Lateral Dispersion Coefficients Research Articles

Investigation on solid dispersion in a CFB dense region with Bluetooth tracking method and MP-PIC simulation

Solid dispersion behavior in a dense region of a six-cyclone pant-leg CFB was investigated experimentally and numerically. The Bluetooth tracking technique was used to measure the solid dispersion characteristics. The numerical simulation was done by MP-PIC model and it was extended to study the influence of tracer particle size on solid dispersion characteristics after it was verified by the tests results. Effects of superficial velocity (Ug), initial bed inventory (Hm) and bed material particle size (dpi) were tested and compared. The results showed that wall constraint in width (x) direction is smaller than depth (y) direction and the dispersion coefficient Dx can be determined by analyzing X2 and dX2/2dt respect to time. The average particle displacement X/X0 increased with Ug, Hm and decreased with dpi. The Dx, in the range of 0.0021m2/s ∼ 0.0108 m2/s, has a linear relationship respect to Ug and Hm. A correlation formula for lateral dispersion coefficient was summarized and its results were compared with the present and literatures' work.

The Impact of Plant Oscillation on Dispersion in Emergent Aquatic Canopies

AbstractFlexible canopies bend and oscillate in both the in‐line and cross‐flow directions due to periodic forcing associated with vortex shedding. The resultant plant motion impacts the vegetation wake structure and, thus, the rate of lateral dispersion in these environments. Despite significant improvements in our understanding of dispersion in rigid canopies, a reliable framework to predict mixing in oscillating canopies is still lacking. This research demonstrates how plant oscillation can profoundly impact rates of lateral mixing in steady flows. The lateral dispersion coefficients were evaluated experimentally, using photographs of injected dye plumes within two types of emergent flexible model vegetation. Results revealed a significant increase in the rates of lateral dispersion (by up to 45%) due to the plant oscillation. A predictive model, based on a redefined vegetation density that incorporates the impact of plant oscillation, was developed that can accurately predict dispersion in emergent canopies. A quantitative prediction of dispersion in oscillating flexible vegetation is a significant step toward a more accurate description of material transport in aquatic environments.

Maximum ground level concentration for Gaussian plume formula using standard and Briggs methods

AbstractThis work aims to determine the maximum concentration and downwind distance at the earth's surface in two methods Briggs and standard for two conditions are slightly unstable and neutral by using the Gaussian equation at different effective heights and wind seeped at (8.9, 8.5 and 8 m/s) under lateral and vertical dispersion coefficient measurement.

Investigation on lateral dispersion characteristics of fuel particles in dense phase zone of a large-scale circulating fluidized bed boiler under combustion conditions

The dispersion characteristics of fuel particles in the dense phase zone in circulating fluidized bed (CFB) boilers have an important influence on bed temperature distribution and pollutant emissions. However, previous research in literature was mostly on small-scale apparatus, whose results could not be applied directly to large-scale CFB with multiple dispersion sources. To help solve this problem, we proposed a novel method to estimate the lateral dispersion coefficient (Dx) of fuel particles under partial coal cut-off condition in a 350 MW supercritical CFB boiler based on combustion and dispersion models. Meanwhile, we carried out experiments to obtain the Dx in the range of 0.1218–0.1406 m2/s. Numerical simulations were performed and the influence of operating conditions and furnace structure on fuel dispersion characteristics was investigated, the simulation value of Dx was validated against experimental data. Results revealed that the distribution of bed temperature caused by the fuel dispersion was mainly formed by char combustion. Because of the presence of intermediate water-cooled partition wall, the mixing and dispersion of fuel and bed material particles between the left and right sides of the furnace were hindered, increasing the non-uniformity of the bed temperature near furnace front wall.

Solids lateral mixing and compartmentalization in dynamically structured gas–solid fluidized beds

An adequate use of gas pulsation can create an ordered, dynamically structured bubble flow in a bed of Geldart B particles. A structured bed is more homogeneous, responds to external control and is scalable. While earlier studies have focused on describing the self-organization of the gas bubbles, the solid mixing and gas–solid contact patterns have remained unclear. In this work, the solids circulation and mixing behavior in structured and unstructured beds at various pulsation frequencies are compared with a traditional fluidized bed operation. The degree of lateral mixing is hereby quantified through an effective lateral dispersion coefficient extracted from CFD-DEM (discrete element modelling) simulations in a thin fluidized bed system. Mixing shows major quantitative and qualitative differences amongst the investigated cases. The coordinated motion of the gas bubbles wraps the solid flow into a series of compartments with minimal interaction, whereby effective lateral dispersion coefficients are an order of magnitude lower than in an unstructured operation. More importantly, unlike a traditional bed, dispersion in a structured bed is driven by advection and is no longer a diffusive process. Compartmentalization decouples the time scales of micro- and macromixing. Every pulse, the compartments rearrange dynamically, causing a level of local axial mixing that is scale-independent. While further work is necessary to fully understand the compartmentalization at a larger scale, the circulation described here indicates that a dynamically structured bed can provide a tight control of mixing at low gas velocities and a narrower distribution of stresses in the solid phase compared to traditional devices.

