Comparison of three separated flow models

 An improved stochastic separated flow (ISSF) model developed by the present authors is compared with two other widely used trajectory models, the deterministic separated flow (DSF) model and the stochastic separated flow (SSF) model, in numerical simulations of gas–particle flows behind a backward-facing step. The DSF and ISSF models are found to need only 250 computational particles to obtain a statistically stationary solution of mean and fluctuating velocities of the particles, while the SSF model requires as many as 10,000 computational particles. Apart from comparing the sensitivity of required computational particles for different models, prediction capability of different models on mean velocities, fluctuating velocities and re-circulation region are also compared in this paper. Predicted results of streamwise mean velocity of particle phase agree well with experimental data for all the three models. For the mean fluctuating velocity of the particle phase, predictions using the ISSF model agree well with experiment data, while the DSF and the SSF models have a significant difference. Only the SSF and the ISSF models are capable of predicting re-circulation regions of the particle phase. As a comparison, the ISSF model has a distinct advantage over the other two models both in terms of accuracy and efficiency. Received 20 October 2001 / Accepted 5 February 2002     

An improved stochastic separated flow model for turbulent two-phase flow

 An improved stochastic separated flow model is proposed to obtain reasonable statistical characteristics of a two-phase flow. Effects of the history of a particle and its current trajectory position on the mean-square fluctuating velocity of the dispersed phase are continuously considered in this model. Comparing with the conventional model, results using the improved model are more reasonable and can also be obtained more easily. Furthermore, the improved model requires less computational particles for simulating dispersed-phase turbulence at the beginning of the stochastic trajectory. In this paper, an application in turbulent two-phase flow of planar mixing layer is carried out. Numerical results including velocity, mean-square fluctuating velocity, particle number density and pdf of fluctuation velocity of dispersed phase are shown to compare well with experimental data.     

Velocity Fluctuations in a Particle-Laden Turbulent Flow over a Backward-Facing Step

Dilute gas-particle turbulent flow over a backward-facing step is numerically simulated. Large Eddy Simulation (LES) is used for the continuous phase and a Lagrangian trajectory method is adopted for the particle phase. Four typical locations in the flow field are chosen to investigate the two-phase velocity fluctuations. Time-series velocities of the gas phase with particles of different sizes are obtained. Velocity of the small particles is found to be similar to that of the gas phase, while high frequency noise exists in the velocity of the large particles. While the mean and rms velocities of the gas phase and small particles are correlated, the rms velocities of large particles have no correlation with the gas phase. The frequency spectrum of the velocity of the gas phase and the small particle phase show the -5/3 decay for higher wave number, as expected in a turbulent flow. However, there is a "rising tail' in the high frequency end of the spectrum for larger particles. It is shown that large particles behave differently in the flow field, while small particles behave similarly and dominated by the local gas phase flow.     

A parametric study of dispersed laminar gas-particle flows through vertical and horizontal channels

Particle diameter, particle phase material density and inlet particle volume fraction are three important parameters governing the flow physics of dispersed gas-particle flows. In this work, an inhouse numerical solver is developed to investigate the effects of particle diameter (Stokes number), particle phase material density, inlet particle volume fraction and inlet phase velocities in the flow characteristics of gas-particle flows through vertical and horizontal channels and also in open domains. It is found that, for a constant inlet particle volume fraction, lower diameter particles attain a higher steady state velocity at any section inside the channel than the higher diameter particles; while the corresponding steady state gas velocity at any section increases with increase in particle diameter. On the other hand, for a constant particle diameter, the steady state gas phase velocity at any section decreases with increase in inlet particle volume fraction. Significant changes in both gas and particle velocity and volume fraction profiles have also been observed with inlet slip, i.e., when the velocities of both the phases at inlet are distinct as opposed to being equal, keeping all other flow and physical parameters invariant.     

The Influence of the Gravity Force on Longwave Marangoni Patterns in Two-Layer Films

An Euler–Euler two-fluid model based on the second-order-moment closure approach and the granular kinetic theory of dense gas-particle flows was presented. Anisotropy of gas-solid two-phase stress and the interaction between two-phase stresses are fully considered by two-phase Reynolds stress model and the transport equation of two-phase stress correlation. Under the microgravity space environments, hydrodynamic characters and particle dispersion behaviors of dense gas-particle turbulence flows are numerically simulated. Simulation results of particle concentration and particle velocity are in good agreement with measurement data under earth gravity environment. Decreased gravity can decrease the particle dispersion and can weaken the particle–particle collision as well as it is in favor of producing isotropic flow structures. Moreover, axial–axial fluctuation velocity correlation of gas and particle in earth gravity is approximately 3.0 times greater than those of microgravity and it is smaller than axial particle velocity fluctuation due to larger particle inertia and the larger particle turbulence diffusions.     

