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.

Residence time distribution of high viscosity fluids falling film flow down outside of industrial-scale vertical wavy wall: Experimental investigation and CFD prediction

The flow behavior of gravity-driven falling film of non-conductive high viscosity polymer fluids on an industrial-scale vertical wavy wall was investigated in terms of film thickness and residence time distribution by numerical simulation and experiment.Falling film flow of high viscosity fluids was found to be steady on a vertical wavy wall in the presence of the large film thickness.The comparison between numerical simulation and experiment for the film thickness both in crest and trough of wavy wall showed good agreement.The simulation results of average residence time of falling film flow with different viscous fluids were also consistent with the experimental results.This work provides the initial insights of how to evaluate and optimize the falling film flow system of polymer fluid.

Distribution, residence time, autotrophic production, and heterotrophic removal of DOP in the Mirs Bay, northern South China Sea

The importance of dissolved organic phosphorus(DOP) as a potential nutrient source for primary producers in marine systems has been recognized for up to eight decades, but currently, the understanding of the biogeochemistry of DOP is in its infancy. In the present study, monthly data between 2000 and 2014 were used to analyze the temporal and spatial distributions of DOP in the Mir Bay, the northern South China Sea. The DOP residence time(TDOP) was also investigated using a simple regression analysis in combination with chlorophyll a(Chl a) measurements while excess DOP(ΔDOP), produced by the biogeochemical processes of autotrophic production and heterotrophic removal, was determined using a two-component mixing mass-balance model in combination with salinity measurements. The results showed that the DOP concentration was(0.017±0.010) mg/L higher in the surface-water compared with the bottom-water and higher in the inner Tolo Harbour and waters adjacent to Shatoujiao compared with the main zone of the bay. Although seasonal changes and annual variability in the DOP were small, the surface DOP concentration was higher in the wet season(April–September)than in the dry season(October–March) due to the impacts of seaward discharges and atmospheric deposition into the bay. Measurement and regression results showed that the DOP release rate from phytoplankton production was about 1.83(gP)/(gChl a) and the TDOP was about 7 d, which implied that the DOP cycle in the bay was rapid. The ΔDOP was calculated from the model to be about 0.000 mg/L in the main zone of the bay and about 0.002 mg/L in the inner Tolo Harbour and waters adjacent to Shaotoujiao, suggesting that the autotrophic production of DOP was almost balanced by the heterotrophic removal in the main zone of the bay and dominated in the inner Tolo Harbour and waters adjacent to Shaotoujiao. In conclusion, the Mirs Bay is very productive and fairly heterotrophic.

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.

RESIDENCE TIME DISTRIBUTION STUDIES WITH TRACER EXPERIMENTS:IMPULSE INJECTION VERSUS STEP CHANGE OF FEED

1 INTRODUCTIONThe popularly used axial dispersion model is mathematically expressed by aone-dimensional partial differential

ON THE RESPONSE FUNCTION AND RESIDENCE TIME DISTRIBUTION OF THE AXIAL DISPERSION MODEL FOR TUBULAR REACTORS

In view of confusion on the residence time distribution and transfer fucntions for dispersion models, the solution of the model subject to possible combinations of closed and open type boundaries at the ends of a chemical reactor is investigated systematically. In particular, some new results are obtained for the closed-open and open-closed types of reactors. It is found that the interchange of boundary conditions for these reactors is not immaterial. In several cases, caution is necessary to distinguish whether the transfer function is applied to the concentration or the flux. When the dispersive flux is notable, measurement techniques must be carefully selected to match the kind of transfer functions derived.

RESIDENCE TIME DISTRIBUTION IN AN OPEN REACTOR:EFFECT OF BACKGROUND REACTANT ON TRACER DISPERSION

A new approach is presented for deriving the residence time distribution(RTD)in open-type reactors with exclusion of residence in the fore section.Inasmuch as failure to predict the con-version of chemical reactions has been evidenced in many occasions,numerical solution of tracerdispersion in the presence of background concentration gradient of reactant is given to demonstratethe strong effect of background reactant on the true RTD a reactant molecule experiences.Withinthe error of computation,the conversion of a first-order chemical reaction under steady state is shownto be equal in both closed and open reactors,despite difference in relevant

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.

Gas Residence Time Distributions in a Spouted Bed

In a spouted bed of 80mm in ID and 1700mm in height, the gas residence time distributions at different radial positions in both spout and annular area were measured with five different kinds of particles as spouting material, air as spouting gas, and hydrogen as tracer. The effects of superficial gas velocity, operating pressure, particle size and its category on gas residence time distribution were discussed. It was found that the gas velocity profile in spout was more uniform than that in annulus. It could be concluded that the gas flow in the spout could be treated as a plug-flow, while that in the annulus inhibited a strong non-ideal flow behavior. Increasing the superficial gas velocity and decreasing the operating pressure, the particle density and its size gave rise to spouting disturbance, thus the measured tracer concentrations vs. time curves fluctuated. The variances of residence time distribution curves could be taken as a measure of the gas fluctuation degree.

