Two-dimensional Bed Research Articles

CFD simulation of a gas–solid fluidized bed with two vertical jets

A computational fluid dynamics (CFD) model is used to investigate the hydrodynamics of a gas–solid fluidized bed with two vertical jets. Sand particles with a density of 2660 kg/m 3 and a diameter of 5.0 × 10 −4 m are employed as the solid phase. Numerical computation is carried out in a 0.57 m × 1.00 m two-dimensional bed using a commercial CFD code, CFX 4.4, together with user-defined Fortran subroutines. The applicability of the CFD model is validated by predicting the bed pressure drop in a bubbling fluidized bed, and the jet detachment time and equivalent bubble diameter in a fluidized bed with a single jet. Subsequently, the model is used to explore the hydrodynamics of two vertical jets in a fluidized bed. The computational results reveal three flow patterns, isolated, merged and transitional jets, depending on the nozzle separation distance and jet gas velocity and influencing significantly the solid circulation pattern. The jet penetration depth is found to increase with increasing jet gas velocity, and can be predicted reasonably well by the correlations of Hong et al. (2003) for isolated jets and of Yang and Keairns (1979) for interacting jets.

Analysis of the radiation heat transfer process of phase change for a liquid droplet radiator in space power systems

The optimization of a space power system is greatly affected by the radiation heat transfer in a liquid droplet radiator (LDR). Radiation heat transfer in a two-dimensional bed of phase-change particle is modeled by solving the radiative transfer equation using the discrete ordinates method and the energy equation using the implicit finite difference method. The Mie theory is used to calculate the radiative properties of the droplet bed, whereas the effective medium theory is used to obtain the optical constants of partial solidification droplets. Multiple factors affect heat flux in the LDR, such as size distribution, flow velocity, phase change of droplets, layer thickness, droplet concentration in the layer, and material type of the work fluid; each of these must be analyzed. Calculations show that once size distribution is neglected, the relative error increases significantly. Size distribution has a remarkably strong effect on heat flux when the flow velocity of the working fluid is above 100 m/s. An increase in flow velocity leads to an increase in the total heat flux for the layer with a fixed volume fraction of droplets. The solidification zone occupies nearly half of the layer, and droplets of different sizes exhibit temperature differences to some extent due to local thermal non-equilibrium among them. Droplet concentration in the layer and the material type of the working fluid have strong effects on heat flux, whereas the thickness of the layer has a mild influence on heat flux.

Effect of coalescence and breakup on bubble size distributions in a two-dimensional packed bed

Bubble size distributions in a two-dimensional packed bed are investigated as a function of axial direction by using image processing techniques with a large number of bubble samples. Two inlet conditions, controlled sized bubbles and uncontrolled sized bubbles, are conducted to study the characteristic behaviors of bubbles. With the uncontrolled sized bubbles, the average bubble size corresponding to the two-dimensional bed is found, and is not affected by decrease or increase of flow rates. With the controlled sized bubbles, dominant bubble breakup and coalescence flows are separately simulated to investigate bubble breakup and coalescence rates. Unique behavior of bubble size distributions for dominant bubble breakup and coalescence has been seen, and changes in bubble size distributions along axial direction are studied with median bubble size. Near the inlet the median changes rapidly due to the dominant bubble mechanism of either coalescence or breakup, and far away from the inlet the median reaches asymptotic value due to the balance of bubble breakup and coalescence. For both dominant breakup and coalescence flows, the asymptotic values are close to the average bubble size. Therefore, the average bubble size, resulting from the balance of bubble coalescence and breakup at far downstream, is irrespective of inlet flow conditions.

Effect of Bed Thickness on the Segregation Behavior of Particle Mixtures in a Gas Fluidized Bed

Discrete particle simulation has been recognized as a useful numerical technique to elucidate the fundamentals of particle−fluid flow, in particular, gas fluidization. In general, it is achieved by combining discrete element method (DEM) for solid flow with computational fluid dynamics (CFD) for continuum gas. Limited by computational capability, such studies are mainly conducted using a two-dimensional (2D) bed in which particles are treated as discs or a pseudo-three-dimensional (3D) bed where the bed thickness is the same as the particle diameter. The loss of one-dimensional motion may significantly affect the flow and related behavior. This paper presents a numerical study of the effect of the front and rear walls of a fluidized bed on the mixing and segregation behavior of particle mixtures. Particle diameters used for simulation are 1 mm for flotsam and 2 mm for jetsam, respectively. Numerical simulations are conducted for two beds of different thicknesses, fluidized at different gas velocities. One...

