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.

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.

Determination and impact factor analysis of hydrodynamic dispersion coefficient within a gravel layer using an electrolyte tracer method

Hydrodynamic dispersion is a measure for describing the process of solute transport in porous media.Characterizing the dispersion of water flow within gravel is essential for the prediction of solute transport especially nonpoint source pollutants migration in alpine watersheds where the land surface is typically covered with gravel.In this study,an integrated model and experimental method using an electrolyte tracer is proposed for determination of the hydrodynamic dispersion coefficient.Two experimental scenarios were designed to measure electrolyte tracer transport processes in both free water flow and gravel layer flow under different slope gradients and transport distances.Subsequently,the measured data were used to simultaneously calculate both the hydrodynamic dispersion coefficient and flow velocity by fitting the experimental data with the mathematical model.Dispersivity,as a critical feature of hydrodynamic dispersion,was determined as well under the two specified scenarios.Finally,the impact mechanisms of the gravel layer and factors related to the dispersion processes were comprehensively analyzed.The results indicate that the presence of a gravel layer significantly reduces flow velocity and the hydrodynamic dispersion coefficient,but increases solute dispersivity.For the flow within gravel layers,with much lower velocity,the positive effect of the gravel layer on dispersivity may be neutralized or even surpassed by the negative effect of flow velocity.The results should be helpful in characterizing the dispersion processes of water flow within gravel layer and hence in predicting solute transport,especially in nonpoint source pollutants migration in alpine watersheds where the land surface is richly covered with gravel.

Inversion of dispersion coeffcient in water quality model using optimal perturbation algorithm

As a primary parameter in the water quality model for shallow bays, the dispersion coefficient is traditionally determined with a trial-and-error method, which is time-consuming and requires much experience. In this paper, based on the measured data of chemical oxygen demand （COD）, the dispersion coefficient is calculated using an inversion method. In the process, the regularization method is applied to treat the ill-posedness, and an operator identity perturbation method is used to obtain the solu- tion. Using the model with an inverted dispersion coefficient, the distributions of COD, inorganic nitrogen （IN）, and inorganic phosphorus （IP） in Bohai Bay are predicted and compared with the measured data. The results indicate that the method is feasible and the inverted dispersion coefficient can be used to predict other pollutant distribution. This method may also be further extended to the inversion of other parameters in the water quality model.

Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers

In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.

Diffusion tensor imaging reveals brain structure changes in dogs after spinal cord injury

Based on the Wallerian degeneration in the spinal cord pathways,the changes in synaptic connections,and the spinal cord-related cellular responses that alter the cellular structure of the brain,we presumed that brain diffusion tensor imaging(DTI)parameters may change after spinal cord injury.However,the dynamic changes in DTI parameters remain unclear.We established a Beagle dog model of T10 spinal cord contusion and performed DTI of the injured spinal cord.We found dynamic changes in DTI parameters in the cerebral peduncle,posterior limb of the internal capsule,pre-and postcentral gyri of the brain within 12 weeks after spinal cord injury.We then performed immunohistochemistry to detect the expression of neurofilament heavy polypeptide(axonal marker),glial fibrillary acidic protein(glial cell marker),and NeuN(neuronal marker).We found that these pathological changes were consistent with DTI parameter changes.These findings suggest that DTI can display brain structure changes after spinal cord injury.

Solute transport characteristics of a deep soil profile in the Loess Plateau,China

Understanding solute transport behaviors of deep soil profile in the Loess Plateau is helpful for ecological construction and agricultural production improvement. In this study, solute transport processes of a deep soil profile were measured by a conservative tracer experiment using 25 undisturbed soil cores （20 cm long and 7 cm diameter for each） continuously sampled from the surface downward to the depth of 500 cm in the Loess Plateau of China. The solute transport breakthrough curves （BTCs） were analyzed in terms of the convection-dispersion equation （CDE） and the mobile-immobile model （MIM）. Average pore-water velocity and dispersion coefficient （or effective dispersion coefficient） were calculated using the CDE and MIM. Basic soil properties and water infiltration parameters were also determined to explore their influence on the solute transport parameters. Both pore-water velocity and dispersion coefficient （or effective dispersion coefficient） generally decreased with increasing depth, and the dispersivity fluctuated along the soil profile. There was a good linear correlation between log-transformed pore-water velocity and dispersion coefficient, with a slope of about 1.0 and an average dispersivity of 0.25 for the entire soil profile. Generally speaking, the soil was more homogeneous along the soil profile. Our results also show that hydrodynamic dispersion is the dominant mechanism of solute transport of loess soils in the study area.

