Comparison of surface tension generation methods in smoothed particle hydrodynamics for dynamic systems

Abstract

Developing robust numerical models of surface tension dominated dynamic multiphase systems is an ongoing challenge, especially in scenarios with large density and viscosity ratios. This is critical to the design and understanding of various physical and engineering systems, such as three-phase fluidized beds, fuel injectors, and drug delivery schemes. Much of the computational work in surface tension dominated multiphase flows has employed the continuum surface force method (CSF) of Brackbill et al. (1992), which recasts surface tension from a surface force to a volumetric force that can be imposed in the vicinity of an interface. The CSF method produces accurate results across a variety of systems, however it relies on the identification of surface normals, which can be unreliable under certain conditions. Alternative methods of simulating surface tension have been proposed. This work uses smoothed particle hydrodynamics (SPH), a particle based computational fluid dynamics method, as the framework for exploring the advantages and disadvantages of the CSF method in comparison to a pairwise forces (PF) method proposed by Tartakovsky and Panchenko (2016). Dynamic systems are modeled and the results are compared to existing test cases from the literature and to analytic solutions derived from fundamental normal mode behavior of bubbles and droplets. Initial studies of droplet-droplet collisions, a physical system for which the PF method is more stable and physically appropriate than the CSF method, are described.