Solid Phase Viscosity Research Articles

Modeling of Ice Slurry Flow through Bend Pipe

In this work, CFD Eulerian multiphase model with KTGFis used to investigate the flow behaviour of the ice slurry in 90° elbow bend pipe. The present model considered the particle-particle collisions along with particle-wall collisions. In the modeling of ice slurry flow various interfacial forces viz. drag force, lift force and turbulence dispersion force are considered. The solid phase viscosity is calculated as a sum of kinetic and collision viscosity component and the turbulence in the ice slurry flow is modeled by the per phase k-model. Simulation has been performed at velocity of 1 m/s, concentration of 10% and particle size of 0.25 mm for the bend radius ratios (R/r) of 2, 2.98 and 5.6. Apart from that, effect of particle size, velocity and concentration on solid particle distribution has also been investigated. Results show that, secondary flow is generated similar to single phase flow which influences the velocity, particle distribution and pressure drop.

A simplified two-fluid model coupled with EMMS drag for gas-solid flows

A simplified two-fluid model (STFM) combined with energy-minimization multi-scale (EMMS) drag was proposed for accurate and fast simulation of gas-solid flows. In the proposed approach, the solid phase viscosity is neglected, the solid phase pressure is calculated with an empirical formulation, and the interphase momentum transfer is modeled with EMMS drag, which takes the effects of meso-scale structures into consideration. Three typical fluidization cases, namely, a 2D circulating fluidized bed, a 3D lab-scale bubbling fluidized bed, and a 3D lab-scale full-loop circulating fluidized bed, were successfully simulated with this approach. The numerical results are compared with those of full two-fluid model (FTFM, i.e., the two-fluid model using the kinetic theory for granular flow to close solid phase stress term), as well as experimental data. Predictions of STFM coupled with EMMS drag are comparable with those of FTFM coupled with EMMS drag, and both agree well with experimental data. However, computational cost of STFM is significantly reduced compared with that of FTFM. It is suggested that drag model has a dominant effect on gas-solid simulation, and the effect of solid phase stress term seems to play a minor role, demonstrating the feasibility and practicality of STFM with EMMS drag for describing the hydrodynamics of heterogeneous gas-solid flows.

Parameter study of a kinetic-frictional continuum model of a disk impeller high-shear granulator

A disk impeller high shear granulator was modeled with a kinetic-frictional continuum model. A parameter study was made and the parameterization of the equations was assessed to investigate if the model is suited for modeling high shear granulation. A dry granule mixing was studied and the parameters investigated were the particle diameter, the angle of internal friction, the particle-particle restitution coefficient, the particle density, the particle velocity boundary condition, the packing limit and the numerical parameter frictional packing limit. All the particle related parameters can be expected to change during a granulation. The flow field prediction of the model is in agreement with the behavior described by Knight et al. (2001), showing a rigid torus. This is in contrast to a discrete element model simulation that predicts inner rotation within the torus (Gantt and Gatzke 2006). The general flow field of this system is fairly insensitive to all parameter changes, except a change to no slip boundary condition for the particle phase, even though several parameters significantly affect the solid phase viscosity. The model was used to predict the change in impeller torque when going from mixing a dry powder to a wet system. It is shown that the models have some potential for qualitative descriptions of the wet state. (

CFD study on hydrodynamics in three-phase fluidized beds—Application of turbulence models and experimental validation

CFD simulations of gas–liquid–solid fluidized beds have been performed in a full three-dimensional, unsteady multiple-Euler framework by means of the commercial software FLUENT. The simulation results were compared with experimental data obtained from laboratory scale three-phase fluidized beds. The significance of implementing accurate numerical schemes, as well as the choice of available k–ε turbulence models (standard, RNG, realizable), solid wall boundary conditions and granular temperature models were investigated. The results indicate that in order to minimize numerical diffusion artifacts and to enable valid discussions on the choice of physical models, third-order numerical schemes need to be implemented. The realizable turbulence formulation was unable to produce the expected solids gulf-stream pattern (i.e., rising solid particles in the core and descending solid particles near the wall) in three-phase fluidized beds whereas the RNG and standard k–ε models were able to better capture depictions of flow patterns. The best prediction of flow characteristics was obtained with a laminar model formulation accounting for the solid phase viscosity and the molecular viscosities of the two fluids.

