Original Research PaperSimulation of the pressure drop across granulated mixtures using a coupled DEM – CFD model
Graphical abstract
Introduction
During the iron ore sintering process, granules are agglomerated by heat exchange and partial fusion that are driven by suction of hot gas through the packed bed of moist granules. The pressure drop over green granules has been used to predict the rate at which the sinter process progresses and the productivity (performance) of the sinter plant. It is well known that granule beds with low pressure drop provide more stable operation and good controllability of the sintering process [1], [2], [3], [4]. In practice, the pressure drop across green granules is generally measured in Japanese Permeability Unit (JPU), and expressed by the relation [5]:where F, A, L and ΔP are flow-rate of gas in m3/min, cross sectional area of the bed in m2, height of the bed in m and pressure drop expressed in mm H2O.
The measurement of the pressure drop through green granules before ignition is carried out experimentally. This technique has remained an “empirical art” in most sinter plants, due to the complexity of the mixtures consisting of moist deformable granules of randomly distributed irregular shapes, structures and sizes. These parameters were known to significantly affect the void fraction, angle of repose and permeability of packed beds [3], [6], [7], [8], [9], [10], [11], [12], [13]. Zhou et al. [14] studied the pressure drop across a sinter bed during a pilot – scale – sintering process. CFD simulations were performed based on the reconstructed real geometry of sinter cakes by X-ray micro-tomography. For simplicity, a sample of 30 * 30 * 30 mm3 was excavated from the sintered zone in the centre region of the sinter cake, where the melt is supposed to solidify and no changes in structure occur. To obtain reliable values of the pressure drop (permeability), it was appropriate to simulate a large size of the sinter cake, which could unfortunately result in huge computational costs. Mitterlehner et al. [15] predicted the fluid flow through a granulated material using the Ergun equation, and adjusting the Ergun constants using the least square fit method. Very good agreement was obtained between the measured and calculated pressure drops.
Coupling of the Discrete Element Method (DEM) with Computational Fluid Dynamics (CFD) has been extensively used in the prediction of flow characteristics through packed beds [16], [17], [18]. Eppinger et al. [18] developed a numerical model of fixed bed reactors with small tube to particle diameter ratios. DEM-code was used to simulate the packing in a fixed bed consisting of randomly packed spherical particles. The fluid domain was meshed and solved with the commercial CFD-code STAR-CCM+. The predicted porosity and pressure drop was in agreement with measured data in the literature. Bai et al. [17] developed a DEM-CFD model for the simulation of the flow field and pressure drop in fixed bed reactors with randomly packed catalyst particles. The predicted pressure drop compared satisfactorily with the experimental measurements with errors of less than 10%, which is acceptable for industrial packed bed reactors [16], [17].
The prediction of the pressure drop through packed beds is significantly affected by the structure of the bed, which in turn is dependent on the particle size distribution and shape and interactions between particles [10], [19], [20], [21], [22], [23]. The difference in particle size can lead to size segregation through the percolation mechanism whereby fines can sift through the voids of larger particles [19]. A narrower particle size distribution results in looser packing than when wider size distributions are used. Particle shape also plays a major role in packing density [24], [25], [26]. Increasing angularity increases the flow resistance of particles and increases the fluid flow across the packing. Spherical shapes are simple to implement in 3D modelling and fast computationally. However, the spheres cannot reproduce the particle interactions that are observed in real-world particles. Spheres roll continuously and have lower shear resistances and lower friction coefficients than those of irregular and non-spherical particles [21], [27], [28], [29].
This paper describes a study on the applicability of using a DEM-CFD coupling model to calculate the pressure drop across a green bed of granules. The design of the packing was simulated using the discrete element method (DEM), in which the effects of the size distribution, shape and adhesion force of moist granules were considered. A multiphase flow model was used to simulate the gas flow through the simulated granule bed. Pressure drop predictions were compared against measured experimental data for granulated mixtures that contained 0–40% concentrate or micropellets respectively. Concentrate is a fine hematite-based (90.3% Fe2O3) iron ore, which is produced through the beneficiation of low-grade iron ore using crushing, milling and dense media separation to upgrade the ore. It has a particle size of less than 0.1 mm. The micropellets (1–4.75 mm in diameter) were produced from concentrate by rolling moist concentrate together with binders, on an inclined disc pelletiser. With the depletion of high-grade lump iron ore, concentrate and micropellets have been identified as alternative raw materials for sintermaking.
Section snippets
DEM – CFD model
The pressure drop across complex packed beds can be simulated by using a coupled DEM-CFD model. The discrete element method is used to simulate the filling process of a column with particles [30]. The motion of a rigid particle is computed by numerically solving the Newton equations for translational and rotational motion (Eqs. (2) and (3)). Computational fluid dynamics has proven to be an alternative to empirical and experimental methods to compute the pressure drop through packed beds [31],
Glass beads
Glass beads with diameters of 3 and 6 mm (Promak Chemicals) were used in this study to validate the coupled DEM-CFD model. The diameter of 30 beads of each group was measured with a digital calliper and their average diameters were calculated. The bulk densities of the glass beads were measured by randomly filling a cylindrical flask (60 mm diameter) with a specific mass of glass beads and measuring the volume. The properties of the glass beads are listed in Table 2.
Raw materials used
Three types of mixtures were
Dynamic properties of glass beads and granulated mixtures
The application of the DEM – CFD model requires the measurement of the dynamic properties of particles (Static friction coefficient, restitution coefficient, Young’s modulus and adhesion force). While there are numerous theoretical and numerical studies on mechanical behaviour of glass beads, only few studies on the behaviour of iron ore granules (agglomerates) are reported in the open literature [22], [23]. These granules are wet, sticky, deformable and heterogeneous, and can easily
Effect of concentrate and micropellet addition on bed permeability
The addition of concentrate or micropellets to the conventional mixture caused a decrease in the bed permeability as the volume fraction of concentrate or micropellets increased (Fig. 9). The presence of concentrate or micropellets resulted in the formation of additional granule structures: Concentrate addition produced granules of Groups I and II, which can potentially deform once packed in a column [52], [54]. This resulted in formation of compact beds with low permeability. The addition of
Conclusions
Experimental measurements and coupled DEM – CFD simulations of pressure drops across beds of iron ore granules were investigated in this study. Based on the experimental results, four structures of iron ore granules were identified. Granules of Group I were formed through adhering of fines around coarse particles. With addition of concentrate, the coalescence of fine material formed granules with pellet-like structure (Group II). The addition of micropellets resulted in the formation of two
Acknowledgements
The authors are grateful to Anglo American Value-in-Use for both financial and technical support, as well as to Dr. Danie de Kock from QfinSoft for technical support.
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