Numerical simulation of aerosol collection in filters with staggered parallel rectangular fibres

 In this paper, filters with rectangular fibres arranged in a staggered and parallel array and placed transverse to the flow are studied numerically. A two- dimensional flow field is obtained by solving Navier–Stokes equations with the control volume method. Periodic boundary conditions are introduced in the calculation. In order to achieve higher accuracy, a second-order upwind scheme is adopted and a fine mesh is arranged near the fibre and the symmetrical plane of the flow field where large gradients in velocity are expected. Particle trajectories are calculated by solving the corresponding Lagrangian equation of motion to obtain the collection efficiency of a single rectangular fibre, in which positions of the approaching particles on the inlet plane of the flow field are randomly distributed according to the Monte-Carlo principle. The simulation considers all the important mechanisms of particle capture including interception, inertial impaction and Brownian motion. Effects of fibre aspect ratio, filter packing density, particulate size and Reynolds number on the collection efficiency are numerically determined. The volumetric packing density ranges from 0.4 to 4% and the particle diameter is from 0.01 μm to 2 μm. Reynolds number based on the height of computational domain varies from 20 to 100 and the aspect ratio is from 0.1 to 10. Simulations with and without Brownian motion are carried out for different Reynolds numbers, packing densities and aspect ratios and the results show that Brownian effects are significant for particles smaller than 1 μm. Received 25 May 2001     

Effect of iodixanol particle size on the mechanical properties of a PMMA based bone cement

Iodixanol (IDX) is a water soluble opacifier widely used in radiographical examinations of blood vessels and neural tissue, and it has been suggested as a potential contrast media in acrylic bone cement. The effect of the iodixanol particle size on the polymerisation process of the bone cement, the molecular weight, and the quasi-static mechanical properties have been investigated in this article. The investigation was performed using radiolucent Palacos powder mixed with 8 wt% of iodixanol with particle sizes ranging from 3 to 20 μm MMD, compared with commercial Palacos R (15 wt% ZrO₂) as control. Tensile, compressive and flexural tests showed that smaller particles (groups with 3, 4, and 5 μm particles) resulted in significantly lower mechanical properties than the larger particles (groups with 15, 16, and 20 μm particles). There was no difference in molecular weight between the groups. The thermographical investigation showed that the IDX cements exhibit substantially lower maximum temperatures than Palacos R, with the 4 μm IDX group having the lowest maximum temperature. The isothermal and the constant rate differential scanning calorimetry (DSC) did not show any difference in polymerisation heat (ΔH) or glass transition temperature (T _g) between radiolucent cement, or cement containing either IDX, or ZrO₂. The findings show that the particle size for a bone cement containing iodixanol should be above 8 μm MMD.     

Anisotropic and Particle-Particle Interaction Effect in a One-Dimensional System of Magnetic Particles

We have studied the effect of the shape anisotropy in a system that consists of a chain of N identical spherical particles each of magnetic dipole moment μ and that has an easy axis. By considering two particle interactions (Dimer Model) we have investigated two different distinct cases depending on the direction of the applied field H and the orientation (ξ) of the easy axis relative to H. We found that for the randomly oriented easy axis (ξ) and for H parallel or perpendicular to the chain the anisotropy has no effect on the ferromagnetic state. For fixed orientation (ξ) an interplay between ferromagnetic-like and anti-ferromagnetic-like behavior exists. The existence of each behavior is strongly dependent on the anisotropy K and the direction of H relative to the chain.     

Vortex simulation for non-axisymmetric collision of a vortex ring with solid particles

This study is concerned with the numerical simulation for the non-axisymmetric collision between a vortex ring and solid particles. The vortex ring convects with its self-induced velocity in a quiescent air, and the half part collides with spherical glass particles. The vortex method for gas-particle two-phase flow proposed by the authors in a prior paper is used for the simulation. The Reynolds number of the vortex ring is 2600, and the particle diameter is 50 μm. The Stokes number, defined as the ratio of the particle response time to the characteristic time of the vortex ring, is 0.74. The simulation clarifies that the particles induce the vortices, having an axis parallel to the convection direction of the vortex ring, inside the vortex ring and that pairs of the positive and negative vortex tubes appear. It also highlights that highly organized three-dimensional vortical structures composed of the streamwise vortices yield the rapid deformation and collapse of the vortex ring.     