On near-wall behavior of particles in a dilute turbulent gas–solid flow using kinetic theory of granular flows

Motion of particles in a dilute turbulent boundary layer, near a flat wall is simulated numerically. Eulerian–Eulerian two-way coupled model is used. Closures for the particulate-phase equations are derived from the kinetic theory of granular flow. One equation model is used to model turbulence in the gas-phase. Effects of inertial parameters of solid-phase such as flow density, material density, particle diameter and free stream velocity are investigated. Furthermore, effects of granular temperature and particulate viscosity on motion of particles are discussed. Simulation results are compared with available numerical and experimental results. Results show that the granular temperature and solid-phase viscosity have a noticeable effect on simulation accuracy especially near the wall. Results are closer to experimental results when implementing the inlet granular temperature which is equal to area-weighted average of granular temperature in the boundary layer. Non-dimensional velocity profiles of solid-phase have a general trend and their dependence on location and free stream velocity is found very weak.

Computational fluid dynamic simulation of ethylene hydrogenation in a fluidised bed of porous catalyst particles

AbstractComputational fluid dynamics (CFD) is used to study the flow behaviour and conversion in a freely bubbling bed of porous cracking catalyst particles fluidised by a mixture of ethylene and hydrogen on the in‐house code FLOTRACS‐MP‐3D. The solid phase viscosity and pressure are modelled on the basis of kinetic theory of granular flows (KTGF). An effective solid density is calculated to account for the inherent porosity of particles. The cohesive inter‐particle forces are incorporated into the CFD model by using an empirical approach proposed in literature. Qualitatively, the CFD model captures the flow behaviour and heat transfer in the bed quite well. On the quantitative front, the variation of conversion with gas velocity is predicted fairly well with the deviation between the predicted and measured conversion remaining within 20%. © 2011 Canadian Society for Chemical Engineering

Simulation of particles and gas flow behavior in a riser using a filtered two-fluid model

Flow behavior of gas and particles is predicted by a filtered two-fluid model by taking into the effect of particle clustering on the interphase momentum-transfer account. The filtered gas–solid two-fluid model is proposed on the basis of the kinetic theory of granular flow. The subgrid closures for the solid pressure and drag coefficient ( Andrews et al., 2005) and the solid viscosity ( Riber et al., 2009) are used in the filtered two-fluid model. The model predicts the heterogeneous particle flow structure, and the distributions of gas and particle velocities and turbulent intensities. Simulated solids concentration and mass fluxes are in agreement with experimental data. Predicted effective solid phase viscosity and pressure increase with the increase of model constant c g and c s . At the low concentration of particles, simulations indicate that the anisotropy is obvious in the riser. Simulations show the subgrid closures for viscosity of gas phase and solid phase led to a qualitative change in the simulation results.

Critical comparison of hydrodynamic models for gas–solid fluidized beds—Part I : bubbling gas–solid fluidized beds operated with a jet

In the Eulerian approach to model gas–solid fluidized beds closures are required for the internal momentum transfer in the particulate phase. Firstly, two closure models, one semi-empirical model assuming a constant viscosity of the solid phase (CVM) and a second model based on the kinetic theory of granular flow (KTGF), have been compared in this part in their performance to describe bubble formation at a single orifice and the time-averaged porosity profiles in the bed using experimental data obtained for a pseudo two-dimensional fluidized bed operated with a jet in the center. Numerical simulations have shown that bubble growth at a nozzle with a jet is mainly determined by the drag experienced by the gas percolating through the compaction region around the bubble interface, which is not much influenced by particle–particle interactions, so that the KTGF and CVM give very similar predictions. However, this KTGF model does not account for the long term and multi particle–particle contacts (frictional stresses) and under-predicts the solid phase viscosity at the wall as well as around the bubble and therefore over-predicts the bed expansion. Therefore, in the later part of the paper, the bubble growth at a single orifice and the time-averaged porosity distribution in the bed predicted by the KTGF model with and without frictional stresses are compared with experimental data. The model predictions by the KTGF are improved significantly by the incorporation of frictional stresses, which are however strongly influenced by the empirical parameters in this model. In Part II the comparison of the CVM and KTGF with experimental results is extended to freely bubbling fluidized beds.

