## Team for Advanced Flow Simulation and Modeling |

For more information: |
## Fluid-Structure Interactions in Interior FlowsIn 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, 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", 3. G.J. Le Beau and T.E. Tezduyar, "Finite Element Computation of
Compressible Flows with the SUPG Formulation", 4. G.J. Le Beau and T.E. Tezduyar, "Finite Element Solution of Flow
Problems with Mixed-Time Integration", 5. T.E. Tezduyar, "Stabilized Finite Element Formulations for
Incompressible Flow Computations", 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",
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", 8. T.E. Tezduyar, "Finite Element Computation of Unsteady
Incompressible Flows Involving Moving Boundaries and Interfaces and
Iterative Solution Strategies", Chapter 3 in 9. S. Mittal and T.E. Tezduyar, "Parallel Finite Element Simulation
of 3D Incompressible Flows--Fluid-Structure Interactions",
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", 11. S.E. Ray, G.P. Wren and T.E. Tezduyar, "Simulation of Compressible
Fluid-Elastic Solid Interactions", AIAA Paper 97-0872, 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", |