Self-assembly of polystyrene microspheres within spatially confined rectangular microgrooves

A convective self-assembly of mono-sized polystyrene spheres with diameters ranging from 262 to 1000 nm was conducted on patterned silicon wafers with one-dimensional, periodic rectangular microgrooves of different widths (0.65–6 μm). The latex beads were driven into the spatially confined microgrooves by the capillary interactions and the confined wall during solvent evaporation, resulting in a range of packing structures. Processing variables including evaporation temperature, particle size (D), groove width (W), and groove height (H) were examined experimentally, and geometrical models were proposed to explain the various packing structures obtained. The degree of spatial freedom for the particles to rearrange themselves in the confined channels is found critical to the assembled particle-packing structure.     

Motion of inertial particles in Gaussian fields driven by an infinite-dimensional fractional Brownian motion

We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between the background fluid velocity and the particle velocity. The fluid velocity satisfies a linear stochastic partial differential equation driven by an infinite-dimensional fractional Brownian motion with an arbitrary Hurst parameter H?∈?(0,?1). The usefulness of such random velocity fields in simulations is that we can create random velocity fields with desired statistical properties, thus generating artificial images of realistic turbulent flows. This model also captures the clustering phenomenon of preferential concentration, observed in real world and numerical experiments, i.e. particles cluster in regions of low-vorticity and high-strain rate. We prove almost sure existence and uniqueness of particle paths and give sufficient conditions to rewrite this system as a random dynamical system with a global random pullback attractor. Finally, we visualize the random attractor through a numerical experiment.     

Interference of separated flows behind backward-facing step in the presence of passive control

The interaction of turbulent separated flows behind a backward-facing step in the presence of a passive miniturbulizer has been experimentally studied using digital particle-tracking velocimetry techniques. It is established that an obstacle placed in front of the step modifies the profiles of velocity and turbulent pulsation and significantly changes the length of a recirculation zone.     

Effect of calcium phosphate glass on bone formation in calvarial defects of Sprague-Dawley rats

The purpose of this study was to investigate the bone regenerative effect of calcium phosphate glass in vivo. We prepared two different sizes of calcium phosphate glass powder using the system CaO-CaF₂-P₂O₅-MgO-ZnO; the particle size of the powders were 400 μm and 40 μm. 8 mm calvarial critical-sized defects were created in 60 male Sprague-Dawley rats. The animals were divided into 3 groups of 20 animals each. Each defect was filled with a constant weight of 0.5 g calcium phosphate glass powder mixed with saline. As controls, the defect was left empty. The rats were sacrificed 2 or 8 weeks after postsurgery, and the results were evaluated using radiodensitometric and histological studies; they were also examined histomorphometrically. When the bigger powders with 400 μm particle were grafted, the defects were nearly completely filled with new-formed bone in a clean healing condition after 8 week. When smaller powders with 40 μm particle were transplanted, new bone formation was even lower than the control group due to a lot of inflammatory cell infiltration. It was concluded that the prepared calcium phosphate glass enhanced the new bone formation in the calvarial defect of Sprague-Dawley rats and it is expected to be a good potential materials for hard tissue regeneration. The particle size of the calcium phosphate was crucial; 400 μm particles promoted new bone formation, while 40 μm particles inhibited it because of severe inflammation.     

Effect of microstructure on Young’s modulus of extruded Al–SiC composites studied by resonant ultrasound spectroscopy

In this work, an attempt was made to correlate the Young’s modulus of SiC particle reinforced aluminum alloy composites, measured by resonant ultrasound method, to reinforcement spatial distribution. Composites were fabricated by extrusion of billets that were previously formed using cold pressing blend of matrix alloy powders and ceramic particles. It has been shown that more aggregated microstructures were generated with an increase in ceramic volume fraction (to 20%) and the matrix alloy powder mean particle size from 40 to 180 μm as well as with a decrease in the reinforcement particle size (3–14 μm). At the same time, ultrasonic wave velocity as well as Young’s modulus diminish with a decrease in SiC content and its particle size, and with increase in matrix alloy particle size. The analysis showed that it could be partly attributed to the higher amount of residual porosity in agglomerated structures. An addition decrease of elastic characteristics was attributed to the increasing influence of mechanically imperfect contacts that formed between ceramic particles in the more aggregated microstructures.     

The Material-Dependent Parameter Controlling the Universal Phase Diagram of Cuprates

The critical temperature T _c in the universal phase diagram of cuprate superconductors is a function of two variables: the hole-doping δ and a material dependent parameter. Here we focus on the behavior of T _c,max as a function of the material dependent parameter (MDP) at the optimum hole doping. We have discussed the correlation between (1) the average Cu—O (planar) distance, or the strain of the Cu—O bond, (2) the nearest-neighbor hopping t′ and (3) the Lifshitz parameter z. These Lifshitz parameter z = μ_{δ = 0.16}−E _vHs which are all material dependent parameters, where μ_{δ = 0.16} is the chemical potential at optimum doping and E_vHs is the energy of the Van Hove singularity, defines the proximity to the Fermi surface topological transition from electron-like to hole-like. The results show that the striped phases occur for z < 0, the highest T _c,max for and the drop of T _c,max for z > 75 meV.     

