Numerical simulation of the gas–solid flow in a bed with lateral gas blasting
Introduction
When gas is laterally blasted into a packed bed, the gas–solid flow shows varying behaviour with the gas velocity. As the gas velocity is increased above a certain value, a void or cavity forms in front of the gas inlet. In blast furnaces, such cavities are called raceways to represent the internal circulating flow of particles [1]. If the gas velocity is further increased above another critical value, then a stable cavity no longer exists, the gas escapes from the packed bed in the form of bubbles, or slugs along the wall where the jet is situated and fluidisation results [2]. In either case, two zones can be identified: a stagnant zone in which particles remain static, and a mobile zone in which particles move in a complex manner.
In modern blast furnaces, most of the coke and injected supplementary fuels are burnt in raceways to provide heat and reducing gases for the smelting process. The size and shape of the raceway are therefore important in distributing these gases and enthalpy to the lower zone of the furnace. Furthermore, these distributions are time-dependent and can be affected by factors such as instability of the raceway boundary and generation of fines among others. For these reasons, raceway phenomena have been extensively studied in the past, as reviewed by Burgess [3]. Although progress has been made to predict the raceway size and shape under various conditions 4, 5, so far there is no predictive model in the literature which considers the transient behaviour of the raceway and various forces acting on individual particles which play an important role in generating fines. As a result, blast furnace models have to be based on simplified raceway geometry and voidage distribution around and within the raceway 4, 6, 7.
In process industries, a moving bed with gas cross-flow is well suited for the continuous catalyst regeneration without removal of the solids from a process. The deactivated catalyst is withdrawn from the reactor and moves through the bed; the reaction gas is blown across the bed through porous walls which are only permeable for the gas to promote reactivation; the reactivated catalyst then feeds back to the reactor. To ensure a continuous operation, it is important to find the critical gas flow rate above which the frictional forces between solids and downstream wall may be strong enough to prevent the bed from moving, giving the so-called “pinning” phenomenon as described by Pilcher and Bridgwater [8]. An attempt has been made by Doyle et al. [9]to model this abnormal solid flow, where the assembly of particles is treated as a continuum porous medium to gas, with an arbitrarily assumed stress distribution within solids. Although comparable with the experiments, the results are very sensitive to the assumptions. Therefore the stress distribution in the assembly of particles is a key factor to predict this upper bound on the flow of reaction gas.
In fact, pinning and cavity formation are two closely related phenomena 8, 9, as are raceway and fluidisation 4, 5. The common feature of these phenomena is the strong gas–solid and solid–solid interactions. These interactions are realised at the individual particle level through a complicated network to transmit various forces among particles and between particles and walls, generating a rich scenario of gas–solid flow patterns in a bed. This warrants a combined approach of Discrete Particle Method and Computational Fluid Dynamics (DPM-CFD) or more generally, a Combined Continuum and Discrete Model (CCDM) to describe the gas–solid flow at such a level [10]. In the past few years, this technique has been applied to model the gas–solid flow in a fluidised bed where its capacity in handling the discrete particle motion has been demonstrated 10, 11, 12, 13.
This paper presents an attempt to apply the CCDM to study the strong localised discrete particle motion in a packed bed caused by lateral gas blasting. It shows that depending on the gas velocity, both raceway and fluidisation can form realistically in the simulations. The results confirm that raceway and fluidisation are two manifestations of gas–solid and solid–solid interactions in a packed bed.
Section snippets
Combined continuum and discrete model
The model development has been published in our previous papers 10, 14, where the detailed discussion about the discrete and continuum models, and their coupling as well can be found. In the following sections, the model is briefly described for the purpose of completeness.
Solution schemes
The explicit time integration method is used to solve the translational and rotational motions of a system of discrete particles in the discrete model [15]. The conventional SIMPLE method [17]is used to solve the equations for the fluid phase in the continuum model. The governing equations are discretized in finite volume form on a uniform, staggered grid. The second-order central difference scheme is used for the pressure gradient and divergence terms. The first-order upwind scheme is used for
Pressure drop vs. gas velocity
As a first step towards a comprehensive understanding of the gas–solid flow by lateral gas blasting, the present work is concerned with one major independent variable, i.e., the gas velocity. To explore its effect on the gas–solid flow behaviour, in total 21 runs of simulation have been carried out, corresponding to the cases with an increasing or decreasing gas velocity. The cases corresponding to increasing gas velocity are simulated under the same boundary and initial conditions outlined in
Conclusions
The gas–solid flow in a bed with lateral gas blasting has been simulated by the Combined Continuum and Discrete Model (CCDM). The results show that depending on the gas velocity, the bed can transform from a fixed bed to a fluidised bed or vice versa via a raceway region, with a pronounced hysteretic effect reflected in either the pressure drop-velocity relationship or raceway size. It is confirmed that the raceway and fluidisation are two manifestations of gas–solid flow in a packed bed and
Nomenclature
cd0 fluid drag coefficient on an isolated particle, dimensionless f force, N ff0 fluid drag force on an isolated particle, N F volumetric fluid–particle interaction force, N m−3 g gravitational acceleration, m s−2 I moment of inertia of particle, kg m2 kc number of particles in a computational cell, dimensionless ki number of particles in contact with particle i, dimensionless m particle mass, kg p pressure, Pa Δp bed pressure drop, Pa Δp̄ mean bed pressure drop, Pa r particle position vector, m R particle radius, m Re
Acknowledgements
The authors are grateful to Australian Research Council (ARC) and BHP for the financial support and High Performance Computing Support Unit of the University of New South Wales for the time allocation in HP Convex machine.
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