Assessment of Fiber Distribution in Steel Fiber Mortar Using Image Analysis

A new test method was introduced to measure fiber distribution in steel fiber reinforced mortar by using image analysis technique. Through specimen preparation, image acquisition, fiber extraction, and measurement of related fiber parameters, quantitative analysis of fiber distribution could be obtained by two parameters, namely dispersion coefficient and orientation factor. Effect of boundaries, size and steel fiber content on fiber distribution was discussed. Results showed that, steel fiber distribution was affected by boundary effect, which would be weakened with the increase of specimen size. If the length and width remained constant, the specimen height had a significant effect on orientation factor of fiber, while its influence on dispersion coefficient was not so obvious. With the increase of steel fiber content, dispersion coefficient decreased slightly, and orientation factor deviated from 0.5.

Longitudinal dispersive coefficient in channels with aquatic vegetation:A review

The determination of longitudinal dispersion coefficient in rivers is necessary for pollution control,environmental risk assessment,and management.In rivers with aquatic vegetation,the flow field is remarkably modified by canopies,which affects velocity profiles and dispersion characteristics dominated by the heterogeneity of the velocity field.The dispersion is deduced from lateral and vertical longitudinal velocity gradients for compound channels with vegetated floodplains and rectangular channels with river-wide vegetation,respectively.Although many efforts have been exerted to clarify the dispersion process in different conditions and predict the diffusion of contaminants in vegetated rivers,no studies have introduced it systematically.This study reviews the dispersion coefficient characteristics,including magnitude,main impacted factors,and relationships with flow and vegetation features,in channels with aquatic canopies considering the variation of impact factors changing with the different vegetation and river morphology scenarios.Several typical methodologies for determining longitudinal dispersion coefficients are also summarized to understand the dispersion processes and concepts.Apart from the pioneer outcomes of previous studies,the review also emphasizes the deficiency of existing studies and suggests possible future directions for improving the theory of dispersion in vegetated channels.

Effect of vegetation on flow structure and dispersion in strongly curved channels

The effect of vegetation on the flow structure and the dispersion in a 180 o curved open channel is studied. The Micro ADV is used to measure the flow velocities both in the vegetation cases and the non-vegetation case. It is shown that the velocities in the vegetation area are much smaller than those in the non-vegetation area and a large velocity gradient is generated between the vegetation area and the non-vegetation area. The transverse and longitudinal dispersion coefficients are analyzed based on the experimental data by using the modified N- zone models. It is shown that the effect of the vegetation on the transverse dispersion coefficient is small, involving only changes of a small magnitude, however, since the primary velocities become much more inhomogeneous with the presence of the vegetation, the longitudinal dispersion coefficients are much larger than those in the non-vegetation case.

DISPERSION OF CYLINDRICAL PARTICLES IN TURBULENT FLOWS

With consideration of the Stokes drag and virtual mass force, the equationsfor mean and fluctuating velocities in rotation and translation were given for rigid cylindricalparticles moving in a turbulent flow. Then the rotational and translational dispersion coefficientsof particle were derived. The relationships between the dispersion, coefficients and flow lengthscale as well as particle characteristic parameters were analyzed. The resulting dispersioncoefficients were proved to decrease as the particle length increases. The conclusions are helpfulfor the further research on the motion of cylindrical particles in turbulent flows.

Dispersion features of pollutants in a compound channel with vegetated floodplains

