Numerical Simulation and Analysis of Particle Mixing and Conduction in Wavy Drums

A thermal discrete element method (DEM) is used to simulate particle mixing and heat conduction inside wavy drums to explore the effects of wavy walls. Sinusoidal configurations with different waves on the walls are simulated. The Lacey mixing index is applied to analyze the mixing characteristics. The driven forces from the wavy wall, either positive/negative or effective driven forces, are analyzed to explain the mechanisms of mixing enhancement in the wavy drum. A new control parameter is proposed to explain the mechanism of mixing enhancement. It is found that a locally oscillating effect exists in wavy drums, which is imparted on the bulk rotating motions of particles and enhances the characteristics of particle mixing and heat conduction significantly. Except over large wave numbers and rotating speeds when the flow regime is deteriorated for mixing, the wavy drum is generally beneficial for mixing augmentation as well as conduction enhancement.     

Mixing and Heat Transfer of Granular Materials in an Externally Heated Rotary Kiln

A heat transfer model based on the discrete element software EDEM and the secondary development tool C++ is developed to simulate the mixing and heat transfer process of particles under different parameters. This model is validated by comparison with experimental data and proved reasonable. It aims to study the heat transfer law of flowing particles in an externally heated rotary kiln and reveal the correlation between mixing and heat transfer from the mechanism. The results show that the combination of the total contact area between adherent particles and the drum wall, the mean temperature difference between adherent particles and the drum wall, the total contact area between particles, and the mean temperature difference between particles affect the heat transfer process. Changes in the temperature differences caused by the mixing rate dominate the heat transfer at different speeds or filling rates.     

Heat transfer in a horizontal rotary drum reactor

The heating of carbohydrates (particle size 15 – 100 μm) has been studied in an industrial scale horizontal drum reactor. The drum was 9.0 m long and had a diameter of 0.6 m. Strips were mounted on the inside wall and the drum was heated externally by steam. Solid movement in the drum was observed in a transparent experimental segment of the drum. From these experiments it became clear that the heat transfer between wall and solids may be described by the penetration model. In separate experiments the product of the effective thermal conductivity of the bulk material and its heat capacity has been determined. The theoretical heat transfer coefficients agree quite well with the experimental values verified by heat transfer measurements in the large-scale drum.The heat transfer coefficients between wall and gas phase and between bulk solid and gas phase have also been measured. The magnitude of the heat transfer coefficient between wall and gas phase indicates a natural convection mechanism.     

Longitudinal mixing in horizontal rotary drum reactors

The longitudinal mixing of sodium carbonate (soda) (mean particle size 137 μm) has been investigated in a laboratory horizontal rotary drum reactor 250 mm in diameter and 600 mm long. The distributions of residence times have been estimated by means of a pulse of a small amount of sodium bicarbonate. The concentration of the tracer at the reactor discharge has been evaluated by thermal decomposition of the samples and by measuring their weight loss.The hold-ups, the mean residence times and the variances of the distribution of residence times were evaluated as a function of the rotational speed of the reactor and the feed rate of the particles. By applying a dispersion model, the Peclet numbers were evaluated from the standardized variances and plotted as a function of the feed rate and rotational speed. The mean residence time of the particles was calculated by means of an extended model of Vahl and Kingma. They correspond with the experiments.     

In-situ monitoring of axial particle mixing in a rotating drum using bulk density measurements

A device is described for measuring changes in the local composition of particulate materials in a rotary mixer by continuously monitoring changes in the bulk density. The bulk density is measured using a small cup mounted to the mixer wall that fills with powder during rotation through the bed of particles in the lower part of the mixer. The mass of material in the cup is measured using a load cell during rotation of the cup above the free surface of the particles, and the cup empties before re-entering the particle bed. For mixing of materials with a difference in either particle density, or packing density, the localised bulk density measurement gives a good measure of mixing progress. The measurement device is demonstrated in a 1 m diameter horizontal rotating drum in which two materials are mixed along the axis of the drum. Measurements of the rate of dispersion along the axis are consistent with other work in inclined rotary kilns and can be fitted with a simple diffusion model for the axial mixing of the two species.     

