Mean Residence Time Of Particles Research Articles

Residence time distribution of ultrafine aerosol particles in a tube with transient and parabolic laminar flow

This paper presents a theoretical investigation concerning the residence time distribution (RTD) of ultrafine monodisperse aerosol particles flowing in a circular tube in laminar flow regime. If a fully developed, parabolic flow (PF) velocity profile is assumed for the whole tube length, the convection-diffusion process undergone by the aerosol particles can be described by means of two parameters, the dimensionless particle diffusion coefficient D and the tube aspect ratio a (radius/length). An additional parameter, the Reynolds number Re, must be taken into consideration when the flow develops starting from a given velocity profile at the tube entrance, which we have assumed to be a uniform (plug) flow. The latter situation is referred to as transient flow (TF). The RTD has been determined using two different variations of a Monte Carlo (MC) technique to simulate the particle trajectory within the tube. The difference between the two MC methods is the assumed distribution of Brownian random displacements of the particles; in both cases the distribution had zero mean and variance 2DΔt, but the distribution was uniform in one method and normal in the other. The simulation results obtained with the two methods were almost coincident. In either PF or TF, even for relatively small values of D the aerosol RTD is quite different from that of the fluid where the particles are suspended. In particular, the dimensionless mean particle residence time, which initially decreases with D, soon attains an asymptotic value of 0.65 for D ≥ 0.3 (the mean residence time of the fluid is 1) in PF; a similar asymptotic value is attained for TF but in this case it depends on the particular combination of a and Re considered. The relative influence of axial diffusion on the RTD is insignificant unless the tube ratio a is of the order of 0.5 (tube with a length equal to its diameter).

Residence Times from Molecular Dynamics Simulations.

In this work, efficient methods are proposed for the calculation, from molecular dynamics trajectories, of residence times (RTs) and related quantities. One of these was designed to obtain RT distributions, from which mean residence times (MRTs), residual time distributions, and mean residual times can be computed. This method does not require the assumptions and approximations made by the most commonly used methods. Its link to the most popular method in the literature is identified. It is shown how the much faster new method can be used as a replacement for the latter and the advantages of doing so. Also, a prescription for estimating the uncertainty in the MRTs obtained though the proposed method is provided. Another even faster method for the calculation of the MRTs, their uncertainties, and the mean residual times is also proposed. It yields exactly the same results as the first one but does not allow to obtain the mentioned distributions. Another very popular method, based on autocorrelation functions, for computing MRTs is analyzed in terms of its assumptions and approximations. An alternative, also based on autocorrelation functions, which is faster and requires fewer assumptions is presented. A prescription for the calculation of the uncertainty of the MRTs obtained with the latter method is also provided. In the literature, there are a few methods to discard short transient escapes. Here, an algorithm is suggested that is much faster than the most used one and allows a more integral treatment of the process. Also, it is more widely applicable because it is a preprocessing step that can be used in conjunction with any of the proposed methods mentioned above. The main disadvantage of these two approaches to discard brief escapes is that the maximum duration allowed for an escape to be considered transient appears as a parameter to be determined for the particular system under study. As an alternative, a parameter-free method of a similar character is also proposed to estimate the mean residence time of particles that reached a constant probability of leaving the region of interest.

Technological assessments on recent developments in fine and coarse particle flotation systems

