on the direction and intensity of the bubble migration is quantitatively analyzed. On this basis, the spatial distribution characteristics of the zero impulse points with the Kelvin impulse equal to zero are explored. The results show that: (1) As the bubble is induced in the symmetric positions, three typical cases of collapse characteristics are summarized according to the bubble morphology, including V-shaped, T-shaped, and ginkgo leaf-shaped. (2) As the bubble incipient position is shifted on the symmetry axis, the Kelvin impulse intensity shows a non-monotonic trend with its direction varying many times. Both the impulse intensity and direction are significantly affected by the arrangement of particles. (3) There are multiple zero impulse points among the three particles, and both the spatial location and the number of the zero impulse points are affected by the arrangement of the particles.

Keywords: Bubble dynamics; High-speed photography; Kelvin impulse; Particle-bubble interaction.

Fig. 1

Schematic diagram of the physical model of the bubble near three spherical particles.

Fig. 2

High-speed photography experimental system.

Fig. 3

Typical bubble dynamics behaviors corresponding to Case 1 with a V-shaped bubble collapse. L* = 5.15, H* = 2.72, x_b* = 0.

Fig. 4

Velocity distribution map of liquid around the bubble and particles corresponding to Case 1 from theoretical results. L* = 5.15, H* = 2.72, x_b* = 0, t* = 0.85.

Fig. 5

The positions of the bubble centroid, characteristic points A and B on the bubble wall change with t* corresponding to Case 1. L* = 5.15, H* = 2.72, x_b* = 0.

Fig. 6

Typical bubble dynamics behaviors corresponding to Case 2 with a T-shaped bubble collapse. L* = 4.38, H* = 2.19, x_b* = 0.

Fig. 7

Velocity distribution map of liquid around the bubble and particles corresponding to Case 2 from theoretical results. L* = 4.38, H* = 2.19, x_b* = 0, t* = 0.85.

Fig. 8

The positions of the bubble centroid, characteristic points A and B on the bubble wall change with t* corresponding to Case 2. L* = 4.38, H* = 2.19, x_b* = 0 mm.

Fig. 9

Typical bubble dynamics behaviors corresponding to Case 3 with a ginkgo leaf-shaped bubble collapse. L* = 4.38, H* = 2.0, x_b* = 0.39.

Fig. 10

Velocity distribution map of liquid around the bubble and particles corresponding to Case 3 from theoretical results. L* = 4.38, H* = 2.0, x_b* = 0.39, t* = 0.85.

Fig. 11

The positions of the bubble centroid, characteristic points A and B on the bubble wall change with t* corresponding to Case 3. L* = 4.38, H* = 2.0, x_b* = 0.39.

Fig. 12

Distribution of the three typical cases in the parameter space formed by H* − x_b*. L* = 4.76.

Fig. 13

Distribution of the three typical cases in the parameter space formed by L* − x_b*. H* = 2.25.

Fig. 14

Kelvin impulse distribution near three particles corresponding to different L*. (a) L* = 5.0; (b) L* = 5.5; (c) L* = 6.0. H* = 4.0.

Fig. 15

Kelvin impulse distribution near three particles corresponding to different H*. (a) H* = 3.5; (b) H* = 4.0; (c) H* = 4.5. L* = 5.0.

Fig. 16

Variation of the Kelvin impulse of the bubble corresponding to different L* with x_b*. H* = 4.0, R_max = 1.0 mm. P₁ and P₂ are the intersection points of the curve and I = 0.

Fig. 17

Variation of Kelvin impulse of the cavitation bubble corresponding to different H* with x_b*. L* = 5.0, R_max = 1.0 mm.

Fig. 18

Variation of P₁ and P₂ coordinates with L*. H* = 4.0.

Fig. 19

Variation of P₁ and P₂ coordinates with H*. L* = 5.0.