Critical comparison of hydrodynamic models for gas–solid fluidized beds—Part II: freely bubbling gas–solid fluidized beds

Correct prediction of spontaneous bubble formation in freely bubbling gas–solid fluidized beds using Eulerian models, strongly depends on the description of the internal momentum transfer in the particulate phase. In this part, the comparison of the simple classical model, describing the solid phase pressure only as a function of a solid porosity by an empirical correlation and assuming the solid phase viscosity constant, which is referred to as the constant viscosity model (CVM), with the more fundamental model based on the kinetic theory of granular flow (KTGF), in which the solid phase properties are described in much more detail in terms of instantaneous binary particle–particle interactions, has been extended for freely bubbling fluidized beds. The performance of the KTGF and the CVM in predicting the hydrodynamics of freely bubbling fluidized beds has been compared with experimental data and correlations taken from the literature. In freely bubbling fluidized beds at relatively low gas velocities, bubble formation is initiated by inelastic particle–particle interactions. When accounting for the dissipation of granular energy by particle collisions, the KTGF predicts much larger bubbles with a much sharper interface in comparison to the CVM. The average bubble size distribution predicted by the KTGF showed better agreement with correlations as well as experimental data from the literature. Although both models showed an increase in the predicted average bubble size with increasing superficial gas velocities, the discrepancy in the predicted bubble size becomes smaller, indicating the growing importance of the gas particle interactions in the bubble formation process at higher gas velocities. The rise velocity predicted by the KTGF and the CVM is approximately the same and in good agreement with correlations available in the literature. Since the KTGF predicts somewhat larger bubbles, also the predicted visible bubble flow is higher in comparison to the CVM. In very dense regions in the fluidized bed the KTGF based on instantaneous binary collisions needs to be extended for additional frictional stresses in addition to the kinetic and collisional transport mechanisms. The extra frictional stresses were implemented via a relatively simple semi-empirical closure model and proved to have a significant influence on the predicted bubble size, rise velocity and visible bubble flow rate, where the model predictions strongly depend on the empirical constants. To further enhance the performance of the KTGF to describe the hydrodynamics of freely bubbling beds a more fundamental description of the frictional stresses on the particle level should be incorporated.

Numerical study on the influence of various physical parameters over the gas–solid two-phase flow in the 2D riser of a circulating fluidized bed

A numerical parametric study was performed on the influence of various physical aspects over the hydrodynamics of gas–solid two-phase flow in the riser of a circulating fluidized bed (CFB). The addressed features were the solid phase viscosity, the gas–solid interface momentum transfer correlations, and the coordinate system. An Eulerian continuum formulation was applied for both phases. The resulting two-fluid model and numerical procedure followed a version of the MICEFLOW code. The simulation results are compared to available experimental data. The effects of the concerning features on the flow behavior are shown, mainly regarding cluster evolution. The flow frequency fluctuations typical to CFB risers were observed. It was also observed that for high values of solid phase viscosity there is an accumulation of solids near the outlet forming large clusters. When those clusters fall down, the instantaneous cross-sectional average solid mass velocity becomes negative. For inviscid solid phase, no cluster formation is observed. The results show the incorrectness of assuming symmetry boundary condition at the axis of the riser when cylindrical coordinates are used. Quite different results were obtained for different correlations for gas–solid interface momentum transfer. Finally, a comparison is presented of predictions from the Illinois Institute of Technology (IIT) hydrodynamic models A and B.

