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

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

Numerical Simulation of Compressible Flows with Interfaces

Compressible interfacial flows exist in a variety of applications: reacting fronts, droplet break up, jets and sprays in high speed, shock passage in foams, etc. These flows behave in a complex multi-scale way including interface deformation, wave interface interaction and complex transport phenomena. In the first section, the interaction of a laminar flame with a compression wave is investigated. More precisely, the evolution of the burning interface is investigated and discussion over different compression waves and their effects on the flame geometry and burning rate are made. In the second part, a numeral framework for simulation of compressible multiphase flows using adaptive wavelet collocation method is developed. This study was originally motivated by the desire for a numerical tool capable of simulating the atomization process during start-up conditions in a supersonic combustor. To model such physics, the solver needs to handle high density ratios, transport terms and capillary effects. The multi-scale behaviour of these flows requires a multi-scale approach. Parallel Adaptive Wavelet Collocation Method (PAWCM) makes use of second generation wavelets to dynamically adapt the grid to localized structures in the flow in time and space. This approach allows the solution to be approximated using a subset of the points that would normally be used with a uniform grid scheme. Thus, computation on this subset is efficient and high levels of data compression is achieved

Application of central-weighted essentially non-oscillatory finite-volume interface-capturing schemes for modeling cavitation induced by an underwater explosion

Cavitation resulting from underwater explosions in compressible multiphase or multicomponent flows presents significant challenges due to the dynamic nature of shock–cavitation–structure interactions, as well as the complex and discontinuous nature of the involved interfaces. Achieving accurate resolution of interfaces between different phases or components, in the presence of shocks, cavitating regions, and structural interactions, is crucial for modeling such problems. Furthermore, pressure convergence in simulations involving shock–cavitation–structure interactions requires accurate algorithms. In this research paper, we employ the diffuse interface method, also known as the interface-capturing scheme, to investigate cavitation in various underwater explosion test cases near different surfaces: a free surface and a rigid surface. The simulations are conducted using the unstructured compressible Navier–Stokes (UCNS3D) finite-volume framework employing central-weighted essentially non-oscillatory (CWENO) reconstruction schemes, utilizing the five-equation diffuse interface family of methods. Quantitative comparisons are made between the performance of both models. Additionally, we examine the effects of cavitation as a secondary loading source on structures, and evaluate the ability of the CWENO schemes to accurately capture and resolve material interfaces between fluids with minimal numerical dissipation or smearing. The results are compared with existing high-order methods and experimental data, where possible, to demonstrate the robustness of the CWENO schemes in simulating cavitation bubble dynamics, as well as their limitations within the current implementation of interface capturing.The authors acknowledge the computing time at Cranfield University Delta2 HPC facility