• Froth flotation of fine and coarse particles is studied, focusing on cell designs. • Generating micro-bubbles, intensive turbulence, and high gas hold-up are advantages of intensified cells. • Scaling up/down procedures for the intensified cells are found unclear. • Positioning the optimum location of discussed cells in flotation circuits is found challenging. After more than a century applying flotation to the mining industry, two completely different strategies have been introduced for processing purposes. One is the classical approach viz. grinding ores to a certain extent (fine particles) and floating them via conventional mechanical and pneumatic cells i.e., Jameson, Imhoflot™ and Reflux™. This strategy continues because mines face declining cut-off grades, complex and poly-mineralized ores, and they are required to achieve an acceptable degree of mineral liberation. The other school of thought deals with coarse particle processes mainly owing to the low energy requirements, that includes SkimAir® flash, fluidized bed and HydroFloat™ cells. There is no study in the literature to comparatively present the recent developments of flotation apparatuses versus the conventional mechanical cells. To cover this knowledge gap in the literature, the present paper endeavors to critically evaluate these concepts from several points of view, including existing technological advancements, water and energy usage, kinetics, and circuit design. A brief introduction of advanced technologies, along with their applications is presented. The data from literature and case studies showed that the Jameson, Imhoflot™ and recently developed Reflux™ flotation cells can be very effective for recovering fine particles owing to their specific hydrodynamic designs, intensive energy dissipation rate and generation of micron-sized bubbles (100–700 µm). Very low (less than a few minutes) mean particle residence time, high gas-hold up (ca. 50–70 %), no agitation and high efficiency of particle-bubble collision were identified as their main advantages compared to traditional mechanical flotation cells. In addition to their common applications in cleaner stage, these cells were used in pre-flotation and scalping (producing final concentrate from the rougher feed) duties. Their main challenges were recognized as relatively unclear procedure on their scale up/down, optimization and simulation. The HydroFloat™ cell was indicated as a promising technology for recovering coarse particle fraction sizes by taking advantage of the fluidized-bed concept with plug-flow dispersion regime, high particle residence time, and limited cell turbulence. We finally concluded that fine particle flotation may remain as the main focus of re-processing tailings dams, while coarse particle treatment should be the focus of this century to reduce total energy consumptions.

Numerical Study and Experimental Validation of Skim Milk Drying in a Process Intensified Counter Flow Spray Dryer

This research presents 3D steady-state simulations of a skim milk spray drying process in a counter-current configuration dryer. A two-phase flow involving gas and discrete phase is modeled using the Eulerian–Lagrangian model with two-way coupling between phases. The drying kinetics of skim milk is incorporated using the Reaction Engineering Approach. The model predictions are found to be in accordance with the experimental temperature measurements with a maximum average error of 5%. The validated computational model is employed further to study the effects of nozzle position, initial spray Sauter Mean Diameter (SMD), air inlet temperature, and feed rate on the temperature and moisture profiles, particle impact positions, drying histories, and product recovery at the outlet. The location of the nozzle upwards (≈23 cm) resulted in maximum product recovery and increased the mean particle residence time at the outlet. A similar trend was observed for the highest feed rate of 26 kg/h owing to the increased spray penetration upstream in the chamber. The maximum evaporation zone was detected close to the atomizer (0–10 cm) when the spray SMD is 38 µm, whereas it shifts upstream (40–50 cm) of the dryer for an SMD of 58 µm. The high air inlet temperature resulted in enhanced evaporation rates only in the initial 10–20 cm distance from the atomizer. The results obtained in this study are beneficial for the development of the novel vortex chamber-based reactors with a counter flow mechanism.

A new method for continuous measurement of residence time distribution in spray drying

The residence time distribution of particles is one of the most important parameters during spray drying, since it directly impacts the thermal damage of a potential product. Due to insufficiencies of previous approaches for measuring the residence time distribution, a new method for continuous measurements was developed. This method simultaneously allows the determination of the residence time distribution of individual particle size fractions. The impact of air mass flow rate and particle size on the residence time distribution during spray drying was investigated. The mean particle residence time decreased with increasing air mass flow rate from 15.8 s for 190 kg/h, to 13.0 s for 210 kg/h and to 7.1 s for 230 kg/h, which is significantly shorter than the mean air residence time of 35.3 s, 31.9 s and 29.1 s, respectively. The mean particle residence time decreased with increasing particle size, with this effect being more pronounced for lower air flow rates. If the particle size is smaller than 105 µm, the presented technique can be transferred to any kind of single-stage spray dryer.

