An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

Abstract

Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the 6-equation model of Saurel et al. [3] as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing methods are implemented and compared. We demonstrate the inadequacy of the traditional 5-equation model of Allaire et al. [1] for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. [2] for representing this phenomenon. Quantitative comparisons between the augmented 5-equation and 6-equation models for three-dimensional bubble collapse problems demonstrate the versatility of pressure-disequilibrium models. Lastly, the performance of pressure disequilibrium model for representing a three-dimensional spherical bubble collapse for different bubble interior/exterior pressure ratios is evaluated for different numerical methods. Pathologies associated with each factor and their origins are identified and discussed.

High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone

“…The present model and numerical method have been validated for 1 D single phase and multi-phase Riemann problems, and several selected multidimensional flows: liquid/ gas shock tube, 8,9,52 surface-tension test, 9,53 and cavitation in air/water mixture. 52 Regarding bubble dynamics, we compared the present numerical modeling results for spherical bubble collapse (on a 3 D grid) with analytical solutions in the weakly compressible limit. 52 The comparison showed a good agreement with discrepancies less than or around one percent.…”

“…52 Regarding bubble dynamics, we compared the present numerical modeling results for spherical bubble collapse (on a 3 D grid) with analytical solutions in the weakly compressible limit. 52 The comparison showed a good agreement with discrepancies less than or around one percent. We also compared (data not shown) maximum pressure at the wall for different standoff distances using the present model and other established models and methods.…”

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

“…We note that the models of Allaire et al [44] and Massoni et al [42] do not include the K term in (2) and thus do not strictly obey the second-law of thermodynamics, nor reproduce the correct mixture speed of sound (9). While MFC also supports these models, accurately representing the sound speed is known to be important for some problems, such as the cavitation of gas bubbles [55]. However, it is also known that the K term can result in numerical instabilities for problems with strong compression or expansion in mixture regions due to its non-conservative nature [55].…”

“…However, ECOGEN is built upon an intrinsically low-order MUSCL scheme that can inhibit both efficient simulation and physically fidelity when compared to the WENO schemes we use here, especially when augmented with our high-order cell-average approximations. This is demonstrated in section 5.4 for an isentropic vortex problem and in section 5.3 and Schmidmayer et al [55] for cavitating gas bubbles. In pursuit of this, MFC was also constructed with a phase-averaged flow model that represent unresolved multi-phase dynamics at the sub-grid level.…”

“…While MFC also supports these models, accurately representing the sound speed is known to be important for some problems, such as the cavitation of gas bubbles [55]. However, it is also known that the K term can result in numerical instabilities for problems with strong compression or expansion in mixture regions due to its non-conservative nature [55]. Thus, the decision of what 5-equation model to use (if any) is problem dependent and left to the user.…”