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.     

Simulation and investigation of periodic deflecting oscillation of gas–solid planar opposed jets

In this study, the Eulerian–Eulerian approach based on kinetic theory of granular flow (KTGF) was used to simulate the gas–solid planar opposed jets. The periodically deflecting oscillation was observed, i.e., the two opposed jets deflect off each other and swing up and down periodically. The system entropy production rate was calculated to explain this periodic oscillation for the first time. It was found that the periodic deflecting oscillation was dominated by a self-adjusting mechanism of planar opposed jets with the combined action of the pressure release and the entrainment of continuous jets. The effects of nozzle separation, initial jet Reynolds number and particle parameters on the oscillation period were analyzed. The period decreases as the jet Reynolds number or mass loading increases, but increases as the nozzle separation or the particle diameter increases. Furthermore, it is found that the residence time of particles was increased by increasing the mass loading.     

A comprehensive review on modeling of pneumatic and flash drying

Pneumatic conveying drying (PCD) is a widely used process in the industries and is a combination of heat and mass transfer and pneumatic handling technology. Drying processes consume large amounts of energy and, therefore, reduction in operating cost will be extremely beneficial for the industry. Many studies have been conducted to model and optimize the pneumatic drying. This review article focuses on the different strategies used in the literature to model pneumatic drying processes. An analysis is provided for the different mathematical modeling and its components such as balance and complementary equations and modeling assumptions. Two-fluid theory, Eulerian granular, and the discrete element method are reviewed as well as gas–solid flow modeling methods. In addition, the numerical methods and the main studied parameters in the field of pneumatic drying are investigated. To this end, heat and mass transfer coefficients, gas and dispersed phase properties are reviewed.     

CFD modeling of a pilot-scale countercurrent spray drying tower for the manufacture of detergent powder

A steady-state, three-dimensional, multiphase computational fluid dynamics (CFD) modeling of a pilot-plant countercurrent spray drying tower is carried out to study the drying behavior of detergent slurry droplets. The software package ANSYS Fluent is employed to solve the heat, mass, and momentum transfer between the hot gas and the polydispersed droplets/particles using the Eulerian–Lagrangian approach. The continuous-phase turbulence is modeled using the differential Reynolds stress model. The drying kinetics is modeled using a single-droplet drying model, which is incorporated into the CFD code using user-defined functions (UDFs). Heat loss from the insulated tower wall to the surrounding is modeled by considering thermal resistances due to deposits on the inside surface, wall, insulation, and outside convective film. For the particle–wall interaction, the restitution coefficient is specified as a constant value as well as a function of particle moisture content. It is found that the variation in the value of restitution coefficient with moisture causes significant changes in the velocity, temperature, and moisture profiles of the gas as well as the particles. Overall, a reasonably good agreement is obtained between the measured and predicted powder temperature, moisture content, and gas temperature at the bottom and top outlets of the tower; considering the complexity of the spray drying process, simplifying assumptions made in both the CFD and droplet drying models and the errors associated with the measurements.     

Modeling of cluster structure-dependent drag with Eulerian approach for circulating fluidized beds

Flow behavior of gas and solids is simulated in combination the gas-solid two-fluid model with a cluster structure-dependent (CSD) drag coefficient model. The dispersed phase is modeled by a Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The drag forces of gas-solid phases are predicted from the local structure parameters of the dense and dilute phases based on the minimization of the energy consumed by heterogeneous drag. The cluster structure-dependent (CSD) drag coefficients are incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. Simulation results indicate that the dynamic formation and dissolution of clusters can be captured with the cluster structure-dependent drag coefficient model. Simulated solid velocity and concentration of particles profiles are in reasonable agreement with experimental results.     

