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shape of this Lissajous is nonlinear with a phase closer to 135°. This is due to shock formation.
The 3-D plot in F) exhibits a loop feature in the first quarter of the cycle.
Wavelet Analysis
Wavelet analysis is applied to points of interest on the wing in Figure 6-33, Figure 6-34,
and Figure 6-35 for the clean-wing Grid0 1Hz pitch case; and in Figure 6-36, Figure 6-37, and
Figure 6-38 for the clean-wing Grid9 8Hz pitch case, 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 6-33 contains the 1Hz Grid0 results at 93% span vs. 67% chord which corresponds
to the shock recovery region as seen in Figure 6-27 C). The time history plot in A) reveals a
fairly periodic response in upper wing surface Cp. The FFT plot in B) shows broad-band energy
for 1-5Hz. The wavelet plot in C) illustrates large energy concentration occurring at 3Hz at
time=0.82 sec and 1.82 sec. The wavelet analysis also confirms a periodic response as predicted
by the FFT.
Figure 6-34 contains the 1Hz Grid0 results at 88% span vs. 72% chord which also
corresponds to shock recovery region as seen in Figure 6-28 C). The time history plot in A) again
reveals a fairly periodic response in upper wing surface Cp. The FFT plot in B) shows a
prominent peak at the input frequency of 1Hz. The wavelet plot in C) illustrates most of the
energy concentration occurring at 1Hz with higher frequency energy occurring on the upstroke
and downstroke of the oscillation. The wavelet analysis also confirms a periodic response as
predicted by the FFT.
Figure 6-35 contains the 1Hz Grid0 results at 88% span vs. 81% chord which also
corresponds to the area aft of shock recovery region as seen in Figure 6-28 C). The time history
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