| Resumo: |
Gas-solid fluidized bed reactors are widely applied in chemical and energy industries, and their design and scale-up are virtually empirical, extremely expensive and time consuming. This scenario has motivated the development of alternative theoretical tools, and two-fluid modeling, where gas and particulate are both treated as interpenetrating continuum phases, has appeared as a most promising approach. Owing to the large domains to be resolved in real-scale fluidized bed reactors, only filtered modeling approaches are feasible, and closure models become necessary to recover sub-grid effects that are filtered by the very coarse numerical grids that are imposed owing to computational limitations. Those closure models, which in hydrodynamic formulations account for filtered interphase momentum exchanges and filtered and residual stresses in the phases, can be derived from results of highly resolved simulations (HRS) performed over small size domains under refined numerical grids. One widely practiced approach consists of applying two-fluid modeling under micro-scale defined closures, generally known as microscopic two-fluid modeling. This approach includes microscopic closures for solid phase stresses derived from the kinetic theory of granular flows (KTGF), which accounts for kinetic-collisional effects only, and is adequate to dilute flows. Otherwise, the conventional KTGF does not account for interparticle friction effects, and its application to dense flow conditions is quite questionable. In this work a literature available modified version of KTGF is applied which also accounts for interparticle friction, and highly resolved simulations are performed for dense flow conditions in order to evaluate the effects of friction over relevant filtered parameters (namely effective drag coefficient, filtered and residual stresses). Ranges of domain average solid volume fractions and gas Reynolds numbers are considered (macro-scale conditions) embracing dense gas-solid fluidized flows from suspensions up to pneumatic transport. The MFIX open source code is used in all the simulations, which are performed over 2D periodical domains for a unique monodisperse particulate. The HRS results (i.e. meso-scale flow fields) are filtered over regions compatible with grid sizes in large scale simulations, and the relevant filtered parameters of concern are derived and classified by ranges of other filtered parameters taken as independent variables (filtered solid volume fraction, filtered slip velocity, and filtered kinetic energy of solid velocity fluctuations, which are referred to as markers). Results show that the relevant filtered parameters of concern are well correlated to all of those filtered markers, and also to all of the imposed macro-scale conditions. Otherwise, interparticle friction showed no significant effects over any filtered parameter. It is recognized that this issue clearly requires further investigation notably regarding the suitability of the markers that were assumed for classifying the filtered results. The current work is intended as a contribution for future developments of more accurate closure models for large scale simulations of gas-solid fluidized flows. |
|---|
