Numerical simulation of super-square patterns in Faraday waves

We report the first simulations of the Faraday instability using the full three-dimensional Navier-Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in rectangular and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of [Douady & Fauve, Europhys. Lett. 6, 221-226 (1988); Douady, J. Fluid Mech. 221, 383-409 (1990)] is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared to the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the center

Effect of surfactants during drop formation in a microfluidic channel: a combined experimental and computational fluid dynamics approach

The effect of surfactants on the flow characteristics during rapid drop formation in a microchannel is investigated using high-speed imaging, micro-particle image velocimetry and numerical simulations; the latter are performed using a three- dimensional multiphase solver that accounts for the transport of soluble surfactants in the bulk and at the interface. Drops are generated in a flow-focusing microchannel, using silicone oil ( 4.6 mPa s) as the continuous phase and a 52 % w/w glycerol solution as the dispersed phase. A non-ionic surfactant (Triton X-100) is dissolved in the dispersed phase at concentrations below and above the critical micelle concentration. Good agreement is found between experimental and numerical data for the drop size, drop formation time and circulation patterns. The results reveal strong circulation patterns in the forming drop in the absence of surfactants, whose intensity decreases with increasing surfactant concentration. The surfactant concentration profiles in the bulk and at the interface are shown for all stages of drop formation. The surfactant interfacial concentration is large at the front and the back of the forming drop, while the neck region is almost surfactant free. Marangoni stresses develop away from the neck, contributing to changes in the velocity profile inside the drop

Effet de la rotation sur les instabilités thermocapillaires dans un pont liquide chauffé latéralement

Dans les procédés de croissance cristalline, la rotation est souvent utilisée comme moyen pour éliminer les défauts d'axisymétrie du chauffage. La rotation du système de chauffage étant en général difficile à mettre en {\oe}uvre, une solution consiste à faire tourner à la fois le cristal et le polycristal soit dans le même sens soit dans des directions opposées. Les vitesses optimales de rotation du cristal et du polycristal sont souvent déterminées empiriquement. A l'aide d'une étude numérique de stabilité linéaire tridimensionnelle puis d'un bilan d'énergie, nous avons cherché à comprendre les effets de rotation sur l'instabilité thermocapillaire en zone flottante. Nous présentons des résultats où nous montrons que la rotation peut avoir des effets surprenants de stabilisation ou de déstabilisation et proposons des pistes pour l'interprétation

Numerical study of oil–water emulsion formation in stirred vessels: effect of impeller speed

The mixing of immiscible oil and water by a pitched blade turbine in a cylindrical vessel is studied numerically. Three-dimensional simulations combined with a hybrid front-tracking/level-set method are employed to capture the complex flow and interfacial dynamics. A large eddy simulation approach, with a Lilly–Smagorinsky model, is employed to simulate the turbulent two-phase dynamics at large Reynolds numbers Re=1802−18 026 . The numerical predictions are validated against previous experimental work involving single-drop breakup in a stirred vessel. For small Re , the interface is deformed but does not reach the impeller hub, assuming instead the shape of a Newton's Bucket. As the rotating speed increases, the deforming interface attaches to the impeller hub which leads to the formation of long ligaments that subsequently break up into small droplets. For the largest Re studied, the system dynamics becomes extremely complex wherein the creation of ligaments, their breakup and the coalescence of drops occur simultaneously. The simulation outcomes are presented in terms of spatio-temporal evolution of the interface shape and vortical structures. The results of a drop size analysis in terms of the evolution of the number of drops, and their size distribution, is also presented as a parametric function of Re

Dynamics of a surfactant-laden bubble bursting through an interface

We study the effect of surfactant on the dynamics of a bubble bursting through an interface. We perform fully three-dimensional direct numerical simulations using a hybrid interface-tracking/level-set method accounting for surfactant-induced Marangoni stresses, sorption kinetics and diffusive effects. We select an initial bubble shape corresponding to a large Laplace number and a vanishingly small Bond number in order to neglect gravity, and isolate the effects of surfactant on the flow. Our results demonstrate that the presence of surfactant affects the dynamics of the system through Marangoni-induced flow, driving motion from high to low concentration regions, which is responsible for the onset of a recirculation zone close to the free surface. These Marangoni stresses rigidify the interface, delay the cavity collapse and influence the jet breakup process

The transition to aeration in turbulent two-phase mixing in stirred vessels

We consider the mixing dynamics of an air–liquid system driven by the rotation of a pitched blade turbine (PBT) inside an open, cylindrical tank. To examine the flow and interfacial dynamics, we use a highly parallelised implementation of a hybrid front-tracking/level-set method that employs a domain-decomposition parallelisation strategy. Our numerical technique is designed to capture faithfully complex interfacial deformation, and changes of topology, including interface rupture and dispersed phase coalescence. As shown via transient, a three-dimensional (3-D) LES (large eddy simulation) using a Smagorinsky–Lilly turbulence model, the impeller induces the formation of primary vortices that arise in many idealised rotating flows as well as several secondary vortical structures resembling Kelvin–Helmholtz, vortex breakdown, blade tip vortices and end-wall corner vortices. As the rotation rate increases, a transition to ‘aeration’ is observed when the interface reaches the rotating blades leading to the entrainment of air bubbles into the viscous fluid and the creation of a bubbly, rotating, free surface flow. The mechanisms underlying the aeration transition are probed as are the routes leading to it, which are shown to exhibit a strong dependence on flow history

Computational fluid dynamics simulations of phase separation in dispersed oil-water pipe flows

The separation of liquid–liquid dispersions in horizontal pipes is common in many industrial sectors. It remains challenging, however, to predict the separation characteristics of the flow evolution due to the complex flow mechanisms. In this work, Computational Fluid Dynamics (CFD) simulations of the silicone oil and water two-phase flow in a horizontal pipe are performed. Several cases are explored with different mixture velocities and oil fractions (15%-60%). OpenFOAM (version 8.0) is used to perform Eulerian-Eulerian simulations coupled with population balance models. The ‘blending factor’ in the multiphaseEulerFoam solver captures the retardation of the droplet rising and coalescing due to the complex flow behaviour in the dense packed layer (DPL). The blending treatment provides a feasible compensation mechanism for the mesoscale uncertainties of droplet flow and coalescence through the DPL and its adjacent layers. In addition, the influence of the turbulent dispersion force is also investigated, which can improve the prediction of the radial distribution of concentrations but worsen the separation characteristics along the flow direction. Although the simulated concentration distribution and layer heights agree with the experiments only qualitatively, this work demonstrates how improvements in drag and coalescence modelling can be made to enhance the prediction accuracy

An AI-based non-intrusive reduced-order model for extended domains applied to multiphase flow in pipes

The modeling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of meters vs a pipe diameter of just a few inches. Approximating CFD models in a low-dimensional space, reduced-order models have been shown to produce accurate results with a speed-up of orders of magnitude. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM), which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by (i) using a domain decomposition approach; (ii) using dimensionality reduction to obtain a low-dimensional space in which to approximate the CFD model; (iii) training a neural network to make predictions for a single subdomain; and (iv) using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we compare Proper Orthogonal Decomposition with several types of autoencoder networks, known for their ability to compress information accurately and compactly. The comparison is assessed with two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network, which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce visually realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1 and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Inspection of the predicted liquid volume fractions shows a good match with the high fidelity model as shown in the results. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the accuracy of our approach