The planting of the vegetation on the floodplain helps the ecological restoration,which is the main form of the river’s ecological corridor.Therefore,the current research of the river dynamics focuses on the water movement under a compound channel with the vegetated floodplains.Two simulated vegetation species are selected in this paper for the flume simulation experiments of the floodplain vegetation,and the compound channel is divided into three subregions in the transverse direction.The Navier-Stokes equation and the eddy viscosity theory are applied to obtain the transverse distribution of the depth-averaged velocity and the results agree well with the experimental data.This paper proposes a new method based on the analytical solution of the flow velocity distribution to calculate the average flow velocity in each section.Calculation results can effectively simulate the average flow velocity of the measured sections.The description of the pollutant transport processes in a moving stream requires a refined determination of the dispersion coefficients in the compound channel.The process of the pollutant concentrations in each zone and the reasons for their occurrence are elucidated on the basis of the experimental results.Simultaneously,the measured values of the longitudinal dispersion coefficients are obtained by the“routing procedure,”and a two-zone model of the pollutant dispersion is constructed on the basis of the hydrodynamic study.The prediction method for the longitudinal dispersion coefficients is also presented.Applying the predicted and measured section average flow velocities to the two-zone model to predict the longitudinal dispersion coefficient,and the average relative errors are only 4.17%,7.15%,respectively.This result indicates that the two-zone model can effectively predict the longitudinal dispersion coefficients.The calculation methods for the longitudinal dispersion coefficients from—various studies are compared.The results reveal that the predicted values of these calculation methods are all larger than the measured values,indicating that the vegetation has a considerable influence on the dispersion process.This study comprehensively shows the dispersion features of the pollutants and provides a theoretical basis for the planning and the design of the vegetated ecological corridors.

Revisit of advection-dispersion equation model with velocity-dependent dispersion in capturing tracer dynamics in single empty fractures

An accurate quantification of the contaminant transport through fractured media is critical for dealing with water-quality related scientific and engineering issues, where the dispersion coefficient is an important and elusive parameter for the solute transport modeling. Many previous studies show that the dispersion coefficient(D) in the standard advection-dispersion equation(ADE) model can be approximated by D=avλ(where a is the dispersivity), a formula to be revisited systematically in this study by laboratory experiments and model analysis. First, a series of tracer transport experiments in single empty fractures are conducted in cases of different hydraulic gradients. Second, the tracer breakthrough curves are determined by simulations based on the ADE model, to obtain the dispersion coefficients corresponding to various fracture roughnesses and flow velocities. A varying trend of λ is analyzed under different flow conditions. Results show that although the standard ADE model cannot be used to characterize the late-time tailing of the tracer BTCs, likely due to the solute retention, this simple model can simulate most of the solute mass dynamics moving through fractures and may therefore provide information for estimating the dispersion in parsimonious models appropriate for the non-Fickian transport. The following three conclusions are drawn:(1) the peak of the breakthrough curves comes earlier with increasing the roughness, according to the ADE simulation,(2) the value of λ generally decreases as the relative roughness of the fracture increases,(3) the value of λ is approximately equal to 2.0 when the dispersion is dominated by the molecular diffusion in the smooth fracture.

Circulation intensity and axial dispersion of non-cohesive solid particles in a V-blender via DEM simulation

In this study, discrete element method （DEM） was employed to simulate the movement of non-cohesive mono-dispersed particles in a V-blender along with particle-particle and particle-boundary interactions. To validate the model, DEM results were successfully compared to positron emission particle tracking （PEPT） data reported in literature. The validated model was then utilized to explore the effects of rotational speed and fill level on circulation intensity and axial dispersion coefficient of non-cohesive particles in the V-blender. The results showed that the circulation intensity increased with an increase in the rotational speed from 15 to 60 rpm. As the fill level increased from 20% to 46%, the circulation intensity decreased, reached its minimum value at a fill level of 34% for all rotational speeds, and did not change significantly at fill levels greater than 34%. The DEM results also revealed that the axial dispersion coefficient of particles in the V-blender was a linear function of the rotational speed. These trends were in good agreement with the experimentallv determined values reported bv previous researchers.

EXPERIMENTAL INVESTIGATIONS ON LONGITUDINAL DISPERSION CHARACTERISTICS OF TIDAL RIVERS

The longitudinal dispersion characteristics of tidal rivers areexperimentally investigated in a water channel. The longitudinal dispersion features and influentialfactors on pollutant in various stages of a tidal period in natural rivers are studied; the valueranges and variation trends of the longitudinal dispersion coefficient are obtained by means ofconcentration measurement. The results can provide important parameters for establishing the waterquality mathematical models in tidal rivers.

