Granular dynamics simulation of cluster formation in dense riser flow

The occurrence of clusters is one of the most characteristic features of dense gas-solid flow in the riser section of a
Circulating Fluidized Bed (CFB). The existence of such clusters has a profound influence on the performance of a
CFB unit as a chemical reactor. It is therefore of great importance to gain more insight into this phenomenon.
Although the existence of clusters (regions of locally higher solid fraction) in dense riser flow is well accepted in the
chemical engineering community, a clear definition is still lacking (Chen, 1995). Clusters were observed
experimentally by (among many others) Horio and Kuroki (1994) using a laser sheet technique. They found that the
clusters had a characteristic parabolic shape. Tsuo and Gidaspow (1990) used a Two-Fluid approach with constant
solids viscosity in order to simulate the riser section of a CFB. They reported the formation of cluster-like structures
as well as the typical core-annulus flow structure where the average solids concentration is considerably higher near
the wall. Other Two-Fluid approaches incorporating the kinetic theory of granular flow (Sinclair and Jackson
(1990), Nieuwland et al. (1996)) did not focus particularly on cluster formation but more on the radial segregation
of solids. This type of model possesses a peculiar dependency on the magnitude of the coefficient of restitution
where a small deviation from unity causes the flow structure to change completely while the agreement with
experimental findings deteriorates. This was (among others) pointed out by Hrenya and Sinclair (1997) who also
reported that when particle phase turbulence was included this dependency became far less pronounced. Tanaka et
al. (1996) performed simulations of gas-solid flow in a vertical duct using the Lagrangian approach for the solid
particles. They employed the Direct Simulation Monte Carlo (DSMC) method to describe the particle dynamics. In
this DSMC method the simulated particles actually represent a certain number of ‘real‘ particles. A Monte Carlo
procedure is invoked to determine the collision partners and the geometry of the collision. Hence this method does
not account for actual particle-particle and particle-wall interaction in a direct way. Moreover the modified Nanbu
method used in their work does not guarantee exact conservation of energy (Frezzotti, 1997) which can be an
important drawback especially since the collision parameters turned out to be of key importance in their simulations.
In this paper we present an extension of our Eulerian Lagrangian simulation technique (Hoomans et al. (1996)) for
dense gas-solid two-phase flow in a riser which features a direct incorporation of the particle-particle and particlewall
interaction.