Methodology for numerical simulations of ellipsoidal particle-laden flows

Despite being relevant in many natural and industrial processes, suspensions of nonspherical particles have been largely underinvestigated compared with the extensive analyses made on the gravity-driven motions of spherical particles. One of the main reasons for this disparity is the difficulty of accurately correcting the short-range hydrodynamic forces and torques acting on complex particles. These effects, also known as lubrication, are essential to the suspension of the particles and are usually poorly captured by direct numerical simulation of particle-laden flows. In this article, we propose a partitioned volume penalization-discrete element method solver, which estimates the unresolved hydrodynamic forces and torques. Corrections are made locally on the surface of the interacting particles without any assumption on the particle global geometry. Numerical validations have been made using ellipsoidal particles immersed in an incompressible Navier-Stokes flow.     

Numerical analysis of complex flow of fibre suspensions in a viscoelastic fluid

Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids. Though short fibre composites are mostly made of polymers, lack of suitable constitutive equations for fibre suspensions in viscoelastic fluids frustrates attempts to simulate flows of these suspensions. A preliminary work done by the author led to a constitutive equation for semiconcentrated fibre suspensions in the Oldroyd-B fluid. This paper describes the mathematical formulation of the flow problems for such a suspension and the numerical procedure to solve them. Some numerical results of flow past a sphere in a tube are also presented. This paper is supported by the University of Melbourne, the National Natural Science Foundation of China and Zhejiang Province.     

Dynamics of fibres in a turbulent flow field – A particle-level simulation technique

A particle-level simulation technique has been developed for modelling the flow of fibres in a turbulent flow field. A single fibre is conceived here as a chain of segments, thus enabling the model fibre to have all the degrees of freedom (translation, rotation, bending and twisting) needed to realistically reproduce the dynamics of real fibres. Equations of motion are solved for each segment, accounting for the interaction forces with the fluid, the contact forces with other fibres and the forces that maintain integrity of the fibre.The motion of the fluid is resolved as a combination of 3D mean flow velocities obtained from a CFD code and fluctuating turbulent velocities derived from the Langevin equation. A case of homogeneous turbulence is treated in this paper.The results obtained show that fibre flocs in air-fibre flows can be created even when attractive forces are not present. In such a case, contacts between fibres, properties of an individual fibre (such as flexibility and equilibrium shapes) and properties of the flow of the carrying fluid are shown to govern the physics behind formation and breaking up of fibre flocs. Highly irregular fibre shapes and stiff fibres lead to strong flocculation.The modelling framework applied in this work aims at making possible a numerical model applicable for designing processes involving transport of fibres by air at industrial scale.     

Fibre suspension rheology: effect of concentration, aspect ratio and fibre size.

Viscosity data for fibre suspensions are produced using cone-and-plate geometry of enhanced dimensions for the reduced influence of fibre-wall interactions. Semi-concentrated suspensions of monodisperse polyamide fibres in silicone oil, with a variety of fibre concentrations (2, 5 and 8%), lengths and diameters, were studied. The suspension viscosity was measured in a range of shear stress in order to study the stress dependence. The study here focuses on the nature of the forces and interactions that contribute to the suspension viscosity. The results show that at sufficiently high stress levels, the suspension viscosity tends to reach a steady-state. At very low stress levels the suspension viscosity increases over time, most likely due to structures formed by adhesive forces. At higher concentrations, the viscosity depends on the absolute size of the fibres, again indicating the presence of non-hydrodynamic interactions.     

Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow

Suspensions in polymeric, viscoelastic liquids have been studied in uniaxial extensional flow. The fibre wind-up technique has been used for this purpose. The effects of particle size and particle volume fraction have been investigated, using monodisperse, spherical particles. The results have been compared with shear flow data on the same materials. The values of the relative extensional viscosities at low stretching rates are in agreement with the relative shear viscosities and relative moduli. This indicates that hydrodynamic forces are stronger than the particle interaction forces. At larger strain rates strain hardening occurs; it is suppressed when particles are added. Small aggregating particles reduce the strain hardening more strongly than larger particles; strain hardening can even be totally eliminated. When further increasing the stretching rate, hydrodynamic effects dominate again and the effect of particle size effect on strain hardening disappears.     

