Cavitation bubble modeling

A collection of python scripts for modeling of cavitation bubbles.

Bubble radial dynamics

The equations are based on the Toegel model¹, which additionally to the radius evolution equation consider heat and mass transport through the interface between the bubble interior and the surrounding liquid. Only acoustic excitation is considered. The obtained temporal data is used to build integrals according to the Louisnard model², which consist of two main categories. First, the damping functions describe the attenuation of the acoustic field due to thermal and viscous losses during the bubble oscillations. Second, the functions needed for the calculation of the primary Bjerknes force responsible for the bubble motion due to acoustic waves.

Coupling to OpenFOAM

The mentioned above and some additional functions are computed in dependence on the equilibrium bubble radius and the acoustic pressure amplitude. The outcomes are saved in form of the 2D interpolation tables readable by OpenFOAM software. Corresponding solvers are provided in the dedicated repository (acousticCavitationOpenFOAM). The material properties are available for two cases:

• A cubic reactor with an emerged sonotrode of 1cm diameter from Nowak³
• A cylindrical tank with an emerged sonotrode of 12cm diameter from Louisnard⁴

Footnotes

1. Toegel, R., Gompf, B., Pecha, R., & Lohse, D. (2000). Does Water Vapor Prevent Upscaling Sonoluminescence? Physical Review Letters, 85(15), 3165–3168. https://doi.org/10.1103/PhysRevLett.85.3165 ↩

2. Louisnard, O. (2012). A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation. Ultrasonics Sonochemistry, 19(1), 56–65. https://doi.org/10.1016/j.ultsonch.2011.06.007 ↩

3. Nowak, T. (2013). Untersuchung von akustischen Strömungen im kHz- und GHz-Bereich [PhD thesis, Georg August University of Göttingen]. ↩

4. Louisnard, O. (2012). A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures. Ultrasonics Sonochemistry, 19(1), 66–76. https://doi.org/10.1016/j.ultsonch.2011.06.008 ↩