TAFSM

Team for Advanced Flow Simulation and Modeling



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Fluid-Structure Interactions in Interior Flows

In this fluid-structure interaction problem, we simulate the flow of a slightly compressible liquid and its interaction with a moving deformable solid. The problem is assumed to be axisymmetric. The fluid is governed by the Navier-Stokes equations for compressible flow and is assumed to be barotropic, which means that the pressure is a function of the density alone. The deformation of the piston is modelled using classical linear elasticity theory.

A sketch of the problem is shown below. A pressure of 50 MPa is imposed on the left boundary, and a pressure of 20 MPa is imposed on the right boundary. The left end of the piston undergoes a forced, sinusoidal translation. The amplitude of the translation is 1.5 mm (the length from the left boundary to the right boundary is 5 cm), and the frequency of the translation is 3 kHz. Although the flow will stay relatively low speed (the highest Mach number is only about 0.4), the fluid must be considered compressible because of the high pressure.

The motion of the piston is large enough that a new fluid mesh must be generated periodically in order to prevent unacceptible mesh deformation. The initial finite element mesh for the fluid consists of 2,489 nodes and 4,696 triangular elements. The mesh for the solid consist of 1,382 nodes and 2,570 triangular elements. These meshes are shown below. At every time step, approximately 14,000 nonlinear equations are solved to update the flow field, and 2,743 equations are solved to update the solid.

The figure below shows the velocity vectors (on the left) and the Mach number (on the right) at five times during one period of oscillation. An analysis of the piston indicates that it undergoes forced vibrations at 3 kHz, and several overtones of 3 kHz. It also vibrates at 13.5 kHz, indicating that 13.5 kHz is a natural frequency of the piston. The mesh generator and flow solver were developed by the T*AFSM.

References:

1. T.E. Tezduyar and T.J.R. Hughes, "Finite Element Formulations for Convection Dominated Flows with Particular Emphasis on the Compressible Euler Equations", AIAA Paper 83-0125, Proceedings of AIAA 21st Aerospace Sciences Meeting, Reno, Nevada (1983).

2. T.J.R. Hughes and T.E. Tezduyar, "Finite Element Methods for First-order Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations", Computer Methods in Applied Mechanics and Engineering, 45 (1984) 217-284.

3. G.J. Le Beau and T.E. Tezduyar, "Finite Element Computation of Compressible Flows with the SUPG Formulation", Advances in Finite Element Analysis in Fluid Dynamics (eds. M.N. Dhaubhadel, M.S. Engelman and J.N. Reddy), FED-Vol. 123, ASME, New York (1991) 21-27.

4. G.J. Le Beau and T.E. Tezduyar, "Finite Element Solution of Flow Problems with Mixed-Time Integration", Journal of Engineering Mechanics, 117 (1991) 1311-1330.

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

6. 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.

7. 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.

8. 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).

9. 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.

10. G. Wren, S. Ray, S. Aliabadi and T. Tezduyar, "Simulation of Flow Problems with Moving Mechanical Components, Fluid-Structure Interactions and Two-Fluid Interfaces", International Journal for Numerical Methods in Fluids, 24 (1997) 1433-1448.

11. S.E. Ray, G.P. Wren and T.E. Tezduyar, "Simulation of Compressible Fluid-Elastic Solid Interactions", AIAA Paper 97-0872, Proceedings of AIAA 35th Aerospace Sciences Meeting, Reno, Nevada (1997).

12. S.E. Ray, G.P. Wren and T.E. Tezduyar, "Parallel Implementations of a Finite Element Formulation for Fluid-Structure Interactions in Interior Flows", Parallel Computing, 23 (1997) 1279-1292.