A minimum volume prediction of spacer based on turbulent dispersion theory: Model and example

During cementing operations involving cement slurry contamination,problems often occur due to the inaccurate calculation of the space fluid volume.This study,based on the turbulent dispersion theory,developed a minimum volume calculation model of spacer fluid to prevent cement slurry contamination.This model was used to analyze influence factors and practical calculations.The results indicated that the minimum volume of spacer fluid increase with the eccentricity of casing and injection rate and decrease with the density of cement slurry.Additionally,the better rheological properties of the cement slurry and spacer fluid would increase the volume of the spacer fluid.Furthermore,this model fitted actual field data better than other heat calculation models.

Axial gas mixing in conical spouted beds with high density particles

Conical spouted beds operating with high-density particles(ρp>2500 kg/m^(3))have recently gained attention because of their potential use as nuclear fuel coaters for next-generation nuclear reactors.In the literature,the number of axial gas mixing studies in conical and conical-cylindrical spouted beds is very limited and all axial mixing studies were carried out with relatively light particles(ρp≤2500 kg/m^(3)).Therefore,the objective of this study was to generate experimental data that can be used to explain the gas axial mixing behavior in conical spouted beds operating with both low-and high-density particles.Experiments were conducted in two(γ=30°,60°)conical spouted beds with three different types of particles:zirconia(ρp=6050 kg/m^(3)),zirconia toughened alumina(ρp=3700 kg/m^(3))and glass beads(ρp=2460 kg/m^(3)).In order to be able to compare experimental data obtained at different conditions,a 1-D convection-diffusion gas mixing model originally developed by San Joséet al.(1995)was implemented to determine the axial dispersion coefficients.The results show that the axial dispersion coefficients range between m^(2)/s and m^(2)/s,increase with superficial gas velocity and are higher than the corresponding dispersion coefficients of fixed beds,lower than the dispersion coefficients of fluidized beds and in the same range with the cylindrical spouted beds reported in the literature.The corresponding Peclet numbers were in the range of 0.6–7.8 for all operating conditions and slightly higher Peclet numbers were obtained with glass beads indicating the relative importance of gas convective transport over gas dispersion for light particles compared to heavy particles.

FLOW BEHAVIOR AND MASS TRANSFER IN THREE-PHASE EXTERNAL-LOOP AIRLIFT REACTORS WITH LARGE PARTICLES

The flow behavior and mass transfer in a three-phase external-loop airlift reactor can be improved by adding large particles. The mass transfer and liquid dispersion behavior for a three-phase external-loop reactor with large particles are studied in terms of the effect of the diameter and loading of the large particles on the liquid dispersion coefficient and mass transfer coefficient, The results showed that increasing the diameter or loading of the large particles tend to decrease dispersion and intensify mass transfer, and that an increase in the diameter of the large particles remarkably decreases the particle loop rate, while the effect of fine particles is much less notable.

Measuring turbulence in a circulating fluidized bed using PIV techniques

This study utilized the particle image velocimetry （P1V） technique, non-invasively near the wall, in the developing region, for the measurements of laminar and turbulent properties during circulation of Geldart B type particles in the U.S. Department of Energy （DOE） National Energy Technology Laboratory （NETL） riser. A novel method was used to measure axial and radial laminar and turbulent solids dispersion coefficients using autocorrelation technique. The instantaneous and hydrodynamic velocities for the solid phase were measured simultaneously in the axial and radial directions using a CCD camera, with the help of a colored rotating transparency. The measured properties, such as laminar and Reynolds stresses, laminar and turbulent granular tempera- tures, laminar and turbulent dispersion coefficients and energy spectra exhibited anisotropy. The mixing in the riser was on the level of clusters. The total granular temperatures were in reasonable agreement with the literature values. However, the axial and radial solids dispersion coefficients measured near the wall were slightly lower than the radially averaged values in the literature.

On controlled propagation of nonautonomous dispersive coupled Whitham-Broer-Kaup equation in shallow water

In this paper,the dispersive coupled Whitham-Broer-Kaup(DCWBK)equation with time-dependent coefficients describing the propagation of the shallow water waves are obtained.The propagation of solitons and elliptic(or chirped)waves can be manipulated by suitable variations of the dispersion coefficient.Here,controllable transmission of the surface waves for soliton similariton pairs with the snoidal backgrounds is considered.It is found that,when the dispersion coefficient is taken as increasing,the velocity is increasing with the dispersion coefficient increasing.While this holds vice versa for the height of propagation wave.