Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T21:36:18.061Z Has data issue: false hasContentIssue false

Theoretical and experimental investigation of an unsteady airfoil in the presence of external flow disturbances

Published online by Cambridge University Press:  01 July 2021

ArunVishnu SureshBabu*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
Albert Medina
Affiliation:
Air Force Research Laboratory, Wright–Patterson AFB, Dayton, OH 45433, USA
Matthew Rockwood
Affiliation:
Air Force Research Laboratory, Wright–Patterson AFB, Dayton, OH 45433, USA
Matthew Bryant
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
Ashok Gopalarathnam
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
*
Email address for correspondence: asuresh2@ncsu.edu

Abstract

While studies on unsteady airfoils in a uniform free stream are abundant, the quest for efficient man-made propulsion and energy harvesting calls for an improved understanding and predictive capability of unsteady airfoils encountering external flow disturbances. In this paper, we conduct experimental and theoretical investigations of the interactions between an airfoil engaged in unsteady motion and external flow disturbances generated by an upstream source. The flow field interactions are experimentally studied using particle-image velocimetry and finite-time Lyapunov exponent techniques. An interesting outcome of the interactions is an interruption of leading-edge vortex (LEV) shedding from the airfoil and a consequent modulation of the lift history, which are dependent on the phase of the disturbances relative to the airfoil kinematics. A low-order model for an unsteady airfoil encountering the disturbances is built upon the leading-edge suction parameter (LESP)-modulated discrete-vortex method (LDVM) developed by Ramesh et al. (J. Fluid Mech., vol. 751, 2014, pp. 500–538). The LDVM distils the determination of the LEV shedding characteristics of unsteady airfoils to a single parameter, the LESP. We show that the LDVM, modified for the current work, is able to predict the effect of the disturbances on the LEV shedding characteristics of the airfoil and the associated lift history in good agreement with experimental observations. In addition to being a predictive tool, the LDVM also augments the experimental study by providing a theoretical framework and various graphical approaches to analyse the flow phenomena from a fundamental perspective and elucidate the role of different factors governing the flow field evolution.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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

