(647a) Spatially-Averaged Models for Moderately Dense Gas-Particle Flows Including a Thermal Energy Balance

Moderately dense gas-particle flows, like fluidized beds or risers, are used for a wide range of applications, from food drying and polymer production to the direct reduction of iron ore. While for small-scale fluidized beds, simulation is quite feasible using averaged equations of motion on the microscale (kinetic-theory based two-fluid model), the occurring physical phenomena cannot be fully numerically analyzed in large scale reactors yet, due to a large range of involved scales. In fluidized bed reactors of several meters in height, the smallest stable structures are usually only several particle diameters wide [1]. By employing coarse enough grids to make a simulation of full-scale reactors possible, mesoscale structures and, thus, their contributions to the gas-solid drag, intra- and interphase heat transfer between the particles and the gas, as well as to other macroscale flow properties, are not resolved. However, the unresolved heterogeneous structures have a significant influence on the macroscale flow properties. The velocity fluctuations around particle clusters give rise to turbulence, i.e. cluster induced turbulence [5,6]. Not accounting for this turbulence leads, for example, to an overestimation the gas-particle heat transfer.

A model accounting for the unresolved terms can be derived by spatially averaging the kinetic theory based two-fluid model equations [4]. The heat transfer coefficient devided by the solids volume fraction can be approximated by its zeroth order Taylor series expansion about the filtered variables. This approximation is used to close the unresolved part of the filtered heat transfer using a concept similar to the drift velocity [2,3]. This so-called drift temperature is the difference between the gas-phase temperature and the gas-phase temperature as seen by the particles. A transport equation for the variance of the temperature of the gas-phase is derived in order to obtain a closure model for the drift temperature.

An a-priori analysis shows that the proposed closure model for the unresolved heat transfer fits well with the predictions obtained by filtering highly resolved fine grid simulation data. In addition, closure models for the other unresolved terms in the filtered thermal energy equation and in the transport equation for the variance of the temperature are validated against the filtered fine-grid simulation data and numerical experiments.

References

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

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