Numerical simulation for the collision between a vortex ring and solid particles

This study is concerned with the numerical simulation for the collision between a vortex ring and an ensemble of small glass particles. The vortex ring, convecting with its self-induced velocity in a quiescent air, collides with the particles. The Reynolds number for the vortex ring is 2600, and the particle diameters are 50 and 200 μm. The Stokes number St for the 50 μm particle is 0.74, while the St for the 200 μm particle is 11.4. Immediately after the collision with the vortex ring, the 50 μm particles surround the vortex ring, forming a dome. It is parallel with the preferential distribution for the particle with St ? 1 around large-scale eddies, which has been measured experimentally and simulated numerically in various free turbulent flows. The 200 μm particles disperse more due to the collision with the vortex ring. This is attributable to the centrifugal effect of large-scale eddy, which has been reported by the numerical simulation for the motion of the particle with St = 10 in a wake flow. The collision between the vortex ring and the particles induces an organized three-dimensional vortical structure. It also reduces the strength and convective velocity of the vortex ring.     

Modelling of heavy and buoyant particle dispersion in a two-dimensional turbulent mixing layer

Heavy and buoyant particle dispersion in the turbulent mixing layer was investigated numerically using a two-phase flow discrete vortex modelling. It was revealed from the modelling that inclusion of two-way momentum coupling is essential for properly modelling heavy particle dispersive transport in turbulent free shear flows. For heavy particles with small Stokes numbers, the dispersion is predominated by the large-scale vortex structures and they exert small influence on the carrier fluid flow. Heavy particles with large St directionally align along the braid region between the neighbouring vortices. However, the lateral dispersion of particles of large St is smaller than that of particles of small St.For buoyant particles with the density being slightly greater than that of the carrier fluid, numerical simulation revealed that the buoyant particles scatter over the whole vortex core rather than collect along the fringes of the vortex. The Lagrangian statistics calculation of buoyant particle dispersion showed that both the inertial and crossing-trajectory effects affect the particle dispersion behaviour and particle eddy diffusivity. The dispersion behaviour of buoyant particles is highly associated with the particle Stokes number. Large St buoyant particles exhibit a larger dispersion. It was also indicated from the numerical simulation that buoyant particles might disperse larger than the fluid tracers. The correlation between the buoyant particle and fluid tracer velocities was affected by including the coupling effect.     

A numerical study of particle wall-deposition in a turbulent square duct flow

The deposition of dense solid particles in a downward, fully developed turbulent square duct flow at Re_τ = 360, based on the mean friction velocity and the duct width, is studied using large eddy simulations of the fluid flow. The fluid and the particulate phases are treated using Eulerian and Lagrangian approaches, respectively. A finite-volume based, second-order accurate fractional step scheme is used to integrate the incompressible form of the unsteady, three-dimensional, filtered Navier-Stokes equations on an 80 × 80 × 128 grid. A dynamic subgrid kinetic energy model is used to account for the unresolved scales. The Lagrangian particle equation of motion includes the drag, lift, and gravity forces and is integrated using the fourth-order accurate Runge-Kutta scheme. Two values of particle to fluid density ratio (ρ_p/ρ_f = 1000 and 8900) and five values of dimensionless particle diameter (d_p/δ × 10⁶ = 100, 250, 500, 1000 and 2000, δ is the duct width) are studied. Two particle number densities, consisting of 10⁵ and 1.5 × 10⁶ particles initially in the domain, are examined.Variations in the probability distribution function (PDF) of the particle deposition location with dimensionless particle response time, i.e. Stokes number, are presented. The deposition is seen to occur with greater probability near the center of the duct walls, than at the corners. The average streamwise and wall-normal deposition velocities of the particles increase with Stokes number, with their maxima occurring near the center of the duct wall. The computed deposition rates are compared to previously reported results for a circular pipe flow. It is observed that the deposition rates in a square duct are greater than those in a pipe flow, especially for the low Stokes number particles. Also, wall-deposition of the low Stokes number particles increases significantly by including the subgrid velocity fluctuations in computing the fluid forces on the particles. Two-way coupling and, to a greater extent, four-way coupling are seen to increase the deposition rates.     

