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4 International Journal of Plasma Environmental Science and Technology Vol.2, No.1, MARCH 2008 boundary layer separation Fig. 10. detachment of the flow. Fig. 11. Experiments showing the dependence of the detachment on the attack angle. experiments made by Wieselsberger [7] concerning a flow around a sphere. On the left part of the figure the Reynolds number is just below the critical value of transition and the separation occurs before the median plane of the sphere. In the right part of the figure the transition has been induced by a thin wire ring soldered on the sphere before the median plane. The instabilities created by the wire induce the transition to the turbulence, then, as we can see, the separation is delayed. Measurements made with these two configurations show a reduction of the drag coefficient as the figure shows a reduction of the "dead-water area". A practical example of this phenomenon is applied to the golf balls whose surface irregularities allows an earlier transition to turbulence which reduces the drag coefficient and then permit a longer drop of the ball. In summary, the turbulent boundary layers are more negative pressure resistant than the laminar ones. Indeed, momentum transfer by convection is much more efficient than by diffusion. Thus, momentum provided in areas close to the wall where the velocity is very small is much more important in turbulent boundary layers than in laminar ones. In consequence, the boundary layer detachment is delayed. Log (CD) critical value of R Log (R) lift coefficient CL stalling drag coefficient CD incidence angle Fig. 12. Evolution of the lift and drag coefficients of an airfoil in terms of the attack angle. F. Effectoftransitionlaminartoturbulenton separation One remarkable phenomenon at the transition between laminar to turbulent is the sudden decrease of the drag coefficient. This is for instance the case of spheres or cylinders submitted to a flow (figure 13). At the critical value of the Reynolds number the drag coefficient suddenly decreases and then increases again for larger Reynolds numbers. This surprising phenomenon is in fact due to the transition which causes the point of separation to move downstream, because, in the case of a turbulent boundary layer, the accelerating influence of the external flow extends further in the boundary layer due to turbulent mixing. We can see in figure 14 photographs of Fig. 13. Sudden decrease of the drag coefficient at the transition laminar to turbulent. Fig. 14. Experiment of drag coefficient reduction on a sphere at the transition. In the case of a plane wing, eddies developed in the separation zone generate a transition zone to a turbulent boundary layer as it can be seen in figure 15 for a plane wing with a flap. We can see in this figure that the transition to the turbulence induces a beneficial reattachment of the boundary layer which finally detach only at the beginning of the fowler.PDF Image | Plasma actuators for aeronautics applications
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