Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-14T00:48:22.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Simulation of Airfoil Vibrations Induced by Turbulent Flow

Published online by Cambridge University Press:  28 November 2014

Miloslav Feistauer ,
Jaromír Horáček  and
Petr Sváček
Miloslav Feistauer*
Affiliation:
Charles University in Prague, Faculty of Mathematics and Physics, Sokolovska 83, 186 75 Praha 8, Czech Republic Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, 182 00 Praha 8, Czech Republic
Jaromír Horáček
Affiliation:
Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, 182 00 Praha 8, Czech Republic
Petr Sváček
Affiliation:
Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, 182 00 Praha 8, Czech Republic Czech Technical University Prague, Faculty of Mechanical Engineering, Karlovo nam. 13, 121 35 Praha 2, Czech Republic
*
*Email addresses:feist@karlin.mff.cuni.cz(M. Feistauer), jaromirh@it.cas.cz(J. Horáček), svacek@marian.fsik.cvut.cz(P. Sváček)
Get access

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. The 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 Reynolds averaged Navier-Stokes equations combined with Spalart-Allmaras or κ–ω turbulence models, coupled with a system of nonlinear ordinary differential equations describing the airfoil motion with consideration of large amplitudes. The time-dependent computational domain and approximation on a moving grid are treated by the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Due to large values of the involved Reynolds numbers an application of a suitable stabilization of the finite element discretization is employed. The developed method is used for the computation of flow-induced oscillations of the airfoil near the flutter instability, when the displacements of the airfoil are large, up to ±40 degrees in rotation. The paper contains the comparison of the numerical results obtained by both turbulence models.

