scholarly journals Numerical Study of Two-Phase Granular Flow for Process Equipment

2000 ◽  
Vol 122 (4) ◽  
pp. 462-468 ◽  
Author(s):  
R. Djebbar ◽  
S. B. Beale ◽  
M. Sayed
Keyword(s):  
Granular Flow ◽  
Solid Phase ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Process Equipment ◽  
Two Phase ◽  
Angle Of Internal Friction ◽  
Phase Liquid ◽  
Multi Phase ◽  
Realistic Geometries

This paper reports on a research program of modeling multi-phase granular flow. Both single-phase granular flow and two-phase liquid/granular flow in a pressure vessel were considered. For the latter case, detailed results based on a viscous/Mohr-Coulomb closure were compared to existing formulations. Idealized test cases indicated that the numerical procedure is sound. Subsequent simulations of two-phase flow using realistic geometries and boundary conditions showed that the pressure distribution in the solid phase is fundamentally different for the Mohr-Coulomb system than for the conventional system. The effect of the angle of internal friction, geometry, and other parameters is discussed. [S0094-9930(00)01204-X]

scholarly journals Axial dispersion of the liquid phase on a three-phase Karr reciprocating plate column

2004 ◽  
Vol 69 (7) ◽  
pp. 581-599 ◽  
Author(s):  
Ljubisa Nikolic ◽  
Vesna Nikolic ◽  
Vlada Veljkovic ◽  
Miodrag Lazic ◽  
Dejan Skala
Keyword(s):  
Liquid Phase ◽  
Gas Flow ◽  
Dispersion Coefficient ◽  
Solid Phase ◽  
Axial Dispersion ◽  
Two Phase ◽  
Three Phase ◽  
Phase Liquid ◽  
Similar Equation ◽  
Plate Column

The influence of the gas flow rate and vibration intensity in the presence of the solid phase (polypropylene spheres) on axial mixing of the liquid phase in a three phase (gas-liquid-solid) Karr reciprocating plate column (RPC) was investigated. Assuming that the dispersionmodel of liquid flow could be used for the real situation inside the column, the dispersion coefficient of the liquid phase was determined as a function of different operating parameters. For a two-phase liquid-solid RPC the following correlation was derived: DL = 1.26(Af)1.42 UL 0.51 ?S 0.23 and a similar equation could be applied with ? 30 % confidence for the calculation of axial dispersion in the case of a three-phase RPC: DL = 1.39(Af)0.47 UL0.42UG0.03 ?S -0.26.

scholarly journals Crystal Growth in Gels from the Mechanisms of Crystal Growth to Control of Polymorphism: New Trends on Theoretical and Experimental Aspects

Crystals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 443 ◽  
Author(s):  
Omar Velásquez-González ◽  
Camila Campos-Escamilla ◽  
Andrea Flores-Ibarra ◽  
Nuria Esturau-Escofet ◽  
Roberto Arreguin-Espinosa ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Solid Phase ◽  
Theory And Practice ◽  
Protein Crystal ◽  
Gel Growth ◽  
Two Phase ◽  
X Ray Crystallography ◽  
Crystal Polymorphism ◽  
Phase Liquid ◽  
Solid System

A gel can be considered to be a two-phase (liquid and solid) system, which lacks flow once it reaches a stationary state. The solid phase is usually a tridimensional polymeric mesh, while the liquid phase is usually found in three forms: contained in great cavities, retained in the capillary pores between micelles, or adsorbed on the surface of a micelle. The influence of the use of gels in crystal growth is diverse and depends on the type of gel being used. A decrease in solubility of any solute in the liquid may occur if the solvent interacts extensively with the polymeric section, hence, the nucleation in gels in these cases apparently occurs at relatively low supersaturations. However, if the pore size is small enough, there is a possibility that a higher supersaturation is needed, due to the compartmentalization of solvents. Finally, this may also represent an effect in the diffusion of substances. This review is divided into three main parts; the first evaluates the theory and practice used for the obtainment of polymorphs. The second part describes the use of gels into crystallogenesis of different substances. The last part is related to the particularities of protein crystal polymorphism, as well as modern trends in gel growth for high-resolution X-ray crystallography.

A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

2021 ◽  
Vol 36 (4) ◽  
pp. 197-217
Author(s):  
Vladislav Balashov
Keyword(s):  
Phase Field ◽  
Solid Phase ◽  
Numerical Study ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Evolutionary Equation ◽  
Two Phase ◽  
Fluid Mixture ◽  
Component Mixture ◽  
Eulerian Description

Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

Experimental and Numerical Study on Growth of Single Vapor Bubble in Upward Flow Through Vertical Mini-Tube

2011 ◽  
Author(s):  
Hiroshi Iwai ◽  
Motohiro Saito ◽  
Yuichi Kami ◽  
Yasuhiro Niina ◽  
Hideo Yoshida
Keyword(s):  
Numerical Study ◽  
Piecewise Linear ◽  
Numerical Procedure ◽  
Mass Conservation ◽  
Surface Force ◽  
Bubble Behavior ◽  
Two Phase ◽  
Intense Evaporation ◽  
Flow Through ◽  
Semi Empirical

A slug flow with phase change in a vertical mini-tube is numerically simulated on the basis of a scheme of continuum mechanics. To formulate two-phase flow, the volume of fluid, VOF, method is employed; the advection of the gas-liquid surface is expressed by the piecewise linear interface calculation, PLIC, scheme, while the effect of surface tension is evaluated by the continuum surface force, CSF, model. Since the treatment of liquid film between a bubble and tube wall is crucially important to properly predict both heat transfer and resulting fluid flow in a mini-tube, a semi-empirical approach based on subsidiary knowledge estimated from a preliminary experiment is newly proposed. Further, an additional numerical procedure is introduced to obtain allowable mass conservation even in the thin-film region with intense evaporation. Consequently, by introducing only one parameter, the physical meaning of which is clear, the bubble behavior is reasonably predicted, and its detailed mechanism is clarified.

