Methods for the Modeling and Simulation of Sprays and Other Interfacial Flows

Abstract

Interfacial multiphase flows involve the motion of at least two fluids separated by surface tension. Atomizing interfacial flows, colloquially known as sprays, are among the most important fluid dynamic systems because of their ubiquity; power generation, delivery of aerosolized medicines, and productive produce farming all depend fundamentally on the detailed control of sprays. Atomization remains poorly understood because of a historical and persisting inability to accurately and affordably measure the dynamics inside and near the spray orifice outlet -- it is therefore desirable to be able to numerically simulate sprays with high fidelity. This dissertation presents computational methods that aim to improve current shortcomings in the modeling and simulation of sprays. Accurately characterizing the interfacial curvature of poorly-resolved liquid structures is addressed by deriving a series of finite particle methods for computing curvature. The methods are verified in analytical curvature tests, and validated against the oscillation frequency of ethanol droplets in air. The finite particle method, leveraging dynamic length scale modification, is demonstrated to out-perform the widely-used height function approach. Tracking the location of interfaces is also addressed, for which a coupled Eulerian-Lagrangian point mass particle scheme is introduced that preserves a well-distributed particle field, can be applied to an arbitrary number of fluids, and does not limit the simulation time step. The Eulerian-Lagrangian method is demonstrated to out-perform contemporary geometric volume of fluid methods at resolutions relevant to spray simulation in a variety of analytical phase tracking tests, and is dynamically evaluated by simulating extending three-phase elliptical regions, droplet dynamics, and Rayleigh-Taylor instabilities. The Eulerian-Lagrangian method is then extended to an approach for consistently and conservatively solving multiphase convection-diffusion problems -- this extension is verified via two analytical heat transfer problems, and robustness is demonstrated by simulating heated air blast atomization. Each of these tests conserves thermal energy and preserves boundedness of the temperature field. This dissertation concludes by outlining paths for consistently and conservatively solving the multiphase Navier-Stokes equations and the multiphase large eddy simulation equations in the coupled Eulerian-Lagrangian point mass particle framework.