Evolution of small sphericity distortion of a~vapor bubble during its supercompression

A. A. Aganin ; D. Yu. Toporkov ; T. F. Khalitova ; N. A. Khismatullina

Matematičeskoe modelirovanie, Tome 23 (2011) no. 10, pp. 82-96.

Résumé

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.

Détail

Keywords: bubble dynamics, cavitation bubble, bubble collapse, stability of the spherical shape.
Mots-clés : acoustic cavitation

Bibliographie

[1] Putterman S. J., Weninger K. P., “Sonoluminescence: How Bubbles Turn Sound into Light”, Annu. Rev. Fluid Mech., 32 (2000), 445–476 | DOI | Zbl

[2] Taleyarkhan R. P., West C. D., Cho J. S., Lahey R. T.(jr.), Nigmatulin R. I., Block R. C., “Evidence for nuclear emissions during acoustic cavitation”, Science, 295 (2002), 1868–1873 | DOI

[3] Brenner M. P. Single-Bubble sonoluminescence, Rev. Modern Physics, 74 (2002), 425–484 | DOI

[4] Nigmatulin R. I., Akhatov I. Sh., Topolnikov A. S., Bolotnova R. Kh., Vakhitova N. K., Lahey R. T.(jr.), Taleyarkhan R., “The theory of supercompression of vapor bubbles and nano-scale thermonuclear fusion”, Phys. Fluids, 17:10 (2005), 107106 | DOI | Zbl

[5] Ilkaev R. I., Garanin S. G., “Issledovanie problem termoyadernogo sinteza na moschnykh lazernykh ustanovkakh”, Vestnik RAN, 76:6 (2006), 503–513

[6] Lebo I. G., Tishkin V. F., Issledovanie gidrodinamicheskoi neustoichivosti v zadachakh lazernogo termoyadernogo sinteza metodami matematicheskogo modelirovaniya, FIZMATLIT, M., 2006, 304 pp.

[7] Aganin A. A., Khalitova T. F., Khismatullina N. A., “Metod chislennogo resheniya zadach silnogo szhatiya nesfericheskogo kavitatsionnogo puzyrka”, Vychislitelnye tekhnologii, 15:1 (2010), 14–32 | Zbl

[8] Nigmatulin R. I., Bolotnova R. Kh., “Shirokodiapazonnoe uravnenie sostoyaniya organicheskikh zhidkostei na primere atsetona”, Doklady RAN, 415:5 (2007), 617–621 | Zbl

[9] Gamalii E. G., “Ustoichivost granitsy kavitiruyuschego puzyrka v neszhimaemoi zhidkosti”, Kratkie soobscheniya po fizike FIAN, 1976, no. 5, 23–27

[10] Gamalii E. G., Lebo I. G., Rozanov V. B., Sergoyan GM., “O razvitii gidrodinamicheskoi neustoichivosti granits sfericheskoi obolochki iz neszhimaemoi zhidkosti”, Kratkie soobscheniya po fizike FIAN, 1987, no. 5, 7–9

[11] Lebo I. G., Rozanov V. B., Stepanov R. V., “Model razvitiya vozmuschenii granits obolochki iz neszhimaemoi zhidkosti”, Matematicheskoe modelirovanie, 9:9 (1997), 83–94 | MR | Zbl

[12] Prosperetti A., “Viscous effects on perturbed spherical flows”, Quart. Appl. Math., 34 (1977), 339–352 | Zbl

[13] Plesset M. S., Prosperetti A., “Bubble dynamics and cavitation”, Ann. Rev. Fluid Mech., 9 (1977), 145–185 | DOI | Zbl

[14] Hilgenfeldt S., Lohse D., Brenner M., “Phase diagrams for sonoluminescing bubbles”, Phys. Fluids, 8 (1996), 2808–2826 | DOI | Zbl

[15] Aganin A. A., Ilgamov M. A., Nigmatulin R. I., Toporkov D. Yu., “Evolyutsiya iskazhenii sferichnosti kavitatsionnogo puzyrka pri akusticheskom sverkhszhatii”, MZhG, 2010, no. 1, 57–69 | Zbl

[16] Lin H., Storey B. D., Szeri A. J., “Rayleigh-Taylor instability of violently collapsing bubbles”, Phys. Fluids, 14 (2002), 2925–2928 | DOI

[17] Hilgenfeldt S., Brenner M., Grossmann S., Lohse D., “Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles”, J. Fluid Mech., 365 (1998), 171–204 | DOI | Zbl

[18] Nigmatulin R. I., Dinamika mnogofaznykh sred, v. 1,2, Nauka, M., 1987

[19] Harten A., Engquist B., Osher S., Chakravarthy S. R., “Uniformly high order accurate essentially nonoscillatory schemes III”, J. Comp. Phys., 71 (1987), 231–303 | DOI | MR | Zbl

[20] Aganin A. A., Ilgamov M. A., Khalitova T. F., “Modelirovanie silnogo szhatiya gazovoi polosti v zhidkosti”, Matematicheskoe modelirovanie, 20:11 (2008), 89–103 | MR | Zbl

[21] Aganin A. A., “Dynamics of a small bubble in a compressible fluid”, Int. J. Numer. Meth. Fluids, 2000, no. 33, 157–174 | 3.0.CO;2-A class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | Zbl