دانلود رایگان مقاله شبیه سازی سوسپانسیون فیبر قابل انعطاف با الگوریتم غوطه ور مقیاس پذیر

Abstract

We present an approach for numerically simulating the dynamics of flexible fibers in a three-dimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev’s pseudo-compressible fluid solver. The fibers are treated as one-dimensional neutrally-buoyant Kirchhoff rods that resist stretching, bending, and twisting, within the generalized IB framework. We perform a careful numerical comparison against experiments on single fibers performed by S.G. Mason and co-workers, who categorized the fiber dynamics into several distinct orbit classes. We show that the orbit class may be determined using a single dimensionless parameter for low Reynolds flows. Lastly, we simulate dilute suspensions containing up to hundreds of fibers using a distributed-memory computer cluster. These simulations serve as a stepping stone for studying more complex suspension dynamics involving aggregation of fibers (or flocculation) and particle sedimentation due to added mass.

6. Conclusions

In this paper, we have presented a parallel immersed boundary algorithm for simulating suspensions of flexible fibers, where individual fibers are modeled as Kirchhoff rods. The novelty of this work derives from its application to multi-fiber suspension flows with non-zero Reynolds number and the inclusion of the full two-way interaction between the fluid and suspended fibers. In our numerical simulations, we reproduce the full range of orbital dynamics observed experimentally by Mason and co-workers for isolated fibers immersed in a linear shear flow. When extending the results to multi-fiber suspensions, we demonstrate through a weak scalability test that the parallel scaling of our algorithm is near optimal and hence shows promise for simulating more complex scenarios such as semi-dilute suspensions and fiber flocculation. In the future, we plan to improve on the underlying model, which will allow us to simulate more realistic fiber suspensions. First, we plan on incorporating the contact forces between fibers such as the frictional forces modeled by Schmid et al. [57]. Second, we will incorporate the effect of added fiber mass using the penalty IB method [58]. After incorporating these extensions, a more extensive comparison to experimental data would be required, comparing quantities such as the specific viscosity of the suspension [4].