Particle dispersion in a turbulent natural convection channel flow

Direct numerical simulations of particle dispersion in the turbulent natural convection flow between two vertical walls kept at constant but different temperatures are reported. It is assumed that the particles do not affect the flow (i.e. the dilute phase approximation is adopted). Particles with different levels of inertia, or Stokes numbers (0.843≤St≤17.45), are tracked according to the drag force imposed by the fluid. The gravity force is included for two cases, St=0.843 and St=17.45. The different levels of turbulence near the wall and near the center of the channel produce, as in isothermal turbulent channel or pipe flow, a larger concentration of particles near the wall. This effect becomes more important, and the deposition velocity of particles on the wall increases, as the particle inertia is increased. The simulations at St=8.38 and St=17.45 predict similar concentration profiles and deposition velocities according to the large inertia of these particles. The deposition velocities, obtained when the gravity force is ignored in the particle equations, follow the trend observed and measured for isothermal turbulent channel flows in the diffusion impaction regime. For the conditions considered, the gravity vector imposes a strong descending motion on the particles and this produces the increase of the particle concentration near the wall and a reduction of the deposition velocities in comparison with the results without the gravity force.     

Detached eddy simulation of particle dispersion in a gas-solid two-phase fuel rich/lean burner flow

To predict the particle dispersion in the burner jet is of great importance in industrial application and in the designing of coal burner with good performance. The objective of this study was to numerically investigate the particle dispersion mechanisms in the gas-solid two-phase jet from a fuel rich/lean burner. The detached-eddy-simulation (DES) approach was employed to study the turbulent flow in the fuel rich/lean separator and the gas-solid multiphase jet from the exit of a fuel rich/lean burner. The vortex shedding process was simulated and its effect on the fuel rich/lean separating performance was evaluated. Combined with the Lagrangian tracking procedure for the particle phase, the coal particles with various Stokes numbers equal to 0.000434, 0.043, 1.08, 4.34 (corresponding to particle diameter 1, 10, 50, 100 μm, respectively) in the gas-solid fuel rich/lean jet were studied, which shows that although there are coherent vortex structures behind the central partition plate, these vorticities are small, the fuel-rich stream and the fuel lean stream will not mix quickly downstream of the exit of the nozzle. The large vortex structures at the jet outer boundary are the main factors that make the small particles to mix together. The coal particles with large Stokes number (St>1) disperse very slowly in the jet flow, which realizes the fuel rich/lean combustion in a rather long distance downstream the exit of the nozzle, resulting in low NO_x emissions.     

Transient, three-dimensional simulation of particle dispersion in flows around a circular cylinder Re = 140-260)

To understand three-dimensional dispersion of particles in the flow around a bluff body, direct numerical simulations of particle-laden wakes of a circular cylinder with Reynolds number ranging from 140 to 260 were performed. The domain decomposition method and high-order finite-difference schemes were applied to solve the fluid flow. A Lagrangian tracking solver was developed to trace the trajectories of each particle in the non-uniform grid system. It is observed that the predicted coherent structures and vortex dislocation frequency agree well with those of previous experimental studies. Particles at low Stokes numbers follow the vortex motion and can disperse into the core regions of the vortex-street and the recirculating region. Particles at larger Stokes numbers try to maintain their own motion, but take on a non-uniform distribution in the wake due to the strong folding effect of shed vortices. But for particles at intermediate Stokes numbers, higher concentration occurs in the outer boundary regions of the vortices as well as the thin band regions connecting adjacent vortex structures. Besides the spanwise vortex structures, the streamwise vortex tubes also have a remarkable effect on particle dispersion, which results in a ‘mushroom’ shape particle distribution in the wake. Furthermore, non-uniform forcing at inlet has additional effect on particle dispersion and mixing.     