Transient Hydrodynamic Dispersion in Rough Open Channels: Theoretical Analysis of Bed-Form Effects

A stochastic Lagrangian approach is proposed to describe dispersion in a two-dimensional low-regime river flow past random bed undulations characterized by the superposition of periodical and stationary exponential correlations, through a suitable time-dependent coefficient. The resulting dimensionless expression depends on the overall resistance factor, which is proportional to the average Peclet number of the process. A graphical analysis shows that the oscillatory transient originating from the periodic component of the bottom elevation pattern is enhanced by reduced global flow resistance, while relatively more intense tracer spreading is associated with wavelike profiles affected by persistent trendless random noise, which also determines the characteristic time needed by the plume to achieve the asymptotic domain. Numerical simulations, validating the first-order analytical approach in a wide range of heterogeneous bed geometries, are also discussed. A semianalytical procedure is finally suggested for the study of depth-averaged transport processes in real three-dimensional streams, based on the use of the derived dispersion coefficient.

Numerical modelling of braided streams in unsteady flow

Braided streams with vegetation growth under unsteady water supply conditions were reproduced using horizontal two-dimensional bed deformation numerical analysis. The effects of both vegetation and the unsteady characteristics of the water supply on the dynamic characteristics of braided streams are investigated. The mechanisms of stream lengthening and the decrease in the number of streams under unsteady flow conditions are discussed. To avoid complete transitions of bed configurations during a flood, tested hydraulic conditions were restricted to those with short-period hydrographs. The results show that wavelengths of submerged bars under unsteady water supply conditions are shorter than those under steady conditions. The results further suggest that both sediment deposition at higher locations and the formation of islands primarily cause stream lengthening under unsteady flow conditions. The wavelength of submerged bars was not a primary cause. Sediment is deposited in smaller channels during floods; the bed at riffles is eroded during low flows. These phenomena force water to flow into larger streams. Consequently, the number of streams decreases under unsteady flow conditions. Furthermore, the presence of vegetation enhances sediment deposition at higher locations and this contributes to a decrease in the number of streams under the condition that vegetation on islands is not completely washed away by floods.

NUMERICAL MODELLING OF BEDFORM DEVELOPMENT

Formation of the initial bedforms, known as sand-wavelets, developing from a flat erodible bed in hydrodynamically smooth flow has been studied numerically. The computational model consists of hydrodynamic and sediment transport equations. The unsteady hydrodynamic equations are solved by Large-Eddy-Simulation (LES) and Immersed-Boundary-Method (IBM) on a non-bodyfitted grid. Dynamics of individual grains are neglected and only bedload is considered, as calculated from Van Rijn's equation (1984, Journal of Hydraulic Engineering, Vol. 110) . Two-dimensional (2D) bed evolution is coupled with the above 3-dimensional (3D) hydrodynamic equations. The computed wavelength agrees with linear stability analysis and with experimental data in the literature. The length of the sand-wavelets is observed to correspond to the disturbance region of bed shear stress caused by discontinuities on the bed surface, as postulated by Yalin (1977, Mechanics of Sediment Transport, Pergamon press) .

NUMERICAL SIMULATIONS OF FLOWS AND BED VARIATIONS IN CHANNELS WITH DIVERSION AND CONFLUENCE

The flow and bed variation in channels with diversion and confluence was investigated experimentally and numerically. The experiments were conducted to obtain the bed variation data of a flow and bed variation in channel with diversion and confluence for verification of the numerical models. The effects of channel width on the bed variation and diversion discharge as well as sediment discharge were also examined from the experimental results. A numerical simulation were also performed by twodimensional bed variation model and verified against the obtained data. It shows that the model has ability to reproduce the bed variation in the channel with diversion and confluence with reasonable accuracy.

