Solid Volume Fraction Profiles Research Articles

Heat-transfer model for the acheson process

The Acheson process is used to manufacture silicon carbide (SiC) in a resistor furnace using petroleum coke and silica as raw materials. The process is highly inefficient, as only 10 to 15 pct of the charge gets converted into silicon carbide. No published attempt has been made to optimize this century-old process by applying mathematical modeling. Therefore, a simultaneous heat- and mass-transfer model has been developed for the resistance-heating furnace, considering silicon carbide formation as a typical carbothermal reaction. Coupled transient partial differential equations have been worked out. These equations have been solved numerically, using the implicit finite-difference method in their nondimensional form, to obtain the profiles of solid temperature and volume fraction reacted in the furnace. The trend of the computed results appears to be realistic; comparison of the results with published experimental work validates the applicability of the model’s predictions. The effects of various parameters on the process have been studied. These include void fraction, power inputs, initial concentration of silicon carbide present in the charge, etc.

An experimental study of cyclone dipleg flow in fluidized catalytic cracking

An experimental study was carried out on the downflow of fine catalysts ( d 50=44 μm) in a straight vertical cyclone dipleg (diameter 80 mm, height 4.6 m) to clarify various types of powder flow which can exist in the dipleg and to measure the amount of gas entrainment down the dipleg under a wide range of operating conditions. In addition, the radial profiles of solids velocity and solids volume fraction were measured at various heights along the dipleg. The axial pressure profiles show that the flow in the dipleg can be divided in regions: inlet, dilute and dense. A flow diagram shows the occurrence of various flow types depending on operating conditions. The flow in the dense region can be fluidized (preferred) or packed. In the dilute region, the solids velocity is higher than the terminal falling velocity of a single particle. This indicates the existence of clusters, the size of which has been estimated. Gas carry-under is generally not significant when the dense region has developed. Once there is a dilute region only, the gas carry-under can become as large as 20 times the volumetric solids flow. The radial profiles of solids velocity and solids volume fraction show that going from dipleg top to dipleg bottom, the rotating annular flow at the dipleg top (cyclone outlet) transforms into a more or less uniform plug flow, both with respect to velocity and to local concentration.

Gas–particle two-phase turbulent flow in horizontal and inclined ducts

Gas–particle two-phase turbulent flows at various loadings in horizontal and inclined ducts are studied. The upgraded thermodynamically consistent two-phase flow model which includes a low Reynolds number fluid-phase turbulence closure is used in the analysis. The governing equations are discretized with the aid of a semi-implicit numerical algorithm. The case of low-concentration gas–particle turbulent flow in a horizontal channel is first analyzed, and the predicted mean velocity and solid volume fraction profiles are favorably compared with the available experimental data. Additional flow properties such as the phasic fluctuation energy and fluctuation energy production and dissipation, as well as the phasic and total normal and shear stress profiles are also presented and discussed. The case of gas–particle flow in a duct with an inclination is then analyzed. Sample model predictions for both dilute and nondilute two-phase turbulent flows under various conditions are presented. The effect of particle diameter on variation of flow properties is also studied.

Determination of the Effect of Enzymes in a Grease Trap

Electrical capacitance volume tomography (ECVT) was conducted to measure instantaneous gas–solid flow structures in a conical spouted bed. The sensor has 24 electrodes/channels and was used to make three-dimensional measurements of the solid volume fraction. Flow structures in the conical spouted bed were analyzed using quantitative ECVT images. Three-dimensional images of gas–solid flow structures and time-averaged vertical and radial solid volume fraction profiles are presented. Different fluidization regimes in spouted beds were characterized by analyzing pressure fluctuation signals and ECVT images. ECVT was shown to be robust and powerful for the three-dimensional visualization and quantitative measurement of a gas–solid fluidization system.

