Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-13T09:59:38.974Z Has data issue: false hasContentIssue false
  • English
  • Français

Variation of leading-edge suction during stall for unsteady aerofoil motions

Published online by Cambridge University Press:  11 August 2020

Shreyas Narsipur Open the ORCID record for Shreyas Narsipur [Opens in a new window] ,
Pranav Hosangadi Open the ORCID record for Pranav Hosangadi [Opens in a new window] ,
Ashok Gopalarathnam Open the ORCID record for Ashok Gopalarathnam [Opens in a new window]  and
Jack R. Edwards
Shreyas Narsipur*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC27695, USA
Pranav Hosangadi
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC27695, USA
Ashok Gopalarathnam
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC27695, USA
Jack R. Edwards
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC27695, USA
*
†Email address for correspondence: shreya@ncsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The suction force at the leading edge of a round-nosed aerofoil is an important indicator of the state of the flow over the leading edge and, often, the entire aerofoil. The leading-edge suction parameter (LESP) is a non-dimensional version of this force. In recent works, the LESP was calculated with good accuracy for attached flows at low Reynolds numbers (10 000–100 000) from unsteady aerofoil theory. In contrast to this ‘inviscid’ LESP, results from viscous computations and experiments are used here to calculate the ‘viscous’ LESP on aerofoils undergoing pitching motions at low subsonic speeds. The LESP formulation is also updated to account for the net velocity of the aerofoil. Spanning multiple aerofoils, Reynolds numbers and kinematics, the cases include motions in which dynamic stall occurs with or without leading-edge vortex (LEV) formation. Inflections in the surface pressure and skin-friction distributions near the leading edge are shown to be reliable indicators of LEV initiation. Critical LESP, which is the LESP value at LEV initiation, was found to be nearly independent of pivot location, weakly dependent on pitch rate and strongly dependent on Reynolds number. The viscous LESP was seen to drop to near-zero values when the flow is separated at the leading edge, irrespective of LEV formation. This behaviour was shown to correlate well with the loss of streamline curvature at the leading edge due to flow separation. These findings serve to improve our understanding and extend the applicability of the leading-edge suction behaviour gained from earlier works.

JFM classification

Boundary Layers: Boundary layer separation Vortex Flows: Vortex dynamics Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A25
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

