Numerical up-scaling approach for the simulation of heat-transfer in randomly packed beds

The objectives of this paper is to report the development and validation of a computational fluid dynamics (CFD) modeling approach to predict heat transfers in arbitrary randomly packed tubular reactors. The capacity of the packed beds to supply or remove heat from the core to the tube walls is indeed critical for the performance of reactors involved in various chemical applications of catalytic reactions. The understanding of the physical mechanisms and the modeling of turbulent heat and mass transfer is thus essential for the design, optimization and scale-up of fixed-bed reactors. For this objective, the heterogeneous catalyst bed can be represented by a macroscopic or homogeneous one where turbulence does exist at the small scales. In this study, an up-scaling approach is considered where the volume averaging procedure is used to derive the macroscopic equations. The flow and turbulent variables are decomposed according to the double decomposition concept within the framework of the volume averaging method. In particular, the dispersive kinetic energy is considered for the modeling of the thermal dispersion term appearing in the macroscopic temperature equation with a k–ε approach. The model is extended for the prediction of the channeling effects near the tube walls. The closure approximations are validated with microscopic simulations performed at the scale of representative elementary volume and comparisons with macroscopic simulations. Several packed bed configurations are considered, and the model predictions for the core heat transfer and the wall heat transfer are also compared to usual correlations when available. The microscopic simulations performed for various particle shapes are also confirming the predominant contribution of the mechanical dispersion to the convective heat transfer. This study is demonstrating the feasibility to predict the global heat transfer inside arbitrary tubular reactors with simple macroscopic simulations as an alternative to complex and computationally expensive microscopic simulations, out of the range of usual engineering tasks