Numerical analysis of flow-induced nonlinear vibrations of an airfoil with three degrees of freedom

Computers and Fluids

Volumn 49, Issue 1, 2011, Pages 110-127

  Feistauer, Miloslav ^a   Horáček, Jaromír ^b   Růžička, Martin ^a   Sváček, Petr ^c  

^a CHARLES UNIVERSITY   (Czech Republic)

^b INSTITUTE OF THERMOMECHANICS   (Czech Republic)

^c CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Aeroelasticity; Arbitrary Lagrangian Eulerian formulation; Finite element method; Flutter instability; Navier Stokes equations; Non linear oscillations; Stabilization for high Reynolds numbers

Indexed keywords

AEROELASTIC SYSTEM; AIRFOIL MOTIONS; ARBITRARY LAGRANGIAN-EULERIAN FORMULATIONS; COMPUTATIONAL DOMAINS; COMPUTATIONAL MESH; DYNAMIC BEHAVIOURS; ELASTIC AXIS; FAR-FIELD VELOCITY; FINITE ELEMENT; FINITE ELEMENT SOLUTION; FINITE-ELEMENT DISCRETIZATION; FLUID-STRUCTURES; FLUTTER INSTABILITY; HIGH REYNOLDS NUMBER; LARGE AMPLITUDE; MOVING GRID; NASTRAN; NON-LINEAR VIBRATIONS; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; NONLINEAR OSCILLATION; NUMERICAL EXPERIMENTS; STRONG COUPLING; THEORETICAL PREDICTION; THREE DEGREES OF FREEDOM; TIME STEP; TIME-DEPENDENT; TWO-DIMENSIONAL INCOMPRESSIBLE VISCOUS FLOW; VERTICAL DIRECTION;

AEROELASTICITY; AIRFOILS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; COUPLED CIRCUITS; DIFFERENTIATION (CALCULUS); FINITE ELEMENT METHOD; FLUID STRUCTURE INTERACTION; FLUTTER (AERODYNAMICS); INCOMPRESSIBLE FLOW; LAGRANGE MULTIPLIERS; MECHANICS; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; REYNOLDS NUMBER; ROTATION; STABILIZATION; SYSTEM STABILITY; VIBRATION ANALYSIS; VISCOUS FLOW;

NAVIER STOKES EQUATIONS;

EID: 79960892694     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2011.05.004     Document Type: Article

References (39)

