A hydrodynamic model for simulating particles with generalised cross-sectional shapes in two-phase flow systems

Abstract

Modeling the motion and interactions of particles with complex shapes in two-phase flow systems presents significant challenges. In this study, we aim to develop an efficient and stable hydrodynamic model for simulating two-phase flow systems involving particles with generalised cross-sectional shapes. Firstly, a geometric representation model (GRM) is developed to precisely characterize arbitrary particle geometries while maintaining uniform Lagrangian points spacing. Next, to overcome traditional limitations, a boundary thickening-based direct forcing Immersed Boundary Method (BTDF-based IBM) and a Characteristic-Based Split (CBS) method have been integrated within the finite element framework for the first time. Unlike iterative IBM, BTDF-based IBM enforces no-slip/no-penetration conditions without iteration, significantly improving efficiency and accuracy. The CBS method can ensure the stability of the flow field using equal-order velocity-pressure interpolation, providing reliable results for accurate particle force and motion calculations. The validity and robustness of our proposed method are demonstrated by the benchmark problems. The method has been applied to simulate two-phase flow systems involving particles with generalised cross-sectional shapes. The results offer new insights into the influence of particle shape and initial orientation on particle-fluid interactions, highlighting the applicability of the method as a powerful tool for simulating particle-fluid interactions in engineering applications.