Structure and properties of sheared fiber suspensions with mechanical contacts

The properties of fiber suspensions are highly sensitive to the suspension microstructure. In dilute or semi-dilute suspensions, nL²d≪1, the fibers' orientation distribution is controlled by hydrodynamic interactions among the fibers. However, direct mechanical contacts among the fibers play an important role in semi-concentrated suspensions, nL²d=O(1). Here, n is the number of fibers per unit volume, L is the fiber length and d is the fiber diameter. We have performed dynamic simulations of fiber suspensions including contact forces that prevent any two fibers from passing through one another. Collisions between the fibers cause them to flip more frequently in the shear flow, leading to a spread of the orientation distribution away from the flow direction. Both this increased orientational dispersion and the direct stress transmitted through the contacts enhance the shear viscosity of the suspension significantly. The contacts also give rise to normal stress differences. The results of the simulation are compared with experiments and the relative importance of contacts and hydrodynamic interactions is discussed.     

Rotational dynamics in dipolar colloidal suspensions: video microscopy experiments and simulations results

The dynamics of field-induced structures in very dilute dipolar colloidal suspensions subject to rotating magnetic fields have been experimentally studied using video microscopy. When a rotating field is imposed the chain-like aggregates rotate with the magnetic field frequency. We found that the size of the induced structures at small rotational frequencies is larger than at zero rotating frequency, i.e. when an uniaxial magnetic field is applied. At higher frequencies, the average size of the aggregates decreases with frequency following a power law with exponent −0.5 as the hydrodynamic friction forces overcome the dipolar magnetic forces, causing the chains break up. A non-thermal molecular dynamics simulations are also reported, showing good agreement with the experiments.     

A review of research on cylindrical particulate flows

The study of cylindrical particulate flows has wide industrial applicability hence received much attention. The purpose of the present paper is to provide a review on our research over the last few years. The research is related to the motion of cylindrical particles in mixing layer, pipe flow, channel flow, converging channel flow; the sedimentation of cylindrical particles in a Newtonian fluid; the structural feature and rheological property of cylindrical particulate suspensions; and the hydrodynamic instability of cylindrical particulate suspensions.     

Rheology of concentrated suspensions containing mixtures of spheres and fibres

Optimising flow properties of concentrated suspensions is an important issue common for many industries. The rheology of concentrated suspensions has therefore been studied intensively both experimentally and theoretically. Most studies have focused on monodisperse and polydisperse suspensions of either spheres or fibres. In practice, most suspensions contain particles that are polydisperse both in size and shape. A mixing rule for such systems is expected to be a powerful tool for engineers and product designers. Therefore in this work, suspensions of spheres, fibres and mixtures thereof were characterised using rotational shear rheometry and in-line image analyses. Thereby, total solids volume concentration and fibre fraction was varied. Results from transient and steady-state shear rheometry are discussed with respect to concentration, fibre fraction, and shear induced microstructure. Experimentally obtained viscosity data were accurately fitted using the model proposed by Farris (T Soc Rheol 12:281, 1968) for mixtures of monodisperse non-interacting spheres of different sizes.Originally presented at the Annual European Rheology Conference 2003, AERC 2003     

纤维悬浮液搅拌流动的数值模拟

由于缺乏适当的本构方程，对纤维悬浮液流动的研究一直局限于纤维的牛顿流体悬浮液。本文采用ＭＵＣＭ模型对作者最近提出的纤维Ｏｌｄｒｏｙｄ－Ｂ流体悬浮液的本构方程作了改进，并对锚式桨搅拌槽的二维Ｏｌｄｒｏｙｄ－Ｂ流体和牛顿流体纤维悬浮液搅拌流动作了数值模拟。模拟的结果表明，本文所用的模型和方法能有效地抑制过大局部应力的影响并合理地处理流体的记忆效应。     

Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling

Elastic buckling of layered/fibre reinforced composites is investigated. Assuming the existence of both shear and transverse modes of failure, the fibre is analysed as a layer embedded in a matrix. Interacting stresses, acting at the interfaces are determined from an exact derived stress field in the matrix. It is shown that buckling can occur only in the shear buckling mode and that the transverse buckling mode is spurious. As opposed to the well known Rosen shear buckling mode solution (predicated on an infinite buckling wavelength), shear buckling is shown to exist under two régimes: buckling of dilute composites with finite wavelengths and buckling of non-dilute composites with infinite wavelengths. Based on the analysis, a model is constructed which defines the fibre concentration at which the transition between the two régimes occurs. The buckling strains are shown to be (approximately) constant for dilute composites and, in the case of very stiff fibres, to have realistic values compatible with elastic behaviour. For the case of non-dilute composites, the strains are found to be in agreement with those given by the Rosen shear buckling solution. Numerical results for the buckling strains and stresses are presented and compared with the Rosen solution. These reveal that the Rosen solution is valid only for the case of non-dilute composites. The investigation demonstrates that elastic buckling may be a dominant failure mechanism of composites consisting of very stiff fibres fabricated in the framework of nano-technology.     

Kinetic theory of colloidal suspensions: morphology, rheology, and migration

Smoluchowski kinetic equation governing the time evolution of the pair correlation function of rigid sphericalparticles suspended in a Newtonian fluid is extended to include particle migration. The extended kinetic equation takes into account three types of forces acting on the suspended particles: a direct force generated by an interparticle potential, hydrodynamic force mediated by the host fluid, and the Faxén-type forces bringing about the across-the-streamline particle migration. For suspensions subjected to externally imposed flows, the kinetic equation is solved numerically by the proper generalized decomposition method. The imposed flow investigated inthe numerical illustrations is the Poiseuille flow. Numerical solutions provide the morphology (the pair correlation function), the rheology (the stress tensor), and the particle migration.     

Micromechanical analysis on tensile properties prediction of discontinuous randomized zalacca fibre/high-density polyethylene composites under critical fibre length

In this research, the tensile properties' performance of compression moulded discontinuous randomized zalacca fibre/high-density polyethylene under critical fibre length was analysed by means of experimental method and micromechanical models. These investigations were used to verify the tensile properties models toward the effect of fibre length and volume fraction on the composites. The experimental results showed that the tensile properties of composites had significantly increased due to the enhancement of fibre length. On the contrary, a decline in the tensile properties was observed with the increase of volume fraction. A comparison was made between the available experimental results and the performances of Tsai-Pagano, Christensen and Cox-Krechel models in their prediction of composites elastic modulus. The results showed that the consideration of fibre's elastic anisotropy in the Cox-Krenchel model had yielded a good prediction of the composites modulus, nevertheless the models could not accurately predict the composites modulus for fibre length study.     

Mechanics of the squeeze flow of planar fibre suspensions

This paper discusses the axisymmetric squeeze flow of concentrated transversely isotropic fibre suspensions in a power-law matrix and relates to the processing of composite materials such as sheet moulding compounds (SMCs) and glass mat thermoplastics (GMTs). A solution to the squeeze flow problem for a transversely isotropic power-law fluid is presented first, followed by a more detailed micromechanical analysis. In the first part of the paper a variational approach is applied to the interpretation of squeeze flow behaviour. This gives a simple expression for the total pressure, which enables the contributions due to extension and shear to be separated. Applying the procedure to GMT data suggests that the dissipation is predominantly extensional, except at very low plate separations. In the second part, a non-local constitutive equation is derived based on a simple drag law for hydrodynamic interactions. This is then used to model the pressure distribution when the effective length of the fibres is comparable to or determined by the dimensions of the squeeze flow plates. The model is shown to describe the observed squeeze flow stresses in both long and short fibre systems and to relate behaviour to the underlying resin flow properties.     