Akbari, M. H. & Price, S. J. 2003 Simulation of dynamic stall for a NACA0012 airfoil using a vortex method. J. Fluids Struct. 17, 855–874.CrossRefGoogle Scholar
Ansell, P. J. & Mulleners, K. 2020 Multiscale vortex characteristics of dynamic stall from empirical mode decomposition. AIAA J. 58 (2), 600–617.CrossRefGoogle Scholar
Beddoes, T. S. 1978 Onset of leading-edge separation effects under dynamic conditions and low Mach number. In Proceedings of the 34th Annual National Forum of the American Helicopter Society.Google 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. Rep. TN 8382. National Aeronautics and Space Administration.Google Scholar
Carr, L. W., McCroskey, W. J., McAlister, K. W., Pucci, S. L. & Lambert, O. 1982 An experimental study of dynamic stall on advanced airfoil sections. Volume 3: hot-wire and hot-film measurements. NASA Tech. Rep. TM 84245. National Aeronautics and Space Administration.CrossRefGoogle Scholar
Carta, F. 1967 a An analysis of the stall flutter instability of helicopter rotor blades. J. Am. Helicopter Soc. 12, 1–18.CrossRefGoogle Scholar
Carta, F. 1967 b Unsteady normal force on an airfoil in a periodically stalled inlet flow. J. Aircraft 4 (5), 416–442.CrossRefGoogle Scholar
Cassidy, D. A., Edwards, J. R. & Tian, M. 2009 An investigation of interface-sharpening schemes for multiphase mixture flows. J. Comput. Phys. 228 (16), 5628–5649.CrossRefGoogle Scholar
Chandrasekhara, M. S., Ahmed, S. & Carr, L. W. 1993 Schlieren studies of compressibility effects on dynamic stall of transiently pitching airfoils. J. Aircraft 30 (2), 213–220.CrossRefGoogle Scholar
Choudhuri, P. G. & Knight, D. D. 1996 Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil. J. Fluid Mech. 308, 195–217.CrossRefGoogle Scholar
Choudhuri, P. G., Knight, D. D. & Visbal, M. R. 1994 Two-dimensional unsteady leading-edge separation on a pitching airfoil. AIAA J. 32 (4), 673–681.CrossRefGoogle Scholar
Corke, T. C. & Thomas, F. O. 2015 Dynamic stall in pitching airfoils: aerodynamic damping and compressibility effects. Annu. Rev. Fluid Mech. 47, 479–505.CrossRefGoogle Scholar
Crimi, P. 1973 Dynamic stall. Tech. Rep. AGARD-AG 172.Google Scholar
Dat, R., Tran, C. T. & Petot, D. 1979 Modele Phenomenologique de Decrochage Dynamique sur Profil de Pale d'Helicoptere. ONERA Tech. Rep. TP 1979-149.Google 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
Edwards, J. R. & Chandra, S. 1996 Comparison of eddy viscosity – transport turbulence models for three-dimensional, shock-separated flowfields. AIAA J. 34 (4), 756–763.CrossRefGoogle Scholar
Ekaterinaris, J. A. & Platzer, M. F. 1998 Computational prediction of airfoil dynamic stall. Prog. Aerosp. Sci. 33 (11–12), 759–846.CrossRefGoogle Scholar
Eldredge, J. D. & Jones, A. R. 2019 Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51, 75–104.CrossRefGoogle Scholar
Eldredge, J. D. & Wang, C. 2010 High-fidelity simulations and low-order modeling of a rapidly pitching plate. AIAA Paper 2010-4281. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Eldredge, J. D. & Wang, C. 2011 Improved low-order modeling of a pitching and perching plate. AIAA Paper 2011-3579. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Eldredge, J. D., Wang, C. J. & Ol, M. V. 2009 A computational study of a canonical pitch-up, pitch-down wing maneuver. AIAA Paper 2009-3687. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Ellington, C. 1999 The novel aerodynamics of insect flight: applications to micro-air vehicles. J. Expl Biol. 202 (23), 3439–3448.Google ScholarPubMed
Ellington, C. P., van den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.CrossRefGoogle Scholar
Epps, B. P. & Greeley, D. S. 2018 A quasi-continuous vortex lattice method for unsteady aerodynamics analysis. AIAA Paper 2018-0815. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Epps, B. P. & Roesler, B. T. 2018 Vortex sheet strength in the Sears, Küssner, Theodorsen, and Wagner aerodynamics problems. AIAA J. 56 (3), 889–904.CrossRefGoogle Scholar
Ericsson, L. E. & Reding, J. P. 1971 Unsteady airfoil stall, review and extension. J. Aircraft 8 (8), 609–616.CrossRefGoogle Scholar
Evans, W. T. & Mort, K. W. 1959 Analysis of computed flow parameters for a set of sudden stalls in low speed two-dimensional flow. NACA Tech. Rep. TN D-85.Google Scholar
Geissler, W. & Haselmeyer, H. 2006 Investigation of dynamic stall onset. Aerosp. Sci. Technol. 10, 590–600.CrossRefGoogle Scholar
