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Temporal Analysis of Transonic Flow Field Characteristics Associated with Limit Cycle Oscillations

Permanent Link: http://ufdc.ufl.edu/UFE0024231/00001

Material Information

Title: Temporal Analysis of Transonic Flow Field Characteristics Associated with Limit Cycle Oscillations
Physical Description: 1 online resource (172 p.)
Language: english
Creator: Pasiliao, Crystal
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Limit Cycle Oscillation (LCO) is a sustained, non-divergent, periodic motion experienced by aircraft with certain external store configurations. Flutter, an instability caused by the aerodynamic forces coupling with the structural dynamics, and LCO are related as evidenced by the accuracy with which linear flutter models predict LCO frequencies and modal mechanisms. However, since the characteristics of LCO motion are a result of nonlinear effects, flutter models do not accurately predict LCO onset speed and amplitude. Current engineering knowledge and theories are not sufficient to provide an analytical means for direct prediction of LCO; instead engineers rely heavily on historical experience and interpretation of traditional flutter analyses and flight tests as they may correlate to the expected LCO characteristics for the configuration of concern. There exists a significant need for a detailed understanding of the physical mechanisms involved in LCO that can lead to a unified theory and analysis methodology. This dissertation aims for a more thorough comprehension of the nature of the nonlinear aerodynamic effects for transonic LCO mechanisms, providing a significant building block in the understanding of the overall aeroelastic effects in the LCO mechanism. Examination of a true fluid-structure interaction (FSI) LCO case (flexible structure coupled with CFD) is considered quasi-incrementally since this capability does not yet exist in the flutter community. The first step in this process is to examine the flow-field during rigid body pitch and roll oscillations, simulating the torsional and bending nature of an LCO mechanism. More complicated configurations and motions will be examined as the state of technology progresses. Through this build-up fluid-structure reaction (FSR) approach, valuable insight is gained into the characteristics of the flow-field during transonic LCO conditions in order to assess any possible influences on the LCO mechanism. This will be accomplished temporally via traditional flow visualization techniques combined with Lissajous and wavelet analyses. By examining the effects that the flow features have on the structure, these analysis techniques lead to the ability to predict whether LCO is expected to occur for particular configurations.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Crystal Pasiliao.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Lind, Richard C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024231:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024231/00001

Material Information

Title: Temporal Analysis of Transonic Flow Field Characteristics Associated with Limit Cycle Oscillations
Physical Description: 1 online resource (172 p.)
Language: english
Creator: Pasiliao, Crystal
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Limit Cycle Oscillation (LCO) is a sustained, non-divergent, periodic motion experienced by aircraft with certain external store configurations. Flutter, an instability caused by the aerodynamic forces coupling with the structural dynamics, and LCO are related as evidenced by the accuracy with which linear flutter models predict LCO frequencies and modal mechanisms. However, since the characteristics of LCO motion are a result of nonlinear effects, flutter models do not accurately predict LCO onset speed and amplitude. Current engineering knowledge and theories are not sufficient to provide an analytical means for direct prediction of LCO; instead engineers rely heavily on historical experience and interpretation of traditional flutter analyses and flight tests as they may correlate to the expected LCO characteristics for the configuration of concern. There exists a significant need for a detailed understanding of the physical mechanisms involved in LCO that can lead to a unified theory and analysis methodology. This dissertation aims for a more thorough comprehension of the nature of the nonlinear aerodynamic effects for transonic LCO mechanisms, providing a significant building block in the understanding of the overall aeroelastic effects in the LCO mechanism. Examination of a true fluid-structure interaction (FSI) LCO case (flexible structure coupled with CFD) is considered quasi-incrementally since this capability does not yet exist in the flutter community. The first step in this process is to examine the flow-field during rigid body pitch and roll oscillations, simulating the torsional and bending nature of an LCO mechanism. More complicated configurations and motions will be examined as the state of technology progresses. Through this build-up fluid-structure reaction (FSR) approach, valuable insight is gained into the characteristics of the flow-field during transonic LCO conditions in order to assess any possible influences on the LCO mechanism. This will be accomplished temporally via traditional flow visualization techniques combined with Lissajous and wavelet analyses. By examining the effects that the flow features have on the structure, these analysis techniques lead to the ability to predict whether LCO is expected to occur for particular configurations.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Crystal Pasiliao.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Lind, Richard C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024231:00001


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TEMPORAL ANALYSIS OF TRANSONIC FLOW FIELD CHARACTERISTICS ASSOCIATED WITH LIMIT CYCLE OSCILLATIONS By CRYSTAL LYNN PASILIAO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1

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This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 2

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To Dodjie 3

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ACKNOWLEDGMENTS I would first like to acknowledge Dr. Ri ck Lind for providing steady guidance and motivation throughout my doctoral experience. I th ank the other members of my committee, Dr. Andreas Haselbacher, Dr. Lawrence Ukeiley, an d Dr. Panos Pardalos for their patience and insight in reviewing my research and providi ng comments on the directions of my work. Additionally, thanks go out to the members of the Air Force SEEK EAGLE Office, specifically Dr. Chuck Denegri, James Dubben, Dr Scott Morton, and David McDaniel, for their continued support. Thanks go to Ben Shirley for providing additional support and funding. Finally, I would like to thank my family fo r their patience and support during these busy past few years. Thanks to my mother, Cindy, si ster, Tiffany, and brother, Austin for always cheering me on. Thanks to my motherand father -in-laws, Helen and Ed for always believing in me. This work would not have been possible wi thout the love, support, and understanding of my husband, Dodjie, who always encouraged me to keep going and picked up all of the parenting responsibilities when I was unable to do my share. I thank my son, Markus, for giving me a reason to smile every day. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................8LIST OF FIGURES .........................................................................................................................9ABSTRACT ...................................................................................................................... .............14CHAPTER 1 INTRODUCTION ................................................................................................................ ..16Motivation ...............................................................................................................................16Approach Overview ............................................................................................................. ...17Contributions ..........................................................................................................................182 FLUTTER AND LIMIT CYCLE OSCILLATIONS .............................................................20Introduction .................................................................................................................. ...........20Dynamic Aeroelasticity ........................................................................................................ ..20Flutter ....................................................................................................................... ...............20Limit Cycle Oscillation ....................................................................................................... ....23LCO Representative Case: F16 .......................................................................................24Current LCO Analysis Techniques .................................................................................25LCO Flight Testing ..........................................................................................................27Previous LCO Research Techniques ......................................................................................30GVT ........................................................................................................................... ......30Doublet-lattice ............................................................................................................... ..31ZAERO ......................................................................................................................... ...31Harmonic Balance ...........................................................................................................31Neural Networks ..............................................................................................................3 2CFD-FASTRAN ..............................................................................................................32CAP-TSD ....................................................................................................................... .32NONLINAE ....................................................................................................................33Other CFD ..................................................................................................................... ..343 ANALYSIS TOOLS .............................................................................................................. .40Introduction .................................................................................................................. ...........40Fluid-Structure Reaction Approach ........................................................................................40Cobalt Flow Solver ............................................................................................................ .....40 5

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4 ANALYSIS TECHNIQUES ..................................................................................................43Introduction .................................................................................................................. ...........43Flow Visualization ............................................................................................................ ......43Lissajous ..................................................................................................................... ............43Wavelet Transform ............................................................................................................. ....445 F-16 TOOL DEVELOPMENT ...............................................................................................48Introduction .................................................................................................................. ...........48Down-Select Methodology .....................................................................................................48Grids and Boundary Conditions .............................................................................................49Time-Step Convergence Study ........................................................................................50Geometric Convergence Study ........................................................................................51Turbulence Model Study .................................................................................................54Preliminary Wind Tunnel Validation ..............................................................................556 F-16 ANALYSIS RESULTS ..................................................................................................70Introduction .................................................................................................................. ...........70Clean-Wing Roll Oscillations .................................................................................................7 1Flow Visualization ...........................................................................................................7 1Lissajous Analysis ...........................................................................................................7 4Wavelet Analysis .............................................................................................................7 7Tip-Launcher Roll Oscillations ..............................................................................................77Flow Visualization ...........................................................................................................7 7Lissajous Analysis ...........................................................................................................8 0Wavelet Analysis .............................................................................................................8 2Clean-Wing Pitch Oscillations ...............................................................................................83Flow Visualization ...........................................................................................................8 3Lissajous Analysis ...........................................................................................................8 7Wavelet Analysis .............................................................................................................9 1Tip-Launcher Pitch Oscillations .............................................................................................93Flow Visualization ...........................................................................................................9 3Lissajous Analysis ...........................................................................................................9 6Wavelet Analysis .............................................................................................................9 8Wing-Only Pitch Oscillations ...............................................................................................100Flow Visualization .........................................................................................................100Lissajous Analysis .........................................................................................................1037 IMPLEMENTATION ...........................................................................................................156Tool Usage and Interpretation ..............................................................................................156Impact on Future Design of Aircraft and Stores ...................................................................1578 CONCLUSIONS AND OBSERVATIONS .........................................................................158 6

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Summary ....................................................................................................................... ........158Future Research Direction ....................................................................................................1 60LIST OF REFERENCES ............................................................................................................ .162BIOGRAPHICAL SKETCH .......................................................................................................172 7

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LIST OF TABLES Table page 5-1 Computational grids examined. .........................................................................................56 8

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LIST OF FIGURES Figure page 2-1 F-16 store stations. ...................................................................................................... .......372-2 F-16 doublet lattice aerodynamic model ............................................................................372-3 F-16 NASTRAN structural model. ....................................................................................382-4 Accelerometer locations on F-16 for flight testing. ...........................................................382-5 Flutter flight test build-up procedur e for altitude vs. Mach vs calibrated air speed. ........394-1 Lissajous phase relationships for various frequency ratios................................................464-2 Morlet mother wavelet. .................................................................................................... ..464-3 Analysis of standa rd 20 Hz sinusoid ..................................................................................475-1 Time step comparison of upper surface Cp vs. non-dimensional chord at 88% span for high sampling rate in red and low sampling rate in blue. ............................................575-2 Viscous, unstructured, full-Scale, F-16 surface mesh on left and computational mesh at 88% span on right. ......................................................................................................... 585-3 Flow results for 8 Hz 0.5 pitch oscillat ions on clean-wing grid s: Grid0 on left and Grid9 on right. ............................................................................................................... .....595-4 Geometric convergence comparison of upper (blue) and lower surface (red) Cp vs. non-dimensional chord at 93% span for clean-wing grids: coarse Grid0 (dashed lines) and fine Grid9 (solid lines). .....................................................................................605-5 Flow results for 8 Hz .5 pitch oscilla tions on tip-launcher grid s: Grid4 on left and Grid8 on right. ............................................................................................................... .....615-6 Geometric convergence comparison of upper (blue) and lower surface (red) Cp vs. non-dimensional chord at 93% span for tip -launcher grids: coarse Grid4 (dashed lines) and fine Grid8 (solid lines). .....................................................................................625-7 Turbulence model comparison of upper (blue) and lower surface (red) Cp vs. nondimensional chord at 88% span for wing-only Wing1 grid: SARC-DDES (solid lines), SA-DDES (dotted lines), and SST-DES (dashes lines). .........................................635-8 CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 96% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). ......................................................................64 9

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5-9 CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 84% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). ......................................................................655-10 CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 72% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). ......................................................................665-11 CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 59% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). ......................................................................675-12 CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 46% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). ......................................................................685-13 CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 32% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). ......................................................................696-1 F-16 wing planform with Spanwise (BL) tap locations indicated by green lines. ...........1056-2 Roll oscillation angle vs. time with nu mbers 1-9 indicating the instantaneous measurements taken during the oscillatory cycle. ...........................................................1056-3 DDES of F-16 in sinusoidal rolling mo tion with instantaneous Mach=1 boundary iso-surface colored by pressure contour for clean-wing Grid0 ........................................1066-4 DDES of F-16 in sinusoidal rolling moti on with instantaneous vorticity magnitude iso-surface colored by pressure contour for clean-wing Grid0 ........................................1076-5 Instantaneous Cp measurements on F-16 Grid0 clean -wing configurations at 93% span ..................................................................................................................................1086-6 Instantaneous Cp measurements on F-16 Grid0 clean -wing configurations at 88% span ..................................................................................................................................1096-7 Lissajous plots of upper surface Cp vs. local displacement during 1Hz roll oscillation for clean-wing Grid0. .......................................................................................................11 06-8 2-D (left column) and 3-D (right column ) Lissajous for Grid0 clean-wing 1Hz roll oscillation ................................................................................................................... ......111 10

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6-9 Lissajous plots of upper surface Cp vs. local displacement during 8Hz roll oscillation for clean-wing Grid0. .......................................................................................................11 26-10 2-D (left column) and 3-D (right column ) Lissajous for clean-wing Grid0 8Hz roll oscillation ................................................................................................................... ......1136-11 Temporal analysis of upper surface Cp for Grid0 8Hz roll oscillation at 93% span vs. 65% chord ........................................................................................................................1146-12 Temporal analysis of upper surface Cp for Grid0 8Hz roll oscillation at 88% span vs. 69% chord ........................................................................................................................1156-13 DDES-SARC of F-16 in sinusoidal 8Hz ro lling motion with instantaneous Mach=1 boundary iso-surface colored by pressure contour ..........................................................1166-14 DDES-SARC of F-16 in sinusoidal 8Hz ro lling motion with instantaneous vorticity magnitude iso-surface colored by pressure contour.........................................................1176-15 Instantaneous Cp measurements on F-16 wing at 98% span for 8Hz roll ........................1186-16 Instantaneous Cp measurements on F-16 wing at 93% span for 8Hz roll ........................1196-17 Instantaneous Cp measurements on F-16 wing at 88% span for 8Hz roll ........................1206-18 Lissajous plots of upper surface Cp vs. local displacement during 8Hz roll oscillation for tip-launcher Grid4. .....................................................................................................12 16-19 2-D (left column) and 3-D (right column) Lissajous for Grid4 tip-launcher 8Hz roll oscillation case .............................................................................................................. ...1226-20 Temporal analysis of upper surface Cp for Grid4 8Hz roll oscillation at 98% span vs. 44% chord. .................................................................................................................... ...1236-21 Temporal analysis of upper surface Cp for Grid4 8Hz roll oscillation at 93% span vs. 67% chord. .................................................................................................................... ...1246-22 Temporal analysis of upper surface Cp fo r Grid4 8Hz roll oscillation at 88% span vs. 70% chord. .................................................................................................................... ...1256-23 Pitch oscillation angle vs. time with numbers 1-9 indicating the instantaneous measurements taken during the oscillatory cycle. ...........................................................1266-24 DDES-SARC of F-16 in sinusoidal pitc hing motion with instantaneous Mach=1 boundary iso-surface colored by pre ssure for clean-wing cases ......................................1276-25 DDES-SARC of F-16 in sinusoidal pitc hing motion with instantaneous vorticity magnitude iso-surface colored by pressure for clean-wing cases ....................................1286-26 Instantaneous Cp measurements on F-16 wing at 98% span ............................................129 11

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6-27 Instantaneous Cp measurements on F-16 wing at 93% span. ...........................................1306-28 Instantaneous Cp measurements on F-16 wing at 88% span. ...........................................1316-29 Lissajous plots of upper surface Cp vs. local displacement during 1Hz pitch oscillation for clean-wing Grid0. .....................................................................................1326-30 2-D (left column) and 3-D (right column ) Lissajous for Grid0 clean-wing 1Hz pitch oscillation case .............................................................................................................. ...1336-31 Lissajous plots of upper surface Cp vs. local displacement during 8Hz pitch oscillation for clean-wing Grid9. .....................................................................................1346-32 2-D (left column) and 3-D (right column ) Lissajous for Grid9 clean-wing 8Hz pitch oscillation case .............................................................................................................. ...1356-33 Temporal analysis of upper surface Cp for Grid0 1Hz pitch oscillation at 93% span vs. 67% chord.................................................................................................................. .1366-34 Temporal analysis of upper surface Cp for Grid0 1Hz pitch oscillation at 88% span vs. 72% chord.................................................................................................................. .1376-35 Temporal analysis of upper surface Cp for Grid0 1Hz pitch oscillation at 88% span vs. 81% chord.................................................................................................................. .1386-36 Temporal analysis of upper surface Cp for Grid9 8Hz pitch oscillation at 98% span vs. 54% chord.................................................................................................................. .1396-37 Temporal analysis of upper surface Cp for Grid9 8Hz pitch oscillation at 93% span vs. 58% chord.................................................................................................................. .1406-38 Temporal analysis of upper surface Cp for Grid9 8Hz pitch oscillation at 88% span vs. 58% chord.................................................................................................................. .1416-39 DDES of F-16 in 8Hz sinusoidal pitching motion with instantaneous Mach=1 boundary iso-surface colored by pressure ........................................................................1426-40 DDES of F-16 in 8Hz sinusoidal pitching motion with instantaneous vorticity magnitude iso-surface colored by pressure ......................................................................1436-41 Instantaneous Cp Measurements on F-16 wing at 98% span ...........................................1446-42 Instantaneous Cp Measurements on F-16 wing at 93% span ...........................................1456-43 Instantaneous Cp Measurements on F-16 wing at 88% span. ..........................................1466-44 Lissajous plots of upper surface Cp vs. local displacement during 8Hz pitch oscillation for tip-launcher Grid8. ....................................................................................147 12

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6-45 2-D (left column) and 3-D (right column) Lissajous for Grid8 tip-launcher 8Hz pitch oscillation case .............................................................................................................. ...1486-46 Temporal analysis of upper surface Cp for Grid8 8Hz pitch oscillation at 98% span vs. 45% chord.................................................................................................................. .1496-47 Temporal analysis of upper surface Cp for Grid8 8Hz pitch oscillation at 93% span vs. 62% chord.................................................................................................................. .1506-48 Temporal analysis of upper surface Cp for Grid8 8Hz pitch oscillation at 88% span vs. 62% chord.................................................................................................................. .1516-49 DDES-SARC of F-16 colored by pressure in 8Hz sinusoidal pitching motion with instantaneous Mach=1 boundary iso-surface ...................................................................1526-50 DDES-SARC of F-16 colored by pressure in 8Hz sinusoidal pitching motion with instantaneous vorticity ma gnitude iso-surface .................................................................1536-51 Instantaneous Cp measurements at 88% span ..................................................................1546-52 Lissajous plots of upper surface Cp vs. local displacement at % span vs. % chord locations during 8Hz pitch oscillatio n for Wing1 (no fuselage). .....................................155 13

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Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TEMPORAL ANALYSIS OF TRANSONIC FLOW-FIELD CHARACTERISTICS ASSOCIATED WITH LIMIT CYCLE OSCILLATIONS By Crystal Lynn Pasiliao May 2009 Chair: Richard C. Lind, Jr. Major: Aerospace Engineering Limit Cycle Oscillation (LCO) is a sustained, non-divergent, periodic motion experienced by aircraft with certain external store configurations. Flutter, an instability caused by the aerodynamic forces coupling with the structural dynamics, and LCO are related as evidenced by the accuracy with which linear flutter models predict LCO frequencies and modal mechanisms. However, since the characteristics of LCO motion ar e a result of nonlinear e ffects, flutter models do not accurately predict LCO onset speed and amplitude. Current engineering knowledge and theories are not sufficient to provide an analytic al means for direct prediction of LCO; instead engineers rely heavily on histor ical experience and interpretation of traditional flutter analyses and flight tests as they may corre late to the expected LCO characte ristics for the configuration of concern. There exists a significant need for a detail ed understanding of th e physical mechanisms involved in LCO that can lead to a unified theory and analys is methodology. This dissertation aims for a more thorough comprehension of the nature of the nonlinear aerodynamic effects for transonic LCO mechanisms, providing a significa nt building block in th e understanding of the overall aeroelastic effects in the LCO mechan ism. Examination of a true fluid-structure interaction (FSI) LCO case (flexible structur e coupled with CFD) is considered quasi14

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15 incrementally since this capability does not yet ex ist in the flutter community. The first step in this process is to perform flui d-structure reaction (FSR) simula tions, examining the flow-field during rigid body pitch and roll oscillations, simu lating the torsional and bending nature of an LCO mechanism. More complicated configurations and motions will be examined as the state of technology progresses. Through this build-up FSR appr oach, valuable insight is gained into the characteristics of the flow-field during transoni c LCO conditions in order to assess any possible influences on the LCO mechanism. This will be accomplished temporally via traditional flow visualization techniques combined with Liss ajous and wavelet analyses. By examining the effects that the flow features have on the struct ure, these analysis techniques will lead to the ability to predict whether LCO is expected to oc cur for particular configurations once true FSI analysis can be conducted.

