Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simulations, of homogeneous bubble distribution in fully periodic domains at relatively low Reynolds numbers have already yielded considerable insight into the dynamics of such flows. Many aspects of the evolution converge rapidly with the size of the systems and results for the rise velocity, the velocity fluctuations, as well as the average relative orientation of bubble pairs have been obtained. The challenge now is to examine bubbles at higher Reynolds numbers, bubbles in channels and confined geometry, and bubble interactions with turbulent flows. We briefly review numerical methods used for direct numerical simulations of multiphase flows, with a particular emphasis on methods that use the socalled "one-field" formulation of the governing equations, and then discuss studies of bubbles in periodic domains, along with recent work on wobbly bubbles, bubbles in laminar and turbulent channel flows, and bubble formation in boiling.

The effect of a few relatively large bubbles injected near the walls on the wall drag in the “minimum turbulent channel” is examined by direct numerical simulations. A front-tracking/finite-volume method is used to fully resolve all flow scales including the bubbles and the flow around them. The Reynolds number, using the friction velocity and the channel half-height, is 135 and the bubbles are 54 wall units in diameter. The results show that deformable bubbles can lead to significant reduction of the wall drag by suppression of streamwise vorticity. Less deformable bubbles, on the other hand, are slowed down by the viscous sublayer and lead to a large increase in drag.

As bubbles rising in a vertical channel with upflow become bigger, it is well known that the void fraction distribution changes in a fundamental way, from a wall peak for small bubbles to a maximum void fraction at the channel center for larger bubbles. Here, we use direct numerical simulations of buoyant bubbles in a turbulent flow to show that it is not the size of the bubbles that matters, but their deformability.

Direct numerical simulations are used to study turbulent bubbly downflows in a vertical channel. All flow scales, including the bubbles and the flow around them, are fully resolved using a front-tracking/finite-volume method. The turbulent bubbly channel flow is driven downward by an imposed constant pressure gradient, and the friction Reynolds number of the flow, based on the friction velocity and half-width of the channel, is 127.3, corresponding to a bulk Reynolds number of 3786 for a flow without bubbles. Three cases with several nearly spherical bubbles are examined. The bubble diameter is 31.8 wall units for all cases but the number of bubbles is varied, giving average void fractions of 1.5%, 3%, and 6%. The lift force on the bubbles drives them away from the walls until the mixture in the center of the channel is in hydrostatic equilibrium. Thus, the flow consists of a core region where the average void fraction and the mean vertical velocity are approximately constant and a bubble-free wall layer. The vertical velocity fluctuations in the wall layer decrease as the void fraction increases and the width of the wall layer decreases, but in the bubble-rich core the velocity fluctuations are higher than for a corresponding single-phase turbulent flow.

Direct numerical simulations of bubbly multiphase flows are used to find closure terms for a simple model of the average flow, using Neural Networks (NNs). The flow considered consists of several nearly spherical bubbles rising in a periodic domain where the initial vertical velocity and the average bubble density are homogeneous in two directions but non-uniform in one of the horizontal directions. After an initial transient motion the average void fraction and vertical velocity become approximately uniform. The NN is trained on a dataset from one simulation and then used to simulate the evolution of other initial conditions. Overall, the resulting model predicts the evolution of the various initial conditions reasonably well.

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.

Purpose -This paper continues the development of a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach -A front-tracking/finite volume method introduced in Part I to simulate the heat transfer and fluid dynamics of the deposition of a polymer filament on a fixed bed is extended by adding an improved model for the injection nozzle, including the shrinkage of the polymer as it cools down, and accounting for stresses in the solid. 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, the shrinkage and the solid stresses.Research limitations/implications -The method presented in the paper focuses on modeling the fluid flow, the cooling and solidification, as well as volume changes and residual stresses, using a relatively simple viscoelastic constitutive model. More complex material models, depending, for example, on the evolution of the configuration tensor, are not included. Practical implications -The ability to carry out fully resolved numerical simulations of the fusion deposition process is expected to be critical for the validation of mathematical models for the material behavior, to help explore new deposition strategies, and to provide the "ground truth" for the development of reduced order models. Originality/value -The paper completes the development of the first numerical method for fully resolved simulation of fusion filament modeling. arXiv:1711.07094v2 [physics.flu-dyn]