Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

Spatial Morphology Evolution Characteristics Analysis of the Resident Population Distribution in Henan, China

The population spatial distribution pattern and its evolving pattern play an important role in regional allocation of social resources and production factors, formulation of regional development plans, construction of a better life society, and promotion of regional economic development. Based on the resident population statistics data of Henan province from 2006 to 2021, with county as the basic study unit, the paper studies the spatial morphology characteristics and its evolution patterns of resident population distribution, by using spatial analysis methods such as population distribution center, standard deviation ellipse, and spatial auto correlation analysis. The results show that: the resident population spatial distribution shows unbalanced state, the population agglomeration areas mainly distribute in the northeast part and north part, where the resident population growth rate is significantly higher than other regions, over time, this trend is gradually becoming significant. The resident population distribution has a trend of centripetal concentration, with the degree and trend of centripetal gradually strengthening. The resident population distribution has obvious directional characteristics, but the significance is not high, the weighted resident population average center is approximately located at (4.13740˚N, 113.8935˚E), and the azimuth of the distribution axis is approximately 11.19˚. The population distribution has obvious agglomeration characteristics, with the built-up areas of Zhengzhou and Luoyang as their centers, where have a significant siphon effect on the surrounding population. The southern and southwestern regions in the province form a relatively stable belt area of Low-Low agglomeration areas.

Modeling on Residence Time Distribution in Subsurface Flow Constructed Wetlands by Multi Flow Dispersion Model

As an important design factor for constructed wetlands,hydraulic retention time and its distribution will affect the treatment performance.Instantaneously injected sodium chloride tracers were used to obtain residence time distributions of the lab scale subsurface flow constructed wetland.Considering the presence of trailing and multiple peaks of the tracer breakthrough curve,the multi flow dispersion model(MFDM)was used to fit the experimental tracer breakthrough curves.According to the residual sum of squares and comparison between the experimental values and simulated values of the tracer concentration,MFDM could fit the residence time distribution(RTD)curve satisfactorily,the results of which also reflected the layered structure of wetland cells,thus to give reference for application of MFDM to the same kind of subsurface flow constructed wetlands.

THE RESIDENCE TIME DISTRIBUTION FOR MULTIFLOW SYSTEM

In this paper,the superposition rule of the residence time distribution functions for the general systemhaving multiple inlet and outlet streams has been described and proved rigorously.For the cascade ves-sels system where the processed material in separate stages may be nonideally mixed in various degrees andthe volumes of separate stages may not be equal,the overall residence time distribution function E(t)and eachE(t)of the flow systems have been derived.The applications of these results to various flow systems havebeen discussed.

Numerical analysis on the transport properties and residence time distribution of ribbon biomass particles in a riser reactor based on CFD-DEM approach

A bended ribbon biomass particle model was developed to explore the dynamic transport properties inside a riser reactor.Residence time distribution(RTD)of the particles was analyzed by using the Eulerian-Lagrange method.The effects of sampling height,particle density,particle size and gas-to-solid mass ratio on RTD were investigated.The coupled Computational Fluid Dynamics and Discrete Element Method(CFD-DEM)model was verified firstly by experimental data on pressure drop and residence time distribution density function.The simulation results demonstrated that the ribbon biomass particles display a typical annular-core spatial distribution during transportation.The RTD of particles exhibit an approximate single-peaked normal distribution.The mean residence time(MRT)can reach up to 0.7 s when the particle density is 1200 kg/m^(3).Particle with higher density has longer mean residence time.The flow patterns are closer to plug flow if particle length over 12 mm.The particle flow pattern is not sensitive to changes in particle density and size,while the gas-to-material mass ratio has a significant impact on it.

