Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
Hostname: page-component-7ccbd9845f-xwjfq Total loading time: 0.429 Render date: 2023-01-31T18:08:31.640Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true
  • English
Journal of Fluid Mechanics Journal of Fluid Mechanics

Article contents

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
Get access Rights & Permissions[Opens in a new window]

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
Check for updates
Copyright
© 2017 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

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.CrossRefGoogle 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.CrossRefGoogle Scholar
Clement, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.CrossRefGoogle Scholar
Dickinson, M. H. & Gotz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174, 45–64.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.CrossRefGoogle Scholar
Graham, J. M. R. 1983 The lift on an aerofoil in starting flow. J. Fluid Mech. 133, 413–425.CrossRefGoogle 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.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.CrossRefGoogle 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.CrossRefGoogle 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.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
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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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 ScholarPubMed
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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Traub, L. W. 2004 Analysis and estimation of the lift components of hovering insects. J. Aircraft 41, 284–289.CrossRefGoogle Scholar
Wagner, H. 1925 Uber die Entstehung des dynamischen Auftriebs von Tragflugeln. Z. Angew. Math. Mech. 5, 17–35.CrossRefGoogle Scholar
Wang, C. & Eldredge, J. D. 2012 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
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432–441.CrossRefGoogle 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.CrossRefGoogle Scholar
Xia, X. & Mohseni, K. 2013 Lift evaluation of a two-dimensional pitching flat plate. Phys. Fluids 25, 091901.CrossRefGoogle Scholar
Zhang, J. 2017 Footprints of a flapping wing. J. Fluid Mech. 818, 1–4.CrossRefGoogle Scholar
11
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Vortex force map method for viscous flows of general airfoils
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Vortex force map method for viscous flows of general airfoils
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Vortex force map method for viscous flows of general airfoils
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *