Integral Equations for Boundary Layers with Streamwise Vortices

Gael De Oliveira Andrade, Nando Timmer, Bas van Oudheusden

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We explore integral boundary layer approximations for shear layer flows with vortex generators. The flow field is decomposed to highlight two phenomena: shear over the wall and vortex-driven mixing of the shear layer. The Navier-Stokes Equations are normalized to identify a new adimensional parameter: the vortex strength number (Vg). Usual boundary layer scales are valid when the
vortex strength number (Vg) is of order one or smaller. New Boundary Layer Equations comprising the effect of streamwise vortex filaments are obtained and integrated accross a periodic vortex cell. The new integral equations share their structure with the original Von Karmann Integral Equations but use different variables. The deduction concludes with an approximate interaction equation for
the construction of generalized closures from the classic set of Swafford turbulent closure relations. The new formulation is solved numerically and it is compatible with future integration in the Xfoil or Rfoil viscous-inviscid airfoil analysis codes.
Original languageEnglish
Title of host publication52nd 3AF International Conference on Applied Aerodynamics
Subtitle of host publication27 – 29 March 2017, Lyon – France
Number of pages13
Publication statusPublished - 2017
Event52nd 3AF International Conference on Applied Aerodynamics - Lyon, France
Duration: 27 Mar 201729 Mar 2017
Conference number: 52


Conference52nd 3AF International Conference on Applied Aerodynamics
Internet address


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