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are calculated from the flow-field by assuming a zero gradient in the cell near the boundary. Therefore, adiabatic solid walls are used for the aircraft surface and the engine duct. The symmetry method applies a tangency condition for the velocity at the boundary. Pressure and density are calculated from the flow-field by assuming a zero gradient in the cell near the boundary. Therefore, symmetry is applied on the symmetry plane for the half-span aircraft. Source boundary conditions are used to create an inflow condition. The conditions specified should inject flow into the grid through this boundary patch. This boundary condition is usually applied to nozzle faces to inject flow through a nozzle or to act as a nozzle exit. Therefore, a source boundary condition based on Riemann invariants is used to create an inflow condition at the engine exhaust. Sink boundary conditions are used to create an outflow condition. The conditions specified should “suck out” flow from the grid through this boundary patch. This boundary condition is usually applied to engine faces to pull flow through an inlet. Therefore, a sink boundary condition is used at the engine face to model the corrected engine mass flow. Time-step Convergence Study Accurate prediction of time-accurate flow about the F-16 requires both a good grid and a proper time step. However, “good” and “proper” are relative terms that need to be examined in light of the flow features of interest. 90 If the aim of the computation is to resolve vortical flow features, the grid of a particular fineness coupled with a specific time step may be adequate. If the goal is to resolve smaller turbulent structures, then a finer grid with a smaller time step may be necessary. A study is carried out for the unsteady flow-field on the F-16 wing while the aircraft is undergoing 8Hz ± 0.5° pitch oscillations in Mach=0.9 flow at 5,000 feet, in order to determine 50
the appropriate time step for the numerical simulations. Such conditions are representative of a straight-and-level LCO. Figure 5-1 shows the upper wing surface pressure coefficient, Cp, at 88% span as a function of non-dimensional chord on the down-stroke of the pitch oscillation, (as indicated by the inset box plot of the airfoil position in the lower portion of the plot), for two time steps, Δt = 0.00025 (low rate in blue) and 0.000025 (high rate in red) seconds. The inset in the lower left-hand portion of Figure 5-1, and similar figures to follow, illustrates the wing motion (horizontal blue line) with respect to the pitch-axis (vertical red line). The starting position of the wing is also illustrated by the horizontal red line. The flow direction is from left to right. These time steps are chosen based on the rule of thumb that aerodynamic features of interest are usually “visible” at non-dimensional time steps of approximately Δt* = 0.01, defined in Equation 5-1; Δ * t = ΔtU ∞ c where U∞ is free-stream velocity and c is the mean aerodynamic chord. The computations are both performed for the same physical time (0.625 seconds, corresponding to 5 cycles of oscillation) by varying the number of iterations for each time step, and each computation is completed with five Newton sub-iterations. No significant changes in the upper wing surface Cp results are evident, as seen in Figure 5-1. There is only slight variation seen in the shock region at 60-75% chord. Therefore, all subsequent calculations are performed with a physical time step of Δt = 0.00025 seconds and 5 Newton sub-iterations. Geometric Convergence Study A geometric convergence study is conducted in order to find the optimal level of refinement for the F-16 undergoing 8 Hz ± 0.5° pitch oscillations in Mach=0.9 flow at 5,000 feet. Five grids are used for the research presented: three half-span and two full-span models all 51 (5-1)
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: (CFD) analyses in order to capture
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 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 (
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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