Towards a Numerical Study of Two-Phase Flow Exhaust Plume Jet

2002 ◽  
Author(s):  
C. Devals ◽  
J.-L. Estivalezes ◽  
G. Jourdan ◽  
L. Houas
Keyword(s):  
Shock Tube ◽  
Two Phase Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Phase Flow ◽  
Two Phase ◽  
Set Up ◽  
Solid Rocket ◽  
Multi Phase

The aim of the present work is to determine experimental drag coefficients for spherical particles accelerated in shock-tube. Then, validations of two phase flow calculations dealing with solid propulsion rocket in supersonic flight are undertaken. First, experiments in the multi-phase vertical-horizontal shock-tube have been set up at IUSTI in Marseille. The drag coefficient is determinated for particle Reynolds numbers less than 50000 and for particle Mach numbers less than 1.14 and is compared with those found in literature. Second, calculation of two phase flow in solid rocket plume has been performed. The particles are tracked with a stochastic one-way coupling lagrangian method.

Numerical Investigation of Sloshing in a Tank: Statistical Description of Experiments and CFD Calculations

2010 ◽  
Author(s):  
Bogdan Iwanowski ◽  
Marc Lefranc ◽  
Rik Wemmenhove
Keyword(s):  
Experimental Data ◽  
Large Scale ◽  
Single Phase ◽  
Stokes Equations ◽  
Numerical Study ◽  
Point Of View ◽  
Navier Stokes ◽  
Two Phase ◽  
Statistical Point ◽  
Phase Liquid

Numerical study of liquid dynamics in an LNG tank is presented. The available data from large scale (1:10) sloshing experiments of 2D section of an LNG carrier reveal large scatter in recorded values of peak pressures. The experimental data is analysed from statistical point of view in order to obtain distributions of the pressure peaks. Then the entire experimental data record is reproduced numerically by CFD simulations and it is shown that pressure peaks obtained numerically display scatter of values as well. A statistical description of the numerically obtained record is provided and compared with description derived from the experimental data. The applied CFD code ComFLOW solves Navier-Stokes equations and uses an improved Volume of Fluid (iVOF) method to track movement of fluid’s free surface. Two different fluid models, single-phase (liquid+void) and two-phase (liquid+compressible gas) can be applied, the latter model being capable of simulating bubbles and gas entrapped in liquid. For low tank filling rate discussed in the paper (10%) the single-phase approach is sufficient. Comparison of statistical properties of experimental and numerical records is offered.

On the role of the ambient fluid on gravitational granular flow dynamics

2010 ◽  
Vol 648 ◽  
pp. 381-404 ◽  
Author(s):  
C. MERUANE ◽  
A. TAMBURRINO ◽  
O. ROCHE
Keyword(s):  
Granular Flow ◽  
Numerical Solutions ◽  
Solid Phase ◽  
Fluid Pressure ◽  
Mixture Theory ◽  
Flow Dynamics ◽  
Solid Particles ◽  
Ambient Fluid ◽  
Two Phase

The effects of the ambient fluid on granular flow dynamics are poorly understood and commonly ignored in analyses. In this article, we characterize and quantify these effects by combining theoretical and experimental analyses. Starting with the mixture theory, we derive a set of two-phase continuum equations for studying a compressible granular flow composed of homogenous solid particles and a Newtonian ambient fluid. The role of the ambient fluid is then investigated by studying the collapse and spreading of two-dimensional granular columns in air or water, for different solid particle sizes and column aspect (height to length) ratios, in which the front speed is used to describe the flow. The combined analysis of experimental measurements and numerical solutions shows that the dynamics of the solid phase cannot be explained if the hydrodynamic fluid pressure and the drag interactions are not included in the analysis. For instance, hydrodynamic fluid pressure can hold the reduced weight of the solids, thus inducing a transition from dense-compacted to dense-suspended granular flows, whereas drag forces counteract the solids movement, especially within the near-wall viscous layer. We conclude that in order to obtain a realistic representation of gravitational granular flow dynamics, the ambient fluid cannot be neglected.

scholarly journals Buoyancy-induced convection of water-based nanofluids in differentially-heated horizontal semi-annuli

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2643-2660
Author(s):  
Alessandro Quintino ◽  
Elisa Ricci ◽  
Emanuele Habib ◽  
Massimo Corcione
Keyword(s):  
Volume Fraction ◽  
Solid Phase ◽  
Numerical Study ◽  
Brownian Diffusion ◽  
Nanoparticle Dispersion ◽  
Two Phase ◽  
Average Temperature ◽  
Effective Dynamic ◽  
Water Based ◽  
The Impact

A two-phase model based on the double-diffusive approach is used to perform a numerical study on natural convection of water-based nanofluids in differentially-heated horizontal semi-annuli, assuming that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum, and energy for the nanofluid, and continuity for the nanoparticles, is solved by the way of a computational code which incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on a wide number of literature experimental data. The pressure-velocity coupling is handled through the SIMPLE-C algorithm. Numerical simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, the cavity size, the average temperature, and the temperature difference imposed across the cavity, as independent variables. It is found that the impact of the nanoparticle dispersion into the base liquid increases remarkably with increasing the average temperature, whereas, by contrast, the other controlling parameters have moderate effects. Moreover, at temperatures of the order of room temperature or just higher, the heat transfer performance of the nanofluid is significantly affected by the choice of the solid phase material.

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