Solids concentration simulation of different size particles in a cyclone separator

To deepen our knowledge of the flow in cyclones, the solids concentrations of different size particles in a scroll cyclone separator were numerically simulated by using the Lagrange approach on the platform of commercial CFD software package, FLUENT 6.1. The numerical calculations visualize that there exists a spiral dust strand near the cyclone wall and a dust ring beneath the cyclone top plate. There are two regions in the radial solids concentration distribution, with which the solids concentration is low in the inner region (r/R(dimensionless radial position) ≤ 0.75) and increases greatly in the outer region (r/R > 0.75). Large particles generally have higher concentration in the wall region and small particles have higher concentration in inner vortex region. The axial distribution of the solids concentration in the inner vortex region (r/R ≤ 0.3) shows that serious fine particle re-entrainment exists within the height of 0.5 D (cyclone diameter) above the dust discharge port. We study the effect of solids particle on the gas flow field by two-way couple. The concepts of back-mixing rate, first escaping rate and second escaping rate are proposed for quantifying the local flow phenomena.     

Numerical Simulation of Particle Dispersion in the Wake of a Circular Cylinder

In this article, numerical simulation of the Navier-Stokes equations was performed for the large-scale structures of a two-dimensional temporally developing cylinder flow and the associated dispersion patterns of particles were simulated. The time-dependent Navier-Stokes equations were integrated in time using a mixed explicit-implicit operator splitting rules. The spatial discretization was processed using spectral-element method. Non-reflecting conditions were employed at the outflow boundary. Particles with different Stokes numbers were traced by the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases.

The simulation results of the flow field agree well with experimental data. Due to the effects of the coherent structures, the particles demonstrate a more organized dispersion process in the space and a periodic dispersion characteristic in the time. Particle dispersion increases with the flow Reynolds number and so does for particle concentration, which is independent of particle size. However, for particles at different Stokes numbers, the dispersion patterns are different. The particles at smaller Stokes number congregate mainly in the vortex core regions and the particles at larger Stokes number disperse much less along the lateral direction with the even distribution. The higher density distribution at the outer boundary of large-scale vortex structure characterizes the dispersion pattern of particles at the Stokes numbers of order of unity. Furthermore, these particles disperse largely along the lateral direction and show the nonuniform distribution of concentration.     

The effect of the generation and handling in the acquired electrostatic charge in airborne particles

The measurement of the charge distribution in laboratory generated aerosols particles was carried out. Four cases of electrostatic charge acquisition by aerosol particles were evaluated. In two of these cases, the charges acquired by the particles were naturally derived from the aerosol generation procedure itself, without using any additional charging method. In the other two cases, a corona charger and an impact charger were utilized as supplementary methods for charge generation. Two types of aerosol generators were used in the dispersion of particles in the gas stream: the vibrating orifice generator TSI model 3450 and the rotating plate generator TSI model 3433. In the vibrating orifice generator, a solution of methylene blue was used and the generated particles were mono-dispersed. Different mono-aerosols were generated with particle diameters varying from 6.0 × 10^− 6 m to 1.4 × 10^− 5 m. In the rotating plate generator, a poly-dispersed phosphate rock concentrate with Stokes mean diameter of 1.30 × 10^− 6 m and size range between 1.5 × 10^− 7 m and 8.0 × 10^− 6 m was utilized as powder material in all tests. In the tests performed with the mono-dispersed particles, the median charges of the particles varied between − 3.0 × 10^− 16 C and − 5.0 × 10^− 18 °C and a weak dependence between particle size and charge was observed. The particles were predominantly negatively charged. In the tests with the poly-dispersed particles the median charges varied fairly linearly with the particle diameter and were negative. The order of magnitude of the results obtained is in accordance with data reported in the literature. The charge distribution, in this case, was wider, so that an appreciable amount of particles were positively charged. The relative spread of the distribution varied with the charging method. It was also noticed that the corona charger acted very effectively in charging the particles.     