The Drying of Sludge in a Cyclone Dryer Using Computational Fluid Dynamics

A control volume-based technique implemented in FLUENT (ANSYS Inc., Canonsburg, PA) computational fluid dynamics (CFD) package was applied along with the kinetic theory of granular flow (KTGF) to simulate the flow pattern and heat and mass transfer processes for sludge material in a large-scale cyclone dryer. The drying characteristics of sludge at the dryer inlet were obtained from a previous study on the drying of sludge in a large-scale pneumatic dryer. User-defined subroutines were added to extend FLUENT's capability to account for mixture properties and to simulate the constant and falling rate drying periods. The convective heat and mass transfer coefficients were modeled using published correlations for Nusselt and Sherwood numbers. Sensitivity analysis was conducted to determine the effect of gas-phase velocity and temperature on the final product outcome. Numerical predictions for the multiphase flow hydrodynamics showed a highly diluted region in the dryer core and a higher concentration of particles close to the wall region, an indication of nonuniform distribution of particles at a cross-sectional area. The numerical predictions for the hydrodynamic profiles qualitatively depicted the flow behavior natural to these designs. The work demonstrated the successful application of CFD in the design stage of a combined pneumatic-cyclone dryer model.     

A combined experimental and computational study of wet granulation in a Wurster fluid bed granulator

A methodology combining theoretical and experimental techniques for analyzing the growth of granules in a fluidized bed granulator was developed. The methodology combines several key features of this complicated process: (i) population balancing (PB) of growth of different granules; (ii) hydrodynamic modeling of the gas-solid mixture flow using Computational Flow Dynamics (CFD); (iii) modeling of contact mechanics and granule formation; (iv) the Stokes number analysis for calculation of successful collisions; (v) well-controlled experimental study of the wet granulation. First, a detailed CFD model of the gas-solid flow and agglomeration (Model CFD-PB) within the Wurster type granulator was developed. Second, a simplified PB model of agglomeration in a homogeneous system (Model H-PB) was developed. The quadrature method of moments (QMOM) was used for solution of PB equations in both models. The kinetic theory of granular flow (KTGF) was employed in both models for calculation of the number of collisions between solid particles of different classes. Success factors, based on the Stokes number analysis, were calculated using results of extensive mesoscale simulations of the formation of realistic three-dimensional virtual granules. Comparison of simulation results of CFD-PB vs. H-PB models allowed evaluation of the KTGF kernel functionality to be used in H-PB model. Next, fluid bed granulation experiments were conducted for typical pharmaceutical excipients (microcrystalline cellulose, mannitol and dicalcium phosphate) with 15% HPC binder solution in a pilot plant Wurster granulator. The observed granule growth was a function of the surface roughness of excipients. Finally, the H-PB model was fitted to the experimental data. The only adjustable parameter of the H-PB model was an effective agglomeration rate constant, which we expect to be mostly related to the binder wetness on the surface of colliding granules.     

Transport in deformable food materials: A poromechanics approach

A comprehensive poromechanics-based modeling framework that can be used to model transport and deformation in food materials under a variety of processing conditions and states (rubbery or glassy) has been developed. Simplifications to the model equations have been developed, based on driving forces for deformation (moisture change and gas pressure development) and on the state of food material for transport. The framework is applied to two completely different food processes (contact heating of hamburger patties and drying of potatoes). The modeling framework is implemented using total Lagrangian mesh for solid momentum balance and Eulerian mesh for transport equations, and validated using experimental data. Transport in liquid phase dominates for both the processes, with hamburger patty shrinking with moisture loss for all moisture contents, while shrinkage in potato stops below a critical moisture content.     

EMMS-based Eulerian simulation on the hydrodynamics of a bubbling fluidized bed with FCC particles

Although great progress has been made in modeling the bubbling fluidization of Geldart B and D particles using standard Eulerian approach, recent studies have shown that suitable sub-grid scale models should be introduced to improve the simulation on the hydrodynamics of Geldart A particles. In this study, the flow structures inside a bubbling fluidized bed of FCC particles are simulated in an Eulerian approach employing the energy minimization multi-scale (EMMS) model (Chemical Engineering Science, 2008, 63: 1553-1571) as the sub-grid scale model for effective inter-phase drag force, using an implicit cluster diameter expression. It was shown that the experimentally found axial and radial solid concentration profiles and radial particle velocity profiles can be well reproduced.     

