Correlation of powder flow properties to interparticle interactions at ambient and high temperatures

A combination of a continuum approach and a particle–particle approach to describe the multi-scale nature of the mechanical properties of bulk solids may be beneficial to scientific and engineering applications. In this paper, a procedure is proposed to estimate the interparticle forces beginning with the bulk flow properties as measured with standardized techniques. In particular, the relationship between interparticle forces and bulk solid tensile strength is adopted based on the microscale approaches of Rumpf (1970) and Molerus (1975). The flow properties of fluid cracking catalyst (FCC), corundum and glass bead powders were all characterized with a modified Schulze ring shear cell capable of operating at temperatures up to 500 °C. The powder test conditions were selected such that the van der Waals forces were the most significant particle–particle interactions. The model equations describe two cases, in which either elastic or plastic deformation of the contact points is assumed. The results indicate that the model provides the correct order of magnitude for the values of the tensile strength when proper values for the mean curvature radius at the contact points are taken into account. A sensitivity analysis for the main parameters in the model was performed. This analysis indicated that the assumption of plastic deformation at contact surfaces coupled with a decrease in porosity justified an increase of the tensile strength with consolidation stress. Furthermore, the effect of temperature on the measured flow behavior can be explained as a change in the strength of the material.     

An experimental and numerical study of the localization behavior of tantalum and stainless steel

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material’s local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length is 870–890 μm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 × 10⁴ s⁻¹ in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the shear section. The numerical results for stainless steel suggest that melting temperature was reached throughout the shear band shortly after peak load. Due to sample geometry, the stress state in the shear zone was not pure shear; a significant normal stress relative to the shear zone basis line was developed.     

Hydrodynamics and energy consumption studies in a three-phase liquid circulating three-phase fluid bed contactor

The hydrodynamics and energy consumption have been studied in a cold flow, bubbling and turbulent, pressurized gas–liquid–solid three-phase fluidized bed (0.15 m ID × 1 m height) with concurrent gas–liquid up flow is proposed with the intention of increasing the gas hold up. The hydrodynamic behaviour is described and characterised by some specific gas and liquid velocities. Particles are easily fluidized and can be uniformly distributed over the whole height of the column. The effect of parameters like liquid flow rate, gas flow rate, particle loading, particle size, and solid density on gas hold up and effect of gas flow rate, solid density and particle size on solid hold up, energy consumption and minimum fluidization velocity has been studied. At the elevated pressures a superior method for better prediction of minimum fluidization velocity and terminal settling velocities has been adopted. The results have been interpreted with Bernoulli’s theorem and Richardson–Zaki equation. Based on the assumption of the gas and liquid as a pretend fluid, a simplification has been made to predict the particle terminal settling velocities. The Richardson–Zaki parameter n′ was compared with Renzo’s results. A correlation has been proposed with the experimental results for the three-phase fluidization.     

Interaction between an incompressible flow and elastic cantilevers of circular cross-section

The purpose of this work is to study the deformation of elastic cantilevers due to hydrodynamic forces by coupled fluid–structure interaction simulations. The cantilever is placed in a rectangular duct and the Reynolds number based on bulk velocity and cantilever diameter is 400. Reduced velocities in the range π/4 to 2π are studied, which covers both un-synchronised motion and the initial branch of synchronisation. The cantilever surface is represented by a virtual boundary method which replaces a solid object in flow by additional force distribution to satisfy local boundary condition. The flow field is solved using a Cartesian finite difference code and the deformation of the cylinder a finite element approach using one-dimensional beam elements is used.     

Axisymmetric simulation of the interaction of a rising bubble with a rigid surface in viscous flow

The interaction between a rising deformable gas bubble and a solid wall in viscous liquids is investigated by direct numerical simulation via an arbitrary-Lagrangian–Eulerian (ALE) approach. The flow field is assumed to be axisymmetric. The bubble is driven by gravity only and the motion of the gas inside the bubble is neglected. Deformation of the bubble is tracked by a moving triangular mesh and the liquid motion is obtained by solving the Navier–Stokes equations in a finite element framework. To understand the mechanisms of bubble deformation as it interacts with the wall, the interaction process is studied as a function of two dimensionless parameters, namely, the Morton number (Mo) and Bond number (Bo). We study the range of Bo and Mo from (2, 6.5 × 10⁻⁶) to (16, 0.1). The film drainage process is also considered in this study. It is shown that the deformation of a bubble interacting with a solid wall can be classified into three modes depending on the values of Mo and Bo.     