Numerical simulation of flow field and residence time of nanoparticles in a 1000-ton industrial multi-jet combustion reactor

In this work,by establishing a three-dimensional physical model of a 1000-ton industrial multi-jet combustion reactor,a hexahedral structured grid was used to discretize the model.Combined with realizable k–εmodel,eddy-dissipation-concept,discrete-ordinate radiation model,hydrogen 19-step detailed reaction mechanism,air age user-defined-function,velocity field,temperature field,concentration field and gas arrival time in the reactor were numerically simulated.The Euler–Lagrange method combined with the discrete-phase-model was used to reveal the flow characteristics of particles in the reactor,and based on this,the effects of the reactor aspect ratios,central jet gas velocity and particle size on the flow field characteristics and particle back-mixing degree in the reactor were investigated.The results show that with the decrease of aspect ratio in the combustion reactors,the velocity and temperature attenuation in the reactor are intensified,the vortex phenomenon is aggravated,and the residence time distribution of nanoparticles is more dispersed.With the increase in the central jet gas velocities in reactors,the vortex lengthens along the axis,the turbulence intensity increases,and the residence time of particles decreases.The back-mixing degree and residence time of particles in the reactor also decrease with the increase in particle size.The simulation results can provide reference for the structural regulation of nanoparticles and the structural design of combustion reactor in the process of gas combustion synthesis.

Residence time distribution and heat/mass transfer performance of a millimeter scale butterfly-shaped reactor

A millimeter scale butterfly-shaped reactor was proposed based on sizing-up strategy and fabricated via femtosecond laser engraving. An improvement of mixing performance and residence time distribution was realized by means of contraction and expansion of the reaction channel. The liquid holdup was greatly increased through connection of multiple mixing units. Structure optimization of the reactor was carried out by computational fluid dynamics simulation, from which the effect of reactor internals on mixing and the influence of parallel branching structure on heat transfer were discussed. The UV–vis absorption spectroscopy was used to determine the residence time distribution in the reactor, and characteristic parameters such as skewness and dimensionless variance were obtained. Further, a chained stagnant flow model was proposed to precisely describe the trailing phenomenon caused by fluid stagnation and laminar flow in small scale reactors, which enables a better fit for the experimental results of the asymmetric residence time distribution. In addition, the heat transfer performance of the reactor was investigated, and the overall heat transfer coefficient was 110–600 W m^(-2)K-1in the flow rate range of 10–40 m L/min.

Application of computational fluid dynamic to model the hydraulic performance of subsurface flow wetlands

A subsurface flow wetland(SSFW)was simulated using a commercial computational fluid dynamic(CFD)code.The constructed media was simulated using porous media and the liquid resident time distribution(RTD)in the SSFW was obtained using the particle trajectory model.The effect of wetland configuration and operating conditions on the hydraulic performance of the SSFW were investigated.The results indicated that the hydraulic performance of the SSFW was predominantly affected by the wetland configuration.The hydr...

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 superfcial 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 infuenced 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.

Hydrodynamic characteristics of a four-compartment periodic anaerobic baffled reactor

Periodic anaerobic baffled reactor （PABR） is a novel reactor based on the design concept of anaerobic baffled reactor （ABR）. Residence time distribution （RTD） studies on both clean and working reactors at the same hydraulic residence time （HRT） of 2 d were carded out to investigate the dead spaces and mixing patterns in PABRs at different organic loading rates （OLRs） in various switching manners and frequencies. The results showed that the fraction of dead space in PABR was similar to that in ABR, which was low in comparison with other reactor designs. Dead space may be divided into two categories, hydraulic and biological. In RTD studies without biomass, the hydraulic dead space in the PABR run in an ＂every second＂ switching manner with T = 2 d was the lowest whereas that in the PABR run in a T = ∞ （ABR） switching manner was the highest. The same trend was obtained with the total dead space in RTD studies with biomass no matter what the OLR was. Biological dead space was the major contributor to dead space but affected decreasingly at higher OLR whichever switching manner the PABR run in. The flow patterns within the PABRs were intermediate between plug-flow and perfectly mixed under all the conditions tested,

Scale-up of bubbling fluidized beds with continuous particle flow based on particle-residence-time distribution

Few studies have investigated scale-up of the residence-time distribution （RTD） of particles in bubbling fluidized beds （BFBs） with continuous particle flow. Two approaches were investigated in this study： first, using well-known scaling laws that require changes in particle properties and gas velocity; second, using a simple approach keeping the same particles and gas velocity for different beds. Our theoretical analysis indicates it is possible to obtain similar RTDs in different BFBs with scaling laws if the plug-flow residence time （tpiug） is changed as m^0.5, where m is the scaling ratio of the bed; however, neither approach can ensure similar RTDs if tplug is kept invariant. To investigate RTD variations using two approaches without changing tplug, we performed experiments in three BFBs. The derivatives dE（θ）/dθ （where E（θ） is the dimensionless RTD density function and θ is the dimensionless time） in the early stage of the RTDs always varied with m 1, which was attributed to the fact that the particle movement in the early stage were mainly subject to dispersion. Using the simple approach, we obtained similar RTDs by separately treating the RTDs in the early and post-stages. This approach guarantees RTD similarity and provides basic rules for designing BFBs.