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CHAPTER 1 INTRODUCTION Motivation Limit Cycle Oscillation (LCO) is a sustai ned non-divergent periodi c motion experienced by aircraft with configurations which often incl ude stores. The external stores consist of any object carried on the aircraft, su ch as a missile, bomb, fuel tank, or pod. The primary concern with regard to LCO relates to the pilots ability to carry out his mission safely and effectively. While experiencing LCO, the pilot may have difficulty reading cockpit gauges and the heads-up display (HUD), and an unexpected LCO condition can lead to premature termination of the mission. There are also concerns regarding th e effects of LCO on the stores and UAVs. These issues include such things as potential degradation in reliability of components, whether or not stores can be safely released during LCO, the possible effects of LCO on target acquisition for smart weapons, and the effects of LCO on w eapon accuracy for unguided weapons. Therefore, the prediction of LCO behavior of fighter aircraft is critical to mission safety and effectiveness, and the accurate determination of LCO onset sp eed and amplitude often requires flight test verification of linear flutter models. The increa sing stores certification demands for new stores and configurations, the associated flight test costs, and the accompanying risk to pilots and equipment all necessitate the development of tools to enhance computation of LCO through modeling of the aerodynamic and struct ural sources of LCO nonlinearities. Flutter, an instability caused by the aerodyna mic forces coupling with the structural dynamics, and LCO are related phenomena. This association is due in part to the accuracy with which linear flutter models predict LCO frequencies and modal mechanisms.1 However, since the characteristics of LCO motion are a result of nonlinear effects, flutter models do not accurately predict LCO onset speed and amplitude. Current engineering knowledge and theories 16

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are not sufficient to provide an analytical mean s for direct prediction of LCO. The current approach relies heavily on historical experience and interpretation of traditional flutter analyses and flight tests as they may corre late to the expected LCO characte ristics for the configuration of concern. There exists a significant need for a detail ed understanding of th e physical mechanisms involved in LCO that can lead to a unified theory and analysis methodology that is capable of predicting LCO responses. Many in the aeroelasti city community believe that LCO is indeed classical flutter at the onset, based on the st rong similarity of the measured LCO deflection characteristics to linear flutter analysis com puted deflections. However, the mechanism that bounds the oscillations still eludes the research community. Preliminary findings suggest that transonic aerodynamics is a potential bounding mechanism for typical LCO. Approach Overview The present work aims to identify flow-field features, such as pressure gradients, flow separation, and shock interactions, using comput ational fluid dynamics (CFD) analyses at known transonic LCO conditions observed in flight tests. The results are used to assess how characteristics in the flow may be influencing the occurrence of LCO. Examination of a true fluid-structure interaction (FSI) LCO case (flexible structure coupl ed with CFD) is considered quasi-incrementally since this capability does no t yet exist in the flutter community. The first step is to perform fluid-structure reaction (FSR) simulations, ex amining the flow-field via CFD analyses on the F-16 wing during prescribed rigid body pitch and ro ll oscillations, simulating the torsional and bending nature of an LCO mechan ism. Two configurations are examined, clean wing without2 and with3 5 tip missile launchers. As the state of CFD FSI codes progress, the wing will be forcefully deformed in bending, to rsion, and complex LCO motions and pylons, launchers, and stores will be added. Through this build-up fluid-structure reaction (FSR) 17

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approach, insight is to be gained into the char acteristics of the flow-field during LCO conditions in order to assess any possible in fluences 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 boundi ng the divergent flutter. Additionally, temporal data analysis techniques will be applied to the resulting time accurate CFD data. Traditional flow visualization t echniques will be utilized in order to capture the overall flow-field features of interest, such as surface pressure variations, Mach=1 boundary and vorticity iso-surfaces, and flow separation. Liss ajous analysis will be applied to the data in order to isolate the phase relationships in regions of interest identified via the flow visualization. Wavelet analysis is also applied at these regions in order to accurately capture the nature of the frequency content of the mechanism. Contributions This dissertation hopes to provide insight into th e fundamental physics that lead to transonic F-16 LCO, and ultimately aid in the de velopment of appropriate analytical prediction models via temporal analysis techniques. In the process of developing the primary contribution of this work, the following contributions will be made: 1. Process which shows: how to use CFD code in a new way with regard to LCO; how to use Lissajous and Wavelet analysis applied to LCO; that this method is not F-16 specific, a nd can be applied to future aircraft. 2. Fundamental understanding of the contribution of elements in th e transonic flow-field to the LCO mechanism: explore the rolls of moving shocks, flow separa tions, pressure gradients, etc. and their effects on wing LCO characteristics; enable theoretical modeling of LCO-prone ai rcraft by discovering what needs to be modeled aerodynamically in order to capture LCO. 2. Understanding the effects of stores on unsteady wing aerodynamics: provide a knowledge tool for missile/air craft designers to avoid LCO conditions; understand the contribution of stores to the fundamental physics behind LCO; reveal the modification of the LCO mechanism due to the stores. 18

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19 4. Contribute to the work of others: add to unsteady pressure database for Cunninghams NONLINAE solver; provide a fluid-structure reaction (FSR) build ing block in the dire ction of understanding the physics for fluid-structure interacti on (FSI) work (Morton and others); identify the shortcomings in reduced-order modeling of LCO (Dukes Harmonic Balance and others).

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CHAPTER 2 FLUTTER AND LIMIT CYCLE OSCILLATIONS Introduction In this section, the characteristics of flu tter and limit cycle oscillations (LCO) will be discussed, as well as techniques for analysis and prediction. Dynamic Aeroelasticity Aeroelasticity is often defined as a science which studies the mutual interaction between aerodynamic and elastic forces.6 Modern aircraft structures are very flexible, and this flexibility is fundamentally responsible fo r the various types of aeroelastic phenomena. Flexibility may have advantages for structural design; however aeroelastic phenomena arise when structural deformations induce additional aerodynamic forces. These additional aerodynamic forces may then give rise to additional structural deform ations which will induce even greater aerodynamic forces. Such interactions can either dampen out a nd lead to a condition of stable equilibrium, or diverge and destroy the structure. The term aeroe lasticity is not completely descriptive since many important aeroelastic phenomena also involve inertial forces. Flutter Flutter is an instability ca used by the aerodynamic forces coupling with the structural dynamics. Flutter can occur in any object within a strong fluid flow that results in a positive feedback occurring between the structure's natura l vibration and the aero dynamic forces. If the energy during the period of aerodyna mic excitation is larger than the natural damping of the system, the level of vibration will increase. The vibration levels are only limited when the aerodynamic or mechanical damping of the object matches the energy input, which often results in large amplitudes and can lead to rapid failure Therefore, structures exposed to aerodynamic forces are carefully designed to avoid flutter. 20

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Classical aircraft flutter is characterize d by the sudden onset of high-amplitude wing oscillations. It is a self -exciting, dynamic instability of the structural components of the aircraft, usually involving the coupling of separate vibration modes, where the forcing function for oscillation is drawn from the airstream. It is of ten destructive. Linear behavior is represented well by linear analysis methods. Classical flutter analyses7 are accomplished in the freque ncy domain and involve solving for the natural vibration frequencies and mode shapes, generalized aerodynamic forces, and modal damping and frequency variations with ve locity. Beginning with the forced vibration governing equation in the spatial/time domain:8 Qqkqcqm (2-1) where = mass matrix, = damping matrix, mc k= stiffness matrix, q= displacement amplitude vector, and the displacement-de pendent applied force is given by: qAICVQ22 1 (2-2) Linear subsonic aerodynamic influence coefficients (AIC) are computed using the doublet-lattice method, where the wing surface is discretized into boxes. Simple harmonic motion is assumed of the form: tieqq (2-3) This results in the forced vibrati on equation in the frequency domain: qAICVqkcim2 22 1 (2-4) Assuming free vibration in the frequency dom ain with no applied force and neglecting damping results in: 02 qkm (2-5) 21

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The eigenvalue solutions of this e quation yield the modal frequencies, and modal deflection amplitudes, q. The free vibration mode shapes can be us ed to diagonalize the left-hand side of Equation 2-4: ...21qq (2-6) rq (2-7) This results in transforming the forced vi bration equation into modal coordinates: rQVrKCiM2 22 1 (2-8) The classical flutter equation is obtained by converting the damp ing term into structural damping: 0 2 1 12 2 rQVKigM (2-9) The Strouhal number defines the reduced frequency as: V b k (2-10) Rearranging the classical flutter equation from Equation 2-9 into eigenvalue form gives: 0 1 1 2 112 1 22 2 2 rI ig kQM k bi i (2-11) Solving this equation yields the freq uency-damping-velocity relationships: 21 igimag realf (2-12) realk b V real imagg real 1 (2-13) 22

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Popular methods for finding the solution to th e flutter equations include the k-method and the p-k method9 in which velocity-damping, V-g, diagra ms and velocity-frequency diagrams are constructed from the roots of the eigenvalues solutions.10 Limit Cycle Oscillation LCO is a sustained, non-divergent, period ic motion experienced by aircraft with configurations which often includ e stores. The external stores consist of any object carried on the aircraft, such as a weapon, fuel tank, or pod. Norton11 provides an excellent overview of LCO of fighter aircraft carrying external stores and its sensitivity to the store carriage configuration and mass properties. The characteristics of LCO mo tion are a result of nonlinear effects that are difficult to model, and prediction of LCO likeli hood is typically performed using linear flutter models. Flutter and LCO are relate d, and this association is due in part to the accuracy with which linear flutter models predict LCO frequencies and modal mechanisms.7 12, 13 However, flutter models do not accurately pred ict LCO onset speed and amplitude. There are two types of LCO, typical and nontypical. Typical LCO is characterized by the gradual onset of sustained limited amplitude wing oscillations where the oscillation amplitude progressively increases with increasi ng Mach number and dynamic pressure.7 12, 13 Non-typical LCO is characterized by the gradual onset of sust ained limited amplitude wing oscillations where the oscillation amplitude does not progressively increase with increasing Mach number. These oscillations may only be present in a limited portion of the flight envelope. Flutter and LCO are known to occur on many fight er aircraft, such as the F-15, F-16, and F-18. Carriage of a missile on the outboard wing st ation of an F-15 leads to traditional flutter, therefore this station is no longer used. The F-18 encounters a 5.6 Hz LCO mechanism for most store configurations, so the developers devised an Active Aero elastic Control device which is 23

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built into the control system and automatically engages when LCO is detected. The F-16 is perhaps the most notorious LCO prone fighter aircraft. LCO Representative Case: F16 The thin, flexible wing supersonic F-16 fighter routinely encounters a range of LCO mechanisms (4-11Hz) for its wide variety of store configurations.14 The F-16 wing is a cropped delta planform blended with the fuselage and is composed of a NACA 64A-204 airfoil with a wingspan of 32 ft, 8 in. The wing aspect ratio is 3.2 and has a leading-ed ge sweep angle of 40 deg. It possesses nine external store stations, as shown in Figure 2-1 : a pair of wingtip missile stations; a pair of underwing missile stations; a pair of generally ai r to ground stations; a pair of stations just outboard of the fuse lage, generally used to carry fuel tanks; and a centerline station. The centerline station is considered not to have a significant eff ect on the aeroelastic characteristics of the F-16. For a given takeoff configuration, thousands of downloads may be possible. For the F-16, wing-store flutter usually takes the form of LCO instead of classical flutter, which is normally divergent and catastrophic. Aerodynamic and stiffness non-linearities limit the amplitude and prevent divergence. Note that th e non-linearities do not cau se the LCO, instead they serve to inhibit divergent flutter by lim iting its amplitude. The F-16 has two primary LCO mechanisms. Others exist but apply only to store loadings peculiar to certain countries. The first type of LCO mechanism consists of configurations containing heavy stores and AIM-9 missiles. The most significant mechanism is heavy stores with high pitch inertia at stations 3/7 and AIM-9s on the wi ngtips. Generally, the characteris tics of these mechanisms are only antisymmetric and occur around 5Hz. The driving LCO mode is a result of a coupling of the wingtip AIM-9 pitch mode and the heavy store pitch mode. The pres ence of other stores affects 24

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LCO amplitude but not the mechanism. The LC O amplitude typically becomes better as tank fuel is burned and if the AIM-9s at stations 2/8 are not present. The second primary type of LCO is for configur ations with long stores at stations 3/7 and empty wingtip launchers. This mechanism is less significant operationally since it only occurs with empty wingtip launchers. Not all of the loadings are restricted but many experience LCO to some degree. The characteristics of the mech anism are only antisymmetric and occur around 79Hz. The driving LCO mode is a result of the coupling of store pitch and antisymmetric first wing bending modes. The presence of other stores affects the LCO amplitude but not the actual mechanism. The primary parameter is pitch inertia of station 3/7 stores, which controls the antisymmetric store pitch frequency. Proximity to the antisymmetric wing bending frequency is critical. Current LCO Analysis Techniques Classical flutter analyses are predominantly used to calculate LCO onset for all the permutations of a given store configuration.1519 These analyses combine14 a linear structural solver with a doublet lattice20 (subsonic) or ZONA5121 (supersonic) aerodynamic method creating a completely linear me thod for predicting an inherently nonlinear LCO phenomenon. This methodology is often good in predicting freque ncy, but can be off by as much as 200 knots in predicting onset speed.7 12 13 These large errors force flutter engineers to rely more on experience and interpolation from similar configur ations to design flight test parameters. This uncertainty requires vast resources for each flig ht test to ensure adequate safety margins.22 This results in a large number of test points requi red to clear the margin of safety expanded operational flight envelope, extend ing the flight flutter testing time, and therefore elevating the associated costs. 25

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Denegri23 provides a detailed description of the lin ear flutter analysis procedure for the F16 to be included herein. The doublet-lattice method aerodynamic model is composed of 13 panels, including the fuselage, inner wings, flaperons, outer wings wingtip launchers, horizontal tails, vertical tail, and rudder, that are subdivided into 616 disc rete boxes. The underwing stores are not modeled aerodynamically, and the only in fluence considered is their effect on the structural mode shapes and frequencies. The wing panel is shown in Figure 2-2 and the NASTRAN structural model is shown in Figure 2-3 The aircraft structure is derived from a finite element model and represented by a lumped mass model. It is composed of 8532 degrees of freedom representing the wing, fusela ge, empennage, underwing stores, pylons, and launchers. By considering only the modal deflecti ons that influence the aerodynamic model, the system reduces to 252 structural points. The free-vibration analyses are conducte d using the Lanczos method of eigenvalue extraction. Aerodynamic influence coefficients are computed for a range of reduced frequencies, Mach numbers, and sir densities. The aerodynamic panels are splined to the vibration modes using the method of Harder and Desmarais.25 The flutter equations are solved using the Laguerre iteration method,26 which is a variation of the classical k-method of fl utter determinant solution. All flexible modes up to 25 Hz, including all f undamental wing modes and several store modes, are retained for the initial flutter analyses. Both symmetric and antisymmetric modes are included in the analyses since a full-span aircraft flutter model is used. A modal deletion study is then performed to isolate the primary modes in the predicted instability mechanism. When interpreting the flutter analysis results, a critical point is considered to be the velocity at which a modal stabil ity curve crosses from stable, which requires negative structural damping to produce neutral stability, to unstable, with positive damping. The analytical flutter 26

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speed for the particular configuration is the critical point associated with the known aeroelastically-sensitive mode. It is considered to be directly comparable to the lowest airspeed at which self-sustained oscillations are encountered in flight. The velocity-sensitivity of a mode is indicated by the slope of the modal damping curve, where steep slopes indicate rapid decreases in stabilizing damping with increased velocity. In classical analysis, a Mach number and density are specified for the aerodynamic solution, and then the damping and frequency varia tions with respect to velocity are determined based on the applied aerodynamic forces for the sp ecified Mach number and density. Several Mach number and density combinations can be examined to determine the critical conditions for a given analysis configuration. A downside of this approach is that it usually does not result in the computed instability speed being consistent with the Mach number and altitude specified, thus resulting in non-matched condition analyses. Even thoug h the aerodynamic and flutter solution velocities from these analyses are not consistent, valuable insight into modal stability characteristics can be obtained for large numbe rs of configurations for a relatively small computational cost. LCO Flight Testing For each store configuration on the F-16, thousands of permutations of a specific configuration are analyzed via flutter analysis an d reduced to the most critical configurations. These are reduced further based on previous flight test results of similar configurations (usually determined via mass properties) and the flutter engineers judgment. However, each new configuration still requires many flight tests in order to ascertain the true flutter/LCO characteristics. Since LCO is so strongly related to, and us ually precedes, an apparent classical flutter response, all testing is conducted as if catastrophic flu tter is imminent.7 Denegri23 provides a 27

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detailed description of the data collection process for a flutter flight test which is included herein. The aircraft is instrumented as shown in Figure 2-4 with an internal ly-mounted package consisting of two vertical and one lateral-directio n accelerometers. The output is telemetered to a ground facility where the incoming data is moni tored and analyzed real -time. The data are presented on video displays in a strip-chart, time-history format with the response amplitudes measured at the peaks in units of gravitationa l acceleration (g). The response amplitudes are also shown in the frequency-domain utilizing spec tral-analysis software to obtain power-spectral density (PSD) plots. The aircraft Mach number, al titude, load factor, fuel condition, and flaperon position are also displayed and monitored. These parameters are instrumental in determining cause and effect relationships of variable aircra ft responses encountered during the course of a flutter flight test. Denegri13 describes the flutter-excitation system (F ES) installed on the test aircraft, which is designed to excite vibration modes in the aircra ft structure by introducing an input signal to the flaperon servoactuators, which move the flaperon a maximum of degrees at frequencies from 2 to 20 Hz. The FES makes it possible to excite and identify specific vibration modes at successively higher speeds to accurately determine damping or structural stability at a specific test condition. The FES can drive the flaperons in two modes, burst or sweep. In the burst mode (frequency dwell), the flaperons are deflected fo r a preselected time peri od at a preselected frequency. In the sweep mode, the excitation fre quency of the flaperons is varied continuously starting at 20 Hz, going down to 2 Hz. In each exc itation mode, the flaperons can be deflected in the same direction (symmetric) or in opposite dir ections (antisymmetric). The FES is controlled and operated by the pilot with the flutter-e xcitation control panel in the cockpit. 28

