The dynamics of a gas bubble in liquid near a rigid surface
A.A. Aganin*, L.A. Kosolapova**, V.G. Malakhov***
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of RAS, Kazan, 420111 Russia
E-mail: *aganin@kfti.knc.ru, **kosolapova@kfti.knc.ru, ***malahov@kfti.knc.ru
Received November 15, 2017
Abstract
The axisymmetric dynamics of a gas bubble in liquid near a plane rigid surface (wall) during its expansion and subsequent compression with the transition to the toroidal phase of motion has been studied. It has been assumed that the liquid is ideal incompressible, its flow being potential. The position of the bubble contour and the potential on it have been found by the Euler method, the fluid velocity on the contour has been derived by the boundary element method. The shape of the bubble, its internal pressure, liquid velocity, and pressure around the bubble have been determined. The pressure profiles on the wall and along the axis of symmetry have been presented. It has been found that at an initial distance d0 between the bubble and the wall less than a certain value d* the thickness of the liquid layer between the bubble and the wall during bubble compression until the moment of transition to the toroidal phase of the motion decreases, while at the initial distance d0 greater than d* it increases. In addition, the liquid layer thickness at the moment of transition to the toroidal phase increases with increasing the initial distance d0 between the bubble and the wall. It has been shown that in the toroidal phase of bubble dynamics the maximum pressure in the liquid near the bubble is located in the region of impact of the cumulative jet on the surface of the liquid layer between the bubble and the wall. In this case, the action of the jet can lead to the appearance of local deformations of the bubble surface (a splash inside the bubble) moving away from the axis of symmetry as the jet displaces the liquid between the bubble and the wall.
Keywords: cavitation bubble, toroidal bubble, potential liquid flow, boundary element method, distance from bubble to wall
Acknowledgments. This study was supported by the Russian Science Foundation (project no. 17-11-01135).
Figure Captions
Fig. 1. Bubble shapes during extension and compression for γ = 0.8 at six points of time t*: 1 – 0, 2 – 1.093, 3 – 1.857, 4 – 2.016, 5 – 2.083, 6 – 2.144 (a) and velocity and pressure fields in the liquid surrounding the bubble at the point of time tc* = 2.144 (b).
Fig. 2. Bubble contours (a), pressure in the bubble (b), and maximum pressure in the liquid (c) for a series of γ values at the point of time tc*.
Fig. 3. Dependencies on γ of the coordinates of the bubble center z* at t* = 0 (line 1) and two points of its surface located on the axis z: being distanced from the wall at t* = tV* (line 2) and close to the wall at t* = tV* (line 3) and t* = tc* (line 4).
Fig. 4. For γ = 0.8 at the points of time tT*: 1 – 0.008, 2 – 0.032, 3 – 0.064, bubble contours in the toroidal phase of motion and the pressure field in the liquid near the bubble (a), pressure profiles along the symmetry axis z (b) and radial pressure profiles on the wall (c).
Fig. 5. For γ = 1.5 at four points of time tT*: 1 – 0, 2 – 0.0032, 3 – 0.0064, 4 – 0.0096, bubble contours in the the toroidal phase of motion and the pressure field in the liquid (a), pressure profiles on the symmetry axisz (b) and radial pressure profiles on the wall (c).
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For citation: Aganin A.A., Kosolapova L.A., Malakhov V.G. The dynamics of a gas bubble in liquid near a rigid surface. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 1, pp. 154–164. (In Russian)
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