The dynamics of a bubble near a local axisymmetric convexity or concavity, cosine-like in the axial section, on a plane rigid wall is studied in the regime with the formation of a cumulative liquid jet directed to the wall. The study is performed by the boundary element method. Main attention is focused on the bubble collapse characteristics at the moment tc when the jet impacts on the bubble surface part near the wall, namely on the jet tip velocity and radius, the internal bubble pressure, the distance between the bubble and the uneven region of the wall, etc. These characteristics are of interest since they to large extent determine the destructive potential of cavitation. The dependences of these characteristics on the radius of the non-plane region of the wall, the depth of the concave region and the height of the convex region, and the local character of the wall unevenness have been investigated. To estimate the effect of the local character of the wall unevenness, the cases of completely concave and convex walls in the form of blunt conical surfaces are used for comparison. It has been found, in particular, that with changing radius of the convex region of the wall, the bubble shape at the moment tc varies significantly: the shape diversity includes the profiles with a gas microcavity in front of the impacting jet tip, an emerging second oppositely-directed jet, and a quite large area of the jet tip impact at its beginning.
Non-spherical dynamics of a bubble during its axisymmetric collapse near a planar rigid wall is considered. The liquid surrounding the bubble is ideal incompressible, its flow is potential. The pressure in the bubble is uniform, and varying with respect to adiabatic law. At the beginning of collapse, the bubble is spheroidal, the liquid is motionless. A numerical technique is applied, which is based on a stepwise method in time for calculating the bubble surface movement and on the boundary element method. The initial stage of the bubble collapse till the moment of contact between some parts of the bubble surface (i.e., till losing its one-connectedness) is considered. The effect of the ratio of the semi-axes of the spheroidal bubble and the initial thickness of the liquid layer between the bubble and the wall on the bubble shape, the pressure and velocity fields in liquid are investigated. The region of the problem parameters (the distance from the wall, the bubble non-sphericity) is outlined, in which the bubble collapses with formation of a cumulative liquid jet impacting on the bubble surface part nearest to the wall. The liquid pressures resulting from the impact are estimated.
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