Flow structure in a fast fluid bed

The focus of this work is the determination of the flow structure which gives rise to the S-shaped profile of axial pressure gradient characteristic of a circulating fluidized bed riser operating at fast fluidization conditions. The flow structure is characterised by measurement of radial profiles of solids momentum and solids volume fraction in a riser 0.09 m in diameter and 7.2 m high using a momentum probe and capacitance tomography. The solids used were sand with a Sauter mean diameter of 100 μm and particle density of 2650 kg/m 3. The core-annalus suspension structure typically found in the upper dilute region of the fast bed is found to extend throughout the S-shaped profile and into the lower dense region. However, the direction of solids flow in the annulus changes from downwards in the upper dilute region to upwards in the lower dense region. The interface between the regions (the middle of the S) is found to be a region of relatively low axial solids momentum throughout the riser cross-section. The fast fluidized bed structure suggested by these observations is presented in the form of a diagram.

Unidirectional Infiltration and Solidification/Remelting of Al-Cu Alloy

Unidirectional, adiabatic infiltration, and solidification/remelting of Al-4.5 wt% Cu alloy in a porous preform is modeled numerically. The model formulation is derived from the fundamental conservation laws. The moving infiltration and remelting fronts are dealt with by the Landau transformation. The transformed governing equations are solved numerically. The solute, temperature, and solid volume fraction profiles are presented for representative parameters. The numerical predictions agree well with previously reported experimental measurements and with the analytical similarity solution. It is observed that the unidirectional infiltration and heat transfer do display the similarity behavior, and the macrosegregation in the casting is strongly dependent on the initial preform temperature, the superheat of inlet metal-matrix, and the applied pressure.

Couette flows of a granular monolayer—an experimental study

An experimental study concerning rapid flows of granular materials in a two-dimensional planar granular Couette flow apparatus is performed. The device is capable of generating particulate flows in the grain-inertia regime at different shearing rates and solid volume fractions. Multi-color spherical glass particles are sheared across an annular test-section for several wall angular velocities. A video recorder is used to record the motion of particles and consecutive images are stored and analyzed by an image processing technique for evaluating individual grain velocities. Experimental data for the mean velocity, the root-mean-square (RMS) fluctuation velocity components and the solid volume fraction profiles are obtained. The resulting mean velocity profiles have a roughly linear variation for the range of solid volume fractions and shear rates studied. The solid volume fraction profiles exhibit non-uniform variations with the highest concentration occurring near the center of the shearing cell. The RMS fluctuation velocities are roughly constant, with the streamwise fluctuation being somewhat larger than the cross-stream direction. The experimentally measured flow properties are in reasonable agreement with the earlier theoretical and simulation results.

97/00561 Similarity of radial profiles of solid volume fraction in a circulating fluidized bed

97/00561 Similarity of radial profiles of solid volume fraction in a circulating fluidized bed

Dynamic Behavior and Solid Volume Fraction Distribution in a Jetting Fluidized Bed.

A reflection-type fiber optic probe was used to measure local solid volume fraction in a cylindrical jetting fluidized bed with a conical distributor using three kinds of particles different in sizes. By analyzing the local voidage fluctuations, the jet contours, and the time-averaged solid volume fraction profiles were studied. The jet extension half angle was found to be much lower than those calculated by Merry’s correlation derived for beds with flat distributors. The solid volume fraction measured on the axis increased almost linearly with the distance from the nozzle. In the annulus, it was about one tenth lower than that at the minimum fluidization. The radial solid volume fraction profile in the jet was found to be parabolic.

Gravity granular flows of slightly frictional particles down an inclined bumpy chute

Gravity-driven granular flow of slightly frictional particles down an inclined, bumpy chute is studied. A modified kinetic model which includes the frictional energy loss effects is used, and the boundary conditions for a bumpy wall with small friction are derived by ensuring the balance of momentum and energy. At the free surface, the condition of vanishing of the solid volume fraction is used. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated. It is shown that steady granular gravity flow down a bumpy frictional chute could be achieved at arbitrary inclination angles. The computational results also show that the slip velocity may vary considerably depending on the granular layer height, the surface boundary roughness, the friction coefficient and the inclination angles. The model predictions are compared with the existing experimental and simulation data, and good agreement is observed. In particular, the model can well predicate the features of the variation of solid volume fraction and fluctuation energy profiles for different particle–wall friction coefficients and wall roughnesses.

