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Numerical simulation of interaction between turbulent flow and a vibrating airfoil. (English) Zbl 1426.74127

Summary: The subject of this paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil. A solid elastically supported airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the stabilized finite element treatment of the Reynolds averaged Navier-Stokes (RANS) approach, the use of turbulence models and the solution of the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. High Reynolds numbers up to \(10^{6}\) require to use a suitable stabilization of the finite element discretization and the application of a turbulence model. We apply the algebraic turbulence model, which was designed by Baldwin and Lomax and modified by Rostand. The developed technique was tested by the simulation of flow past a flat rigid plate and the computation of pressure distribution around a rotating airfoil with prescribed motion. Finally, the method was applied to the simulation of flow induced airfoil vibrations.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76F99 Turbulence
76M10 Finite element methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows
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[1] Akbari, H.M., Price, S.J.: Simulation of the flow over elliptic airfoils at large angles of attack. J. Fluid Struct. 14, 757–777 (2000) · doi:10.1006/jfls.2000.0297
[2] Akbari, H.M., Price, S.J.: Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method. J. Fluid Struct. 14, 855–874 (2003) · doi:10.1016/S0889-9746(03)00018-5
[3] Baldwin, D., Lomax, T.: Thin layer approximation and algebraic model for separated turbulent flows. AIAA Paper, pp. 78–257 (1978)
[4] Benetka, J.: Measurement of an oscillating airfoil in slotted measurement spaces with various heights. Technical Report Z-2610/81, Aeronautical Research and Test Institute, Prague, Letňany (1981) (in Czech)
[5] Benetka, J., Kladrubský, J., Valenta, R.: Measurement of NACA 0012 profile in a slotted measurement section. Technical Report R-2909/98, Aeronautical Research and Test Institute, Prague, Letňany (1998) (in Czech)
[6] Cebeci, T., Smith, A.M.O.: Analysis of Turbulent Boundary Layers. Academic Press, New York (1974) · Zbl 0342.76014
[7] Davis, T.A.: UMFPACK V4.0. http://www.cise.ufl.edu/research/sparse/umfpack , University of Florida
[8] Dervieux, A. (eds): Fluid–Structure Interaction. Kogan Page Science, London (2003)
[9] Dixon, R.C.: High Reynolds number investigation of an Onera model of the NACA 0012 airfoil section. Raport Technique de Laboratoire LTR-HA-5X5/0069, OT, Canada, January (1975)
[10] Dolejší, V.: Anisotropic mesh adaptation technique for viscous flow simulation. East West J Numer Math 9, 1–24 (2001) · Zbl 1056.76045
[11] Dolejší, V.: ANGENER V3.0. http://www.karlin.mff.cuni.cz/dolejsi/angen/angen.htm . Charles University in Prague, Faculty of Mathematics and Physics
[12] Dowell, E.H.: A Modern Course in Aeroelasticity. Kluwer, Dodrecht (1995) · Zbl 0846.73001
[13] Dubcová, L.: Numerical simulation of interaction of fluids and solid bodies. Master Degree Thesis, Charles University Prague, Faculty of Mathematics and Physics, Prague (2006) (in Czech)
[14] Farhat, C., Lesoinne, M., Maman, N.: Mixed explicit/implicit time integration of coupled aeroelastic problems: three field formulation, geometric conservation and distributed solution. Int. J. Numer. Methods Fluids 21, 807–835 (1995) · Zbl 0865.76038 · doi:10.1002/fld.1650211004
[15] Feistauer, M.: Mathematical Methods in Fluid Dynamics. Longman, Harlow (1993) · Zbl 0819.76001
[16] Foias, C., Manley, O., Rosa, R., Temam, R.: Navier–Stokes Equations and Turbulence. Cambridge University Press, Cambridge (2001) · Zbl 0994.35002
[17] 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. 177, 243–267 (2005) · Zbl 1063.76054 · doi:10.1016/j.cam.2004.09.017
