Modeling surface tension dominated interfacial dynamics using smoothed particle hydrodynamics
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This work describes the development of a numerical model to simulate multiphase flows with surface tension dominated interfacial dynamics. Multiphase flows are ubiquitous in nature and throughout mechanical systems and the interfacial dynamics within these flows can significantly impact overall system characteristics. Given the limited number of analytic solutions and the potential expense and constraints of experimental work, numerical simulations can provide tools to aid in the fundamental understanding and optimization of such systems. Multiphase flows, especially those with large parameter gradients and geometric deformations, pose a number of unique numerical challenges that require careful consideration of numerical stability, flexibility and efficiency. Many multiphase flow models have difficulty representing large parameter gradients and geometric deformations simultaneously. They also frequently distinguish fluid and gas phases by evolving a volume fraction, but do not have the capability of solving different governing equations in each phase. This work uses smoothed particle hydrodynamics (SPH), a Lagrangian particle based method uniquely capable of accommodating large geometric deformations and arbitrary numbers of fluids, to model transient surface tension dominated dynamics of droplets and bubbles under a variety of circumstances. Existing implementations of multiphase SPH are plagued by technical challenges that are addressed here in order to develop a more robust formulation for physically realistic parameters that can be applied to a broad range of multiphase systems. The simulation of droplets and bubbles, which are inherently dynamic, multiphase and characterized by an interface, is first considered in the context of fundamental droplet and bubble behavior. The deformations of isolated droplets and bubbles under body forces and surface tension are modeled and the results verified and validated. Then the acquired numerical insight is applied to more complicated systems, including drop-drop collisions and bubble deformations in constrained environments. Two fundamentally different surface tension formulations are studied and observations regarding their optimal usage are made.