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university of florida thesis or dissertation formatting template

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frequency <strong>of</strong> 8Hz. The wavelet plot in C) reveals most <strong>of</strong> the energy concentration occurring at<br />

8Hz as expected, with the higher frequency harmonics participating on the upstroke and<br />

downstroke <strong>of</strong> the oscillation. The wavelet analysis confirms a periodic response as predicted by<br />

the FFT.<br />

Figure 6-22 contains the results at 88% span vs. 70% ch<strong>or</strong>d and which c<strong>or</strong>responds to the<br />

shock recovery region as seen in Figure 6-17 C). The time hist<strong>or</strong>y plot in A) reveals a fairly<br />

periodic response in upper wing surface Cp, with the top <strong>of</strong> the peaks being flat and the bottom<br />

sharp. The FFT plot in B) shows a prominent peak at the input frequency <strong>of</strong> 8Hz with smaller<br />

peaks at some harmonics. The wavelet plot in C) confirms a mostly periodic response seen in the<br />

FFT with most <strong>of</strong> the energy concentration occurring at 8Hz and energy from the harmonics<br />

contributing on the upstrokes and downstrokes <strong>of</strong> the oscillations. However, it does reveal that<br />

the second green peak at time=0.35 seconds is larger than the first one at time=0.28 seconds due<br />

to the higher frequency energy concentration <strong>of</strong> the 16Hz harmonic.<br />

Flow Visualization<br />

Clean-Wing Pitch Oscillations<br />

In <strong>or</strong>der to emulate the t<strong>or</strong>sional nature <strong>of</strong> an LCO mechanism, the next step in the FSR<br />

flow-field break-down is to perf<strong>or</strong>m f<strong>or</strong>ced, rigid-body pitch oscillations with the clean-wing F-<br />

16. Time-accurate solutions are run at Mach=0.9, 5,000 feet, f<strong>or</strong> 1Hz ±2° and 8Hz ±0.5° angles<br />

<strong>of</strong> attack at initial AOA=1.34° (trimmed flight). The 1Hz ±2° case, though not a flutter practical<br />

study, is considered f<strong>or</strong> its unsteady aerodynamic characteristics, and coarse refinement Grid0 is<br />

acceptable f<strong>or</strong> use in <strong>or</strong>der to capture the overall trends <strong>of</strong> the mechanism. The 8Hz ±0.5° m<strong>or</strong>e<br />

accurately emulates the t<strong>or</strong>sional nature <strong>of</strong> an LCO mode at a realistic LCO frequency, theref<strong>or</strong>e<br />

the fine refinement Grid9 is used. As previously mentioned, unsteady wing surface pressure<br />

coefficients, Cp, are extracted at every iteration from the upper and lower-wing surfaces at<br />

83

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