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Denegri23 explains the flutter flight test profile included herein. Testing typically begins at 10,000 feet mean-sea-level (MSL) altitude and a low Mach number and progresses in increments beyond the desired carriage envelope This progression is then re peated at 5,000 and 2,000 feet MSL. At these altitudes, full data sets are obtained which consist of collection of random atmospheric excitation data, constant frequency excitation of the flaper on control surface, and elevated load factor maneuver. If needed, test points are accomplished at higher altitudes in order to better define the envelope. An illustration of the testing envelope is provided in Figure 2-5 Random atmospheric excitation data is collected while the aircraft is flown in a straightand-level, trimmed condition. If random atmosp heric turbulence does not sufficiently excite the aircraft structure, an FES sweep is performed. The data are analyzed real-time in the control room using spectral analysis software and the fr equency content is eval uated to determine the presence of any critical modes. The FES is then tuned to oscillate the flaperon at the critical frequency. A symmetrically-loaded turn of incremen tally increasing load factor is also performed to determine the effects of increas ed load factor and angle of atta ck on the flutter characteristics. A symmetric pull-up maneuver is sometimes used for test points during dive maneuvers. Denegri13 observed that in most LCO flight tests, the free vibration modes that make up the predicted flutter mechanism show the largest deflections at the wing-tip. These modes are antisymmetric (with both inboard and outboard wing motion) and the re sulting motion at the wing-tips has both bending and twisting components w ith little flexible motion at the wing-root. These modes impart a rolling moment to the aircraft fuselage, thus establishing an energy transfer path for antisymmetric LCO. Based on these observations, this dissertation will attempt to recreate these wing-tip motions via com putational fluid dynamics (CFD) analyses. 29

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It is interesting to note that there are recent in stances in flight testi ng where two flight tests with nearly identical configurations (except for slight aerodynamic differences with the underwing missiles) display a dramatic disparity in LCO response characteris tics. It appears that the differing LCO responses can be attributed to subtle aerodynamic differences in the underwing missiles. These unexpected flight test re sults have lead to the accidental discovery of a previously unknown LCO sensitivity. Previous LCO Research Techniques It is widely accepted in the flutter engineering community that LCO is triggered by the same mechanisms that initiate flutter and that the nonlinear interaction of the structural and aerodynamic forces acting on the aircraft structure produce finite amplitude oscillations, rather than the unbounded oscillations predicted by dynamica lly linear flutter theory. However, there is substantial disagreement as to which of these sources is the major contributing factor to the bounding mechanism.27 There are many approaches to investigating the cause of LCO. Most of them will be covered in this section. GVT As of yet, there is no direct evidence for a ny structural nonlinearities in the F-16. That is, no ground vibration test (GVT) is reportedly conduc ted at various excitation levels to test for stiffness or damping nonlinearities. However, it is known that the conn ection between the store and pylon is inherently nonlinear. Northington 28, 29 is currently performi ng nonlinear structural deflection testing in order to explore structural nonlinea rities and hysteretic behaviors contributing to the LCO mechanism. 30

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Doublet-lattice Denegri1 7 12, 13 analyzes the F-16 using double-lattice method aerodynamics and classical flutter analysis. He shows a correlation to LCO-sensitive configurations but is not able to give response amplitude characteristics. ZAERO Toth30 and Chen31 32 approach the LCO prediction from a structural perspective and assume that nonlinear structural damping is the significant factor. They present two F-16 aircraft configurations that differ only in the missile launchers carrie d underwing and on the wingtip. A more refined aerodynamic model of the aircraft and stores is used in ZAERO that leads to an improvement in the solution results. Their result s show a humped damping curve with stability transitions that correlate to the onset and subseq uent cessation of the LC O measured during flight testing. They also find that ZONAs modal-based Transonic Aerodynamic Influence Coefficient (ZTAIC) matrix can correlate classical flutter, typical LCO, and non-typical LCO based on V-g (flutter speed vs. damping) plots. By examining the shape of the unstable mode in the V-g diagram, flutter engineers should be able to descri be the type of LCO the ai rcraft will exhibit in flight. These results are encouraging for the ca ses examined. However, their work addresses a category of LCO behavior where th e oscillation onset occurs at a relatively low subsonic Mach number. In this case, the linear aerodynamic assumption is quite va lid but may not prove quite as useful for the purely transonic cases (such as those presented in this dissertation). Harmonic Balance Thomas3341 performs F-16 LCO calculations using a harmonic balance (HB) approach. HB provides a computationally efficient method for modeling the nonlinear unsteady aerodynamic forces created by finite amplitude moti ons of the wing. From this frequency domain 31

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solution, Thomas is able to show LCO amplitude and stability characteristics that correlate reasonably well with flight test results. Neural Networks Johnson42 46 investigates the use of artificial neural networks (ANN) to model aircraft LCO behavior. The initial neural network designs perform well in predicting amplitude and frequency over a range of Mach numbers for the flutter and typical LCO type configurations. However they do not predict the decreasing amplitude characte r that the non-typical LCO cases exhibit at higher Mach numbers. Dawson47 49 evaluates subsequent neural network designs utilizing an analytical eigenvector descriptor feature atte mpting to improve the predictive capability with respect to non-typical LCO predictions. This network design performs well in predicting the LCO amplitudes of all types of aeroelastic conditions, including non-typical LCO. CFD-FASTRAN The Air Force SEEK EAGLE Office (AFSEO) explores the commercial CFD Fluidstructure Interaction (FSI) solver, CFD-FASTRAN.50 AFSEO attempts to show that CFDFASTRAN can accurately run a transient-aeroelastic F-16 wing and launcher case joined by overset grids. The grids are created and succe ssfully used by CFD-FASTRAN in steady cases, but the results still need to be confirmed. AFSE O is unable to validate ESI Groups ability to run transient aeroelastic problems. CAP-TSD Batina51 60 uses a transonic small-disturbance a pproach to investigate a full-span F-16 aircraft with a clean-wing (no st ores/pylons/launchers) configurat ion. He examines steady flow conditions as well as rigid-body pi tch oscillations of the entire aircraft and shows that the transonic small-disturbance theo ry provided a viable solution fo r aeroelastic applications on fighter aircraft. Haller61 accomplishes further transonic small-disturbance evaluations based on 32

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Batinas work and uses an F-16 half-span model with the Computational Aeroelasticity Program Transonic Small-Disturbance (CAP-TSD). He ex amines steady flow solutions and compares these to wind-tunnel test results.62 Pitt63 applies the CAP-TSD approach to transonic flutter analysis of the F-15 and F/A-18. Denegri64 65 applies the medium-fidelity time-domain computational physics approach of CAP-TSD to LCO prediction and extends the stea dy CAP-TSD analysis of Batina and Haller and the transonic flutter analysis of Pitt by examining a typical F-16 LCO test case.23 24 Discrepancies between the aerodynamic model a nd the wind tunnel and CFD results are noted and may be the primary causes of the observed differences between the aeroelastic computational and flight test results. Denegri co ntinues to apply the CAP-TSD approach in the Medium-Fidelity Flutter Analysis Tool (MEDFFAT).66 MEDFFAT overcomes the linear transonic physics limitations of current co mmercial off-the-shelf (COTS) software by automatically generating transonic computational gr ids for the aircraft and its stores based on a single linear panel model, solving the nonlinear aeroelastic equations, and interpolating the solutions between the aircraft and stores grids. NONLINAE Cunningham develops NONLINAE, a semi-empiric al method for LCO prediction based on his observation of shock induced trailing e dge separation (SITES) during LCO wind tunnel testing.6772 He shows that nonlinear aerodynamic forces arising from SITES are a dominant mechanism in transonic LCO. He investigates several transonic LCO cases and demonstrates success with an analytical approach, NONLINAE, which uses both steady and unsteady windtunnel data for the aerodynamic forces and a li near dynamics model for the structural motions. His time lag-based model shows good correlation to test results for configurations that exhibit 33

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LCO at elevated angles of attack.73 75 Cunningham's work establishes the foundation that LCO is predominantly an aerodynamic phenomenon.76 Other CFD Melville examines F-16 flutter and LCO cases using a time-domain CFD approach.77 78 His primary goal is to show the feas ibility of using CFD for LCO pred iction. He only performs shortduration time-domain solutions, which prove to be impractical for the large number of external store configuration runs that must be analyzed. Farhat also examines the F-16 using CFD but only considers store configura tions that do not exhibit si gnificant dynamic aeroelastic sensitivities.79 No LCO results are reported in his wo rk. Dowell concludes that the principal aerodynamic nonlinearity for LCO is flow separati on, and in order to adequately model flow separation, the aerodynamic CFD model must in clude some representation of the viscous boundary layer, such as the RANS (Re ynolds Averaged Navier-Stokes) model.27 Tang80 investigates the effect of nonlinear ae rodynamics on transonic LCO characteristics of a two-dimensional supercritical wing with the NLR 7301 section using a CFD time-marching method. He concludes that the presentation of the viscous effects, including turbulence modeling, plays an important role on the accurate prediction of shock and LCO; and a small initial perturbation appears to produce large amplitude LCO at small mean pitch angle and plunge while a large amplitude initial perturbatio n produces small (or negligible) amplitude LCO at larger mean values. Bendiksen81 explores the mechanisms responsible for limiting the energy flow from the fluid to the structure theoretical ly and by performing Euler-based calculations. He concludes that in order to predict LCO it is necessary for a computational code to model the energy exchange between the fluid and the structure correctly a nd with sufficient spatial and temporal accuracy. 34

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As a result of Denegris previous discoveries through F-16 flight testing that differences in LCO response characteristics are associated with subtle aerodynamic differences of underwing missiles, Dubben82 performs time-accurate CFD analyses using Beggar83 87 and shows that these slight aerodynamic differences have a significant effect on the wing pressure distribution in the vicinity of the underwing missile. Moran88 examines a combination of the CFD co de Beggar with the Fluid And Structure Interaction Toolkit (FASIT) and the Finite Elem ent Analysis (FEA) solver NASTRAN in order to develop a fully-coupled FSI capability. He succe ssfully couples Beggar and FASIT to perform structurally steady-state solutio ns of FASIT deformed grids. He examines steady-state bending due to aerodynamic loading, as predicted by NASTRAN, for various F-16 wingtip deflections with a few store configurations. Maxwell89 also investigates differe nt LCO behaviors seen in flight test for relatively similar missiles. He examines several F-16 mo dels including underwing aerodynamic effects of varying complexity in an attempt to find a quick to obtain an indication of this kind of different behavior. These range from simple interference panels, to the inclusion of bodies and airfoil shapes and incorporation of CFD steady pressure distributions. He determines that none of the aerodynamic models investigated are able to prod uce the kinds of indications of flight test differences that are traditionally produced by linear flutter analysis. Morton90 performs a study of the flow-field characteristics of the F-16XL using the commercial high fidelity CFD code Cobalt. Very good agreement with flight test is found in almost all cases and the unsteadiness is documen ted with flow-field visualization and unsteady surface pressure coefficient data. 35

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Parker91 92 discovers that the nonlinear aerodynamic source of LCO on the Goland wing is shock motion and the periodic appearance/disappear ance of shocks. It is determined that the combination of strong trailing-edge and lambda shocks which periodically appear/disappear, limit the energy flow into the structure. This mechanism quenches the growth of the flutter, resulting in a steady limit-cycle oscillation. U nderwing and tip stores are added to the Goland wing to determine how they affected limit-cycle oscillation. It is found that the aerodynamic forces on the store transfer additional energy into the structure increasing the amplitude of the limit-cycle oscillation. However, it is also f ound that the underwing store interferes with the airflow on the bottom of the wing, which limits the amplitude of the limit-cycle oscillation. Parker also attempts to examine an F-16 store-configuration LCO case93 but is unable to complete the computation. Morton94 is currently developing Kestrel under the DoD CREATE-AV program. Kestrel is a CFD code based upon the AF RL research code AVUS95 that is targeted to the need of simulating multi-disciplinary physics such as fluid-structure interactions, inclusion of propulsion effects, moving control surfaces, and coupled flight control systems. It will be designed to address these needs for fixed-wing aircraft in flight regimes ranging from subsonic through supersonic flight, including maneuvers, multi-aircraft configurations, and operational conditions. It also utilizes McDaniels96 algebraic deforming mesh algorit hm which will allow for LCO type motions. 36

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Figure 2-1. F-16 store stations. Figure 2-2. F-16 doublet lattice aerodynamic model.23 37

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Figure 2-3. F-16 NASTRAN structural model. Figure 2-4. Accelerometer loca tions on F-16 for flight testing.23 38

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Figure 2-5. Flutter flight test build-up procedur e for altitude vs. Mach vs. calibrated air speed. 39

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CHAPTER 3 ANALYSIS TOOLS Introduction This section will address the analysis tools ut ilized for the research to include the fluidstructure reaction (FSR) approach to limit cycl e 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 (fle xible structure coupled with CFD) must be considered quasi-incrementally since this capa bility does not yet exist in the aeroelasticity community. By imposing a particular motion to th e structure, and therefore removing a degree of freedom from the system, a fluidstructure 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 moti ons; and adding pylons, launchers, and stores in order to increase the complexity of the configuration. Through this buildup FSR approach, insight will be gained into the ch aracteristics of the flow-field during transonic LCO conditions in order to assess any possibl e 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, eff ectively 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

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Stokes (RANS) equations on hybrid unstructured grids of arbitrary cell topology. It is fundamentally based on Godunovs97 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 accur acy is obtained through a Least Squares Reconstruction. A Newton sub-iteration method is us ed 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, Menters baseline,101 Menters Shear Stress Transport (SST),101 SST with DES,102 and the 1998 Wilcox k.103 All turbulence models are extensively validated. Strang104 validates the numerical method on a number of pr oblems, including the SA model, which forms the core for the DES model available in Cobalt. Tomaro105 converts the code from explicit to implicit, enabling CFL numbers as high as 106. Grismer106 parallelizes the code, with a demonstrated linear speed-up on as many as 4,000 processors. Cobalt uses an Arbitrary Lagrangian-Euleria n (ALE) formulation to perform rigid-body grid movement, where the grid is neither stationa ry 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 su ch as cell volume and face area remain constant and equal to the values in the original grid. Th e 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

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METIS (ParMetis) domain decom position library of Karypis107 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

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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 flowfield features. Built-in iso-surface capability is us ed 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-dimensiona l chord location plots are utilized in regions of inte rest. 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 gr aph of the system of parametric equations: )sin( datAx (4-1) )sin( btBy (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 execut es two motions simultaneously perpendicular to one another in a plane, it traces out a two-dimensional trajectory that lies within a rectangle. If 43

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there is no relation between the two motions, the point does not return to its original position, and its trajectory fills up the re ctangle by its repeated passages. However, recognizable stationary patterns emerge whenever the two motions are either of the same frequency or if the ratio of their frequencies is a rational number and the in itial phases are a simple fraction of 2 .109 Historically, Lissajous figures are used in electrical and mechanical engineering. A signal generator generates one signal of known frequency, and an oscilloscope compares the known signal with an unknown by combining them at righ t angles to each other. If there is a small difference between the frequencies, one of the patterns is maintained for a few oscillations. It will gradually change to another pattern as the phase difference between the orthogonal vibrations changes. If the frequencies are 1 and 2, then one motion gains 12 periods/second on the other. Hence, the cycle of patterns repeats after 1/( 12) seconds. Timing the repetition cycle of the patterns accurately gives the difference in the two frequencies. Lissajous figures used this way are very va luable in comparing frequencies, calibrating frequency sources, and obtaining the natural frequencies of mechanical components. Lissajous figures are also applie d in aeroelasticity as an indi cation of flutter during flight and wind tunnel testing. Pitch rate vs. pitch and plunge rate vs. plunge are plotted resulting in a circular Lissajous figure.91 This method provides a quantitative measure of the coupling between the torsion and bending motions that occur as flutter is approached.110 Wavelet Transform The wavelet is originally in troduced by French geophysicist Jean Morlet as a tool for signal analysis in the applications for the seis mic phenomena. It is now developed in various fields of science and applied in practical engin eering. The wavelet transf orm has two parameters, one is the scale that co rresponds to frequencies and the other is the position th at corresponds to time. A Fourier transform maps a signal into the frequency domain so information concerning 44

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time-localization cannot be dete rmined; conversely, the wavelet provides a tool for timefrequency localization. The varia tion in frequency that occurs with time can indicate several characteristics including nonlin earity and associated LCO.111 Wavelet transforms can take the form of eith er a discrete wavelet transform (DWT) or a continuous wavelet transform (CWT). Wavelet tr ansforms relate an input signal to a basis function defined as the mother wavelet, similar to how the fast-Fourier transform (FFT) relates the input signal to a superposit ion of cosine terms when it transforms a signal from the time domain to the frequency domain. Since wavelets are of finite length, wavelet analysis can identify nearly instantaneous frequency changes in the signal while the FFT cannot due to its relation to an infinite time signal. 112 This property of wavelets allows the wavelet transform to simultaneously display the three relevant dimensi ons of time, frequency, and magnitude, as seen in Figure 4-3 for a 20Hz sinusoid. The additional time information ca n be particularly useful in the analysis of non-linear and time-varying systems.113 The Morlet wavelet is commonly used when de aling with dynamic systems, such as those with nonlinearities and time-v arying structural dynamics.112 114 The Morlet wavelet is selected for this research since it mo re closely resembles the dynamics of a system, as seen in Figure 4-2 so it is anticipated that it will provide the best fit for the data. The basic equations for the mother wavelet, the Morlet wavelet, and the frequenc y corresponding to the magnitude and scale output are seen in Equations 4-3, 4-4, and 4-5 respectively. t ett5cos22/1 (4-3) atata /1, (4-4) affs796.0 (4-5) 45

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Figure 4-1. Lissajous phase relations hips for various frequency ratios. Figure 4-2. Morlet mother wavelet. 46

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A B C D E Figure 4-3. Analysis of standard 20 Hz sinusoid. A) Time histor y. B) Fast Fourier transform. Wavelet analysis: C) Magnitude vs. time D) Magnitude vs. frequency, and E) Frequency vs. time views. 47

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CHAPTER 5 F-16 TOOL DEVELOPMENT Introduction The tool development necessary for the speci fic F-16 cases analyzed will be discussed, such as the reasons for analyzing a particul ar configuration based up previous limit cycle oscillation (LCO) flight testing; as well as the turbulence model, temporal, and spatial convergence studies necessary for a valid soluti on. Preliminary wind tunnel comparison results will also be presented for the purpose of model and code validation. Down-Select Methodology Previous flight testing experience shows which analytically-predicted flutter solutions manifest in LCO; however, as previously menti oned, this classical flut ter-analysis method is not capable of modeling nonlinear eff ects. Therefore, flutter flight testing is the only sure way of determining true LCO response char acteristics. Due to the high cost associated with flutter flight testing, accompanied with the large possible numbe r of configurations that the F-16 can carry, it is vital that the fewest number of representa tive LCO cases are chosen for flight testing. Representative in the sense that the flight flutte r test results can clear ot her related downloads of the configuration. This decision is usually based on historical flight test results and how they correspond to traditional flutter analysis. However, recent flight testing shows that nearly identical configurations, predicted to have similar LCO results based on the traditional flutte r analysis, result in drastically higher than expected LCO amplitudes. The only differences in the configurations are slight aerodynamic differences, such as missile length, missile fin shape, and missile body shape. Therefore, these are the types of configurations that are most served by performing computational fluid dynamics 48

