COMPUTATIONAL FLUID DYNAMICS FOR DENSE GAS-SOLID FLUIDIZED BEDS: A MULTI-SCALE MODELING STRATEGY

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissipative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1 ) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow,and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

Determination of the interparticle void volume in packed beds via intraparticle Donnan exclusion

Interparticle void volumes and porosities of packed capillaries have been determined using intraparticle Donnan exclusion of a small, unretained, co-ionic tracer (nitrate ions). The operational domain of this approach has been characterized for bare silica, reversed-phase, and strong cation-exchange materials (with different particle sizes and intraparticle pore sizes) in dependence of the mobile phase ionic strength. Interparticle porosities agree well with those analyzed by inverse size-exclusion chromatography (ISEC). Limitations to the use of Donnan exclusion (electrostatic exclusion) and ISEC (mechanical exclusion) arise as either type of exclusion becomes noticeable also in the cusp regions between the particles, or as the intraparticle pores are so large that complete electrostatic and size-exclusion are difficult to realize. Our data confirm that intraparticle Donnan exclusion presents a most simple, fast, and reliable approach for the analysis of packing densities.     

General methods to render macroporous stationary phases nonporous and deformable,exemplified with agarose and silica beads and their use in high-performance ion-exchange and hydrophobic-interaction chromatography of proteins

Summary New general methods for the preparation of nonporous beads from macroporous beads are described. One method is based on filling the inner volume of the beads with a solution of a monomer which binds to the matrix at the same time as it is allowed to polymerize. The method is illustrated with agarose and silica as matrices and glycidol as monomer. In an alternative, but principally similar method, we first attached allyglycidyl ether to agarose via the epoxide groups and then allowed acrylamide to react with the immobilized allyl groups during polymerization. In an analogous way, nonporous silica beads were prepared by coupling -methacryloxypropyltrimethoxy silane to the macroporous beads followed by polymerization of acrylamide or N-methylolacrylamide on the immobilized methacryl groups. The latter monomer has the advantage of giving a polymer rich in OH groups, which can be used for crosslinking or/and attachment of different ligands (the glycidol polymers have the same advantage).The nonporous agarose beads have chromatographic properties similar to those of the previously described nonporous agarose beads prepared by shrinkage and subsequent crosslinking. For instance, the beds are compressible, which favors the resolution: compressed beds of large beads give the same or higher resolution than do beds of small beads. Another similarity is that the resolution is independent of flow rate or is even enhanced upon an increase in flow rate, maybe in part owing to the generation of a flow pattern which transports the solute from one bead to another faster than does diffusion. These similarities are demonstrated by anion-exchange and hydrophobic-interaction chromatography of proteins. Even the nonporous silica beads are somewhat deformable owing to the relatively thick polymer coating and share with the nonporous agarose beads the attractive relation between resolution and flow rate. In addition, in comparison with naked silica beads they exhibit very little protein adsorption and are more pH stable. A compressed bed of nonporous, coated 30–45 m silica beads gave in an HIC experiment a resolution comparable to that obtained with a bed of noncompressed, nonporous 1.5-m silica beads, which give a very high resolution, as shown by Unger and coworkers [5].     

A note on a boundary condition for spouted beds

The boundary condition, zero solids pressure at the top of a particle bed of maximum spoutable height, Hm, is shown to eliminate any resort to empiricism in the derivation of the fluid velocity in the annulus of a spouted bed for which both viscous and inertial effects are taken into account. The same boundary condition fails when applied to a spouted bed for which the bed height H 〈 Hm, especially when H 〈 0.8Hm.     

A Semi-empirical Correlation for Pressure Drop in Packed Beds of Spherical Particles

The effect of a confining wall on the pressure drop of fluid flow through packed beds of spherical particles with small bed-to-particle diameter ratios was investigated to develop an improved pressure drop correlation. The dependency of pressure loss on both wall friction and increased porosity near the wall was accounted for by using a theoretical approach. A semi-empirical model was created based upon the capillary-orifice model, which included a wall correction factor for the inertial pressure loss. In this model, packed beds were treated as a bundle of capillary tubes whose orifice diameter in the core region was different from that of the wall region. Using this model, a new pressure drop correlation was obtained, based on the Ergun equation and applicable for a wide range of Reynolds numbers (10⁻²–10³). The proposed correlation was compared with previous correlations, as well as with experimental data. This correlation showed close agreement with the experimental data for both low- and high-Reynolds number regimes and for a wide range of bed-to-particle diameter ratios. The ratio of the pressure drop in finite packing to that in homogeneous packing was then calculated. This ratio clearly shows how the wall effect depends on the Reynolds number and the bed-to-particle diameter ratio.     

A CFD Model for Fluid Dynamics in a Gas-fluidised Bed

A modified particle bed model derived from the two-fluid momentum balance equations was employed to predict the gas-fluidised bed behaviour. Additional terms are included in both the fluid and the particle mo-mentum balance equations to take into account the effect of the dispersed solid phase. This model has been extended to two-dimensional formulations and has been implemented in the commercial code CFX 4.3. The model correctly simulates the homogeneous fluidisation of Geldart Group A and the bubbling fluidisation of Geldart Group B in gas-solid fluidised beds.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.