Transient thermal behaviour of a cylindrical wood particle during devolatilization in a bubbling fluidized bed

This work proposes a transient heat transfer model to predict the thermal behaviour of wood in a heated bed of sand fluidized with nitrogen. The 2-D model in cylindrical coordinates considers wood anisotropy, variable fuel properties, fuel particle shrinkage, and heat generation due to drying and devolatilization. The influence of initial fuel moisture content, thermal diffusivity, particle geometry, shrinkage, external heat transfer coefficient, chemical reaction kinetics and heats of reaction on temperature rise is presented. The cylindrical wood particles chosen for the study have length (l) = 20 mm, diameter (d) = 4 mm and l = 50 mm and d = 10 mm, both having an aspect ratio (l/d) of 5. The bed temperature is 1123 K. The model prediction is validated using measurements obtained from literature. The temperature rise in the wood particle is found to be sensitive to changes in the moisture content and thermal diffusivity and heat of reaction (in larger particles) while it is less sensitive to the external heat transfer coefficient and chemical kinetics. Also shrinkage is found to have a compensating effect and it does not have any significant influence on the temperature rise. Beyond an aspect ratio of three, the wood particle behaves as a 1-D cylinder.     

Drag of non-spherical solid particles of regular and irregular shape

The drag of a non-spherical particle was reviewed and investigated for a variety of shapes (regular and irregular) and particle Reynolds numbers (Re_p). Point-force models for the trajectory-averaged drag were discussed for both the Stokes regime (Re_p ? 1) and Newton regime (Re_p ? 1 and sub-critical with approximately constant drag coefficient) for a particular particle shape. While exact solutions were often available for the Stokes regime, the Newton regime depended on: aspect ratio for spheroidal particles, surface area ratio for other regularly-shaped particles, and min-med-max area for irregularly shaped particles. The combination of the Stokes and Newton regimes were well integrated using a general method by Ganser (developed for isometric shapes and disks). In particular, a modified Clift-Gauvin expression was developed for particles with approximately cylindrical cross-sections relative to the flow, e.g. rods, prolate spheroids, and oblate spheroids with near-unity aspect ratios. However, particles with non-circular cross-sections exhibited a weaker dependence on Reynolds number, which is attributed to the more rapid transition to flow separation and turbulent boundary layer conditions. Their drag coefficient behavior was better represented by a modified Dallavalle drag model, by again integrating the Stokes and Newton regimes. This paper first discusses spherical particle drag and classification of particle shapes, followed by the main body which discusses drag in Stokes and Newton regimes and then combines these results for the intermediate regimes.     

Orthogonal design process optimization and single factor analysis for bimodal acoustic agglomeration

Acoustic agglomeration is proved as a promising pretreatment to control the emission of fine particles. As to removal of coal-fired fly ash particles (first mode), this paper investigates the combination of acoustic agglomeration with the addition of lime seed particles (second mode). The bimodal acoustic agglomeration can improve agglomeration efficiency significantly. Orthogonal designs are carried out for the first time to optimize the agglomeration conditions. The factors range as follows: acoustic frequency, f = 1000-1800 Hz; sound pressure level, SPL = 135-150 dB; residence time, t = 3-7 s, lime seed particle mass fraction, m_lime% = 30%-90%. The results of difference analysis and analysis of variance reveal that frequency is the dominant factor and the optimal conditions are: f = 1400 Hz, SPL = 150 dB, t = 4 s, m_lime% = 30%. In addition, the detailed influences of single factor on agglomeration efficiency are investigated.     

