This paper presents a computational analysis on forced vibration and fluid-structure interaction in compressible flow regimes. A so-called staggered approach is pursued where the fluid and structure are integrated in time by distinct solvers. Their interaction is then taken into account by a coupling algorithm. The unsteady fluid motion is simulated by means of an explicit time-accurate solver. For the fluid-structure interaction problems which are considered here the effects due to the viscosity can be neglected. The fluid is hence modeled by the Euler equations for compressible inviscid flow. Unstructured grids are used to discretise the fluid domain. These grids are particularly suited to simulate unsteady flows over complex geometries by their capacity of being dynamically refined and unrefined. Dynamic mesh adaptation is used to enhance the computational precision with minimal CPU and memory constraints. Fluid-structure interaction involves moving boundaries. Therefore the Arbitrary Lagrange Euler method (ALE-method) is adopted to solve the Euler equations on a moving domain. The deformation of the mesh is controlled by means of a spring analogy in conjunction with a boundary correction to circumvent the principle of Saint Venant. To take advantage of the differences between fluid and structure time scales, the fluid calculation is subcycled within the structural time step. Numerical results are presented for large rotation, pitching oscillation and aeroelastic motion of the NACA0012 airfoil. The boundary deformation is validated by comparing the numerical solution for a flat plate under supersonic flow with the analytical solution.

1.
Bathe K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, NJ.
2.
Batina
J. T.
,
1990
, “
Unsteady Euler Airfoil Solutions Using Unstructured Dynamic Meshes
,”
AIAA Journal
, Vol.
28
, No.
8
, pp.
1381
1388
.
3.
Bendiksen O. O., 1991, “A New Approach to Computational Aeroelasticity,” AIAA Paper 91-0939-CP.
4.
Bisplinghoff R. L., Ashley H., 1962, Principles of Aeroelasticity, Dover Publications, New York, NY.
5.
Blom F. J., 1996, “Comparison of Different Mesh Displacement Algorithms on Unstructured Meshes,” IMHEF Report T-196–13, EPF-Lausanne.
6.
Donea
J.
,
Guiliani
S.
,
Halleux
J. P.
,
1982
, “
An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interactions
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
33
, pp.
689
723
.
7.
Farhat, C., 1995, “High Performance Simulation of Coupled Nonlinear Transient Aeroelastic Problems,” Cosmase Course, EPF-Lausanne.
8.
Farhat C., Lin T, Y., 1990, “Transient Aeroelastic Computations Using Multiple Moving Frames of Reference,” AIAA paper, 90–3053-CP.
9.
Farhat, C., Maman N., Lesoinne M., 1994, “Mixed Explicit/Implicit Time Integration of Coupled Aeroelastic Problems: Three-Field Formulation, Geometric Conservation Law and Distributed Solution,” Center for Aerospace Structures 94–17, University of Colorado.
10.
Houbolt J. C, 1958, “A Study of Several Aerothermoelastic Problems of Aircraft Structures in High-Speed Flight,” Ph.D. thesis, ETH-Zurich.
11.
Landon R. H., 1982, “NACA0012 Oscillatory and Transient Pitching,” Compendium of Unsteady Aerodynamic Measurements, Dataset 3, AGARD-R-702.
12.
Piperno S., 1995, “Simulation nume´rique de phe´nomenes d’interaction fluide-structure,” PhD. thesis, Ecole Nationale Des Fonts et Chausse´es, France.
13.
Rausch R. D., Batina J. T., Yang H. T. Y., 1989, “Euler Flutter Analysis of Airfoils Using Unstructured Dynamic Meshes,” AIAA Paper 89–1384-CP.
14.
Richter R., Leyland P., 1993, “Precise Pitching Airfoil Computations by Use of Dynamic Unstructured Meshes,” AIAA Paper 93–2971.
15.
Thomas
P. D.
,
Lombard
C. K.
,
1997
, “
Geometric Conservation Law and its Application to Flow Computations on Moving Grids
,”
AIAA Journal
, Vol.
17
, No.
10
, pp.
1030
1037
.
16.
Weaver W., Timoshenko S. P., Young D. H., 1990, Vibration Problems in Engineering, 5th edition, Wiley.
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