Advanced Heat Transfer Model for Eulerian–Lagrangian Simulations of Industrial Gas–Solid Flow Systems

The discrete element method (DEM), coupled with computational fluid dynamics (CFD), has been developed to simulate complex solid–fluid flow systems. Today, the DEM is regarded as an established approach, with extensive applications in industrial systems. Heat transfer modeling might be essential to the DEM for industrial applications. However, existing heat transfer models of the DEM have fundamental limitations. These issues arise from the soft spring model inherent in the DEM, where heat conduction is mathematically influenced by the spring constant values. Therefore, current heat transfer models require complex modeling, namely, consideration of the contact state such as contact area and duration, to estimate heat conduction. Moreover, the current heat transfer models exhibit poor compatibility with scaling laws, such as the coarse-grained DEM, leading to amplify temperature errors relative to motion errors. To address these challenges, we develop a novel heat transfer model based on an Eulerian framework within DEM simulations. In our approach, the Eulerian description is applied to the heat transfer calculation, while particle motion is simulated by the DEM. Notably, heat conduction in the solid phase is captured through a simple setup by specifying the void fraction rather than modeling the contact state. The adequacy of the proposed heat transfer model is demonstrated through validation tests in gas–solid flow systems, showing that the temperature distribution is independent of the particle contact state. Furthermore, the proposed model exhibits strong compatibility with the coarse-grained DEM, maintaining accuracy even at reduced computational costs. These results establish the new model’s reliability and universality, positioning it as a promising standard for DEM-CFD simulations in industrial applications.