(133g) Sub-Grid Deconvolution Approach for Filtered Two-Fluid Models and the Application to Fluidized Beds

Highly resolved two-fluid model (TFM) simulations of gas-solid flows in vertical periodic channels have been performed to study closures for the filtered drag force and the Reynolds-stress-like contribution stemming from the convective terms. An approximate deconvolution model (ADM, [1]–[3]) for the large-eddy simulation of turbulent gas-solid suspensions is detailed and subsequently used to reconstruct those unresolved contributions in an a priori manner. With such an approach, an approximation of the unfiltered solution is obtained by repeated filtering allowing the determination of the unclosed terms of the filtered equations directly. A priori filtering shows that predictions of the ADM model yield fairly good agreement with the fine grid TFM simulations for various filter sizes and different particle sizes. In particular, strong positive correlation (ρ > 0.98) is observed at intermediate filter sizes for all sub-grid terms, even though the filtered drag force has been approximated by drift velocity correction ([1], [4]).

This ADM-TFM approach is implemented in an a-posteriori manner for the coarse grid simulation of a fluidized bed of Geldart type B particles and is verified against highly-resolved TFM simulations. Furthermore, different regularization methods, which account for the sub-filter scale (SFS) contribution, are presented and discussed with respect to their predictiveness and stability. It is shown that employing an appropriate rheological model for the solid phase considerably improves stability without removing too much energy from the resolved scales. The ADM-TFM predictions are in fairly good agreement with the fine grid reference case and do not show a notable grid-dependency. Compared to TFM simulations using the same grid resolution, the ADM-TFM approach does only require marginally more computational resources [5].Finally, the application to the coarse-grid simulation of large-scale fluidized beds is discussed.

References:

[1] S. Schneiderbauer and M. Saeedipour, “Approximate deconvolution model for the simulation of turbulent gas-solid flows: An a-priori analysis,” Phys. Fluids, vol. 30, no. 2, p. 023301, 2018.

[2] S. Vincent, M. Tavares, S. Fleau, S. Mimouni, M. Ould-rouiss, and J. Estivalezes, “A priori filtering and LES modeling of turbulent two-phase flows application to phase separation,” Comput. Fluids, vol. 176, pp. 245–259, 2018.

[3] S. Stolz and N. A. Adams, “An approximate deconvolution procedure for large eddy simulation.,” Phys. Fluids., vol. 11, no. 7, pp. 1699–1701, 1999.

[4] A. Ozel, Y. Gu, C. C. Milioli, J. Kolehmainen, and S. Sundaresan, “Towards fitered drag force model for non-cohesive and cohesive particle-gas flows,” Phys. Fluids, vol. 29, no. October, p. 103308, 2017.

[5] S. Schneiderbauer and M. Saeedipour, “Numerical simulation of turbulent gas-solid flow using an approximate deconvolution model,” Int. J. Multiph. Flow, vol. 114, pp. 287–302, 2019.