REFERENCES

Alaminos-Quesada, J. & Fernandez-Feria, R. 2017 Effect of the angle of attack on the transient lift during the interaction of a vortex with a flat plate. Potential theory and experimental results. J. Fluids Struct. 74, 130141.CrossRefGoogle Scholar
Beal, D.N., Hover, F.S., Triantafyllou, M.S., Liao, J.C. & Lauder, G.V. 2006 Passive propulsion in vortex wakes. J. Fluid Mech. 549, 385402.CrossRefGoogle Scholar
Binder, A., Forster, W., Mach, K. & Rogge, H. 1987 Unsteady flow interaction caused by stator secondary vortices in a turbine rotor. Trans. ASME J. Turbomach. 109 (2), 251256.CrossRefGoogle Scholar
Cheng, M., Liu, G. & Lam, K. 2001 Numerical simulation of flow past a rotationally oscillating cylinder. Comput. Fluids 30 (3), 365392.CrossRefGoogle Scholar
Choi, J., Colonius, T. & Williams, D.R. 2015 Surging and plunging oscillations of an airfoil at low Reynolds number. J. Fluid Mech. 763, 237253.CrossRefGoogle Scholar
Choudhry, A., Mo, J., Arjomandi, M. & Kelso, R. 2014 Effects of wake interaction on downstream wind turbines. Wind Engng 38 (5), 535547.CrossRefGoogle Scholar
Dickinson, M.H., Lehmann, F.-O. & Sane, S.P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284 (5422), 19541960.CrossRefGoogle ScholarPubMed
Ellington, C.P., Van Den Berg, C., Willmott, A.P. & Thomas, A.L.R. 1996 Leading-edge vortices in insect flight. Nature 384 (6610), 626630.CrossRefGoogle Scholar
Faure, T.M., Dumas, L. & Montagnier, O. 2020 Numerical study of two-airfoil arrangements by a discrete vortex method. Theor. Comput. Fluid Dyn. 34 (1), 79103.CrossRefGoogle Scholar
Fletcher, T.M. & Brown, R.E. 2007 Modelling the interaction of helicopter main rotor and tail rotor wakes. Aeronaut. J. 111 (1124), 637643.CrossRefGoogle Scholar
Gopalkrishnan, R., Triantafyllou, M.S., Triantafyllou, G.S. & Barrett, D. 1994 Active vorticity control in a shear flow using a flapping foil. J. Fluid Mech. 274, 121.CrossRefGoogle Scholar
Graftieaux, L., Michard, M. & Grosjean, N. 2001 Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12, 1422.CrossRefGoogle Scholar
Green, M.A., Rowley, C.W. & Smits, A.J. 2011 The unsteady three-dimensional wake produced by a trapezoidal pitching panel. J. Fluid Mech. 685, 117145.CrossRefGoogle Scholar
Haller, G. 2001 Distinguished material surfaces and coherent structures in 3D fluid flows. Physica D 149, 248277.CrossRefGoogle Scholar
Huang, Y. & Green, M.A. 2015 Detection and tracking of vortex phenomena using Lagrangian coherent structures. Exp. Fluids 56 (7), 147.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. NASA Ames/Stanford University Center for Turbulence Research Report CTR-S88, pp. 193–207.Google Scholar
Jefferies, R.W. & Rockwell, D. 1996 Interactions of a vortex with an oscillating leading edge. AIAA J. 34 (11), 24482450.CrossRefGoogle Scholar
von Kármán, T. & Sears, W. 1938 Airfoil theory for non-uniform motion. J. Aeronaut. Sci. 5, 379390.CrossRefGoogle Scholar
Katz, J. & Plotkin, A. 2000 Low-Speed Aerodynamics. Cambridge Aerospace Series.Google Scholar
Küssner, H. 1936 Zusammenfassender bericht über den instationären auftrieb von flügeln (summary report on the nonstationary lift of wings). Luftfahrtforschung 13 (12), 410424.Google Scholar
Lefebvre, J.N. & Jones, A.R. 2019 Experimental investigation of airfoil performance in the wake of a circular cylinder. AIAA J. 57 (7), 28082818.CrossRefGoogle Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comput. Phys. 37 (3), 289335.CrossRefGoogle Scholar
Li, C., Yang, W., Xu, X., Wang, J., Wang, M. & Xu, L. 2017 Numerical investigation of fish exploiting vortices based on the Kármán gaiting model. Ocean Engng 140, 718.CrossRefGoogle Scholar
Li, J., Bai, C.-Y. & Wu, Z.-N. 2014 A two-dimensional multibody integral approach for forces in inviscid flow with free vortices and vortex production. Trans. ASME J. Fluids Engng 137 (2), 021205.CrossRefGoogle Scholar
Li, J., Wang, Y., Graham, M. & Zhao, X. 2020 a Vortex moment map for unsteady incompressible viscous flows. J. Fluid Mech. 891, A13.CrossRefGoogle Scholar
Li, J. & Wu, Z.-N. 2015 Unsteady lift for the wagner problem in the presence of additional leading/trailing edge vortices. J. Fluid Mech. 769, 182217.CrossRefGoogle Scholar
Li, J. & Wu, Z.-N. 2016 A vortex force study for a flat plate at high angle of attack. J. Fluid Mech. 801, 222249.CrossRefGoogle Scholar
Li, J. & Wu, Z.-N. 2018 Vortex force map method for viscous flows of general airfoils. J. Fluid Mech. 836, 145166.CrossRefGoogle Scholar
Li, J., Zhao, X. & Graham, M. 2020 b Vortex force maps for three-dimensional unsteady flows with application to a delta wing. J. Fluid Mech. 900, A36.CrossRefGoogle Scholar
Li, S. & Sun, Z. 2015 Harvesting vortex energy in the cylinder wake with a pivoting vane. Energy 88, 783792.CrossRefGoogle Scholar
Liao, J.C., Beal, D.N., Lauder, G.V. & Triantafyllou, M.S. 2003 a The Kármán gait: novel body kinematics of rainbow trout swimming in a vortex street. J. Expl Biol. 206 (6), 10591073.CrossRefGoogle Scholar