Numerical Investigation of Residence Time Distribution for the Characterization of Groundwater Flow System in Three Dimensions

How to identify the nested structure of a three-dimensional(3D)hierarchical groundwater flow system is always a difficult problem puzzling hydrogeologists due to the multiple scales and complexity of the 3D flow field.The main objective of this study was to develop a quantitative method to partition the nested groundwater flow system into different hierarchies in three dimensions.A 3D numerical model with topography derived from the real geomatic data in Jinan,China was implemented to simulate groundwater flow and residence time at the regional scale while the recharge rate,anisotropic permeability and hydrothermal effect being set as climatic and hydrogeological variables in the simulations.The simulated groundwater residence time distribution showed a favorable consistency with the spatial distribution of flow fields.The probability density function of residence time with discontinuous segments indicated the discrete nature of time domain between different flow hierarchies,and it was used to partition the hierarchical flow system into shallow/intermediate/deep flow compartments.The changes in the groundwater flow system can be quantitatively depicted by the climatic and hydrogeological variables.This study provides new insights and an efficient way to analyze groundwater circulation and evolution in three dimensions from the perspective of time domain.

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution(RTD)in an impinging stream reactor,a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed.The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions.The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux,but is almost independent of gas flux.As the liquid flux and the gas flux increase,the liquid dispersion coefficient of center-to-wall decreases.The axial liquid dispersion coefficient is much larger than that of center-to-wall,which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.

Optimization of residence time distribution in RCDG and an assessment of its applicability in continuous manufacturing

Knowledge of residence time is a critical aspect in developing control and material diversion strategies for continuous manufacturing processes in pharmaceutical manufacturing.Dry granulation is a promising continuous granulation technique as it is fast and economical.In this study,a step-change method to determine residence time in roll compaction/dry granulation is introduced.The factors roll speed and rotational speed of the impeller in the powder inlet unit of the compactor were evaluated using a central composite circumscribed statistical design of experiments in order to optimize the residence time.The fill volume in the compactor was varied exemplarily.It was found that high roll speed,low rotational speed of the impeller and low fill volume in the compactor are beneficial to generate fast transition through the compactor.The impact of roll speed increase was estimated.It can be concluded that despite fast residence time in the process,high roll speed and its subsequent high material throughput can generate a large amount of material that has to be discarded if material diversion is required.

Control strategy and methods for continuous direct compression processes

We presented a control strategy for tablet manufacturing processes based on continuous direct compression.The work was conducted by the experts of pharmaceutical companies,machine suppliers,academia,and regulatory authority in Japan.Among different items in the process,the component ratio and blended powder content were selected as the items requiring the control method specific to continuous manufacturing different from the conventional batch manufacturing.The control and management of the Loss in Weight(LIW)feeder were deemed the most important,and the Residence Time Distribution(RTD)model were regarded effective for setting the control range and for controlling of the LIW feeder.Based on these ideas,the concept of process control using RTD was summarized.

Determining axial dispersion coefficients of pilot-scale annular pulsed disc and doughnut columns

In this study,a computational fluid dynamics(CFD)method was adopted to calculate axial dispersion coefficients of annular pulsed disc and doughnut columns(APDDCs).Passive tracer was uniformly injected by pulse input at the continuous phase inlet,and its concentration governing equation was solved in liquid–liquidtwo-phase flow fields.The residence time distributions(RTDs)were obtained using the surface monitoring technique.The adopted RTD–CFD method was verified by comparing the axial dispersion coefficient between simulation and experimental results in the literature.However,in pilot-scale APDDCs,the axial dispersion coefficients predicted by the CFD–RTD method were approximately three times larger than experimental results determined by the steady-state concentration profile method.This experimental method was demonstrated to be insensitive to the variation of the axial dispersion coefficient.The CFD–RTD method was more recommended to determine the axial dispersion coefficient.It was found that the axial dispersion coefficient increased with an increase in pulsation intensity,column diameter,and plate spacing,but was little affected by the throughput.