Granular temperature: Comparison of Magnetic Resonance measurements with Discrete Element Model simulations

The Discrete Element Model (DEM) is a very promising modelling strategy for two-phase granular systems. However, owing to a lack of experimental measurements, validation of numerical simulations of two-phase granular systems is still an important issue. In this study, a small two-dimensional gas-fluidized bed was simulated using a Discrete Element Model. The dimensions of the simulated bed were 44 × 10 × 120 mm and the fluidized particles had a diameter d p = 1.2 mm and density ρ p = 1000 kg m − 3 . The influence of different drag-force correlations was investigated. Preliminary numerical experiments were also performed to study the effects of (i) the coefficient of restitution and (ii) the modelled transverse thickness of the two-dimensional bed. Experimental measurements were made using Magnetic Resonance (MR), with the comparisons between DEM simulations and experimental measurements performed on the basis of the time-averaged velocity and granular temperature profiles of the particles. It was found that the DEM simulations of the time-averaged vertical velocity of the particles agreed well with the MR measurements. The drag-force correlation proposed by [R. Beetstra, M.A. van der Hoef and J.A.M. Kuipers, Drag force of intermediate Reynolds number flow past mono- and bidispersed arrays of spheres. AIChE Journal, 53, 489–501 (2007).] showed the best agreement with the experimental data. Fair agreement was found if the granular temperature calculated by the DEM simulations was compared with MR measurements. At lower fluidization velocities and closer to the distributor the DEM simulations under-predicted both the velocity and the granular temperature measurements using MR.

Formation Processes and Configuration of Channel-Flow Dominated Alluvial Deltas by Numerical Simulation

A horizontal two-dimensional mobile bed model for simulating the formation of river-dominated deltas in the river mouth or reservoir is presented, which is composed of shallow water equations, sediment transport formula, and a sediment continuity equation. Geometry similarity of river deltas during the processes of formation is discussed. Stability analysis and sensitivity analysis of parameters in the model are analyzed, which indicates that bed configuration is sensitive to the incipient-motion criteria of bed — load particles. The effect of gravity component on the initiation of sediment movement, therefore, is recommended to be considered in the modeling. The bed configuration including the reverse slope in the longitudinal profile and concave in the transverse profiles are correctly simulated with help from the correction of incipient-motion criteria. Simulation results are verified with a series of experiments and are consistent with series geometric functions and dimensionless profiles inducted from experimental data. This reflects the great reliability of the model. Historical topographical records of two typical in-land deltas depicting their earlier developmental stages are discussed to show the usefulness of this study.

Influence of vibrational wave form on intruder clustering

It has recently been shown that, within a two-dimensional granular bed subjected to sinusoidal, vertical vibration, neutrally buoyant intruders attract each other over a distance of up to five intruder diameters. The interaction between these intruders is the net result of attractive and repulsive forces which occur at different parts of the vibration cycle. Here we show that these forces may be manipulated by altering the vibration wave form to vary the strength of the overall attraction, or even to produce a weak repulsion. This ability is important for controlling the mixing of larger grains held within a granular bed.

Visualization of the rise of a bubble in a two-dimensional air-fluidized bed

Visualization of the rise of a bubble in a two-dimensional air-fluidized bed

PREDICTION OF MINIMUM SPOUTING VELOCITY IN TWO-DIMENSIONAL FLAT BOTTOM SPOUTED BEDS

ABSTRACT Spouted beds have been used in industry for operations such as drying, catalytic reactions, and granulation. Conventional cylindrical spouted beds suffer from the disadvantage of scaleup. Two-dimensional beds have been proposed by other authors as a solution for this problem. Minimum spouting velocity has been studied for such two-dimensional beds. A force balance model has been developed to predict the minimum spouting velocity and the maximum pressure drop. Effect of porosity on minimum spouting velocity and maximum pressure drop has been studied using the model. The predictions are in good agreement with the experiments as well as with the experimental results of other investigators.

