A continuum model for transport phenomena in convective flow of solid–liquid phase change material suspensions

Heat and mass transport is modeled in convective flow of a dilute binary mixture of a continuous fluid with mono-dispersed particles (PCM suspensions), in which solid–liquid phase change can take place. The model is based on the mixture continuum approach together with an approximate enthalpy formulation, in which the temporal and spatial variations of phase change fraction in the particles are considered explicitly. Derivations are given for a set of equations governing conservation of mass, momentum, species, and energy of the suspensions, as well as the evolution of phase change fraction of the dispersed particles.     

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.     

Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

Predicting gas–liquid flow in a mechanically stirred tank

Computational fluid dynamics (CFD) provides a method for investigating the highly complex fluid flow in mechanically stirred tanks. Although there are quite a number of papers in the literature describing CFD methods for modelling stirred tanks, most only consider single-phase flow. However, multiphase mixtures occur very frequently in the process industries, and these are more complex situations for which modelling is not as well developed. This paper reports on progress in developing CFD simulations of gas–liquid mixing in a baffled stirred tank. The model is three-dimensional and the impeller region is explicitly included using a Multiple Frames of Reference method to account for the relative movement between impeller and baffles. Fluid flow is calculated with a turbulent two-fluid model using a finite-volume method. Several alternative treatments of the multiphase equations are possible, including various expressions for drag and dispersion forces, and a number of these have been tested. Variation in bubble size due to coalescence and break-up is also modelled. The CFD simulation method has been used to model a gas-sparged tank equipped with a Rushton turbine, and simulation results are compared with experimental data. Results to date show the correct pattern of gas distribution and the correct trends in local bubble size in the tank. Further work is needed to improve the quantitative agreement with experimental data.     

A phase field approach to solidification and solute separation in water solutions

We propose a phase field model for the solid–liquid phase transition in a water-salt (sodium chloride) solution in the absence of macroscopic motion, under possibly non-isothermal conditions. A thermodynamic approach based on a free energy functional is assumed. The model consists of three evolution equations: a time-dependent Ginzburg–Landau equation for the solid–liquid phase change, a diffusion equation of the Cahn–Hilliard kind for the solute dynamics and the heat equation for the temperature change. The proposed system is aimed to contribute to the modelling of the brine channels formation in the ice of the polar seas.     

Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.     

Modeling of local particle accumulation in disperse flows with kinematic singularities

The aim of the study is to model the formation of local particle accumulation zones near several typical kinematic singularities. The flows considered are: (i) a steady two–dimensional flow with localized vorticity of the Kelvin cat's eye type (vortex in a mixing layer), (ii) a steady axisymmetric flow formed by a vortex filament normal to a plane in viscous fluid (simple model of tornado), (iii) a neighbourhood of a zero acceleration point in two–dimensional unsteady (harmonic) flow. From parametric numerical calculations, we investigated the inertial mechanisms of forming local particle accumulation zones and found the threshold values of governing parameters separating qualitatively different particle velocity and density patterns. In particular, it is shown that the zero–acceleration point can either “attract” or “scatter” the particles. Zones of concentrated vorticity are typically devoid of particles. In the tornado–like flow, an axisymmetric “cup-shaped” particle accumulation region is formed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling aspects of flow and solute transport simulations in water disinfection tanks

Water disinfection tanks such as chlorine and ozone contactors typically consist of multiple compartments featuring a serpentine flow pattern. Due to the complex hydrodynamics, the design and optimization of these tanks are often carried out by employing computational fluid dynamics (CFD) simulations. The present study demonstrates the influence of certain modeling aspects when the widely used Reynolds-Averaged Navier Stokes (RANS) based CFD approach to predict hydrodynamics and disinfection performance is employed. Three different contact tank geometries are examined numerically using RANS. The time-averaged velocity predictions are reasonably accurate when compared to validation data. However, in baffled contact tanks, the time-averaged flow differs quite significantly from the instantaneous flow, with the consequence that RANS-based models require careful calibration of the turbulent mixing parameter, i.e., the turbulent Schmidt number, when computing transport of solutes.     

Modeling Sediment Deposition Patterns Arising From Suddenly Released Fixed-Volume Turbulent Suspensions

