Computationally generated constitutive models for particle phase rheology in gas-fluidized suspensions

2018 ◽  
Vol 860 ◽  
pp. 318-349 ◽  
Author(s):  
Yile Gu ◽  
Ali Ozel ◽  
Jari Kolehmainen ◽  
Sankaran Sundaresan
Keyword(s):  
Kinetic Theory ◽  
Granular Materials ◽  
Particle System ◽  
Constitutive Models ◽  
Particle Collision ◽  
Particle Phase ◽  
Particle Volume ◽  
Volume Fractions ◽  
Mechanical Methods ◽  
Rate Of Dissipation

Developing constitutive models for particle phase rheology in gas-fluidized suspensions through rigorous statistical mechanical methods is very difficult when complex inter-particle forces are present. In the present study, we pursue a computational approach based on results obtained through Eulerian–Lagrangian simulations of the fluidized state. Simulations were performed in a periodic domain for non-cohesive and mildly cohesive (Geldart Group A) particles. Based on the simulation results, we propose modified closures for pressure, bulk viscosity, shear viscosity and the rate of dissipation of pseudo-thermal energy. For non-cohesive particles, results in the high granular temperature $T$ regime agree well with constitutive expressions afforded by the kinetic theory of granular materials, demonstrating the validity of the methodology. The simulations reveal a low $T$ regime, where the inter-particle collision time is determined by gravitational fall between collisions. Inter-particle cohesion has little effect in the high $T$ regime, but changes the behaviour appreciably in the low $T$ regime. At a given $T$, a cohesive particle system manifests a lower pressure at low particle volume fractions when compared to non-cohesive systems; at higher volume fractions, the cohesive assemblies attain higher coordination numbers than the non-cohesive systems, and experience greater pressures. Cohesive systems exhibit yield stress, which is weakened by particle agitation, as characterized by $T$. All these effects are captured through simple modifications to the kinetic theory of granular materials for non-cohesive materials.

Macroscopic description of arbitrary Knudsen number flow using Boltzmann–BGK kinetic theory. Part 2

2010 ◽  
Vol 658 ◽  
pp. 294-309 ◽  
Author(s):  
HUDONG CHEN ◽  
STEVEN A. ORSZAG ◽  
ILYA STAROSELSKY
Keyword(s):  
Relaxation Time ◽  
Kinetic Theory ◽  
Closed Form ◽  
Knudsen Number ◽  
Constitutive Models ◽  
Spatial Dimension ◽  
Scalar Transport ◽  
Constant Relaxation Time ◽  
Number Flow ◽  
Short Times

We extend our previous analysis of closed-form equations for finite Knudsen number flow and scalar transport that result from the Boltzmann–Bhatnagar–Gross–Krook (BGK) kinetic theory with constant relaxation time. Without approximation, we obtain closed-form equations for arbitrary spatial dimension and flow directionality which are local differential equations in space and integral equations in time. These equations are further simplified for incompressible flow and scalars. The particular case of no-flow scalar transport admits analytical solutions that exhibit ballistic behaviour at short times while behaving diffusively at long times. It is noteworthy that, even with constant relaxation time BGK microphysics, quite complex macroscopic descriptions result that would be difficult to obtain using classical constitutive models or continuum averaging.

Wear Behavior of In Situ Mg2Si Particle-Dispersed Magnesium Alloys

2017 ◽  
Vol 909 ◽  
pp. 100-105
Author(s):  
Kazunori Asano
Keyword(s):  
Magnesium Alloys ◽  
High Speed ◽  
Wear Behavior ◽  
Particle Dispersion ◽  
Dry Sliding Wear ◽  
Wear Loss ◽  
Mg2si Particle ◽  
Particle Volume ◽  
Volume Fractions

Magnesium alloys, in which the in-situ Mg2Si particles were dispersed, were fabricated by a casting process, and the dry sliding wear behavior of the alloys was investigated. Optical microscopy revealed that the polygonal Mg2Si particles were homogeneously dispersed in the alloys. Mg2Si particle volume fractions in the alloys were 7 and 11 vol%. Although the wear loss of the alloy decreased due to the particle-dispersion, there was no difference in the wear loss between the alloys with different volume fractions. The worn surfaces of the particle-dispersed alloys were covered with the crumbled Mg2Si particles, which would prevent seizure between the alloy and the steel counterpart, leading to an improvement in the wear resistance of the alloy. The particle-dispersion slightly decreased the scatter of the coefficient of friction during the wear for the low sliding speed and load, but the effect of the dispersion was not clearly observed for the high speed and load.

