Re<1: For small velocities, the current lines are symmetrical. There are two break points A1 and A2. It is flow crawling



  Re=4: When Re increases, the separation appears at back of the sphere along a circle S in conjunction with a vortex ring on the center axis of the sphere .


 Re=10 Increasing Re, the vortex increases in size to occupy the entire rear of the sphere and the circle of separation S is substantially diametrical l.

 Re=14, The tourbillon stands and takes a helical shape, while the sphere is subjected to a transverse force turning around. flow is more permanent but permanent medium .


Re=100, It is a circle of separation at 10 ° on the front of the sphere. Behind The sphere wake is an area where the speed varies statistically around a mean value zero .


Re =(1Oe5 à 10e6), The circle of detachment moves abruptly back and the wake is reduced .

 

Assume that :

• for Re <(1Oe5 to 10e6), the delamination occurs in laminar boundary layer

• for Re > (1Oe5 to 10e6), the delamination occurs in turbulent boundary layer .

• For Re = (1Oe5 to 10e6)
  there is delamination at the transition boundary layer. The value of Re depends greatly on the surface condition of the sphere . It lowers the value of " Re abrupt displacement of the circle of detachment " By increasing the roughness of the sphere , This precipitates the onset of the turbulent boundary layer.

Change drag coefficient (cd in English or Cx in french) of a sphere (full line)

and a disc (dashed) versus Reynolds number