Team for Advanced Flow Simulation and Modeling
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Flow Induced Vibrations of a Cantilevered, Flexible PipeIn this fluid-structure interaction problem, we simulate the 3D flow in a cantievered, flexible pipe and the response of the pipe to this flow. The deformation of the pipe, assumed to be planar, is governed by the Bernoulli-Euler theory. This limits the reliability of our results to small deformations of the pipe. It is known that beyond a certain critical inflow velocity, the pipe exhibits flow-induced oscillations. In this simulation the Reynolds number, based on the pipe diameter and the inflow velocity at the pipe centerline, is 1000. The length of the pipe is 20 times its diameter.
The finite element mesh consists of 20,449 nodes and 18,720 hexahedral elements. At every time step 145,298 nonlinear equations are solved to update the flow field. The structural part of the problem involves solution of 240 equations at every time step.
The figure below shows the flow field in the pipe section in its plane of motion during a full period of oscillations. The images on the left show the pressure field, and the ones on the right show the lateral component of the velocity in the plane of motion of the pipe. The pipe exhibits the second mode of cantilevered beam oscillations. The flow solver and flow visualization software were developed by the T*AFSM.
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. S. Mittal and T.E. Tezduyar, "A Finite Element Study of Incompressible Flows Past Oscillating Cylinders and Airfoils", International Journal for Numerical Methods in Fluids, 15 (1992) 1073-1118.
5. T.E. Tezduyar, "Finite Element Computation of Unsteady Incompressible Flows Involving Moving Boundaries and Interfaces and Iterative Solution Strategies", Chapter 3 in Special Course on Unstructured Grid Methods for Advection Dominated Flows, AGARD-R-787, NATO Advisory Group for Aerospace Research and Development, Neuilly Sur Seine, France (1992).
6. S. Mittal and T.E. Tezduyar, "Parallel Finite Element Simulation of 3D Incompressible Flows--Fluid-Structure Interactions", International Journal for Numerical Methods in Fluids, 21 (1995) 933-953.
7. T. Tezduyar, "Advanced Flow Simulation and Modeling", Flow Simulation with the Finite Element Method (in Japanese), Springer-Verlag, Tokyo, Japan (1998).
8. T. Tezduyar, "CFD Methods for Three-Dimensional Computation of Complex Flow Problems", Journal of Wind Engineering and Industrial Aerodynamics, 81 (1999) 97-116.
9. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation of Complex Flow Problems", Parallel Computing, 25 (1999) 2039-2066.