Solid Velocity Profiles Research Articles

Numerical investigation of slush nitrogen flow in a horizontal pipe

Slush nitrogen is a cryogenic two-phase fluid containing solid particles in liquid nitrogen, and the flow of slush nitrogen in a horizontal pipe is investigated using the 2D Eulerian–Eulerian multiphase approach. The per-phase k–ε turbulence model is used in the study to model the turbulent two-phase flow, and the motion of solid phase is modeled by the kinetic theory of granular flow to account for both particle–particle and particle–wall interactions. The 2D multiphase model is firstly validated with solid volume fraction and velocity profile data of several different slurry flows from the open literature, and then is further applied to studying slush nitrogen flow in a horizontal pipe, and the numerical solid velocity profiles are compared with the experimental data. The effects of the flow velocity and the mean solid volume fraction on the flow characteristics of slush nitrogen are investigated numerically in this study.

Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle

In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.

Numerical and experimental studies on the flow multiplicity phenomenon for gas–solids two-phase flows in CFB risers

The flow multiplicity phenomenon in circulating fluidized bed (CFB) risers, i.e. under the same superficial gas velocity and solids circulation rate, the CFB risers may sometimes exhibit multiple flow structures, was numerically and experimentally investigated in this study. To investigate the flow multiplicity phenomenon, the experiments of gas–solids two-phase flows in a 2-D CFB riser with different flow profiles at the inlet of the CFB riser were conducted. Specially designed gas inlet distributors with add-ons are used to generate different flow profiles at the inlet of the CFB rise. The CFD model using Eulerian–Eulerian approach with k–ε turbulence model for each phase was employed to numerically analyze the flow multiplicity phenomenon. It is experimentally and numerically proved that for gas–solids two-phase flows, the flow profiles in the fully-developed region are dominated by the flow profiles at the inlet. The solids concentration profile is closely coupled with the velocity profile, and the inlet solids concentration and velocity profiles can largely influence the fully-developed solids concentration and velocity profiles.

Theoretical and numerical studies on the flow multiplicity phenomenon for gas–solids two-phase flows in CFB risers

The dependence of the fully-developed flow profiles on the inlet flow conditions for gas–solids two-phase flows, i.e. the flow multiplicity phenomenon, in circulating fluidized bed (CFB) risers was proposed and discussed in this article. The flow multiplicity phenomenon for gas–solids two-phase flows was first proved mathematically based on the conservation equations of mass and momentum. Then the CFD model using Eulerian–Eulerian approach with k– ε turbulence model for each phase was further adopted to analyze the details of this flow multiplicity phenomenon. It is theoretically and numerically revealed that for gas–solids two-phase flows, the flow profiles in the fully-developed region are always dominated by the flow profiles at the inlet. The solids concentration profile is closely coupled with the velocity profile, and the inlet solids concentration and velocity profiles can largely influence the fully-developed concentration and velocity profiles.

A fast first order model of a rough annular shear cell using cellular automata

The motivation of the current work is to simulate granular phenomena in a rough annular shear cell without load using a physics-based cellular automata (CA) modeling approach. A simple yet powerful two-dimensional (2D) cellular automata model was developed to model granular flows inside a 2D annular shear cell from a tribological perspective. Physics-based equations developed from first-principles to model collisions have been adopted to form the cellular automata local rules of interaction. This combines the computational efficiency of CA modeling with the accuracy and generalization of first-principle physics modeling. The local flow properties—solid fraction, velocity and granular temperature profiles- were predicted from the CA simulation and compared to the granular shear cell experiments. The resulting steady-state CA model profiles show good agreement with the experimental results. The ability of the CA model to probe the effect of each granular flow property is demonstrated by performing parametric studies of the particle–particle coefficient of restitution and roughness factor.

Eulerian–Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer

Numerical simulation of fully developed hydrodynamics of a riser and a downer was carried out using an Eulerian–Lagrangian model, where the particles are modeled by the discrete element method (DEM) and the gas by the Navier–Stokes equations. Periodic flow domain with two side walls was adopted to simulate the fully developed dynamics in a 2D channel of 10 cm in width. All the simulations were carried out under the same superficial gas velocity and solids holdup in the domain, starting with a homogenous state for both gas and solids, and followed by the evolution of the dynamics to the heterogeneous state with distinct clustering in the riser and the downer. In the riser, particle clusters move slowly, tending to suspend along the wall or to flow downwards, which causes wide residence time distribution of the particles. In the downer, clusters still exist, but they have faster velocities than the discrete particles. Loosely collected particles in the clusters move in the same direction as the bulk flow, resulting in plug flow in the downer. The residence time distribution (RTD) of solids was computed by tracking the displacements of all particles in the flow direction. The results show a rather wide RTD for the solids in the riser but a sharp peak RTD in the downer, much in agreement with the experimental findings in the literature. The ensemble average of transient dynamics also shows reasonable profiles of solids volume fraction and solids velocity, and their dependence on particle density.