Continuous versus discrete modelling of heat transfer to agitated beds

Heating of free-flowing particles by contact with the wall of a rotary drum without inserts has been simulated in two dimensions by means of the thermal version of the Discrete Element Method (DEM). The results are in qualitative agreement with existing experimental data and with the classical penetration model (PM) for the following limiting cases: heat transfer controlled by a contact resistance at the wall of the drum; heat transfer to agitated beds with significant bed-side resistance; heat transfer to the stagnant bed. The latter can be used to establish an equivalence (calibration) between the discrete (DEM) and the continuous (PM) modelling approach. Thermal mixing times can be derived from asymptotic overall heat transfer coefficients obtained via thermal DEM for agitated beds. They are found to be significantly smaller than purely mechanical mixing times. For the investigated conditions, they are also much smaller than previous recommendations based on the PM. The ability of thermal DEM to provide information not accessible to the penetration model, like temperature distributions, is discussed. It is pointed out that a decrease of the high computational cost of the method is necessary in order to enhance its applicability.     

Solids mixing and residence time distribution in a horizontal rotary drum reactor

For the design of a rotary drum reactor, knowledge of the mechanism of both heat transfer and the dispersion of the solids is important. In this contribution the movement of solids in a horizontal rotary drum is investigated. Residence time distribution measurements were performed in an industrial scale reactor. Also, in model sections of this reactor, the behaviour of solids was studied visually. In the model sections the rotational speed of the drum, the number and height of the strips on the reactor wall and the angle between strip and wall, as well as the degree of filling, were varied.Model sections 0.60 and 1.40 m in diameter were used: the length of the industrial scale drum was 9.0 m, its diameter 0.60 m.Potato starch, particle size range from 15 to 100 μm, was used as the solid material.It was shown that in a drum provided with strips for rotational speeds above 5 r.p.m. and a degree of filling less than 15%, the transverse mixing was virtually completed within 2 revolutions of the drum. At these speeds and degrees of filling the extent of axial mixing is still very low as was shown by the residence time distribution measurements, the length of a mixing unit being 0.1 m or less.     

A CORRELLATION FOR CYLINDER-TO-BED HEAT TRANSFER IN AERATED VIBRATED BEDS OF SMALL PARTICLES

ABSTRACT

Beds of alumina particles (d_p= 27 μm and 100 μm) were vibrated in the vertical direction at frequencies frdm 0–25 Hz and half-amplitudes from 0–4 mm. Air flow rate through a single-hole or multiple-holes bottom plate varied from 0 to 2 times the minimum fluidizing velocity. The contact heat transfer coefficients at resonance are much higher than those in packed beds and in vibrated fluidized beds (up to 1.2 times). The high heat transfer rates are due to enhanced particle mobility which reaches a maximum at the resonant point. A simple semi-empirical correlation is developed for contact heat transfer which is based on particle mobility. Heat transfer coefficients are correlated with frequency using amplitude, bed height and particle size as adjustable parameters. The correlation is found explain the observed trends in the data reasonably well over the range of parameters studied.     

Particle Suspension in a Rotating Drum Chamber When the Influence of Gravity and Rotation are Both Significant

In recent years, rotating chambers have been found to be an effective method of retaining particles suspended in the air for an extended period of time. Rotating drum chambers have the potential of providing a stable atmosphere of well-characterized inhalable particles for periods lasting from hours to days for use in inhalation toxicology studies. To aid in planning for the use of rotating drum chambers in inhalation studies, we created a model that describes (a) the concentration of particles in the chamber under various conditions and (b) the particle sizes for which gravity and rotation influence particle dynamics. Previous publications describe the suspension / deposition of particles when the rotational effect is dominant, but do not describe particle suspension / deposition when gravitational settling is significant as occurs when such drum chambers are operated at optimal conditions for retaining the highest fraction of particles over time. By using the limiting trajectory of particles, the fraction of particles that remain suspended in a 1-m diameter rotating drum chamber was derived for forces of gravity only, rotation only, and gravity plus rotation. For particles between 0.5 and 1 μm in diameter and for suspension times of < 96 h, there was no loss of the suspended particles for drum rotation rates from 0.1 to 10 rpm. For 2- and 5-μm diameter particles, > 98% and 91%, respectively, remain suspended after 96 h under optimal rotation of the drum chamber. Optimal rotation rates were independent of particle size for particles < 10 μm in diameter (agreeing with Gruel et al. [1987] even though we predicted suspended fractions higher by > 30% for 10-μm particles after 96 h). For 20-μm diameter particles and suspension times < 96 h, the maximum suspended fraction occurred for drum rotation rates between 0.3 and 0.5 rpm. The particles > 2 μm can be selectively removed from an airborne particle size distribution in time periods of < 15 h when the rotational rate is > 5 rpm.     

