In this paper, the transient settling dynamics of a spherical particle sedimenting in a linearly stratified fluid is investigated by performing fully resolved direct numerical simulations. The settling behaviour is quantified for different values of Reynolds, Froude and Prandtl numbers. It is demonstrated that the transient settling dynamics is correlated to the induced Lagrangian drift of flow around the settling particle. A simplified model is provided to predict the maximum velocity of the settling particle in linearly stratified fluids. The peak velocity can be followed by the oscillation of the settling velocity and the particle can even reverse its direction of motion before reaching to its neutrally buoyant level. The frequency of oscillation of settling velocity scales with the Brunt–Väisälä frequency and the motion of the particle can lead to the formation of secondary and tertiary vortices following the primary vortex.

Purpose -This paper presents a first step toward developing a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach -A front-tracking/finite volume method previously developed for simulations of multiphase flows is extended to model the injection of hot polymer and its cooling down. Findings -The accuracy and convergence properties of the new method are tested by grid refinement and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, contact area and reheat region when new filaments are deposited on top of previously laid down filaments. Research limitations/implications -The present paper focuses on modeling the fluid flow and the cooling. The modeling of solidification, volume changes and residual stresses will be described in Part II. Practical implications -The ability to carry our fully resolved numerical simulations of the fusion deposition process is expected to help explore new deposition strategies and to provide the "ground truth" for the development of reduced order models. Originality/value -The present paper is the first fully resolved simulation of the deposition in fusion filament modeling.

Direct Numerical Simulations of multiphase flows have progressed rapidly over the last decade and it is now possible to simulate, for example, the motion of hundreds of deformable bubbles in turbulent flows. The availability of results from such simulations should help advance the development of new and improved closure relations and models of the average or large-scale flows. We review recent results for bubbly flow in vertical channels, discuss the difference between upflow and downflow and the effect of the bubble deformability and how the resulting insight allowed us to produce a simple description of the large scale flow, for certain flow conditions. We then discuss the need for the development of numerical methods for more complex situations, such as where the flow creates spontaneous thin films and threads, or where additional physical processes take place at a rate that is very different from the fluid flow. Recent work on capturing localized small-scale processes using embedded analytical models, focusing on the mass transfer from bubbles in liquids with low mass diffusivity, suggests one approach. We conclude by discussing immediate needs for progress on the theoretical framework for describing the large-scale motion of multiphase flows and the need for multiscale methods to capture physical processes taking place at diverse length and time scales.

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