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Three-dimensional boundary layer and vortex wake over a cone at high angle of attack: study of asymmetries

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An experimental investigation of the flow over a one at a large angle of attack is reported. First, the study was focused on the wall shear stress measurement, including the localization of the separation. Secondly, the mean flow field in the whole wake of the cone was measured, as well as the velocity fluctuations. Results indicate that the separation and the fluctuations are asymmetrical in a certain way, whereas the mean flow field is approximately symmetrical. Finally, the different parts of the flow can be easily determined using vorticity calculations.

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C :

vortex core

D :

diffusion coefficient for the polarographic solution

D :

cone diameter for the rotation plane of the electrochemical probes

D :

separation point

F :

function F (sin α) = (K 1-K 2)/(K 1+K 2)

G :

function G(sin α) = (K 1+K 2)/(K 1+K 2)(α = 90dg)

g :

bidimensional gain of the electrochemical probe (constant for each probe)

K 1, K 2 :

mass transfer coefficients for differential probes

Re x :

Reynolds number based on the X length, and relative to the forward upstream velocity

\(\vec S\) :

wall velocity gradient vector

S :

wall velocity gradient modulus

S :

enclosing saddle point

S x :

azimuthal component of the wall velocity gradient (perpendicular to a generator)

S z :

longitudinal component of the wall velocity gradient (along a generator)

U :

mean value of the forward upstream velocity

U i :

component number i of the velocity vector in the (X, Y, Z) coordinates

X, Y, Z :

cone cartesian coordinates

\(\tilde X,\tilde Y,\tilde Z\) :

non-dimensional cone cartesian coordinates (relative to D)


incidence (part 1) angle between the wall velocity gradient and the neutral axis of the electrochemical probe (except part 1)

α r :

relative incidence α/0 c


velocity circulation


wavelength of the laser beam


kinematic viscosity


azimuthal angle

θ c :

cone semi-apex angle


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Menet, J.L., Menart, B. & Tournier, C. Three-dimensional boundary layer and vortex wake over a cone at high angle of attack: study of asymmetries. Experiments in Fluids 14, 224–232 (1993). https://doi.org/10.1007/BF00194012

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  • Vortex
  • Boundary Layer
  • Shear Stress
  • Vorticity
  • Flow Field