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CHAPTER 3 ANALYSIS TOOLS Introduction This section will address the analysis tools utilized for the research to include the fluid- structure reaction (FSR) approach to limit cycle oscillation (LCO) study and the computational fluid dynamics (CFD) flow solver Cobalt. Fluid-Structure Reaction Approach Fluid-structure interaction (FSI) occurs when a fluid interacts with a solid structure, exerting pressure that may cause deformation in the structure and, thus, alter the flow of the fluid itself. Examination of a true FSI LCO case (flexible structure coupled with CFD) must be considered quasi-incrementally since this capability does not yet exist in the aeroelasticity community. By imposing a particular motion to the structure, and therefore removing a degree of freedom from the system, a fluid-structure reaction (FSR) case is examined. The first step is to compute the transonic flow-field on the F-16 wing during rigid body pitch and roll oscillations, simulating the torsional and bending nature of an LCO mechanism. The next steps would involve deforming the wingtip in bending, torsion, and complex LCO motions; and adding pylons, launchers, and stores in order to increase the complexity of the configuration. Through this build- up FSR approach, insight will be gained into the characteristics of the flow-field during transonic LCO conditions in order to assess any possible influences on the LCO mechanism. It is hypothesized that these flow features interact with the structure in a way that limits the magnitude of an LCO mechanism, effectively bounding the divergent flutter. Cobalt Flow Solver Computations are performed using Cobalt, a commercial, cell-centered, finite volume CFD code. It solves the unsteady, three-dimensional, compressible Reynolds-averaged Navier 40
Stokes (RANS) equations on hybrid unstructured grids of arbitrary cell topology. It is fundamentally based on Godunov’s 97 first-order accurate, exact Riemann solver. The exact Riemann solver is replaced with an inviscid flux function that alleviates the inherent shortcomings of Riemann methods, namely the ‘slowly-moving shock’ and ‘carbuncle’ problems, while retaining their inherent advantages, most notably the exact capture of stationary contact surfaces. Second-order spatial accuracy is obtained through a Least Squares Reconstruction. A Newton sub-iteration method is used in the solution of the system of equations to improve time accuracy of the point-implicit method. Cobalt has eight turbulence models available: Spalart-Allmaras (SA), 98 SA with rotation and curvature corrections (SARC), 99 SA with Delayed Detached Eddy Simulation (DDES), 100 SARC with DDES, Menter’s baseline, 101 Menter’s Shear Stress Transport (SST), 101 SST with DES, 102 and the 1998 Wilcox k-ω. 103 All turbulence models are extensively validated. Strang 104 validates the numerical method on a number of problems, including the SA model, which forms the core for the DES model available in Cobalt. Tomaro 105 converts the code from explicit to implicit, enabling CFL numbers as high as 106. Grismer 106 parallelizes the code, with a demonstrated linear speed-up on as many as 4,000 processors. Cobalt uses an Arbitrary Lagrangian-Eulerian (ALE) formulation to perform rigid-body grid movement, where the grid is neither stationary nor follows the fluid motion but is reoriented without being deformed. The coordinate values change, but the relative positions between the grid points are unchanged. As a result, terms such as cell volume and face area remain constant and equal to the values in the original grid. The motion can include both translation and rotation. Complex motions can be defined by specifying arbitrary rotations and displacements of the grid in a motion file. This file then forms part of the required input deck for Cobalt. The parallel 41
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: Figure 2-5. Flutter flight test bui
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
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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
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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)
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A B Figure 6-14. DDES-SARC of F-16
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Figure 6-18. Lissajous plots of upp
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-Cp (Non-dimensional) Frequency (Hz
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-Cp (Non-dimensional) A Frequency (
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A B D Figure 6-40. DDES of F-16 in
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Impact on Future Design of Aircraft
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The size of the Mach=1 iso-surface
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these cases in order to identify th
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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
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121. Travin, A. K., Shur, M. L., Sp
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