Multi-fluid modeling of heat transfer in bubbling fluidized bed with thermally-thick particles featuring intra-particle temperature inhomogeneity

The multi-fluid model has been widely used to study heat transfer between gas and solid in bubbling fluidized beds. However, zero-dimensional (0D) model has been commonly used. The model assumes a uniform tem-perature distribution, which is only reasonable for thermally-thin particles (Biot number (Bi) < 1). However, one-dimensional (1D) model considering intra-particle temperature inhomogeneity inside particles is difficult to be implemented in multi-fluid model. To solve this issue, a corrected coefficient is introduced to quantitively feature the effects of intra-particle temperature inhomogeneity inside particles on external heat transfer, which forms a corrected 0D model. The corrected coefficient is correlated as a binary function of Bi and dimensionless temperature. The results of particle-scale modeling show that temperature profiles predicted by the corrected 0D model are the same as those of the 1D model for both thermally-thin and thermally-thick particles, while the 0D model overestimates heat transfer between particles and surrounding gas. The corrected 0D model is further implemented in the multi-fluid model to simulate particle cooling and heating process in bubbling fluidized beds. The results predicted by CFD simulations with both the 0D and the corrected 0D models are in good agreement with the experimental data of thermally-thin particles. For both the cooling and heating processes, a significant difference is observed for thermally-thick particles, indicating the importance of considering intra-particle temperature inhomogeneity in multi-fluid modeling. Consistent with the results of particle-scale modeling, the corrected 0D model predicts a smaller heat transfer rate between the gas and solid phases, as compared to the 0D model. Additionally, computational efficiency of the corrected 0D model is comparable to that of the 0D model.