Active Load

Transcript

AIRCRAFT DESIGN WITH ACTIVE LOAD ALLEVIATION AND NATURAL LAMINAR FLOW A DISSERTATION SUBMITTED TO THE DEPARTMENT OF AERONAUTICS & ASTRONAUTICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Jia Xu March 2012 http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/hz528zb1688 © 2012 by Jia Xu. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Ilan Kroo, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Juan Alonso I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Antony Jameson Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract In this thesis we incorporate maneuver load alleviation (MLA), gust load alleviation (GLA), and natural laminar flow (NLF) into aircraft conceptual design. While existing conceptual design frameworks tend to reduce the impact of these technologies to empirical weight and drag corrections, the present work uses physics-based methods to capture the dynamic interplay among natural laminar flow and load alleviation. The results demonstrate that the simultaneous application of MLA and GLA can tilt the balance of the transonic Mach-sweep-thickness (MT) trade in favor of high aspect ratio, low-sweep natural laminar flow wings. A minimum cost turbulent aircraft designed concurrently with MLA and GLA control systems can achieve a significant 10% reduction in fuel burn and 3.4% reduction in cost relative to a baseline design without load control. The fuel and cost savings grow to 15% and 5% respectively when we introduce natural laminar flow into the design process. Sensitivity studies confirm that the control and actuator requirements of eective active load alleviation are consistent with the performance parameters of modern aircraft. Results also suggest that the combination of aggressive active load control and low-sweep NLF wing can be a viable alternative to a 3-D NLF wing design or complex active laminar flow control (LFC) schemes. Finally, the aeroservoelastic conceptual design framework developed in this thesis can serve as a platform for assessing future aircraft configurations and operational paradigms aimed at reducing aircraft fuel consumption and environmental impact. iv This dissertation is dedicated to my parents Sarah and Yan; and to my loving wife, Donna v Acknowledgments My deepest gratitude goes to my advisor, Professor Ilan Kroo, who has taught me by example to seek out interesting questions and pursue them with rigor, intensity and integrity. I shall miss the precious ah-ha moments in our conversations about research and aircraft design I would like to thank my committee members Professor Jameson and Professor Alonso. I shall miss my discussions with Professor Jameson on all things airplane. It was my honor and pleasure to be his course assistant in the well-loved Case Studies in Aircraft Design. Professor Alonso has always been there with incisive comments and timely encouragement. I am deeply grateful for the long discussions on both research and career paths. It is also entirely possible that I only learned aerodynamics by working with him on AA200B. I want to thank Dr. Steve Smith for serving on my oral committee and for his leadership and insights in the NASA NRA that ultimately led to this thesis. Professor David Freyberg responded enthusiastically to my last-minute request for an oral examination chair. I am grateful for his time and for his questions and perspectives in the examinations. I am deeply indebted to the members of the Aircraft Design Group. Most of all I thank Tristan Flanzer, Andrew Ning, Geo Bower and Emily Schwartz. The FYI team eort was a highlight of my years at Stanford. I am grateful and proud to have you all as friends. While we were cruelly robbed of our 30,000 e prize money, what I cherish in its place are the priceless adventures and laughters – I will always vi have Paris with my friends. I reserve a very special thanks to Tristan and Elyssa, for feeding me, for listening, and for being such awesome human beings. My best wishes for the two of you in all of life’s journeys. My experience at Stanford would be rendered incomplete – perhaps all too literally – without the words of wisdom and encouragement from Mathias Wintzer and Sara Smoot. I shall miss our long conversations. The same is true of former ADG members Peter Sturdza, Dev Rajnarayan and Brian Roth. And many thanks go to Alex Haas and Alex Stoll for the enlightening discussions. A special thanks Aero/Astro alum Prasun Bansal for his joviality, hospitality, and for his long, arduous journey across the Himalayas (by Boeing 777) to my wedding. I am indebted to the miracle workers in the Aero/Astro oce. I want to give a big thanks to Jay Subramanian and Robin Murphy for their patience with my consistent procrastinations on all matters paperwork and deadline. I thank Ralph Levine, the departmental manager, for his constant encouragements, and for lunch. I am grateful for the generous support from the National Science Foundation, the NASA Subsonic Fixed Wing Program and Airbus. I owe much to mentors and ad- vocates beyond Stanford: Professor Jewel Barlow at the University of Maryland, Professors P.K.Yeung, Jerry Seitzman and Carol Senf at Georgia Tech, and Professor Christopher Coker at the LSE. I am forever indebted to the Marshall Aid Commemo- ration Commission for the opportunity of a lifetime to study in the UK. Most importantly, none of this would have been possible without the unconditional love and