Dispersion polymerization of 2-hydroxyethyl methacrylate stabilized by a hydrophilic/CO2-philic poly(ethylene oxide)-b-poly(1,1,2,2-tetrahydroperfluorodecyl acrylate) (PEO-b-PFDA) diblock copolymer in supercritical carbon dioxide

Dispersion polymerization of 2-hydroxyethyl methacrylate (HEMA) has been successfully performed in supercritical carbon dioxide at P=370 bar and T=65 °C with azobis(isobutyronitrile) as initiator and a hydrophilic/CO₂-philic poly(ethylene oxide)-b-poly(1,1,2,2-tetrahydroperfluorodecyl acrylate) (PEO-b-PFDA) block copolymer as steric stabilizer. The PEO-b-PFDA (2K/21K) block copolymer was synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization. Spherical particles of poly(HEMA) were obtained in the range of 200-400 nm diameter size with a narrow particle size distribution (D_w/D_n<1.1). The effect of the stabilizer concentration on the dispersion polymerization was investigated from 20 w/w% down to 3.5 w/w% versus HEMA. Precipitation polymerization in the absence of stabilizer lead to the formation of large aggregates of partially coalesced particles whereas discrete spherical particles of poly(HEMA) were obtained by dispersion polymerization even at low concentration of PEO-b-PFDA (3.5 w/w% versus HEMA).     

Prediction of single particle settling velocities through liquid fluidized beds

Single particle settling velocities through water fluidized beds of mono-sized glass spheres (d_p = 0.645, 1.20, 1.94, 2.98 and 5 mm in diameter) were studied experimentally using a column, 40 mm in diameter. The settling spherical particles (D_p = 10 and 19.5 mm) had different densities (1237 to 8320 kg/m³), while the settling particles (D_p = 5 and 2.98 mm) were glass spheres. The pseudo-fluid model, which considers a liquid fluidized bed as a homogenous pseudo-fluid, predicts single particle settling velocities quite well if the ratio D_p/d_p is larger than about 10. With decreasing ratio D_p/d_p, the overall friction between the settling particle and the fluidized media increases. A method for predicting single particle settling velocities through a liquid fluidized bed is proposed and discussed. Following the approach of Van der Wielen et al. [L.A.M. Van der Wielen, M.H.H Van Dam, K.C.A.M. Van Luyben, On the relative motion of a particle in a swarm of different particles, Chem. Eng. Sci. 51 (2006) 995-1008], the overall friction is decomposed into a particle-fluid and a particle-particle component. The effective buoyancy force is calculated using the transition function proposed by Ruzicka [M.C. Ruzicka, On buoyancy in dispersion, Chem. Eng. Sci. 61 (2006) 2437-2446]. A simple model for predicting the collision force is proposed, as well as a correlation for the collision coefficient. The mean absolute deviation between the experimental and calculated slip velocities was 5.08%.     

Experimental study and simulation of vibrated fluidized bed drying

The paper addresses numerical simulation for the case of convective drying of seeds (fine-grained materials) in a vibrated fluidized bed, analyzing agreement between the numerical results and the results of corresponding experimental investigation. In the simulation model of unsteady simultaneous one-dimensional heat and mass transfer between gas phase and dried material during drying process it is assumed that the gas-solid interface is at thermodynamic equilibrium, while the drying rate (evaporated moisture flux) of the specific product is calculated by applying the concept of a “drying coefficient”. Mixing of the particles in the case of vibrated fluidized bed is taken into account by means of the diffusion term in the differential equations, using an effective particle diffusion coefficient. Model validation was done on the basis of the experimental data obtained with narrow fraction of poppy seeds characterized by mean equivalent particle diameter (d_S,d = 0.75 mm), re-wetted with required (calculated) amount of water up to the initial moisture content (X₀ = 0.54) for all experiments. Comparison of the drying kinetics, both experimental and numerical, has shown that higher gas (drying agent) temperatures, as well as velocities (flow-rates), induce faster drying. This effect is more pronounced for deeper beds, because of the larger amount of wet material to be dried using the same drying agent capacity. Bed temperature differences along the bed height, being significant inside the packed bed, are almost negligible in the vibrated fluidized bed, for the same drying conditions, due to mixing of particles. Residence time is shorter in the case of a vibrated fluidized bed drying compared to a packed bed drying.     

