(137c) Three-Dimensional Computational Fluid Dynamic Study of a Gas-Solid Riser Based On the Kinetic Theory of Granular Flow

Fluidized beds are widely used in many operations in chemical, metallurgical, energy generation and especially petrochemical industries. Major applications are fluid catalytic cracking (FCC) risers and CFB combustor systems. Although fluidized beds are successfully and widely used in commercial industrial operations, much remains to be done due to the complexity of the gas-solid flow. No analytical tools that describe the influences of complex geometries, chemical reaction, internal reflux and heat transfer on the flow pattern in fluidized beds are available. With the increased availability of computers, mathematical models have been applied to predict the behavior of a fluidized bed and several models have been proposed. Gidaspow et al. (2004) carried out an extensive review of the models developed for the fluidized bed reactors and Peirano and Leckner (1998) reviewed turbulent gas-solid flow modeling in circulating fluidized beds.

Gas-particle two-fluid models, which treated the particle phase as a continuous fluid based on the Eulerian method, were widely employed in modeling gas-solid flow in the past several decades. A fundamental problem encountered in modeling the hydrodynamics of a gas-solid fluidized bed by the two-fluid method is how to include the stress of the particle phase in the particulate momentum equation. In the more recent two-fluid models, for the particle phase in dense gas-particle flow, the kinetic theory of granular flow has received attention and its use in Eulerian simulations has increased (Jenkins and Savage, 1983; Ding and Gidaspow, 1990; Gidaspow, 1994; Hrenya and Sinclair, 1997; Samuelsberg and Hjertager, 1996; Mathiesen et al., 2000). The kinetic theory of granular flow is based on the kinetic theory of gases, first developed by Chapman and Cowling (1970). In this theory, the inter particle interactions are taken into account by adding the contribution of collisions between particles (Jenkins and Savage, 1983), which are the main mechanism of transport due to particulate phase properties. The kinetic theory of granular flow is able to predict core-annulus flows in CFBs, an experimentally well-established flow regime described in the literature (Gidaspow, 1994). However, several model features in predicting core-annulus flows, as boundary conditions and model parameters, are not well understood, as investigated by Benyahia and O'Brien (2007). The appropriated boundary condition for the solids velocity must be a partial slip condition, between free slip and no slip conditions.

The present study aims to simulate a transient three-dimensional two-phase flow model, based on the kinetic theory of granular flow (KTGF), to predict the behavior of a gas-solid fluidized bed, using a computational fluid dynamics technique. The model is based on an Eulerian description of the two phases, gas and particles, and is composed of a set of mass conservation and momentum equations for each phase. In this model, the k-epsilon turbulence model and multiphase mixture are used. In order to describe the behavior of several particles in a continuum, the kinetic theory of granular flow was used. The conservation equations for the solid phase are based on the kinetic theory for granular flow (Gidaspow, 1994). As wall boundary conditions for the solid phase, it was used the Johnson and Jackson (1987) slip boundary condition, expressed in terms of a specularity coefficient.

In order to validate the present numerical results, we compared them with the experimental results of Samuelsberg and Hjertager (1996). The simulations were carried out for the riser section of a circulating fluidized bed similar to that used by Samuelsberg and Hjertager (1996) and Mathiesen et al. (2000). In this study, just the riser section was simulated. The riser section is 1m high with an inner diameter of d = 0.032m. A secondary air supplier, positioned 0.05m above the gas inlet, feeds the solid back into the riser. The secondary gas inlet and the gas outlet have a diameter of 0.008m. The initial bed height is 0.05m and the initial solid volume fraction is 0.61.

The riser section is modeled and simulated in a three-dimensional Cartesian coordinate system. Numerical predictions were obtained using the finite volume approach through the FLUENT code, a CFD software by ANSYS, and the ICEM CFD code to generate the numerical grid. Numerical tests were conducted in order to optimize the computational grid. A grid of approximately 300,000 control volumes was considered satisfactory considering the precision of the results (10-4) and the computation time consumed. The time step used in all simulations was 10-5s.

At the primary gas inlet, the superficial gas velocity, Vsup, was 1.42m/s. At the secondary gas inlet, the gas velocity and volume fraction were 0.05m/s and 0.6, respectively, and the particle volume fraction was 0.4. A constant solids flux at the secondary gas inlet was 0.01 Kg/s. At the outlet, atmospheric pressure was prescribed. At the walls, no-slip conditions were used for the gas phase. The simulation results were computed through time-averaged distribution of flow variables. All the simulations were run for 15 s of real time.

The experimental results of Samuelsberg and Hjertager (1996) and the present numerical results to the solid radial velocity profiles in the riser section were compared. These demonstrated that the mathematical modeling of this problem was adequate, especially to the solid phase. The profiles were in good agreement with the experimental points, also the near wall region, which is known to be a challenging aspect of CFD simulations.