(224a) Spatially-Averaged Models for Heat Transfer in Gas-Solid Flows

Gas-solid flows, like fluidised beds or risers, are used in industry for a wide range of applications, from food drying and polymer production to the direct reduction of iron ore. While for small scale fluidised beds, simulation is quite feasible, the occurring physical phenomena cannot be fully numerically analysed in large scale reactors yet, due to a large range of involved scales. In fluidised bed reactors of several meters, the smallest stable structures are usually only several particle diameters wide [1]. Thus, the microscopic behaviour of individual particles, i.e. gas-solid drag, intraphase and interphase heat transfer between the particles and the gas as well as collisions cannot be fully resolved due to computational limitations. However, the unresolved heterogeneous structures have a significant influence on the flow properties. The velocity fluctuations around particle clusters give rise to turbulence, i.e. cluster induced turbulence [6, 7]. An overestimation of the gas-solid drag force by not accounting for this turbulence leads to an overestimation of the bed expansion [5].

A model accounting for the unresolved terms can be derived by spatially averaging the kinetic theory based two-fluid model equations [4]. The filtered gas-solid drag can be, for example, approximated by the filtered drag coefficient times the filtered slip velocity corrected by a drift velocity [2, 3]. The drift velocity can be seen as the gas-phase velocity fluctuations seen by the particles. Additionally, it is also shown in [3] that the filtered drag force depends on the turbulent kinetic energies of both phases, as well as strongly on bulk density fluctuations. Closures for the turbulent kinetic energies and the bulk density fluctuations are derived [4, 8].

The spatially averaged two-fluid model will be extended to include a model for heat transfer and, therefore, filtered energy equations are derived. 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 similar construct as the drift velocity. That is that the temperature difference between both phases is corrected by a ‘drift temperature’ stemming from phase averaging. Closure models for this ‘drift temperature‘ as well as for the other unresolved terms in the filtered equations for the thermal energy balance are derived following the concepts outlined in [4]. Finally, a comparison shows fairly good agreement of the presented closure models with the fine grid data.

References

[1] Agrawal K, Loezos PN, Syamlal M, Sundaresan S. The role of meso-scale structures in rapid gas-solid flows. J. Fluid Mech. 2001;445:151–185.

[2] Ozel A, Gu Y, Milioli CC, Kolehmainen J, Sundaresan, S. Towards filtered drag force model for non-cohesive and cohesive particle-gas flows. Phys. Fluids 2017;29:103308.

[3] Schneiderbauer S, Saeedipour M. Approximate deconvolution model for the simulation of turbulent gas-solid flows: An a priori analysis. Phys. Fluids 2018;30:023301.

[4] Schneiderbauer S. A spatially-averaged two-fluid model for dense large-scale gas-solid flows. AIChE J. 2017;63(8):3544-3562.

[5] Schneiderbauer S, Puttinger S, Pirker S. Comparative analysis of subgrid drag modifications for dense gas-particle flows in bubbling fluidized beds. AIChE J. 2013;59(11):4077-4099.

[6] Fox RO. On multiphase turbulence models for collisional fluid-particle flows. J. Fluid Mech. 2014;742:368-424.

[7] Capecelatro J, Desjardins O, Fox RO. Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics. Phys. Fluids 2016;28(3):033306.

[8] Capecelatro J, Desjardins O, Fox RO. Numerical study of collisional particle dynamics in cluster-induced turbulence. J. Fluid Mech. 2014;747:R2.