Gas-particle flows in fluidized and circulating fluidized beds are inherently unstable, and they manifest fluctuations in velocities and local suspension density over a wide range of length and time scales. In riser flows, these fluctuations are associated with the random motion of the individual particles (typically characterized through the granular temperature) and with the chaotic motion of particle clusters, which are repeatedly formed and broken apart. The two-fluid model equations are able to capture these clusters in a robust manner; however, to resolve the clusters at all length scales, extremely fine spatial grids are necessary [1]. Due to computing limitations, the grid size used in simulating industrial scale gas-particle flows is invariably much larger than the length scales of the finer particle clusters. Such coarse-grid simulations for industrial scale gas-particle flows will clearly not resolve the structures which exist on sub-grid length scales; however, these small-scale unresolved structures affect the resolved flow characteristics. We pursue a filtered equations approach in which the influence of the small scale structures appears as residual correlations for which constitutive models should be constructed. If constructed properly, the filtered equations should produce a solution with the same macroscopic features as the finely resolved kinetic theory model results; however, as the filtered equations place less stringent requirements on the grid resolution than the original two-fluid model equations, they would be easier to solve.

In a recent study [2], we extracted closures for the filtered two-fluid models by filtering the statistical “data” generated through highly resolved MFIX simulations in large periodic domains – employing a kinetic theory based two-fluid model with Wen & Yu drag for uniformly sized particles [3,4]. We found that both the filtered drag coefficient decreased systematically with increasing filter width, whereas the particle-phase stresses increased with increasing filter width.

The objectives of the present study are two-fold:

(a) What boundary conditions should be used with the filtered equations at bounding walls?

(b) How do the solutions of filtered model equations compare with those of the kinetic theory based model which were used to generate the closures for the filtered equations?

We have completed several 2-D simulations with different boundary conditions at the vertical walls and have found that as filter size increases, the boundary conditions which should be employed with filtered equations approach free slip conditions for both phases.

In order to evaluate the filtered two-fluid models, we have run a number of simulations of the filtered two-fluid models and compared the results predicted by such simulations with those from finely resolved simulations of the kinetic theory based two-fluid model. Through these comparisons, we assess the filtered two-fluid and bring forth their strengths and weaknesses.

The details of these results will be described in the presentation.

References:

[1] Agrawal, K., Loezos, P. N., Syamlal, M. & Sundaresan, S. 2001 The role of meso-scale structures in rapid gas-solid flows. J. Fluid Mech. 445, 151 – 185.

[2] Igci Yesim, Andrews, A.T. IV, Sundaresan S., Pannala S. & O'Brien T. 2008 Filtered two-fluid models for fluidized gas particle suspensions. AIChE J. 54, 1431-1448.

[3] Gidaspow, D., 1994 Multiphase Flow and Fluidization, Academic Press, CA. 31-58, 197 – 238.

[4] Syamlal, M., Rogers, W. & O'Brien, T. J., 1993 MFIX Documentation, U.S. Department of Energy, Federal Energy Technology Center, Morgantown, WV.