Models presented in several recent papers [1–3] dealing with particle transport by, and deposition from, bottom gravity currents produced by the sudden release of dilute, well‐mixed fixed‐volume suspensions have been relatively successful in duplicating the experimentally observed long‐time, distal, areal density of the deposit on a rigid horizontal bottom. These models, however, fail in their ability to capture the experimentally observed proximal pattern of the areal density with its pronounced dip in the region initially occupied by the well‐mixed suspension and its equally pronounced local maximum at roughly the one‐third point of the total reach of the deposit. The central feature of the models employed in [1–3] is that the particles are always assumed to be vertically well‐mixed by fluid turbulence and to settle out through the bottom viscous sublayer with the Stokes settling velocity for a fluid at rest with no re‐entrainment of particles from the floor of the tank. Because this process is assumed from the outset in the models of [1–3], the numerical simulations for a fixed‐volume release will not take into account the actual experimental conditions that prevail at the time of release of a well‐mixed fixed‐volume suspension. That is, owing to the vigorous stirring that produces the well‐mixed suspension, the release volume will initially possess greater turbulent energy than does an unstirred release volume, which may only acquire turbulent energy as a result of its motion after release through various instability mechanisms. The eddy motion in the imposed fluid turbulence reduces the particle settling rates from the values that would be observed in an unstirred release volume possessing zero initial turbulent energy. We here develop a model for particle bearing gravity flows initiated by the sudden release of a fixed‐volume suspension that takes into account the initial turbulent energy of mixing in the release volume by means of a modified settling velocity that, over a time scale characteristic of turbulent energy decay, approaches the full Stokes settling velocity. Thereafter, in the flow regime, we assume that the turbulence persists and, in accord with current understanding concerning the mechanics of dense underflows, that this turbulence is most intense in the wall region at the bottom of the flow and relatively coarse and on the verge of collapse (see [22]) at the top of the flow where the density contrast is compositionally maintained. We capture this behavior by specifying a “shape function” that is based upon experimental observations and provides for vertical structure in the volume fraction of particles present in the flow. The assumption of vertically well‐mixed particle suspensions employed in [1–5] corresponds to a constant shape function equal to unity. Combining these two refinements concerning the settling velocity and vertical structure of the volume fraction of particles into the conservation law for particles and coupling this with the fluid equations for a two‐layer system, we find that our results for areal density of deposits from sudden releases of fixed‐volume suspensions are in excellent qualitative agreement with the experimentally determined areal densities of deposit as reported in [1, 3, 6]. In particular, our model does what none of the other models do in that it captures and explains the proximal depression in the areal density of deposit.     

Dispersion of solid particles in turbulant flow through pipe expansions

Studies of the effects upon gas-liquid two-phase flows of pipefittings such as expansions, contractions, bends, and valveshave usually concentrated upon pressuredrop correlations andhave not attempted to determine changes in the distributionsof the gas and liquid phases caused by the fitting. However,it is known that such information is important if, for example,flow separators, which divide the gas and liquid phases in avariety of industrial processes, are to function efficiently.It is therefore important to gain an understanding of the influenceupon phase distributions of the common pipe fittings mentionedabove, which will be found in almost any industrial pipeworksystem. As a first step, the dispersion of solid particles carriedby turbulent gas flows through a pipe expansion has been modellednumerically. The commercial fluid-flow code CFDS-FLOW{smalltilde}hDas been used to model the gas flow, together with aneddy interaction model for determination of the motion of thesolid particles. Mean particle velocities and root-mean-squarevalues of the particle velocity fluctuations, as well as particleconcentrations, are evaluated and compared with recent experimentalresults. The influence of different eddy-length and eddy-lifetimespecifications upon the dispersion of particles of various sizesis investigated. It is found that the different eddy characteristicshave little effect on predicted mean particle velocities, whereasfluctuations in particle velocities and particle concentrationare sensitive to the changes made. By comparing the resultswith experimental data, it is possible to draw conclusions aboutthe relative merits of the different eddy specifications.     

Numerical simulation of ice formation in a reservoir

The one-dimensional formulation is considered of a two-phase Stefan problem of heat flow with an unknown phase transition temperature that depends on the concentration of impurity. A numerical method is described for implementing the constraints that the heat and mass conservation are given on the unknown nonstationary boundary between the liquid and solid phases. Some examples are included of simulations for the sodium chloride solutions of different concentrations.     

CFD of turbulent transport of particles behind a backward-facing step using a new model—k-ε-Sp

The k-ε-S_p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models (k-ε-A_p, k-ε-k_p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.     

悬浮固粒对二维混合层流动失稳特性的影响*

本文在不可压缩二维混合层流动方程的基础之上,通过添加固粒的作用项,推导得到了修正的瑞利方程;然后用数值计算方法解其特征方程,得到了悬浮固粒的质量密度、固粒和气流的速度比值以及Stokes数不同时二维混合层流动中扰动频率与空间增长率的关系曲线,给出了关于悬浮固粒对流场失稳特性影响的几个重要结论。     

Simulations of thixotropic liquids

In thixotropic liquids the rheological properties depend on the liquid’s deformation history. Clay suspensions (as encountered in oil sands mining) are a prominent example. Activated clay particles form a network. As a consequence of (ionic) transport limitations, the network is not an instantaneous feature; it takes time to build up, and also to break down, the latter as a result of deformation in the liquid. In this paper a procedure for detailed simulations of flow of viscous thixotropic liquids is outlined. The local viscosity of the liquid relates to the level of integrity of the network. The time-dependence of the liquid’s rheology is due to the finite rate with which the network in the liquid builds up or breaks down. This concept has been incorporated in a lattice-Boltzmann discretization of the flow equations. With this methodology the way thixotropic liquids are mobilized in mixing tanks and the drag force experienced by dense assemblies of coarse particles (e.g. sand) in thixotropic liquids have been studied.     

