Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T18:50:07.203Z Has data issue: false hasContentIssue false

Vortex formation on a pitching aerofoil at high surging amplitudes

Published online by Cambridge University Press:  27 October 2020

Luke R. Smith*
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD20742, USA
Anya R. Jones
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD20742, USA
*
Email address for correspondence: lsmith1@umd.edu

Abstract

In many applications, conventional aerofoils are subject to a number of simultaneous motions that complicate the prediction of flow separation. The purpose of this work is to evaluate the impact of a large-amplitude free-stream oscillation on the timing of vortex formation for a simultaneously surging and pitching wing. Experimental flow field measurements were obtained on a NACA 0012 aerofoil over a wide range of surge amplitudes ($1.50 \leq \lambda \leq 2.25$) and reduced frequencies ($0.1 \leq k \leq 0.3$). Particular attention was paid to how various mechanisms of flow separation, specifically the velocity induced by the trailing wake and unsteady effects in the boundary layer, were impacted by a change in the properties of the surge motion. In the regime where $k \leq 0.3$, a change in the surge kinematics primarily manifested as a change in the relative strength of the trailing wake. Boundary layer unsteadiness was found to have a negligible influence on the timing of vortex formation in the same flow regime. Thus, the timing of leading-edge vortex formation was well predicted by a combination of an unsteady inviscid flow solver and a quasi-steady treatment of the boundary layer, a promising result for low-order predictions of vortex behaviour in unsteady aerofoil flows.

Type
JFM Papers
Copyright
© The Author(s), 2020. 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

