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In this work, a novel discretization of the incompressible Navier-Stokes equations for a gas-liquid flow is developed. Simulations of gas-liquid flows are often performed by discretizing time with a predictor → pressure → corrector approach and the phase interface is represented by a volume of fluid (VOF) method. Recently, unsplit, geometric VOF methods have been developed that use a semi-Lagrangian discretization of the advection term within the predictor step. A disadvantage of the current methods is that an alternative discretization (e.g. finite volume or finite difference) is used for the divergence operator in the pressure equation. Due to the inconsistency in discretizations, a flux-correction to the semi-Lagrangian advection term is required to achieve mass conservation, which increases the computational cost and reduces the accuracy. In this work, we explore the alternative of using a semi-Lagrangian discretization for the divergence operators in both the advection term and the pressure equation. The proposed discretization avoids the need to use a flux-correction to the semi-Lagrangian advection term as mass conservation is achieved through consistent discretization. Additionally, avoiding the flux-correction improves the accuracy while reducing the computational cost of the advection term semi-Lagrangian discretization. 

In this work, a novel discretization of the incompressible Navier-Stokes equations for a gas-liquid flow is developed. Simulations of gas-liquid flows are often performed by discretizing time with a predictor → pressure → corrector approach and the phase interface is represented by a volume of fluid (VOF) method. Recently, unsplit, geometric VOF methods have been developed that use a semi-Lagrangian discretization of the advection term within the predictor step. A disadvantage of the current methods is that an alternative discretization (e.g. finite volume or finite difference) is used for the divergence operator in the pressure equation. Due to the inconsistency in discretizations, a flux-correction to the semi-Lagrangian advection term is required to achieve mass conservation, which increases the computational cost and reduces the accuracy. In this work, we explore the alternative of using a semi-Lagrangian discretization for the divergence operators in both the advection term and the pressure equation. The proposed discretization avoids the need to use a flux-correction to the semi-Lagrangian advection term as mass conservation is achieved through the consistent discretization. Additionally, avoiding the flux-correction improves the accuracy while reducing the computational cost of the advection term semi-Lagrangian discretization. 

Electrostatic rotary bell atomizers are commonly used in several engineering applications, including the automobile industry. A high-speed rotating nozzle operating in a strong background electric field atomizes paint into charged droplets that range from a few micrometers to tens of micrometers in diameter. The atomization process directly determines the droplet size and droplet charge distributions which subsequently control the transfer efficiency and the surface finish quality. We have previously developed a tool to perform high fidelity simulations of near-bell atomization with electrohydrodynamic effects. In this work, we perform simulations employed with a droplet ancestry extraction tool to analyze previously inaccessible information and understand the physical processes driving atomization. We find that the electric field accelerates breakup processes and enhances secondary atomization. The total number of droplets, the ratio of secondary to primary droplets, and the ratio of coalescence to breakup activity are all much higher when operating in an electric field. We analyze the droplet velocity, local Weber number and charge density statistics to understand the complex physics in electrically assisted breakup. The results of the study have helped us gain insights into the physics of atomization in electrostatic rotary sprays. 

When an electrolyte jet is injected through a grounded nozzle into a region with an electric field, non-axisymmetric whipping instabilities are often observed in the jet. These instabilities are characterized by large scale violent, chaotic and quick whips of the jet. This system is numerically modeled using an electrohydrodynamic formulation that includes the Nernst-Planck model for ion transport with an aim to investigate the origin and propagation of the instabilities in the jet. Simulating this process will help gain an in-depth insight into the complex physical phenomena that occur. In this article, the formulation and modeling of electrolyte jets using a Poisson–Nernst–Planck (PNP) model is discussed. 

Understanding the process of primary and secondary atomization in liquid jets is crucial in describing spray distribution and droplet geometry for industrial applications and is essential in the development of physics-based low-fidelity atomization models. Significant advances in numerical modelling and computational resources allows research groups to conduct detailed numerical simulations of these flows. However, the large size of the datasets produced by highfidelity simulations limit researchers’ ability to analyze them. Consequently, the process of a coherent liquid core breaking into droplets has not been analyzed in simulation results even though a complete description of the jet dynamics exists. The present work applies a droplet physics extraction technique to high-fidelity simulations to track breakup events and data associated with the local flow. The data on the atomization process is stored in a Neo4j graphical database providing an easily accessible format. Results will provide a robust, quantitative description of the process of atomization and the details on the local flow field will be useful in the development of low-fidelity atomization models. 

Rotary Bell Atomizers (RBA) are extensively used as paint applicators in the automotive industry. Atomization of paint is achieved by a bell cup rotating at speeds of 40k-60k RPM in the presence of a background electric field. Automotive paint shops amount up to 70% of the total energy costs [Galitsky et. al., 2008], 50% of the electricity demand [Leven et. al., 2001] and up to 80% of the environmental concerns [Geffen et al., 2000] in an automobile manufacturing facility. The atomization process in an RBA affects droplet size and velocity distribution which subsequently control transfer efficiency and surface finish quality. Optimal spray parameters used in industry are often obtained from expensive trial-and-error methods. In this work, three-dimensional near-cup atomization (primary and secondary breakup) are simulated computationally using a high-fidelity volume-of-fluid transport scheme that includes an electrohydrodynamic effects. The influence of fluid properties (viscosity ratio, flow rate and charge density), nozzle rotation rate and bell potential on atomization are investigated by performing a parametric study. This cost-effective method of research aims to identify the ideal spray parameters to achieve maximum transfer efficiency.