Gas-particle flow of cohesive aluminium powders during laser metal deposition – Experimental and numerical investigation

This paper investigates particle dynamics both inside and outside a Laser Metal Deposition nozzle of a Directed Energy Deposition processing head, i.e. a Laser Metal Deposition (LMD) nozzle, by way of high-speed imaging and particle tracking as well as through computer simulations that account for particle collision and van der Waals forces. It is shown that the particle accumulation phenomena observed experimentally with cohesive aluminium powders can be qualitatively reproduced numerically. It is also demonstrated that such computer simulations can yield the correct order of magnitude for particle velocities, which is rarely reported in the literature and usually unknown for any given LMD system. This work thus paves the way towards more accurate simulations of gas-particle flows in LMD nozzles, especially with cohesive powders.     

Foaming behavior of Ti6Al4V particle-added aluminum powder compacts

The foaming behavior of 5 wt.% Ti6Al4V (Ti64) particle (30–200 μm)-added Al powder compacts was investigated in order to assess the particle-addition effects on the foaming behavior. Al compacts without particle addition were also prepared with the same method and foamed. The expansions of Ti64 particle-added compacts were measured to be relatively low at small particle sizes and increased with increasing particle size. At highest particle size range (160–200 μm), particle-added compacts showed expansion behavior similar to that of Al compacts without particle addition, but with lower expansion values. Expansions studies on 30–45 μm size Ti64-added compacts with varying weight percentages showed that the expansion behavior of the compacts became very similar to that of Al compact when the particle content was lower than 2 wt.%. However, Ti64 addition reduced the extent of drainage. Ti64 particles and TiAl₃ particles formed during foaming increased the apparent viscosity of the liquid foam and hence reduced the flow of liquid metal from cell walls to plateau borders. The reduced foamability in the compacts with the smaller size Ti64 addition was attributed to the relatively high viscosities, due to the higher cumulative surface area of the particles and higher rate of TiAl₃ formation between liquid Al and Ti64 particles.     

Magnetic properties of Fe78.4Si9.5B9Cu0.6Nb2.5 nanocrystalline alloy powder cores

The microstructure and morphology of nanocrystalline Fe_78.4Si_9.5B₉Cu_0.6Nb_2.5 alloy powders prepared by ball milling technique were characterized by X-ray diffraction and scanning electron microscopy studies. The effective permeability (μ_e), quality factor (Q), DC bias property, and core losses of the corresponding powder cores were tested using low capacitance resonator meter and B–H analyzer in the range of 1–1000 kHz. The results show that the relative density and compression strength of the powder cores increased with increasing particle size. Powder cores from large size particles (150–300 μm) were found to exhibit higher μ_e and core loss, but lower Q level when compared to samples of small size ones (5–40 μm). Moreover, the μ_e of powder cores with large particles reached a peak value with the addition of 2 wt% glass binder. The Q value was also found to be proportional to the binder content except 10 wt%, while its peak position was shifted toward higher frequency.     

Granular configurations, motions, and correlations in slow uniform flows driven by an inclined conveyor belt

The present experimental study examines the behaviour of slow granular flows, focusing on the details of particle patterns and motions over the depth of a sheared layer. A conveyor belt circuit enclosed in an inclined flume is used to generate steady uniform open-channel flows of dry granules. Particle positions near the transparent sidewall are extracted from video sequences. The Voronoï diagram is then used to characterise the configurations formed by neighbouring grains and to assist particle tracking over successive frames. This allows a qualitative visualisation of the internal structure of the flowing layer, as well as quantitative measurements of lattice defect density and granular velocities at different depths. The response of the depth profiles to different conveyor belt speeds is examined. In addition to the mean and fluctuating velocities, we probe the time and space correlations of the fluctuations.     

Investigation of wear products of high-nitrogen manganese steels

The wear rate of hydrogenated specimens of high-nitrogen cold-worked manganese steels is five times larger than that of nonhydrogenated ones. In the absence of hydrogenation, the size of the wear products ranges from 25 to 40 μm at P = 400 N and from 40 to 100 μm at P = 500 N. For hydrogenated specimens, the size of the wear products is above 350 μm under a load of 250 N and ranges from 600 to 1000 μm at P = 400 N. The morphology of the wear products demonstrates an excellent microrelief, which indicates that fracture occurs by different mechanisms of fracture during the formation of a particle under friction conditions. On the products, we detected dimples in which, probably, particles containing σ-type intermetallics, carbides, and nitrides, which cause the initiation of cracks under both sliding friction and rolling friction, spalled.