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LCO at elevated angles of attack. 73-75 Cunningham's work establishes the foundation that LCO is predominantly an aerodynamic phenomenon. 76 Other CFD Melville examines F-16 flutter and LCO cases using a time-domain CFD approach. 77,78 His primary goal is to show the feasibility of using CFD for LCO prediction. He only performs short- duration time-domain solutions, which prove to be impractical for the large number of external store configuration runs that must be analyzed. Farhat also examines the F-16 using CFD but only considers store configurations that do not exhibit significant dynamic aeroelastic sensitivities. 79 No LCO results are reported in his work. Dowell concludes that the principal aerodynamic nonlinearity for LCO is flow separation, and in order to adequately model flow separation, the aerodynamic CFD model must include some representation of the viscous boundary layer, such as the RANS (Reynolds Averaged Navier-Stokes) model. 27 Tang 80 investigates the effect of nonlinear aerodynamics on transonic LCO characteristics of a two-dimensional supercritical wing with the NLR 7301 section using a CFD time-marching method. He concludes that the presentation of the viscous effects, including turbulence modeling, plays an important role on the accurate prediction of shock and LCO; and a small initial perturbation appears to produce large amplitude LCO at small mean pitch angle and plunge while a large amplitude initial perturbation produces small (or negligible) amplitude LCO at larger mean values. Bendiksen 81 explores the mechanisms responsible for limiting the energy flow from the fluid to the structure theoretically and by performing Euler-based calculations. He concludes that in order to predict LCO it is necessary for a computational code to model the energy exchange between the fluid and the structure correctly and with sufficient spatial and temporal accuracy. 34
As a result of Denegri’s previous discoveries through F-16 flight testing that differences in LCO response characteristics are associated with subtle aerodynamic differences of underwing missiles, Dubben 82 performs time-accurate CFD analyses using Beggar 83-87 and shows that these slight aerodynamic differences have a significant effect on the wing pressure distribution in the vicinity of the underwing missile. Moran 88 examines a combination of the CFD code Beggar with the Fluid And Structure Interaction Toolkit (FASIT) and the Finite Element Analysis (FEA) solver NASTRAN in order to develop a fully-coupled FSI capability. He successfully couples Beggar and FASIT to perform structurally steady-state solutions of FASIT deformed grids. He examines steady-state bending due to aerodynamic loading, as predicted by NASTRAN, for various F-16 wingtip deflections with a few store configurations. Maxwell 89 also investigates different LCO behaviors seen in flight test for relatively similar missiles. He examines several F-16 models including underwing aerodynamic effects of varying complexity in an attempt to find a quick to obtain an indication of this kind of different behavior. These range from simple interference panels, to the inclusion of bodies and airfoil shapes and incorporation of CFD steady pressure distributions. He determines that none of the aerodynamic models investigated are able to produce the kinds of indications of flight test differences that are traditionally produced by linear flutter analysis. Morton 90 performs a study of the flow-field characteristics of the F-16XL using the commercial high fidelity CFD code Cobalt. Very good agreement with flight test is found in almost all cases and the unsteadiness is documented with flow-field visualization and unsteady surface pressure coefficient data. 35
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 and 18: are not sufficient to provide an an
Page 19 and 20: 4. Contribute to the work of others
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: Batina’s work and uses an F-16 ha
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
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
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shape of this Lissajous is nonlinea
Page 93 and 94:
occurring at harmonics, and assumes
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 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:
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:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
A B D Figure 6-40. DDES of F-16 in
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Impact on Future Design of Aircraft
Page 159 and 160:
The size of the Mach=1 iso-surface
Page 161 and 162:
these cases in order to identify th
Page 163 and 164:
15. Dawson, K. S., and Sussinham, J
Page 165 and 166:
41. Thomas, J. P., Dowell, E. H., a
Page 167 and 168:
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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