3D Eulerian-Eulerian modeling of a screw reactor for biomass thermochemical conversion. Part 1: Solids flow dynamics and back-mixing

Three-dimensional (3D) computational fluid dynamics (CFD) simulations were performed to study solids flow dynamics and solids back-mixing behavior in a screw reactor (designed for thermal conversion of dry biomass particles) based on the Eulerian-Eulerian method. Simulation results were compared against experimental data with respect to filling degree and mean residence time of particles. The mean deviations for filling degree and for mean residence time between simulation and experiment were about 0.01 and 11.4 s, respectively, which shows that the model is reasonably accurate in predicting solids flow behavior in the screw reactor. The solids flow dynamics inside the reactor were discussed. The solids residence time distribution (RTD) was calculated and the degree of solids back-mixing in the forward transportation direction of the reactor was analyzed. It was found that solids being flung over the shaft and solids back-leakage, resulting from the low solids forward transportation velocity at the clearance between the flight and the bottom shell of the screw reactor, were responsible for solids back-mixing. The degree of solids back-mixing can be reduced at higher screw rotating speeds when keeping inlet mass flow rate of solids constant.

Numerical Simulations of a Gas–Solid Two-Phase Impinging Stream Reactor with Dynamic Inlet Flow

Fluid flow characteristics and particle motion behavior of an impinging stream reactor with dynamic inlet flow (both inlet velocity patterns exhibit step variation) are investigated and discussed with the computational fluid dynamics–discrete element method (CFD–DEM). The effect of T (variation period of the dynamic inlet flow) and ∆u (inlet velocity difference) on the motion characteristics of single and multiple particles, as well as the mean particle residence time, are studied and discussed. The research results indicate that, compared with the traditional impinging stream reactor (both inlet velocities are equal and constant) with equal mean inlet velocity (um) within one period, the impinging surface is instantaneously moving and the flow regime is varied with time in the impinging stream reactor with dynamic inlet flow. The impinging stream reactor with dynamic inlet flow provides higher cost performance over the traditional impinging stream reactor, under equal um, in terms of single-particle residence time. Moreover, three new particle motion modes exist in multi-particle motions of the impinging stream reactor with dynamic inlet flow; particles are accelerated by the original or reverse fluid and perform oscillatory motion at least once after an interparticle collision. Whether it is a single particle or multi-particles, the mean particle residence time reaches a maximum value when T/2 is approximately equal to the first particle acceleration time, since the maximum axial kinetic energy increases in every oscillatory motion compared with traditional impinging stream, and the number of oscillatory motions is increasing. The mean residence time of a particle in the impinging stream reactor with a dynamic inlet flow increases with increasing ∆u, since the dynamic inlet conditions and increasing ∆u can continuously supply more energy to particles and thus cause more particles to enter one of the three new modes of particle motion.

Soil Particle Transport and Mixing Near a Hillslope Crest: 2. Cosmogenic Nuclide and Optically Stimulated Luminescence Tracers

We examine probabilistic elements of how cosmogenic nuclide (e.g., 10Be) concentrations and optically stimulated luminescence (OSL) particle ages are distributed within a soil mantle near a hillslope crest as a consequence of disturbance‐driven transport and particle mixing. We use an Eulerian‐Lagrangian algorithm in which fluctuating particle motions, representing depth‐dependent mixing, are superimposed on a two‐dimensional mean motion. The intensity of mixing is characterized by a Péclet number involving the vertical speed of particles entering the soil mantle at the soil‐bedrock interface, the mechanically active soil thickness, and a particle diffusivity at the soil surface. With weak mixing, the vertical profile of 10Be concentration reflects the strong influence of the mean motion in which particles spend much of their lives in the higher part of the soil column with higher 10Be production rates. With increasing mixing intensity, the profile becomes linear, then uniform, and the vertically averaged concentration is larger than that expected with one‐dimensional motion. With weak mixing, particles possessing a finite OSL age tend to remain near the soil surface; with increasing mixing they become more uniformly distributed with depth. Depth‐interval‐averaged OSL ages increase linearly with depth and then become uniform with strong mixing. With moderate to strong mixing, the probability distribution of OSL ages is approximately exponential with an average much less than the mean residence time of particles. The formulation is consistent with profiles of 10Be concentrations and interval‐averaged OSL particle ages compiled from published data, suggesting moderate to strong mixing in the cases examined.

