Horizontal gas mixing in rectangular fluidized bed:A novel method for gas dispersion coefficients in various conditions and distributor designs

In a rectangular fluidized bed combustor, the tracer gas is injected continuously into the bed from a point source at the center of the distributor plate. In this study, a general governing equation is formulated for tracer gas dispersion in the bed. An analytical solution is derived to estimate the dispersion coefficients, Dxand Dy, in a horizontal plane. The concentration profiles at different sampling heights with various gas velocities are plotted.Subsequently, to estimate the dispersion coefficients, surface fitting of the obtained analytical solution to the experimental data is performed. The dispersion coefficients obtained from this model are compared with those of a conventional model. Additionally, the effect of walls, bed height and gas injection rate on the dispersion coefficients in a horizontal plane is investigated, and the effect of distributor design on the dispersion coefficients in a horizontal plane is investigated with different tracer positions. It is found that Dxand Dyare nearly equivalent at a lower tracer gas ratio of the injected gas to the total gas flow rate. It is also demonstrated that the effect of bed height on Dxis minor. This model is also able to estimate the dispersion coefficients in the case of a multihorizontal nozzle distributor.

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.

Use of axial dispersion model for determination of Sherwood number and mass transfer coefficients in a perforated rotating disc contactor

The mass transfer process in a perforated rotating disk contactor(PRDC) using a toluene-acetone-water system was investigated.The volumetric overall mass transfer coefficients are calculated in a PRDC column.Both mass transfer directions are considered in experiments.The influences of operating variables containing agitation rate,dispersed and continuous phase flow rates and mass transfer in the extraction column are studied.According to obtained results,mass transfer is significantly dependent on agitation rate,while the dispersed and continuous phase flow rates have a minor effect on mass transfer in the extraction column.Furthermore,a novel empirical correlation is developed for prediction of overall continuous phase Sherwood number based on dispersed phase holdup,Reynolds number and mass transfer direction.There has been great agreement between experimental data and predicted values using a proposed correlation for all operating conditions.

High-Order Dispersion Coefficients for Alkali-metal Atoms

High-order dispersion coefficients C9, C11, C12, and C13 for the ground-state alkali-metals were calculated by combining the 1-dependent model potential of alkali-metal atoms and linear variation method based on B-spline basis functions. The results were compared.

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.

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.

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.

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.

Experimental Study on Dispersion Coefficient of Dredger Fill in Reclamation Region

In order to satisfy the demand of land use, reclamation engineering has been undertaken in coastal cities for a long time. To study the contaminant transport in the reclamation districts, robust and accurate estimation of dispersion coefficient is essential. In this study, the continuous sodium chloride （NaC1） solution with constant concentration was introduced into the column filled with the dredger fill to get the breakthrough curves （BTCs）. Inverse error function method （IEFM） and CXTFIT program were used for estimating dispersion coefficient. Results showed that the difference between the dispersion coefficients estimated by IEFM and CXTFIT program was slight. The main reason was that the BTC was not strictly linear. IEFM performed poorly in the nonlinear area, while the CXTFIT performed well over the entire BTCs. Moreover, the dispersion coefficient of dredger fill was small. The dispersion property of dredger fill would result in the slow migration of contaminants in the dredger fill.

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.

Impact of Soil Water Flux on Vadose Zone Solute Transport Parameters

The transport processes of solutes in two soil columns filled with undisturbed soil material collected from an unsaturated sandy aquifer formation in Belgium subjected to a variable upper boundary condition were identified from breakthrough curves measured by means of time domain reflectometry (TDR). Solute breakthrough was measured with 3 TDR probes inserted into each soil column at three different depths at a 10 minutes time interval. In addition, soil water content and pressure head were measured at 3 different depths. Analytical solute transport models were used to estimate the solute dispersion coefficient and average pore-water velocity from the observed breakthrough curves. The results showed that the analytical solutions were suitable in fitting the observed solute transport. The dispersion coefficient was found to be a function of the soil depth and average pore-water velocity, imposed by the soil water flux. The mobile moisture content on the other hand was not correlated with the average pore-water velocity and the dispersion coefficient.

Lateral Solids Mixing in the Dense Zone of a Circulating Fluidized Bed

Lateral solid mixing was investigated experimentally in the dense zone of a 900mm×100mm×5.2m rectangular circulating fluidized bed riser.Using heated tracer injection,the lateral solid dispersion was determined by measuring the temperature response at different lateral positions. Furthermore, a one-dimensional dispersion model,which describes the solid mixing in the dense zone,is presented.The experimental results were used to determine the lateral particle dispersion coefficient under various operating conditions. A correlation of dispersion coefficient with bed height, gas velocity,and particle size is also proposed.

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.

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.