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consisting of viscous, rigid, full-scale models of the F-16. Three of these grids are seen in Figure 5-2. The left side of the figures shows the surface grid on the wing and the right side the computational grid at 88% span station. The engine duct is modeled and meshed up to the engine face for all cases. The initial grid examined, listed in Table 5-1 as Grid0, models the forebody bump, diverter, and ventral fin. The wing-tip missile and corresponding attachment hardware and the nose boom are not modeled. This computational grid is identical to the grid used by Dean 116 and Görtz 117 for their development of an efficient computational method for accurately determining static and dynamic stability and control (S&C) characteristics of a high-performance aircraft. This grid is also extensively validated by Dean for whole aircraft forces and moments against the ATLAS database provided by the aircraft manufacturer. The half-span aircraft surface grid comprises 1.09 million points (3.42 million cells) and is considered the “coarse” grid examined, as it is the lowest refinement. The cells are concentrated in the strake vortex and quarter-chord regions, as seen in Figure 5-2 A) and D). The medium-refinement grid is listed as Grid4 in Table 5-1. The half-span version of Grid4 consists of 1.77 million points (5.6 million cells) and models the same components as Grid0, but adds the fuselage gun-port and leading-edge antennae in addition to the tip launcher and attachment hardware. Grid4, seen in Figure 5-2 B) and E), has uniform refinement over the entire wing with source surfaces in tip and strake vortex regions. Grid9 is the fine-refinement clean-wing aircraft grid in Table 5-1 consisting of 3.08 million points (9.0 million cells). Grid8 is the fine-refinement grid in Table 5-1 that models the aircraft with tip launcher and consists of 3.18 million points (9.27 million cells). Both Grid8 and Grid9 model the forebody bump, diverter, ventral fin, fuselage gun-port, and leading-edge antennae. 52
Wing1, is the wing-only (no fuselage) fine-refinement grid in Table 5-1 containing the tip launcher with 2.25 million points (5.87 million cells). Grid8, Grid9, and Wing1 have fine refinement along the LE and shock transition region with finer spacing in the boundary layer, source surfaces in the tip and strake vortex regions, along the TE separation region, and in the engine plume. Grid8 is shown in Figure 5-2 C) and F), and is representative of the spacing seen for all of the fine level grids. Computations are performed on all grids and the computational results are compared in Figure 5-3 and Figure 5-4 for the clean-wing grids Grid0 (coarse) and Grid9 (fine); and in Figure 5-5 and Figure 5-6 for the tip-launcher grids Grid4 (medium) and Grid8 (fine). For the clean- wing cases, Figure 5-3 A) and C) illustrate the Mach=1 boundary iso-surface, and B) and D) show the vorticity magnitude iso-surface. The results for coarse Grid0 are in the left column and those for fine Grid9 are in the right column. Based on these results, it can be seen that refinement in the grid leads to better capturing of separation and oscillation in the shock region. These results are also seen in Figure 5-4 for the instantaneous Cp measurements plotted against non- dimensional chord at 93% span on the down-stroke of the pitch oscillation, (as indicated by the box plot of the airfoil position in the lower portion of the plot), in the 50-60% chord region. Similarly for the tip-launcher cases, Figure 5-5 A) and C) illustrate the Mach=1 boundary iso-surface, and B) and D) show the vorticity magnitude iso-surface. The results for medium Grid4 are in the left column and those for fine Grid8 are in the right column. Based on these results, it can be seen that refinement in the grid again leads to better capturing of separation and oscillation in the shock region. These results are also seen in Figure 5-6 for the instantaneous Cp measurements plotted against non-dimensional chord at 93% span on the down-stroke of the 53
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 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: the appropriate time step for the n
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 and 92: 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 (
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Page 131 and 132:
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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
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
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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
Page 171 and 172:
121. Travin, A. K., Shur, M. L., Sp
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