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(CFD) analyses in order to capture the nonlinearities in the LCO mechanism not captured by traditional flutter analysis. For this dissertation, an 8Hz mode is chosen, as this is representative of a typical straightand-level LCO mechanism. Additionally, based on actual flight test accelerometer data, .5 of displacement is chosen as a reasonable wingtip displacement. Grids and Boundary Conditions The grids used for this research consist of vi scous, full-scale models of the F-16. Half-span grids are required for the pitch cases, full-span for the roll cases, and different grids are required for each configuration change. The boundary conditions are symmetry (half-span only), adiabatic solid wall for the surface of the aircraft and the engine duct, and modified Riemann invariants for the far-field boundaries. The exact Ri emann solver is replaced with an inviscid flux function that alleviates the inherent shortcomings of Riem ann methods, namely the slowly-moving shock and carbuncle problems, while retaining their inherent advantages, most notably the exact capture of stationary contact surfaces.106 Far-field boundary conditions should be appl ied at outer boundaries. The outer boundaries need to be far enough away so they do not influence the area of intere st of the simulation. Typically, the boundaries should be six to eigh t characteristic body lengths away from the configuration of interest. Far-field boundary cond ition types are used for regions of inflow and outflow. Solid wall boundary conditions should be applied where there is no flow through boundaries. There are two broad cate gories of solid walls: slip and no-slip. A slip wall enforces the tangency condition, and a no-slip wall enfo rces no relative velocity at the surface. The adiabatic no-slip method applies a zero relative velocity at the boundary. Pressure and density 49

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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 veloci ty 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 a pplied on the symmetry plane for the half-span aircraft. Source boundary conditions are used to crea te 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 Riem ann 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-f ield 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

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the appropriate time step for the numerical simu lations. 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 lo wer portion of the plot), for two time steps, t = 0.00025 (low rate in blue) and 0.000025 (h igh 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 th e pitch-axis (vertical red line). The starting position of the wing is also illustrated by the horizont al red line. The flow direction is from left to right. These time steps are chosen based on th e rule of thumb that aerodynamic features of interest are usually visible at non-di mensional time steps of approximately t* = 0.01, defined in Equation 5-1; ctUt* (5-1) where U is free-stream velocity and c is the mean aerodynamic chord. The computations are both performed fo r the same physical time (0.625 seconds, corresponding to 5 cycles of oscillation) by va rying the number of iterations for each time step, and each computation is completed with five Ne wton 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 subseque nt calculations are performed with a physical time step of t = 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 presen ted: three half-span and two full-span models all 51

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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 surf ace grid on the wing and the right side the computational grid at 88% span station. The engi ne 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 Dean116 and Grtz117 for their development of an efficient computational met hod for accurately determining static and dynamic stability and control (S&C) characteristics of a hi gh-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) a nd is considered the coarse grid examined, as it is the lowest refinement. The cells are conc entrated 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 leadin g-edge antennae in add ition 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 poi nts (9.27 million cells). Both Grid8 and Grid9 model the forebody bump, diverter, ventral fin, fu selage gun-port, and l eading-edge antennae. 52

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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 ce lls). Grid8, Grid9, and Wing1 have fine refinement along the LE and shock transition re gion 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 (c oarse) and Grid9 (fine); and in Figure 5-5 and Figure 5-6 for the tip-launcher grids Grid4 (medium) and Grid8 (fine). For the cleanwing cases, Figure 5-3 A) and C) illustrate the Mach=1 boundary iso-surface, and B) and D) show the vorticity magnitude isosurface. The results for coarse Gr id0 are in the left column and those for fine Grid9 are in the right column. Base d on these results, it can be seen that refinement in the grid leads to better capturing of separa tion and oscillation in the shock region. These results are also seen in Figure 5-4 for the instantaneous Cp measurements plotted against nondimensional chord at 93% span on the down-stroke of the pitch oscillati on, (as indicated by the box plot of the airfoil position in the lower porti on 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 c hord at 93% span on the down-stroke of the 53

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pitch oscillation, (as indicated by the box plot of the airfoil position in th e lower portion of the plot), in the 50-68% chord region. Based upon the results in the s hock location and behavior obser ved 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 wa y to more oscillatory behavior in the shock. Hence, it is decided that increa sed refinement in the shock region and along the leading edge is necessary. Theref ore, all new computations are conducted with the fine Grid8, Grid9, and Wing1. Turbulence Model Study A turbulence model study is conducted in orde r 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 appropriat e 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 cu rvature corrections (SARC)99 with DDES, and Menters Shear Stress Transport (SST)101 with DES.102 Detached eddy simulation (DES) is a modification of a Reynolds-averaged NavierStokes (RANS) mode l in which the model switches to a subgrid scale formulation in regions fine enough for la rge 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 soluti on. As the turbulent length scale exceeds the grid dimension, the regions are solved using th e 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 th e two equation SST model) behaves as a hybrid RANS-LES model. Delayed Detached-Eddy Simu lation (DDES) is a hybrid RANS-LES model 54

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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 mode ls and the results are presented in Figure 5-7 for the instantaneous Cp measurements plotted against non-dime nsional chord at 88% span on the downstroke of the pitch oscillation, (as indicated by the box plot of the airf oil position in the lower portion of the plot). No significan t changes in the wing surface Cp results are evident. There is only minor variation seen in the shock regi on 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 th e 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, Coba lt CFD steady surface-pressures are compared with those of Elbers118 and Sellers119 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 2.5x106 per foot. This configuration is also used by Cunningham for un steady wind-tunnel testing at high angles of attack.68 Sellers steady wind tunnel c onfiguration 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 2.0x106 per foot. 55

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Results are chosen from both sets of wi nd tunnel data at Mach=0.9, and AOA=1.5 for Elbers and AOA=1.0 for Sellers. CFD results are run at Mach=0.9, AOA=1.34 (trimmed flight condition), at 5,000 feet for a full scale F16C with tip LAU-129 launchers. It can be seen in the instantaneous Cp measurements plotted against non-d imensional chord at various span locations in Figure 5-8 Figure 5-9 Figure 5-10 Figure 5-11 Figure 5-12 and Figure 5-13 that despite the differences in configuration, the re sults match closely, particularly in the shock region. Therefore based on these in itial indirect comparison results, confidence can be had in the accuracy of CFD models and code used for the research at hand. In the future, direct comparisons can easily be made once the appropriate store models are generated. Table 5-1. Computational grids examined. Grid# Wing Components Refinement Level #points #cells Half-span Full-span Half-span Full-span Grid0 Clean coarse 1.09E+06 2.07E+06 3.42E+06 6.85E+06 Grid4 Tip Launcher/ LE Antennae medium 1.77E+06 3.97E+06 5.60E+06 14.2E+06 Grid8 Tip Launcher/ LE Antennae fine 3.18E+06 9.27E+06 Grid9 LE Antennae fine 3.08E+06 9.00E+06 Wing1 Tip Launcher/ LE Antennae fine 2.25E+06 5.87E+06 56

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Figure 5-1. Time step comparison of upper surface Cp vs. non-dimensional chord at 88% span for high sampling rate in red a nd low sampling rate in blue. 57

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D A E B F C Figure 5-2. Viscous, unstructured, full-Scale, F16 surface mesh on left and computational mesh at 88% span on right for: A) & D) Gri d0; B) & E) Grid4; C) & F) Grid8. 58

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C A D B Figure 5-3. Flow results for 8 Hz 0.5 pitch os cillations on clean-wing grids: Grid0 on left and Grid9 on right, illustrating: A) & C) Mach=1 iso-surface; B) & D) Vorticity magnitude iso-surface. 59

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60 Figure 5-4. Geometric convergence comparis on of upper (blue) and lower surface (red) Cp vs. non-dimensional chord at 93% span for cleanwing grids: coarse Grid0 (dashed lines) and fine Grid9 (solid lines).

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C A D B Figure 5-5. Flow results for 8 Hz .5 pitch os cillations on tip-launcher grids: Grid4 on left and Grid8 on right, illustrating: A) & C) Mach=1 iso-surface; B) & D) Vorticity magnitude iso-surface. 61

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Figure 5-6. Geometric convergence comparis on of upper (blue) and lower surface (red) Cp vs. non-dimensional chord at 93% span for tip -launcher grids: coarse Grid4 (dashed lines) and fine Grid8 (solid lines). 62

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Figure 5-7. Turbulence model comparison of upper (blue) and lower surface (red) Cp vs. nondimensional chord at 88% span for wingonly Wing1 grid: SARC-DDES (solid lines), SA-DDES (dotted lines), and SST-DES (dashes lines). 63

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Figure 5-8. CFD vs. wind tunnel comparis on of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 96% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). 64

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Figure 5-9. CFD vs. wind tunnel comparis on of upper (blue) and lower (red) surface Cp vs. nondimensional chord at 84% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). 65

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Figure 5-10. CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. non-dimensional chord at 72% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). 66

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Figure 5-11. CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. non-dimensional chord at 59% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). 67

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Figure 5-12. CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. non-dimensional chord at 46% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles). 68

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69 Figure 5-13. CFD vs. wind tunnel comparison of upper (blue) and lower (red) surface Cp vs. non-dimensional chord at 32% span for: Coba lt CFD tip-launcher Grid8 (solid lines), Sellers tip AIM-9 wind tunnel model (das hed-dotted lines), and Elbers underwing AIM-120 wind tunnel model (open circles).

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CHAPTER 6 F-16 ANALYSIS RESULTS Introduction In order to emulate the torsional and bendi ng nature of a limit cy cle oscillation (LCO) mechanism, the first step in the flow-field break -down is to perform forced, rigid-body pitch and roll oscillations. Cobalts bu ilt in oscillation motion-type is ut ilized for this purpose. This method applies sinusoidal motions to the grid, and can include both translational and rotational oscillations. The form of th e applied motion is given by tf Ati 2 sin (6-1) where t is the angle motion with respect to time in degrees, i is the initial angle in degrees, A is the amplitude in degrees, f is the frequency in Hertz (Hz), and t is solution time in seconds. Cobalt also incorporates a ramp-up time (the tim e at which the displacem ent reaches 99% of its amplitude) in order to ramp displacement from 0.0. The unsteady oscillations are simulated using the delayed detached eddy simulation (DDES) version120 121 of the Spalart-Allmaras (SA) oneequation turbulence model with ro tation correction (DDES-SARC) to predict the effects of fine scale turbulence. Fully turbulent flow is assume d. The outer (physical) time step is set to t = 0.00025 sec., corresponding to a non-dimensional time step of t* = 0.01. The number of Newton sub-iterations is set to 5. The temporal damping coeffici ents for advection and diffusion are set to 0.05 and 0.0, respectively. The unst eady numerical simulations are initialized by 3,000 iterations of steady-state solutions computed with the DDES-SARC turbulence model. An additional 7,000 iterations are run for a steady, time-accurate solution, for convergence to a sufficiently steady-state. All computations are run on up to 256 CPUs on the Jaws supercomputing system at the Maui High Performance Computing Center (MHP CC). Jaws is a Dell PowerEdge 1955 blade 70

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server cluster comprised of 5, 120 processors in 1,280 nodes. Each node contains two Dual Core 3.0 GHz 64-bit Woodcrest CPUs, 8GB of RAM, and 72GB of local SAS disk. Additionally, there is 200TB of shared disk available. The nodes are connected via Cisco Infiniband, running at 10Gbits/sec (peak). Jaws has a theoretical peak performance of 62.4 TFlops, and maximal LINPACK performance of 42.39 TFlops. The steady simulation took approximately 237 CPU hours (1.6 wall clock hours) on 128 processors and the time-accurate simulation took 1,124 CPU hours (8.85 wall clock hours) on 128 processors. Unsteady wing-surface pressure coefficients, Cp, are extracted from the upper and lower wing surfaces at various butt line (BL) locations, as shown in Figure 6-1 These tap sites are analogous to a physical pressure tap, and are evenly distri buted from the leading edge (LE) to the trailing edge (TE), 100 on the upper su rface and 100 on the lower surface. Clean-Wing Roll Oscillations Flow Visualization The first step in the fluid-structure react ion (FSR) build-up approach is to perform prescribed roll oscillations in order to emulate the bending natu re of an LCO mechanism. For this, the full-span Grid0 F-16 model is used. Time-accurate solutions are run at Mach=0.9, 5,000 feet, for 1Hz and 8Hz .5 roll angles at initial AOA=1.34 (trimmed flight). Looking from the aircraft tail to the aircraft nose, the aircraft rolls left-wing-up first. For the simplicity of 2-D rendition, 9 points in the oscillatory cy cle are chosen for display of the Cp, as shown in Figure 62 The 1Hz case, though not a flutter practical study, is c onsidered for its unsteady aerodynamic characteristics. The primary purpose of exploring this frequency-amplitude combination is to determine the impact of these parameters on the LCO mechanism. The 8Hz .5 more accurately emulates the bending na ture of an LCO mode at a reasonable LCO frequency. 71

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Figure 6-3 and Figure 6-4 illustrate a sequence of images visualizing the flow computed on the left wing (looking aft forward) for the sinusoidal rolling motion depicting Mach = 1 boundary and instantaneous vorticity magnitude is o-surfaces, respectively, with the pressure coloring the aircraft surface. The roll angle is sh own as a function of time in the lower right-hand corner in each set of images. Th e left set of images, A) and B), display the 1Hz case results, and the 8Hz .5 case results are presented in C) and D) on the right. Looking at Figure 6-3 it is difficult to see a difference in the Mach=1 isosurface as the aircraft rolls. Upon animation, it maintains a fairly constant size for the 1Hz case and appears to grow in size at the top of the roll oscillation for the 8Hz .5 case. The grow th of this iso-surface for the 8Hz .5 case appears to lag behind the rolling motion of th e aircraft, which is indicative of a phase shift/hysteresis in the flow. This iso-surface also maintains a mos tly constant position on the aft portion of the wing, parallel to the TE. As the aircraft rolls left-wing-down, the Mach=1 isosurface begins to wrap around the wingtip at the LE to the bottom surface of the wing. Figure 6-4 displays evidence of the vortices comi ng off of the strake in the cave-like feature on the inboard portion of the wing for both cases. Thes e vortices remain stationary despite the motion of the aircraft when an imated. Indication of the wing tip vortices strengthening can be seen at the peak of the ro lling cycle, and diminish ing at the bottom of the cycle, so that the strength of the vortices is offs et asymmetrically on the wingtips. There is also a delay in the strengthening of the tip vortex. It ac tually develops further as the wing begins to roll down, and delays its shrinking until the wing ha s already begun its downward rolling motion. This indicates a lag in the flows reaction to the rolling motion. The instantaneous Cp measurements plotted against non-dimensional chord are plotted in Figure 6-5 at 93% span and in Figure 6-6 at 88% span on the left wing for one developed cycle 72

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of oscillation. The 88% span location is chosen as the region of interest due to its vicinity to the underwing missile launcher location and will be discussed most extensively. Due to the symmetry of the aircraft and motion, time-accurate pressure measurements are only taken on one wing of the aircraft. Although the rolling motion indu ces span-wise flow that differs from right wing to left wing at an instant in time, the symme try of the motion results in similar flow results overall on each wing. Results for the 1Hz ca se are shown in A) upper and B) lower surfaces; and the 8Hz .5 case results are illustrated in C) upper and D) lower surfaces. Each numbered line (1-9) corresponds to the time-accurate locati on, in degrees, during the sinusoidal rolling cycle, indicated by the corres ponding line color give n in the legend in the upper right-hand corner. It is interesting to note from Figure 6-5 and Figure 6-6 that the Cp on both the upper and lower surface overlap for cycle angles 0 and 360, but do not for cycle angle 180. One would expect, from a quasi-static perspec tive, that the coefficients would be the same for all of these cycle angles since they are at the same absolute roll angle. However, it seems that only those roll angles which correspond to the same direction of motion overlap; i.e., cycle angles 0 and 360 indicate left-wing-up roll, whereas cycle angle 180 corresponds to left-wing-down roll. This mismatching trend is prominent for all similar roll angles, and is indicative of the pressure hysteresis in the flow. For the 1Hz case on bo th the upper and lower surfaces in A) and B), cycle angles 0 and 360, 45 and 315, 90 and 270, and 135 and 225 are paired, leaving cycle angle 180 alone through the 60% chord region, where they all converge. However, for the 8Hz .5 case on the upper surface in C) and D), cycle angles 0 and 360 are paired with cycle angle 45 and cycle angles 180 and 225 are paired through the 60% chord region. 73

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Additionally, cycle angles 90 and 315 and cycle angles 135 and 270 are near one another throughout this region. The cycle angles begin to criss-cross aft of the 60% chord region and converge in the 85% chord region. On the lower surface in D), cycle angles 0 and 360, 45 and 315, 90 and 270, and 135 and 225 are pair ed, leaving cycle angle 180 alone through the 20% chord region. All of the cycle angles then converge from the 40% chord region aft. These behaviors can most likely be attributed to the flow-fields inability to keep up with the motion of the structure, indicating a lag in the flow, and pressure hysteresis in the flow. From the 85% chord region and aft, there is very little pressure variation seen. The lower surface has quite large pressure variations through the cycle on the forward 25% chord, but these variations are not as large for the 1Hz .0 case. The upper half of the cycle also has a disproportionately larger variance than the downward half of the cycle as well. Finally, the full back half of the lower surface has very litt le difference in Cp throughout the cycle. Upon more closely examining Figure 6-5 and Figure 6-6 and animating the Cp for all iterations, a suction build-up with increasing roll angle is observed on the upper surface at the 60-85% chord location. As roll angle decreases, th ere is a subtle loss of suction which progresses from the aft portion of the wing forward. This resu lt is an indication of the hysteresis behavior in the shock structure. The build-up and loss is not as rapid for the 1Hz .0 case, and motion is more smooth and rolling. One would expect this roll only contributes lift through the plunging velocity. Lissajous Analysis Lissajous plots of -Cp vs. local vertical displacement for one complete oscillation cycle are examined from the upper surface of the wing at various chord vs. span locations, shown in Figure 6-7 and Figure 6-8 for the 1Hz case, and in Figure 6-9 and Figure 6-10 for the 8Hz .5 case, to examine linearity and phase relationships. -Cp is chosen as the dependent variable 74

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since it is proportional to lift, and the upper su rface of the airfoil is being examined. Local vertical displacement is chosen as the independent variable as opposed to angle of attack (AOA), or some other more typical aerodynamic parameter, due to the fact that as this work continues to more complex motions, i.e. vibration and fl utter modes, comparison will be made in a straightforward manner with the same technique. A low-pass filter is applied to the data at 100Hz to filter out the noise due to turbulence effects. The left-hand side of Figure 6-7 and Figure 6-9 corresponds to the LE of the wing, and the right -hand side corresponds to the TE of the wing. The top of the figures corresponds to the wingtip a nd the bottom to the root of the wing. The lefthand side of Figure 6-8 and Figure 6-10 corresponds to the same 2D Lissajous plots seen in Figure 6-7 and Figure 6-9 and the right-hand side corresponds to the 3-D Lissajous plots with time being the third dimension. The red circle in all figures indicates th e starting point of the cycle, and the black arrows indi cate the direction of rotation. It can be seen in Figure 6-7 that there is a 90 (circle) phase shift over most of the wing. The direction of rotation on the forward portion of the wing is counter-clockwise and transitions to clockwise on the aft portion of the wing. Near this directional rota tion change (and along the TE), regions on the wing resembling figure-eights and other odd shapes are observed. These do not indicate a harmonic that is normally asso ciated with figure-eights but a continuous phase variation within 1 cycle. Since th e solution is cyclically steady, solutions at 0 are identical to 360 solutions, any time lag that shows up during a cycle has to be made up and that fallbehind and catch-up nature leads to the phase variation within a cycle that is shown here. This continuous phase variation within a single cycle al so accounts for the other odd shapes that are not simple ovals. There is also a significant amount of noise along the TE. 75

