A compressible semi-resolved computational fluid dynamics-discrete element method coupling model for fluid–solid systems with heat transfer

Compressible particle-laden systems are widely present in various natural phenomena and engineering applications. This study focuses on developing a compressible semi-resolved computational fluid dynamics-discrete element method (CFD-DEM) coupling model with heat transfer. The model can simulate gas–solid and liquid–solid systems across a range of dilute to dense patterns. A semi-resolved model is developed by combining the diffusion-based smoothing method and the volume-averaged weighted function interpolation method, removing the restriction of the grid size to particle diameter ratio in unresolved models. The volume-averaged Navier–Stokes equation is introduced for variable density flows in the fluid phase. All closed terms and assumptions are discussed. Special attention is paid to the improved energy conservation equation for the fluid phase and the modified pressure Poisson equations that are suitable for high-speed thermal particulate flows. Particle motion is tracked using DEM, which considers the translation, rotation, collision, and heat transfer processes of the particles. The numerical simulation results are compared with several experimental findings, validating the effectiveness of the compressible CFD-DEM coupling model. The proposed model introduces new ideas and methods for investigating the mechanisms and engineering applications of compressible fluid–solid systems.