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METIS (ParMetis) domain decomposition library of Karypis 107 is also incorporated into Cobalt. New capabilities include rigid-body and six degree-of-freedom (6-DOF) motion, equilibrium air physics, and overset grids. A coupled aeroelastic simulation capability is also being developed. 42
CHAPTER 4 ANALYSIS TECHNIQUES Introduction This section will discuss the various data analysis techniques used to determine the significance of flow characteristics. These methods include traditional flow visualization using FieldView along with novel implementation of Lissajous analysis and Wavelet transforms. Flow Visualization FieldView, 108 a commercial flow visualization software, is chosen to examine the flow- field features. Built-in iso-surface capability is used to explore instantaneous vorticity magnitude and Mach = 1 boundary iso-surfaces. Time-accurate videos of the motion are also created in FieldView. Traditional surface pressure coefficient, Cp, versus non-dimensional chord location plots are utilized in regions of interest. These plots are also animated time accurately in order to capture the transient nature of the shock motion and oscillation. Lissajous A Lissajous figure (or Bowditch curve) is the graph of the system of parametric equations: x = Asin( at + d) (4-1) y = B sin(bt) (4-2) which describe complex harmonic motion. This family of curves is investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857. From the shape of the Lissajous pattern, the phase difference between the two signals can be determined, as well as the frequency ratio. Figure 4-1 shows Lissajous patterns for various frequency ratios and phase shifts. In Lissajous figures, when a point executes two motions simultaneously perpendicular to one another in a plane, it traces out a two-dimensional trajectory that lies within a rectangle. If 43
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: Stokes (RANS) equations on hybrid u
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
Page 91 and 92: shape of this Lissajous is nonlinea
Page 93 and 94:
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
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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
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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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-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
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
Page 145 and 146:
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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
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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
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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