A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h0 and length x0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ=x0/h0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λcrit ), the dynamics of the current is significantly influenced by λ. We conjecture that λcrit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λcrit ) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ1/4 when λ<λcrit

Resolved simulations of submarine avalanches with a simple soft-sphere / immersed boundary method

Physical mechanisms at the origin of the transport of solid particles in a fluid are still a matter of debate in the physics community. Yet, it is well known that these processes play a fundamental role in many natural configurations, such submarines landslides and avalanches, which may have a significant environmental and economic impact. The goal here is to reproduce the local dynamics of such systems from the grain scale to that of thousands of grains approximately. To this end a simple soft-sphere collision / immersed-boundary method has been developed in order to accurately reproduce the dynamics of a dense granular media collapsing in a viscous fluid. The fluid solver is a finite-volume method solving the three-dimensional, time-dependent Navier-Stokes equations for a incompressible flow on a staggered. Here we use a simple immersed-boundary method consisting of a direct forcing without using any Lagrangian marking of the boundary, the immersed boundary being defined by the variation of a solid volume fraction from zero to one. The granular media is modeled with a discrete element method (DEM) based on a multi-contact soft-sphere approach. In this method, an overlap is allowed between spheres which mimics the elasto-plastic deformation of real grain, and is used to calculate the contact forces based on a linear spring model and a Coulomb criterion. Binary wall-particle collisions in a fluid are simulated for a wide range of Stokes number ranging from 10-¹ to 10⁴. It is shown that good agreement is observed with available experimental results for the whole range of investigated parameters, provided that a local lubrication model is used when the distance of the gap between the particles is below a fraction of the particle radius. A new model predicting the coefficient of restitution as a function of the Stokes number and the relative surface roughness of the particles is proposed. This model, which makes use of no adjustable constant, is shown to be in good agreement with available experimental data. Finally, simulations of dense granular flows in a viscous fluid are performed. The present results are encouraging and open the way for a parametric study in the parameter space initial aspect ratio - initial packing

A numerical investigation of constant-volume non-Boussinesq density currents

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents of density ρc, released from a lock of height h₀ and length x₀ into a ambient of height H and density ρₐ, is considered. We use two dimensional Navier-Stokes simulations to cover a wide range of density ratio ρc/ρₐ (for both "heavy"-bottom and "light"-top currents) and geometric ratios (H*=H/h₀, λ=x₀/h₀). To our knowledge, the ranges of parameters and times of propagation considered here were not covered in previous experimental or numerical studies. In the first part, we set the lock aspect ratio to λ=18.75, and vary the density ratio 10-⁴<ρc/ρₐ<10⁴ and initial depth ratio 1≤H*≤50. The Navier-Stokes results are compared with predictions of a shallow-water model, in the regime of constant-speed (slumping) phase. Good agreement is observed in a large region of the parameter space (ρc/ρₐ; H*). The larger discrepancy is observed in the range of high-H* and low-ρc/ρₐ for which the shallow-water model overpredicts the velocity of the current. Two possible reasons are suspected, namely the fluid motion in the ambient fluid which is not accounted for in the model, and the choice of the model for the front condition. In the second part, we set the initial depth ratio to H*=10, and vary the density ratio 10-²<ρc/ρₐ<10² and lock aspect ratio 0.5≤λ≤18.75. In particular, we derive novel insights on the influence of the lock aspect ratio λ=x₀/h₀ on the shape and motion of the current in the slumping stage. It is shown that a critical value exists, λcrit; the dynamics of the current is significantly influenced by λ if below λcrit. We present a simple analytical model which support the observation that for a light current the speed of propagation is proportional to λ¼ when λ<λcrit

Visualization of toner ink adsorption at bubble surfaces

Flotation deinking involves interactions between inks particles and bubbles surfaces. These interactions are very difficult to observe directly or to quantify in bench-scale experiments or mill operations, making it difficult to evaluate effects of process conditions such as bubble size and solution chemistry on deinking efficiency. This paper presents images and measurements of toner ink interactions with bubble surfaces in laboratory-scale flotation processes. Stable adsorption of toner ink was observed at surfaces of stationary and suspended bubbles for several system chemistries. Interactions of toner particles and bubbles were quantified by high magnification and high temporal resolution digital videos obtained in bubble flow facilities creating both stationary and flowing bubbles. Large (>200 micron), flat toner particles adsorbed to bubble surfaces by single contact points. Smaller toner particles formed very stable complexes in fatty acid chemistries. Desorption of toner ink from bubble surfaces was not observed, even for vigorous flows. Bubbles were observed to be fully covered with toner after 4 minutes of residence time in the suspending bubble flow facility. Initial estimates indicate that bubbles with diameters of approximately 1 mm carry more than 1 mg of ink per bubble

Teaching in the lab through virtual reality [Apprendere in laboratorio tramite la realtà virtuale]