PROCESS OF FLUSHING SEDIMENT THROUGH RESERVOIR AND THE NUMERICAL SIMULATION

The process of flushing sediment through reservoirs was investigated experimentally and numerically. The experiments were conducted to obtain the bed variation data of the flushing sediment for verification of the numerical models. The effects of gate of flushing and horizontal shape of the reservoir on the bed variation and sediment discharge through the gate were also examined from the experimental results. A numerical simulation of the flushing sediments were also performed by two-dimensional bed variation model and verified against the obtained data. It shows that the model has ability to reproduce the process of the flushing sediments, but the more improvement is needed to predict the flushing process with reasonable accracy.

INFLUENCE OF SLOPE FAILURE PROCESS ON FLOOD AND SEDIMENT RUNOFF IN A MOUNTAIN RIVER

A heavy rainfall often causes slope failures and landslides. The earth mass produced by a large scale slope failure buries a valley, and sometimes forms a landslide dam. Water and sediment runoff process in the river channel are strongly affected by the formation and deformation of landslide dams. In a report of the natural disaster 2004, the earth mass sometimes breaks into several blocks, and each block starts to move separately. Such slope failure process seems to influence on the landslide dam formation. I apply 2-D hybrid debris flow model to the landslide dam formation process, and investigate the influence through the calculations in different occurrence timing of slope failure. The model was proposed to explain the runoff process of the soil block including the fluidization phenomenon, which is composed of the usual two-dimensional debris flow model and a tracking model for soil block movement as solid. The deformation process of landslide dam and the water and sediment runoff process are calculated by a usual two-dimensional bed variation model.

Flow patterns and wall stresses in a moving granular filter bed with an asymmetric louvered-wall and obstacles

This study investigated the flow patterns and wall stresses in a two-dimensional asymmetric louvered-wall moving granular filter bed with an obstacle placed at each stage of the granular filter bed. The obstacles utilized were: (1) a single vertical plate and (2) a wedge-shaped obstacle comprising a left-vertical-plate and a right-inclined-plate. A digital camcorder was used to record the flow pattern histories of the granular solids in the moving granular filter bed. The instantaneous vertical velocity distribution at a certain height from the bottom of the third stage in a two-dimensional asymmetric louvered-wall granular filter bed was determined from two successive flow images. The static stresses and the variations in the dynamic wall stresses with time were obtained using a two-directional pressure gauge, which could simultaneously measure the normal and shear stresses of the granular solids. The preliminary theoretical study of the obstacle's placement in the asymmetric louvered-wall moving granular filter bed was proposed. The magnitude of the average dynamic normal stress on the convergent section of the louvered-wall greatly exceeds that on the vertical section of the louvered-wall. A wedge-shaped obstacle (or a single vertical plate) placed at a proper location, which causes two asymmetric flowing streams in the granular bed, may increase the velocity and refreshing rate of the filter granules in the quasi-stagnant zone near the louvered-wall and further the overall dust collection efficiency of the filter granules because the central flowing core above exit is not evident in the granular bed. Additionally, a wedge-shaped obstacle installed at an appropriate location, which consists of a left-vertical-plate and a right-inclined-plate, satisfies the following requirements: (1) it keeps the granules in the left part of the granular bed away from the obstacle, preventing interference therewith; (2) it shrinks stagnant zone and declines the normal stress on the convergent section of the louvered-wall in the right part of the granular bed; and (3) it solves the potential problem of a roof-type insert, on which the stagnant zone may sit.

Bubble characteristics in a two-dimensional vertically vibro-fluidized bed

Measurement of bubble size and local average bubble rise velocity was carried out in a vertically sinusoidal vibro-fluidized bed. Glass beads of Geldart group B particles were fluidized at different gas velocities, while the bed was vibrated at different frequencies and amplitudes to study their effects on the bubble behavior. This is compared with the case of no vibration in a two-dimensional bed and it is concluded that with vibration the local average bubble size, d bav, decreases significantly, especially at minimum bubbling velocity. The average bubble size increases slightly with increasing vibration frequency and amplitude. The local average bubble rise velocity is higher than that with no vibration, though with increasing vibration frequency and amplitude, it does not change significantly.