The effect of different particle residence time distributions on the chemical looping combustion process

A model for chemical looping combustion has been developed to allow the effect of different residence time distributions of oxygen carrier particles in the air and fuel reactors to be investigated. The model envisages two, coupled fluidised bed reactors with steady circulation of particles between them. The results show that the process is sensitive to the residence time distributions, particularly when the mean residence time of particles in the reactors is similar to the time required for them to react completely. Under certain operating conditions, decreasing the variance of the residence time distribution, leads to a greater mean conversion of the particles by the time they leave the reactors and higher mean rates of reaction in the beds. In this way the required inventory and circulation rate of solids could be reduced, which would lower the capital and operating costs of a CLC process. Since the residence time distribution of solids is important, it should be taken into account when modelling or designing a chemical looping combustion process, e.g. by using a tanks-in-series model. This work indicates that if the number of tanks, N ≤ 5, knowing N to the nearest integer is generally sufficient, unless a high degree of accuracy is needed. As N increases, the sensitivity of the coupled system decreases, so for N > 5, knowing the value to the nearest 5 or 10 tanks is sufficient. This is valid whether N is the same or different in the two reactors. Chemical looping combustion is one example of a reactor-regenerator system, so the results are also relevant for other processes of this type, such as fluidised catalytic cracking.

Numerical study of particle mixing in a lab-scale screw mixer using the discrete element method

This study employs the discrete element method (DEM) to simulate particulate flow and investigate mixing performance of a lab-scale double screw mixer. The simulation employs polydispersed biomass and glass bead particles based on experiments conducted in previous studies. Visual examination of particle distribution and statistical analysis of particle residence times of experimental data served as model validation. Statistical analysis indicates a maximum 9.8% difference between the experimental and simulated biomass particle mean residence time, and visual observations suggest the simulation captures the particle mixing trends observed in the experiments. Results indicate that the particle mean mixing time, non-dimensionalized by ideal flow time in the plug flow reactor, varies between 1.008 and 1.172, and it approaches 1 with increasing biomass feed rate. The mixing index profile in the axial direction shows a mixing-demixing-mixing oscillation pattern. Increasing screw pitch length is detrimental to mixing performance; decreasing the solid particle feed rate reduces the mixing degree; and increasing the biomass to glass bead size ratio decreases mixing performance. A comparison of a binary, single-sized biomass and glass particles mixture to a multicomponent mixture indicates that the binary system has similar mixing pattern as a multicomponent system. These findings demonstrate that DEM is a valuable tool for the design and simulation of double screw mixing systems.

Experimental investigation and correlation of the Bodenstein number in horizontal fluidized beds with internal baffles

In many branches of industry, there is a high demand for the formation or the conditioning of particulate products. In many cases the fluidized bed technology is applied due to its robustness and intensity of heat and mass transfer. Furthermore, many producers look for a continuous process for economic reasons instead of a batch process with high labor and dead-time. These continuous processes, however, hold the disadvantage of a particle residence time distribution (RTD) and therefore a distribution of particle properties. To minimize the spread of the RTD vertical baffles can be installed into the system, causing an influence on the particle transport behavior. To investigate this influence several experiments have been conducted, varying relevant parameters, such as superficial gas velocity, particle diameter, the kind and placement as well as the number of internal baffles, the height of the exit weir and the apparatus itself (pilot and lab-scale plant). From the experiments different influences of the varied parameters on the Bodenstein number, as a measure of convective to dispersive transport, are shown. Based on these trends an empirical correlation for the Bodenstein number is developed and compared to the experimentally determined Bodenstein numbers. Furthermore a correlation for apparent bed porosity is proposed, which uses the set exit weir height instead of the unknown bed height to predict the particle holdup mass and thus the particle mean residence time. It is shown, that both correlations fit well with the experimentally determined values. Finally a prediction of the RTD is shown from the correlated Bodenstein number and the mean particle residence time.

Sensitivity of chemical-looping combustion to particle reaction kinetics

A simple simulation for chemical-looping combustion (CLC) is discussed: two, coupled fluidised reactors with steady circulation of particles of oxygen carrier between them. In particular, the sensitivity of CLC to different particle kinetics is investigated. The results show that the system is relatively insensitive to different kinetics when the mean residence time of particles in each reactor is greater than the time taken for them to react completely.

