Eulerian-Lagrangian approach to modeling heat transfer in gas-particle mixtures: volume-averaged equations, multi-scale modeling and comparison with numerical experiments
Résumé
In this paper, a macro-scale model is proposed to describe heat transfer in a dilute gas-particle mixture. The continuous phase is described by a filtered Eulerian approach while the dispersed one is represented as Lagrangian particles. The filtered model, which is obtained using an up-scaling methodology, consists of a macroscopic heat transfer model for the continuous phase with a matrix of heat exchange coefficients that captures both particle-particle and particle-fluid interactions. The up-scaling methodology further provides closure problems that link these coefficients to the particle scale and can be used to calculate the matrix explicitly. The validity of lumped and diagonal approximations of the matrix is studied, therefore providing a direct link between our approach and classical models of dilute gas-particle mixtures considering that the temperature field in the vicinity of each particle is not influenced by the presence of other particles. We also discuss the influence of the number of particles in the REV (Representative Elementary Volume) on the solution of the closure problems and compare numerical solutions of the exchange coefficients with analytical results obtained in the case of an isolated particle. Finally, we study a model system with immobile particles in a purely diffusive case and compare results of the macro-scale representation to those obtained from numerical experiments for different volume fractions.We show good agreement of our model with the numerical experiments and discuss the accuracy of lumped and diagonal approximations.
Origine : Fichiers produits par l'(les) auteur(s)