This contribution proposes a reflection on a virtual training experience carried out in a uni- versity through the use of 3D viewers. The project arose in response to the need posed by the pandemic period to reduce interaction and the use of tools. Hence, the idea of experimenting with laboratory didactics through virtual reality. The research group started to reflect on the experience, trying to systematize an interpretative view that overcomes certain classical an- timonies (real/virtual; concrete world and imaginary world). What emerges is an interpretative matrix that is still in progress and is intended to serve as a key for identifying possible lines of didactic action, beyond forcing positions in the given categories. Without claiming to be a systematicreview,theworkaimstoofferstartingpointforreflection amoreintegratedview of the use of virtual reality in education

An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics

We report on the development and applications of an interface-capturing method aimed at computing threedimensional incompressible two-phase flows involving high density and viscosity ratios, together with capillary effects. The numerical approach borrows some features to the Volume of Fluid method (since it is essentially based on the transport of the local volume fraction of the liquid) as well as to the Level Set technique (as no explicit reconstruction of the interface is carried out). The transport of the volume fraction is achieved by using a flux-limiting Zalesak scheme and the fronts are prevented from spreading in time by a specific strategy in which the velocity at nodes crossed by the interface is modified to keep the thickness of the transition region constant. As shown on several test cases, this algorithm allows the interface to deform properly while maintaining the numerical thickness of the transition region within three computational cells whatever the structure of the local flow field. The full set of governing equations is then used to investigate some fundamental aspects of bubble dynamics. More precisely we focus on the evolution of shape and rise velocity of a single bubble over a wide range of physical parameters and on head-on and side-by-side interactions between two rising bubbles

Hydrodynamic structures of droplets in square micro-channels

This paper reports on numerical simulations of the hydrodynamics inside droplets in rectangular micro-channels. We use a finite-volume/front-capturing method that allows us to perform two- and three-dimensional simulations with a reasonable cost. The numerical method is an interface-capturing technique without any interface reconstruction. Therefore no complex or expensive interface tracking is needed. Droplet interface deformation and velocity fields inside both droplets and continuous phase can then be followed. This study leads to important results about droplet deformation and inner streamlines for mass and heat transfer studies. More particularly, the capillary number seems to have a great influence on the liquid/liquid flow hydrodynamics whatever is the channel width

Effect of schmidt number on the structure and propagation of density currents

The results of a numerical study of two- and three-dimensional Boussinesq density currents are described. They are aimed at exploring the role of the Schmidt number on the structure and dynamics of density driven currents. Two complementary approaches are used, namely a spectral method and a finite-volume interface capturing method. They allow for the first time to describe density currents in the whole range of Schmidt number 1 ≤ Sc ≤ ∞ and Reynolds number 102 ≤ Re ≤ 104. The present results confirm that the Schmidt number only weakly influences the structure and dynamics of density currents provided the Reynolds number of the flow is large, say of 0(104) or more. On the contrary low- to moderate-Re density currents are dependant on Sc as the structure of the mixing region and the front velocities are modified by diffusion effects. The scaling of the characteristic density thickness of the interface has been confirmed to behave as (ScRe)-½. Three-dimensional simulations suggest that the patterns of lobes and clefts are independent of Sc. In contrast the Schmidt number is found to affect dramatically (1) the shape of the current head as a depression is observed at high-Sc, (2) the formation of vortex structures generated by Kelvin-Helmholtz instabilities. A criterion is proposed for the stability of the interface along the body of the current based on the estimate of a bulk Richardson number. This criterion, derived for currents of arbitrary density ratio, is in agreement with present computed results as well as available experimental and numerical data

Transition from spherical cap to toroidal bubbles

Large gas bubbles rising under the effect of buoyancy are known to adopt either a spherical cap shape or to undergo a topological transition after which they become toroidal. We carry out an axisymmetric numerical investigation of the evolution of such large bubbles in the presence of both capillary and viscous effects. The numerical approach is of the volume of fluid type (it solves the Navier-Stokes equations on a fixed grid and transports the local volume fraction of one of the fluids), but does not involve any explicit reconstruction of the interface. The transition from spherical cap to toroidal bubbles is studied in the parameter space built on the Bond (Bo) and Archimedes (Ar) numbers, which compare the strength of inertial effects to that of capillary and viscous effects, respectively. Preliminary tests show that the position of this transition is very sensitive to the grid resolution; these tests are used to select grid characteristics that yield grid-independent results. Two markedly different transition scenarios, corresponding to the limit of large Ar and large Bo, respectively, are then identified. In the first case, the front of the bubble is pierced by an upward jet coming from the rear of the bubble. In contrast, in the limit of large Bo, a downward jet develops at the front part and pierces the rear of the bubble, unless viscous effects are sufficient to stabilize the front. We also determine the position of the transition for intermediate values of Bo and Ar and discuss the connection between present axisymmetric results and experimental situations in which the bubble is followed by a turbulent wake. We finally examine a puzzling feature of these large bubbles which is that, given an initial gas volume, the final bubble topology appears to depend dramatically on the initial conditions. Indeed, we find that initially oblate bubbles may result in stable spherical cap bubbles for values of Bo and Ar well beyond those for which initially spherical bubbles of similar volume undergo the topological transition. This remarkable influence of the initial shape is shown to be due to the influence of the oblateness on both the bubble acceleration and the hydrostatic pressure difference between the two bubble poles