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A vortex force study for a flat plate at high angle of attack

Published online by Cambridge University Press:  19 July 2016

Juan Li  and
Zi-Niu Wu
Juan Li
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Zi-Niu Wu*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The vortex force is studied for a flat plate at arbitrarily large angle of attack. A suitable vortex force approach, adapted from a previous work, is used to study the vortex force and to build a vortex force line map to identify the force effect of any potential vortex. This map can be used exactly for a potential point vortex and approximately for a concentrated leading-edge vortex (LEV) or trailing-edge vortex (TEV); the latter are shown to have a non-potential vortex core. By means of this map, we identify a force-producing critical region, due to pressure suction, above the front and rear parts of the plate for an LEV and a TEV, respectively. The impulsively started flow problem is used as an application, with validation by computational fluid dynamics. The force variation in time is decomposed into four repeatable stages (force release, force enhancement, stall and force recovery) in close relation to the individual and combined effect by an LEV and a TEV. A pressure distribution analysis shows that force enhancement is due to pressure suction by an LEV, while stall and force recovery are respectively due to the upwash effect (which reduces the pressure below the plate) of a new TEV right off the plate and the pressure suction of this TEV having now moved above the plate. A viscous effect causes a small-amplitude oscillation on the force curves by promoting multiple small-scale LEVs.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 222 - 249
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Copyright
© 2016 Cambridge University Press 