Simultaneous measurements of the solid particles velocity and concentration profiles in two phase flow by pulsed ultrasonic doppler velocimetry

In this experimental study, the pulsed ultrasonic Doppler velocimetry was used to measure simultaneously the local velocity and the local concentration in a flow of solid-liquid suspension in a horizontal pipe. In order to distinguish between the Doppler signals coming from the continuous phase, water and those of the glass bead particles larger than the Kolmogorov length scale and the wavelength of the ultrasonic wave, a threshold is imposed on the integral of the power spectral density of the Doppler signal. The new approach measurement of the local concentration was used. It consists of counting a number NP of the Doppler signals of the solid particles crossing the measurement volume and a number NPt of the Doppler signals of the solid particles crossing the control volume. The concentration profile is then represented by the ration NP / NPt. The results obtained show that the suspension of fine particles, which represents a tracer, behaves as a homogenous fluid. For large particles, we confirmed the existence of the slip velocity and the effects of both concentration and size particle on the turbulence. The use of two distinct measurement volumes allows the direct determination of the turbulent length scales. The results show that the turbulence characteristics of the carried fluid are modified by the presence of the solid particles.

Horizontal laminar flow of coarse nearly-neutrally buoyant particles in non-Newtonian conveying fluids: CFD and PEPT experiments compared

The horizontal flow of coarse particle suspensions in non-Newtonian carrier fluids was numerically simulated using an Eulerian–Eulerian CFD model. This study was concerned with nearly-neutrally buoyant particles of 5 and 10 mm diameter conveyed by fluids of Ellis rheology in laminar flow, in a 45 mm diameter pipe at concentrations up to 41% v/v. CFD predictions of solid phase velocity profiles and passage times were compared to experimental data obtained by a Positron Emission Particle Tracking (PEPT) technique and Hall effect sensors, and a very good agreement was obtained considering the complexity of the flows studied. CFD predictions of solid–liquid pressure drop were compared to a number of relevant correlations gleaned from the literature. Only one of them showed a good agreement over the whole range of conditions studied. Other correlations generally showed large deviations from CFD, and their limitations in predicting the influence of solids concentration and particle size have been demonstrated. Overall, it emerged that for the flows studied, CFD was capable of giving predictions of pressure drop which were probably better and more reliable than the correlations available in the literature.

Characterization of an annular fluidized bed

The annular fluidized bed is a new technology consisting of a large central nozzle surrounded by a stationary fluidized bed. Due to the moderate primary gas fluidization of the annulus, the solids overflow at the upper edge of the central nozzle is mixed into the high upward velocity central secondary gas stream and transported into the mixing chamber. With this geometrical configuration, the process combines the advantages of the stationary fluidized bed (long solids residence time) and of the circulating fluidized bed (good heat and mass transfer). This paper presents the determination of the operating range of the system and the characterization of the solids mixing behaviour above the central nozzle in order to develop scale-up rules for the industrial application of the annular fluidized bed. The local radial solids concentration, velocity and mass flux profiles are investigated by capacitance probe measurements in a laboratory rig and a pilot plant of inside diameter 0.19 m and 0.74 m, respectively. The geometric and operating parameters varied are the diameter of the central nozzle, the gas velocity in the annulus and in the central nozzle and the pressure drop in the mixing chamber.

Modelling and simulation of a gas–solids dispersion flow in a high-flux circulating fluidized bed (HFCFB) riser

Radial solids velocity profiles were computed on seven axial levels in the riser of a high-flux circulating fluidized bed (HFCFB) using a two-phase 3-D computational fluid dynamics model. The computed solids velocities were compared with experimental data on a riser with an internal diameter of 76 mm and a height of 10 m, at a high solids flux of 300 kg m −2 s −1 and a superficial velocity of 8 m s −1. Several hundreds of experimental and numerical studies on CFBs have been carried out at low fluxes of less than 200 kg m −2 s −1, whereas only a few limited useful studies have dealt with high solids flux. The k– ɛ two-phase turbulence model was used to describe the gas–solids flow in an HFCFB. The model predicts a core–annulus flow in the dilute and developed flow regions similar to that found experimentally, but in the region of highest solids concentration it is somewhat overpredicted at the level close to the inlet.

