Integral Equations for Boundary Layers with Streamwise Vortices

Gael De Oliveira Andrade; Nando Timmer; Bas van Oudheusden

Integral Equations for Boundary Layers with Streamwise Vortices

Gael De Oliveira Andrade, Nando Timmer, Bas van Oudheusden

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific

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Abstract

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 language	English
Title of host publication	52nd 3AF International Conference on Applied Aerodynamics
Subtitle of host publication	27 – 29 March 2017, Lyon – France
Number of pages	13
Publication status	Published - 2017
Event	52nd 3AF International Conference on Applied Aerodynamics - Lyon, France Duration: 27 Mar 2017 → 29 Mar 2017 Conference number: 52 http://3af-aerodynamics2017.com/

Conference

Conference	52nd 3AF International Conference on Applied Aerodynamics
Country/Territory	France
City	Lyon
Period	27/03/17 → 29/03/17
Internet address	http://3af-aerodynamics2017.com/

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Cite this

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title = "Integral Equations for Boundary Layers with Streamwise Vortices",

abstract = "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 thevortex 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 forthe 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.",

author = "{De Oliveira Andrade}, Gael and Nando Timmer and {van Oudheusden}, Bas",

year = "2017",

language = "English",

booktitle = "52nd 3AF International Conference on Applied Aerodynamics",

note = "52nd 3AF International Conference on Applied Aerodynamics ; Conference date: 27-03-2017 Through 29-03-2017",

url = "http://3af-aerodynamics2017.com/",

}

Integral Equations for Boundary Layers with Streamwise Vortices. / De Oliveira Andrade, Gael; Timmer, Nando ; van Oudheusden, Bas.
52nd 3AF International Conference on Applied Aerodynamics: 27 – 29 March 2017, Lyon – France. 2017. FP59-AERO2017-deoliveira.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific

TY - GEN

T1 - Integral Equations for Boundary Layers with Streamwise Vortices

AU - De Oliveira Andrade, Gael

AU - Timmer, Nando

AU - van Oudheusden, Bas

N1 - Conference code: 52

PY - 2017

Y1 - 2017

N2 - 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 thevortex 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 forthe 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.

AB - 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 thevortex 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 forthe 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.

UR - http://resolver.tudelft.nl/uuid:bd89fe29-b042-4241-a4d4-c002a8a2cb1a

M3 - Conference contribution

BT - 52nd 3AF International Conference on Applied Aerodynamics

T2 - 52nd 3AF International Conference on Applied Aerodynamics

Y2 - 27 March 2017 through 29 March 2017

ER -

Integral Equations for Boundary Layers with Streamwise Vortices

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