The residence-time distribution （RTD） and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematic...The residence-time distribution （RTD） and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematical model as well as three-dimensional computational fluid dynamics （CFD） model was established to analyze the flow regions of feedwells on an industrial scale. The concept of RTD, although a well-known method for the characterization of mixing behavior in conventional mixers and reactors, is still a novel measure for the characterization of mixing in feedwells. Numerical simulation results show that the inlet feed rate and the aspect ratio of feedwells are the most critical parameters which affect the RTD of feedwell. Further simulation experiments were then carried out. Under the optimal operation conditions, the volume fraction of dead zone can reduce by10.8% and an increasement of mixing flow volume fraction by 6.5% is also observed. There is an optimum feed inlet rate depending on the feedwell design. The CFD model in conjunction with the RTD analysis then can be used as an effective tool in the design, evaluation and optimization of thickener feedwell in the red mud separation.展开更多
A wedge-shaped planar mass-flow hopper system was modelled using stress-field theory as found in the literature, The authors present governing equations for stress and velocity fields under a radial- flow assumption i...A wedge-shaped planar mass-flow hopper system was modelled using stress-field theory as found in the literature, The authors present governing equations for stress and velocity fields under a radial- flow assumption in a converging hopper. The velocity in the silo above the hopper is modelled as plug flow, Two set-ups are modelled, one where powder layers in the hopper are assumed to be flat, and the second in which the layers are heaped at some characteristic angle, The ejection times and residence-time distributions are calculated and presented for a range of heap angles. For realistic heap angles, the spread of the residence-time distribution decreases with increasing heap angle; in one case, the spread is halved to a well-defined limit. At this limit （the critical heap angle） the geometry of the hopper can be optimised to minimise the spread of the residence-time distribution, and hence to minimise predicted mixing in the system. We present examples of curves for a variety of parameters that minimise the predicted mixing in the hopper-silo system.展开更多
India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its ne...India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor,Pakistan.The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries.The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries(notably non-pharmaceutical interventions).Numerical simulations of the basic model indicate that,based on the current baseline levels of the control and mitigation strategies implemented,the pandemic trajectory in India is on a downward trend.This downward trend will be reversed,and India will be recording mild outbreaks,if the control and mitigation strategies are relaxed from their current levels.By early September 2021,our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies,while Pakistan(where the pandemic is comparatively milder)could see over 24,000 cumulative deaths at current mitigation levels.The basic model was extended to assess the impact of back-and-forth mobility between the two countries.Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan,with daily mortality in Pakistan peaking in mid-August to mid-September of 2021.Under the respective baseline control scenarios,our simulations show that the backand-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022,respectively.展开更多
To predict the particle size and layer-thickness distributions(LTDs)in a continuously operated horizontal fluidized-bed granulation process,two alternative models were considered.A one-dimensional two-zone model was p...To predict the particle size and layer-thickness distributions(LTDs)in a continuously operated horizontal fluidized-bed granulation process,two alternative models were considered.A one-dimensional two-zone model was proposed,which describes with population-balance equations the particle growth in a spraying zone that is separated from the drying zone.The residence-time distribution(RTD)was calculated from a literature correlation and was coupled with a population-balance model via a tank-in-series model with reflux.A two-dimensional,one-zone population-balance model,which was based directly on the RTD and the feed particle-size distribution(PSD)was also used.Granulation experiments were conducted and analyzed microscopically and with a camera optical device to determine the sample PSDs.LTDs over the particle population were derived from the PSDs and were analyzed directly by micro-computer-tomography.To compare the simulated data with the experimentally determined distributions,the PSDs were converted to LTDs.The good agreement shows that both methods are suitable to determine the PSD from an RTD of an arbitrary granulation process in a horizontal fluidized bed.Improvement appears necessary with regards to the LTD spread.展开更多
基金Project (50876116) supported by the National Natural Science Foundation of China
文摘The residence-time distribution （RTD） and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematical model as well as three-dimensional computational fluid dynamics （CFD） model was established to analyze the flow regions of feedwells on an industrial scale. The concept of RTD, although a well-known method for the characterization of mixing behavior in conventional mixers and reactors, is still a novel measure for the characterization of mixing in feedwells. Numerical simulation results show that the inlet feed rate and the aspect ratio of feedwells are the most critical parameters which affect the RTD of feedwell. Further simulation experiments were then carried out. Under the optimal operation conditions, the volume fraction of dead zone can reduce by10.8% and an increasement of mixing flow volume fraction by 6.5% is also observed. There is an optimum feed inlet rate depending on the feedwell design. The CFD model in conjunction with the RTD analysis then can be used as an effective tool in the design, evaluation and optimization of thickener feedwell in the red mud separation.
文摘A wedge-shaped planar mass-flow hopper system was modelled using stress-field theory as found in the literature, The authors present governing equations for stress and velocity fields under a radial- flow assumption in a converging hopper. The velocity in the silo above the hopper is modelled as plug flow, Two set-ups are modelled, one where powder layers in the hopper are assumed to be flat, and the second in which the layers are heaped at some characteristic angle, The ejection times and residence-time distributions are calculated and presented for a range of heap angles. For realistic heap angles, the spread of the residence-time distribution decreases with increasing heap angle; in one case, the spread is halved to a well-defined limit. At this limit （the critical heap angle） the geometry of the hopper can be optimised to minimise the spread of the residence-time distribution, and hence to minimise predicted mixing in the system. We present examples of curves for a variety of parameters that minimise the predicted mixing in the hopper-silo system.
基金One of the authors(ABG)acknowledge the support,in part,of the Simons Foundation(Award#585022)the National Science Foundation(Grant Number:DMS-2052363)Another author(SS)acknowledges the support of the Fulbright Scholarship.
文摘India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor,Pakistan.The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries.The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries(notably non-pharmaceutical interventions).Numerical simulations of the basic model indicate that,based on the current baseline levels of the control and mitigation strategies implemented,the pandemic trajectory in India is on a downward trend.This downward trend will be reversed,and India will be recording mild outbreaks,if the control and mitigation strategies are relaxed from their current levels.By early September 2021,our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies,while Pakistan(where the pandemic is comparatively milder)could see over 24,000 cumulative deaths at current mitigation levels.The basic model was extended to assess the impact of back-and-forth mobility between the two countries.Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan,with daily mortality in Pakistan peaking in mid-August to mid-September of 2021.Under the respective baseline control scenarios,our simulations show that the backand-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022,respectively.
基金the Forschungs-Gellschaft Verfahrens-Technik(GVT-IGF project no.17633 N)the German Federal Ministry of Science and Education(BMBF,WIGRATEC+project No.03WKCI4B).
文摘To predict the particle size and layer-thickness distributions(LTDs)in a continuously operated horizontal fluidized-bed granulation process,two alternative models were considered.A one-dimensional two-zone model was proposed,which describes with population-balance equations the particle growth in a spraying zone that is separated from the drying zone.The residence-time distribution(RTD)was calculated from a literature correlation and was coupled with a population-balance model via a tank-in-series model with reflux.A two-dimensional,one-zone population-balance model,which was based directly on the RTD and the feed particle-size distribution(PSD)was also used.Granulation experiments were conducted and analyzed microscopically and with a camera optical device to determine the sample PSDs.LTDs over the particle population were derived from the PSDs and were analyzed directly by micro-computer-tomography.To compare the simulated data with the experimentally determined distributions,the PSDs were converted to LTDs.The good agreement shows that both methods are suitable to determine the PSD from an RTD of an arbitrary granulation process in a horizontal fluidized bed.Improvement appears necessary with regards to the LTD spread.