A microscopic study on the mixing process of binary solids in bubbling fluidized bed

A novel method for measuring the micro mixing ratio of binary solids in dense fluidizations is developed. The mixing process within a bubbling fluidized bed that can be assumed as one mixing cell is resolved. Dispersion coefficient and mixing index methods are applied to characterize the mixing process. Results show that diffusion has an important effect on mixing at the bottom and top of the fluidized bed. Meanwhile, convection is the principal mechanism of mixing at the center. The lateral micro dispersion coefficient is between 0.005 m/s and 0.03 m/s. The vertical micro dispersion coefficient is approximately twice as that in the lateral direction. A new mixing index is proposed to evaluate the micro mixing quality of binary solids. The time required to reach uniform mixing in the lateral direction is more than twice as that in the vertical direction.

Experimental Quantification of the Lateral Mixing of Binary Solids in Bubbling Fluidized Beds

A novel experimental method for the lateral mixing of binary solids in bubbling fluidized beds was developed based on the capacitance probe technique. The evolutions of local mixing ratios in a fluidized bed which can be assumed as one mixing cell were analyzed in detail. The solids mixing within one mixing cell was resolved and the effect of convection and diffusion mechanism on lateral mixing was evaluated individually. The results show that at lower part of the fluidized bed, convection plays a more important role in the mixing process near the wall; meanwhile, diffusion is very important for the mixing around the center line. This is opposite with that at the higher part. A lateral micro dispersion coefficient was proposed to characterize the lateral mixing within the mixing cell and the value is generally between 0.005 and 0.025 m/s. A new mixing index was proposed to evaluate the lateral mixing quality of binary solids. It was found that at the lower part of the fluidized bed, the best mixing is acquired at the half radius, whereas mixing at the center line is the worst. At the higher part, solid mixing is better when increasing the distance from the wall. The influences of gas velocity and static bed on the lateral mixing were also discussed from a microscopic perspective.

A comprehensive uncertainty analysis of model-estimated longitudinal and lateral dispersion coefficients in open channels

The complexity of pollutant-mixing mechanism in open channels generates large uncertainty in estimation of longitudinal and lateral dispersion coefficients (Kx and Ky). Therefore, Kx and Ky estimation in rivers should be accompanied by an uncertainty analysis, a subject mainly ignored in previous studies. We introduce a method based on thorough analysis of different calibration datasets, resampled from a global database of tracer studies, to determine the uncertainty associated with five applicable intelligent models for estimation of Kx and Ky (model tree, evolutionary polynomial regression (EPR), gene-expression programming, multivariate adaptive regression splines (MARS), and support vector machine (SVM)). Our findings suggest that SVM gives least uncertainty in both Kx and Ky estimation, while EPR and MARS generate most uncertainty in Kx and Ky estimation, respectively. By considering significant uncertainty in the model estimations, we suggest that the methodology we introduce here for uncertainty determination of the models be incorporated in empirical studies on estimation of Kx and Ky in rivers.

Modeling the motion of fuel particles in a fluidized bed

A semiempirical model for the mixing of fuel particles in a fluidized bed is presented and validated against experimental data from the literature regarding lateral fuel mixing. The model of fuel particle mixing categorizes the fluidized bed into three mixing zones: a rising bubble wake solid zone, an emulsion zone with sinking bulk solids, and a splash zone located above the dense bed. In the emulsion zone, the axial motion of the fuel particle is described by a force balance, applying a viscoplastic stress model, i.e., with a dominant yield stress and only a minor contribution of the shear stress, using an empirical expression from the literature. In the lateral direction, the model is divided into so-called ‘recirculation cells’, which are crucial for the lateral mixing.Comparisons of the modeled and measured lateral dispersion coefficients of different fuel types measured in three different large-scale fluidized bed units under both hot and cold conditions (covering a broad range of coefficients: 10−4–10−1 m2/s) reveal satisfactory agreement. The validated model was used to investigate how the lateral mixing of fuel particles depends on the excess gas velocity, the bed height, and the lateral distribution of bubbles over the bed cross-section (which is typically uneven in industrial FB furnaces), as well as the size and density of the fuel particles.