Residence Time Distribution at Laminar Pulsatile Flow in a Straight Pipe

This paper deals with the problem of theoretical identification of the residence time distribution （RTD） characteristics of a straight pipe at laminar pulsatile flow, if tracer diffusion can be neglected. This situation is typical for micro-apparatuses （e.g. fluidic element） and also for flow in large arteries. Residence time distribution based on velocity profiles at pulsatile flow of a Newtonian liquid in a rigid pipe will be derived theoretically and compared with the well known results for a constant flow rate E（τ） = τ-^2/2τ^3 at τ 〉 τ^-/2, where E （τ） is differential distribution, x is residence time and τ^- is the mean residence time. The following part of the paper deals stimulus response experimental techniques using tracers. The principal problem related to laminar and convection dominated pulsatile flows is discussed： Can the impulse response also be identified with the actual residence time distribution in the case of variable flow？ The general answer is no, and differences between RTD and impulse responses are evaluated as a function of the frequency and amplitude of pulsatile flows.

Residence time distribution of wood chips in a semi-industrial multiple hearth furnace using RFID tracers Author links open overlay panel

In continuous biomass torrefaction plants,the products'yields,composition and homogeneity highly depend on the residence time of particles.A characterization of particle residence time distribution(RTD)was therefore carried out in an industrial-scale multiple hearth furnace on poplar wood chips using radio frequency identification tracers.The effects of operating conditions,namely,mass flow rate of biomass,shaft speed of the rabbling system and interdental length on the RTD were studied.The increase of shaft speed and mass flow rate reduces particles’mean residence time.Lowering the length between two successive teeth also increases the bed speed.Uncontrollable biomass accumulation(also called“bulldozing”)was observed during several tests.This phenomenon is favored by a high mass flow rate of resources,a small interdental length between the teeth and a low shaft speed.RTD measurements were compared to the axial dispersion model.For all tests,the Peclet number is ranging between 20 and 62,indicating that the multiple hearth furnace cannot be modelled as an ideal plug flow reactor.

Analysis model of internal residence time distribution for fluid flow in a multi-strand continuous casting tundish

The external residence time distribution(RTD)curve is extensively used to characterise fluid flow within the single-strand continuous casting tundish.Dead volume fraction determination typically relies on the external RTD curve to reveal macroscopic fluid flow behaviour.Based on the external RTD to effectively assess dead volume fractions and other fluid characteristics under conditions of internal non-uniform flow,an internal RTD was introduced.In a smooth pipe under laminar flow conditions,the dead region occupies 25%of the total volume,which is defined as the space between the pipe wall and a radius of 0.866 R0(where R0 is the radius of pipe).Under turbulent flow conditions,the dead region only occupies 0.38%of the reactor’s internal volume,spanning from the pipe wall to a radius of 0.00189 R0.The results obtained using the external RTD method are consistent with the theoretical analysis.Experimental trials involving water were conducted to examine the flow of molten steel within a five-strand tundish.Subsequently,an analysis approach employing internal RTD was employed to evaluate fluid mixing within a multi-flow continuous casting tundish.Using the internal RTD method,the analysis revealed that the whole dead zone volume fraction of the intermediate package decreased from 26.9%to 18.9%after the addition of the flow control device.The dead volume fraction can be accurately depicted by utilising the internal mean RTD function.The association between the internal RTD function and the external average RTD can be effectively employed to scrutinise the response curve of the tracer within a system exhibiting uneven flow distribution.

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.

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.

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.

An Estimation Method for Kill Probability Based on Random Residence Time Series

Relations between statistical residence time series and effective shooting are analyzed in accordance with the properties of the random residence time of maneuver targets crossing shot area in a given time. An estimation method for kill probability is proposed, which solves the probability of number of residence times satisfied effective shooting in given time. Some expressions and their approximate formulae of kill probability are derived, under known the distribution of residence time series. Theoretical analysis and simulation results show that this method is suitable for evaluating the hit ability of fire system for maneuver targets in random shooting.

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.

The Relationship Between Hysteresis and Liquid Flow Distribution in Trickle Beds

Experiments were conducted on a trickle bed with 0.283m ID to elucidate the relationship between hysteretic phenomena and liquid distribution. The hysteresis of pressure drop and the variance of radial liquid distribution were observed simultaneously. Residence time distribution (RTD), holdup and mean residence time (RT) of liquid phase were also found to demonstrate hysteresis of the same nature. RTD, liquid holdup and mean RT calculated with a simple model from the distribution of liquid flow rate show characteristics consistant with the experimental data, suggesting that the hyteretic phenomena originate from the multiplicity and nonuniformity of liquid flow distribution.

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.

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.