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of phase. Figure 6-10 B) and D) are individual Lissajous figures taken at 88% span vs. 69%
chord location, which also corresponds to shock recovery region as seen in Figure 6-6 C).
Similarly, another odd figure-eight-like shape due to the continuous phase variation is seen. The
3-D plot in D) is similar to that in C), with the loop feature happening later in the cycle.
Wavelet Analysis
Wavelet analysis is applied to points of interest on the wing in Figure 6-11 and Figure 6-
12, for the Grid0 8Hz roll 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 6-11 contains the results at 93% span vs. 65% chord and Figure 6-12 is at 88%
span vs. 69% chord. Both of these locations correspond to the shock recovery regions as
previously mentioned.
From both figures, the time history plots in A) reveal a fairly sinusoidal response in upper
wing surface Cp. The FFT plots in B) both show a prominent peak at the input frequency of 8Hz
and smaller peaks at the harmonics. The wavelet plots in C) are also very similar and reveal most
of the energy concentration occurring at 8Hz as expected, with the higher frequency harmonics
participating on the upstroke and downstroke of the oscillation. The wavelet analysis confirms a
periodic response as predicted by the FFT.
Flow Visualization
Tip-Launcher Roll Oscillations
In order to emulate the bending nature of an LCO mechanism, the FSR flow-field break-
down is extended by performing a forced, rigid-body roll oscillation for a more refined F-16
Grid4 with tip launchers, LE edge antennae, and gun port. An 8Hz ±0.5° rigid-body roll
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