Experimental Study on Dispersion of Unconfined Aquifer in a Site of Jilin City

Dispersion parameter is an important parameter for the establishment of groundwater solute transport model.The dispersion test uses sodium chloride as a tracer,which was conducted in a site in Jilin City.The standard curve comparison method was used to solve the dispersion parameters of the aquifer under the natural flow field.The test results show that under the natural flow field,the longitudinal dispersion of unconfined aquifer in Jilin City is 0.400m,and the lateral dispersion is 1.933×10-5~6.557×10-3m;while the vertical dispersion coefficient is 0.246m2d,the lateral dispersion coefficient is 1.191×10-5~4.039×10-3m2d.The above results can provide an important parameter basis for the establishment of groundwater solute transport model,the accurate prediction of temporal and spatial variation of pollutant concentration in groundwater and the formulation of groundwater pollution prevention and control scheme.

Experimental Investigations on Lateral Dispersion Coefficients of Fuel Particles in Large-Scale Circulating Fluidized Bed Boilers with Different Coal Feeding Modes

The dispersion characteristics of fuel particles over the bed have always been a key consideration in the design of fluidized beds. However, the lateral fuel dispersion coefficients (Dsr) reported in the previous literature widely ranged from 10−4 to 10−1 m2/s, which were hard to be directly applied in large-scale CFB (circulating fluidized bed) boilers with wider bed width (close to 30 m) and variable coal feeding modes. To solve this problem, field tests were conducted on the first 600 MW CFB boiler in this paper, and the distributions of flue gas composition and flue gas temperature were obtained near the coal feeding port under four working conditions. The dispersion characteristics of fuel particles were analyzed in detail combined with the dispersion model. In addition, a new method based on bed heat balance was also proposed to estimate Dsr and applied in a 300 MW CFB boiler with a different coal feeding mode. The results revealed that Dsr through the local heat balance method ranged from 0.10–0.35 m2/s, which were 9–18% higher than the values through the dispersion model. Compared with the coal feeding port immersed in the bed, Dsr of the fuel particles fed into the splash zone increased by about 34.7%. Dsr under the coal feeding mode of a screw feeder with pressurized air ranged from 0.12–0.16 m2/s, which were lower than Dsr under the coal feeding method of importing fuel into circulating ash. The method and results in this paper could expand the applicability of fuel dispersion, and provide the most direct guidance for the design and optimization of coal feeding ports in large-scale CFB boilers.

Experimental study of lateral dispersion in flexible aquatic canopy with emergent blade-like stems

This paper quantitatively investigates the role of flexibility of blade-like stems and, in particular, the occurrence of stem resonance on lateral dispersion in emergent aquatic canopies. Two sets of experiments are presented: single-stem and canopy tests. In the first set, the flow around single blade-like flexible model stems and the proximity to a resonant state are studied. Wake areas behind four model stems with distinct flexibilities are measured by particle image velocimetry for stem Reynolds numbers between 350 and 850. A single flexible emergent stem bends and oscillates in in-line and cross-flow directions due to periodic forcing associated with the vortex shedding. The plant motion, especially at resonance, affects the width of the wake area and, hence, the extent to which a tracer is dispersed laterally around a stem. The results show that the oscillation amplitude of a stem increases significantly as the vortex shedding frequency approaches the natural frequency of the stem in the corresponding direction. As a result, the size of the wake area is greater for the resonated stems. In the second set of the experiments, lateral dispersion in two different flexible model canopies was measured. The results show that the proximity to a resonant state is the major factor describing the variation of the lateral dispersion coefficient in the experiments for the tested Reynolds numbers and canopies. The dispersion coefficient increases as the vortex shedding frequency approaches the natural frequency of stems in either direction.

Solid residence time distribution in a cross-flow dense fluidized bed with baffles

