Etude et développement d'un actionneur plasma à décharge à ...

Annexes
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Figure 7 Temporal evolution of the vy velocity component along different slices at (1) y/C=0.13, (2)
y/C=0.075, (3) y/C=-0.015 and (4) y/C=-0.125
The estimation of the frequency of the vortex shedding is not easy if it is based on the temporal evolution
only. To overcome this drawback, the single-point temporal correlation functions based on vy are computed at
R τ over the whole PIV field is performed by a spatial
each point of the PIV grid while the estimation of ( )
22
averaging of the correlation functions:
R
22
( τ )
=
nk
nj
∑∑
k = 1 j = 1
nk
nj
∑∑
k = 1 j = 1
22
22
( k , j , τ )
R x y
( k , j ,0)
R x y
where nk and nj refer to the maximal indices of the PIV grid in the x and y direction, respectively. Finally, a
repetitive flow patterns occurring during the sequence acquisition could be identified and would result in regular
peaks in the spatially averaged correlation function. The figure 8 shows the single-point correlation function
averaged over the whole PIV field. This figure reveals a correlation peak oscillating at approximately 90 Hz. A
manual estimation of the vortex shedding frequency estimated from sequences of located eddy such the one
shown in figure 6 confirms that a repetitive flow pattern is reproduced at a frequency ranging between 80 and
100 Hz. One can remark that this shedding frequency corresponds to a reduced frequency, F + , ranging from 0.8
up to 1. This reduced frequency range corresponds pretty well with the results published in previous studies
reporting that optimal effects in term of lift coefficient are measured when the airflow is forced with nonstationary
actuation operated at a reduced frequency near unity [7, 11, 34]. This may be explained by the fact
that a reduced frequency of one approximately corresponds to the frequency of the natural vortex shedding.
Figure 8 Temporal cross-correlation based on spatially averaged single-point correlations for the baseline
flow
B. Flow Controlled by a Quasi-steady Actuation
As previously mentioned, the quasi-steady actuation consists of applying a sine waveform having an
amplitude of 18 kV at 1.5 kHz. The resulting time-averaged flow field when the actuator is switched on is shown
in figure 9. This confirms the authority of the control strategy. The airflow is now reattached along the suction
side up to 70% of the chord length (Figure 9a) while the turbulent intensity is largely reduced in the free shear
layer region (Figure 9b). However, the leading edge of the airfoil presents high turbulent intensity, probably due