Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T07:32:14.040Z Has data issue: false hasContentIssue false

Parameters influencing vortex growth and detachment on unsteady aerodynamic profiles

Published online by Cambridge University Press:  26 May 2015

A. Widmann*
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Flughafenstr. 19, 64347 Griesheim, Germany
C. Tropea
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Flughafenstr. 19, 64347 Griesheim, Germany
*
Email address for correspondence: [email protected]

Abstract

Experiments with a pitching and plunging airfoil are conducted in order to investigate the mechanisms responsible for the formation and detachment of leading edge vortices (LEVs). The chord length is varied from 90 to 180 mm, keeping all other non-dimensional parameters constant, specifically the Reynolds number (17 000), the Strouhal number (0.25), the reduced frequency (0.5) and the effective angle of attack history. It is shown that the mechanism of vortex detachment changes with chord length, evident in a corresponding change in flow topology. One mechanism scales with chord length, the other is attributed to viscous effects in the boundary layer. For the latter mechanism a new scaling of the LEV circulation is introduced. A second experiment investigates the influence of the reduced frequency on the LEV circulation and detachment mechanisms, again keeping all other non-dimensional parameters constant.

Type
Papers
Copyright
© 2015 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

Afanasyev, Y. D. 2006 Formation of vortex dipoles. Phys. Fluids 18, 037103.CrossRefGoogle Scholar
Baik, Y. S., Bernal, L. P., Granlund, K. & Ol, M. V. 2012 Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J. Fluid Mech. 709, 132.CrossRefGoogle Scholar
Betz, A. 1950 Wie entsteht ein Wirbel in einer wenig zähen Flüssigkeit? Naturwissenschaften 37, 193196.CrossRefGoogle Scholar
Buckingham, E. 1914 On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345376.CrossRefGoogle Scholar
Dabiri, J. O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 1733.CrossRefGoogle Scholar
Dabiri, J. O. & Gharib, M. 2005 Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111136.CrossRefGoogle Scholar
DeVoria, A. C. & Ringuette, M. J. 2012 Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp. Fluids 52, 441462.CrossRefGoogle Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30, 101115.CrossRefGoogle Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. 1994 Vortex interactions with walls. Annu. Rev. Fluid Mech. 26, 573616.CrossRefGoogle Scholar
Domenichini, F. 2011 Three-dimensional impulsive vortex formation from slender orifices. J. Fluid Mech. 666, 506520.CrossRefGoogle Scholar
Fage, A. & Johansen, F. C. 1928 XLII. The structure of vortex sheets. Lond. Edinb. Dublin Phil. Mag. J. Sci. 5, 417441.CrossRefGoogle Scholar
Foss, J. F. 2004 Surface selections and topological constraint evaluations for flow field analyses. Exp. Fluids 37, 883898.CrossRefGoogle Scholar
Gerrard, J. H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401413.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.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, 14221429.CrossRefGoogle Scholar
Jones, A. R. & Babinsky, H. 2010 Unsteady lift generation on rotating wings at low Reynolds numbers. J. Aircraft 47, 10131021.CrossRefGoogle Scholar
Jones, A. R. & Babinsky, H. 2011 Reynolds number effects on leading edge vortex development on a waving wing. Exp. Fluids 51, 197210.CrossRefGoogle Scholar
Kaden, H. 1931 Aufwicklung einer unstabilen Unstetigkeitsfläche. Ing.-Arch. 2, 140168.CrossRefGoogle Scholar
Krueger, P. S., Dabiri, J. O. & Gharib, M. 2006 The formation number of vortex rings formed in uniform background co-flow. J. Fluid Mech. 556, 147166.CrossRefGoogle Scholar
McCroskey, W. J. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14, 285311.CrossRefGoogle Scholar
Nudds, R. L., Taylor, G. K. & Thomas, A. L. R. 2004 Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds. Proc. R. Soc. Lond. B 271, 20712076.CrossRefGoogle ScholarPubMed
Pedrizzetti, G. 2010 Vortex formation out of two-dimensional orifices. J. Fluid Mech. 655, 198216.CrossRefGoogle Scholar
Raffel, M., Willert, C. E., Wereley, S. T. & Kompenhans, J. 2007 Particle Image Velocimetry. Springer.CrossRefGoogle Scholar
Ringuette, M. J., Milano, M. & Gharib, M. 2007 Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J. Fluid Mech. 581, 453468.CrossRefGoogle Scholar
Rival, D. E., Kriegseis, J., Schaub, P., Widmann, A. & Tropea, C. 2014 Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry. Exp. Fluids 55, 18.CrossRefGoogle Scholar
Rival, D. E., Manejev, R. & Tropea, C. 2010 Measurement of parallel blade–vortex interaction at low Reynolds numbers. Exp. Fluids 49, 8999.CrossRefGoogle Scholar
Rival, D. E., Prangemeier, T. & Tropea, C. 2008 The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight. Exp. Fluids 46, 823833.CrossRefGoogle Scholar
Roshko, A.1954 On the drag and shedding frequency of two-dimensional bluff bodies – Technical Note 3169. Tech. Rep. National Advisory Committee for Aeronautics.Google Scholar
Sattari, P., Rival, D. E., Martinuzzi, R. J. & Tropea, C. 2012 Growth and separation of a start-up vortex from a two-dimensional shear layer. Phys. Fluids 24, 114.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2001 Boundary Layer Theory. Springer.Google Scholar
Triantafyllou, M. S., Techet, A. H. & Hover, F. S. 2004 Review of experimental work in biomimetic foils. IEEE J. Ocean. Engng 29 (3), 585594.CrossRefGoogle Scholar
Wojcik, C. J. & Buchholz, H. J. 2014 Vorticity transport in the leading-edge vortex on a rotating blade. J. Fluid Mech. 743, 249261.CrossRefGoogle Scholar