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Figure 6-8 A) and C) are individual Lissajous figures taken at 93% span vs. 64% chord location, which corresponds to the shock recovery region as seen in Figure 6-5 A). In this region, a great deal of unsteadiness is observed along with the previo usly mentioned odd figure-eightlike shape due to the continuous phase variation. The 3-D plot in C) reveals that the Cp varies little time, although the signal is noisy. The sinusoidal shape is due to the fact that the local vertical displacement is sinusoidal. Figure 6-8 B) and D) are individual Lissajous figures taken at 88% span vs. 81% chord location, which corresponds to the region aft of the shock recovery as seen in Figure 6-6 A). Similarly, a great deal of unst eadiness and another odd figure-eight-like shape due to the continuous phase variation is seen. The 3-D plot in D) is similar to that in C). Figure 6-9 shows the set of Lissajous plots for th e 8Hz .5 case. Most of the plots are open in nature. Much of the forward portion of th e wing exhibits the 90 pha se shift seen in the 1Hz case. However, upon movement inboard toward the wing root, a more elliptical behavior emerges. Near the tran sition from counter-clockwise to clockwise rotation, regions of 180 phase shift are seen. Observa tion of the figure-eights and othe r odd shapes are seen in this region, indicating a continuous phase variation within 1 cycle. However, there is no noise observed along the TE as is seen in the 1Hz case. Overall, th e Lissajous figures for both roll oscillation cases differ significantly at and aft of the shock region. Figure 6-10 A) and C) are individual Lissajous figures taken at 93% span vs. 65% chord location, which corresponds to the shock recovery region as seen in Figure 6-5 C). In this region, an odd figure-eight-like shape due to the continuous phase variati on is observed which is much different from the one seen with the 1Hz case. Th e 3-D plot in C) provides more insight as to how the Cp varies with time. Notably, a loop feature is seen occurring in the first half of the cycle. This is due to both the sinusoidal response of the Cp and the local displacement being out 76

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of phase. Figure 6-10 B) and D) are individual Lissajous figures taken at 88% span vs. 69% chord location, which also corresponds to shock recovery region as seen in Figure 6-6 C). Similarly, another odd figure-eight-like shape due to the continuous phase variation is seen. The 3-D plot in D) is similar to that in C), w ith the loop feature happening later in the cycle. Wavelet Analysis Wavelet analysis is applied to points of interest on the wing in Figure 6-11 and Figure 612, for the Grid0 8Hz roll case in order to gain further insight into the temporal nature of the results. In each set of figures, A) gives the time history of the Cp variation, B) shows the fast Fourier transform (FFT) of the da ta, and C) illustrates the wave let transform view of frequency vs. time. Figure 6-11 contains the results at 93% span vs. 65% chord and Figure 6-12 is at 88% span vs. 69% chord. Both of these locations correspond to the shock recovery regions as previously mentioned. From both figures, the time history plots in A) reveal a fairly sinusoidal response in upper wing surface Cp. The FFT plots in B) both show a promin ent peak at the input frequency of 8Hz and smaller peaks at the harmonics. The wavelet plots in C) are also very similar and reveal most of the energy concentration occurring at 8Hz as expected, with the higher frequency harmonics participating on the upstroke and downstroke of th e oscillation. The wavelet analysis confirms a periodic response as predicted by the FFT. Tip-Launcher Roll Oscillations Flow Visualization In order to emulate the bending nature of an LCO mechanism, the FSR flow-field breakdown is extended by performing a forced, rigidbody roll oscillation fo r a more refined F-16 Grid4 with tip launchers, LE edge antennae, and gun port. An 8Hz .5 rigid-body roll 77

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oscillation is examined at the same flow conditions (Mach=0.9, 5,000 feet, initial AOA=1.34) for direct comparison to the clean-wing Grid0 case. Figure 6-13 and Figure 6-14 illustrate a sequence of images visualizing the flow computed on the left wing for the sinusoidal rolling motion depicting instantaneous Mach = 1 boundary and vorticity magnitude iso-surfaces, respectively, colored by pressure. The roll angle is shown as a function of time in the lower right -hand corner in each se t of images. The right set of images, A) and B), display the tip-launche r Grid4 case results, and the clean-wing Grid0 comparisons are presented in C) and D). The addition of the tip launcher and LE antennae significantly influence the nature of the Mach=1 and vorticity magnitude iso-surfaces where expected for this case, such as the cave created by the LE antennae and the wrinkle due to the tip launcher. Looking at Figure 6-13 A) and B), it is difficult to see a difference in the Mach=1 isosurface as the aircraft rolls. Upon animation, the growth of this iso-surface appears to lag behind the rolling motion of the aircraft, which is indicative of a phase shift/hysteresis in the flow. This iso-surface also maintains a mostly constant position on the aft portion of the wing, parallel to the TE. As the aircraft rolls left-wing-down, the Mach=1 iso-surface begins to wrap around the wingtip at the LE to the bottom surface of the wi ng. Upon animation of the tip-launcher case, it is revealed that as the aircraft pitches nos e-down, the Mach=1 iso-surface completely wraps around the wingtip at the LE to the bottom surface of the wing and surrounds the LE antennae. It should be noted that the shock on th e front of the engine is due to faults with the engine model resulting in a throttle chop flow feature that will be resolved in future simulations. Vortices are also observed in Figure 6-14 rotating along the tip launcher, co rresponding to the rolling up and down of the wing. 78

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The instantaneous Cp measurements plotted against non-dimensional chord are plotted in Figure 6-15 at 98% span, in Figure 6-16 at 93% span, and in Figure 6-17 at 88% span on the left wing (looking aftforward) for one developed cycle of oscillation. The 88% span location is chosen as the region of interest due to its vici nity to the underwing miss ile launcher location and will be discussed most extensively. Due to the symmetry of the aircraft, time-accurate pressure measurements are only taken on one wing of the ai rcraft. Results for the Grid4 tip-launcher case are shown in A) upper and B) lower surfaces; and the Grid0 clean-wing case results are illustrated in C) upper and D) lower surfaces. Each numbered line (1-9) corresponds to the timeaccurate location, in degrees, during the sinusoidal rolling cycle, indicated by the corresponding line color given in the legend in the upper right-hand corner. Upon comparison of the tip-launcher case in Figure 6-17 A) and B) with the clean-wing case in C) and D), it is seen in both cases that the same roll a ngles, which correspond to the same direction of motion, overlap; i.e., cycle angl es 0 and 360 indicate left -wing-up roll, whereas cycle angle 180 corresponds to left-wing-down roll. This mismatching trend is prominent for all similar roll angles, and is indi cative of the pressure hysteresis in the flow. However, on the upper surface, a more defined shock character is observed in the 60-70% chord region for the tiplauncher case. This effect may be attributed to refinements in the grid. Upon closer examination of Figure 6-17 and animation of the Cp for all iterations, a suction build-up with increasing roll angle is observed on the upper surf ace at the 60-85% chord location reveals; similar to the one seen with the increasing AOA of the pitch oscillation. As roll angl e decreases, there is a loss of suction which progresses from the aft portion of the wing forward. The motion of this loss is much more subtle than that seen for the pitch cas es. This result is an indication of the hysteresis behavior in the shock structure. 79

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Significant pressure differences also occur on th e lower surface for the tip-launcher case in the 0-30% chord region. Similar results are enco untered on both the upper and lower surfaces for BL locations closer to the tip launcher. This result may be indicative of the aerodynamic influence of the tip launcher. With this in mind, the pressure distributions are examined for more inboard BL locations, and noticed a significant influence due to the LE antennae (located at BL154) as far inboard as BL146. This effect is unexpected given how relatively small this component is on the aircraft. Based on this significant influence from a small component, it is hypothesized that small aerodynamic differences betw een stores can cause significant changes in the flow-field, possibly influencing the occurr ence of LCO. This may explain why nearly identical configurations have different LCO flight test results which are not predicted by classical flutter analyses. Lissajous Analysis Figure 6-18 and Figure 6-19 show the set of Lissajous plots (-Cp vs. local displacement from the upper surface of the airfoil at various chord vs. span locations) for the rolling, 8Hz .5, case, to examine linearity and phase relationships. -Cp is chosen as the dependent variable since it is proportional to lift, and the upper su rface of the airfoil is being examined. Local vertical displacement is chosen as the independe nt variable as opposed to AOA, or some other more typical aerodynamic parameter, due to the fact that as this work continues to more complex motions, i.e. vibration and flutter modes, comparison will be made in a straightforward manner with the same technique. A low-pass filter is applied to the data at 100 Hz to filter out the noise due to turbulence effects. The left-hand side of Figure 6-18 corresponds to the LE of the wing, and the right-hand side corresponds to the TE of the wing. The top of the figures corresponds to the wingtip and the bottom to the root of the wing. The left-hand side of Figure 6-19 corresponds to the same 2-D Lissajous plots seen in Figure 6-18 and the right-hand side corresponds to the 380

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D Lissajous plots with time being the third dimens ion. The red circle in all figures indicates the starting point of the cycle, and the black ar rows indicate the direction of rotation. The orientation of the Lissajous plots for the tip-launcher case in Figure 6-18 is slightly different from the clean-wing case seen in Figure 6-9 since the tip-launcher plots include two extra span stations, one on the tip launcher (BL183) and one at 100% span (BL180). However, the overall trends are similar. Most of the plot s are circular in nature. Much of the forward portion of the wing exhibits a 90 phase shift. However, upon m ovement inboard toward the wing root, a more elliptical beha vior is seen. Near the transition from counter-clockwise to clockwise rotation on the right po rtion of the plot, regions of 180 phase shift emerge. The figure-eights and other odd sh apes are also seen for the tip-launcher case, indicating a continuous phase variation within 1 cycle. These occur most prominently in the tip launcher and LE antennae locations, and along the TE. Figure 6-19 A) and D) are individual Lissajous figures taken at 98% span vs. 44% chord location, which corresponds to the secondary shoc k region ahead of the primary shock as seen in Figure 6-15 C). In this region, an odd circular shap e forms due to the continuous phase variation caused by the formation of this secondary shock, which is due to the tip launchers presence. The 3-D plot in C) provides more insight as to how the Cp varies with time. Notably, a loop feature is seen occurring in the last quarter of the cycle. Figure 6-19 B) and E) are individual Lissajous figures taken at 93% span vs. 67% chord locatio n, which corresponds to shock recovery region as seen in Figure 6-16 C). The phase relationship for this figure is close to 45 with some unsteadiness due to the shock transition. The 3D plot in E) shows a loop feature happening in the last half of the cycle. Figure 6-19 C) and F) are individual Li ssajous figures taken at 88% span vs. 70% chord location, which also corres ponds to shock recovery region as seen in Figure 81

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6-17 C). The shape of this Lissajous in C) is simila r to B), but with a phase closer to 15; also with some unsteadiness due to the shock transition. The 3-D plot in F) is similar to that in E), with the la slightly different shape in the loop feature. Wavelet Analysis Wavelet analysis is applied to points of interest on the wing in Figure 6-20 Figure 6-21 and Figure 6-22 for the Grid4 8Hz roll case with tip launc hers in order to gain further insight into the temporal nature of the results. In each set of figures, A) gives the time history of the Cp variation, B) shows the fast Fourier transform (F FT) of the data, and C) illustrates the wavelet transform view of frequency vs. time. Figure 6-20 contains the results at 98% span vs. 44% chord and which corresponds to the secondary shock region ahead of the primary shock as seen in Figure 6-15 C). The time history plot in A) reveals a fairly sinus oidal response in upper wing surface Cp. However, a double-peak is seen in the data around time= 0.45 seconds. The FFT plot in B) shows a prominent peak at the input frequency of 8Hz, and assumes a periodic re sponse. The wavelet plot in C) reveals various non-periodic features that are no t seen in the FFT. There is a c oncentration of 20 Hz energy at time=0.3-0.35 sec. Also in this region and at 0.45 seconds, the energy concentration at 8Hz goes to a dark red color at the center of the circle, indicating more 8Hz energy content than for other cycles. This explains the sharpness of the peaks in the time history plot in A) at these times. At 0.2 seconds, the 8Hz energy concentration is only indicated by a pink circle, meaning less energy. Also, the double-peak feature seen in the time history plot in A) manifests in the sshaped region seen near 0.45 sec. Figure 6-21 contains the results at 93% span vs 67% chord, corresponding to the shock recovery region seen in Figure 6-16 C). The time history plot in A) reveals a fairly sinusoidal response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input 82

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frequency of 8Hz. The wavelet plot in C) reve als most of the energy c oncentration occurring at 8Hz as expected, with the hi gher frequency harmonics part icipating on the upstroke and downstroke of the oscillation. The wavelet analysis confirms a periodic response as predicted by the FFT. Figure 6-22 contains the results at 88% span vs. 70% chord and which corresponds to the shock recovery region as seen in Figure 6-17 C). The time history plot in A) reveals a fairly periodic response in upper wing surface Cp, with the top of the peaks being flat and the bottom sharp. The FFT plot in B) shows a prominent pe ak at the input frequenc y of 8Hz with smaller peaks at some harmonics. The wavelet plot in C) confirms a mostly periodi c response seen in the FFT with most of the energy c oncentration occurring at 8Hz and energy from the harmonics contributing on the upstrokes and downstrokes of th e oscillations. However, it does reveal that the second green peak at time=0.35 seconds is larg er than the first one at time=0.28 seconds due to the higher frequency energy conc entration of the 16Hz harmonic. Clean-Wing Pitch Oscillations Flow Visualization In order to emulate the torsional nature of an LCO mechanism, the next step in the FSR flow-field break-down is to perform forced, ri gid-body pitch oscillations with the clean-wing F16. Time-accurate solutions are run at Mach=0.9 5,000 feet, for 1Hz and 8Hz .5 angles of attack at initial AOA=1.34 (tri mmed flight). The 1Hz case, though not a flutter practical study, is considered for its unsteady aerodynamic ch aracteristics, and coarse refinement Grid0 is acceptable for use in order to capture the overall trends of the mechanism. The 8Hz .5 more accurately emulates the torsional nature of an LC O mode at a realistic LCO frequency, therefore the fine refinement Grid9 is used. As previ ously mentioned, unsteady wing surface pressure coefficients, Cp, are extracted at every iteration from the upper and lower-wing surfaces at 83

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various span locations. For simplicity of 2-D rendition, 9 points in the oscillatory cycle are chosen for display of the Cp, as shown in Figure 6-23 Figure 6-24 and Figure 6-25 illustrate a sequence of images visualizing the flow computed for the sinusoidal pitching-motion depicting in stantaneous Mach = 1 boundary and vorticity magnitude iso-surfaces, respectively, colored by pressure. The AOA is shown as a function of time in the lower right-hand corner in each set of images. The left set of images, A) and B), display the 1Hz Grid0 case results, and the 8H z .5 Grid9 case results are presented in C) and D). Each figures perspective is from the top of the left wing. It is seen from Figure 6-24 that the Mach=1 iso-surface is maximum in size at the top of the oscillation. Throughout the oscillation, the aft extent of the upper-surface Mach=1 iso-surface maintains a mostly constant position on the aft po rtion of the wing, parallel to the TE. At the peak of the oscillatory cycle, there is a not able break-up of the M ach=1 iso-surface along the wingtip in the 1Hz case. This result is du e to the wingtip vortical structure seen in Figure 625. Evidence of the vortices coming off of the stra ke is noticed in the cave-like feature on the inboard portion of the wing. Upon animation of th e 1Hz case, it is revealed that as the aircraft pitches nose-down, the Mach=1 iso-surface completely wraps around the wingtip at the LE to the bottom surface of the wing and spreads along the LE. A Mach=1 boundary iso-surface also develops on the lower fuselage of the aircraft as the aircraft pitches nose-down and joins the Mach=1 iso-surface that wraps around the wing. In contrast, the Mach=1 iso-surface is not as large for the 8Hz .5 case, does not spread all the way along the LE to the root of the wing, and does not develop on the fuselage. Figure 6-25 also displays evidence of the strong wi ng-tip vortices manifesting at the peak of the sinusoidal cycle. Upon animation of both the upper and lower wing surfaces, the strake 84

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vortex is observed travelling outboard with noseup pitch and inboard with nose-down pitch. Additionally, animation of the lowe r surface of the aircraft reveals strong vortices coming off of the engine inlet oscillating in a similar manner. Vortices for the 8Hz .5 case exhibit decreased strength and an inertial lag when compared to the 1Hz case, which are indicative of more phase shift/hysteresis. Fuselage effects are not expected be a factor during an actual LCO mode, where the fuselage is relatively stationary and the motion is primarily concentrated in the outer portions of the wing/wingtip. However, it is anticipated that there may be similar flow manifestations attributed to the launchers/pyl ons/stores once they are added, and that the character of these iso-surfaces may change. The instantaneous Cp measurements plotted against non-dimensional chord are plotted in Figure 6-26 at 98% span, in Figure 6-27 at 93% span, and in Figure 6-28 at 88% span on the left wing (looking aftforward) for one developed cycle of oscillation. The 88% span location is chosen as the region of interest due to its vici nity to the underwing miss ile launcher location and will be discussed most extensively. Results for the 1Hz Grid0 case are shown in A) upper and B) lower surfaces; and the 8Hz Grid9 case results ar e illustrated in C) upper and D) lower surfaces. Each numbered line (1-9) corresponds to the time-accurate location, in degrees, during the sinusoidal rolling cycle, indicated by the corr esponding line color given in the legend in the upper right-hand corner. For example, line 1 is at 0 (green, solid line), line 2 is at 45 (blue, dashed line), line 3 is at 90 (purple, dotted line), etc. It is worthy to note from Figure 6-28 that the Cp on both the upper and lower surface overlap for 0 and 360 cycle angles, but do not fo r 180. One would expect, from a quasi-static perspective, that the coefficients would be the same for all of thes e cycle angles since they are at the same absolute AOA. For the 1Hz case in Figure 6-28 A) and B) it seems that the cycle 85

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angles corresponding to the downward motion of th e cycle overlap, whereas the cycle angle on the upward motion is offset. This same trend hol ds true for cycle angles 45 and 135 and cycle angles 225 and 315, and is indicative of the pre ssure hysteresis in the flow. However, for the 8Hz .5 case in Figure 6-28 C) and D), cycle angles 0 and 360 are paired with cycle angle 225 throughout the 0-50% chord location and aft of the 80% chord location. Additionally, cycle angles 45 and 180, 90 and 135, and 270 and 315 form pairs from the 0-50% chord location and aft of the 80% chord location. This result is most likely an indication that the flow-field is unable to keep up with the motion of the structure, indicating a lag in the flow. It can also be seen from Figure 6-28 that in the 65-75% chord region on the upper surface, there is a noteworthy suction lo ss feature for cycle angles 22 5, 270, and 315, corresponding to the ascension, peak, and descension of the positiv e peak of the pitch oscillation. From the 75% chord region and aft, there is very little pre ssure variation. The lower surface has quite large pressure variations through the cycle on the forw ard 25% chord, but these variations are not as large for the 8Hz .5 case. The upper half of the cycle also has a disproportionately larger variance than the downward half of the cycle as well. Finally, the full back half of the lower surface has very litt le difference in Cp throughout the cycle. Additiona lly, it is observed that the lower amplitude pitch oscillation, .5 vice 2, results in a more constant upper LE suction region (5-25% chord). This brings out unsteady characteristics due to motion and not as much due to pressure variation through the cycle. Upon examining Figure 6-28 and animating the Cp for all iterations on the upper surface, a rapid suction build-up with increasing AOA is revealed at the 50-70% chord location. As AOA decreases, there is a rapid loss of suction which progresses from the aft portion of the wing forward. The motion of this lo ss resembles that of a double hinge d door slamming shut; the first 86

