Summary
This paper presents numerical approaches for computing fluid/structure interactions in a transonic flow using Euler/Navier-Stokes solvers. The first method concerns the flutter simulation using the linearized Euler equations in the frequency domain. The second method concerns the direct fluid structure coupling in the time domain.
The Euler/Navier-Stokes equations are solved on a multi-block structured mesh and are based on an ALE formulation. Specific tools are developed for the mesh deformations. A Finite Element Formulation is used to model the structural part of the aeroelastic problem. The use of a modal reduction for the structure and a dual timestep technique to simulate the unsteady aerodynamics reduces considerably the CPU times without detracting from the accuracy and the robustness of the simulations. These numerical methods are applied for static aeroelasticity and flutter prediction for complex civil and military configurations in transonic flow. The tools are tested for a Limit Cycle Oscillations (LCO) problem in 2D.
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References
W.F. Ballhaus and P.M. Goorjian: “Implicit Finite-Difference Computations of Unsteady Transonic Flows about Airfoil”, AIAA Journal Vol.15, No. 12,77, pp. 1728–1735.
E. Balmès: “Experimental and Analytical Structural Dynamic Toolbox”, Matlab User’s Guide, January 1997.
K. J. Bathe: “Finite element procedures in engineering analysis”, Prentice Hall, Englewood Cliffs, New Jersey 07632, 1982, pp. 512.
J.T. Batina: “Unsteady Euler airfoil solution using unstructured dynamic meshes”, AIAA Paper 89–0115.
R.M. Bennet, J.T. Batina and H.J. Cunningham: “Wing Flutter Calculations with the CAP-TSD Unsteady Transonic Small-Disturbance Program”, Journal of Aircraft, Vol. 26, No. 9, Sept. 1989, pp. 876–882.
R. Collercandy: “Multigrid Strategy for Euler and Navier Stokes computations for flows around complex aerospace configurations”, Proceedings of the ECCOMAS 98 Conference, Athens, 1998.
V. Couaillier: “Numerical simulation of separated turbulent flows based on the solution of RANS/low Reynolds two-equation model”, AIAA Paper 99–0154, 37th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, January 11–14, 1999.
B. Darras: “Identification de systèmes vibrants par la méthode du décrément aléatoire”, Revue française de mécanique, numéro 58–59, pp. 21–27, 1976.
R. Dat and J.L. Meurzec: “Sur les calculs de flottement par la méthode dite du ‘balayage en fréquence réduite’ ”, La Recherche Aérospatiale No. 133, Nov.-Dec. 1969.
A. Dugeai, A. Madec and A.S. Sens: “Numerical unsteady aerodynamics for turbomachinery aeroelasticity”, 9th International Symposium of Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, Lyon, France, September 4–7, 2000.
J. Donea: “Arbitrary Lagrangian-Eulerian Finite Element Methods”, Computational Methods for Transient Analysis. Edited by T. Belytschko and T.J.R. Hughes. Elsevier Sciences Publisher B.V. (1983) pp. 473–516.
C. Farhat and M. Lesoinne: “Fast staggered algorithms for the solution of threedimensional nonlinear aeroelastic problem”, 85th AGARD SMP Meeting, Aalborg, Denmark, November 13–16, 1997.
P. Girodroux-Lavigne, J.P. Grisval, S. Guillemot, M. Henshaw, A. Karlsson, V. Selmin, J. Smith, E. Teupootahiti and B. Winzell: “Comparative of advanced fluidstructure interaction methods in the case of a highly flexible wing (Results from the UNSI Program)”, International Forum on Aeroelasticity and Structural Dynamics, Madrid, Spain, June, 2001.
P.A. Gnoffo: “A finite volume adaptive grid algorithm applied to planetary entry flowfields”, AIAA Journal, Vol. 21, number 9, pp 1249–1254 (1983).
J.P. Grisval and J.L. Meurzec: “Couplage direct fluide structure en aéroélasticité transsonique”, 73rd Meeting of the AGARD Structures and Materials Panel, San Diego, CA, USA, October 7–11, 1991, AGARD Proceedings 507, ONERA TP 1991205.
J.P. Grisval, C. Sauvignet and Z. Johan: “Aeroelasticity calculation using a finite element method”, International Forum on Aeroelasticity and Structural Dynamics, Rome, Italy, June 17–20, 1997.
J.P. Grisval, C. Liauzun and Z. Johan: “Aeroelasticity simulations in turbulent flows”, International Forum on Aeroelasticity and Structural Dynamics, Williamsburg, USA, June 22–25, 1999.