Liao, J.C., Beal, D.N., Lauder, G.V. & Triantafyllou, M.S. 2003 b Fish exploiting vortices decrease muscle activity. Science 302 (5650), 15661569.CrossRefGoogle ScholarPubMed
Liao, Q., Dong, G.J. & Lu, X.Y. 2004 Vortex formation and force characteristics of a foil in the wake of a circular cylinder. J. Fluids Struct. 19 (4), 491510.CrossRefGoogle Scholar
Lissaman, P.B.S. & Shollenberger, C.A. 1970 Formation flight of birds. Science 168 (3934), 10031005.CrossRefGoogle Scholar
McCune, J.E., Lam, C.G. & Scott, M.T. 1990 Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver. AIAA J. 28 (3), 385393.CrossRefGoogle Scholar
Medina, A., SureshBabu, A., Rockwood, M.P., Gopalarathnam, A. & Anwar, A. 2019 Theoretical and experimental study of wake encounters on unsteady airfoils. AIAA Paper 2019-0898.CrossRefGoogle Scholar
Muscutt, L.E., Weymouth, G.D. & Ganapathisubramani, B. 2017 Performance augmentation mechanism of in-line tandem flapping foils. J. Fluid Mech. 827, 484505.CrossRefGoogle Scholar
Narsipur, S., Hosangadi, P., Gopalarathnam, A. & Edwards, J.R. 2020 Variation of leading-edge suction during stall for unsteady aerofoil motions. J. Fluid Mech. 900, A25.CrossRefGoogle Scholar
Okajima, A., Takata, H. & Asanuma, T. 1975 Viscous flow around a rotationally oscillating circular cylinder. NASA STI/Recon Tech. Rep. N 76.Google Scholar
Perrin, R., Braza, M., Cid, E., Cazin, S., Barthet, A., Sevrain, A., Mockett, C. & Thiele, F. 2007 Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD. Exp. Fluids 43, 341355.CrossRefGoogle Scholar
Pitt Ford, C.W. & Babinsky, H. 2013 Lift and the leading-edge vortex. J. Fluid Mech. 720, 280313.CrossRefGoogle Scholar
Ramesh, K., Gopalarathnam, A., Granlund, K., Ol, M.V. & Edwards, J.R. 2014 Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding. J. Fluid Mech. 751, 500538.CrossRefGoogle Scholar
Rival, D., Manejev, R. & Tropea, C. 2010 Measurement of parallel blade–vortex interaction at low Reynolds numbers. Exp. Fluids 49 (1), 8999.CrossRefGoogle Scholar
Rockwood, M.P. & Medina, A. 2020 Controlled generation of periodic vortical gusts by the rotational oscillation of a circular cylinder and attached plate. Exp. Fluids 61, 65.CrossRefGoogle Scholar
Rockwood, M.P., Taira, K. & Green, M.A. 2017 Detecting vortex formation and shedding in cylinder wakes using Lagrangian coherent structures. AIAA J. 55 (1), 1523.CrossRefGoogle Scholar
Sears, W.R. 1941 Some aspects of nonstationary airfoil theory and its practical application. J. Aeronaut. Sci. 104108.CrossRefGoogle Scholar
Shao, X. & Pan, D. 2011 Hydrodynamics of a flapping foil in the wake of a d-section cylinder. J. Hydrodyn. 23 (4), 422430.CrossRefGoogle Scholar
Shyy, W., Aono, H., Chimakurthi, S.K., Trizila, P., Kang, C.-K., Cesnik, C.E.S. & Liu, H. 2010 Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 46 (7), 284327.CrossRefGoogle Scholar
Streitlien, K., Triantafyllou, G.S. & Triantafyllou, M.S. 1996 Efficient foil propulsion through vortex control. AIAA J. 34 (11), 23152319.CrossRefGoogle Scholar
SureshBabu, A., Ramesh, K. & Gopalarathnam, A. 2019 Model reduction in discrete-vortex methods for unsteady airfoil flows. AIAA J. 57 (4), 14091422.CrossRefGoogle Scholar
Tadokoro, M., Yokoyama, H. & Iida, A. 2017 Effects of wake-turbine blade interactions on power production of wind turbines. AIP Conf. Proc. 1807, 020002.CrossRefGoogle Scholar
Theodorsen, T. 1935 General theory of aerodynamic instabililty and the mechanism of flutter. NACA Tech. Rep. NACA-TR-496. National Advisory Committee for Aeronautics.Google Scholar
Toming, G., Chambers, L. & Kruusmaa, M. 2014 Experimental study of hydrodynamic forces acting on artificial fish in a von Kármán vortex street. Underwater Technol. 32 (2), 8191.CrossRefGoogle Scholar
Vatistas, G.H., Kozel, V. & Mih, W.C. 1991 A simpler model for concentrated vortices. Exp. Fluids 11 (1), 7376.CrossRefGoogle Scholar
Wagner, H. 1925 Über die entstehung des dynamischen auftriebes von tragflügeln. Z. Angew. Math. Mech. 5, 1735.CrossRefGoogle Scholar
Wang, C. & Eldredge, J.D. 2013 Low-order phenomenological modeling of leading-edge vortex formation. Theor. Comput. Fluid Dyn. 27 (5), 577598.CrossRefGoogle Scholar
Wei, Z.A. & Zheng, Z.C. 2017 a Energy-harvesting mechanism of a heaving airfoil in a vortical wake. AIAA J. 55 (12), 40614073.CrossRefGoogle Scholar
Wei, Z.A. & Zheng, Z.C. 2017 b Fluid-structure interaction simulation on energy harvesting from vortical flows by a passive heaving foil. Trans. ASME J. Fluids Engng 140 (1), 011105.Google Scholar
Wu, J., Chen, Y.L. & Zhao, N. 2015 Role of induced vortex interaction in a semi-active flapping foil based energy harvester. Phys. Fluids 27 (9), 093601.CrossRefGoogle Scholar
Zhang, I., Su, Y., Yang, L. & Wang, Z. 2010 Hydrodynamic performance of flapping-foil propulsion in the influence of vortices. J. Mar. Sci. 9 (2), 213219.Google Scholar
Zhang, Z., Wang, Z. & Gursul, I. 2020 Lift enhancement of a stationary wing in a wake. AIAA J. 58 (11), 46134619.CrossRefGoogle Scholar
Zhao, Q., Sheng, C. & Afjeh, A. 2014 Computational aerodynamic analysis of offshore upwind and downwind turbines. J. Aerodyn 2014, 860637.CrossRefGoogle Scholar