A 3-dimensional Eulerian–Eulerian CFD simulation of a hydrocyclone

Hydrocyclones are used in mineral industries for classification and separation of solid particles of different sizes and densities suspended in water medium. In the present study an Eulerian–Eulerian CFD simulation of a solid–liquid hydrocyclone has been carried out taking into account two solid phases and one liquid phase. The average size of the larger particle was 0.6117 and that of the smaller particle was 0.09875 mm. Three separate momentum balance equations for the three phases have been considered unlike that in the mixture model where a single momentum equation is solved for the three phases. Two turbulent models i.e. the Reynolds stress model (RSM) and the standard k–ε model were studied. Comparison of the two turbulence models showed slight variation in prediction of the velocity profile and the separation efficiency. The maximum deviation between the two models was observed near the wall where the stress was maximum for larger size particles.     

3D gradient corrected SPH for fully resolved particle–fluid interactions

Fully resolved fluid–solid coupling is explored with the gradient corrected weakly compressible SPH methodology being used to simulate an incompressible Newtonian fluid as well as being used to obtain the coupling force information required to accurately represent these interactions. Gradient correction allows for the application of the Neumann boundary condition required to describe the pressure fields at solid interfaces, as well as symmetry boundary conditions for velocity (where applicable) without the use of ghost or mirrored particles. A scaling study is performed by investigating the drag on an infinitely long cylinder at different smoothed particle hydrodynamics (SPH) resolutions, with finer resolution scales showing good correlation to other studies. The drag characteristics of several particle shapes and topologies are also investigated making use of both convex and non-convex particle shapes. Clear distinction for both the fluid and solid particle responses for the various solid particle shapes are observed. Boundary effects are also explored with results showing a strong responses to changing domain geometry aspect ratios. A many particle system with two different particle shapes are simulated to investigate bulk behaviour of the different solids falling under gravity in a fluid. All results presented in this paper are obtained from full 3D simulations.     

Interaction of a finite-size particle with the moving lid of a cavity

The motion of a solid particle in a lid-driven cavity is investigated. If the tangential velocity of the lid is large the streamlines are dense near the moving lid and the finite size of a particle can have a profound effect on its trajectory. To assess this effect different particle-motion models are examined: inertial point particles (Maxey–Riley equation) one-way coupled to the flow and finite-size particles the flow around which is fully resolved (two-way coupling). We compare the corresponding trajectories with those obtained using the particle–surface interaction model originally introduced by Hofmann and Kuhlmann [Phys. Fluids 23, 0721106 (2011)]. The finite-size effect on the particle's trajectory is quantified and discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact and approximate expressions for resistance coefficients of a colloidal sphere approaching a solid surface at intermediate Reynolds numbers

A mathematical model has been developed to describe the force of liquid flow acting on a colloidal spherical particle as it approaches a solid surface at intermediate-Reynolds-number-flow regime. The model has incorporated bispherical coordinates to determine a stream function for the flow disturbed by the sphere. The stream function was then used to derive the flow force on the particle as a function of the inter-surface separation distance. The force equation was related to the modified Stokes equation to obtain an exact analytical expression for the correction factor to the Stokes law. Finally, a rational approximation is presented, which is in good agreement with the exact numerical result, and can be readily applied to more general particle–surface interactions involving short-range hydrodynamics associated with colloidal particles in the near vicinity of a large solid collector surface at intermediate Reynolds number of the supporting flow.     

Numerical modeling of interaction between surface radiation and natural convection of atmospheric aerosol in presence of transverse magnetic field

After the era of industrialization, technology is developing daily since the last century. Urbanization, communication, and transportation have grown rapidly and simultaneously deforestation and volcanic eruptions take place on a large scale. As result every moment tons of foreign particles like soot, dust, ash, and bio-fuel contaminants are released into the atmosphere. These contaminants mix with air and various green house gases, form a blanket structure in atmosphere. This mixture of ultrafine particle suspension with atmospheric air is known as aerosol. In the present study, numerical simulations of hydrodynamic single cell buoyant convection of atmospheric aerosol sample enclosed within a gray enclosure in the presence of a transverse magnetic field and surface radiation is addressed. Flow of the aerosol over deserts and industrial belts is a practical example of such a condition, where the thermal radiation emanating from the surface, affects the flow mechanism of the aerosol transport. The emphasis of the present study is only on carbon-black solid particles of a size in the nanometer range present in atmospheric air. The aerosol is treated as nanofluid for the numerical simulation. A comprehensive study on the controlling parameters that affect the flow and heat transfer characteristics are delineated. The governing equations are solved using modified MAC method and SIMPLER algorithm has been used to solve pressure velocity coupling employing relaxation technique. The transport equation for surface radiation is solved using the net radiation method. The cross string method is used to evaluate the view factor. The most striking result is that the heat transfer rate increases with increase in the volume fraction of the carbon-black particles, which has an adverse effect on both the climate and living creatures. The results are presented in tabular and graphical form. The heat transfer and flow characteristics are depicted in the form of isotherms and streamlines revealing the physics of this complex phenomenon.