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near 70% chord and the second ne ar 60% chord. This result is an indication of the hysteresis behavior in the shock structure. The build-up and loss is not as rapid for the 8Hz .5 case, and the doubled-hinged, door-like motion is more smooth and rolling. For th e 1Hz case, this trend is reversed in the 0-10% chord location, where with increas ing AOA, there is lower suction than with decreasing AOA. This result may be a result of higher relative AOA as the nose pitches down and a vertical component of velo city contributes to a higher local AOA, and therefore more suction. This region also contains a second hump, seen in cycle angles 225, 270, and 315, and the biggest overall pressure vari ations, which are not seen for the 8 Hz .5 case. This result is most likely due to the smalle r amplitude of oscillation. It is hypothesized at this point that the greatest contribution to the shock motion for the 1Hz case is due to the significant pressure variation in the 0-10% portion of the airfoil. For the 8Hz case, the LE surface pressure variation is rather small and the hypot hesized contributor to the shock motion is the plunging motion (causing a velocity vector addition AOA change). Lissajous Analysis Lissajous plots of -Cp vs. local displacement are genera ted from the upper surface of the airfoil at various chord vs. span locations in order to examine the linearity and phase relationships. -Cp is chosen as the dependent variable si nce it is proportional to lift, and the upper surface of the airfoil is being examined. Local displacement is chosen as the independent variable as opposed to AOA, or some other more typical aerodynamic parameter, due to the fact that as this work continues to more comple x motions, i.e. vibration and flutter modes, comparison will be made in a straightforward manner with the same technique. A low pass filter is applied to the data at 100 Hz to filter out the noise due to turbulence effects. Figure 6-29 and Figure 6-30 illustrate the Lissajous plots for the 1Hz case, and the 8Hz .5 results are seen in Figure 6-31 and Figure 6-32 The left-hand side of Figure 6-29 and 87

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Figure 6-31 corresponds to the LE of the wing, and th e right-hand side corresponds to the TE of the wing. The top of the figure co rresponds to the wingtip and the bottom to the root of the wing. The left-hand side of Figure 6-30 and Figure 6-32 corresponds to the same 2-D Lissajous plots seen in Figure 6-29 and Figure 6-31 respectively; and the right-ha nd side corresponds to the 3-D Lissajous plots with time being the third dimensi on. The red circle in al l figures indicates the starting point of the cycle, and the black arrows indicate the direction of rotation. It can be seen in the lower left-hand portion of Figure 6-29 that there is a 0 (diagonal line downward to the left) phase shift region with counter-clockwise rotation. Progressing aft, the phase abruptly shifts to 180 (diagonal line downw ard to the right) with clockwise rotation. This shift is indicative of the pitch axis. Once in th e 63% chord region, the Lissajous plots begin to open up, indicating the shock structure region. The plots then flip back to a 0 shift in the 78% chord region upon aft and inboard progression. However, in the outboard region, the phase remains at 180 and takes on a highly odd shape. This odd shape is also seen along the LE upon outboard movement from the 68% span section, and all along the tip of the wing. Any plot that is not a symmetric oval about an arbitrary axis is the resu lt of a phase variation within 1 cycle. The figure-eight plot is not a harmonic, as is normally associated with figure-eights, but the result of the phase ch anging sign. The phase changes from a lead to a lag, or vice-versa. Since the solution is cyclically steady, solutions at 0 are identical to 360 solutions, any time lag that shows up during a cycle has to be mad e up and that fall-beh ind and catch-up nature leads to the phase variation within a cycle that is shown here. The re gion beginning at the top (tip) in the 23-28% chord region and extending at the bottom (root) to the 43-48% chord-region, indicates a transition from clockw ise to counter-clockwise rotation. Increased suction (increased lift) is seen with increased di splacement (increase in AOA) in front of the pitch axis, as is 88

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expected from a lift curve slope. Aft of the pitch axis the vertical displ acement is opposite in sign to AOA. This leads to a 180 out of phase lift curve slope plot. Figure 6-30 A) and D) are individual Lissajous figures taken at 93% span vs. 67% chord location, which corresponds to the shock recovery region as seen in Figure 6-27 C). In this region, an odd figure-eight shape forms due to the continuous phase variation caused by the shock transition. The 3-D plot in D) provides more insight as to how the Cp varies with time. Notably, a loop feature is seen occu rring in the last quarter of the cycle. This is due to the large and fast Cp variation occurring at th is point in the cycle. Figure 6-30 B) and E) are individual Lissajous figures taken at 88% span vs. 72% ch ord location, which also corresponds to shock recovery region as seen in Figure 6-28 C). The phase relationship for this figure is close to 15 with some nonlinear, figure-eight aspects due to the shock transition. The 3-D plot in E) shows a loop feature happening in the last half of the cycle since the Cp jump is more prolonged. Figure 6-30 C) and F) are individual Lissajous figures ta ken at 88% span vs. 81% chord location, which corresponds to the area aft of shoc k recovery region as seen in Figure 6-28 C). The shape of this Lissajous is also a nonlinear, figure-eight, but with a phase closer to 145. The 3-D plot in F) has a more s-shaped feature with a small loop occurr ing in the last part of the cycle due a doublesinusoidal-like response in the Cp. Figure 6-31 shows that the set of Lissajous plots for the 8Hz .5 case is very different from the 1Hz case. Most of the plots are open in nature and do not display the nonlinear nature shown previously. In the lower left-hand po tion of the plot, a 0 phas e shift is again seen with counter-clockwise rotation, but it opens up to a 45 (ellipse up to the right) phase shift along the LE. As in the 1Hz plot this maps out the pitch axis. The phase then shifts to 180 with clockwise rotation and begins to open up upon af t movement. However, the shift to clockwise 89

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rotation is delayed for the area in 32-46% span and 28-58% chord. Fewer regions on the wing where the Lissajous plots form a figure-eight sh ape are observed, indicating a continuous phase variation within 1 cycle. The transition from clockwise to counter-cloc kwise rotation is again seen. However, this transition occurs much fart her aft for the 8Hz .5, in the 53-73% chord region. Aft of this change the phase changes to 90 (circle). Figure 6-32 A) and D) are individual Lissajous figures taken at 98% span vs. 54% chord location, which corresponds to the sh ock transition region as seen in Figure 6-26 C). In this region, a figure-eight shape forms due to the co ntinuous phase variation caused by the oscillatory behavior in the shock transition region. The figure-eight plot is not a harmonic, as is normally associated with figure-eights, but the result of th e phase changing sign; from a lead to a lag, or vice-versa. The shape of the figure-eight provides insight into phase/time lag. A fat top or bottom shows where Cp is lagging behind the motion; alte rnatively a narrow top or bottom indicates where the Cp is leading the motion, trying to catch up. The transition across the shock is indicated by the change in lift (i.e., the change in value of Cp shown by position of starting red circle). An increase in -Cp is ahead of shock, whereas decrease in -Cp is behind shock. The 3-D plot in C) provides more insight as to how the Cp varies with time, with an s-shape. Figure 6-32 B) and E) are individual Lissajous figures taken at 93% span vs. 58% chord location, which corresponds to s hock recovery region as seen in Figure 6-27 C). In this region, a figure-eight shape also forms due to the conti nuous phase variation caused by the oscillatory behavior in the shock transition region. The 3D plot in E) shows an s-shaped feature. Figure 632 C) and F) are individual Liss ajous figures taken at 88% span vs. 58% chord location, which corresponds to the region ahead of the shock recove ry region as seen in Figure 6-28 C). The 90

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shape of this Lissajous is nonlinear with a phase cl oser to 135. This is due to shock formation. The 3-D plot in F) exhibits a loop feat ure in the first quarter of the cycle. Wavelet Analysis Wavelet analysis is applied to points of interest on the wing in Figure 6-33 Figure 6-34 and Figure 6-35 for the clean-wing Grid0 1Hz pitch case; and in Figure 6-36 Figure 6-37 and Figure 6-38 for the clean-wing Grid9 8Hz pitch case, in order to gain further insight into the temporal nature of the results. In each set of figures, A) gives the time history of the Cp variation, B) shows the fast Fourier transform (FFT) of th e data, and C) illustrates the wavelet transform view of frequency vs. time. Figure 6-33 contains the 1Hz Grid0 results at 93 % span vs. 67% chord which corresponds to the shock recovery region as seen in Figure 6-27 C). The time history plot in A) reveals a fairly periodic response in upper wing surface Cp. The FFT plot in B) shows broad-band energy for 1-5Hz. The wavelet plot in C) illustrate s large energy concentra tion occurring at 3Hz at time=0.82 sec and 1.82 sec. The wavelet analysis also confirms a periodic response as predicted by the FFT. Figure 6-34 contains the 1Hz Grid0 results at 88% span vs. 72% chord which also corresponds to shock recovery region as seen in Figure 6-28 C). The time history plot in A) again reveals a fairly periodic re sponse in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input frequency of 1Hz. The wavelet plot in C) illustrates most of the energy concentration occurring at 1Hz with higher frequency energy occurring on the upstroke and downstroke of the oscillation. The wavelet analysis also confirms a periodic response as predicted by the FFT. Figure 6-35 contains the 1Hz Grid0 results at 88% span vs. 81% chord which also corresponds to the area aft of shoc k recovery region as seen in Figure 6-28 C). The time history 91

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plot in A) reveals a fairly periodic response in upper wing surface Cp, with a double sinusoidal shape. The FFT plot in B) shows a peak at the input frequency of 1H z, with a larger peak at 2Hz. The wavelet plot in C) illustrates large energy concentrations occurring at 1Hz with the higher frequency 2Hz energy overlapping and particip ating on the upstroke and downstroke of the oscillation. The wavelet analysis also confir ms a periodic response as predicted by the FFT. Figure 6-36 contains the 8Hz Grid9 results at 98% span vs. 54% chord and which corresponds to the shock tran sition region as seen in Figure 6-26 C). The time history plot in A) reveals a saw-tooth shaped response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input fr equency of 8Hz with smaller pe aks occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals non-pe riodic features that are not seen in the FFT, such as higher frequency energy concentrations on the end of the cycle occurring when the Cp drops dramatically, such as at time=0.25 sec and 0.37 sec. Figure 6-37 contains the 8Hz Grid9 results at 93% span vs. 58% chord and which corresponds to the shock recovery region as seen in Figure 6-27 C). The time history plot in A) reveals an even more exaggerated saw-t ooth shaped response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input frequency of 8Hz with smaller peaks occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals non-periodic features that are not seen in the FFT, such as higher frequency energy concentrations on the end of the cycle occurring when the Cp drops dramatically, such as at time=0.25 sec and 0.38 sec. Figure 6-38 contains the 8Hz Grid9 results at 88% span vs. 58% chord and which corresponds to the region ahead of the shock recove ry region as seen in Figure 6-28 C). The time history plot in A) reveals a wide peak vs. sharp trough response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at th e input frequency of 8H z with smaller peaks 92

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occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals nonperiodic features that are not seen in the FFT. The blue region at time=0.23 sec corresponds to the wide peak region and consists of a range of fr equencies, whereas the green region at time=0.3 sec corresponds to the narrow trough region a nd consists of one, clear frequency. Tip-Launcher Pitch Oscillations Flow Visualization The FSR flow-field break-down is now extended by performing forced, rigid body pitch oscillation for a fine F-16 Grid8 with forebody bum p, diverter, ventral fin, fuselage gun port, leading edge antenna, and tip launchers. An 8Hz .5 rigid-body pitch oscillation is examined at the same flow conditions (AOAi=1.34, Mach=0.9, 5000 feet) with the same turbulence model (DDES-SARC) for direct comparison to the clean-wing Grid9 case. Figure 6-39 and Figure 6-40 illustrate a sequence of images visualizing the flow computed for 8Hz .5 sinusoidal pitching motion depi cting instantaneous Mach = 1 boundary and vorticity magnitude iso-surfaces colored by pressure, respectively, at the upward stroke (between pitch angles of 135 and 180) of the 8 Hz .5 si nusoidal pitching cycle. The left set of images, A) upper and B) lower surfaces, display the tip-l auncher Grid8 case results, and the clean-wing Grid9 comparisons are presented in C) upper and D) lower surfaces. The AOA is shown as a function of time in the center of each pair of images. Additionally, BL159 (88% span location) is indicated along the LE of each of the images for reference purposes. Just like for the roll cases, it can be seen from that the addition of the tip launcher significantly influences the nature of the Mach =1 boundary and vorticity magnitude iso-surfaces for the pitch cases. It is observed from Figure 6-39 that the trends between the tip-launcher and clean-wing cases are similar; such as the Mach=1 iso-surfaces at their maximum sizes at the top of the oscillation, and that the aft extent of the upper-surface Mach=1 iso-surface maintains a 93

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mostly constant position on the aft portion of the wing, parallel to the TE. Differences are expected in the tip-launcher region, such as th e small secondary shock aft of the primary shock near the tip launcher due to the tip launcher not ch seen in the roll oscillation case. The most interesting difference, however, is aft of the shock on the inboard portion of the wing where apparent separation of the shock is evident. This is much more visible upon animation. For the clean-wing case, this separation appears to occu r all the way out to the wing tip and be much more significant overall. For the tip-launcher case it looks like the separation begins to occur near the tip, but then interacts with the secondary s hock due to the launcher, resulting in less separation. This same trend is s een at the inboard separation. Upon animation of Figure 6-39 C) and D), the clean-wing case reveals that as the aircraft pitches nose-down, the Mach=1 iso-surface wrap s around the wingtip at the LE extending about one-half the length of the wing. This surface then wraps around the bottom surface of the wing at the LE, and continues along the LE, tapering off well inboard. Upon animation of the tiplauncher case in Figure 6-39 A) and B), it is revealed that as the aircraft pitches nose-down, the Mach=1 iso-surface is inhibited from wrapping around the wingtip at the LE by the tip launcher. It wraps around the tip launcher at about one-half the way down the tip. The shock along the LE still wraps around the bottom surface of the wing. For both cases, the presence of LE antenna causes the shock to snake along the bottom surface of the wing and connect to the base of the LE antenna just like for the roll case. However, it also appears that the forward shock on the LE antenna attaches to the shock on the LE edge of the wing. From animation of Figure 6-40 A) and B), vortices are seen rotating along the tip launcher, corresponding to the pitching up and down of the aircraft. Rotation in the LE antenna vortex is also apparent as the aircraft is pitching up a nd down. The tip vortex and LE antenna vortex share 94

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the same direction of rotation on the upper surface, but are contra on the lower surface. The LE antenna vortex diminishes on the upper surface as the aircraft pitches down and grows as it pitches up. Additionally, th ere is much more activity from th e strake vortex on inboard portion of the wing. This feature may be contributing to the inboard separation of the shock seen previously. This may be strong evidence of shockinduced separation. Additionally, this type of flow feature may play an important role in the LCO mechanism. The instantaneous Cp measurements plotted against non-dimensional chord are plotted in Figure 6-41 at 98% span, in Figure 6-42 at 93% span, and in Figure 6-43 at 88% span on the left wing (looking aftforward) for one developed cycle of oscillation. The 88% span location is chosen as the region of interest due to its vici nity to the underwing miss ile launcher location and will be discussed most extensively. Results fo r the Gird8 tip-launcher case are shown in A), upper surface, and B), lower surface; and the Gri d9 clean-wing comparison results are illustrated in C), upper surface, and D), lower surface. Each numbered line (1-9) corresponds to the timeaccurate oscillation cycle angle, in degrees, during the sinusoida l pitching cycle, indicated by the corresponding cycle angle color given in th e legend in the upper right-hand corner. In Figure 6-43 the Cp on both the upper and lower surface overlap for 0 and 360 cycle angles, but do not for 180. Similar to the cl ean-wing pitching case, from a quasi-static perspective it can be expected that the coeffici ents would be the same for all of these cycle angles since they are at the same absolute AOA. Upon comparison of the tip-launcher case and the clean-wing case, the same cycl e angles create pairs, indicating the same inability of the flowfield to keep up with the motion of the structur e, indicating a lag in the flow. The same suction loss feature is observed for cycle angles 225, 270, and 315, corresponding to the ascension, peak, and descension of the positive peak of the pitch oscillation in the 65-75% chord region on 95

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the upper surface. However, on the upper surface, th ere is a more defined shock character in the 60-70% chord region for the tip-launcher case. There is also see a shift aft in the shock location. These features are attributed to the presence of the tip launcher. Upon examining Figure 6-43 and animating the Cp for all iterations on the upper surface, a rapid suction build-up with increasing AOA is revealed at the 50-70% chord location. As AOA decreases, there is a rapid loss of suction which progresses from the aft portion of the wing forward. The motion of this loss resembles that of a double hinged door slamming shut; the first near 70 % chord and the second near 60% chord. This is an indication of the hysteresis beha vior in the shock structure. Significant pressure differences occur on the lower surface for the both cases in the 0-30% chord region. Similar results where encountered on for the Grid4 tip-launcher case with LE antenna. This is indicative of the aerodynamic influence of the LE antenna. Based on this significant influence from a small component, sm all aerodynamic differences between stores can cause significant changes in the flow-field, pos sibly influencing the occurrence of LCO. This may explain why nearly identical configurations ha ve different LCO flight test results which are not predicted by classical flutter analyses. Howeve r, it is known from f light testing experience that the LE antenna is not a driving force behind the LCO mechanism. Therefore, future grids will most likely not include the LE antenna so as to avoid distraction from the true contribution to the LCO mechanism. Lissajous Analysis Figure 6-44 shows the set of Lissajous plots (-Cp vs. local displacement from the upper surface of the airfoil at various chord vs. span locations) for one cycle of pitching 8Hz .5 oscillation. A low pass filter is applied to th e data at 100 Hz to filter out the noise due to turbulence effects. The top of the figure is the ti p launcher, the bottom the wing root; and the left side is the LE and the right side the TE of the wi ng. The red circles indica te the starting point of 96

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the roll cycle, and the black arrows indicate the di rection of rotation of th e Lissajous. The set of Lissajous plots for the tip-launcher case is slig htly different from the clean-wing case seen in Figure 6-31 First, the tip-launcher plots include two ex tra span stations, one on the tip launcher and one at the LE antennae. The Lissajous figures for the pitch oscillation cases are very different from the roll oscillation cases. However, the overall trends are similar for the tiplauncher Grid8 and clean-wing Grid9 pitch cases. In the lower left-hand potion of the plot, a 0 to 45 phase shift is observed with counter-clock wise rotation. The phase suddenly shifts to 180, essentially mapping out the pitch axis. There is also a corresponding phase shift on the tip launcher (LAU) for Grid8 at the 13% chord location indicative of the pitch axis. The phase then shifts to 180 with clockwise rotation, with a delayed shift in the 42-59% span, 28-68% chord region, and begins to open up aft along the wing with 90 phase shift along the inboard, TE portion of the wing. The phase maintains a 180 phase shift near and along the tip for Grid8. A transition from clockwise to counter-clockwise rotation is apparent in the 78% chord region at the root and extending back to the 68% c hord region near the tip. This shift in rotational direction can be attributed to th e shock transition. It is interesting to note that the rotational directions for the pitch cases are opposite of those of th e roll cases. This has to do with the roll beginning left-wing-up and the pi tch beginning left-wing-down. Additionally, the region of change is much further forward moving toward the tip launcher. The tip-launcher plots show a more narrow nature in the shock transition regi on than the rounder clean-wing case, and a more open nature near the tip. There are also a few re gions on the wing, mostly near the tip launcher and shock transition, where the Lissajous plots fo rm a figure-eight shape, indicating a continuous phase variation within 1 cycle. Overall, the Li ssajous figures for both pitch oscillation cases differ significantly near the tip (88-1 00% span) and shock transition region. 97