[18] Gilliatt, H.C., Strganac, T.W., Kurdila, A.J.: An investigation of internal resonance in aeroelastic systems. Nonlinear Dyn. 31, 1–22 (2003) · Zbl 1026.70023 · doi:10.1023/A:1022174909705
[19] Girault, V., Raviart, P.-A.: Finite Element Methods for the Navier–Stokes Equations. Springer, Berlin (1986) · Zbl 0585.65077
[20] Gresho, P.M., Sani, R.L.: Incompressible Flow and the Finite Element Method. Wiley, Chichester (2000) · Zbl 0988.76005
[21] Heo, H., Cho, Y.H., Kim, D.J.: Stochastic control of flexible beam in random flutter. J. Sound Vib. 267, 335–354 (2003) · Zbl 1236.74203 · doi:10.1016/S0022-460X(03)00184-6
[22] Holmes, P., Marsden, J.E.: Bifuraction to divergence and flutter in flow-induced oscillations: an infinite dimensional analysis. In: Banks, S.P., Pritchard, A.J. (eds.) Control of Distributed Parameter Systems, Proceedings of 2nd IFAC Symposium. Coventry, pp. 133–145 (1977)
[23] Horáček, J.: Nonlinear formulation of oscillations of a profile for aero-hydroelastic computations. In: Dobiáš, I. (ed.) Dynamics of Machines. Institute of Thermomechanics, AS CR, Prague, pp. 51–56 (2003) (ISBN 80-85918-81-1)
[24] John, V.: Large Eddy Simulation of Turbulent Incompressible Flows. Springer, Berlin (2004) · Zbl 1035.76001
[25] Le Tallec, P., Mouro, J.: Fluid structure interaction with large structural displacements. Comput. Methods Appl. Mech. Eng. 190, 3039–3067 (2001) · Zbl 1001.74040 · doi:10.1016/S0045-7825(00)00381-9
[26] Lojcjanskij, L.G.: Mechanics of Fluids and Gases. Nauka, Moscow (1978) (in Russian)
[27] Lube, G.: Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems. Numer. Anal. Math. Model. Banach Center Publications 29, 85–104 (1994) · Zbl 0801.76046
[28] Naudasher, E., Rockwell, D.: Flow-Induced Vibrations. A.A. Balkema, Rotterdam (1994)
[29] 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. 95, 115–138 (1992) · Zbl 0756.76047 · doi:10.1016/0045-7825(92)90085-X
[30] Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2005) · Zbl 1201.76303
[31] Randall, D.A.: Reynolds Averaging. Selected notes, Department of Atmospheric Science, Colorado State University (2003)
[32] Rostand, P.: Algebraic turbulence models for the computation of two-dimensional high speed flows using unstructured grids. NASA CR-181741 (1988)
[33] Schlichting, H., Gersten, K.: Boundary Layer Theory, 8th edn. Springer, Berlin (2000) · Zbl 0940.76003
[34] Schlichting, H., Gersten, K.: Grenzschicht-Theorie, 10th edn. Springer, Berlin (2006)
[35] Singh, S.N., Brenner, M.: Limit cycle oscillation and orbital stability in aeroelastic systems with torsional nonlinearity. Nonlinear Dyn. 31, 435–450 (2003) · Zbl 1062.70592 · doi:10.1023/A:1023264319167
[36] Spalart, P.R., Allmaras, S.R.: A one equation turbulence model for aerodynamic flows. Rech Aérosp 1, 5–21 (1994)
[37] Stanišić, M.M.: The Mathematical Theory of Turbulence. Springer, New York (1988)
[38] Sváček, P., Feistauer, M.: Application of a stabilized FEM to problems of aeroelasticity. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K.(eds) Numerical Mathematics and Advanced Applications, ENUMATH 2003, pp. 796–805. Springer, Berlin (2004) · Zbl 1216.76035
[39] Sváček, P., Feistauer, M., Horáček, J.: Numerical simulation of flow induced airfoil vibrations with large amplitudes. J. Fluid Struct. 23, 391–411 (2007) · doi:10.1016/j.jfluidstructs.2006.10.005
[40] Triebstein, H.: Steady and unsteady transonic pressure distributions on NACA 0012. J. Aircr. 23, 213–219 (1986) · doi:10.2514/3.45291
[41] Tuncer, I.H., Wu, J.C., Wang, C.M.: Theoretical and numerical studies of oscillating airfoils. AIAA J. 28(9), 1615–1624 (1990) · doi:10.2514/3.25260
[42] Turek, S.: Efficient Solvers for Incompressible Flow Problems: An Algorithmic and Computational Approach. Springer, Berlin (1999) · Zbl 0930.76002
[43] White, F.M.: Viscous Fluid Flow. Mc Graw-Hill, New York (2006)
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