tireless patience of my parents. My dream may have be an impossible one without their courage to start life anew in this once foreign land. And they, more than anyone else, have had to endure too many Christmases, thanksgivings and Chinese New Years without their son by their side. Finally, I could not have walked this far without the constant, enveloping love of my dear wife Donna. And the journey would be rendered meaningless without her. Thanks to Donna I live with the joy and anticipation of a soon-to-be father. Why vii built airplanes if not to see the faces of our loved ones that much faster; why travail in life if not to see the same people made happy and safe. Finally, it bears mention that this thesis would not be complete without Donna’s patience, encouragements, warm hugs, and her timely realization that the deadline for thesis submission is in fact in two weeks. viii Contents Abstract iv v Acknowledgments vi 1 Introduction 7 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Natural Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Maneuver Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Gust Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Design Framework 15 2.1 Aircraft Parameterization . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Mission Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3 Wing Design 20 3.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 High Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5 Inverse Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5.1 Pressure Distribution . . . . . . . . . . . . . . . . . . . . . . . 29 ix 3.5.2 Airfoil Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5.3 Boundary Layer Solution . . . . . . . . . . . . . . . . . . . . . 35 4 Active Load Alleviation 38 4.1 MLA and GLA Parameterization . . . . . . . . . . . . . . . . . . . . 38 4.2 Maneuver Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3 Gust Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3.1 GLA Parameterization . . . . . . . . . . . . . . . . . . . . . . 41 4.3.2 Gust Load Design Criteria . . . . . . . . . . . . . . . . . . . . 42 4.3.3 Gust Encounter Simulation . . . . . . . . . . . . . . . . . . . 46 4.3.4 Structural Dynamics . . . . . . . . . . . . . . . . . . . . . . . 47 5 Design Studies 54 5.1 Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.2 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.4 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.5 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6 Results 60 6.1 Turbulent Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1.1 Point Optimizations . . . . . . . . . . . . . . . . . . . . . . . 61 6.1.2 Mach Number Sweeps . . . . . . . . . . . . . . . . . . . . . . 68 6.2 Laminar Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.2.1 Point Optimizations . . . . . . . . . . . . . . . . . . . . . . . 70 6.2.2 Mach Number Sweeps . . . . . . . . . . . . . . . . . . . . . . 77 6.3 Turbulent and Laminar Comparison . . . . . . . . . . . . . . . . . . . 78 7 Sensitivity Studies 81 7.1 NLF Wing Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.2 MLA and GLA Control Surface Deflection . . . . . . . . . . . . . . . 85 7.3 GLA Control Surface Bandwidth . . . . . . . . . . . . . . . . . . . . 87 x 7.4 GLA with Only Ailerons . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.5 Lower Surface Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . 90 7.6 Gate Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 8 Conclusions and Future Work 98 A Airfoil Inverse Design 101 B Numerical Solution of Second-Order ODEs 105 C Cost Model 107 C.1 Direct Operating Cost . . . . . . . . . . . . . . . . . . . . . . . . . . 108 C.1.1 Fuel Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 C.1.2 Pilot Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 C.1.3 Depreciation and Insurance Costs . . . . . . . . . . . . . . . . 109 C.1.4 Maintenance Cost . . . . . . . . . . . . . . . . . . . . . . . . . 110 C.2 Indirect Operating Cost . . . . . . . . . . . . . . . . . . . . . . . . . 111 Bibliography 113 xi List of Tables 2.1 Engine parameters for the PW-2037 (reference engine deck) and CFM- 56-7B27 turbofans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.1 Key cost assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2 Summary of all optimization variables. . . . . . . . . . . . . . . . . . 57 5.3 Summary of all optimization constraints. . . . . . . . . . . . . . . . . 59 6.1 Summary of optimized Mach 0.78 turbulent aircraft design parameters. 62 6.2 Summary of Mach 0.78 high sweep NLF aircraft parameters. . . . . . 72 xii List of Figures 1.1 The Boeing Sugar Volt – part of the NASA N+3 advanced subsonic transport study. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Representative airfoil geometries and C p distributions. . . . . . . . . . 10 1.3 A plot of NLF transition as a function of wing sweep based on the results of historical laminar flow experiments. 2 . . . . . . . . . . . . . 10 1.4 An illustration of typical compressibility drag rise trend as a function of streamwise t/c and wing sweep. . . . . . . . . . . . . . . . . . . . . 11 1.5 Lift distribution for conventional and MLA aircraft at the same ma- neuver load factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 The design mission profile and flight conditions. . . . . . . . . . . . . 