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plot in A) reveals a fairly periodic response in upper wing surface Cp, with a double sinusoidal shape. The FFT plot in B) shows a peak at the input frequency of 1Hz, with a larger peak at 2Hz. The wavelet plot in C) illustrates large energy concentrations occurring at 1Hz with the higher frequency 2Hz energy overlapping and participating on the upstroke and downstroke of the oscillation. The wavelet analysis also confirms a periodic response as predicted by the FFT. Figure 6-36 contains the 8Hz Grid9 results at 98% span vs. 54% chord and which corresponds to the shock transition region as seen in Figure 6-26 C). The time history plot in A) reveals a saw-tooth shaped response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input frequency of 8Hz with smaller peaks occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals non-periodic features that are not seen in the FFT, such as higher frequency energy concentrations on the end of the cycle occurring when the Cp drops dramatically, such as at time=0.25 sec and 0.37 sec. Figure 6-37 contains the 8Hz Grid9 results at 93% span vs. 58% chord and which corresponds to the shock recovery region as seen in Figure 6-27 C). The time history plot in A) reveals an even more exaggerated saw-tooth shaped response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input frequency of 8Hz with smaller peaks occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals non-periodic features that are not seen in the FFT, such as higher frequency energy concentrations on the end of the cycle occurring when the Cp drops dramatically, such as at time=0.25 sec and 0.38 sec. Figure 6-38 contains the 8Hz Grid9 results at 88% span vs. 58% chord and which corresponds to the region ahead of the shock recovery region as seen in Figure 6-28 C). The time history plot in A) reveals a wide peak vs. sharp trough response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input frequency of 8Hz with smaller peaks 92
occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals non- periodic features that are not seen in the FFT. The blue region at time=0.23 sec corresponds to the wide peak region and consists of a range of frequencies, whereas the green region at time=0.3 sec corresponds to the narrow trough region and consists of one, clear frequency. Flow Visualization Tip-Launcher Pitch Oscillations The FSR flow-field break-down is now extended by performing forced, rigid body pitch oscillation for a fine F-16 Grid8 with forebody bump, diverter, ventral fin, fuselage gun port, leading edge antenna, and tip launchers. An 8Hz ±0.5° rigid-body pitch oscillation is examined at the same flow conditions (AOAi=1.34°, Mach=0.9, 5000 feet) with the same turbulence model (DDES-SARC) for direct comparison to the clean-wing Grid9 case. Figure 6-39 and Figure 6-40 illustrate a sequence of images visualizing the flow computed for 8Hz ±0.5° sinusoidal pitching motion depicting instantaneous Mach = 1 boundary and vorticity magnitude iso-surfaces colored by pressure, respectively, at the upward stroke (between pitch angles of 135° and 180°) of the 8 Hz ±0.5° sinusoidal pitching cycle. The left set of images, A) upper and B) lower surfaces, display the tip-launcher Grid8 case results, and the clean-wing Grid9 comparisons are presented in C) upper and D) lower surfaces. The AOA is shown as a function of time in the center of each pair of images. Additionally, BL159 (88% span location) is indicated along the LE of each of the images for reference purposes. Just like for the roll cases, it can be seen from that the addition of the tip launcher significantly influences the nature of the Mach=1 boundary and vorticity magnitude iso-surfaces for the pitch cases. It is observed from Figure 6-39 that the trends between the tip-launcher and clean-wing cases are similar; such as the Mach=1 iso-surfaces at their maximum sizes at the top of the oscillation, and that the aft extent of the upper-surface Mach=1 iso-surface maintains a 93
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TEMPORAL ANALYSIS OF TRANSONIC FLOW
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To Dodjie 3
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TABLE OF CONTENTS ACKNOWLEDGMENTS .
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Summary ...........................