Solids motion at horizontal tube surfaces in a large gas-solid fluidized bed

The motion of fluidized particles at the surface of 38 mm diameter horizontal tubes, immersed in a 1.2 m square bed of silica sand (U_mf = 0.3 m/s), fluidized at 0.9 m/s has been observed using photographic techniques (200 fps). It is shown that the solids motion is different for centrally located tubes and those adjacent to a side wall. Data on particle velocity and surface contact are presented and the degree of particle contact at various zones around the tube circumference is shown to vary in a similar manner to published localized heat transfer rates.     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

ABSTRACT

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

Quantifying lateral solids mixing in a fluidized bed by modeling the thermal tracing method

Thermal tracing is a simple method for studying solids mixing in fluidized beds. However, the measurement of temperatures is influenced by both mixing and heat transfer, which limits its usefulness for inferring mixing quantitatively. In this work, a semiempirical model is developed to quantify lateral solids mixing in fluidized beds. The model couples the tracer mass balance, the enthalpy balance of tracers and bed particles, and the response dynamic of thermometers. A series of tests is pezrformed in a lab‐scale fluidized bed, with particle sizes of 0.28–0.45, 0.45–0.6, 0.6–0.8, and 0.8–1.0 mm, and fluidizing velocity from 0.3 to 2.3 m/s. By evaluating the measured transient temperatures using the model, the lateral dispersion coefficient (D_sr) is determined to be between 0.0002 and 0.0024 m²/s. Its reliability is confirmed by bed collapse experiments. Finally, the values of D_sr is compared with a collection of data in the literature. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Numerical correlation for thermal conduction in packed beds

The numerical conduction of heat in packed beds of particles is investigated, including the effects of inter-particle microasperity gaps and deformation contacts. A detailed numerical model of two half spheres in contact with interstitial fluid is constructed, including asperity (roughness) gaps and deformation contacts on the respective orders of 5 μm and 100 μm for 1 mm particle diameters. The resulting heat flux distributions at the diametrical planes of the particles are integrated to yield the overall thermal conductance, K, or resistance, R = 1/K, between the two diametrical planes. The results show K to be strongly dependent on the interstitial fluid gap and the deformation contact diameter, as well as on fluid and solid conductivities. The effective bed conductivity, k_e, is determined as a function of K and the void fraction, and correlated in terms of bed parameters. The resulting k_e correlation agrees well with published experimental data over a wide range of substances and temperatures.     

Reactive melt blending of modified polyamide and polypropylene: Assessment of compatibilization by fractionated crystallization and blend morphology

The melting and crystallization behavior of nonreactive and reactive melt‐mixed blends of polypropylene and carboxylic‐modified polyamide (mPA) as the dispersed phase was investigated. It was found that the size of the mPA particles decreases and the crystallization behavior of the mPA particles changes in dependence on the mixing time of the blends with oxazoline‐modified PP (mPP). This indicates that an in situ reaction occurs between the oxazoline groups of mPP and the carboxylic acid groups of mPA, resulting in a compatibilizing effect. In blends with mPP, the crystallization of the dispersed mPA phase splits into two steps. Below a critical particle size, the mPA does not crystallize at temperatures typical for bulk crystallization. These finely dispersed mPA particles crystallize coincidently with the PP phase, and this part increases with increasing mixing time. Analysis of the crystallization heat of both steps in connection with the particle volume distribution permits the estimation of the critical particle size to be ≤4 μm. These investigations showed that the effect of fractionated crystallization can be used to follow the morphology development and to evaluate the efficiency of compatibilizing interfacial reactions during processing. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 3445–3453, 2002     

