Insights from high-fidelity modeling of industrial rotary bell atomization.

The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.

The Voronoi Implicit Interface Method for computing multiphase physics.

We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method's accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann's law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.

Multiscale modeling of membrane rearrangement, drainage, and rupture in evolving foams.

Modeling the physics of foams and foamlike materials, such as soapy froths, fire retardants, and lightweight crash-absorbent structures, presents challenges, because of the vastly different time and space scales involved. By separating and coupling these disparate scales, we have designed a multiscale framework to model dry foam dynamics. This leads to a predictive and flexible computational methodology linking, with a few simplifying assumptions, foam drainage, rupture, and topological rearrangement, to coupled interface-fluid motion under surface tension, gravity, and incompressible fluid dynamics. Our computed results match theoretical analyses and experimentally observed physical effects, including thin-film drainage and interference, and are used to study bubble rupture cascades and macroscopic rearrangement. The developed multiscale model allows quantitative computation of complex foam evolution phenomena.