Analytical and numerical techniques to predict carbon nanotubes properties

In this paper, two different approaches for modeling the behaviour of carbon nanotubes are presented. The first method models carbon nanotubes as an inhomogeneous cylindrical network shell using the asymptotic homogenization method. Explicit formulae are derived representing Young’s and shear moduli of single-walled nanotubes in terms of pertinent material and geometric parameters. As an example, assuming certain values for these parameters, the Young’s modulus was found to be 1.71 TPa, while the shear modulus was 0.32 TPa. The second method is based on finite element models. The inter-atomic interactions due to covalent and non-covalent bonds are replaced by beam and spring elements, respectively, in the structural model. Correlations between classical molecular mechanics and structural mechanics are used to effectively model the physics governing the nanotubes. Finite element models are developed for single-, double- and multi-walled carbon nanotubes. The deformations from the finite element simulations are subsequently used to predict the elastic and shear moduli of the nanotubes. The variation of mechanical properties with tube diameter is investigated for both zig-zag and armchair configurations. Furthermore, the dependence of mechanical properties on the number of nanotubules in multi-walled structures is also examined. Based on the finite element model, the value for the elastic modulus varied from 0.9 to 1.05 TPa for single and 1.32 to 1.58 TPa for double/multi-walled nanotubes. The shear modulus was found to vary from 0.14 to 0.47 TPa for single-walled nanotubes and 0.37 to 0.62 for double/multi-walled nanotubes.     

CFD-DEM simulation of spouting of corn-shaped particles

Three dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) were used to investigate the flow of corn-shaped particles in a cylindrical spouted bed with a conical base. The particle motion was modeled by the DEM, and the gas motion by the k-? two-equation turbulent model. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas–particle interactions in terms of momentum exchange. The corn-shaped particles were constructed by a multi-sphere method. Drag force, contact force, Saffman lift force, Magnus lift force, and gravitational force acting on each individual particle were considered in establishing the mathematical modeling. Calculations were carried out in a cylindrical spouted bed with an inside diameter of 200 mm, a height of 700 mm, and a conical base of 60°. Comparison of simulations with experiments showed the availability of the multi-sphere method in simulating spouting action with corn-shaped particles, but it depended strongly on the number and the arrangement of the spherical elements. Gas–solid flow patterns, pressure drop, particle velocity and particle concentration at various spouting gas velocity were discussed. The results showed that particle velocity reaches a maximum at the axis and then decreases gradually along the radial direction in the whole bed. Particle concentration increases along the radial direction in the spout region but decreases in the fountain region, while it is nearly constant in the annulus region. Increasing spouting gas velocity leads to larger pressure drop, remarkably increased speed of particle moving upward or downward, but decreased particle concentration.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.     

Numerical investigation of particle deposition inside aero-shielded solar cyclone reactor: A promising solution for reactor clogging

Solar cracking of methane is considered to be an attractive option due to its CO₂ free hydrogen production process. Carbon particle deposition on the reactor window, walls and exit is a major obstacle to achieve continuous operation of methane cracking solar reactors. As a solution to this problem a novel “aero-shielded solar cyclone reactor” was created. In this present study the prediction of particle deposition at various locations for the aero-shielded reactor is numerically investigated by a Lagrangian particle dispersion model. A detailed three dimensional computational fluid dynamic (CFD) analysis for carbon deposition at the reactor window, walls and exit is presented using a Discrete Phase Model (DPM). The flow field is based on a RNG k–ε model and species transport with methane as the main flow and argon/ hydrogen as window and wall screening fluid. Flow behavior and particle deposition have been observed with the variation of main flow rates from 10–20 L/min and with carbon particle mass flow rate of 7 × 10⁻⁶ and 1.75 × 10⁻⁵ kg/s. In this study the window and wall screening flow rates have been considered to be 1 L/min and 10 L/min by employing either argon or hydrogen. Also, to study the effect of particle size simulations have also been carried out (i) with a variation of particle diameter with a size distribution of 0.5–234 μm and (ii) by taking 40 μm mono sized particles which is the mean value for the considered size distribution. Results show that by appropriately selecting the above parameters, the concept of the aero-shielded reactor can be an attractive option to resolve the problem of carbon deposition at the window, walls and exit of the reactor.     