18 3.1 The wing break sections that define the planform and twist. The innermost section (÷ = 0) corresponds to the wing root. The next section defines the wing-fuselage intersection. . . . . . . . . . . . . . . 21 3.2 The wing structure box configuration. . . . . . . . . . . . . . . . . . . 21 3.3 The parameterization of the wing box cross section. . . . . . . . . . . 22 3.4 An illustration of wing aerodynamic control points and C lmax constraints. 23 3.5 Section C lmax as a function of t/c and Mach number. The airfoil is in its clean configuration and the chord Reynolds number is fixed at 20 million. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.6 Section C lmax as a function of t/c and wing sweep in degrees. The airfoil is in its clean configuration and the chord Reynolds number is fixed at 20 million. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 xiii 3.7 Section C lmax as a function of the t/c and flap deflection in degrees. The Reynolds number is fixed at 20 million. . . . . . . . . . . . . . . 26 3.8 Wing static stress constraints. . . . . . . . . . . . . . . . . . . . . . . 27 3.9 The aileron reversal constraint placed on the outboard deflections ” 4 . 28 3.10 The wing breakpoints with inverse design sections highlighted. The blue sections can be designed for NLF while the red wing-fuselage inter- section is always assumed to be turbulent to account for the dominant role of attachment line instabilities. . . . . . . . . . . . . . . . . . . . 29 3.11 An illustration of the airfoil C p parameterization with important pres- sure features labeled. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.12 The inverse deisgn C p parametrization with the pressure variables la- beled in blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.13 Example wing section pressure distributions at selected spanwise loca- tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.14 Example wing section geometry at selected spanwise locations. . . . . 35 4.1 The wing control surfaces are defined by the wing break sections. . . 39 4.2 The wing static and dynamic stress design constraints are collocated with y-position of the aerodynamic control points. . . . . . . . . . . . 41 4.3 The 1–Cosine gust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4 Positive 1–Cosine vertical gust fields at dierent gust gradient lengths H. 44 4.5 Positive 1–Cosine vertical gust fields at dierent gust encounter alti- tudes z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.6 Aircraft dynamics through gust encounters. . . . . . . . . . . . . . . 47 4.7 Control surface deflection time history for each trailing edge channel. 48 4.8 Control deflection rate laminar MLA+GLA design. . . . . . . . . . . 48 4.9 Dynamic wing stresse constraints. . . . . . . . . . . . . . . . . . . . . 53 5.1 Examples of the high-sweep turbulent and low-sweep NLF aircraft families. The transition fronts are shown in green. . . . . . . . . . . . 55 xiv 6.1 The optimized Mach 0.78 turbulent aircraft with dierent levels of active load alleviation. . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.2 A comparison of the optimized turbulent aircraft. The performance metrics and configuration parameters are normalized against the corre- sponding values of the Mach 0.78 turbulent baseline. . . . . . . . . . 63 6.3 A comparison of the optimized turbulent wing planforms. All parame- ters are normalized by their values in the Mach 0.78 turbulent baseline. 65 6.4 Turbulent wing and skin thickness distributions. . . . . . . . . . . . . 65 6.5 Comparisons of the turbulent maneuver C l (solid lines) and C lmax (dashed lines) distributions. . . . . . . . . . . . . . . . . . . . . . . . 66 6.6 Maneuver and gust bending stresses for the optimized turbulent designs at Mach 0.78. The wing bending stresses ‡ are normalized by the allowable stress ‡ a . The gust stresses represent the maximum values encounter by each wing section at all gust gradient lengths. . . . . . . 67 6.7 A plot of the relative operating cost of optimized turbulent designs as functions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. . 69 6.8 A plot of the relative fuel burn of optimized turbulent designs as func- tions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. . 70 6.9 The optimized Mach 0.78 turbulent aircraft with dierent levels of active load alleviation. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.10 A comparison of the optimized laminar aircraft. The performance metrics and configuration parameters are normalized by those of the Mach 0.78 turbulent baseline. . . . . . . . . . . . . . . . . . . . . . . 72 6.11 A comparison of the optimized laminar wing planforms. All parameters are normalized by their values in the Mach 0.78 turbulent baseline. . 74 6.12 Laminar wing and skin thickness distributions. . . . . . . . . . . . . . 74 6.13 Laminar wing C l and C lmax distributions. . . . . . . . . . . . . . . . . 75 xv 6.14 Maneuver and gust bending stresses for the optimized laminar designs at Mach 0.78. The wing bending stresses ‡ are normalized by the allowable stress ‡ a . The gust stresses represent the maximum values encounter by each wing section at all gust gradient lengths. . . . . . . 76 6.15 A plot of the relative cost of optimized laminar designs as functions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. . . . . 77 6.16 A plot of the relative fuel burn of optimized laminar designs as functions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. . . . . 