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

The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. A solid airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rot...

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Published in:	Computers & fluids Vol. 49; no. 1; pp. 110 - 127
Main Authors:	Feistauer, Miloslav, Horáček, Jaromír, Růžička, Martin, Sváček, Petr
Format:	Journal Article
Language:	English
Published:	Kidlington Elsevier Ltd 01.10.2011 Elsevier
Subjects:	Aeroelasticity Airfoils Arbitrary Lagrangian–Eulerian formulation Computation Computational methods in fluid dynamics Computer simulation Dynamical systems Exact sciences and technology Finite element method Fluid dynamics Flutter instability Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Navier-Stokes equations Non-linear oscillations Physics Solid mechanics Stabilization for high Reynolds numbers Structural and continuum mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Finite element method Navier–Stokes equations Arbitrary Lagrangian–Eulerian formulation Non-linear oscillations Flutter instability Aeroelasticity Stabilization for high Reynolds numbers Euler Lagrange equation Non linear oscillation Viscous fluid Unsteady flow Fluid structure interaction Modeling Large Reynolds number Flap Navier Stokes equation Numerical simulation Incompressible fluid Aerofoil Mesh generation
ISSN:	0045-7930, 1879-0747
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Abstract	The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. A solid airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the finite element solution of the Navier–Stokes equations coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent computational domain and a moving grid are treated by the arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations. High Reynolds numbers require the application of a suitable stabilization of the finite element discretization. With the aid of numerical experiments we analyze the convergence of the method, if the computational mesh is refined and the time step is successively decreased. Also the effect of the loose (weak) and strong coupling of the flow and structure problems is tested. The applicability of the method is demonstrated by the comparison with NASTRAN computations and the solution of the coupled fluid–structure problem with increasing far-field velocity up to and behind the flutter instability. The developed method can be used in theoretical prediction of dynamic behaviour of aeroelastic systems especially when the system stability has been lost.
AbstractList	The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. A solid airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the finite element solution of the Navier-Stokes equations coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent computational domain and a moving grid are treated by the arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. High Reynolds numbers require the application of a suitable stabilization of the finite element discretization. With the aid of numerical experiments we analyze the convergence of the method, if the computational mesh is refined and the time step is successively decreased. Also the effect of the loose (weak) and strong coupling of the flow and structure problems is tested. The applicability of the method is demonstrated by the comparison with NASTRAN computations and the solution of the coupled fluid-structure problem with increasing far-field velocity up to and behind the flutter instability. The developed method can be used in theoretical prediction of dynamic behaviour of aeroelastic systems especially when the system stability has been lost.
Author	Horáček, Jaromír Růžička, Martin Sváček, Petr Feistauer, Miloslav
Author_xml	– sequence: 1 givenname: Miloslav surname: Feistauer fullname: Feistauer, Miloslav email: feist@karlin.mff.cuni.cz organization: Charles University Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic – sequence: 2 givenname: Jaromír surname: Horáček fullname: Horáček, Jaromír email: jaromirh@it.cas.cz organization: Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, 182 00 Praha 8, Czech Republic – sequence: 3 givenname: Martin surname: Růžička fullname: Růžička, Martin email: mart.in.ruza@seznam.cz organization: Charles University Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic – sequence: 4 givenname: Petr surname: Sváček fullname: Sváček, Petr email: svacek@marian.fsik.cvut.cz organization: Czech Technical University Prague, Faculty of Mechanical Engineering, Karlovo nám. 13, 121 35 Praha 2, Czech Republic
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Keywords	Finite element method Navier–Stokes equations Arbitrary Lagrangian–Eulerian formulation Non-linear oscillations Flutter instability Aeroelasticity Stabilization for high Reynolds numbers Euler Lagrange equation Non linear oscillation Viscous fluid Unsteady flow Fluid structure interaction Modeling Large Reynolds number Flap Navier Stokes equation Numerical simulation Incompressible fluid Aerofoil Mesh generation
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SubjectTerms	Aeroelasticity Airfoils Arbitrary Lagrangian–Eulerian formulation Computation Computational methods in fluid dynamics Computer simulation Dynamical systems Exact sciences and technology Finite element method Fluid dynamics Flutter instability Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Navier-Stokes equations Non-linear oscillations Physics Solid mechanics Stabilization for high Reynolds numbers Structural and continuum mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Title	Numerical analysis of flow-induced nonlinear vibrations of an airfoil with three degrees of freedom
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