The residence time distribution (RTD) of particles in a gas-solid dense fluidized bed with a continuous solid flow operation and baffles needs much more focus for the purpose of the wide industrial applications. The available models of solid RTD are not adequate in this case due to the additional convective diffusion induced by the cross-flow of the solid feeding and the complex geometry caused by the baffles. To address this problem, this work applied a two-phase Eulerian-Eulerian model combined with the species transport equation to predict solid RTD in a dense fluidized bed. The effects of the continuous solid feeding and baffles were considered. The solid dispersion coefficient Ds in the species transport equation was calculated by an analytical solution from kinetic theory of granular flow. Ds only needs the value at a molecular level due to the fact that the computational fluid dynamics (CFD) model is able to reproduce the RTD procedure exactly same as the practical experiments. To validate the established CFD model, a series of 3D lab-scale cold flow experiments were conducted in the free and baffled beds for the bed material with various severe non-spherical shapes. The measurement included the solid hydrodynamic characteristics at the outlet of the outflow pipe and solid RTD of the system. The reasonable agreement between the CFD prediction and experimental data demonstrated the good performance of the CFD model. 1D plug flow with dispersion model and the tanks-in-series model were further used to fit the calculated RTD curves. The estimated lateral dispersion coefficient of solids locates in a rational range compared with the data collected extensively from the literature. The results showed that the lateral dispersion coefficient of solids decreases when the baffles are installed.

Lateral dispersion in deflected emergent aquatic canopies

Understanding the mechanism of dispersion within plants is essential for proper operation of natural and constructed treatment wetlands. Plant deflection induced by the current drag modifies the flow and dispersion within an aquatic canopy. In this study, we look at the effect of the deflection angle of the plants on transverse dispersion. Experiments were carried out in a current flume on an array of inclined solid rods representing a deflected emergent canopy. The stem Reynolds number varied between 90 and 360, normalized stem densities between 0.011 and 0.033, and the inclination angles between 0° and 45°. The plume development was recorded using image processing technique. A special post-processing analysis was proposed to handle the discontinuities in the light intensity profile as a result of the light blocking effect of inclined cylinders. The results indicate that the dispersion coefficient increases with the inclination angle as well as vegetation density. However, the effects disappear at Reynolds numbers higher than 240. The effect of inclination angle on lateral dispersion coefficient is effectively described by the associated increase in the actual vegetation density, so the inclination angle and stem density can be combined into one single parameter. Based on a regression analysis, a compact equation is proposed for dispersion coefficient as a function of Reynolds number, stem angle, and vegetation density.

Dispersion characteristics of dissimilar materials in a fluidized bed with unevenly distributed fluidizing air

Large-scale internally circulating flows of gas and particles might form under unevenly distributed fluidized air in a fluidized bed. Compared with bed materials, the present study investigated dissimilar particles with different sizes and density moving and mixing through the developed image technique in an internally circulating fluidized bed (ICFB). The concentrations of the tracer particles were obtained by the image analysis method. The inhomogeneity degree and lateral dispersion coefficients of the tracer particles were also calculated, with the results indicating that the degree of inhomogeneity decreases with the increasing dispersed time. The lateral dispersion coefficients of tracer particles with a lower density (for a similar diameter) are larger than those with a higher density. It is clear that the different air distribution methods play an important role in the lateral dispersion of the tracer particles.

Magnetic tracking of a fuel particle in a fluid-dynamically down-scaled fluidised bed

The mixing of a fuel particle in a fluid-dynamically down-scaled bubbling fluidised bed was studied using magnetic particle tracking. Both the resulting steady-state fuel distributions and the underlying mixing dynamics (fuel velocity field) were investigated. The experimental set-up applied resembles the mixing of an anthracite coal particle in a bed with a cross-section of 0.85×0.85m2 operated at 900°C with fluidisation velocities in the range of 0.16–0.45m/s and bed heights in the range of 0.25–0.35m. Four different gas distributors with variable pressure drops and orifice configurations were investigated.For the cases studied, 7.5min of sampling time at a sampling frequency of 20Hz was found to be sufficient to resolve the spatial distribution of the tracer. However, to provide a reliable estimate of the mixing dynamics, a sampling frequency of at least 100Hz was required, together with a sampling time of approximately 20s.Results on axial mixing showed improved mixing with increasing fluidisation velocity and bed height. The lateral dispersion coefficients were in the order of 10−3–10−2m2/s (on an up-scaled basis), increased with fluidisation velocity, and were only moderately influenced by the configuration of the gas distributor.

Experimental study on the characteristic mixing time of solids and its link with the lateral dispersion coefficient in bubbling fluidized beds

An experimental relation between the characteristic mixing time of solids and the lateral dispersion coefficient in a bubbling fluidized bed is established in this work. To do that, experiments were carried out in a pseudo-2D fluidized bed using glass beads as bed material. The glass beads have the same density and diameter but half of them are painted in black to make them distinguishable. At the beginning of each experiment, the particles were placed in a completely lateral segregated state and then the fluidizing air was suddenly injected while images were recorded. The images were processed to obtain the mixing index evolution with time. Two different regions where differentiated in the evolution of the lateral mixing with time: a region dominated by convective mixing and a region governed by diffusive mixing. Both the start-up time and the total solids mixing time were characterized. The total solids mixing time was found to have a potential relation with the excess gas velocity and it was found to be independent of the particle size. This total solids mixing time was compared to the residence time of the bubbles in the bed and it was showed that the axial solids mixing is two orders of magnitude faster than the lateral solids mixing. This result justifies the use of the 1D Fickian-type diffusion equation to fit the experimental data of the mixing index obtaining the values of the lateral dispersion coefficient. Finally, the experimental values of the total solids mixing time were compared to the experimental values of the lateral dispersion coefficient and a straightforward relation between both parameters was provided.

