Stable monolithic immersed boundary projection method for particle sedimentation with heat transfer at density ratios near unity

Abstract

This study proposes a highly stable and efficient monolithic immersed boundary projection method with staggered time discretization for particle sedimentation with heat transfer at density ratios near unity. To achieve the implicit coupling of fluid and solid motion, the proposed method uses a monolithic approach that incorporates temperature, fluid velocities, particle velocities, momentum forcing, energy forcing, and pressure. Subsequently, a two-step approximate lower–upper decomposition is used to decouple the complex large system. Two-dimensional and three-dimensional (3D) single particle sedimentation at various Grashof numbers and density ratios verifies the ability of the proposed method to handle particle sedimentation at density ratios near unity. Moreover, the proposed method demonstrates its clear advantages by successfully addressing both stability issues and spurious oscillations. Furthermore, simulation with the proposed method was performed for 3D two- and multi-particle sedimentation with heat transfer to demonstrate the robustness of the proposed method. The investigation of the effects of density ratio and Grashof numbers on particle sedimentation reveals a significant influence of buoyancy force, particularly for relatively lighter particles. An increase in the drag coefficient for multi-particle sedimentation is observed, owing to interactions between particles, and the Grashof number exerts a pronounced influence, particularly at low-density ratios.