Numerical Simulation of Gas−Solid Dynamics in a Circulating Fluidized-Bed Riser with Geldart Group B Particles

Circulating fluidized-bed (CFB) risers with Geldart group B particles have found significant application in combustion reactions. The present work attempts to study the solids flow dynamics in a CFB riser that is operated with group B particles, using computational fluid dynamics (CFD) techniques. The key feature in the present study is that the various closure schemes in the CFD model have been evaluated against data from non-invasive experimental techniques: computer automated radioactive particle tracking (CARPT) for solids velocity field and computed tomography (CT) for solids holdup. Since solids flow in a riser is multiscale in character, in addition to the measured averaged solids velocity profiles and solids fraction profiles in the experimental section, mean granular temperature profiles have also been compared. Two flow regimes (viz., fast fluidization and dilute phase transport) have been considered in this study.

Filtered gas–solid momentum transfer models and their application to 3D steady-state riser simulations

To account for meso-scale phenomena in coarse grid simulations, correlation terms appearing in the filtered gas–solid flow equations have to be modeled. Possible approaches to describe filtered gas–solid momentum transfer are evaluated via a mixture speed of sound test. In contrast to the effective drag coefficient closure model for the filtered drag force, the generalized added mass closure model for the correlation between the solid volume fraction and the gas phase pressure gradient shows an acceptable behavior. Furthermore, the generalized added mass may become determining in describing filtered gas–solid momentum transfer when sufficiently coarse grids are used. 3D steady-state riser simulations demonstrate the impact of the generalized added mass based description of filtered gas–solid momentum transfer on the calculated gas–solid flow behavior, in particular on the gas–solid slip velocity profile.

Factorial Modeling for Transient Solid Particle Velocity in a Fluidized Bed Combustor Cold Model

ABSTRACT Transient hydrodynamics phenomena in the fluidized bed combustor (FBC) freeboard have been critical in the past two decades. Within a 152 mm ID FBC cold model, solid particle transient velocities were measured and analyzed with the assistance of advanced laser-based particle image velocimetry (PIV) instrumentation. Two layers of swirling secondary air were injected into the cold model. The PIV system was applied to the FBC cold model to visualize transient solid particle velocity. A series of transient solid particle velocity profiles were generated for the factorial analysis. In each profile, the solid particle velocity vectors (Vx and Vy) for 10 × 10 grids were generated. Analysis of variance (ANOVA) was used to determine the significant factors that affect transient solid particle velocities, time, and position coordinates. Then, the 1010 factorial design method was used to develop a specific empirical model of transient solid particle velocity in the FBC freeboard, which was in the shape of Vx = f1(t, x, y) and Vy = f2(t, x, y). This unique factorial analysis method proved to be a very effective and practical method to evaluate experimental conditions and analyze experimental results in the FBC systems.

Experimental investigation of the hydrodynamics in a liquid–solid riser

AbstractLiquid–solid fluid dynamics has been investigated in a 6‐in. (0.15 m) “cold‐flow” circulating fluidized bed riser using non‐invasive flow monitoring methods. Gamma‐ray computed tomography (CT) was used to measure the time‐averaged cross‐sectional solids volume fraction distributions at several elevations. The time‐averaged mean and “fluctuating” solids velocity fields were quantified using the computer‐automated radioactive particle tracking (CARPT) technique. The experimental equipment, protocol of implementation, and data analysis have been discussed briefly, with particular emphasis on the specific features in the use of these techniques for studying high‐density turbulent flows as in a liquid–solid riser. The experimental study examines nine operating conditions, that is, three liquid superficial velocities and three solids flow rates. The solids holdup profile is found to be relatively uniform across the cross section of the riser, with marginal segregation near the walls. The time‐averaged solids velocity profiles are found to have a negative component at the walls, indicating significant solids backmixing. Detailed characterization of the solids velocity fields in terms of RMS velocities, kinetic energies, Hurst exponents, residence time distributions, trajectory length distributions, dispersion coefficients, and so forth are presented. Comparative and symbiotic analyses of the results were used to develop a coherent picture of the solids flow field. In addition, the work also serves to demonstrate the power and versatility of these flow‐imaging techniques in studying highly turbulent and opaque multiphase systems. © 2005 American Institute of Chemical Engineers AIChE J, 51: 802–835, 2005

Solids motion and holdup profiles in liquid fluidized beds

Non-invasive gamma rays-based techniques, computer tomography and computer-aided radioactive particle tracking, were used to measure solid holdup and solid velocity profiles in liquid–solid fluidized beds. The time averaged velocity measurements indicated that multiple circulation cells exist in the column. The solid motion was upward in the center and downward near the walls in the fully developed part of the column. The flow pattern is reversed in the entry region of the column. The solid holdup values increase slightly with the increase in radial position in the fully developed region. The average values of holdup in the column were in agreement with other measurements and with the modified Richardson–Zaki equation. The solids mean velocities and eddy diffusivities increase with increase in liquid superficial velocity, column size, particle size and density. Distributor-type affects the mean velocity and turbulence parameters while the column height has a relatively minor effect. The solids motion and turbulence parameters presented here are useful for validation of CFD models.

