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

Direct numerical simulations of mass transfer in square microchannels for liquid-liquid slug flow

Microreactors for the development of liquid-liquid processes are promising technologies since they are supposed to offer an enhancement of mass transfer compared to conventional devices due to the increase of the surface/volume ratio. But impact of the laminar flow should be negative and the effect is still to be evaluated. The present work focuses on the study of mass transfer in microchannels by means of 2D direct numerical simulations. We investigated liquid-liquid slug flow systems in square channel of 50 to 960 μm depth. The droplets velocity ranges from 0.0015 to 0.25 m/s and the ratio between the channel depth and the droplets length varies between 0.4 and 11.2. Droplet side volumetric mass transfer coefficients were identified from concentration field computations and the evolution of these coefficients as a function of the flow parameters and the channel size is discussed. This study reveals that mass transfer is strongly influenced by the flow structure inside the droplet. Moreover, it shows that the confinement of the droplets due to the channel size leads to an enhancement of mass transfer compared to cases where the droplets are not constrained by the walls

A fundamental approach to predicting mass transfer coefficients in bubble column reactors

Includes bibliographical references.A bubble column reactor is a vertical cylindrical vessel used for gas-liquid reactions. Bubble Columns have several applications in industry due to certain obvious advantages such as high gas-liquid interfacial area, high heat and mass transfer rates, low maintenance requirements and operating costs. On the other hand, attempts at modelling and simulation are complicated by lack of understanding of hydrodynamics and mass transfer characteristics. This complicates design scale-up and industrial usage. Many studies and models have attempted to evolve understanding of the hydrodynamic complexity in Bubble Columns reactors. A closer look at these studies and models reveals a variety of solution methods for different systems (Frössling, 1938; Clift et al., 1978; Hughmark, 1967; Dutta, 2007; Ranz and Marshall, 1952; Benitez, 2009; Buwa et al., 2006; Suzzia et al., 2009; Wylock et al., 2011). Numerous correlations (Frössling, 1938; Clift et al., 1978; Hughmark, 1967; Dutta, 2007; Ranz and Marshall, 1952; Benitez, 2009; Buwa et al., 2006) exist but to date in literature, there is no general approach to determining accurate estimates of average mass transfer coefficient values. Good estimates of the average mass transfer coefficient will improve the predictive capacity of the associated models. Recent attempts at modelling micro-scale bubble-fluid interaction resulted in the Bubble Cell Model, BCM, (Coetzee et al., 2009) which simulates the velocity vector field around a single gas bubble in a flowing fluid stream using a Semi-Analytical model. The aim of the present study is to extend the BCM applications by integrating the mass balance into the framework to predict the average mass transfer coefficient in bubble columns. A nitrogen-water steady state system was simulated in an axisymmetric grid where mass transfer occurs between the gas and liquid

Numerical Simulation of Convective-Radiative Heat Transfer

This book presents numerical, experimental, and analytical analysis of convective and radiative heat transfer in various engineering and natural systems, including transport phenomena in heat exchangers and furnaces, cooling of electronic heat-generating elements, and thin-film flows in various technical systems. It is well known that such heat transfer mechanisms are dominant in the systems under consideration. Therefore, in-depth study of these regimes is vital for both the growth of industry and the preservation of natural resources. The authors included in this book present insightful and provocative studies on convective and radiative heat transfer using modern analytical techniques. This book will be very useful for academics, engineers, and advanced students

Mass or heat transfer inside a spherical gas bubble at low to moderate Reynolds number

Mass (or heat) transfer inside a spherical gas bubble rising through a stationary liquid is investigated by direct numerical simulation. Simulations were carried out for bubble Reynolds number ranging from 0.1 to 100 and for Péclet numbers ranging from 1 to 2000. The study focuses on the effect of the bubble Reynolds number on both the interfacial transfer and the saturation time of the concentration inside the bubble. We show that the maximum velocity Umax at the bubble interface is the pertinent velocity to describe both internal and external transfers. The corresponding Sherwood (or Nusselt) numbers and the saturation time can be described by a sigmoid function depending on the Péclet number Pemax = Umaxdb/D (db and D being the bubble diameter and the corresponding diffusion coefficient)

Improved micro-contact resistance model that considers material deformation, electron transport and thin film characteristics

This paper reports on an improved analytic model forpredicting micro-contact resistance needed for designing microelectro-mechanical systems (MEMS) switches. The originalmodel had two primary considerations: 1) contact materialdeformation (i.e. elastic, plastic, or elastic-plastic) and 2) effectivecontact area radius. The model also assumed that individual aspotswere close together and that their interactions weredependent on each other which led to using the single effective aspotcontact area model. This single effective area model wasused to determine specific electron transport regions (i.e. ballistic,quasi-ballistic, or diffusive) by comparing the effective radius andthe mean free path of an electron. Using this model required thatmicro-switch contact materials be deposited, during devicefabrication, with processes ensuring low surface roughness values(i.e. sputtered films). Sputtered thin film electric contacts,however, do not behave like bulk materials and the effects of thinfilm contacts and spreading resistance must be considered. Theimproved micro-contact resistance model accounts for the twoprimary considerations above, as well as, using thin film,sputtered, electric contact

Bubble formation from a flexible hole submerged in an inviscid liquid

In the waste water treatment industry, a novel gas sparger based on flexible membranes has been used for the last ten years. The objective of the present work is to study the bubble formation generated from a flexible orifice (membrane). Firstly, the membranes are characterised with regard to their properties: wetting critical surface tension, expanding hole diameter, orifice coefficients, flexibility, critical and elastic pressures. The bubble formation phenomenon in an inviscid liquid at rest is studied experimentally for different membranes and gas flow rates. The variation in the bubble diameter, the bubble centre of gravity and the bubble spread on the membrane are determined as a function of time. An analytic model is proposed to describe the bubble growth and its detachment at a flexible orifice. This theoretical approach, developed by Teresaka & Tsuge (1990) for rigid orifices, is adapted to take into account the membrane features (elastic behaviour and wettability). The predicted bubble diameters at detachment agree with the experimental measurements; however, the model underestimates slightly the bubble formation times. The calculation of the various forces acting on the bubble in the vertical direction indicates that the real forces governing the bubble growth are the buoyancy force, the surface tension force, and near detachment the inertial force