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Flow physics and dynamics of flow-induced pitch oscillations of an airfoil

Published online by Cambridge University Press:  27 August 2019

Karthik Menon Open the ORCID record for Karthik Menon [Opens in a new window]  and
Rajat Mittal Open the ORCID record for Rajat Mittal [Opens in a new window]
Karthik Menon
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Rajat Mittal*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

We conduct a computational study of flow-induced pitch oscillations of a rigid airfoil at a chord-based Reynolds number of 1000. A sharp-interface immersed boundary method is used to simulate two-dimensional incompressible flow, and this is coupled with the equations for a rigid foil supported at the elastic axis with a linear torsional spring. We explore the effect of spring stiffness, equilibrium angle-of-attack and elastic-axis location on the onset of flutter, and the analysis of the simulation data provides insights into the time scales and mechanisms that drive the onset and dynamics of flutter. The dynamics of this configuration includes complex phenomena such as bifurcations, non-monotonic saturation amplitudes, hysteresis and non-stationary limit-cycle oscillations. We show the utility of ‘maps’ of energy exchange between the flow and the airfoil system, as a way to understand, and even predict, this complex behaviour.

JFM classification

Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 582 - 613
Copyright
© 2019 Cambridge University Press 

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References

Abbott, I. H. & Von Doenhoff, A. E. 1959 Theory of Wing Sections, Including A Summary of Airfoil Data. Courier Corporation.Google Scholar
Akbari, M. H. & Price, S. J. 2003 Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method. J. Fluids Struct. 17 (6), 855–874.10.1016/S0889-9746(03)00018-5Google Scholar
Amiralaei, M. R., Alighanbari, H. & Hashemi, S. M. 2010 An investigation into the effects of unsteady parameters on the aerodynamics of a low Reynolds number pitching airfoil. J. Fluids Struct. 26 (6), 979–993.10.1016/j.jfluidstructs.2010.06.004Google Scholar
Argentina, M. & Mahadevan, L.2005 Fluid-flow-induced flutter of a flag. Tech. Rep. 6.10.1073/pnas.0408383102Google Scholar
Ashraf, M. A., Young, J. & Lai, J. C. S. 2011 Reynolds number, thickness and camber effects on flapping airfoil propulsion. J. Fluids Struct. 27 (2), 145–160.10.1016/j.jfluidstructs.2010.11.010Google Scholar
Bhat, S. S. & Govardhan, R. N. 2013 Stall flutter of NACA 0012 airfoil at low Reynolds numbers. J. Fluids Struct. 41, 166–174.10.1016/j.jfluidstructs.2013.04.001Google Scholar
Blackburn, H. M. & Karniadakis, G. E. 1993 Two- and three-dimensional simulations of vortex-induced vibration of a circular cylinder. In 3rd International Offshore & Polar Engineering Conference, Singapore, 1977, pp. 715–720.Google Scholar
Brunton, S. & Rowley, C. 2009 Modeling the unsteady aerodynamic forces on small-scale wings. In 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, p. 1127.Google Scholar
Dimitriadis, G. & Li, J. 2009 Bifurcation behavior of airfoil undergoing stall flutter oscillations in low-speed wind tunnel. AIAA J. 47 (11), 2577–2596.10.2514/1.39571Google Scholar
Dowell, E. H. 1966 Nonlinear oscillations of a fluttering plate. AIAA J. 4 (7), 1267–1275.10.2514/3.3658Google Scholar
Dowell, E. H. & Hall, K. C. 2001 Modeling of fluid–structure interaction. Annu. Rev. Fluid Mech. 33 (1), 445–490.10.1146/annurev.fluid.33.1.445Google Scholar
Ducoin, A. & Young, Y. L. 2013 Hydroelastic response and stability of a hydrofoil in viscous flow. J. Fluids Struct. 38, 40–57.10.1016/j.jfluidstructs.2012.12.011Google Scholar
Eldredge, J. D. & Jones, A. R. 2019 Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51, 75–104.10.1146/annurev-fluid-010518-040334Google Scholar
Ericsson, L. E. & Reding, J. P. 1988 Fluid mechanics of dynamic stall. Part I. Unsteady flow concepts. J. Fluids Struct. 2 (1), 1–33.10.1016/S0889-9746(88)90116-8Google Scholar
Gharali, K. & Johnson, D. A. 2013 Dynamic stall simulation of a pitching airfoil under unsteady freestream velocity. J. Fluids Struct. 42, 228–244.10.1016/j.jfluidstructs.2013.05.005Google Scholar
Ghias, R., Mittal, R. & Dong, H. 2007 A sharp interface immersed boundary method for compressible viscous flows. J. Comput. Phys. 225 (1), 528–553.10.1016/j.jcp.2006.12.007Google Scholar
Hall, K. C. 1994 Eigenanalysis of unsteady flows about airfoils, cascades, and wings. AIAA J. 32 (12), 2426–2432.10.2514/3.12309Google Scholar
Holmes, P. & Marsden, J. 1978 Bifurcation to divergence and flutter in flow-induced oscillations: an infinite dimensional analysis. Automatica 14 (4), 367–384.10.1016/0005-1098(78)90036-5Google Scholar
Hover, F. S., Techet, A. H. & Triantafyllou, M. S. 1998 Forces on oscillating uniform and tapered cylinders in crossflow. J. Fluid Mech. 363, 97–114.10.1017/S0022112098001074Google Scholar
Jones, K. D. & Platzer, M. F. 1996 Time-domain analysis of low-speed airfoil flutter. AIAA J. 34 (5), 1027–1033.10.2514/3.13183Google Scholar