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LIST OF FIGURES Figure page 2-1 F-1
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6-9 Lissajous plots of upper surfac
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6-45 2-D (left column) and 3-D (rig
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incrementally since this capability
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are not sufficient to provide an an
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4. Contribute to the work of others
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Classical aircraft flutter is chara
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Popular methods for finding the sol
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LCO amplitude but not the mechanism
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speed for the particular configurat
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Denegri 23 explains the flutter fli
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Doublet-lattice Denegri 1, 7,12,13
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Batina’s work and uses an F-16 ha
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As a result of Denegri’s previous
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Figure 2-1. F-16 store stations. Fi
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Figure 2-5. Flutter flight test bui
Page 41 and 42: Stokes (RANS) equations on hybrid u
Page 43 and 44: CHAPTER 4 ANALYSIS TECHNIQUES Intro
Page 45 and 46: time-localization cannot be determi
Page 47 and 48: A B C D E Figure 4-3. Analysis of s
Page 49 and 50: (CFD) analyses in order to capture
Page 51 and 52: the appropriate time step for the n
Page 53 and 54: Wing1, is the wing-only (no fuselag
Page 55 and 56: similar to DES but with modificatio
Page 57 and 58: Figure 5-1. Time step comparison of
Page 59 and 60: A B Figure 5-3. Flow results for 8
Page 61 and 62: A B Figure 5-5. Flow results for 8
Page 63 and 64: Figure 5-7. Turbulence model compar
Page 65 and 66: Figure 5-9. CFD vs. wind tunnel com
Page 67 and 68: Figure 5-11. CFD vs. wind tunnel co
Page 69 and 70: Figure 5-13. CFD vs. wind tunnel co
Page 71 and 72: server cluster comprised of 5,120 p
Page 73 and 74: of oscillation. The 88% span locati
Page 75 and 76: since it is proportional to lift, a
Page 77 and 78: of phase. Figure 6-10 B) and D) are
Page 79 and 80: The instantaneous Cp measurements p
Page 81 and 82: D Lissajous plots with time being t
Page 83 and 84: frequency of 8Hz. The wavelet plot
Page 85 and 86: vortex is observed travelling outbo
Page 87 and 88: near 70% chord and the second near
Page 89 and 90: expected from a lift curve slope. A
Page 91: shape of this Lissajous is nonlinea
Page 95 and 96: the same direction of rotation on t
Page 97 and 98: the roll cycle, and the black arrow
Page 99 and 100: B) shows the fast Fourier transform
Page 101 and 102: is that shock separation aft of the
Page 103 and 104: on the upper surface, a much larger
Page 105 and 106: Figure 6-1. F-16 wing planform with
Page 107 and 108: A C B Figure 6-4. DDES of F-16 in s
Page 109 and 110: Cp (Non-dimensional) Cp (Non-dimens
Page 111 and 112: -Cp (Non-dimensional) A -Cp (Non-di
Page 115 and 116: -Cp (Non-dimensional) A Time (sec)
Page 117 and 118: A B Figure 6-14. DDES-SARC of F-16
Page 121 and 122: Figure 6-18. Lissajous plots of upp
Page 123 and 124: -Cp (Non-dimensional) Frequency (Hz
Page 125 and 126: -Cp (Non-dimensional) A Frequency (
Page 127 and 128: A B Figure 6-24. DDES-SARC of F-16
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A B D Figure 6-40. DDES of F-16 in
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Cp (Non-dimensional) Cp (Non-dimens
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Figure 6-44. Lissajous plots of upp
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-Cp (Non-dimensional) A Time (sec)
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-Cp (Non-dimensional) A Time (sec)
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A B Figure 6-50. DDES-SARC of F-16
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Figure 6-52. Lissajous plots of upp
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Impact on Future Design of Aircraft
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The size of the Mach=1 iso-surface
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these cases in order to identify th
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15. Dawson, K. S., and Sussinham, J
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41. Thomas, J. P., Dowell, E. H., a
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67. Cunningham, A. M., Jr., and den
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93. Parker, G. H., Maple, R. C., an
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121. Travin, A. K., Shur, M. L., Sp
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