TAFSM

Team for Advanced Flow Simulation and Modeling



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Water Sloshing in a Vibrating Container

Here we perform a 3D study of sloshing in a container subjected to vertical vibrations. The experimental and theoretical evidence indicates the existence of multiple solution branches when the horizontal cross-section of the container is nearly square. Depending on the frequency of the vibrations, the competing wave modes interact, generating complex periodic, as well as chaotic, wave behavior.

The mesh consists of 7,056 nodes and 6,000 quadrilinear brick elements which result in 52,878 equations that are solved iteratively. The simulation was carried out on a CM-200. The figures below show the free-surface displacement and the pressure field at two instants during the simulation.

The horizontal cross section of the tank is a W x H rectangle, where W = 0.1778 m and H = 0.18934 m. The water level, initially flat, is at D = 0.127 m from the bottom of the tank. The side and bottom boundaries are assumed to be boundaries which allow slip. The open surface of the water is assumed to be free from normal and shear stresses, and it moves consistently with the normal component of the fluid velocity at the surface. The external forces acting on the fluid consist of a sinusoidal vertical excitation A*g*sin(w*t), with w = 2*pi*f, f = 4.00 Hz, and A such that the amplitude of the oscillations remains at 1 mm. The mesh generator, flow solver, and flow visualization software (based on BoB) were developed by the T*AFSM.

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. M. Behr and T.E. Tezduyar, "Finite Element Solution Strategies for Large-Scale Flow Simulations", Computer Methods in Applied Mechanics and Engineering, 112 (1994) 3-24.

5. T. Tezduyar, "Advanced Flow Simulation and Modeling", Flow Simulation with the Finite Element Method (in Japanese), Springer-Verlag, Tokyo, Japan (1998).

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. I. Guler, M. Behr and T.E. Tezduyar, "Parallel Finite Element Computation of Free-Surface Flows", Computational Mechanics, 23 (1999) 117-123.

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