Predicting the local heat and mass transfer rate in fluidization processes is an important task for laboratory experiments, as well as for industrial plant design, operation, and optimization. While predicting the heat (or mass) transfer rate is already a formidable task on its own, heat and mass transfer inside the particles even complicate the situation. The Biot number, relating the external to the intra-particle heat (or mass) flux, is a dimensionless number that helps in quantifying the relevance of intra-particle transport phenomena. However, modeling the effect of the Biot number on the local heat and mass transfer process is still challenging.
In this study we will present two strategies that can be used to model the effect of the Biot number in fixed and fluidized particle beds: our first strategy is based on integral heat and mass balances for the gas and particle phase. These balance equations are spatially discretized using a one-dimensional finite-difference approach. We use a second-order implicit formulation for temporal discretization, as well as a robust technique to treat the exchange terms for an efficient integration of the equations. Our model considers particle and gas-phase dispersion to account for the effect of pseudo-turbulence and the agitation by bubbles in case of fluidized beds.
Our second strategy is based on a CFD-DEM simulation approach, which accounts for intra-particle temperature (and concentration) gradients using the ParScale package. While the LIGGGHTS®/CFDEM® package is used to integrate the governing equations for fluid and particle flow, the newly established ParScale package (https://github.com/CFDEMproject/ParScale-PUBLIC) is used to resolve intra-particle profiles. The advantage of our second approach is that we are able to compute particle and (meso-scale) gas dispersion rates directly, as well as to access intra-particle temperature (and concentration) profiles of all particles. Finally, we will compare the two modeling strategies, present a workflow for the calibration of the simple 1D model, as well as highlight operating regimes in which Biot number effects must be accounted for.
Figure: Temperature at the particle surface (hemi-spheres) as well as at the center of each particle (spheres) in a fluidized bed (fluidization at 2.3 times the minimal fluidization velocity, mean Biot number 1.7)
Acknowledgement and Disclaimer
SR and TP acknowledge funding through the NanoSim project (http://www.sintef.no/projectweb/nanosim), as well as the “NAWI Graz” project by providing access to dcluster.tugraz.at.
LIGGGHTS® and CFDEM® are registered trade marks of DCS Computing GmbH, the producer of the LIGGGHTS® and CFDEM® software.