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pitch oscillation, (as indicated by the box plot of the airfoil position in the lower portion of the plot), in the 50-68% chord region. Based upon the results in the shock location and behavior observed with the coarse Grid0, progressively refined grids are created. First, a uniform grid spacing is applied over the surface of the wing, resulting in Grid4. This increased refinement gave way to more oscillatory behavior in the shock. Hence, it is decided that increased refinement in the shock region and along the leading edge is necessary. Therefore, all new computations are conducted with the fine Grid8, Grid9, and Wing1. Turbulence Model Study A turbulence model study is conducted in order to find the appropriate turbulence model to use within the Cobalt CFD code for the F-16 undergoing 8 Hz ± 0.5° pitch oscillations in Mach=0.9 flow at 5,000 feet. The most appropriate turbulence models of the eight available are determined to be the Spalart-Allmaras (SA) 98 with Delayed Detached Eddy Simulation (DDES), 100 SA with rotation and curvature corrections (SARC) 99 with DDES, and Menter’s Shear Stress Transport (SST) 101 with DES. 102 Detached eddy simulation (DES) is a modification of a Reynolds-averaged Navier–Stokes (RANS) model in which the model switches to a subgrid scale formulation in regions fine enough for large eddy simulation (LES) calculations. Regions near solid boundaries and where the turbulent length scale is less than the maximum grid dimension are assigned the RANS mode of solution. As the turbulent length scale exceeds the grid dimension, the regions are solved using the LES mode. Therefore the grid resolution is not as demanding as pure LES, thereby considerably cutting down the cost of the computation. The Spalart-Allmaras model, a single equation RANS-based model, with DES acts as LES with a wall model. DES based on other models (like the two equation SST model) behaves as a hybrid RANS-LES model. Delayed Detached-Eddy Simulation (DDES) is a hybrid RANS-LES model 54
similar to DES but with modifications to reduce the influences of ambiguous grid densities in the numerical results. SARC contains modifications to the original SA model to account for the effect of system rotation and/or streamline curvature. The Cp is the quantity of most interest for this research, therefore other parameters such as skin friction coefficient and velocity profiles are not closely examined. Flow results are run on the Wing1 wing-only grid for all three models and the results are presented in Figure 5-7 for the instantaneous Cp measurements plotted against non-dimensional chord at 88% 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). No significant changes in the wing surface Cp results are evident. There is only minor variation seen in the shock region on the upper surface at 60-75% chord, shock region on the lower surface at 10-15% chord, and near the TE on both upper and lower surfaces for the SST-DES model. Therefore, any of the three turbulence models can be used with confidence. The SARC-DDES turbulence model is chosen for the research. Preliminary Wind Tunnel Validation For the purpose of model validation, Cobalt CFD steady surface-pressures are compared with those of Elbers’ 118 and Sellers’ 119 wind-tunnel results. Elbers’ steady wind-tunnel configuration consists of a 1/9-scale F-16A with tip 16S210 or AMRAAM launchers and four underwing AMRAAMS evaluated at a Mach range of 0.90-0.96 in 0.01 increments and an AOA range of 0-10°, in 1° increments, with a unit Reynolds number held at 2.5x10 6 per foot. This configuration is also used by Cunningham for unsteady wind-tunnel testing at high angles of attack. 68 Sellers’ steady wind tunnel configuration consists of a 1/9-scale F-16C with tip AIM-9 missiles on a 16S210 launcher evaluated at a Mach range of 0.6-1.2 in 0.1 increments and an AOA range of 0-26°, in 1° increments, with a constant Reynolds number of 2.0x10 6 per foot. 55
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 and 52: the appropriate time step for the n
Page 53: Wing1, is the wing-only (no fuselag
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
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Cp (Non-dimensional) Cp (Non-dimens
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-Cp (Non-dimensional) A -Cp (Non-di
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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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A B D Figure 6-40. DDES of F-16 in
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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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