Flow and migration of nanoparticle in a single channel

A numerical simulation based on a combined Euler and Lagrange method is investigated in this work to simulate the flow and migration of nanoparticles in a single channel. The motion of discrete nanoparticles is determined by the Lagrangian trajectory method based on the Newton’s second law that includes the influence of the body force, various hydrodynamic forces, the Brownian motion and the thermophoresis force. The coupling of discrete particles with continuous flow is realized through the modification of the source term of the continuous equation. The results reveal the two-phase flow nature of nanoparticle suspensions and their implications to the convective heat transfer of nanofluids.     

Stress–strain and fracture behaviour of 0°/90° and plain weave ceramic matrix composites from tow multi-axial properties

A computationally economic finite-element-based multi-linear elastic orthotropic materials approach has been developed to predict the stress–strain and fracture behaviour of ceramic matrix composites with strain-induced damage. The finite element analysis utilises a solid element to represent a homogenised orthotropic medium of a heterogeneous uni-directional tow. The non-linear multi-axial stress–strain behaviour has been discretised to multi-linear elastic curves, which have been implemented by a user defined subroutine or UMAT in the commercial finite element package, ABAQUS. The model has been used to study the performance of two CMC composites: a SiC (Nicalon) fibre/calcium aluminosilicate (CAS) matrix 0°/90° cross-ply laminate Nicalon/CAS; and, a carbon fibre/carbon matrix–SiC matrix (C/C–SiC) plain weave laminate DLR-XT. The global stress–strain curves with catastrophic fracture behaviour and effects of fibre waviness have been predicted. Comparisons have been made between the predictions and experimental data for both materials. The predicted results when fibre waviness is taken into account compare well with the experimental data.     

Rheology of pulp suspensions using ultrasonic Doppler velocimetry

Conventional rheometry coupled with local velocity measurements (ultrasonic Doppler velocimetry) are used to study the flow behaviour of various commercial pulp fibre suspensions at fibre mass concentrations ranging from 1 to 5 wt.%. Experimental data obtained using a stress-controlled rheometer by implementing a vane in large cup geometry exhibits apparent yield stress values which are lower than those predicted before mainly due to existence of apparent slip. Pulp suspensions exhibit shear-thinning behaviour up to a high shear rate value after which Newtonian behaviour prevails. Local velocity measurements prove the existence of significant wall slippage at the vane surface. The velocimetry technique is also used to study the influence of pH and lignin content on the flow behaviour of pulp suspensions. The Herschel–Bulkley constitutive equation is used to fit the local steady-state velocity profiles and to predict the steady-state flow curves obtained by conventional rheometry. Consistency between the various sets of data is found for all suspensions studied, including apparent yield stress, apparent wall slip and complete flow curves.     

Thixotropy, yielding and ultrasonic Doppler velocimetry in pulp fibre suspensions

This paper reports thixotropy in concentrated pulp fibre suspensions and studies their transient flow behaviour using conventional rheometry coupled with a velocimetry technique. Specifically, an ultrasonic Doppler velocimeter is used in conjunction with a rate-controlled rheometer to deduce the local velocity profiles of pulp fibre suspensions. Pulp suspensions are found to exhibit a plateau in their flow curves where a slight increase in the shear stress generates a jump in the corresponding shear rate, implying the occurrence of shear banding. The velocity profiles were found to be discontinuous in the vicinity of the yielding radius where the Herschel–Bulkley model failed to predict the flow. Shear history and the time of rest prior to the measurement were found to play a significant role on the rheology and the local velocity profiles of pulp suspensions.     

Lubricated revolute joints in rigid multibody systems

The main purpose of this work is to present a general methodology for modeling lubricated revolute joints in constrained rigid multibody systems. In the dynamic analysis of journal-bearings, the hydrodynamic forces, which include both squeeze and wedge effects, generated by the lubricant fluid, oppose the journal motion. The hydrodynamic forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation, written for the dynamic regime. The hydrodynamic forces built up by the lubricant fluid are evaluated from the system state variables and included into the equations of motion of the multibody system. Numerical examples are presented in order to demonstrate the use of the methodologies and procedures described in this work.