1. Badia S., Codina R. On some fluid-structure iterative algorithms using pressure segregation methods. Application to aeroelesticity. Int J Numer Methods Eng 2007, 72:46-71.
2. Badia S., Nobile F., Vergara C. Fluid-structure partioned procedures based on Robin transmission conditions. J Comput Phys 2008, 227:7027-7051.
3. Bisplinghoff R.L., Ashley H., Halfman R.L. Aeroelasticity 1996, Dover, New York.
4. Bolotin V.V. Nonconservative problems of the theory of elastic stability 1963, Macmillan, New York.
5. Brezzi F., Falk R.S. Stability of higher-order Hood-Taylor methods. SIAM J Numer Anal 1991, 28:581-590.
6. Brezzi F., Fortin M. Mixed and hybrid finite element method. Springer series in computational mathematics 15 1991, Springer-Verlag, New York.
7. Ciarlet P.G. The finite element method for elliptic problems 1979, North-Holland, Amsterdam.
8. Chung K.W., He Y.B., Lee B.H.K. Bifurcation analysis of a two-degree-of-freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation-incremental method. J Sound Vib 2009, 320:163-183.
9. Davis T.A. A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans Math Soft 2004, 30:165-195.
10. T.A.Davis, UMFPACK V4.0, University of Florida..
11. Dessi D., Mastroddi F. A nonlinear analysis of stability and gust response of aeroelastic systme. J Fluid Struct 2008, 24:436-445.
12. Aeroelasticity of plates and shells 1974, Kluwer, Dordrecht. E.H. Dowell (Ed.).
13. Dowell E.H. A modern course in aeroelasticity 1995, Kluwer, Dodrecht.
14. Farhat C., van der Zee K.G., Geuzaine P. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Comput Methods Appl Mech Eng 2006, 195:1973-2001.
15. Fernández M.A., Gerbeau J.-F. Algorithms for fluid-structure interaction problems. Modeling and simulation of the circulatory sestem 2009, 307-346. Springer-Verlag Italia. L. Formaggia, A. Quarteroni, A. Veneziani (Eds.).
16. Gelhard T., Lube G., Olshanskii M.A., Starcke J.H. Stabilized finite element schemes with LBB-stable elements for incompressible flows. J Comput Appl Math 2005, 177:243-267.
17. Grandmont C. Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. SIAM J Math Anal 2008, 40:716-737.
18. Guidorzi M., Padula M., Plotnikov P.I. Hopf solutions to a fluid-elastic interaction model. Math Models Methods Appl Sci 2008, 18:215-269.
19. Hoffmann K.H., Starovoitov V.N. On a motion of a solid body in a viscous fluid. Two-dimensional case. Adv Math Sci Appl 1999, 9:633-648.
20. Horáček J., Sváček P., Růžička M., Feistauer M. Contribution to finite element modelling of airfoil aeroelastic instabilities. Appl Comput Mech 2007, 1:43-52.
21. Jones D.P., Roberts I., Gaitonde A.L. Identification of limit cycles for piecewise nonlinear aeroelastic systems. J Fluid Struct 2007, 23:1012-1028.
22. Librescu L., Marzocca P. Advances in the linear/nonlinear control of aeroelastic structural systems. Acta Mech 2005, 178:147-186.
23. Librescu L., Marzocca P., Silva W.A. Aeroelasticity of 2-D lifting surfaces with time-delayed feedback control. J Fluid Struct 2005, 20:197-215.
24. Losík V, Čečrdle J. Aeroelastic analysis of a verifying model of an airplane construction with three degrees of freedom - part I. Research Report No. V-1833/3210/05. Aircraft Research and Test Institute (ARTI), Prague-Letany, 2005 [in Czech].
25. Losík V, Čečrdle J. Flutter computation of 3-DOF wing profile model. Technical Report P-PL-0061/07. Aircraft Research and Test Institute (ARTI), Prague-Letany, 2007 [in Czech].
26. Lube G. Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems. Numer Anal Methods Model 1994, 29:85-104.
27. Na S., Librescu L., Kim M.-H., Jeong I.-J., Marzocca P. Robust aeroelastic control of flapped wing systems using a sliding mode observer. Aerosp Sci Technol 2006, 10:120-126.
28. Naudasher E., Rockwell D. Flow-induced vibrations 1994, A.A. Balkema, Rotterdam.
29. Neustupa J. Existence of a weak solution to the Navier-Stokes equation in a general time-varying domain by the Rothe method. Math Methods Appl Sci 2009, 32:653-683.
30. Nomura T., Hughes T.J.R. An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Comput Methods Appl Mech Eng 1992, 95:115-138.
31. Paidoussis M.P. Fluid-structure interactions. Slender structures and axial flow 1998, vol. I. Academic Press, San Diego.
32. Paidoussis M.P. Fluid-structure interactions. Slender structures and axial flow. 2004, vol. II. Elsevier, Academic Press, London, UK.
33. Peters D.A. Two-dimensional incompressible unsteady airfoil theory - an overview. J Fluid Struct 2008, 24:295-312.
34. Růžička M., Feistauer M., Horáček J., Sváček P. Interaction of incompressible flow and a moving airfoil. Electron Trans Numer Anal 2008, 32:123-133.
35. Shim J.-H., Na S., Chung C.-H. Aeroelastic response of an airfoil-flap system exposed to time-dependent disturbances. KSME Int J 2004, 18:560-572.
36. Sváček P., Feistauer M., Horáček J. Numerical simulation of flow induced airfoil vibrations with large amplitudes. J Fluid Struct 2007, 23:391-411.
37. Taylor C., Hood P. A numerical solution of the Navier-Stokes equations using the finite element technique. Comput Fluids 1973, 1:73-100.
38. Verfürth R. Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal Numer/Numer Anal 1984, 18:175-182.
39. Witteveen J.A.S., Bijl H. An unsteady adaptive stochastic finite elements formulation for rigid-body fluid-structure interaction. Comput Struct 2008, 86:2123-2140.