Simulation of dynamic transport of flexible ribbon particles in a rotary dryer

Flexible ribbon particles are a special type of particles, and there is relatively little research on their processing in a rotary dryer. In the present study, dynamic transport of flexible ribbon particles in a laboratory rotary drum was investigated. First, a box-chain model in three dimensions was established for flexible ribbon particles. Each particle was represented as a long and thin piece, divided into several rigid segments and connected by joint constraints. Periodic boundaries were considered along with constraints, torque, gravity, friction, collision force and air drag force during the drum rotation. Then, dynamic behavior of certain particles was investigated through numerical simulation, which vividly represents particle flexibility, multi-particle entanglement and multiple particle collisions. Based on this model, residence time of particles and mean residence time of particles in the drum were discussed in terms of key variables, including rotational velocity, drum slopes and initial velocity of air flow. The results clearly show the variation trend and the effects of variables on the residence time and dynamic behavior of particles in the drum. Lastly, selected results were compared with our previous experimental results and other relevant findings, and reasonable agreements between these results validate the numerical approach. The presented method and results could provide guides for the further study of flexible ribbon particles as well as other flexible particles.

Simulation of flow and drying characteristics of high-moisture particles in an impinging stream dryer via CFD-DEM

ABSTRACTImpinging stream dryer (ISD) is an alternative for drying high-moisture particulate materials. Due to the complex multiphase transport phenomena that take place within an ISD, use of a reliable computational model instead of a tedious experimental route to aid the design of the dryer is desirable. In the present study, computational fluid dynamics were used in combination with the discrete element method (CFD-DEM) to predict, for the first time, the multiphase transport phenomena within a coaxial ISD; results from a model that does not consider particle-particle interactions (CFD) were also obtained and compared with those from the CFD-DEM model. In all cases, high-moisture particles having negligible internal transport resistance were assumed. Both models were used to simulate the gas-particle motion behavior, particle mean moisture content, particle mean residence time, and particle residence time distribution. The simulated results from both models were compared with the experimental data whenever possible. The results showed that the CFD-DEM model could be utilized to predict the particle motion behavior and led to more physically realistic results than the CFD model. The CFD-DEM model also gave predictions that were in better agreement with the experimental mean particle residence time and moisture content data.

Wood chips flow in a rotary kiln: Experiments and modeling

Rotary kilns are well suited for processing woody biomass by torrefaction to produce bioenergy. One of the key issues for process design lies in the flow pattern modeling. The Saeman model is classically used to predict the mean residence time (MRT) and the bed depth profile of powder materials in rotary kilns. Its ability to describe wood chips flow arises. In the present study, residence time distribution (RTD) experiments are conducted with raw and torrefied wood chips. Effects of operating parameters – kiln slope, rotational speed and inlet flow-rate – on the average residence time, the variance and the mean solid hold-up are discussed. A plug flow with small extent of dispersion is emphasized, even if some segregation phenomena are highlighted. Torrefaction did not evidence any significant influence on the flow pattern. With a discrepancy of 20% between the measured and computed mean residence time, the predictive capacity of the classical Seaman model proved to be insufficient. The model is adapted to predict accurately the load profile and the mean residence time of particles with parallelepiped form. The discrepancy between experimental and calculated results is so reduced from 20% to 5% for the MRT and from 25% to 5% for the mean solid hold-up.

Onset velocity of circulating fluidization and particle residence time distribution: A CFD–DEM study

Until now, the onset velocity of circulating fluidization in liquid–solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superficial liquid velocity, and is reported to be only dependent on the liquid and particle properties. This study presents a new approach to calculate the onset velocity using CFD–DEM simulation of the particle residence time distribution (RTD). The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity. Our results are in reasonable agreement with experimental data. The simulation indicates that the onset velocity is influenced by the density and size of particles and weakly affected by riser height and diameter. A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity. The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity, but influence the particle RTD, showing some humps and trailing. The particle RTD is found to be related to the particle trajectories, which may indicate the complex flow structure and underlying mechanisms of the particle RTD.

