TAFSM

Team for Advanced Flow Simulation and Modeling



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For more information:
  tezduyar@gmail.com

2-5 Spheres Falling in a Liquid Filled Tube

These simulations involve multiple spheres falling in a liquid filled tube. Between 2 to 5 spheres with different initial arrangements are allowed to fall with their dynamics determined by the fluid forces acting on them. They may also collide if any two spheres get too close to each other. Due to the requirement that there may be any number of spheres at any location, a 3D automatic mesh generator is used to discretize the domain. Also, due to the arbitrary motions of the spheres, a mesh moving scheme which handles the movement of the mesh automatically is used. In this scheme, the movement of the mesh is governed by the equations of linear elasticity. New meshes are created with the automatic mesh generator as often as needed to avoid reaching unacceptable levels of mesh distortion.

In one of the simulations, there are two spheres initially in a staggered arrangement. As the spheres fall, the trailing sphere is attracted to the low-pressure region in the wake of the leading sphere. The two spheres eventually collide and then separate. The two spheres then fall side by side throughout the rest of the simulation. The location of the spheres at five instants during the simulation can be seen in the figure on the left.

                           
In another simulation, there are five spheres initially in a slightly jumbled pentagon arrangement. As the spheres fall, they eventually rearrange themselves into the exact pentagon arrangement which seems to be the most stable state for five spheres. The location of the spheres at five instants during the simulation can be seen in the figure on the right. Both the unstructured mesh generator and flow solver were developed by the T*AFSM.

Movies of each of these simulations were also made.

Two Sphere Simulation

Five Sphere Simulation

References:

1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1991) 1-44.

2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces--The DSD/ST Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339-351.

3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces--The DSD/ST Procedure: II. Computation of Free-surface Flows, Two-liquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353-371.

4. A.A. Johnson and T.E. Tezduyar, "Simulation of Multiple Spheres Falling in a Liquid-Filled Tube", Computer Methods in Applied Mechanics and Engineering, 134 (1996) 351-373.

5. A.A. Johnson and T.E. Tezduyar, "3D Simulation of Fluid-Particle Interactions with the Number of Particles Reaching 100", Computer Methods in Applied Mechanics and Engineering, 145 (1997) 301-321.

6. T. Tezduyar, "CFD Methods for Three-Dimensional Computation of Complex Flow Problems", Journal of Wind Engineering and Industrial Aerodynamics, 81 (1999) 97-116.

7. A. Johnson and T. Tezduyar, "Advanced Mesh Generation and Update Methods for 3D Flow Simulations", Computational Mechanics, 23 (1999) 130-143.

8. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation of Complex Flow Problems", Parallel Computing, 25 (1999) 2039-2066.

9. A. Johnson and T. Tezduyar, "Methods for 3D Computation of Fluid-Object Interactions in Spatially-Periodic Flows", Computer Methods in Applied Mechanics and Engineering, 190 (2001) 3201-3221.