ISSN 2658–5782
DOI 10.21662
Electronic Scientific Journal

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им. Р.Р. Мавлютова

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Davletshin A.I., Khalitova T.F. Numerical simulation of single vapor bubble dynamics in a liquid in an intense acoustic field. Multiphase Systems. 13 (2018) 4. 127–135.
2018. Vol. 13. Issue 4, Pp. 127–135
DOI: 10.21662/mfs2018.4.018
Numerical simulation of single vapor bubble dynamics in a liquid in an intense acoustic field
Davletshin A.I., Khalitova T.F.
Institute of Mechanics and Engineering, Kazan Scientific Center of the RAS, Kazan


The possibility of increasing the calculation efficiency by the joint use of two models of the dynamics of a single weakly-nonspherical vapor bubble under its strong collapse in liquid is studied. In both models the motion of liquid and vapor is split into a spherical component and its small nonspherical perturbation. The models differ in the description of the spherical component. In the first (simplified) model, it is described by a system of ODE together with partial differential equations in temperature, derived under the assumption of weak compressibility of liquid and bubble homobaricity. In the second model, one-dimensional gas dynamics equations are applied. The advantage of the simplified model consists in determining a numerical solution with much-less computer time costs in comparison with what is required for the numerical integration of gas dynamics equations. The assumptions used in the simplified model in the final stage of collapse become incorrect, and, as a result, the numerical solution errors increase. Therefore, the simplified model is applied at the beginning of bubble collapse, whereas the gas dynamics equations are used at its end. Within this approach, the numerical solution in the final stage of collapse is dependent on the moment of transition to the gas dynamics equations. It is shown that satisfactory description of evolution of bubble sphericity distortion is achieved when the transition is made under the condition that the Mach number M of vapor in the vicinity of the bubble surface is less than 0.4. Satisfactory resolution of the shock wave in the bubble is attained when the transition is performed at M<0.2.


vapor bubble collapse,
shock waves,
small nonsphericity of bubble

Article outline

Purpose: Improving the efficiency of calculations of single weakly nonspherical vapor bubble dynamics in liquid in an intense acoustic field by jointly applying different models. Investigation of applicability of such models.

Methodology: The model and numerical technique is an effective combination of two models and techniques of calculatinng the dynamics of a weakly-nonspherical bubble, in which the liquid and vapor motion is split into a spherical component and its small non-spherical perturbation. To describe the spherical component of bubble dynamics at the beginning of bubble collapse, a simplified model is used, in which the ODE system is solved together with two heat-conduction equations, whereas gas dynamics equations are applied at the end of collapse. Effects of viscosity, surface tension, evaporation and condensation at the interface are taken into account. The variation of a small non-spherical perturbation of the bubble surface is described by an ordinary second-order differential equation.

Findings: The errors of using a simplified model in the initial stage of vapor bubble collapse in an intense acoustic field have been studied in order to identify opportunities for improving the efficiency of calculations. It is shown that the simplified modeling with satisfactory error in resolving the radial convergence of shock waves can be applied until the Mach number of the vapor on the bubble surface is less than 0.2, whereas a satisfactory description of the growth in the bubble non-sphericity amplitude is achieved using the simplified modeling until the Mach number is less than 0.4. With the use of the simplified model, the computer time costs are reduced by 3 and 5 times, respectively.

Originality/value: The use of a simplified model of dynamics of a single weakly-nonspherical vapor bubble in liquid makes it possible to increase the calculations efficiency by several times. This can be used in studying the growth of small perturbations of the sphericity of a single vapor bubble in an intense acoustic field.


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