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

Shear Flow Analysis of Nanosize Particle Flow Behavior Using Kinetic Theory

2005 ◽  
Vol 277-279 ◽  
pp. 939-944
Author(s):  
Hae Ryung Kim ◽  
Jaihyun Seu ◽  
Hamid Arastoopour
Keyword(s):  
Shear Flow ◽  
Kinetic Theory ◽  
Flow Behavior ◽  
Flow Analysis ◽  
Particle Diameter ◽  
Particle Flow ◽  
Particle Collision ◽  
Simple Shear Flow ◽  
Particle Force ◽  
Nanosize Particle

Nanosize particle flow is significantly affected by inter-particle force. Due to the inter-particle force, the most significant characteristic of nanosize particle flow may become the formation of agglomerates or clusters which considerably affects the flow patterns. The formation of agglomerates or clusters results in a reduction in the number and an increase in the size of particles, both of which directly affect the frequency of inter-particle collisions and, in turn, the particle phase properties such as viscosity and pressure, as well as gas/particle drag force in gas/particle flow systems. In this present work, we focus our attention on the verification of nanosize particle flow behavior due to the formation of agglomerates or clusters under different fluctuation of flow and inelasticity of particle collision. By extending the application of the cohesive model using kinetic theory to nanosize particle flow system, we performed the homogeneous simple shear flow analysis using various fluctuation energy and restitution coefficient. The predicted flow properties, such as particle diameter growth, agreed well with the expected trends.

Treatment of Cork Wastes in a Conical Spouted Bed Reactor

2006 ◽  
Vol 4 (1) ◽  
Author(s):  
Maria J San Jose ◽  
Sonia Alvarez ◽  
Alvaro Ortiz de Salazar ◽  
Alberto Morales ◽  
Javier Bilbao
Keyword(s):  
Granular Materials ◽  
Particle System ◽  
Previous Knowledge ◽  
Spouted Bed ◽  
Experimental Conditions ◽  
Glass Spheres ◽  
Geometric Factors ◽  
Hydrodynamic Study

The applicability of conical spouted bed reactors for the treatment of cork caps has been studied by means of a hydrodynamic study with homogeneous beds of cork of different size in different experimental conditions. The validity of the ranges of the geometric factors of the contactor and of the contactor-particle system for stable spouting established in previous papers and of the equation for the calculation of the minimum spouting velocity proposed for granular materials and glass spheres has been proven for beds consisting of cork. The suitable design of the conical spouted bed reactor for the combustion of cork wastes requires the previous knowledge of the ranges of the geometric factors of the contactor and of the contactor-particle system for stable spouting.

Comparative Evaluation of Algorithms for Achieving Ultrapacked Thermal Greases: Microstructural Models and Effective Behavior

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Sukshitha Achar P. L ◽  
Huanyu Liao ◽  
Ganesh Subbarayan
Keyword(s):  
Heuristic Algorithms ◽  
Volume Fraction ◽  
Augmented Lagrangian Method ◽  
Random Network ◽  
Optimization Algorithms ◽  
Particle Packing ◽  
Computational Time ◽  
Particle Volume ◽  
Volume Fractions ◽  
Number Of Particles