A cell-based constitutive model for embryonic epithelia and other planar aggregates of biological cells

Embryonic epithelia are shown to have in common with plastic materials a number of key characteristics, including fabric evolution, “yielding”, “particle” (cell) rearrangement, energy dissipation, dependence of stress on fabric and irreversibility of deformation. The strains apparent at the tissue level can be large (several hundred percent over the course of 5–10 h), and are possible because of in-plane cell rearrangement. We propose a cell-based constitutive model, the first of its kind, to relate in-plane stresses, tissue deformations, evolution of cellular fabric (cell size, shape and orientation), mitosis and cell rearrangement. The governing equations are based on results from finite element models, statistical mechanics analyses and experiments. The constitutive model overcomes drawbacks of existing finite element models where cells are modeled using multiple elements, and it confirms that tissue fabric is a primary determinant of stress and deformation. Fabric predictions made using the model are as good as the available data, even when strain histories are complex or multiple biological processes are active simultaneously. The model provides insights into the mechanics of embryonic epithelia and other labile biological tissues, and it sets the stage for future computational studies of whole embryos.     

Lagrangian particle dispersion in turbulent flow over a wall mounted obstacle

Large-eddy simulations (LES) of particle-laden turbulent flows are presented in order to investigate the effects of particle response time on the dispersion patterns of a space developing flow with an obstruction, where solid particles are injected inside the wake of an obstacle [Vincont, J.Y., Simoens, S., Ayrault M., Wallace, J.M., 2000. Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and downstream of an obstacle. J. Fluid Mech. 424, 127–167]. The numerical method is based on a fully explicit fractional step approach and finite-differences on Cartesian grids, using the immersed boundary method (IBM) to represent the existence of solid obstacles. Two different turbulence models have been tested, the classical Smagorinsky turbulence model and the filtered structure function model. The dispersed phase was modelled either by an Eulerian approach or a Lagrangian particle tracking scheme of solid particles with Stokes numbers in the range St = 0–25, assuming one-way coupling between the two phases. A very good agreement was observed between the Lagrangian and Eulerian approaches. The effect of particle size was found to significantly differentiate the dispersion pattern for the inhomogeneous flow over the obstacle. Although in homogeneous flows like particle-laden turbulent channels near-wall particle clustering increases monotonically with particle size, for the examined flow over an obstacle, preferential concentration effects were stronger only for an intermediate range of Stokes numbers.     

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method (DEM) of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3–6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated. The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.     

Constraint strength and axial/radial particle velocity profiles for an integrated riser outlet

To study axial/radial profiles of particle velocity in the affected region of an integrated riser outlet, a cold model was developed for the integrated riser reactor combining the gas–solid distributor with the fluidized bed. Constraints, related to the gas–solid distributor and the upper fluidized bed, imposed on the particle flow in the riser outlet region, were investigated experimentally. The experimental results showed that with increasing superficial gas velocity, these constraints have strong influences on particle flow behavior, the particle circulation flux in the riser, and the height of the static bed material of the upper fluidized bed. When the constraints have greater prominence, the axial profile of the cross-sectionally averaged particle velocity in the outlet region initially increases and then decreases, the rate of decrease being proportional to the constraint strength. Along the radial direction of the outlet section, the region where the local particle velocity profile tends to decrease appears near the dimensionless radius r/R = 0.30 initially and then, with increasing constraint strength, gradually extends to the whole section from the inner wall. Based on the experimental data, an empirical model describing the constraint strength was established. The average relative error of the model is within 7.69%.     

