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.

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The design and control of blast furnace (BF) ironmaking must be optimized in order to be competitive and sustainable, particularly under the more and more demanding and tough economic and environmental conditions. To achieve this, it is necessary to understand the complex multiphase flow, heat and mass transfer, and global performance of a BF under different conditions. Mathematical modeling, often coupled with physical modeling, plays an important role in this area. This paper reviews the recent developments in this direction. The emphasis is given to mathematical models for different BF regions from the top charging system, body, and finally down to raceway and hearth. The needs for the further research and developments are also discussed.

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Dense-phase pneumatic transportation of bulk materials in the form of slug flow has become a very important technology in industry. In order to understand the underlying mechanisms of slug flow, this paper presents a numerical study of slug flow in horizontal pneumatic conveying by means of discrete particle simulation. To be computationally efficient, the motion of discrete particles is three-dimensional and the flow of continuum gas is two-dimensional, and periodic boundary conditions are applied to both gas and solid phases horizontally. The proposed numerical model is qualitatively verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. Then the influence of operational conditions such as gas and solid flowrates on slug behavior is numerically investigated. It is shown that slug velocity linearly increases with gas flowrate but is not sensitive to solid flowrate, and slug length increases with both gas and solid flowrates. The results qualitatively agree with the experimental observations. Finally, forces governing the gas-solid flow are analyzed on different length scales. It is shown that the movement of a slug is macroscopically controlled by the axial particle-fluid and particle-wall interactions, whereas the particleparticle interaction microscopically causes a slug to sweep up particles in a settled layer. The magnitudes of these interaction forces increase with gas and solid flowrates.

Pneumatic conveying is an important technology in industries to transport bulk materials from one location to another. Different flow regimes have been observed in such a transportation process depending on operational conditions, but the underlying fundamentals are not clear. This paper presents a three-dimensional numerical study of vertical pneumatic conveying by a combined approach of discrete element model for particles and computational fluid dynamics for gas. The approach is verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. It is shown that flow regimes usually encountered in vertical pneumatic conveying and their corresponding phase diagram can be reproduced. Then forces governing the behavior of particles, such as the particle-particle, particle-fluid, and particle-wall forces, are analyzed in detail. It is shown that the roles of these forces vary with flow regimes. A new phase diagram is proposed in terms of the key forces, which can successfully identify dilute-phase flow and dense-phase flow in vertical pneumatic conveying.