دانلود رایگان مقاله چارچوب جفت DF-IBM/NSCD برای شبیه سازی برهمکنش ذرات غوطه ور

Abstract

Immersed granular flows are present widely in different domains under different forms (at various scales) such as in nature (rivers, muds, atmosphere, blood...), and in many industrial applications (detergents, cosmetics, etc...). Studying such flows properly requires one to represent well the physics behind their dynamics: the fluid/solid interactions (FSI), the solid/solid interactions (SSI) and the coupling mechanisms at various scales. In this work, a new coupling framework to simulate immersed granular flows has been developed. The FSI has been modeled using a direct-forcing immersed boundary method (DF-IBM) and implemented in the parallelized “PELICANS” C++ library. In this DF-IBM, all the mathematical equations, including the direct-forcing term, are discretized, both in space and time, and solved iteratively via a finite-volume and projection methods on Eulerian Grids. A sharp-edge interface, that can be smoothed, is used to represent the fluid/solid transition. The modeling of the multiple SSI at the grain’s scale is based on the Non-Smooth Contact Dynamics (NSCD) approach developed in the “LMGC90” open-source library. The coupling of the two softwares “PELICANS” and “LMGC90”, called Xper, provides an efficient framework to simulate and study dense immersed granular flows by taking into account, both advanced contact laws between grains, and hydrodynamic interactions. We address in this paper the effects of imposing a fluid-ring numerically (or fluid-mesh-cells) around two settling solid disks on modifying their dynamics. The DF-IBM approach implemented in Xper is validated, on a 2D flow over a stationary rigid cylinder benchmark, and on the settling of a rigid buoyant sphere in an incompressible laminar fluid at different Reynolds numbers. The numerical results are in good agreement with experimental and numerical data from the literature.

5. Conclusion

A Direct-Forcing Immersed Boundary Method (DF-IBM) is used and implemented in the parallelized numerical framework named PELICANS. This was to take into account for the presence of stationary and moving rigid bodies that are immersed in a fluid (Fluid–Structure Interactions). The numerical implementation is validated by simulating the transient 2D flow around a stationary cylinder at two different Reynold’s numbers (20 and 100). Good results are obtained in computing the drag and lift coefficients, and the pressure difference using a PTIT (Penalization Term Integration Technique) inside the immersed body. These results have been characterized by studying the effect of the diameter-to-space-step ratio (DSS) on numerical precision. We found that a DSS of 20 was fair to obtain results that are close to the benchmark data provided by Turek and Schafer [ ¨ 18] for the 2D flow over a stationary cylinder. For multiple contacts (Solid–Solid Interactions) between immersed rigid bodies, the PELICANS framework was coupled to the Contact-Mechanics framework named LMGC90 and the resulting package is named Xper. The 3D settling of a sphere has been simulated at different Reynolds numbers (between 1.5 and 32.2) using Xper to test the validity of the numerical package as a whole. Satisfactory results are obtained for the settling velocity values compared to the experimental and numerical data found in the literature [26,1]. This indicates the primary validity of Xper in simulating immersed granular flows in 3D. Finally, the effect on the contacts dynamics is addressed by imposing numerical fluid cells around two identical settling cylindrical particles in a stationary fluid as it is usually done by many authors in literature. We found that, imposing this numerical fluid ring (of thickness of the order of a one mesh space) around the particle (as done usually by most authors using different numerical methods to avoid numerical difficulties) to neglect friction alters the particles trajectories. This is a new finding that implies that imposing at all even a very small fluid ring, the obtained dynamics cannot correspond well to the “real” phenomena because the friction due to direct solid-to-solid contacts is present. Moreover, a Coulomb’s friction coefficient of 0.5 has shown to have a great effect on the particles dynamics after contact.