CFD–DEM simulation of the pneumatic conveying of fine particles through a horizontal slit

Fine particles play a significant role in many industrial processes. To study the dynamic behavior of fine particle and their deposition in rock fractures, the pneumatic conveying of fine particles (approximately 100 μm in diameter) through a small-scale horizontal slit (0.41 m × 0.025 m) was studied, which is useful for the sealing technology of underground gas drainage in coal mining production. The CFD–DEM method was adopted to model the gas-particle two-phase flow; the gas phase was treated as a continuum and modeled using computational fluid dynamics (CFD), particle motion and collisions were simulated using the DEM code. Then, the bulk movement of fine particles through a small-scale horizontal slit was explored numerically, and the flow patterns were further investigated by visual inspection. The simulation results indicated that stratified flow or dune flow can be observed at low gas velocities. For intermediate gas velocities, the flow patterns showed pulsation phenomena, and dune flow reappeared in the tail section. Moreover, periodic flow regimes with alternating thick and sparse stream structures were observed at a high gas velocity. The simulation results of the bulk movement of fine particles were in good agreement with the experimental findings, which were obtained by video-imaging experiments. Furthermore, the calculated pressure drop versus gas velocity profile was investigated and compared with relative experimental findings, and the results showed good agreement. Furthermore, the particle velocity vectors and voidage distribution were numerically simulated. Selected stimulation results are presented and provide a reference for the further study of fine particles.     

Dynamic crushing of sandwich panels with prismatic lattice cores

The dynamic out-of-plane compressive response of stainless steel corrugated and Y-frame sandwich cores have been investigated for impact velocities ranging from quasi-static to 200 ms⁻¹. Laboratory-scale sandwich cores of relative density 2.5% were manufactured and the stresses on the front and rear faces of the dynamically compressed sandwich cores were measured using a direct impact Kolsky bar. Direct observational evidence is provided for micro-inertial stabilisation of both topologies against elastic buckling at impact velocities below 30 ms⁻¹. At higher impact velocities, plastic waves within the core members result in the front face stresses increasing with increasing velocity while the rear face stresses remain approximately constant. While the finite element calculations predict the rear face stresses and dynamic deformation modes to reasonable accuracy, the relatively slow response time of the measurement apparatus results in poor agreement between the measured and predicted front face stresses. The finite element calculations also demonstrate that material strain-rate effects have a negligible effect upon the dynamic compressive response of laboratory-scale and full-scale sandwich cores.     

Computational study of steady streaming from oscillating microbubbles with uniform and wavy wall motions

Steady streaming flow fields of a 5 μm bubble oscillating with uniform radial wall motion and a 500 μm bubble oscillating with wavy wall motion were simulated using a computational fluid dynamics method that incorporated fluid–structure interactions. The steady streaming flow fields for both bubbles were calculated, and they exhibited upward jet flow with two symmetrical counter-rotating vortices. The maximum streaming velocity ranged from a few to tens of millimeters per second. The simulated flow fields were compared with the theory and experimental measurements using particle image velocimetry. The simulation results agreed well with the theoretical and experimental data. Therefore, the proposed computational method would provide a useful tool to predict steady streaming flow fields of oscillating bubbles.     

Discrete element-embedded finite element model for simulation of soft particle motion and deformation

The motion and deformation of soft particles are commonly encountered and important in many applications. A discrete element-embedded finite element model (DEFEM) is proposed to solve soft particle motion and deformation, which combines discrete element and finite element methods. The collisional surface of soft particles is covered by several dynamical embedded discrete elements (EDEs) to model the collisional external forces of the particles. The particle deformation, motion, and rotation are independent of each other in the DEFEM. The deformation and internal forces are simulated using the finite element model, whereas the particle rotation and motion calculations are based on the discrete element model. By inheriting the advantages of existing coupling methods, the contact force and contact search between soft particles are improved with the aid of the EDE. Soft particle packing is simulated using the DEFEM for two cases: particle accumulation along a rectangular straight wall and a wall with an inclined angle. The large particle deformation in the lower layers can be simulated using current methods, where the deformed particle shape is either irregular in the marginal region or nearly hexagonal in the tightly packed central region. This method can also be used to simulate the deformation, motion, and heat transfer of non-spherical soft particles.