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References

Anderson, J. D. 2007 Fundamentals of Aerodynamics, 4th edn. McGraw-Hill.Google Scholar
Ansari, S., Zbikowski, R. & Knowles, K. 2006 Non-linear unsteady aerodynamic model for insect-like flapping hover. Part 2: implementation and validation. J. Aerosp. Engng 220, 169–186.Google Scholar
Bomphrey, R. J., Lawson, N. J., Harding, N. J., Taylor, G. K. & Thomas, A. L. R. 2005 The aerodynamics of Manduca sexta: digital particle image velocimetry analysis of the leading-edge vortex. J. Expl Biol. 208, 1079–1094.CrossRefGoogle ScholarPubMed
Bomphrey, R. J., Taylor, G. K. & Thomas, A. L. R. 2009 Smoke visualization of free-flying bumble bees indicates independent leading-edge vortices on each wing pair. Exp. Fluids 46, 811–821.Google Scholar
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.Google Scholar
Clement, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.Google Scholar
Choudhry, A., Leknys, R., Arjomandi, M. & Kelso, R. 2014 An insight into the dynamic stall lift characteristics. Exp. Therm. Fluid Sci. 58, 188–208.CrossRefGoogle Scholar
Darakananda, D., Eldredge, J., Colonius, T. & Williams, D. R. 2016 A vortex sheet/point vortex dynamical model for unsteady separated flows. In 54th AIAA Aerospace Sciences Meeting (AIAA SciTech), 4–8 January 2016, San Diego, CA, USA, p. 2072. American Institute of Aeronautics and Astronautics.Google Scholar
Dickinson, M. H. & Gotz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174, 45–64.CrossRefGoogle Scholar
Harbig, R. R., Sheridan, J. & Thompson, M. C. 2013 Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J. Fluid Mech. 717, 166–192.CrossRefGoogle Scholar
Hemati, M. S., Eldredge, J. D. & Speyer, J. L. 2014 Improving vortex models via optimal control theory. J. Fluids Struct. 49, 91–111.Google Scholar
Howe, M. S. 1995 On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high Reynolds numbers. Q. J. Mech. Appl. Maths 48, 401–425.Google Scholar
Graham, J. M. R. 1980 The forces on sharp-edged cylinders in oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 97, 331–346.Google Scholar
Graham, J. M. R. 1983 The lift on an aerofoil in starting flow. J. Fluid Mech. 133, 413–425.Google Scholar
Johansson, L. C., Engel, S., Kelber, A., Heerenbrink, M. K. & Hedenstrom, A. 2013 Multiple leading edge vortices of unexpected strength in freely flying hawkmoth. Nat. Sci. Rep. 3, 3264.Google Scholar
Jones, M. A. 2003 The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441.CrossRefGoogle Scholar
Knowles, K., Wilkins, P. C., Ansari, S. A. & Zbikowski, R. W. 2007 Integrated computational and experimental studies of flapping-wing micro air vehicle aerodynamics. In 3rd International Symposium on Integrating CFD and Experiments in Aerodynamics, 20–21 June 2007, US Air Force Academy, CO, USA, Cranfield University.Google Scholar
Li, G. J. & Lu, X. Y. 2012 Force and power of flapping plates in a fluid. J. Fluid Mech. 712, 598–613.Google Scholar
Li, J., Bai, C. Y. & Wu, Z. N. 2015a A two-dimensional multibody integral approach for forces in inviscid flow with free vortices and vortex production. Trans. ASME J. Fluids Engng 137, 021205; Paper No: FE-13-1671.Google Scholar
Li, J., Bai, C. Y. & Wu, Z. N. 2015b Unsteady lift for the Wagner problem of starting flow at large AoA. In ASME 2015 International Mechanical Engineering Congress and Exposition, 13–19 November 2015, Houston, TX, USA, American Society of Mechanical Engineers, V001T01A010.Google 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, 182–217.Google Scholar
Lu, Y., Shen, G. X. & Lai, G. J. 2006 Dual leading-edge vortices on flapping wings. J. Expl Biol. 209, 5005–5016.Google Scholar
Michelin, S. & Smith, S. G. L. 2009 An unsteady point vortex method for coupled fluid–solid problems. Theor. Comput. Fluid Dyn. 23, 127–153.Google Scholar
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics, 4th edn. chaps. 5, 9 and 13, Macmillan.Google Scholar
Muijres, F. T., Johansson, L. C., Barfield, R., Wolf, M., Spedding, G. R. & Hedenstrom, A. 2008 Leading-edge vortex improves lift in slow-flying bats. Science 319, 1250–1253.Google Scholar
Nitsche, M. & Xu, L. 2014 Circulation shedding in viscous starting flow past a flat plate. Fluid Dyn. Res. 46 (6), 061420.Google Scholar
Pierce, D. D. 1961 Photographic evidence of the formation and growth of vorticity behind plates accelerated from rest in still air. J. Fluid Mech. 11, 460–464.CrossRefGoogle Scholar
Pitt Ford, C. W. & Babinsky, H. 2013 Lift and the leading-edge vortex. J. Fluid Mech. 720, 280–313.CrossRefGoogle Scholar
Polhamus, E. C. 1971 Predictions of vortex lift characteristics by a leading-edge suction analogy. J. Aircraft 8, 193–198.CrossRefGoogle Scholar
Pullin, D. I. & Wang, Z. J. 2004 Unsteady forces on an accelerating plate and application to hovering insect flight. J. Fluid Mech. 509, 1–21.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, 500–538.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Streitlien, K. & Triantafyllou, M. S. 1995 Force and moment on a Joukowski profile in the presence of point vortices. AIAA J. 33, 603–610.CrossRefGoogle Scholar
Wagner, H. 1925 Uber die Entstehung des dynamischen Auftriebs von Tragflugeln. Z. Angew. Math. Mech. 5, 17–35.Google Scholar
Wang, C. & Eldredge, J. D. 2013 Low-order phenomenological modeling of leading-edge vortex formation. Theor. Comput. Fluid Dyn. 27, 577–598.CrossRefGoogle Scholar
Wang, Z. J. 2000 Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323–341.CrossRefGoogle Scholar
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid Mech. 37, 183–210.CrossRefGoogle Scholar
Widmann, A. & Tropea, C. 2015 Parameters influencing vortex growth and detachment on unsteady aerodynamic profiles. J. Fluid Mech. 773, 432–459.Google Scholar
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432–441.Google Scholar
Wu, J. Z., Lu, X. Y. & Zhuang, L. X. 2007 Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286.Google Scholar
Xia, X. & Mohseni, K. 2013 Lift evaluation of a two-dimensional pitching flat plate. Phys. Fluids 25, 091901.Google Scholar
Xu, L. & Nitsche, M. 2014 Scaling behaviour in impulsively started viscous flow past a finite flat plate. J. Fluid Mech. 756, 689–715.Google Scholar