Discrete particle simulation of particulate systems: A review of major applications and findings

Review of discrete particle modeling of fluidized beds

Extensive lattice-Boltzmann simulations were performed to obtain the drag force for random arrays of monodisperse and bidisperse spheres. For the monodisperse systems, 35 different combinations of the Reynolds number Re (up to Re = 1,000) and packing fraction were studied, whereas for the bidisperse systems we also varied the diameter ratio (from 1:1.5 to 1:4) and composition, which brings the total number of different systems that we considered to 150. For monodisperse systems, the data was found to be markedly different from the Ergun equation and consistent with a correlation, based on similar type of simulations up to Re = 120. For bidisperse systems, it was found that the correction of the monodisperse drag force for bidispersity, which was derived for the limit Re = 0, also applies for higher-Reynolds numbers. On the basis of the data, a new drag law is suggested for general polydisperse systems, which is on average within 10% of the simulation data for Reynolds numbers up to 1,000, and diameter ratios up to 1:4

Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres

Gas-solid fluidized beds are widely applied in many chemical processes involving physical and/or chemical transformations, and for this reason they are the subject of intense research in chemical engineering science. Over the years, researchers have developed a large number of numerical models of gas-fluidized beds that describe gas-solid flow at different levels of detail. In this review, we discriminate these models on the basis of whether a Lagrangian or a Eulerian approach is used for the gas and/or particulate flow and subsequently classify them into five main categories, three of which we discuss in more detail. Specifically, these are resolved discrete particle models (also called direct numerical simulations), unresolved discrete particle models (also called discrete element models), and two-fluid models. For each of the levels of description, we give the general equations of motion and indicate how they can be solved numerically by finite-difference techniques, followed by some illustrative examples of a fluidized bed simulation. Finally, we address some of the challenges ahead in the multiscale modeling of gas-fluidized beds

Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy

The approach of combining computational fluid dynamics (CFD) for continuum fluid and the discrete element method (DEM) for discrete particles has been increasingly used to study the fundamentals of coupled particle–fluid flows. Different CFD–DEM models have been used. However, the origin and the applicability of these models are not clearly understood. In this paper, the origin of different model formulations is discussed first. It shows that, in connection with the continuum approach, three sets of formulations exist in the CFD–DEM approach: an original format set I, and subsequent derivations of set II and set III, respectively, corresponding to the so-called model A and model B in the literature. A comparison and the applicability of the three models are assessed theoretically and then verified from the study of three representative particle–fluid flow systems: fluidization, pneumatic conveying and hydrocyclones. It is demonstrated that sets I and II are essentially the same, with small differences resulting from different mathematical or numerical treatments of a few terms in the original equation. Set III is however a simplified version of set I. The testing cases show that all the three models are applicable to gas fluidization and, to a large extent, pneumatic conveying. However, the application of set III is conditional, as demonstrated in the case of hydrocyclones. Strictly speaking, set III is only valid when fluid flow is steady and uniform. Set II and, in particular, set I, which is somehow forgotten in the literature, are recommended for the future CFD–DEM modelling of complex particle–fluid flow.

Discrete particle simulation of particle–fluid flow: model formulations and their applicability

We report on lattice-Boltzmann simulations of slow fluid flow past mono- and bidisperse random arrays of spheres. We have measured the drag force on the spheres for a range of diameter ratios, mass fractions and packing fractions; in total, we studied 58 different parameter sets. Our simulation data for the permeability agrees well with previous simulation results and the experimental findings. On the basis of our data for the individual drag force, we have formulated new drag force relations for both monodisperse and polydisperse systems, based on the Carman?Kozeny equations; the average deviation of our binary simulation data with the new relation is less than 5%. We expect that these new relations will significantly improve the numerical modelling of gas?solid systems with polydisperse particles, in particular with respect to mixing and segregation phenomena. For binary systems with large diameter ratios (1:4), the individual drag force on a particle, as calculated from our relations, can differ by up to a factor of five compared with predictions presently favoured in chemical engineering.

R Beetstra

Papers

Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres

Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force

Numerical study of segregation using a new drag force correlation for polydisperse systems derived from lattice-Boltzmann simulations

A Lattice-Boltzmann simulation study of the drag coefficient of clusters of spheres