(647e) A Cascading Approach to Develop a Filtered Drag Force Model for Large-Scale Gas-Particle Flows

Gas-particle flows in fluidized beds are inherently unstable with multiscale structures. These systems can be studied with Two-Fluid Model (TFM) which solves continuum equations of motion for both fluid and particle phases. When a small mesh size up to a few particle diameters is used, TFM can resolve the fine multiscale structures such as bubbles and clusters fairly accurately. However, simulations with small mesh grid size become prohibitively expensive for larger scale systems, leading to the development of filtered Two-fluid model (fTFM). fTFM requires accurate filtered drag model to account for the significant sub-grid contribution to homogeneous drag force, which originates from inhomogenieties within the filtering volume^1-4.

Recently we have developed a neural-network-based filtered drag model from a dense fluidized bed case⁵. Compared to previous modeling attempts for filtered drag force model, we included an additional marker, gas-phase pressure gradient, which is identified through theoretical derivation and budget analysis. Validation tests through a priori analysis show high prediction accuracy, and a posteriori analysis with coarse grid size up to 27dp show good agreement between fine- and coarse-grid simulations. In the present study, we further investigate how this neural-network-based filtered drag model can be improved by incorporating filter size and Froude number, to make this model more generally applicable, and efficient for fTFM simulations.

Most industrial devices are very large and grid sizes used to simulate flows in these units are invariably much larger than the range considered in our neural-network based filtered drag model. In fact, most computationally developed coarse models are based on rather small fine grid simulations, and they essentially extrapolate filter size effect to these larger systems, whose accuracy is not established. In the present study, we set out to examine how drag correction changes with filter size for larger filter sizes. We approach this problem through cascading, where one performs one or more additional rounds of filtering of the fTFM. Cascading also allows us to examine how the dominant physics changes with scale.

Briefly, the fine-grid simulations are first used to develop the closures for an fTFM. This fTFM is then solved with coarser grids, whose size is in the range of the first round of filtering, to generate computational data which is further filtered to get drag corrections which are now valid for even larger filter sizes. This procedure is repeated until we reach a mesh grid size of desired level of coarsening for most large industrial systems. We first validate this approach rigorously and then examine how drag correction changes with filter size for large filter sizes.

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

[2] Igci, Y., Andrews, A. T., Sundaresan, S., Pannala, S., & O'Brien, T. (2008). Filtered two‐fluid models for fluidized gas‐particle suspensions. AIChE Journal, 54(6), 1431-1448.

[3] Ozel, A., Fede, P., & Simonin, O. (2013). Development of filtered Euler–Euler two-phase model for circulating fluidised bed: high resolution simulation, formulation and a priori analyses. International Journal of Multiphase Flow, 55, 43-63.

[4] Parmentier, J., Simonin O., & Delsart,O. (2012) A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed." AIChE Journal 58.4: 1084-1098.

[5] Jiang, Y., Kolehmainen, J., Gu, Y., Kevrekidis, Y. G., Ozel, A., Sundaresan, S. (2019) Neural-network-based filtered drag model for gas-particle flows. Powder Technology, 346, 403-413