Jumper, E. J., Dimmick, R. L. & Allaire, A. J. S. 1989 The effect of pitch location on dynamic stall. J. Fluids Engng 111 (3), 256–262.10.1115/1.3243639Google Scholar
Kumar, S., Navrose & Mittal, S. 2016 Lock-in in forced vibration of a circular cylinder. Phys. Fluids 28, 113605.10.1063/1.4967729Google Scholar
Lee, T. & Gerontakos, P. 2004 Investigation of flow over an oscillating airfoil. J. Fluid Mech. 512, 313–341.10.1017/S0022112004009851Google Scholar
Leontini, J. S., Stewart, B. E., Thompson, M. C. & Hourigan, K. 2006 Predicting vortex-induced vibration from driven oscillation results. Appl. Math. Model. 30 (10), 1096–1102.10.1016/j.apm.2005.05.017Google Scholar
McCroskey, W. J. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14, 285–311.10.1146/annurev.fl.14.010182.001441Google Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. & von Loebbecke, A. 2008 A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227 (10), 4825–4852.10.1016/j.jcp.2008.01.028Google Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37 (1), 239–261.10.1146/annurev.fluid.37.061903.175743Google Scholar
Morse, T. L. & Williamson, C. H. K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid. Mech. 634, 5–39.10.1017/S0022112009990516Google Scholar
Morse, T. L. & Williamson, C. H. K. 2006 Employing controlled vibrations to predict fluid forces on a cylinder undergoing vortex-induced vibration. J. Fluids Struct. 22 (6-7), 877–884.10.1016/j.jfluidstructs.2006.04.004Google Scholar
Mueller, T. J. & DeLaurier, J. D. 2003 Aerodynamics of small vehicles. Annu. Rev. Fluid Mech. 35 (1), 89–111.10.1146/annurev.fluid.35.101101.161102Google Scholar
Olivieri, S., Boccalero, G., Mazzino, A. & Boragno, C. 2017 Fluttering conditions of an energy harvester for autonomous powering. Renewable Energy 105, 530–538.10.1016/j.renene.2016.12.067Google Scholar
Onoue, K. & Breuer, K. S. 2016 Vortex formation and shedding from a cyber-physical pitching plate. J. Fluid Mech. 793, 229–247.10.1017/jfm.2016.134Google Scholar
Onoue, K. & Breuer, K. S. 2018 A scaling for vortex formation on swept and unswept pitching wings. J. Fluid Mech. 832, 697–720.10.1017/jfm.2017.710Google Scholar
Onoue, K., Song, A., Strom, B. & Breuer, K. S. 2015 Large amplitude flow-induced oscillations and energy harvesting using a cyber-physical pitching plate. J. Fluids Struct. 55, 262–275.10.1016/j.jfluidstructs.2015.03.004Google Scholar
Orchini, A., Mazzino, A., Guerrero, J., Festa, R. & Boragno, C. 2013 Flapping states of an elastically anchored plate in a uniform flow with applications to energy harvesting by fluid–structure interaction. Phys. Fluids 25 (9), 97105.10.1063/1.4821808Google Scholar
Patil, M. J. & Hodges, D. H. 2004 On the importance of aerodynamic and structural geometrical nonlinearities in aeroelastic behavior of high-aspect-ratio wings. J. Fluids Struct. 19 (7), 905–915.10.1016/j.jfluidstructs.2004.04.012Google Scholar
Peng, Z. & Zhu, Q. 2009 Energy harvesting through flow-induced oscillations of a foil. Phys. Fluids 21 (12), 1–9.10.1063/1.3275852Google Scholar
Poirel, D., Harris, Y. & Benaissa, A. 2008 Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers. J. Fluids Struct. 24 (5), 700–719.10.1016/j.jfluidstructs.2007.11.005Google Scholar
Poirel, D., Métivier, V. & Dumas, G. 2011 Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers. J. Fluids Struct. 27 (8), 1262–1277.10.1016/j.jfluidstructs.2011.05.009Google Scholar
Ramesh, K., Murua, J. & Gopalarathnam, A. 2015 Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding. J. Fluids Struct. 55, 84–105.10.1016/j.jfluidstructs.2015.02.005Google Scholar
Sarpkaya, T. 1978 Fluid forces on oscillating cylinders. NASA STI/Recon Tech. Rep. A 78, 275–290.Google Scholar
Seo, J. H. & Mittal, R. 2011 A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comput. Phys. 230 (19), 7347–7363.10.1016/j.jcp.2011.06.003Google Scholar
Shyy, W., Lian, Y., Tang, J., Viieru, D. & Liu, H. 2007 Aerodynamics of Low Reynolds Number Flyers, vol. 22. Cambridge University Press.Google Scholar
Staubli, T. 1983 Calculation of the vibration of an elastically mounted cylinder using experimental data from forced oscillation. J. Fluids Engng 105 (2), 225–229.10.1115/1.3240968Google Scholar
Strogatz, S. H. 2018 Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press.10.1201/9780429492563Google Scholar
Theodorsen, T.1935 General theory of aerodynamic instability and the mechanism of flutter NACA Report No. 496. Tech. Rep., US National Advisory Committee for Aeronautics.Google Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36 (1), 413–455.10.1146/annurev.fluid.36.050802.122128Google Scholar
Williamson, C. H. K. & Govardhan, R. 2008 A brief review of recent results in vortex-induced vibrations. J. Wind Engng Ind. Aerodyn. 96 (6-7), 713–735.10.1016/j.jweia.2007.06.019Google Scholar
Young, J., Lai, J. C. S. & Platzer, M. F. 2014 A review of progress and challenges in flapping foil power generation. Prog. Aerosp. Sci. 67, 2–28.10.1016/j.paerosci.2013.11.001Google Scholar