Challenges of Simulating Droplet Coalescence within a Spray

This article reports various challenges that have been encountered in the process of developing validated Lagrangian and Eulerian models for simulating particle agglomeration within a spray dryer. These have included the challenges of accurately measuring droplet coalescence rates within a spray, and modeling properly the gas-droplet and droplet-droplet turbulence interactions. We have demonstrated the relative versatility and ease of implementation of the Lagrangian model compared with the Eulerian model, and the accuracy of both models for predicting turbulent dispersion of droplets and the turbulent flow-field within a simple jet system. The Lagrangian and Eulerian droplet coalescence predictions are consistent with each other, which implies that the numerical aspects of each simulation are handled properly, suggesting that either approach can be used with confidence for future spray modeling. However, it is clear that considerable research must be done in the area of particle turbulence modeling and accurate measurement of particle agglomeration rates before any Computational Fluid Dynamics tool can be employed to accurately predict particle agglomeration within a spray dryer.     

循环硫化床上升管中动态行为的拟流体模拟

The kinetic theory of granular flow (KTGF) is modified to fit the Einstein′s equation for effective viscosity of dilute flow. A pseudo-fluid approach based on this modified KTGF is used to simulate the dynamic formation and dissipation of clusters in a circulating fluidized bed riser. The agglomeration of particles reduces slip velocity within particle clusters, and hence results in two reverse trends: discrete particles are lifted by air while particle clusters fall down along the wall. The dynamic equilibrium of these two types of motion leads to the characteristic sigmoid profile of solid concentration along the longitudinal direction. The predicted solid velocity, lateral and longitudinal profiles of solid volume fraction and annulus thickness are in reasonable agreement with experimental results.     

聚合物涂膜干燥研究进展

评述了人们对于聚合物涂膜形成过程及干燥机理的认识 ,并以涂膜干燥过程的模拟、涂膜缺陷的形成、扩散系数的测定及估算等方面的研究进展为依据 ,讨论了聚合物涂膜干燥过程中需要进一步研究和开发的领域     

3D simulation of effect of geometry on minimum fluidization velocity and flow regimes in a spout-fluidized bed

Spout–fluid beds are used for a variety of processes involving particulate solids, like coating, drying, granulation and etc. The spout–fluidized bed combines a number of favorable properties of both spouted and fluidized beds. In this study, the Granular Eulerian model is used in 3-D hydrodynamic simulation of spout fluidized bed for calculation of minimum fluidization velocity. The results of simulation were compared with experimental data and good agreement was obtained. Then the effect of geometry on minimum fluidization velocity was studied. Also a review of flow regimes in different spout fluidized bed geometries was studied.     

Analysis of Particle Transport and Deposition of Micron-Sized Particles in a 90° Bend Using a Two-Fluid Eulerian–Eulerian Approach

Two-phase flows involving dispersed particle and droplet phases are common in a variety of natural and industrial processes, such as aerosols, blood flow, emulsions, and gas-catalyst systems. For sufficiently dilute particle/aerosol phases, a simplified one-way coupling is often assumed, in which the continuous primary phase is unaffected by the presence of the dispersed secondary phase and standard CFD methods can be applied. To predict the transport and deposition of the particle phase, typically a Lagrangian particle-tracking or Eulerian one-fluid/two-phase drift-flux approach is used. Here, a full two-fluid Eulerian modeling approach is presented for coarse particles (>1 μm), in which transport equations are numerically solved for both particle-phase continuity and particle-phase momentum. Simulation results were obtained for a laminar flow regime (Re 100 and 1000) in a 90° elbow, and the effects of grid topology and resolution were investigated. Additionally, gravity effects were considered for both Re cases. Results using this full two-fluid Eulerian approach were validated against experimental data and other computational studies. One key novel contribution of this work is presentation of a simple algorithm for stabilizing the Eulerian particle-phase equation. To the authors' knowledge, this is the first study documenting a full two-fluid Eulerian approach for dilute particle phases in laminar flow on unstructured (prism/tetrahedral) meshes. The results show the potential of the two-fluid approach for providing a useful alternative to the more typical Lagrangian approach for prediction of coarse-particle transport and wall deposition.

Copyright 2015 American Association for Aerosol Research     

Eulerian–Lagrangian Simulation and Experimental Validation of Pneumatic Conveying Dryer

This paper explores numerical and experimental studies on the performance of a pneumatic conveying dryer. The four-way coupling Eulerian–Lagrangian approach is utilized in the numerical study and the experimental study is carried out in a pilot-scale vertical pneumatic conveying dryer of diameter 8.1 cm and 4.5 m length. The effects of Reynolds number, particle size, solid mass flow rate, and inlet gas temperature on the dryer performance are investigated. It is found that the present model predictions agree well with the experimental data. Generally, it is concluded that the drying rate increases as the Reynolds number increases, while increasing the particle size or the solid mass flow rate decreases the drying rate.     