Keywords

74F1076D0576F6065N30Fluid-structure interactionflow induced vibrationsReynolds averaged Navier-Stokes equationsturbulence modelsfinite element methodcoupling algorithm
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 1 , January 2015 , pp. 146 - 188
Copyright
Copyright © Global Science Press Limited 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Badia, S, Codina, R (2007) On some fluid-structure iterative algorithms using pressure segregation methods. Application to aeroelesticity, Int. J. Numer. Meth. Engr. 72:46–71.Google Scholar
[2]Baxevanou, CA, Chaviaropoulos, PK, Voutsinas, SG, Vlachos, NS (2008) Evaluation study of a Navier-Stokes CFD aeroelastic model of wind turbine airfoils in classical flutter. J. Wind Engr. Ind. Aerod. 96:1425–1443.CrossRefGoogle Scholar
[3]Brezzi, F, Falk, RS (1991) Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28:581–590.CrossRefGoogle Scholar
[4]Brezzi, F, Fortin, M (1991) Mixed and Hybrid Finite Element Method. Springer Series in Computational Mathematics 15, Springer-Verlag, New York.Google Scholar
[5]Caracoglia, L (2011) Simulation of linear and non-linear propagation effects of a random turbulence field on bridge flutter instability. J. Wind Engr. Ind. Aerod. 99(9):945–954.CrossRefGoogle Scholar
[6]Ciarlet, PG (1979) The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam.Google Scholar
[7]Codina, R (1993) A discontinuity capturing crosswind-dissipation for the finite element solution of the convection diffusion equation. Comput. Meth. Appl. Mech. Engr. 110:325342.Google Scholar
[8]Dolejší, V (2001) ANGENER V3.0. Faculty of Mathematics and Physics, Charles University in Prague.Google Scholar
[9]Dolejší, V (2001) Anisotropic mesh adaptation technique for viscous flow simulation. East-West J. Numer. Math. 9:1–24.Google Scholar
[10]Dowell, EH (1995) A Modern Course in Aeroelasticity. Kluwer Academic Publishers, Dodrecht.Google Scholar
[11]Dubcová, L, Feistauer, M, Horáček, J, Sváček, P (2008) Numerical simulation of airfoil vibrations induced by turbulent flow. J. Comput. Appl. Math. 218(1):34–42.Google Scholar
[12]Dubcová, L, Feistauer, M, Horáček, J, Sváček, P (2009) Numerical simulation of interaction between turbulent flow and a vibrating airfoil. Comput. Visual. Sci. 12:207–225.Google Scholar
[13]Farhat, C, Lesoinne, M, Maman, N (1995) Mixed explicit/implicit time integration of coupled aeroelastic problems: Three field formulation, geometric conservation and distributed solution. Int. J. Numer. Meth. Fluids 21:807–835.Google Scholar
[14]Feistauer, M, Horáček, J, Růžička, M, Sváček, P (2011) Numerical analysis of flow induced nonlinear vibrations of an airfoil with three degrees of freedom. Comput. Fluids 49:110–127.Google Scholar
[15]Foias, C, Manley, O, Rosa, R, Temam, R (2001) Navier-Stokes Equations and Turbulence. Cambridge University Press, Cambridge.Google Scholar
[16]Geissler, W (2003) Numerical study of buffet and transonic flutter on the NLR 7301 airfoil. Aerosp. Sci. Tech. 7:540–550.Google Scholar
[17]Gelhard, T, Lube, G, Olshanskii, MA, Starcke, JH (2005) Stabilized finite element schemes with LBB-stable elements for incompressible flows. J. Comput. Appl. Math. 177:243–267.CrossRefGoogle Scholar
[18] GMSH, http://www.geuz.org/gmsh.Google Scholar
[19]Geuzaine, C, Remacle, JF (2009) Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Meth. Engr. 79(11):1309–1331.Google Scholar
[20]Horáček, J, Sváček, P, Růžička, M, Feistauer, M (2007) Contribution to finite element modelling of airfoil aeroelastic instabilities. Appl. Comput. Mech. 1:43–52.Google Scholar
[21]John, V, Knobloch, P (2007) On spurious oscillations at layers diminishing (SOLD) method for convection-diffusion equations, Part I - A review. Comput. Meth. Appl. Mech. Engr. 196:2197–2215.Google Scholar
[22]Khadra, K, Angot, P, Parneix, S, Caltarigone, J-P (2000) Fictitious domain approach for numerical modelling of Navier-Stokes equations. Int. J. Numer. Meth. Fluids 34:651–684.Google Scholar
[23]Kok, JC (1999) Resolving the dependence on free-stream values for the k-omega turbulence model, National Aerospace Laboratory, NLR Report p. 20.Google Scholar
[24]Langthjem, MA, Morita, H, Nakamura, T, Nakano, M (2006) A flexible rod in annular leakage flow: Influence of turbulence and equilibrium offset, and analysis of instability mechanisms. J. Fluids Struct. 22(5):617–645Google Scholar
[25]Le Tallec, P, Mouro, J (2001) Fluid structure interaction with large structural displacements. Comput. Meth. Appl. Mech. Engr. 190:3039–3067.Google Scholar