Gormont, R. E. 1973 A mathematical model of unsteady aerodynamics and radial flow for application to helicopter rotors. Army Air Mobility Research and Develpment Laboratory TR 767240.Google Scholar
Granlund, K., Ol, M. V. & Bernal, L. 2011 Experiments on pitching plates: force and flowfield measurements at low Reynolds numbers. AIAA Paper 2011-0872. American Institute of Aeronautics and Astronautics.Google Scholar
Granlund, K., Ol, M. V., Garmann, D. J., Visbal, M. R. & Bernal, L. 2010 Experiments and computations on abstractions of perching. AIAA Paper 2010-4943. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Gupta, R. & Ansell, P. J. 2019 Unsteady flow physics of airfoil dynamic stall. AIAA J. 57 (1), 165–175.CrossRefGoogle Scholar
Gursul, I. 2005 Review of unsteady vortex flows over slender delta wings. J. Aircraft 42 (2), 299–319.CrossRefGoogle Scholar
Hill, J. L., Shaw, S. T. & Qin, N. 2004 Investigation of transition modelling for a aerofoil dynamic stall. In Proceedings of the 24th International Congress of Aeronautical Sciences, Yokohama, Japan.Google Scholar
Hirato, Y., Shen, M., Gopalarathnam, A. & Edwards, J. R. 2019 Vortex-sheet representation of leading-edge vortex shedding from finite wings. J. Aircraft 56 (4), 1626–1640.CrossRefGoogle Scholar
Hou, W., Darakananda, D. & Eldredge, J. D. 2019 Machine-learning-based detection of aerodynamic disturbances using surface pressure measurements. AIAA J. 57 (12), 5079–5093.CrossRefGoogle Scholar
Huyer, S. A., Simms, D. & Robinson, M. C. 1996 Unsteady aerodynamics associated with a horizontal-axis wind turbine. AIAA J. 34 (7), 1410–1419.CrossRefGoogle Scholar
Jones, K. & Platzer, M. 1998 On the prediction of dynamic stall onset on airfoils in low speed flow. In Proceedings of the 8th International Symposium on Unsteady Aerodynamics and Aeroelasticity of Turbomachines, pp. 797–812. Kluwer.CrossRefGoogle Scholar
Katz, J. 1981 Discrete vortex method for the non-steady separated flow over an airfoil. J. Fluid Mech. 102, 315–328.CrossRefGoogle Scholar
Katz, J. & Plotkin, A. 2000 Low-Speed Aerodynamics. Cambridge Aerospace Series. Cambridge University Press.CrossRefGoogle Scholar
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
Larsen, J. W., Nielsen, S. R. K. & Krenk, S. 2007 Dynamic stall model for wind turbine airfoils. J. Fluids Struct. 23 (7), 959–982.CrossRefGoogle Scholar
Leishman, J. G. 1990 Dynamic stall experiments on the NACA 23012 aerofoil. Exp. Fluids 9, 49–58.CrossRefGoogle Scholar
Leishman, J. G. 2002 Principles of Helicopter Aerodynamics, Cambridge Aerospace Series. Cambridge University Press.Google Scholar
Leishman, J. & Beddoes, T. 1989 A semi-empirical model for dynamic stall. J. Am. Helicopter Soc. 34 (3), 3–17.Google Scholar
Liu, Z., Lai, J. C., Young, J. & Tian, F.-B. 2016 Discrete vortex method with flow separation corrections for flapping-foil power generators. AIAA J. 55 (2), 410–418.CrossRefGoogle Scholar
McAlister, K. W. & Carr, L. W. 1978 Water-tunnel experiments on an oscillating airfoil at $Re = 21,\!000$. NASA Tech. Rep. TM 78446. National Aeronautics and Space Administration.Google Scholar
McAlister, K. W., Carr, L. W. & McCroskey, W. J. 1978 Dynamic stall experiments on the NACA0012 airfoil. NASA Tech. Rep. TP 1100. National Aeronautics and Space Administration.Google Scholar
McAlister, K. W., Pucci, S. L., McCroskey, W. J. & Carr, L. W. 1982 An experimental study of dynamic stall on advanced airfoil sections. Volume 2: pressure and force data. NASA Tech. Rep. TM 84245. National Aeronautics and Space Administration.Google Scholar
McCroskey, W. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14, 285–311.CrossRefGoogle Scholar
McCroskey, W. J. 1981 The phenomenon of dynamic stall. NASA Tech. Rep. TM 81264. National Aeronautics and Space Administration.Google Scholar
McCroskey, W. J., Carr, L. W. & McAlister, K. W. 1976 Dynamic stall experiments on oscillating airfoils. AIAA J. 14 (1), 57–63.CrossRefGoogle Scholar
McCroskey, W. J., McAlister, K. W., Carr, L. W. & Pucci, S. L. 1982 An experimental study of dynamic stall on advanced airfoil sections. Volume 1: summary of the experiment. NASA Tech. Rep. TM 84245. National Aeronautics and Space Administration.Google Scholar
Morris, W. J. & Rusak, Z. 2013 Stall onset on aerofoils a low to moderately high Reynolds number flows. J. Fluid Mech. 733, 439–472.CrossRefGoogle Scholar
Mulleners, K. & Raffel, M. 2012 The onset of dynamic stall revisited. Exp. Fluids 52, 779–793.CrossRefGoogle Scholar