Influence of particle size on electrochemical performances of pyrite FeS2 for Li-ion batteries

Well-crystallized FeS₂ powders are synthesized via solid state reaction. Influence of particle size on electrochemical performances has been conducted. Compared with other anode materials, FeS₂ powder with mean particle size of 0.28 μm exhibits high coulombic efficiency, initial discharge specific capacity, low polarization and enhanced electrode process kinetics. The enhanced electrochemical properties are attributed to the dense powder packing, better electrical contact and relative stable structure during cycling process. Smaller FeS₂ particles (0.078 and 0.071 μm) have difficulty in dispersing and mixing with carbon black and binder and less dense packing state, leading to a decrease of reactive contact surface area and poor electrochemical performance.     

KINETIC CHARACTERISTICS OF A BATCH ADSORBER OR AN ION EXCHANGE DEVICE OPERATED UNDER NONISOTHERMAL CONDITIONS

Abstract

A model was formulated for a batch adsorber or ion exchange device with heat generation inside the bulk liquid due to mixing or electrical heating and due to heat of adsorption. Internal and external particle mass and heat transfer gradients and heat transfer through the vessel wall were included. The effective diffusion coefficient was taken to be temperature dependent. Numerical calculations (by orthogonal collocation) give conditions for the existence of intra particle nonisothermity and show the effect of mixing and process temperature on adsorption kinetics.     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

A multiple radioactive particle tracking technique to investigate particulate flows

Radioactive particle tracking is a nonintrusive technique that has been successfully used to study the flow dynamics in a wide range of reactors and blenders. However, it is still limited to the tracking of only one tracer at a time. A multiple radioactive particle tracking (MRPT) technique that can determine the trajectory of two free or restricted (attached to the same particle) moving tracers in a system is introduced. The accuracy (<5 mm) and precision (<5 mm) of the proposed technique is evaluated by tracking two stationary tracers and two moving tracers. The results confirm the reliability and validity of the MRPT technique when the two tracers have the same isotope and the distance between them is not too small (>2 cm). The tracking of two sticking tracers at the two ends of a cylindrical particle in a rotating drum is also considered to illustrate the potential of this characterization method. © 2014 American Institute of Chemical Engineers AIChE J, 61: 384–394, 2015     

Use of High-Gradient Magnetic Fields for the Separation of Macromolecules

Abstract

High gradient magnetic field separation (HGMS) has been used to separate several types of > 1 μm sized ferro- or paramagnetic particles from bulk streams. The majority of the studies have been carried out using a single ferromagnetic wire or wire mesh to produce the field gradients necessary for particle capture. The purpose of this paper is to examine the possibility of using HGMS on < 1 μm entities for the purpose of macromolecular separations. Preliminary experimental results demonstrate that HGMS techniques can be used to capture 0.1 μm diam latex beads from a paramagnetic salt solution passing through a columnar bed of ferro-magnetic spheres.     

Granular flow in a rotating drum with gaps in the side wall

This paper presents a numerical investigation of the motion of bi-sized particles in a short rotating drum by using Discrete Element Method (DEM). The side wall of the drum has equally spaced gaps whose width is just between the two particle diameters. One end wall of the drum is fixed while the other rotates with the side wall. Small particles are fed into the drum continuously at the center region in the axial direction. The effect of rotating speed on the volumetric holdup and residence time of small particle is investigated. A critical rotating speed is found, below which the decrease of rotating speed will increase the volumetric holdup and the residence time of the small particles sharply. A jump in the axial distribution of the outflow rate of the small particles is observed at the region adjacent to the fixed end wall. The flow pattern inside the drum is analyzed. In the region between the fixed end wall and the feeding point, all small particles, on average, move towards the fixed end wall. While in the region between the rotating end wall and the feeding point, the small particles curve away the rotating end wall in the upper part of the charge and return to this wall in the lower part. The particle temperature distributions at different rotating speeds are explored to understand the flow behavior observed in these simulations.