A numerical study on flow and pollutant transport in Singapore coastal waters

Intensive economic and shipping activities in Singapore Strait have caused Singapore coastal waters to be under high risk of water pollution. A nested three-dimensional unstructured-grid SUNTANS model is applied to Singapore coastal waters to simulate flow and pollutant transport. The small domain (~50m resolution) Singapore coastal model is nested within a large domain (~200m resolution) regional model. The nested model is able to predict water surface elevations and velocities with high R2 values of 0.96 and 0.91, respectively. Model results delineate the characteristics of circulation pattern in Singapore coastal waters during the Northeast and Southwest monsoons. The pollutants are modeled as passive tracers, and are released at six key sailing locations Points 1–6 in Singapore coastal waters and are named as Passive Tracers 1–6, respectively. Our results show that the rate of dispersion is twice as large for the Northeast monsoon compared to the Southwest monsoon due to differences in large-scale monsoons and small-scale local winds. The volume averaged concentration (VAC) diminishes faster and the local flushing time is shorter during the Northeast monsoon than the Southwest monsoon. Dispersion coefficients K and the VAC decreasing rate are maximum for Tracers 2 and 3 with shortest local flushing time due to the strong surrounding currents and abrupt bathymetry changes near Senang and St. John Islands. Dispersion coefficients K and the VAC decreasing rate are minimum for Tracer 1 due to weak currents induced by the semi-enclosed coastline near Tuas. It is found that both the lateral dispersion coefficient Ky and the compound dispersion coefficient K obey a “4/3-law”, which defines a linear correlation between dispersion coefficients and 4/3-power of selected length scale.

An analysis of error propagation in AERMOD lateral dispersion using Round Hill II and Uttenweiller experiments in reduced averaging times

ABSTRACTDispersion modelling was proved by researchers that most part of the models, including the regulatory models recommended by the Environmental Protection Agency of the United States (AERMOD and CALPUFF), do not have the ability to predict under complex situations. This article presents a novel evaluation of the propagation of errors in lateral dispersion coefficient of AERMOD with emphasis on estimate of average times under 10 min. The sources of uncertainty evaluated were parameterizations of lateral dispersion (), standard deviation of lateral wind speed () and processing of obstacle effect. The model’s performance was tested in two field tracer experiments: Round Hill II and Uttenweiller. The results show that error propagation from the estimate of directly affects the determination of , especially in Round Hill II experiment conditions. After average times are reduced, errors arise in the parameterization of , even after observation assimilations of , exposing errors on Lagrangian Time Scale parameterization. The assessment of the model in the presence of obstacles shows that the implementation of a plume rise model enhancement algorithm can improve the performance of the AERMOD model. However, these improvements are small when the obstacles have a complex geometry, such as Uttenweiller.

Measuring fuel mixing under industrial fluidized-bed conditions – A camera-probe based fuel tracking system

This work presents and applies a camera-based fuel tracking system for quantification of the motion of individual fuel particles at the surface of bubbling fluidized beds operated under hot conditions. In particular a bubbling fluidized bed with a cross section of 1.44m2 operated at 800°C is investigated. Mixing of wood pellets and wood chips is investigated by feeding batches of fuel and applying multi particle tracking to the videos recorded by a specially designed camera probe. The influence of the bulk solids cross-flow and fluidization velocity on the mixing of fuel particles is analyzed.It is shown that the new fuel tracking method can withstand industrial conditions. Applying the method gives reproducible results and yields lateral dispersion coefficients in the range 10−3–10−2m2/s for both pellets and wood chips. The lateral mixing of the fuel increases with fluidization velocity and, to a minor extent, with the cross-flow of bulk solids. As observed in previous work, the location of fuel particles on the bed surface confirms the existence of preferred bubble paths, and these are smeared out by the cross-flow of bulk solids. The vertical mixing is hindered by the cross-flow of bulk solids, while it is enhanced by fluidization velocity, which is in agreement with previous research.