Narsipur, S. 2017 Low-order modeling of dynamic stall on airfoils in incompressible flow. PhD thesis, North Carolina State University, Raleigh, NC.Google Scholar
Narsipur, S., Gopalarathnam, A. & Edwards, J. R. 2018 Low-order modeling of airfoils with massively separated flow and leading-edge vortex shedding. In Proceedings of the AIAA Aerospace Science Meeting, Kissimmee, FL, 2018-0813.Google Scholar
Narsipur, S., Gopalarathnam, A. & Edwards, J. R. 2019 Low-order model for prediction of trailing-edge separation in unsteady flow. AIAA J. 57 (1), 191–207.CrossRefGoogle Scholar
Ol, M., Bernal, L., Kang, C. & Shyy, W. 2009 Shallow and deep dynamic stall for flapping low Reynolds number airfoils. Exp. Fluids 46 (5), 883–901.CrossRefGoogle Scholar
Peters, D. A., Karunamoorthy, S. & Cao, W.-M. 1995 Finite state induced flow models. I – two-dimensional thin airfoil. J. Aircraft 32 (2), 313–322.CrossRefGoogle Scholar
Ramesh, K. 2020 On the leading-edge suction and stagnation-point location in unsteady flows past thin aerofoils. J. Fluid Mech. 886, A13.CrossRefGoogle Scholar
Ramesh, K., Gopalarathnam, A., Edwards, J. R., Ol, M. V. & Granlund, K. 2013 An unsteady airfoil theory applied to pitching motions validated against experiment and computation. J. Theor. Comput. Fluid Dyn. 27 (6), 843–864.CrossRefGoogle Scholar
Ramesh, K., Gopalarathnam, A., Granlund, K., Ol, M. V. & Edwards, J. R. 2014 Discrete-vortex method with novel shedding criterion for unsteady airfoil flows with intermittent leading-edge vortex shedding. J. Fluid Mech. 751, 500–538.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. J. Theor. Comput. Fluid Dyn. 32 (2), 109–136.CrossRefGoogle 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.CrossRefGoogle Scholar
Ramsay, R. R., Gregorek, G. M. & Hoffmann, M. J. 1996 Effects of grit roughness and pitch oscillations on the S801 airfoil. National Renewable Energy Laboratory Report NREL/TP-442-7818.CrossRefGoogle Scholar
Selig, M. S., Donovan, J. F. & Fraser, D. B. 1989 Airfoils at Low Speeds. Soartech 8, SoarTech Publications.Google Scholar
Sharma, A. & Visbal, M. 2019 Numerical investigation of the effect of airfoil thickness on onset of dynamic stall. J. Fluid Mech. 870, 870–900.CrossRefGoogle Scholar
Sheng, W., Galbraith, R. A. M. & Coton, F. N. 2006 A new stall-onset criterion for low speed dynamic-stall. J. Solar Energy Engng 128 (4), 461–471.CrossRefGoogle Scholar
Sheng, W., Galbraith, R. A. M. & Coton, F. N. 2008 A modified dynamic stall model for low Mach numbers. J. Solar Energy Engng 130 (3), 31013–31023.CrossRefGoogle Scholar
Spalart, P. R. & Allmaras, S. R. 1992 A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Spentzos, A., Barakos, G., Badcock, K., Richards, B., Wernert, P., Schreck, S. & Raffel, M. 2004 CFD investigation of 2D and 3D dynamic stall. In Proceedings of the AHS 4the Decennial Specialist's Conference on Aeromechanics, San Francisco, California, USA. American Helicopter Society International.Google Scholar
Taha, H. & Rezaei, A. S. 2019 Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem. J. Fluid Mech. 868, 141–175.CrossRefGoogle Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Tech. Rep. 496.Google Scholar
Visbal, M. R. & Garmann, D. J. 2019 Dynamic stall of a finite-aspect-ratio wing. AIAA J. 57 (3), 962–977.CrossRefGoogle Scholar
Visbal, M. R. & Shang, J. S. 1989 Investigation of the flow structure around a rapidly pitching airfoil. AIAA J. 27 (8), 1044–1051.CrossRefGoogle Scholar
Wagner, H. 1925 Über die Entstehung des dynamischen Auftriebes von Tragflügeln. Z. Angew. Math. Mech. 5 (1), 17–35.CrossRefGoogle Scholar
Wang, C. & Eldredge, J. 2013 Low-order phenomenological modeling of leading-edge vortex formation. J.Theor. Comput. Fluid Dyn. 27 (5), 577–598.CrossRefGoogle Scholar
Wernert, P., Geissler, W., Raffel, M. & Kompenhaus, J. 1996 Experimental and numerical investigations of dynamic stall on a pitching airfoil. AIAA J. 34 (5), 982–989.CrossRefGoogle Scholar
Xia, X. & Mohseni, K. 2017 Unsteady aerodynamics and vortex-sheet formation of a two-dimensional airfoil. J. Fluid Mech. 830, 439–478.CrossRefGoogle Scholar
Yan, Z., Taha, H. E. & Hajj, M. R. 2014 Geometrically-exact unsteady model for airfoils undergoing large amplitude maneuvers. Aerosp. Sci. Technol. 39, 293–306.CrossRefGoogle 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.CrossRefGoogle Scholar
Supplementary material: File

Narsipur et al. supplementary material

Narsipur et al. supplementary material

Download Narsipur et al. supplementary material(File)
File 205 MB