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Figure 6-45 A) and D) are individual Lissajous figures taken at 98% span vs. 45% chord location, which corresponds to the primary shock formation region as seen in Figure 6-41 C). In this region, an odd circular shape forms due to the continuous phase variation caused by the formation of the shock in the tip launchers pres ence. The 3-D plot in C) provides more insight as to how the Cp varies with time, revealing a loop feature in the firs t quarter of the cycle. Figure 6-45 B) and E) are individual Lissajous figures taken at 93% span vs. 62% chord location, which corresponds to the shock recovery region as seen in Figure 6-42 C). In this region, a figure-eight shape forms due to the co ntinuous phase variation caused by the oscillatory behavior in the shock transition region. The figure-eight plot is not a harmonic, as is normally associated with figure-eights, but the result of th e phase changing sign; from a lead to a lag, or vice-versa. The shape of the figure-eight provides insight into phase/time lag. A fat top or bottom shows where Cp is lagging behind the motion; alte rnatively a narrow top or bottom indicates where the Cp is leading the motion, trying to catch up. The transition across the shock is indicated by the change in lift (i.e., the change in value of Cp shown by position of starting red circle). An increase in -Cp is ahead of shock, whereas decrease in -Cp is behind shock. The 3-D plot in C) provides more insight as to how the Cp varies with time, with an s-shape. Figure 6-45 C) and F) are individual Lissajous figures taken at 88% span vs. 62% chord location, which corresponds to the region ahead of the shock recovery region as seen in Figure 643 C). The shape of this Lissajous is nonlinear with a phase closer to 135. This is due to shock formation. The 3-D plot in F) exhibits a l oop feature in the first quarter of the cycle. Wavelet Analysis Wavelet analysis is applied to points of interest on the wing in Figure 6-46 Figure 6-47 and Figure 6-48 for the tip-launcher Grid8 8Hz pitch case, in order to gain further insight into the temporal nature of the results. In each set of figures, A) gives the time history of the Cp variation, 98

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B) shows the fast Fourier transform (FFT) of th e data, and C) illustrates the wavelet transform view of frequency vs. time. Figure 6-46 contains the 8Hz Grid8 results at 98% span vs. 45% chord and which corresponds to the primary shock formation region as seen in Figure 6-41 C). The time history plot in A) reveals a nearly, noi sy sinusoidal response with wider peaks than troughs in upper wing surface Cp. The FFT plot in B) shows a prominent p eak at the input frequency of 8Hz with smaller peaks occurring at harmonics, and assume s a periodic response. The wavelet plot in C) reveals the primary energy concentrations at 8H z with higher frequency energy concentrations on the upstroke and downstroke of the cycle. Th e wavelet also verifies a periodic response predicted by the FFT. Figure 6-47 contains the 8Hz Grid8 results at 93% span vs. 62% chord and which corresponds to the shock recovery region as seen in Figure 6-42 C). The time history plot in A) reveals a saw-tooth shaped response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at the input fr equency of 8Hz with smaller pe aks occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals non-pe riodic features that are not seen in the FFT, such as higher frequency energy concentrations on the end of the cycle occurring when the Cp drops dramatically, such as at time=0.25 sec and 0.38 sec. These are nonsymmetric responses compared to the times when the Cp is building at time=0.17, 0.3, and 0.43 sec. Figure 6-48 contains the 8Hz Grid8 results at 88% span vs. 62% chord and which corresponds to the region ahead of the shock recove ry region as seen in Figure 6-43 C). The time history plot in A) reveals a wide peak vs. sharp trough response in upper wing surface Cp. The FFT plot in B) shows a prominent peak at th e input frequency of 8H z with smaller peaks 99

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occurring at harmonics, and assumes a periodic response. The wavelet plot in C) reveals nonperiodic features that are not seen in the FFT. The blue region at time=0.21 sec corresponds to the wide peak region and consists of a range of fr equencies, whereas the green region at time=0.3 sec corresponds to the narrow trough region a nd consists of one, clear frequency. Wing-Only Pitch Oscillations Flow Visualization In order to examine the effect of the fuselage the next step in the FSR approach is to perform forced, rigid body pitch oscillation for a refined F-16 wing-only Wing1 with LE edge antenna and tip launcher. Motion is prescribed for 8Hz.5 rigid-body pitch oscillation at the same flow conditions ( i=1.34, Mach=0.9, altitude=5k feet) with the same turbulence model (DDES-SARC) as the tip-launcher aircra ft Grid8 for direct comparison. Figure 6-49 and Figure 6-50 illustrate images visualizing the flow computed on the left wing (looking aft-forward) at the upward stroke (between pitch angles of 135 and 180) of the 8Hz .5 sinusoidal pitching cycle. These imag es depict the instantaneous Mach = 1 boundary ( Figure 6-49 ) and vorticity magnitude=50 ( Figure 6-50 ) iso-surfaces with the aircraft surface colored by pressure. The AOA is shown as a func tion of time in the upper half in each set of images. Additionally, BL159 is indicated along th e LE of each of the images for reference purposes. The left set of images in display the Wing1 wing-only case results for the upper surface in A) and lower surface in B), and the Gr id8 aircraft comparisons are presented on the right for the upper surface in C) and lower surface in D). In Figure 6-49 A), it is seen that the Mach=1 boundary iso-surface is much larger for the wing-only case than for the aircraft case in C) The small secondary shock aft of the primary shock near the tip launcher due to the tip launcher notch is still se en but it is smaller than it is with the aircraft in C). The most interesting difference between the wing-only and aircraft cases 100

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is that shock separation aft of the shock on the in board portion of the wing is not seen. This is due to the absence of the oscillati ng strake vortex. Therefore, it wi ll be highly interesting to see in future bending, torsion, and complex LCO mo tion analysis what role the strake vortex will play. In realistic LCO motions, there is negligible pitching of the fuselage, with most of the motion isolated to the outboard portion of the wi ng. Therefore, there will be no oscillation in the strake vortex. Upon animation of the tip-launcher case in Figure 6-49 C) and D), it is revealed that as the aircraft pitches nose-down, the Mach=1 isosurface is inhibited from wrapping around the wingtip at the LE by the tip launcher. It wraps ar ound the tip launcher at about one-half the way down the tip, and extends along the LE along the lower surface, attaching to the base of the LE antenna. Animating Figure 6-49 A) and B), the wing-only case reveal s that as the aircraft pitches nose-down, the Mach=1 iso-surface is not inhibi ted by the presence of the tip launcher from wrapping around the wingtip due to the increase in size of the iso-surface. This shock wraps around the tip extending about one-half the length of the wing. The iso-surface then wraps around the bottom surface of the wing at the LE, but is much smaller than the aircraft case and does not wrap around the bottom surface all the way to the base of the LE antenna. Additionally, it appears that the forward shock on the LE antenna does not attach to the shock on the LE edge of the wing as it does for the aircraft case. From animation of Figure 6-50 vortices are seen rotating along the tip launcher, corresponding to the pitching up and down of the aircraft. Rotation in the LE antenna vortex is also evidenced as the aircraft is pitching up and down. The tip vortex and LE antenna vortex share the same direction of rotation on the uppe r surface for both wing-only and aircraft cases; but are contra on the lower surface for the aircraft case and the same but with a small lag for the 101

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wing-only case. The LE antenna vortex diminishes on the upper surface as the aircraft pitches down and grows as it pitches up. Additionally, much lower pressures across the wing-only case are present due to the increased strength and si ze of the Mach=1 iso-surface. A more substantial amount of separation can be seen aft of the shock transition on the upper surface for the wingonly case when examining the vortic ity magnitude iso-surface in Figure 6-50 A) and C). This may be strong evidence of shock-induced separation. Additionally, this type of flow feature may play an important role in the LCO mechanism. Figure 6-51 shows the instantaneous Cp measurements plotted against non-dimensional chord taken at 89% span (BL159) for the one de veloped cycle of oscillation. Results for the wing-only case are shown in A) upper surface, and B) lower surface; and the aircraft comparison results are illustrated in C) upper surface and D) lower surface. Each numbered line (1-9) corresponds to the time-accurate oscillation cy cle angle, in degrees, during the sinusoidal pitching cycle, indicated by the corresponding cycl e angle color given in the legend in the upper right-hand corner. In Figure 6-51 it is seen that the Cp on both the upper and lower surface overlap for 0 and 360 cycle angles, but do not for 180. One would e xpect, from a quasi-static perspective, that the coefficients would be the same for all of these cycle angles since they are at the same absolute AOA. Upon comparison of the wing-only case and the aircraft case, the same cycle angles pairing are evident, indicating the same inability of the flow-field to keep up with the motion of the structure, indicating a lag in the flow The same suction loss feature is apparent for cycle angles 225, 270, and 315, corresponding to the ascension, peak, and descension of the positive peak of the pitch oscillation in the 65-75% chord region on the upper surface. However, 102

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on the upper surface, a much larger shock characte r in the 60-70% chord region is evident for the tip-launcher case. However, there is not mu ch of a shift in the shock location. Upon examining Figure 6-51 and animating the Cp for all iterations on the upper surface, a rapid suction build-up with increasing AOA is revealed at the 50-70% chord location. As AOA decreases, there is a rapid loss of suction which progresses from the aft portion of the wing forward. The motion of this lo ss resembles that of a double hinge d door slamming shut; the first near 70% chord and the second near 60% chord. This is an indicat ion of the hysteresis behavior in the shock structure. The character of this motion is the same at this particular BL location for both cases, with the magnitudes of the overall Cp for the wing-only case larger for the upper surface and smaller for the lower surface. Looki ng at inboard BL locations in the shock separation region for the aircra ft case and comparing the Cp at the same location for the wingonly, the same oscillatory behavior is not evident in the shock attributed to the separation. For the future purposes of this FSR work using prescribed motion, the lack of inboard shock separation should not be a problem when consider ing the flow at the outboard locations of the wing, such as BL159. However, when the time comes to examine LCO with a coupled, FSI code, modeling of the entire aircraft may be necessary to determine the importance of the presence of the strake vortex. Lissajous Analysis Figure 6-52 shows the set of Lissajous plots (-Cp vs. local displacement from the upper surface of the airfoil at various chord vs. span locations) for one cycle of rolling 8 Hz .5 oscillation. A low pass filter is applied to th e data at 100 Hz to filter out the noise due to turbulence effects. The top of the figure is the ti p launcher, the bottom the wing root; and the left side is the LE and the right side the TE of the wi ng. The red circles indica te the starting point of the roll cycle, and the black arrows indicate the direction of rotation of the Lissajous. 103

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The overall trends of the Lissajous figures ar e similar for the wing-only Wing1 and aircraft Grid8 pitch cases. In the lower le ft-hand potion of the plot, there is a 0 to 45 phase shift with counter-clockwise rotation. The phase suddenly shifts to 180, essentially mapping out the pitch axis. There is also a corresponding phase shift on the tip launcher (L AU) at the 13% chord location indicative of the pitch ax is. It is interesting to note that the Lissajous along the tip launchers is 180 out of phase from the 8-38% ch ord region. This may be attributed to the increased strength of the shock and, therefore, more wrapping of the shock around the wing-tip. The phase then shifts to 180 with clockwise rotation, and begins to open up aft along the wing with 90 phase shift along the inboard, TE portion of the wing. The phase maintains a 180 phase shift near and along the ti p aft of 48% chord. A transition from clockwise to counter-clockwise rotation is apparent in the 78% chord region at the root and extending back to the 68% c hord region near the tip. This shift in rotational direction can be attributed to the shock transi tion. There are also a few regions on the wing, mostly near the tip launcher and shock transition, where the Lissajous plots form a figure-eight shape, indicating a continuous phase variation within 1 cycle. Overall, the Lissajous figures for both pitch oscillation cases differ most signific antly along the forward portion of the tip launcher and in the shock transition region. 104

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105 Figure 6-1. F-16 wing planform with Spanwise (BL) tap locations i ndicated by green lines. Figure 6-2. Roll oscillation angle vs. time w ith numbers 1-9 indicat ing the instantaneous measurements taken during the oscillatory cycle.

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C A D B Figure 6-3. DDES of F-16 in sinusoidal rolling motion with instanta neous Mach=1 boundary iso-surface colored by pressure contour for clean-wing Grid0: A) & B) 1Hz case and C) & D) 8Hz case. 106

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A C D B Figure 6-4. DDES of F-16 in sinusoidal rolling motion with instantaneous vorticity magnitude iso-surface colored by pressure contour for clean-wing Grid0: A) & B) 1Hz case and C) & D) 8Hz case. 107

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Cp (Non-dimensional) A Non-dimensional Chord Location (x/c) C Non-dimensional Chord Location (x/c) Cp (Non-dimensional) D B Figure 6-5. Instantaneous Cp measurements on F-16 Grid0 clean -wing configurations at 93% span for: 1Hz .0 roll A) Upper and B) Lower and 8Hz .5 roll C) Upper and D) Lower surfaces; with lines 1-9 corresponding to roll angle (). 108

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Cp (Non-dimensional) A Non-dimensional Chord Location (x/c) C Non-dimensional Chord Location (x/c) Cp (Non-dimensional) D B Figure 6-6. Instantaneous Cp measurements on F-16 Grid0 clean -wing configurations at 88% span for: 1Hz .0 roll A) Upper and B) Lower and 8Hz .5 Roll C) Upper and D) Lower surfaces; with lines 1-9 corresponding to roll angle (). 109

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Figure 6-7. Lissajous plots of upper surface Cp vs. local displacement during 1Hz roll oscillation for clean-wing Grid0. 110

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C A -Cp time time Local Vertical Displacement -Cp (Non-dimensional) -Cp (Non-dimensional) Disp -Cp Disp Figure 6-8. 2-D (left column) and 3-D (right column) Lissajous for Grid0 clean-wing 1Hz roll oscillation at: A) & C) 93% span vs. 64% chord and B) & D) 88% span vs. 81% chord. Local Vertical Dis p lacementD B 111

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Figure 6-9. Lissajous plots of upper surface Cp vs. local displacement during 8Hz roll oscillation for clean-wing Grid0. 112

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113 -Cp (Non-dimensional) Time (sec) -Cp Disp Local Vertical Dis p lacementC A -Cp (Non-dimensional) Time (sec) -Cp Disp B D Figure 6-10. 2-D (left column) and 3-D (right column) Lissajous for clean-wing Grid0 8Hz roll oscillation at: A) & C) 93% span vs. 65% chord and B) & D) 88% span vs. 69% chord. Local Vertical Displacement

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Figure 6-11. Temporal analysis of upper surface Cp for Grid0 8Hz roll oscillation at 93% span vs. 65% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) C 114

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) C Time (sec) Figure 6-12. Temporal analysis of upper surface Cp for Grid0 8Hz roll oscillation at 88% span vs. 69% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. 115

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C A D B Figure 6-13. DDES-SARC of F-16 in sinusoidal 8H z rolling motion with instantaneous Mach=1 boundary iso-surface colored by pressure cont our for: A) & B) Grid4 tip-launcher case and C) & D) Grid0 clean-wing case. 116

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C A D B Figure 6-14. DDES-SARC of F-16 in sinusoidal 8H z rolling motion with in stantaneous vorticity magnitude iso-surface colored by pressure contour for: A) & B) Grid4 tip-launcher case and C) & D) clean-wing case. 117

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) C A Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) Figure 6-15. Instantaneous Cp measurements on F-16 wing at 98% span for 8Hz roll for Grid4 tip-Launcher case A) Upper and B) Lower and Grid0 clean-wing case C) Upper and D) Lower surfaces; with lines 19 corresponding to roll angle (). D B 118

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) C Non-dimensional Chord Location (x/c) A Cp (Non-dimensional) D Non-dimensional Chord Location (x/c) B Non-dimensional Chord Location (x/c) Figure 6-16. Instantaneous Cp measurements on F-16 wing at 93% span for 8Hz roll for Grid4 tip-Launcher case A) Upper and B) Lower and Grid0 clean-wing case C) Upper and D) Lower surfaces; with lines 19 corresponding to roll angle (). 119

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) C Non-dimensional Chord Location (x/c) A Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Figure 6-17. Instantaneous Cp measurements on F-16 wing at 88% span for 8Hz roll for Grid4 tip-Launcher case A) Upper and B) Lower and Grid0 clean-wing case C) Upper and D) Lower surfaces; with lines 19 corresponding to roll angle (). B Non-dimensional Chord Location (x/c) D 120

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Figure 6-18. Lissajous plots of upper surface Cp vs. local displacement during 8Hz roll oscillation for tip-launcher Grid4. 121

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-Cp (Non-dimensional) Time (sec) -Cp Disp Local Vertical Dis p lacementD A -Cp (Non-dimensional) Time (sec) -Cp Disp E B Local Vertical Displacement -Cp (Non-dimensional) Time (sec) -Cp Disp C F Figure 6-19. 2-D (left column) and 3-D (right co lumn) Lissajous for Grid4 tip-launcher 8Hz roll oscillation case at: A) & D) 98% span vs. 44% chord, B) & E) 93% span vs. 67% chord, and C) & F) 88% span vs. 70% chord. Local Vertical Displacement 122

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123 -Cp (Non-dimensional) Ma g nitude Fre q uenc y ( Hz ) A Time ( sec ) Frequency (Hz) B Time (sec) Figure 6-20. Temporal analysis of upper surface Cp for Grid4 8Hz roll oscillation at 98% span vs. 44% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot.C

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Figure 6-21. Temporal analysis of upper surface Cp for Grid4 8Hz roll oscillation at 93% span vs. 67% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot.A Ti m e ( sec ) Frequency (Hz) B Time (sec) -Cp (Non-dimensional) C Ma g nitude Fre q uenc y ( Hz ) 124

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A Figure 6-22. Temporal analysis of upper surface Cp for Grid4 8Hz roll oscillation at 88% span vs. 70% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. B Time (sec) Frequency (Hz) C 125

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126 1 2 3 4 5 6 7 8 9 Figure 6-23. Pitch oscillation angle vs. time w ith numbers 1-9 indicating the instantaneous measurements taken during the oscillatory cycle.

