Separated Flows
Wakes and Cavities
Flow past 3D bluff-bodies
Bifurcation scenario
• 2D flows
• 3D axisymetric
• 3D non-axisymetric
Laminar Sphere Re < 500
Bifurcation in a sphere wake
Re = 210
SAxi
Re = 270
SPS
UPS
Thompson et al. (2001)
z
x
Fabre et al. (2008)
Sakamoto & Haniu (1990)
y
x
Steady
Axisymmetric
Steady
Planar Symmetry
 =
Unsteady
Planar Symmetry
 =
3
3
Symmetries and aerodynamics force
• Symmetry breaking :
 lift
 additionnal drag
0.9
Pier (2008)
0.8
Cx SAxi SPS
0.7
UPS
0.6
150 200 250 300 350
Re
0.08
SPS
0.06
Cz
UPS
0.04
0.02
Pier (2008)
SAxi
0150 200 250 300 350
Re
1.0 Plan x = D , Re = 250 |Ω *\
x
0.4
0.5
0.3
0
z/D
0.2
-0.5
0.1
Thompson et al. (2001)
0
-1.0
-1.0
0
1.0 4
y/D
4
Re > 104
Turbulent sphere
• Planar symmetry, vortex loops shedding
W becomes random as
Re increases beyond 104
Total averaging
z y
x
z
y
Conditionnal averaging
with W=0
 z1 - Ux  



θW  atan
 y 1 - U  
x 
 
Angular position of the
velocity loss
Recovering of the planar
symmetry
Drag of a sphere
non-axisymmetric body
• Reflectionnal Symmetry
non-axisymmetric body
• Reflectionnal Symmetry breacking
non-axisymmetric body
• Reflectionnal Symmetry breaking
non-axisymmetric body
• At large Re (up to 107), restores RS but ...
or
randomly
The role of induced drag
The two flaps angle allows to
thin the wake
Why an optimum since we
expect the thinner the wake
the lower the drag ?
Induced drag
The optimum is a compromised between
thin wake and weak longitudinal vortices
No angles
Lower Drag
High Drag