Numerical and experimental investigation of flow and scour around a circular pile

The flow around a vertical circular pile exposed to a steady current is studied numerically and experimentally. The numerical model is a three-dimensional model. The model validation was achieved against new experimental data (which include two-component laser-Doppler anemometry (LDA) flow measurements and the hot-film bed shear stress measurements, and reported in the present paper) and the data of others, and a k-w turbulence model was used for closure. The model does not have a free-surface facility and therefore is applicable only to cases where the Froude number is small (Fr < 0(0.2)). The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the pile. The influence on the horseshoe vortex of three parameters, namely the boundary-layer thickness, the Reynolds number and the bed roughness, was investigated. In the latter investigation, the steady solution of the model was chosen. A study of the influence of the unsteady solution on the previously mentioned flow processes was also carried out. The ranges of the parameters covered in the numerical simulations are: The boundary-layer-thickness-to-pile-diameter ratio is varied from 2 x 10 -2 to 10 2 , the pile Reynolds number from 10 2 to 2 × 10 6 , and the pile diameter-to-roughness ratio from 2 to about 10 3 . The amplification of the bed shear stress around the pile (including the areas under the horseshoe vortex and the lee-wake region) was obtained for various values of the previously mentioned parameters. The steady-state flow model was coupled with a morphologic model to calculate scour around a vertical circular pile exposed to a steady current in the case of non-cohesive sediment. The morphologic model includes (i) a two-dimensional bed load sediment-transport description, and (ii) a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The results show that the present numerical simulation captures all the main features of the scour process. The equilibrium scour depth obtained from the simulation agrees well with the experiments for the upstream scour hole. Some discrepancy (up to 30 %) was observed, however, for the downstream scour hole. The calculations show that the amplification of the bed shear stress around the pile in the equilibrium state of the scour process is reduced considerably with respect to that experienced at the initial stage where the bed is plane.

Fluidization of fine powders in fluidized beds with an upward or a downward air jet

The hydrodynamic behavior of fine powders in jet-fluidized beds was studied numerically and experimentally. The starting point of numerical simulation was the generalized Navier-Stokes (N-S) equations for the gas and solids phases. The κ- ɛ turbulence model was used for high-speed gas jets in fluidized beds. Computation shows that a suitable turbulence model is necessary to obtain agreement between the simulation and literature experimental data for a high-speed gas jet. The model was applied to simulating the fluidization of fine powders in fluidized beds with an upward or a downward air jet. An empirical cohesion model was obtained by correlating the cohesive force between fine particles using a cohetester. The cohesion model was embedded into the two-fluid model to simulate the fluidization of fine powders in two-dimensional (2-D) beds. To study the fluidization behavior of fine and cohesive powders with a downward jet, experiments were performed in a 2-D bed. Agreement between the computed time-averaged porosity and measured data was obtained. With an upward jet in the bed center, the measured and computed porosities show a dilute central core, especially at very high jet velocities. Based on our experiments and computations, a downward jet located inside the bed is recommended to achieve better mixing and contacting of gas and solids.

Velocity measurements in a developed open channel flow in the presence of an upstream perturbation

The effect of a near-free surface disturbance imposed on an open channel flow in the presence of low and high background turbulence is studied using a two-component laser Doppler anemometer. A bluff body located near the entrance of the flume was used to generate the free surface disturbance and the velocity characteristics were measured at a downstream location where the flow is fully developed. Experiments were conducted in two sets of flow fields. In the first set, the basic condition was an undisturbed open channel flow on a smooth bed, which is then compared with a flow with free surface disturbance. In this set, the turbulence levels are relatively lower and comparable with typical laboratory flume conditions. In the second set, the basic condition is a flow over a train of fixed two-dimensional bed forms, which is then compared with a flow with both bed forms and free surface disturbance. In the presence of the bed forms, there is continuous generation and sustenance of turbulence resulting in significantly higher background turbulence levels. The turbulence levels in the second set are comparable to natural open channel flows. Within the first set, though the mean profiles in inner coordinates are nearly identical, differences can be noticed in the mean defect profiles, while the Coles' parameter and the normalized turbulence levels are reduced in the presence of the free surface disturbance. Furthermore, quadrant decomposition indicates that in the presence of the free surface disturbance, three of the four quadrants are significantly altered. In the second set, the increased background turbulence due to the existing shear layer dynamics has an overwhelming influence on the flow characteristics while the free surface disturbance has a secondary role.