[26]Lian, Y, Steen, J, Trygg-Wilander, M, Shyy, W (2003) Low Reynolds number turbulent flows around a dynamically shaped airfoil. Comput. Fluids 32:287–303.Google Scholar
[27]Lojcjanskij, LG (1978) Mechanics of Fluids and Gases. Nauka, Moscow (in Russian).Google Scholar
[28]Losík, V, Čečrdle, J (2005) 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-Letňany, 22p. (in Czech).Google Scholar
[29]Losík, V, Čečrdle, J (2007) Flutter computation of 3-DOF wing profile model. Technical report P-PL-0061/07, Aircraft Research and Test Institute (ARTI), Prague-Letňany, 12p. (in Czech).Google Scholar
[30]Lube, G (1994) Kowalski, Jan Krzysztof (ed.) et al., Numerical Analysis and Mathematical Modelling. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 29:85–104.CrossRefGoogle Scholar
[31]Mannini, C, Šoda, A, Schewe, G (2010) Unsteady RANS modelling of flow past a rectangular cylinder: Investigation of Reynolds number effects. Comput. Fluids 39:1609–1624.CrossRefGoogle Scholar
[32]Mannini, C, Šoda, A, Vo, R, Schewe, G (2010) Unsteady RANS simulations of flow around a bridge section. J. Wind Engr. Ind. Aerod. 98:742–753.Google Scholar
[33]Matsuzaki, Y, Torii, H (1990) Response characteristics of a two-dimensional wing subjected to turbulence near the flutter boundary. J. Sound Vib. 136(2):187–199.Google Scholar
[34]Naudasher, E, Rockwell, D (1994) Flow-Induced Vibrations. A.A. Balkema, Rotterdam.Google Scholar
[35]Nomura, T, Hughes, TJR (1992) An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body, Comput. Meth. Appl. Mech. Engr. 95:115–138.Google Scholar
[36]Poirel, DC, Price, SJ (1996) Numerical investigation of the stability and post-flutter response of a 2D nonlinear airfoil in longitudinal atmospheric turbulence. Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 1:204–214.Google Scholar
[37]Poirel, D, Price, SJ (2003) Random binary (coalescence) flutter of a two-dimensional linear airfoil. J. Fluids Struct. 18:23–42.Google Scholar
[38]Poirel, D, Price, SJ (2007) Bifurcation characteristics of a two-dimensional structurally nonlinear airfoil in turbulent flow. Nonlinear Dynamics, 48(4):423–435.CrossRefGoogle Scholar
[39]Poirel, D, Méitivier, V, Dumas, G (2011) Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers. J. Fluids Struct. 27:1262–1277.Google Scholar
[40]Pope, SB (2000) Turbulent Flows. Cambridge University Press, Cambridge.Google Scholar
[41]Salvatori, L, Spinelli, P (2006) Effects of structural nonlinearity and along-span wind coherence on suspension bridge aerodynamics: Some numerical simulation results. J. Wind Engr. Ind. Aerod. 94(5):415–430.Google Scholar
[42]Schlichting, H, Gersten, K (2000) Boundary Layer Theory (8th edition). Springer, Berlin.Google Scholar
[43]Schlichting, H, Gersten, K (2006) Grenzschicht-Theorie (10th edition). Springer, Berlin.Google Scholar
[44]Spalart, PR, Allmaras, SR (1994) A one equation turbulence model for aerodynamic flows. Recherche Aérospatiale 1:5–21.Google Scholar
[45]Srinivasan, GR, Ekaterinaris, JA, Mc Croskey, WJ (1995) Evaluation of turbulence models for unsteady flows of an oscillating airfoil. Comput. Fluids 24(7):833–861.Google Scholar
[46]Stanišić, MM (1988) The Mathematical Theory of Turbulence. Springer, New York.CrossRefGoogle Scholar
[47]Sváček, P, Feistauer, M, Horáček, J (2007) Numerical simulation of flow induced airfoil vibrations with large amplitudes. J. Fluids Struct. 23:391–411.Google Scholar
[48]Taylor, C, Hood, P (1973) A numerical solution of the Navier-Stokes equations using the finite element technique. Comput. Fluids 1:73–100.Google Scholar
[49]Verfürth, R (1984) Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO, Anal. Numr. 18:175–182.Google Scholar
[50]Wang, B, Zha, GC (2011) Detached-eddy simulation of transonic limit cycle oscillations using high order schemes. Comput. Fluids 52:58–68.Google Scholar
[51]Weber, S, Jones, KD, Ekaterinaris, JA, Platzer, MF (2001) Transonic flutter computations for the NLR 7301 supercritical airfoil. Aerosp. Sci. Tech. 5:293–304.Google Scholar
[52]Wilcox, DC (1993) Turbulence Modeling for CFD. DCW Industries, La Canada, California.Google Scholar
[53]Zhao, D, Zhang, Q, Tan, Y (2009) Random flutter of a 2-DOF nonlinear airfoil in pitch and plunge with freeplay in pitch. Nonlinear Dynamics 58(4):643–654.Google Scholar
[54]Zhao, DM, Zhang, QC, Wang, W (2009) Random bifurcation and power spectrum analysis of a 2-DOF airfoil with freeplay nonlinearity in pitch. J. Vib. Shock 28(6):86–89.Google Scholar