Geodesic
Evolution of small sphericity distortion of a~vapor bubble during its supercompression
Matematičeskoe modelirovanie, Tome 23 (2011) no. 10, pp. 82-96

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Possibility of using two models to study evolution and maximum increase in amplitude of small distortions of sphericity of a bubble during its strong compression in a liquid is investigated. The investigation is performed in conditions of experiments on acoustic cavitation of deuterated acetone. The first (full hydrodynamic) model is based on the two-dimensional equations of gas dynamics. They are valid in every stage of the bubble compression. But its using is related to large consumption of computational time. The second (simplified) model is derived by splitting the liquid and vapor flows into the spherical part and its small non-spherical perturbation. To describe the spherical component, one-dimensional version of the two-dimensional model is used in this model. The advantage of the simplified model over the full one is its many (tens of) times less consumption of computational time. At the same time, the evolution of the non-spherical perturbation in this model is described with utilizing a number of assumptions validity of which is justified only at the initial stage of the bubble compression. It is therefore logical to apply the simplified model at the initial low-speed stage of the bubble compression while the full hydrodynamic one at its final high-speed stage. It has been shown that such a combination allows one to significantly reduce the computational time. It has been found that the simplified model alone can be used to evaluate estimates of maximum increase of amplitude of small distortions of sphericity of a bubble during its compression.
Keywords: bubble dynamics, cavitation bubble, bubble collapse, stability of the spherical shape.
Mots-clés : acoustic cavitation 
@article{MM_2011_23_10_a5,
     author = {A. A. Aganin and D. Yu. Toporkov and T. F. Khalitova and N. A. Khismatullina},
     title = {Evolution of small sphericity distortion of a~vapor bubble during its supercompression},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {82--96},
     publisher = {mathdoc},
     volume = {23},
     number = {10},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_10_a5/}
}
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A. A. Aganin; D. Yu. Toporkov; T. F. Khalitova; N. A. Khismatullina. Evolution of small sphericity distortion of a~vapor bubble during its supercompression. Matematičeskoe modelirovanie, Tome 23 (2011) no. 10, pp. 82-96. http://geodesic.mathdoc.fr/item/MM_2011_23_10_a5/