Challenges of Simulating Droplet Coalescence within a Spray

Abstract

This article reports various challenges that have been encountered in the process of developing validated Lagrangian and Eulerian models for simulating particle agglomeration within a spray dryer. These have included the challenges of accurately measuring droplet coalescence rates within a spray, and modeling properly the gas–droplet and droplet-droplet turbulence interactions. We have demonstrated the relative versatility and ease of implementation of the Lagrangian model compared with the Eulerian model, and the accuracy of both models for predicting turbulent dispersion of droplets and the turbulent flow-field within a simple jet system. The Lagrangian and Eulerian droplet coalescence predictions are consistent with each other, which implies that the numerical aspects of each simulation are handled properly, suggesting that either approach can be used with confidence for future spray modeling. However, it is clear that considerable research must be done in the area of particle turbulence modeling and accurate measurement of particle agglomeration rates before any Computational Fluid Dynamics tool can be employed to accurately predict particle agglomeration within a spray dryer.     

Drying kinetics of cork planks in a cork pile in the field

Moisture content is one important parameter in the trading of raw cork planks after harvesting. This study presents a mathematical modeling of the drying curve of raw cork planks in a cork pile in the field, under natural sun drying conditions. Experimental data were obtained by following the water loss (i.e. by daily weighing) of 97 cork planks positioned in nine points within a cork pile. Immediately after harvesting, the raw cork planks had a mean moisture content in a dry basis of 40.4% and after 20-day drying 16.6%. The drying process of the cork planks showed three phases: drying was very fast in the first 2 days; in the next 2–15 days there was a decreasing drying rate; and a final phase, after 15 days in the cork pile, with a slightly decreasing drying rate. Mathematical modeling provided a direct relation between moisture content and drying time. After comparing sixteen empirical drying models, the Modified Henderson and Pabis model showed the best fit. According to this model, the cork planks are commercial dry (14% moisture content in a wet basis) 15 days after harvest.     

Multiphase modeling of intermittent drying using the spatial reaction engineering approach (S-REA)

Several schemes of energy minimization of drying process including intermittent drying have been attempted. Intermittent drying is conducted by applying different heat inputs in each drying period. An effective and physically meaningful drying model is useful for process design and product technology. The lumped reaction engineering approach (L-REA) has been shown previously to be accurate to model the intermittent drying In L-REA, the REA (reaction engineering approach) is used to describe the global drying rate. In this study, the REA is used to model the local evaporation/condensation rate and combined with the mechanistic drying models to yield the spatial reaction engineering approach (S-REA), a non-equilibrium multiphase drying model. The accuracy of the S-REA to model the intermittent drying under time-varying drying air temperature is evaluated here. In order to incorporate the effect of time-varying drying air temperature, the equilibrium activation energy and boundary condition of heat balance implement the corresponding drying settings in each drying period. The results of modeling using the S-REA match well with the experimental data. The S-REA can yield the spatial profiles of moisture content, concentration of water vapor, temperature and local evaporation/condensation rate so that better understanding of transport phenomena of intermittent drying can be obtained. It is argued here that the REA can describe the local evaporation rate under time-varying external conditions well. The S-REA is an effective non-equilibrium multiphase approach for modeling of intermittent drying process.     

Influence of convective intermittent drying schemes on drying induced stress–strain of a 3D clay object

Drying process of industrial green in-process products especially those susceptible to cracking, need great care, and optimally arrangement of parameters of convective drying. Intermittent drying is a new technique in drying area and is a promising solution for product quality enhancement. The intermittent drying with variable air temperature and the intermittent drying with variable air humidity are the most used techniques. The current study is devoted to 3D modeling and simulation of intermittent drying with variations of both air humidity and temperature and it is then compared with each of the cases of the intermittent drying with variable air temperature and the intermittent drying with variable air humidity. It was observed that the best dried product quality was obtained in intermittent drying with periodic changes of air temperature. Vapor condensation in the intermittent drying with variable air humidity is an undesirable phenomenon that significantly reduces the effectiveness of this process.