Determination of the adhesion force between particles and a flat surface, using the centrifuge technique

By using a centrifuge technique, the influence of powdery material particle size on the adhesion force particle-surface was determined. In order to achieve this, the adhesion of phosphatic rock (ρ_p = 3.090 kg m^− 3) and of manioc starch particles (ρ_p = 1.480 kg m^− 3) on a steel surface were studied. A microcentrifuge that reached a maximum speed rotation of 14000 rpm and which contained specially designed centrifuge tubes was used. There tubes contained the flat surface where the test particles were deposited. The powder particles were dispersed on these disks and the particles detachment were performed using diverse centrifugal speeds. The graphics of particle percentages still adhering on the surface of the disks as a function of the applied detachment force showed that the profile of adhesion force followed a log-normal distribution. The adhesion force increased with particle size. The manioc starch particles presented adhesion forces greater than those for the phosphatic rock particles for all particle sizes studied. The results obtained were compared with the theory proposed by Derjaguin, Muller and Toporov whose theoretical adhesion presented values close to the experimental data for the phosphatic rock particles adhesion on the stainless steel surface. On the contrary, the theoretical values were lower than the experimental ones for the manioc starch particles maybe due to the small roughness of these particles, their physical properties (softer and deformable material) and/or specific chemical interactions since the organic composition of the manioc starch particles that can dominate the adhesion force. Finally, the separation distance among the surfaces in contact (Z₀) was estimated in approximately 1.0 × 10^− 9 m for the phosphatic rock and 5.0 × 10^− 10 m for the manioc starch. These results were weakly dependent on the particle size range.     

Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

Novel electrically conductive α-β SiAlON/TiCN composites

Electrically conductive α-β SiAlON/TiCN composites were produced in the form of a segregated network in a ceramic matrix structure. A continuous 3D network of conductive TiCN particles was successfully achieved by mechanically coating spray-dried SiAlON granules with varying amounts of nano sized TiCN (0-10 vol.%) particles. For comparison, the same SiAlON matrix was incorporated with 25 vol.% micron sized TiCN particles to give a particle reinforced composite. Densification, together with mechanical and electrical properties of the composites produced were discussed in terms of conventional and novel approach. Fully dense composites were obtained by gas pressure sintering (GPS) under a nitrogen pressure of 100 bar at a peak temperature of 1990 °C. The electrical resistivity of the SiAlON (1 × 10¹³ Ω m) matrix material was drastically reduced with the addition of only 5 vol.% TiCN (18 × 10⁻⁴ Ω m) to the composites prepared by the coating method.     

Pyrolysis of wheat straw in a thermogravimetric analyzer: Effect of particle size and heating rate on devolatilization and estimation of global kinetics

The influence of different parameters such as particle size, initial weight of the sample, and heating rate on the devolatilization of wheat straw particles have been studied using thermogravimetric analysis. In addition, the variations in proximate analysis with different particle sizes of wheat straw have also been investigated. Results show that the curves corresponding to the third stage of pyrolysis differ for variations in particle size, initial weight, and heating rate of the pyrolysis process. A devolatilization model with three parallel nth-order reactions has been considered to determine the global kinetic parameters using thermogravimetric data. The kinetic parameters such as activation energy (kJ/mol), frequency factor (1/min), and order of the reaction for the three stages considered in devolatilization model were E₁ = 69, E₂ = 78, E₃ = 80; k₀₁ = 2.57 × 10¹², k₀₂ = 3.97 × 10⁷, k₀₃ = 3.17 × 10⁶; and n₁ = 2.3, n₂ = 0.65, n₃ = 2.7, respectively. It was noted from the order of the reaction that the second stage of the pyrolysis curve corresponds to the degradation of cellulose and hemicellulose, and the third stage to the lignin degradation.