Wavy Instability in Liquid-Fluidized Beds

Experiments on the primary wavy instability in a liquid-fluidized bed are designed to test the two-phase flow governing equations. The wave is shown to saturate along the bed. The saturated wave can be well described as a cnoidal wave. The solid-phase viscosity and pressure which are unknown in the two-phase model are deduced from the shape of the saturated wave. The validity of the two-phase Newtonian model is then questioned.

The viscosity of germanium during substrate relaxation upon thermal anneal

Thin-film heterostructures experience structural relaxation when subjected to post-deposition thermal heat treatment. The rate of relaxation, elastic effects, and inelastic effects on the stress and deformation of the structure are determined by the physical properties of the materials, in particular, the solid-phase viscosity. During relaxation, movement of defects causes an increase of viscosity with time at a constant rate as these defects are annihilated. Experimental anneals have been performed on structures with polycrystalline silicon films on (111) germanium substrates, in which the substrate relaxes during thermal annealing. A numerical analysis of the experimental results has determined values for the viscosity and viscosity rate of (111) germanium wafers. In addition, four zones of the relaxation process have been identified, and results indicate that the increasing viscosity with time has a larger effect at lower furnace ramp-up rates.

On the effect of various momentum transfer coefficient models on bubble dynamics in a rectangular gas fluidized bed

In this paper a computational study of the effect of various gas—solid momentum transfer coefficient models on the bubble formation in a gas fluidized bed is presented. The numerical scheme developed is implicit in the gas—solid momentum transfer terms. The bed is modeled to be composed of gas and particulate phases. Beyond the minimum fluidization conditions the excess gas passes through the bed as bubbles. In addition to the gravitational effects on the solid particles, the overall behavior is characterized by the interphase momentum transfer and the pressure and viscosity of the solid phase. The momentum transfer coefficient is modeled for the flow around spherical particles and the solids pressure is modeled based on kinetic theory. The solid-phase viscosity is considered to be constant and a value of 1 Pa s is used as reported in the literature. The computations are performed for a two-dimensional rectangular bed of particles 500 μm in diameter. The bed has a single air jet in the middle at the bottom while the secondary air at minimum fluidization velocity comes in uniformly through the rest of the distributor. A jet velocity to distributed velocity ratio of 40:1 is used in the computations. The computations are started from minimum fluidization conditions and show the formation, growth, detachment, rise and subsequent bursting of the first bubble in the freeboard region. The results are presented in terms of void fraction contours. The computations are carried out for longer real times and the subsequent bubble dynamics is discussed. For different momentum transfer coefficients the bed was observed to demonstrate quite different behaviors after the collapse of the first bubble. For the prescribed flow rate only the first bubble was seen to be well defined and the gas tended to channel through a slender jet thereafter. A lower jet velocity case as well as uniformly fluidized case are also discussed for comparison purposes.

Computer simulation of the hydrodynamics of a two-dimensional gas-fluidized bed

A first principles model of a gas-fluidized bed has been applied to calculate the hydrodynamics of a two-dimensional (2-D) bed with an orifice in the middle of a porous plate distributor. The advanced hydrodynamic model is based on a two fluid model approach in which both phases are considered to be continuous and fully interpenetrating. Conservation equations for mass, momentum and thermal energy have been solved numerically by a finite difference technique on a mini-computer. Our computer model calculates the porosity, the pressure, the fluidum phase temperature, the solid phase temperature and the velocity fields of both phases in 2-D Cartesian or axisymmetrical cylindrical coordinates. The new feature of the present model is the incorporation of Newtonian behaviour in the gas and solid phases. Our preliminary calculations indicate that the sensitivity of the computed bubble size with respect to the bed rheology (i.e. the solid phase viscosity) is quite small. However the bubble shape appears to be much more sensitive to the bed rheology. Results of the calculations have been compared with data obtained from an experimental cold-flow model (height: 1000 mm, width: 570 mm, depth: 15 mm).