Numerical modeling of the dynamics of bubble oscillations subjected to fast variations in the ambient pressure with a coupled level set and volume of fluid method

Abstract

A numerical method for modeling and understanding the dynamics of bubble oscillations subjected to fast variations in the ambient pressure is proposed under low Mach number conditions. In the present work, the method uses a single-fluid continuum formalism of weakly compressible axisymmetric Navier-Stokes equations for the numerical simulation of liquid-gas flows with surface tension and adopts the interface capturing approach based on a coupled level set and volume of fluid (CLSVOF) method for describing the moving and deformed interfaces. To demonstrate the efficacy of the proposed method, first, the numerical results of the radial oscillations of a spherical gas bubble are tested with the numerical solutions of Rayleigh-Plesset equation. Then, the numerical method is applied to reproduce the growth and subsequent collapse of a bubble in an infinite liquid medium observed in experiments. Finally, the numerical simulation of the interaction of two oscillating bubbles at small separation distance is evaluated in response to a moderate step change in the ambient pressure. It is shown that two deformable bubbles undergo coupled radial and oscillatory translational motions which eventually results in the bubbles' attraction and coalescence caused by the secondary Bjerknes forces. The numerical predictions show very good accuracy with the experimental and numerical results reported in the literature.

Numerical simulation of a confined cavitating gas bubble driven by ultrasound

“…Comparison of the equivalent radius history of the present VOF simulation result with numerical data 83 and experimental data 88 . The equivalent RPE solutions using the different p ac are included for reference.…”

“…Fig. 2(a) compares the results obtained using the present VOF model with the experimental data 88 and the CLSVOF simulation 83 . Note that the numerical and analytical results have been shifted by 68 µs to match the time at which the expansion wave reaches the bubble in the experiments.…”

“…The Tait exponent γ l = 7 and the Tait pressure B = 331 MPa. 83 Similarly, the pressure p and density ρ g of the gas are related through the polytropic equation of state:…”

“…The computed bubble radius history is compared with the experimental data of Rodríguez-Rodríguez, Casado-Chacón, and Fuster 88 . This case has also been numerically simulated using a Coupled Level-Set Volume-Of-Fluid (CLSVOF) method by Chakraborty 83 . Therefore, this is an excellent verification exercise because it allows for a comparison of the present model with experimental results, 88 numerical solution to the analytical RPE in Eq.…”

Acoustic-driven Oscillations of a Bubble in a Narrow Gap

“…where 0, and 0 are the density and pressure of the liquid at atmospheric conditions, respectively; the Tait exponent = 7 and the Tait pressure = 331 MPa as in [18]. Similarly, the pressure and density of the gas are related through the polytropic equation of state:…”