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6-17 C). The shape of this Lissajous in C) is similar to B), but with a phase closer to 15°; also
with some unsteadiness due to the shock transition. The 3-D plot in F) is similar to that in E),
with the la slightly different shape in the loop feature.
Wavelet Analysis
Wavelet analysis is applied to points of interest on the wing in Figure 6-20, Figure 6-21,
and Figure 6-22, for the Grid4 8Hz roll case with tip launchers in order to gain further insight
into the temporal nature of the results. In each set of figures, A) gives the time history of the Cp
variation, B) shows the fast Fourier transform (FFT) of the data, and C) illustrates the wavelet
transform view of frequency vs. time.
Figure 6-20 contains the results at 98% span vs. 44% chord and which corresponds to the
secondary shock region ahead of the primary shock as seen in Figure 6-15 C). The time history
plot in A) reveals a fairly sinusoidal response in upper wing surface Cp. However, a double-peak
is seen in the data around time=0.45 seconds. The FFT plot in B) shows a prominent peak at the
input frequency of 8Hz, and assumes a periodic response. The wavelet plot in C) reveals various
non-periodic features that are not seen in the FFT. There is a concentration of 20 Hz energy at
time=0.3-0.35 sec. Also in this region and at 0.45 seconds, the energy concentration at 8Hz goes
to a dark red color at the center of the circle, indicating more 8Hz energy content than for other
cycles. This explains the sharpness of the peaks in the time history plot in A) at these times. At
0.2 seconds, the 8Hz energy concentration is only indicated by a pink circle, meaning less
energy. Also, the double-peak feature seen in the time history plot in A) manifests in the s-
shaped region seen near 0.45 sec.
Figure 6-21 contains the results at 93% span vs. 67% chord, corresponding to the shock
recovery region seen in Figure 6-16 C). The time history plot in A) reveals a fairly sinusoidal
response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input
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