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A D C B Figure 6-24. DDES-SARC of F-16 in sinusoidal pitching motion with instantaneous Mach=1 boundary iso-surface colored by pressure for clean-wing cases: A) & B) Grid0 1 Hz .0 case and C) & D) Grid9 8 Hz .5 case. 127

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A D C B Figure 6-25. DDES-SARC of F-16 in sinusoidal pitching motion with instantaneous vorticity magnitude iso-surface colored by pressure fo r clean-wing cases: A) & B) Grid0 1 Hz .0 case and C) & D) Grid9 8 Hz .5 case. 128

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) A Non-dimensional Chord Location (x/c) C Cp (Non-dimensional) B Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) Figure 6-26. Instantaneous Cp measurements on F-16 wing at 98% span for Grid0 clean-wing 1Hz .0 pitch A) Upper and B) Lower and Grid9 8Hz .5 pitch C) Upper and D) Lower surfaces; where Lines 1-9 correspond to cycle angle (). D 129

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) A Non-dimensional Chord Location (x/c) C Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) B D Figure 6-27. Instantaneous Cp measurements on F-16 wing at 93% span for Grid0 clean-wing 1Hz .0 pitch A) Upper and B) Lower and Grid9 8Hz .5 pitch C) Upper and D) Lower surfaces; where Lines 1-9 correspond to cycle angle (). 130

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) C A Cp (Non-dimensional) Figure 6-28. Instantaneous Cp measurements on F-16 wing at 88% span for Grid0 clean-wing 1Hz .0 pitch A) Upper and B) Lower and Grid9 8Hz .5 pitch C) Upper and D) Lower surfaces; where Lines 1-9 correspond to cycle angle (). D Non-dimensional Chord Location (x/c) B Non-dimensional Chord Location (x/c) 131

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Figure 6-29. Lissajous plots of upper surface Cp vs. local displacement during 1Hz pitch oscillation for clean-wing Grid0. 132

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A -Cp (Non-dimensional) -Cp (Non-dimensional) Time (sec) -Cp Disp Local Vertical Dis p lacementD E F Time (sec) Time (sec) -Cp Disp B Local Vertical Displacement -Cp (Non-dimensional) -Cp Disp C Figure 6-30. 2-D (left column) and 3-D (right column) Lissajous for Grid0 clean-wing 1Hz pitch oscillation case at: A) & D) 93% span vs. 67% chord, B) & E) 88% span vs. 72% chord, and C) & F) 88% span vs. 81% chord. Local Vertical Displacement 133

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Figure 6-31. Lissajous plots of upper surface Cp vs. local displacement during 8Hz pitch oscillation for clean-wing Grid9. 134

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-Cp (Non-dimensional) Time (sec) -Cp Disp Local Vertical Dis p lacementD A -Cp (Non-dimensional) Time (sec) -Cp Disp E B Local Vertical Displacement -Cp (Non-dimensional) Time (sec) -Cp Disp C F Figure 6-32. 2-D (left column) and 3-D (right column) Lissajous for Grid9 clean-wing 8Hz pitch oscillation case at: A) & D) 98% span vs. 54% chord, B) & E) 93% span vs. 58% chord, and C) & F) 88% span vs. 58% chord. Local Vertical Displacement 135

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136 -Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Time (sec) C Figure 6-33. Temporal analysis of upper surface Cp for Grid0 1Hz pitch oscillation at 93% span vs. 67% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot.

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Figure 6-34. Temporal analysis of upper surface Cp for Grid0 1Hz pitch oscillation at 88% span vs. 72% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) C 137

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-Cp (Non-dimensional) Ma g nitude A Time ( sec ) Frequency (Hz) Fre q uenc y ( Hz ) B Figure 6-35. Temporal analysis of upper surface Cp for Grid0 1Hz pitch oscillation at 88% span vs. 81% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot.C Time (sec) 138

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Figure 6-36. Temporal analysis of upper surface Cp for Grid9 8Hz pitch oscillation at 98% span vs. 54% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) C 139

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Time (sec) Figure 6-37. Temporal analysis of upper surface Cp for Grid9 8Hz pitch oscillation at 93% span vs. 58% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot.C 140

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) C Figure 6-38. Temporal analysis of upper surface Cp for Grid9 8Hz pitch oscillation at 88% span vs. 58% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) 141

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A D C B Figure 6-39. DDES of F-16 in 8Hz sinusoidal pitching motion with instantaneous Mach=1 boundary iso-surface colored by pressure for: Grid8 tip-launcher case A) Upper & B) Lower surfaces and Grid9 clean-wing case C) Upper & D) Lower surfaces. 142

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C A B D Figure 6-40. DDES of F-16 in 8Hz sinusoidal pitching motion with instantaneous vorticity magnitude iso-surface colored by pressure fo r: Grid8 tip-launcher case A) upper & B) lower surfaces and Grid9 clean-wing case C) upper & D) lower surfaces. 143

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) C Non-dimensional Chord Location (x/c) A Cp (Non-dimensional) D Non-dimensional Chord Location (x/c) B Non-dimensional Chord Location (x/c) Figure 6-41. Instantaneous Cp Measurements on F-16 wing at 98% span for 8Hz pitch Grid8 tiplauncher case A) Upper and B) Lower and Grid9 clean-wing case C) Upper and D) Lower surfaces; where lines 1-9 correspond to cycle angle (). 144

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) A C Cp (Non-dimensional) D Non-dimensional Chord Location (x/c) B Non-dimensional Chord Location (x/c) Figure 6-42. Instantaneous Cp Measurements on F-16 wing at 93% span for 8Hz pitch Grid8 tiplauncher case A) Upper and B) Lower and Grid9 clean-wing case C) Upper and D) Lower surfaces; where lines 1-9 correspond to cycle angle (). 145

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Cp (Non-dimensional) Cp (Non-dimensional) Non-dimensional Chord Location (x/c) Non-dimensional Chord Location (x/c) A C Figure 6-43. Instantaneous Cp Measurements on F-16 wing at 88% span for 8Hz pitch Grid8 tiplauncher case A) Upper and B) Lower and Grid9 clean-wing case C) Upper and D) Lower surfaces; where lines 1-9 correspond to cycle angle (). D Non-dimensional Chord Location (x/c) B Non-dimensional Chord Location (x/c) 146

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Figure 6-44. Lissajous plots of upper surface Cp vs. local displacement during 8Hz pitch oscillation for tip-launcher Grid8. 147

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-Cp (Non-dimensional) Time (sec) -Cp Disp Local Vertical Dis p lacementD A B -Cp (Non-dimensional) -Cp (Non-dimensional) E Time (sec) Time (sec) -Cp -Cp Disp Local Vertical Displacement Disp C F Figure 6-45. 2-D (left column) and 3-D (right column) Lissajous for Grid8 tip-launcher 8Hz pitch oscillation case at: A) & D) 98% span vs. 45% chord, B) & E) 93% span vs. 62% chord, and C) & F) 88% span vs. 62% chord. Local Vertical Displacement 148

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149 -Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Figure 6-46. Temporal analysis of upper surface Cp for Grid8 8Hz pitch oscillation at 98% span vs. 45% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) C

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) Figure 6-47. Temporal analysis of upper surface Cp for Grid8 8Hz pitch oscillation at 93% span vs. 62% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) C 150

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-Cp (Non-dimensional) Ma g nitude Time ( sec ) Fre q uenc y ( Hz ) A B Frequency (Hz) C Figure 6-48. Temporal analysis of upper surface Cp for Grid8 8Hz pitch oscillation at 88% span vs. 62% chord. A) Time history. B) Fast Fourier transform. C) Wavelet frequency vs. time plot. Time (sec) 151

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C A D B Figure 6-49. DDES-SARC of F-16 colored by pre ssure in 8Hz sinusoidal pitching motion with instantaneous Mach=1 boundary iso-surface for Wing1 (no fuselage) A) Upper and B) Lower surfaces; and Grid8 half-aircr aft C) Upper and D) Lower surfaces. 152

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C A D B Figure 6-50. DDES-SARC of F-16 colored by pre ssure in 8Hz sinusoidal pitching motion with instantaneous vorticity magnitude iso-su rface for Wing1 (no fuselage) A) Upper and B) Lower surfaces; and Grid8 half-aircr aft C) Upper and D) Lower surfaces. 153

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Cp (Non-dimensional) Non-dimensional Chord Location (x/c) C Non-dimensional Chord Location (x/c) A Cp (Non-dimensional) D Non-dimensional Chord Location (x/c) B Non-dimensional Chord Location (x/c) Figure 6-51. Instantaneous Cp measurements at 88% span for 8Hz pitch: Wing1 (no fuselage) A) Upper and B) Lower surfaces; and Grid8 half-aircraft C) Upper and D) Lower surfaces; where lines 1-9 correspond to cycle angle (). 154

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155 Figure 6-52. Lissajous plots of upper surface Cp vs. local displacement at % span vs. % chord locations during 8Hz pitch oscilla tion for Wing1 (no fuselage).

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CHAPTER 7 IMPLEMENTATION Tool Usage and Interpretation The Lissajous figures provide key insight in to the highly non-sinus oidal tracking of the surface pressure coefficient, Cp, with respect to aircraft motion. Once a Lissajous of interest is identified in the localized sense, the Lissajous analysis procedure can be applied to the entire region in order to discover the same feature in other areas. For example, in order to identify the shock oscillation transition on a nother portion of the wing, Lissa jous is applied to the wing plotting all Cp vs. a single reference Cp. Areas where these two signals are in phase indicates the same phenomena is occurring. Therefore, once a known limit cycle oscillation (LCO) configuration is analyzed and compared to a known non-LCO configuration, comparisons can determine where the LCO indicative phase relati onship occurs on the wing and what it looks like. This information can be used to analy ze unknown configurations and determine whether LCO will occur. Wavelet analysis is a key component in identifying the localized frequency differences at any point in time. A single LCO mechanism cannot be simply represented by a single periodic response at one frequency. For example, an 8Hz LCO mode may be the combination of a 20Hz and a 6Hz localized response. Similarly to the Li ssajous analysis, once a wavelet of interest is identified from a known LCO configuration, th e same analysis method can be applied to a known non-LCO configuration. Comparisons can de termine where the LCO indicative frequency combination occurs on the wing and what it looks like. This information can be used to analyze unknown configurations and determ ine whether LCO will occur. 156

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157 Impact on Future Design of Aircraft and Stores The prediction of LCO behavior of fighter ai rcraft is critical to mission safety and effectiveness, and the accurate determination of LCO onset speed and amplitude often requires flight test verification of linea r flutter models. The increasing stores certification demands for new stores and configurations, and the associated flight test costs, necessitate the development of tools to enhance computation of LCO thr ough modeling of the aerodynamic and structural sources of LCO nonlinearities. Once the state of fl uid-structure interaction (FSI) codes advances, the temporal analysis techniques applied in this dissertation, namely the Lissajous and wavelet plots, can be applied in order to identify LCO conditions and design new stores such that they avoid an LCO condition. These methods can also be applied when develo ping new store-carrying fighter aircraft such as the F-35. Many of th e unexpected problems encountered by the F-16 (also the F-15 and F-18) can be avoided altogether fo r this new aircraft, dr astically reducing the required number of flight tests, associated cost s, and the risks encountered by the pilots flying the aircraft in such dangerous conditions.

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CHAPTER 8 CONCLUSIONS AND OBSERVATIONS Summary Unsteady fluid-structure reaction (FSR) comput ational fluid dynamics (CFD) solutions of a viscous, rigid, full-scale F-16 are computed a nd analyzed for prescribed rigid-body pitch and roll oscillations for tip-launcher, clean-wing, and wing-only cases, simulating the torsional and bending nature of limit cycle osci llation (LCO) mechanisms, respec tively. There are a number of interesting features seen in the flow upon examining the surf ace pressure coefficient, Cp, Mach=1 iso-surface, vorticity magnitude iso-surf ace, Lissajous, and wavelet plots for 1Hz 2.0 and 8Hz 0.5 pitch and roll oscillations. Significant shock-induced separation and tip and strake (aircraft cases) vortices are observed for all motion cas es. Lagging trends relative to aircraft/wing motion are exhibited for all cases when animating the vorticity magnitude, Mach=1 boundary, and surface Cp; and when examining the Lissajous plots of -Cp vs. local displacement and associated wavelet transform plots. The F-16 aircraft roll cases indicate that the presence of the tip launcher has a significant effect on the strength and location of the shoc k on the upper surface of the wing. Additionally, the strake vortices maintained a relatively constant posit ion and magnitude throughout the oscillatory cycle. The tip vortices also exhibited a lag in their growth with respect to the aircraft motion. F-16 aircraft pitch cases exhibit signif icant inboard shock separation. The presence of the tip launcher during the pitch oscillation lim its the amount of inboard separation seen; and again shows strengthening and relocation of the shock on the wing. The strake vortices demonstrate a much more active oscillatory natu re during pitch oscillat ion, and it is believed they are a factor in the inboard shock separation. It is seen in the pitch cases that the vortices motion also lags behind that of the aircraft. 158

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The size of the Mach=1 iso-surface is larger for the F-16 wing-only pitch case with tip launchers since it is not bounded by the fuselage. However, the overall oscillatory behavior and location of the shock are very similar to the ai rcraft case with tip launc hers. There is also no evidence of inboard shock separation. The lack of inboard shock sepa ration for the wing-only case reveals the influence of the st rake vortices. It will be highly interesting to see in future bending, torsion, and complex LCO motion analysis what role the strake vortex will play. In realistic LCO motions, there is negligible pitching of the fuselage, with most of the motion isolated to the outboard portion of the wing. Therefore, there will be no oscillation in the strake vortex. However, separation is seen aft of the shock transition on the upper surface for this and all other cases when examining the vorticity magnitude iso-surfaces. This may be strong evidence of shock-induced separation. This type of flow feature may play an important role in the LCO mechanism. Overall, with the addition of the tip launc her, leading edge (LE) antenna, and grid refinement, alterations are to be expected in th e flow-field in the tip-launcher, LE antenna, and refined regions. However, upon examining the unsteady Cp on the wing, it is surprising to see a significant influence on the part of the LE antenna. Based on this noteworthy effect from a small component, small aerodynamic differences between stores can cause substa ntial changes in the flow-field, possibly influencing the occurrence of LCO. This ma y explain why nearly identical configurations have different LC O flight test results which are not predicted by classical flutter analyses. It is expected that the addition of pylons, launchers, and stores will add further complexity and insight into the contribution of these components on the LCO mechanism. However, it is known from flight testing experien ce that the LE antenna is not a driving force behind the LCO mechanism. 159

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The Lissajous figures provide key insight into the highly non-sinusoi dal tracking of the Cp with respect to aircraft motion. Additionally, the wavelet analysis is a key component in identifying the localized frequency differences at any point in time. Temporal analysis techniques such as these are vi tal at uncovering the non-periodic behavior in the response. Once the state of FSI codes is capable of accurately modeling a true LCO mechanism, these techniques will be crucial in identifying the underlyi ng physics that would be otherwise missed by frequency-domain-based techniques that are currently relied upon. The work presented here supports additional FSR study into realistic, transonic aeroelastic motions such as prescribed bending, torsion, and complex (LCO) motion, as well as the addition of pylons, launchers, and stores. As these complex ities are added, the flow-field features should develop and interact differently, leading to varying pressure di stributions, shock locations and strengths, and vortical structures on the wing; and resulting in added time and flow inertia lags. Features such as these could be pa rticipating in the LCO mechanism. Future Research Direction Increasingly more complex conf igurations will be analyzed in order to acquire more knowledge as to how and which flow-field charact eristics may be contribu ting to the occurrence of transonic LCO. Deformation of the wingtip in bending, torsion, and combined bending/torsion motions (effectively simulating the LCO mechanism), respectively, is next on the agenda. Through this build-up approach, understanding is hoped to be gleaned of how small configuration changes to the aircraft, such as adding pylons/launchers/stores, influence the characteristics of the flow-field during transoni c LCO conditions; and ultimately how these flowfield characteristics may influen ce on the LCO mechanism. Other parameters, such as the Mach number and altitude, will then be varied in order to capture more diverse LCO conditions. Temporal analysis techniques such as the Lissaj ous and wavelet transforms will be applied to 160

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161 these cases in order to identify the underlying nature of the LCO mechanism. Ultimately, fluidstructure interaction (FSI) codes will be needed for predictive LCO capability. For the purpose of further validation, once th e store/pylon/launcher grids are generated, direct comparison of steady surface pressures to those of Elbers118 and Sellers119 wind tunnel results will be conducted, as well as unstea dy surface pressures to those of Cunninghams68 rigid body wind tunnel pitch oscillation results.

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LIST OF REFERENCES 1. Bunton, R. W., and Denegri, C. M., Limit Cy cle Oscillation Characteristics of Fighter Aircraft, Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 916-918. 2. Pasiliao, C. L., and Dubben, J. A., Analysis of CFD Pressure Coefficients on the F-16 Wing Associated with Limit Cycle Oscill ations, AIAA Paper 2008-0409, January 2008. 3. Pasiliao, C. L., and Dubben, J. A., Determi nation of Flow Field Ch aracteristics of F-16 Wing Associated with Limit Cycle Oscillations Using CFD, Proceedings of the NATO RTO Symposium AVT-152 on Limit-Cycle Oscillations and other Amplitude-Limited, Self-Excited Vibrations Norway, May 2008. 4. Pasiliao, C. L., and Dubben, J. A., CFD Ba sed Determination of Transonic Flow Field Characteristics of F-16 Wing Associated with LCO, AIAA-2009-1084, January 2009. 5. Pasiliao, C. L., and Dubben, J. A., Transient Analysis of Transonic Flow Field Characteristics of F-16 Wing Associated with LCO, Abstract Accepted to Proceedings of the IFASD Conference Seattle, WA, June 2009. 6. Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., Aeroelasticity Mineola, NY: Dover Publications, Inc., 1955. 7. Denegri, C. M., Jr., and Cutchins, M. A., Eva luation of Classical Flutter Analysis for the Prediction of Limit Cycle Oscillatio ns, AIAA Paper 1997-1021, April 1997. 8. Denegri, C. M., Jr., Fundamentals of Fl utter Engineering, Air Force SEEK EAGLE Office Training Materials, Eglin AFB, FL, June 2003. 9. Hassig, H. J., An Approximate True Damping Solution of the Flutter Equation by Determinant Iteration, AIAA Journal of Aircraft Vol. 3, No. 11, 1971, pp. 885-889. 10. Ward, D. T., and Strganac, T. W., Introduction to Flight Test Engineering 2nd Ed., Dubuque, IA: Kendall/Hunt Company, 2001, pp. 218-250. 11. Norton, W. J., Limit Cycle Oscilla tion and Flight Flutter Testing, 21st Annual Symposium Proceedings Society of Flight Test Engin eers, Lancaster, CA, 1990, pp. 3.41.4-12. 12. Denegri, C. M., Jr., Limit Cycle Oscillati on Flight Test Results of a Fighter with External Stores, Journal of Aircraft Vol. 37, No. 5, 2000, pp. 761-769. 13. Denegri, C. M., Jr., Limit Cycle Oscillati on Flight Test Results of a Fighter with External Stores, AIAA Paper 2000-1394, April 2000. 14. Dreyer, C. A., and Shoch, D. L., F-16 Flut ter Testing at Eglin Air Force Base, AIAA Paper 86-9819, April 1986. 162

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BIOGRAPHICAL SKETCH Crystal Lynn Pasiliao was born in Oklahom a in 1979. After graduating from Yukon High School, Crystal attended the University of Oklahoma receiving a Bachelor of Science in aerospace engineering in 2003. Crystal then bega n work at the Air Force SEEK EAGLE Office at Eglin AFB, Florida as a Flutter Engineer. It is here that she met and married her husband, Dr. Eduardo Pasiliao, Jr in 2006; resulting in the birth of thei r son, Markus, in 2007. Crystal continued her education at the University of Fl orida receiving a Master of Science in aerospace engineering in 2005. Upon obtaining her M.S., Crystal pursued a docto ral degree under the advisement of Dr. Richard Lind, Jr. Crystal's research involved the unde rstanding of Limit Cycle Oscillation (LCO) flow-field physics. She rece ived her Ph.D. in the spring of 2009. Upon graduation, Crystal continued her work at th e Air Force SEEK EAGLE Office at Eglin AFB, Florida pursuing her research in the field of aircraft LCO. 172