Lagrangian modeling of the particle residence time in indoor environment

This study develops a new methodology to investigate the particle residence time in indoor environment with the Lagrangian modeling. So far, the particle residence time has been only developed in terms of the Eulerian-based advection-diffusion approach, which is easy to use but is only valid for the transport of fine, neutrally buoyant, non-inertial particles that exactly follow indoor airflows. However, for practical indoor air pollution problems, there exists a wide range of particle sizes. To extend the engineering application range of the particle residence time, a new Lagrangian-based approach, which adopts the kernel concentration estimation method, is herein proposed to model the particle residence time in indoor environment. This new approach can transfer Lagrangian particle trajectories into an Eulerian form of particle concentrations at a given point, and thus provide the mean particle residence time. The commonly used Eulerian-based advection-diffusion approach is also considered for numerical comparison. Two representative particle sizes of 10-μm coarse particles and 1-μm fine particles are input into the two approaches to investigate the effect of particle size on the mean particle residence time. The simulated results indicate that this new Lagrangian approach can give more reasonable prediction on the particle residence time than the Eulerian-based advection-diffusion approach.

Numerical Simulation of Multiphase Transport Phenomena During Impinging Stream Drying of a Particulate Material

The objective of the present study was to employ an existing three-dimensional computational fluid dynamic model to investigate the multiphase transport phenomena in a coaxial impinging stream dryer. The continuous-phase equations were solved in the Eulerian frame, while the discrete-phase equations were solved in the Lagrangian frame. Two-way coupling between the continuous and dispersed phases was taken into account in the model. Standard k-ϵ and realizable k-ϵ turbulence models were compared in order to decide which model could better represent the turbulent behavior of the flow in the ISD, while the stochastic approach was used to treat the effect of turbulence on the particle motion. Simulated mean particle moisture content and air humidity ratio at the dryer outlet as well as the particle mean residence time were compared with the experimental data. The results indicated that the model could predict the experimental results within ±10%, with the realizable turbulence model performing better than the standard model. The effects of various parameters including the inlet air velocity, inlet air temperature, material feed flow rate, and impinging distance on the transport and performance behavior of the dryer were then numerically investigated and discussed.

Impact of process parameters on critical performance attributes of a continuous blender—A DEM‐based study

AbstractA discrete element method‐based computational study carried out to study the effect of impeller design, speed, and input feed rate on the performance of a continuous powder blender is presented. The blender performance was characterized using the mean particle residence time, the residence time distribution, the number of blade passes experienced by the powder, and the mean centered variance. The powder residence time decreased with increasing impeller speed; however, the number of blade passes experienced a maximum at an intermediate speed. The effects of feed rate and impeller design were more prominent at lower speeds. Lower feed rate resulted in the powder experiencing higher number of blade passes. The number of blade passes was also higher for the alternate blade pattern when compared to the forward pattern. The computational findings were compared with an experimental study which showed that the model captured the essential flow dynamics well. © 2012 American Institute of Chemical Engineers AIChE J, 2012

Simulation of Blood Flow and Nanoparticle Transport in a Stenosed Carotid Bifurcation and Pseudo-Arteriole

Numerical simulation of flow through a realistic bifurcated carotid artery geometry with a stenosis has been conducted for comparison to experimental measurements. The behaviour of simplified therapeutic nanoparticles in relatively low concentration was observed using a discrete particle approach. The role of size (diameters from 500 nm to 50 nm) in determining particle residence time and the potential for both desirable and undesirable wall interactions was investigated. It was found that mean particle residence time reduced with decreasing particle diameter, and the percentage of particles experiencing one or more wall interactions increased simultaneously. Further simulations were conducted on a scaled-down version of the geometry which approximated the size and flow conditions of an arteriole with capillary branches, and in this instance the mean residence time increased with decreasing particle diameter, owing largely to the greater influence of Brownian motion. 33% of all 50 nm particles were involved in wall interactions, indicating that smaller particles would have a greater ability to target, for instance, cancerous tumours in such regions.