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approach, insight is to be gained into the characteristics of the flow-field during LCO conditions in order to assess any possible influences on the LCO mechanism. It is hypothesized that these flow features interact with the structure in a way that limits the magnitude of an LCO mechanism, effectively bounding the divergent flutter. Additionally, temporal data analysis techniques will be applied to the resulting time accurate CFD data. Traditional flow visualization techniques will be utilized in order to capture the overall flow-field features of interest, such as surface pressure variations, Mach=1 boundary and vorticity iso-surfaces, and flow separation. Lissajous analysis will be applied to the data in order to isolate the phase relationships in regions of interest identified via the flow visualization. Wavelet analysis is also applied at these regions in order to accurately capture the nature of the frequency content of the mechanism. Contributions This dissertation hopes to provide insight into the fundamental physics that lead to transonic F-16 LCO, and ultimately aid in the development of appropriate analytical prediction models via temporal analysis techniques. In the process of developing the primary contribution of this work, the following contributions will be made: 1. Process which shows: • how to use CFD code in a new way with regard to LCO; • how to use Lissajous and Wavelet analysis applied to LCO; • that this method is not F-16 specific, and can be applied to future aircraft. 2. Fundamental understanding of the contribution of elements in the transonic flow-field to the LCO mechanism: • explore the rolls of moving shocks, flow separations, pressure gradients, etc. and their effects on wing LCO characteristics; • enable theoretical modeling of LCO-prone aircraft by discovering what needs to be modeled aerodynamically in order to capture LCO. 2. Understanding the effects of stores on unsteady wing aerodynamics: • provide a knowledge tool for missile/aircraft designers to avoid LCO conditions; • understand the contribution of stores to the fundamental physics behind LCO; • reveal the modification of the LCO mechanism due to the stores. 18
4. Contribute to the work of others: • add to unsteady pressure database for Cunningham’s NONLINAE solver; • provide a fluid-structure reaction (FSR) building block in the direction of understanding the physics for fluid-structure interaction (FSI) work (Morton and others); • identify the shortcomings in reduced-order modeling of LCO (Duke’s Harmonic Balance and others). 19
Page 1 and 2: TEMPORAL ANALYSIS OF TRANSONIC FLOW
Page 3 and 4: To Dodjie 3
Page 5 and 6: TABLE OF CONTENTS ACKNOWLEDGMENTS .
Page 7 and 8: Summary ...........................
Page 9 and 10: LIST OF FIGURES Figure page 2-1 F-1
Page 11 and 12: 6-9 Lissajous plots of upper surfac
Page 13 and 14: 6-45 2-D (left column) and 3-D (rig
Page 15 and 16: incrementally since this capability
Page 17: are not sufficient to provide an an
Page 21 and 22: Classical aircraft flutter is chara
Page 23 and 24: Popular methods for finding the sol
Page 25 and 26: LCO amplitude but not the mechanism
Page 27 and 28: speed for the particular configurat
Page 29 and 30: Denegri 23 explains the flutter fli
Page 31 and 32: Doublet-lattice Denegri 1, 7,12,13
Page 33 and 34: Batina’s work and uses an F-16 ha
Page 35 and 36: As a result of Denegri’s previous
Page 37 and 38: Figure 2-1. F-16 store stations. Fi
Page 39 and 40: 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
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of oscillation. The 88% span locati
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since it is proportional to lift, a
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of phase. Figure 6-10 B) and D) are
Page 79 and 80:
The instantaneous Cp measurements p
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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
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near 70% chord and the second near
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expected from a lift curve slope. A
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shape of this Lissajous is nonlinea
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occurring at harmonics, and assumes
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the same direction of rotation on t
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the roll cycle, and the black arrow
Page 99 and 100:
B) shows the fast Fourier transform
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is that shock separation aft of the
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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 113 and 114:
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 119 and 120:
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Figure 6-18. Lissajous plots of upp
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-Cp (Non-dimensional) Frequency (Hz
Page 125 and 126:
-Cp (Non-dimensional) A Frequency (
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A B D Figure 6-40. DDES of F-16 in
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Page 151 and 152:
Page 153 and 154:
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Page 157 and 158:
Impact on Future Design of Aircraft
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The size of the Mach=1 iso-surface
Page 161 and 162:
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
Page 169 and 170:
93. Parker, G. H., Maple, R. C., an
Page 171 and 172:
121. Travin, A. K., Shur, M. L., Sp
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