NUMERICAL SIMULATION OF GRANULAR COUETTE FLOWS BETWEEN TWO ROUGH PARALLEL PLATES

ABSTRACT This paper presents a numerical method for calculating the granular Couette flows between two parallel plates. A kinetic model which includes the frictional energy loss effects is employed, and the equations of motion are solved using a numerical iterative method. The boundary conditions are satisfied by ensuring the balance of momentum and energy at such boundaries. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated under a variety of conditions. The mean velocity profiles are compared with the molecular dynamic simulation results, and good agreement is observed. The study shows that the slip velocity may vary considerably depending on the surface roughness, coefficient of restitution and friction coefficient.

Analysis of rapid shear flows of granular materials by a kinetic model including frictional losses

A kinetic model for granular flow which includes frictional losses is used to analyze several rapid flow problems. Granular Couette flows between two parallel plates, gravity flows down a rough inclined chute and a vertical channel, and granular motions on the top of a vibrating plate are studied in detail. The equations of motion are solved using a fourth-order Runge—Kutta numerical scheme. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated under a variety of conditions. Particular attention was given to the effects of friction coefficient. The results are compared with the available experimental and simulation data and good agreement is observed. The study also shows that under certain conditions a plug flow regime might form for which the granular assembly moves as a rigid body.

A computer code for analyzing transient three-dimensional rapid granular flows in complex geometries

A computer code for simulating transient multidimensional free-surface rapid granular flows in regions with complex geometries is developed. The discrete-element computational scheme, which utilizes the integral form of the governing equations of motion, and a special discretization technique are used. The computational algorithm of the code also uses an explicit composite time-splitting integration method. The recently developed constitutive equations obtained from a kinetic model for rapid granular flows are used in the computer code. The computer code is capable of predicting the mean velocity, solid volume fraction and fluctuation energy profiles, as well as the surface elevation of rapid granular flows in complex geometries of industrial interest. The computational model is used and several transient nonuniform granular flows are analyzed. These include gravity flow down an inclined chute and three-dimensional flows around a block in a channel.

A kinetic model for rapid granular flows of nearly elastic particles including interstitial fluid effects

Rapid flow of nearly elastic granular materials is considered. The kinetic equation governing the evolution of the first-order distribution function including the fluid drag force is presented. Moments of the kinetic equation are used to establish the basic conservation laws for the mean granular motion. Using a simple model, the particle—fluid interactions are analyzed. The collision operator is approximated by the BGK relaxation model and the Chapman—Enskog iteration scheme is used for solving the kinetic equation. The first-order particulate distribution function is determined and the constitutive equations for the kinetic parts of the particulate stress tensor and fluctuation energy flux vector are formulated. Extension of the model to high concentration flows is considered. Contributions of the collisional transport of momentum and energy to the stress tensor and the energy flux vectors are included. The system of equations governing the mean granular velocity, solid volume fraction and fluctuation energy profiles are obtained. The special case of a simple shear flow is considered. The dependence of the normal and shear stresses on the solid volume fraction and coefficient of restitution are studied and the results are compared with the other models and the experimental data. It is shown that when the turbulent fluctuation of the fluid phase is negligible, the fluid drag reduces the particulate stresses. The results also show a reasonable agreement with the experimental data.

A turbulence model for rapid flows of granular materials part II. Simple shear flows

Using the one-equation turbulence model of Part I, rapid flows of granular materials are studied. The equations governing the transport of mass, linear momentum and fluctuation energy are considered. For simple shear flows, the dependences of the stress—shear rate relationship on the coefficient of restitution and solid volume fraction are studied. Couette and gravity flows of granular materials in rapid flow regimes are analyzed. Velocity, solid volume fraction and fluctuation energy profiles are calculated. The results are compared with those of the other theoretical models and the existing experimental data. It is shown that the predictions of the turbulence model agree reasonably well with the experimental data.