Modelling Heterogeneous Slurry Flows at High Velocities

AbstractExperiments have been conducted with sand slurries of median diameter 0.09 mm and 0.27 mm in a laboratory test pipeline 0.103 m in diameter. In addition to pressure gradient measurements as functions of mean velocity and in‐situ solids concentration, concentration and velocity profiles have been obtained. The measurements show that the pipeline friction is lower than expected at high velocities. This deviation is of the type that has been predicted in recent theoretical work by Wilson and coworkers. A correlation for the slurry friction at high velocities has been obtained. This correlation has been used to modify the model for predicting friction of heterogeneous slurries at velocities above the deposition condition.

Expansion Behavior of a Binary-Solid Liquid Fluidized Bed with Large Particle Size Difference

The overall expansion of two dissimilar solid particle species with over a tenfold difference in their size and substantial density difference is investigated for different compositions of the fluidized bed. Contrary to the widely held notion that the total bed height would be the sum of the heights of the two segregated mono-component beds, the actual bed heights were, in fact, found to be lower. This volume contraction is found to strongly depend upon the mixing behavior prevailing in the binary-solid fluidized bed. At the complete mixing of the two solid species, the bed-contraction versus liquid velocity profile shows a global maximum. As a result, the overall bulk density profiles are similarly affected. Moreover, it is found that correlations meant for predicting the porosity of the packing of binary particle mixtures can be satisfactorily extended to binary-solid fluidized beds where solid species differ significantly in size.

Bubble-Wake Model for Radial Velocity Profiles of Liquid and Solid Phases in Three-Phase Fluidized Beds

The effects of particle size (0.4−2.3 mm), liquid (0.006−0.01 m/s), and gas (0.01−0.14 m/s) superficial velocities on liquid velocity in the radial direction have been determined by electric conductivity probes in a three-phase fluidized bed (0.254 m i.d. × 2.0 m height). The local liquid and solid velocity profiles in the radial direction can be determined from the proposed bubble-wake model. The velocities of liquid and solid phases can be expressed as a function of bubble velocity, phase holdups, and liquid velocity in the liquid fluidized region. Both the volume ratios of liquid and solid in the wake to the bubble phases decrease with an increase in the gas velocity but increase with an increase in the liquid velocity.

On viscous momentum transfer by solids in gas–solids flow through risers

Applying the two-fluid concept, momentum transfer by solids in gas–solids flow through risers is described in terms of solids-phase shear viscosity. Viscosities for glass- and FCC-particles are estimated from literature data on radial profiles of solids concentration and solids velocity in two CFB-risers. Results are compared with simple kinetic theory of granular flow, leading to unreasonable high values of granular temperature. In contrast to kinetic theory, results also indicate a decrease of viscosity with increasing shear rate. Therefore, it is proposed to assume particle clusters as momentum transferring structures. Qualitative analysis of viscosity results by adopting kinetic theory to clusters suggests cluster size decrease with increasing shear rate. These results indicate importance of local shear rate on structure of aggregative solids flow.

A six-electrode local probe for measuring solids velocity and volumefraction profiles in solids-water flows

This paper describes the design and construction of a localsix-electrode conductivity probe which can be used in solids-water pipeflows to simultaneously measure the local solids volume fraction and thelocal solids axial velocity. Using finite element analysis, the probeelectrode geometry was designed so that the regions of the solids-watermixture that were interrogated by the probe were optimal for measurementof the volume fraction and for cross correlation velocity measurement. Theprobe was used, in conjunction with a computer controlled traversingmechanism, to obtain distributions of the local solids volume fraction andthe local solids axial velocity both in vertical upward and in upwardinclined solids-water flows. Such distributions can be used to validatevolume fraction and velocity profiles obtained using dual-plane electricalresistance tomography systems. Experimental results indicated that thesix-electrode probe can be used to estimate the local solids volumefraction in vertical upward solids-water flows with a mean absolute errorof approximately 0.01. Experimental results also indicated that thesix-electrode probe can be used to measure the local axial solids velocitywith a mean error of 2% of the reading.