(701f) Spatially-Averaged Two-Fluid Models for Heat and Mass Transfer

Clusters are observed to form in gas-particle flows in the presence of a mean body force, such as gravity. Simulations on coarse grids are commonly used to predict the macroscale flow properties of moderately dense gas-particle flows such as full-scale fluidized beds or risers. However, often these grids are too coarse to resolve the mesoscale particle clusters, which can only be a few particle diameters wide [1]. As was shown in many previous studies, the influence of these mesoscale structures on the macroscale flow properties is important, i.e. the bed expansion is severely overestimated if drag models derived for homogeneous suspensions are applied [2]. Therefore, various studies focused on deriving models for the drag reduction. Our approach, for example, is based on spatial averaging, which allows us to model the unresolved contributions in coarse grid simulations [3,4]. However, although various works focused on the drag-force correction, a significantly smaller number discusses heat and mass transfer corrections [5], which are also needed in order to correctly predict the thermodynamics and reactions in coarse-grid simulations.

Previously, we conducted an a priori study on the influence of the particle clusters on the interphase heat transfer [6]. We showed that the resolved transfer can be corrected by a construct similar to the drift velocity [7], which we called drift temperature. This drift temperature is essentially the gas-phase temperature fluctuations as seen by the particles. We expressed it as a function of the variance of the gas-phase temperature and the variance of the solid volume fraction scaled by linear correlation coefficients and derived transport equations for these variances. Furthermore, our a priori analysis showed, that the correlation coefficients can be determined locally and dynamically in coarse grid simulations through the application of test-filters [8].

In a consecutive a posteriori study, we considered different test cases of lab-scale fluidized beds as well as unbound fluidization and validated the previously derived models for momentum and heat transfer. Therefore, we implemented the derived SATFM turbulence models in a modified solver based on the OpenFoam [9] solver twoPhaseEulerFoam [10]. We observed, that the overall heat transfer is overestimated in coarse grid simulations, similar to the overprediction of the drag force. The corrections based on our spatially-averaged approach are in good agreement with the measurements of the interphase heat transfer based on fine-grid simulations of the same cases (see Figure 1).
Furthermore, we expanded this approach to mass transfer, where, as a first step, we again conducted an a priori study and found that a similar drift scalar approach can be used.

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] Schneiderbauer, S., Pirker, S., 2014. Filtered and heterogeneity based subgrid modifications for gas-solid drag and solids stresses in bubbling fluidized beds. AIChE J. 60(3), 839–854.
[3] Schneiderbauer, S., 2017. A Spatially-Averaged Two-Fluid Model for Dense Large-Scale Gas-Solid Flows. AIChE J. 63 (8), 3544–3562.
[4] Rauchenzauner S., Schneiderbauer S., 2020. A dynamic Anisotropic Spatially-Averaged Two-Fluid Model for moderately dense gas-particle flows, IJMF 126, 103237.
[5] Sundaresan S., Ozel A., Kolehmainen J., 2018. Toward Constitutive Models for Momentum, Species, and Energy Transport in Gas–Particle Flows, Annu. Rev. Chem. Biomol. Eng. 9 (1), 61–81.
[6] Rauchenzauner S., Schneiderbauer S., 2020. A dynamic Spatially Averaged Two-Fluid Model for heat transport in moderately dense gas–particle flows. Physics of Fluids 32, 063307.
[7] Parmentier, J.-F., Simonin, O., Delsart, O., 2012. A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed. AIChE J. 58 (4), 1084– 1098.
[8] Lilly, D. K., 1992. A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.
[9] OpenFoam v6 User Guide, The OpenFOAM Foundation, https://cfd.direct/openfoam/user-guide-v6
[10] twoPhaseEulerTurbFoam is available on github, https://github.com/ParticulateFlow/pfmFOAM-public