BIRS Workshop Lecture Videos
Kinetic Theory of Granular Flows & Multiscale CFD Modeling of Fluidized Beds Mills, Patrick
Talk: Keynote Abstract: Fluidized bed reactors are widely used in the chemical processing, petroleum refining, power generation, specialty materials and waste conversion industries for carrying out gas-solids catalyzed and gas-solid non-catalytic reactions. However, fluidized beds also present outstanding challenges in understanding the gas-solids mixing, contacting patterns, gas-particle and particle-particle interactions as well as the combined effects of these phenomena on gas-phase homogeneous and gas-solid heterogeneous reactions. Computational fluid dynamics (CFD) has emerged as an approach for more rational design and scale-up of fluidized bed reactors. However, CFD models require parameters based upon phenomenological models. Two types of simulation methods, i.e., Eulerian-Eulerian and Eulerian-Lagrangian, are described in this presentation. For the Eulerian method (also called two-fluid model, or TFM), in which the discrete solid particles are assumed as a continuous granular phase interpenetrated with the gas, constitutive models are needed for closure of the solids phase stress tensor. The most commonly used models are derived from the kinetic theory for granular flow (KTGF), (e.g., Jenkins and Savage, 1983; Lun et al., 1984; Gidaspow, 1994). These models assume that during an inelastic collision, only the normal component of the relative velocity is decreased, while the tangential component remains unaltered due to the assumption of smooth particles. Here, it is assumed that the velocity magnitude that is dampened is due to an inelastic collision between two smooth or nearly smooth particles, rather than just the normal velocity component. Based on this assumption, new phenomenological models arise for solids pressure, shearing and bulk viscosity, thermal conductivity, and most importantly for the dissipation rate, which is found to be almost twice as large as the original one. The proposed models reduce to those for dense gases (Chapman and Cowling, 1970) when the coefficient of restitution e is equal to one, as does Gidaspow (1994). The stress tensor now becomes asymmetric without the need to assume a different restitution coefficient in the tangential direction, and to add transport equations for angular velocity and rotational fluctuation energy, as indicated by Lun and Savage (1987) and Lun (1991). Therefore, the proposed models predict less underestimated dissipation rate without extra complexity. The models are implemented in OpenFOAM to simulate a fluidized bed. These show that the new collision model provides an improved the prediction of the solids volume fraction without extra computational cost. In the Lagrangian or DEM (discrete element method) approach, the effort is motivated by Bhusarapu’s (2005) pioneering finding using CARPT (computer-aided radioactive particle tracking) that the traditional tracer method for measuring solids residence time distribution (RTD) cannot capture the actual residence time due to inability to distinguish the time that a particle temporarily spends out of the riser after first entry to or before last exit from the riser. By implementing the algorithm developed in this work to record separately the time that each particle actually spends in the riser, Lagrangian simulation is performed for a small circulating fluidized bed in OpenFOAM. The results clearly demonstrate the difference between RTD obtained from simulated traditional tracer method and that from the Lagrangian approach. Other information can be extracted as well such as the first passage time distribution, macromixing index, and interchange coefficient between a core region and an annular region, if a core-annulus model is used. Opportunities for other advancements by including other multiphysics will also be summarized.
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