Hydraulic modeling of an anaerobic expanded bed reactor for municipal sewage treatment

Anaerobic expanded bed reactor(AEBR) is mostly used for the treatment of fairly low strength wastewaters. Since the performance of AEBR largely depends on its hydraulic characteristics, residence time distribution(RTD) method is commonly used for investigation of the hydraulic characteristics of AEBR under different ascending velocity of mixed liquor. In this paper, a pilot-scale AEBR reactor is investigated for treatment of municipal sewage in which lithium chloride is used as a tracer. The results show that the AEBR could be considered as the superimposition of several constant stirred tank reactors(CSTR) and the increase of hydraulic up-flow velocity could increase the number of the CSTR and decrease the volume rate of the dead zone. The optimal up-flow velocity of the investigated AEBR was approximately 1.9 m/h in the municipal sewage treatment.

Influence of Swimming Pool Design on Hydraulic Behavior: A Numerical and Experimental Study

A swimming pool can be considered as a chemical reactor with specific hydraulic and macro-mixing characteristics. The nature of flow into the pool depends on various characteristics, such as water inlets and outlets (number and position), pool geometry, and flow rate. This study investigates how swimming pool design affects hydraulic behavior based on experimental and computational fluid dynamics studies (CFD). This paper does not describe the hydraulic behavior of all existing swimming pools, however the cases studied here are representative of pool designs widely used in Europe and the United States. The model developed, based on the principle of a stirred reactor, could be used as a first approach in describing the hydraulic behavior of regular pools. This model is suitable for the study of physical and chemical phenomena with long characteristic times. Other, more advanced, models were shown to be more suitable to the case of fast chemical processes.

Measurement,Modelling and Analysis of Residence Time Distribution Characteristics in a Continuous Hydrothermal Reactor

Understanding the residence time distribution(RTD)of a continuous hydrothermal reactor is of great significance to improve product quality and reaction efficiency.In this work,an on-line measurement system is attached to a continuous reactor to investigate the characteristics of RTD.An approach that can accurately fit and describe the experimental measured RTD curve by finding characteristic values is proposed for analysis and comparison.The RTD curves of three experiment groups are measured and the characteristic values are calculated.Results show that increasing total flow rate and extending effective reactor length have inverse effect on average residence time,but they both cause the reactor to approach a plug flow reactor and improve the materials leading.The branch flow rate fraction has no significant effect on RTD characteristics in the scope of the present work except the weak negative correlation with the average residence time.Besides,the natural convection stirring effect can also increase the average residence time,especially when the forced flow is weak.The analysis reveals that it is necessary to consider the matching of natural convection,forced flow and reactor size to control RTD when designing the hydrothermal reactor and working conditions.

Physical and numerical investigation on fluid flow and inclusion removal behavior in a single-strand tundish

Aiming at the problem that the existence of inclusions in the tundish continuous casting process can easily lead to quality defects of the slab,the stainless steel continuous casting tundish was taken as the research object.The effects of flow control device,inclusion density and inclusion size on the mixing characteristics of molten steel and inclusion behavior in tundish were studied.The results showed that compared with the tundish without flow control device,the average residence time of molten steel was prolonged by about 49 s,the dead zone volume fraction was reduced by 8.93%,and the piston fluid integral rate was increased by 12.68%.In the turbulence inhibitor(TI)tundish with weir-dam combination,the removal rate of inclusions with a density of 2700 kg m^(-3) and a particle size of 5 lm is 63.32%,while the removal rate of large inclusions with a density of 150μm could reach 89.04%.When the inclusion particle size was 10-50μm and the density was 2700-4500 kg m^(-3),the effect of inclusion density on inclusion removal rate was small.At the same time,when weir-dam combination TI tundish was set,the inclusions were mainly limited to the slag-metal interface of the first and second chambers of the tundish.The removal rate of inclusions in the first chamber was generally improved,with 10μm inclusions accounting for 47.67% and 150μm inclusions accounting for 60.69%.Furthermore,it has the best effect on the removal of small-size inclusions,especially those less than 70μm.