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Vortex force map method for viscous flows of general airfoils

Published online by Cambridge University Press:  11 December 2017

Juan Li  and
Zi-Niu Wu Open the ORCID record for Zi-Niu Wu [Opens in a new window]
Juan Li
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China Institute of Aeroengine, Tsinghua University, Beijing 100084, PR China
Zi-Niu Wu*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China Institute of Aeroengine, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: ziniuwu@tsinghua.edu.cn
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Abstract

In a previous paper, an inviscid vortex force map approach was developed for the normal force of a flat plate at arbitrarily high angle of attack and leading/trailing edge force-producing critical regions were identified. In this paper, this vortex force map approach is extended to viscous flows and general airfoils, for both lift and drag forces due to vortices. The vortex force factors for the vortex force map are obtained here by using Howe’s integral force formula. A decomposed form of the force formula, ensuring vortices far away from the body have negligible effect on the force, is also derived. Using Joukowsky and NACA0012 airfoils for illustration, it is found that the vortex force map for general airfoils is similar to that of a flat plate, meaning that force-producing critical regions similar to those of a flat plate also exist for more general airfoils and for viscous flow. The vortex force approach is validated against NACA0012 at several angles of attack and Reynolds numbers, by using computational fluid dynamics.

JFM classification

Wakes/Jets: Separated flows Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 145 - 166
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Copyright
© 2017 Cambridge University Press 

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References

Andersen, A., Bohr, T., Schnipper, T. & Walther, J. H. 2017 Wake structure and thrust generation of a flapping foil in two-dimensional flow. J. Fluid Mech. 812, R4.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
Choudhry, A., Leknys, R., Arjomandi, M. & Kelso, R. 2014 An insight into the dynamic stall lift characteristics. Exp. Therm. Fluid Sci. 58, 188–208.Google Scholar
Clement, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.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
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
Graham, J. M. R. 1983 The lift on an aerofoil in starting flow. J. Fluid Mech. 133, 413–425.Google Scholar
Graham, W. R., Pitt Ford, C. W. & Babinsky, H. 2017 An impulse-based approach to estimating forces in unsteady flow. J. Fluid Mech. 815, 60–76.Google 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
Hsieh, C. T., Kung, C. F., Chang, C. C. & Chu, C. C. 2010 Unsteady aerodynamics of dragonfly using a simple wing–wing model from the perspective of a force decomposition. J. Fluid Mech. 663, 233–252.Google 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
Lee, J. J., Hsieh, C. T., Chang, C. C. & Chu, C. C. 2012 Vorticity forces on an impulsively started finite plate. J. Fluid Mech. 694, 464–492.CrossRefGoogle 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. & 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
Li, J. & Wu, Z. N. 2016 A vortex force study for a flat plate at high angle of attack. J. Fluid Mech. 801, 222–249.CrossRefGoogle Scholar
Jones, M. A. 2003 The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441.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
Nabawy, M. R. A. & Crowther, W. J. 2014 On the quasi-steady aerodynamics of normal hovering flight part II: model implementation and evaluation. J. R. Soc. Interface 11 (94), 20131197.Google Scholar
Pitt Ford, C. W. & Babinsky, H. 2013 Lift and the leading-edge vortex. J. Fluid Mech. 720, 280–313.Google Scholar
Polhamus, E. C. 1971 Predictions of vortex lift characteristics by a leading-edge suction analogy. J. Aircraft 8, 193–198.Google 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.Google 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
Saffman, P. G. & Sheffield, J. S. 1977 Flow over a wing with an attached vortex. Stud. Appl. Maths 57, 107–117.Google Scholar
Streitlien, K. & Triantafyllou, M. S. 1995 Force and moment on a Joukowsky profile in the presence of point vortices. AIAA J. 33, 603–610.Google Scholar
Thielicke, W., Kesel, A. B. & Stamhuis, E. J. 2011 Reliable force predictions for a flapping-wing micro air vehicle: a ‘vortex-lift’ approach. Intl J. Micro Air Vehicle 3, 201–215.Google Scholar
Traub, L. W. 2004 Analysis and estimation of the lift components of hovering insects. J. Aircraft 41, 284–289.Google 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. 2012 Low-order phenomenological modeling of leading-edge vortex formation. Theor. Comput. Fluid Dyn. 27, 577–598.Google Scholar
Wang, Z. J. 2000 Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323–341.Google Scholar
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid Mech. 37, 183–210.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
Zhang, J. 2017 Footprints of a flapping wing. J. Fluid Mech. 818, 1–4.Google Scholar