J.P. Grisval and C. Liauzun: “Application of the finite element method to aeroelasticity”, Revue européenne des éléments finis. Vol. 8, no 5–6, pages 553–579, septembre 1999.
G.P. Guruswamy, P.M. Goorjian and E.L. Tu: “Transonic Aeroelasticity of Wings with Tip Stores”, Journal of Aircraft, Vol. 24, No. 10, Oct. 1987, pp. 688–695 and AIAA Paper 86–1007.
G.P. Guruswamy and C. Byun: “Fluid structural interactions using Navier Stokes flow equations coupled with shell finite element structures”, AIAA 24th Fluid Dynamics Conference, July 6–9, 1993, Orlando, FL, USA, AIAA-93–3087.
R.L. Harder and R.N. Desmarais: “Interpolation using surface splines”, Journal of Aircraft, February 1972.
E.M. Lee-Rausch and J.T. Batina: “Wing flutter boundary prediction using unsteady Euler aerodynamic method”. AIAA-93–1422-CP.
J.C. Le Balleur and P. Girodroux-Lavigne: “Calculation of fully three-dimensional separated flows with an unsteady viscous-inviscid interaction method”, Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, California States University, Long-Beach, USA January 13–15, 1992, ONERA TP 1992–01.
N. Liamis: “Méthodes implicites de résolution des équations d’Euler pour des écoulements tridimensionnels instationnaires dans des turbomachines”, Thèse, Université de Paris VI, 4 Octobre 1993.
J.L. Meurzec, A.S. Sens and J.P. Grisval: “Flutter prediction using an aerodynamic finite element method”, International Forum on Aeroelasticity and Structural Dynamics 1995, Manchester, U.K., June 26–28, 1995, ONERA TP 1995–64.
G.D. Mortchelewicz and A.S. Sens: “Solution of 3-D Euler Equations with Unstructured Meshes for Aeroelasticity Problems.”, International Symposium on Aeroelasticity and Structural Dynamics, Aachen, Germany, June 3–6, 1991, and TP Onera No. 1991–62.
G.D. Mortchéléwicz: “Application des équations d’Euler linéarisées à la prévision du flottement”, AGARD report 822, 85th Meeting of the AGARD Structures and Material Panel, Aalborg, Denmark, October 14–15, 1997.
G.D. Mortchéléwicz: “Flutter simulation using the linearized Euler equations”, 39th Israel Annual Conference on Aerospace Sciences, Tel Aviv, Haifa, Israel, February 17–18, 1999.
G.D. Mortchéléwicz: “Flutter simulations”, Aerospace Science & Technology No. 4 (2000), pp. 33–40.
G.D. Mortchéléwicz: “Flutter simulation using the linearized Euler equations”, 41st Israel Annual Conference on Aerospace Sciences, Tel Aviv, Israel, February 21–22, 2001.
O. Rouzaud and A. Plop: “2D unsteady Navier Stokes computations at ONERA for prediction of dynamic stall”, 24th European Rotorcraft Forum, Marseille, France, September 15–17, 1998.
O. Rouzaud, S. Plot and V. Couaillier: “Numerical simulation of buffeting over airfoil using dual time stepping method”, European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, September 11–14, 2000.
G. Schewe and H. Deyhle: “Experiments on transonic flutter of a two-dimensional supercritical wing with emphasis on the non-linear effects”, Proceedings of the Royal Aeronautical Society conference on “Unsteady Aerodynamics”, London, United Kingdom, July 17–18, 1996.
D.M. Schuster, J. Vadyak and E. Atta: “Static Aeroelastic Analysis of Fighter Aircraft Using a Three Dimensional Navier-Stokes Algorithm ”, Journal of Aircraft, Vol. 27, No. 9, Sep. 1990, pp. 820–825.
A.M. Vuillot, V. Couaillier and N. Liamis: “3D turbomachinery Euler and Navier-Stokes calculation with multidomain cell-centered approach”, AIAA Paper 93–2576, Monterey, California, June 28-July 1, 1993.
H. Zingel et al.: “Measurement of steady and unsteady airloads on a stiffness scaled model of a modern transport aircraft wing”, International Symposium on Aeroelasticity and Structural Dynamics, Aachen, Germany, June 3–6, 1991, and DGLR-Bericht 91–06, 1991, pp. 120–131.
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Grisval, JP. (2003). Numerical Simulation in Aeroelasticity For Complex Configurations in a Transonic Flow. In: Barton, N.G., Periaux, J. (eds) Coupling of Fluids, Structures and Waves in Aeronautics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44873-0_6
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DOI: https://doi.org/10.1007/978-3-540-44873-0_6
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