Abstract In this work, we develop and evaluate algorithms for generating ultrapacked microstructures of particles. Simulated microstructures reported in the literature rarely contain particle volume fractions greater than 60%. However, commercially available thermal greases appear to achieve volume fractions in the range of 60–80%. Therefore, to analyze the effectiveness of commercially available particle-filled thermal interface materials (TIM), there is a need to develop algorithms capable of generating ultrapacked microstructures. The particle packing problem is initially posed as a nonlinear programming problem, and formal optimization algorithms are applied to generate microstructures that are maximally packed. The packing efficiency in the simulated microstructure is dependent on the number of particles in the simulation cell; however, as the number of particles increases, the packing simulation is computationally expensive. Here, the computational time to generate microstructures with large number of particles is systematically evaluated first using optimization algorithms. The algorithms include the penalty function methods, best-in-class sequential quadratic programming method, matrix-less conjugate gradient method as well as the augmented Lagrangian method. Heuristic algorithms are next evaluated to achieve computationally efficient packing. The evaluated heuristic algorithms are mainly based on the drop-fall-shake (DFS) method, but modified to more effectively simulate the mixing process in commercial planetary mixers. With the developed procedures, representative volume elements (RVE) with volume fraction as high as 74% are demonstrated. The simulated microstructures are analyzed using our previously developed random network model to estimate the effective thermal and mechanical behavior given a particle arrangement.

FUNDAMENTALS OF THE SQUEEZE-FLOW BETWEEN A HEAT SINK AND A FLIP-CHIP

2008 ◽  
Vol 32 (3-4) ◽  
pp. 467-486 ◽  
Author(s):  
M.A. Marois ◽  
M. Lacroix
Keyword(s):  
Heat Sink ◽  
Flip Chip ◽  
String Model ◽  
Thermal Interface Material ◽  
Squeeze Flow ◽  
Back Side ◽  
Two Dimensional ◽  
Particle Volume ◽  
Volume Fractions ◽  
Drop Flow

The paper presents the fundamentals of the squeeze-flow of the thermal interface material (TIM) that takes place during the pressing of a heat sink to the back side of a flip-chip is studied. A two-dimensional string model is developed for predicting the time-varying plate separation and squeeze-rate in terms of the squeeze force. The predictions are compared to a one-dimensional string model and to a squeeze-drop flow model. Results indicate that the flow resulting from the squeezing of a string of TIM between two rigid plates is truly two-dimensional. The effect of surface tension and of the heat transfer is found to be negligible under the assembly conditions. The flow behaviour of the TIM with suspensions of high thermal conductivity particles is also investigated. It is shown that the fluid remains Newtonian for particle volume fractions smaller than 30%. For volume fractions larger than 30%, the fluid becomes Non-Newtonian during the early stages of the squeezing process, i.e. for t ≤ 1s. In the later stages however (t > 10s), the fluid may be considered Newtonian.

Numerical Study of Forced Convection of Nanofluids in a Microchannel Heat Sink

2008 ◽  
Author(s):  
Parisa Vaziee ◽  
Omid Abouali
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Heat Sink ◽  
Volume Fraction ◽  
Numerical Study ◽  
Heat Removal ◽  
Al2o3 Nanoparticles ◽  
Microchannel Heat Sink ◽  
Particle Volume ◽  
Volume Fractions

Effectiveness of the microchannel heat sink cooled by nanofluids with various particle volume fractions is investigated numerically using the latest theoretical models for conductivity and viscosity of the nanofluids. Both laminar and turbulent flows are considered in this research. The model of conductivity used in this research accounts for the fundamental role of Brownian motion of the nanoparticles which is in good agreement with the experimental data. The changes in viscosity of the nanofluid due to temperature variation are considered also. Final results are compared with the experimental measurements for heat transfer coefficient and pressure drop in microchannel. Enhancement in heat transfer is achieved for laminar flow with increasing of volume fraction of Al2O3 nanoparticles. But for turbulent flow an enhancement of heat removal was not seen and using higher volume fractions of nanoparticles increases the maximum substrate temperature. Pressure drop is increased with using nanofluids because of the augmentation in the viscosity and this increase is more noticeable in higher Reynolds numbers.

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