Beddoes, T. S. 1979 A qualitative discussion of dynamic stall. AGARD Rep. 679.Google Scholar
Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412 (6848), 729733.CrossRefGoogle Scholar
Carr, L. W., McAlister, K. W. & McCroskey, W. J. 1977 Analysis of the development of dynamic stall based on oscillating airfoil experiments. NASA Tech. Note TN D-8382.Google Scholar
Cebeci, T., Platzer, M. F., Hang, H. M. & Chen, H. H 1993 An inviscid-viscous interaction approach to the calculation of dynamic stall initiation on airfoils. J. Turbomach. 115 (4), 111.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
Deparday, J. & Mulleners, K. 2019 Modeling the interplay between the shear layer and leading edge suction during dynamic stall. Phys. Fluids 31 (10), 107104.CrossRefGoogle Scholar
Dunne, R. & McKeon, B. 2015 Dynamic stall on a pitching and surging airfoil. Exp. Fluids 56, 157.CrossRefGoogle Scholar
Dunne, R., Schmid, P. & McKeon, B. 2016 Analysis of flow timescales on a periodically surgingpitching airfoil. AIAA J. 54 (11), 34213433.CrossRefGoogle Scholar
Dwyer, H. A. & McCroskey, W. J. 1971 Crossflow and unsteady boundary-layer effects on rotating blades. AIAA J. 9 (8), 14981505.CrossRefGoogle Scholar
Eldredge, J. D. & Jones, A. R. 2019 Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51 (1), 75104.CrossRefGoogle Scholar
Ellington, C. P., van den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626630.CrossRefGoogle Scholar
Gharali, K., Gharaei, E., Soltani, M. & Raahemifar, K. 2018 Reduced frequency effects on combined oscillations, angle of attack and freestream oscillations, for a wind turbine blade element. J. Renew. Energy 115, 252259.CrossRefGoogle Scholar
Gharali, K. & Johnson, D. A. 2013 Dynamic stall simulation of a pitching airfoil under unsteady freestream velocity. J. Fluids Struct. 42, 228244.CrossRefGoogle Scholar
Granlund, K. O., Ol, M. V. & Jones, A. R. 2016 Streamwise oscillation of airfoils into reverse flow. AIAA J. 54 (5), 16281636.CrossRefGoogle Scholar
Greenberg, J. M. 1947 Airfoil in sinusoidal motion in a pulsating stream. NACA Tech. Rep. 1326.Google Scholar
Hess, J. L. 1990 Panel methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 22, 255274.CrossRefGoogle Scholar
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
Kirk, P. B. & Jones, A. R. 2018 Vortex formation on surging airfoils with application to reverse flow modeling. J. Fluid Mech. 859, 5988.CrossRefGoogle Scholar
Kocher, A., Cummings, R., Tran, S. & Sahni, O. 2017 Large eddy simulation of surging airfoils with moderate to large streamwise oscillations. In 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas. AIAA Paper 2017-1006.Google Scholar
Kriegseis, J., Kinzel, M. & Rival, D. E. 2013 On the persistence of memory: do initial conditions impact vortex formation? J. Fluid Mech. 736, 91106.CrossRefGoogle Scholar
Leishman, J. G. & Beddoes, T. S. 1989 A semi-empirical model for dynamic stall. J. Am. Helicopter Soc. 34 (3), 317.Google Scholar
Lind, A. H., Trollinger, L. N., Manar, F. H., Chopra, I. & Jones, A. R. 2018 Flowfield measurements of reverse flow on a high advance ratio rotor. Exp. Fluids 59, 185.CrossRefGoogle Scholar
Lock, R. C. & Williams, B. R. 1987 Viscous-inviscid interactions in external aerodynamics. Prog. Aerosp. Sci. 24 (2), 51171.CrossRefGoogle Scholar
Lorber, P. F. & Carta, F. O. 1988 Airfoil dynamic stall at constant pitch rate and high Reynolds number. J. Aircraft 25 (6), 548556.CrossRefGoogle Scholar
Manar, F. & Jones, A. R. 2019 Evaluation of potential flow models for unsteady separated flow with respect to experimental data. Phys. Fluids 4 (3), 034702.CrossRefGoogle Scholar
Manar, F. H. 2018 Measurements and modeling of the unsteady flow around a thin wing. PhD thesis, University of Maryland, College Park.Google Scholar
Mancini, P., Manar, F., Granlund, K., Ol, M. V. & Jones, A. R. 2015 Unsteady aerodynamic characteristics of a translating rigid wing at low Reynolds numbers. Phys. Fluids 27, 123102.CrossRefGoogle Scholar
McAlister, K. W., Lambert, O. & Petot, D. 1984 Application of the ONERA model of dynamic stall. NASA Tech. Paper 2399.Google Scholar
McCroskey, W. J. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14, 285311.CrossRefGoogle Scholar
Medina, A. & Jones, Anya R. 2016 Leading-edge vortex burst on a low-aspect-ratio rotating flat plate. Phys. Rev. Fluids 1, 044501.CrossRefGoogle Scholar
Medina, A., Ol, M. V., Greenblatt, D., Muller-Vahl, H. & Strangfeld, C. 2018 High-amplitude surge of a pitching airfoil: complementary wind- and water-tunnel measurements. AIAA J. 56 (4), 17031709.CrossRefGoogle Scholar
Milne-Thompson, L. M. 1938 Theoretical Hydrodynamics, 1st edn. Macmillan.Google Scholar
Panah, A. E., Akkala, J. M. & Buchholz, J. H. J. 2015 Vorticity transport and the leading-edge vortex of a plunging airfoil. Exp. Fluids 56, 160.CrossRefGoogle Scholar
Parker, C. M. & Leftwich, M. C. 2016 The effect of tip speed ratio on a vertical axis wind turbine at high Reynolds numbers. Exp. Fluids 57, 74.CrossRefGoogle Scholar
Ramesh, K., Gopalarathnam, A., Granlund, K. & Ol, M. V. 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
Ramesh, K., Gopalarathnam, A., Granlund, K., Ol, M. V. & Edwards, J. R. 2012 Theoretical modeling of leading edge vortices using the leading edge suction parameter. In 30th AIAA Applied Aerodynamics Conference, New Orleans, Louisiana.CrossRefGoogle Scholar
Ramesh, K., Granlund, K., Ol, M. V., Gopalarathnam, A. & Edwards, J. R. 2017 Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows. Theor. Comput. Fluid Dyn. 32, 109136.CrossRefGoogle Scholar
Ramos-Garcia, N., Sorensen, J. N. & Shen, W. Z. 2014 A strong viscous-inviscid interaction model for rotating airfoils. Wind Energy 17 (12), 19571984.CrossRefGoogle Scholar
Riley, N. 1975 Unsteady laminar boundary layers. SIAM Rev. 17 (2), 274297.CrossRefGoogle Scholar
Schlichting, H. 2017 Boundary Layer Theory, 9th edn. Springer.CrossRefGoogle Scholar
Sears, W. R. 1938 A systematic presentation of the theory of thin airfoils in non-uniform motion. PhD thesis, California Institute of Technology.Google Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Tech. Rep. 496.Google Scholar
Wang, C. & Eldridge, J. D. 2013 Low-order phenomenological modeling of leading-edge vortex formation. Theor. Comput. Fluid Dyn. 27 (5), 577598.CrossRefGoogle Scholar
Wang, Q. & Zhao, Q. 2016 Unsteady aerodynamic characteristics investigation of rotor airfoil under variational freestream velocity. Aerosp. Sci. Technol. 58, 8291.CrossRefGoogle Scholar
Wojcik, C. J. & Buchholz, J. H. J. 2014 Vorticity transport in the leading-edge vortex on a rotating blade. J. Fluid Mech. 743, 249261.CrossRefGoogle Scholar
Wong, J. G. & Rival, D. E. 2015 Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles. J. Fluid Mech. 766, 611625.CrossRefGoogle Scholar