Jet dynamics of a cavitation bubble near unequal-sized dual particles

Abstract

The jet dynamics of a cavitation bubble near unequal-sized dual particles is investigated employing OpenFOAM, and the effects of the jets on the particles are quantitatively analyzed in terms of their pressure impacts. Different from single-particle cases, the necks that evolve between dual particles are closely linked to the formation mechanism of the jets. Based on the simulation results, the jet dynamics can be divided into five scenarios: (1) the contraction of the annular depression produced by the collision of the two necks causes the bubble to split into two daughter bubbles and generates a single jet inside each daughter bubble; (2) the annular depression impacts the particle, leading to the bubble to fracture and producing a single jet inside a daughter bubble; (3) the bubble is split by a single neck constriction and produces a single jet; (4) the bubble is split by a single neck constriction and generates two jets; and (5) the bubble is split by the contraction of two necks and produces four jets together with three daughter bubbles. As the bubble-particle distance or the radius ratio of the dual particles increases, the maximum force on the small particle generated by the bubble decreases.

Keywords: Cavitation bubble dynamics; Cavitation bubble–particle interactions; Jet dynamics; OpenFOAM.

Fig. 1

Schematic diagram of the positional relationship between the bubble and the unequal-sized dual particles.

Fig. 2

Schematic diagram of computational domain and grid.

Fig. 3

Variations in bubble equivalent radius for different maximum grid sizes. γ = 0.89. δ = 1.33. R_max = 1.14 mm. R_LP = 2.00 mm.

Fig. 4

Comparison of experimental and simulated results. (a) Variations in bubble shapes obtained from experiments. (b) Variations in bubble shapes obtained from simulations. (c) Variations in feature point locations as a function of dimensionless time, where d denotes the distance from the feature point to the bubble inception. γ = 0.89. δ = 1.33. θ = 1.75. R_max = 1.14 mm. R_LP = 2.00 mm.

Fig. 5

Comparison of present numerical method with bubble dynamics theory and experiments for a bubble near a rigid wall. (a) Bubble radius vs. time. (b) Bubble migration vs. time. R_max = 0.768 mm. The distance between the bubble inception and the wall is 2.02R_max. The data for theory and experiments are

Fig. 6

Categorization of the jet behavior in terms of γ and δ. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 7

Evolution of the jets for scenario 1. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.25. δ = 2.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 8

Variations in surface pressure and force on particles with time for scenario 1. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.25. δ = 2.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 9

Evolution of the jets for scenario 2. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.25. δ = 6.00. θ = 2.00. R_max = 1.00 mm. R_pL = 2.00 mm.

Fig. 10

Variations in surface pressure and force on particles with time for scenario 2. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.25. δ = 6.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 11

Evolution of the jets for scenario 2. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.35. δ = 6.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 12

Variation of surface pressure and force on particles with time for scenario 2. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.35. δ = 6.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 13

Evolution of the jets for scenario 3 during the bubble collapse stage. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.35. δ = 10.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 14

Variations in surface pressure and force on particles with time for scenario 3. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.35. δ = 10.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 15

Temporal evolution of the jet velocity for scenario 3. γ = 0.35. δ = 10.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 16

Velocity of the jet as it pierces the bubble for scenario 3. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 17

Evolution of the jets for scenario 4. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.50. δ = 2.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 18

Variations in surface pressure and force on particles with time for scenario 4. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.50. δ = 2.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 19

Evolution of the jets for scenario 4. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.25. δ = 11.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 20

Variations in surface pressure and force on particles with time for scenario 4. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.25. δ = 11.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 21

Evolution of the jets for scenario 5. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. γ = 0.50. δ = 1.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 22

Variations in surface pressure and force on particles with time for scenario 1. (a) Surface pressure of small particle. (b) Surface pressure of large particle. (c) Forces exerted on the two particles. γ = 0.50. δ = 1.00. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 23

Jet dynamics for particle sizes smaller than the bubble. (a) γ = 0.25. (b) γ = 0.35. (c) γ = 0.50. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. δ = 2.00. θ = 0.40. R_max = 1.00 mm. R_LP = 2.00 mm.

Fig. 24

Jet dynamics for particle sizes larger than the bubble. (a) γ = 0.34. (b) γ = 0.68. (c) γ = 1.08. (d) γ = 1.35. Gray regions indicate particles, white region indicates the bubble. The left and right sides of each subplot show the pressure and velocity distributions of the liquid, respectively, with velocity vectors indicated by black arrows. δ = 1.00. θ = 4.05. R_max = 0.74 mm. R_LP = R_SP = 3.00 mm.

Fig. 25

Variations in maximum force exerted by the bubble on the particles for various γ and δ during the bubble collapse stage. (a) Small particle. (b) Large particle. θ = 2.00. R_max = 1.00 mm. R_LP = 2.00 mm.