A dynamic Spatially-averaged Two-fluid Model for heat transfer in gas-solid flows
Sprache des Vortragstitels:
14th International Conference on Computational Fluid Dynamics In the Oil & Gas, Metallurgical and Process Industries
Sprache des Tagungstitel:
In gas-solid flows meso-scale particle clusters are forming due to the momentum coupling between the two phases in the presence of a mean body force, such as gravity. In simulations of full-scale gas-particle reactors, such as fluidized beds or risers, coarse numerical grids are employed in order to reduce computational resources. These coarse grids do not resolve the heterogeneous mesoscale structures, which can be only a few particle diameters wide. These have, however, a significant influence on the macroscopic flow properties. The interphase heat transfer and the drag force, for example, are severely overestimated if the unresolved mesoscale structures are not accounted for. In particular, the velocity fluctuations around particle clusters give rise to turbulence, i.e. cluster induced turbulence. We derive a model accounting for the unresolved terms by spatially-averaging the kinetic theory based two-fluid model equations including a thermal energy balance equation.
The effective heat transfer coefficient divided by the solid volume fraction is approximated by its zeroth order Taylor series expansion about the filtered variables. This gives rise to a construct similar to the drift velocity. This drift temperature is a measure for the sub-filter heterogeneity. It represents the gas-phase temperature fluctuations seen by the particles and can be expressed as a correlation between the solid volume fraction variations and the gas-phase temperature fluctuations, i.e. the turbulent internal energy. Therefore, we derived transport equations for the turbulent internal energies of the phases. In addition, we employ a dynamic adjustment of the correlation coefficients by using test-filters in coarse-grid simulations.
The developed closure models show good agreement with the predictions obtained by filtering fine-grid, two-fluid model simulation data. Finally, we performed an a posteriori verification of the developed models, which lead to satisfying results.