78 6.17 A comparison of the optimized MLA+GLA aircraft parameters. The displayed parameters are normalized by the value of the Mach 0.78 turbulent baseline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.18 Relative cost of turbulent and laminar designs as functions of Mach number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.19 Relative fuel burn of turbulent and laminar designs as functions of Mach number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.1 Optimized high-sweep NLF design at Mach 0.78. . . . . . . . . . . . . 82 7.2 Comparison of high-sweep laminar-25 aircraft. . . . . . . . . . . . . . 83 7.3 Comparison of high-sweep laminar-25 MLA+GLA aircraft. . . . . . . 84 7.4 Optimized aircraft cost as functions of Mach number. . . . . . . . . . 84 7.5 Optimized aircraft fuel burn as functions of Mach number. . . . . . . 85 7.6 Optimized MLA+GLA aircraft costs as functions of maximum load alleviation control surface deflections. . . . . . . . . . . . . . . . . . . 86 7.7 Optimized MLA+GLA aircraft fuel burns as functions of maximum load alleviation control surface deflections. . . . . . . . . . . . . . . . 86 7.8 MLA+GLA aircraft cost trends as functions of maximum allowable load alleviation control surface deflection rates. . . . . . . . . . . . . 87 7.9 MLA+GLA aircraft fuel burn trends as functions of maximum allowable load alleviation control surface deflection rates. . . . . . . . . . . . . 88 xvi 7.10 GLA using only outboard control surfaces. . . . . . . . . . . . . . . . 89 7.11 Laminar MLA+GLA aircraft cost trends with dierent GLA control allocations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.12 Laminar MLA+GLA aircraft fuel burn trends with dierent GLA con- trol allocations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.13 Comparison of the MLA+GLA aircraft designed with turbulent and laminar bottom surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.14 Comparison of the MLA+GLA aircraft designed with turbulent and laminar bottom surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.15 Cost trends for the Laminar MLA+GLA aircraft with turbulent and laminar bottom surfaces. The results of the Turbulent MLA+GLA are included for reference. . . . . . . . . . . . . . . . . . . . . . . . . . . 92 7.16 Duel burn trends for the Laminar MLA+GLA aircraft with turbulent and laminar bottom surfaces. The results of the Turbulent MLA+GLA are included for reference. . . . . . . . . . . . . . . . . . . . . . . . . 92 7.17 A comparison of gate-constrained aircraft.(b<120 ft) . . . . . . . . . 93 7.18 A comparison of the turbulent aircraft designed with and without gate constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 7.19 A comparison of the Turbulent MLA+GLA aircraft designed with and without gate constraints. . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.20 A comparison of the Laminar MLA+GLA aircraft designed with and without gate constraints. . . . . . . . . . . . . . . . . . . . . . . . . . 96 A.1 Example airfoil optimization geometry, C p and boundary layer momen- tum thickness results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.2 Optimized airfoil transition and C dp as a function of C l and Mach Œ . The section t/c and Re c are fixed at 9% and 20 million respectively. . 103 A.3 Optimized airfoil transition and drag as a function of t/c and Mach Œ . The C l and Re c are fixed at 0.4 and 20 million respectively. . . . . . . 104 A.4 Optimized airfoil transition and drag as a function of Re c and Mach Œ . The C l and t/c are fixed at 0.4 and 9% respectively. . . . . . . . . . . 104 xvii Nomenclature x aircraft Aircraft design variables x CG Vector of longitudinal center-of-gravity positions for all flight conditions x GLA GLA design variables x mission Mission variables x MLA MLA design variables x pressure Pressure design variables x transition Transition design variables x wing Wing design variables ¯ C Modal damping matrix ¯ K Modal stiness matrix ¯ M Modal mass matrix ¯ Q Orthonormal basis for modal decomposition C Global damping matrix K Global stiness matrix L Triangular Cholesky factorization matrix M e Element mass matrix M Global mass matrix u Generalized displacement dCp dx l Lower surface airfoil pressure gradient dCp dx u Upper surface airfoil pressure gradient D T Drag-to-thrust ratio Ÿ if Inflation index 1 2 ‹ Kinematic viscosity c Mean aerodynamic chord C p Canonical pressure coecient ˜ C p l Airfoil lower surface C p in sweep-taper system ˜ C p u Airfoil upper surface C p in sweep-taper system ˜ u l Airfoil lower surface velocity in sweep-taper system ˜ u u Airfoil upper surface velocity in sweep-taper system A Element cross section area AR Trapezoidal wing aspect ratio c a Airplane cost (excluding engines) c a The airplane cost c e Engine cost c ce engine material cost per flight hour c he engine material cost per flight cycle c tic Estimated ticket cost D a Depreciation period (years) E Young’s modulus F Generalized forces f Modal forcing F g Gust alleviation factor H Boundary layer shape factor h Gust gradient length h c Second segment climb gradient H te Shape factor at trailing edge I Cross-section inertia I ra Insurance rate K e Element stiness matrix k d GLA derivative gain k p GLA proportional gain L Element length l land Landing field length 3 l to Balanced takeo field length LF Load factor) M dd Airfoil drag divergence Mach number M land Landing Mach number M to Takeo Mach number n Load factor N e Number of engines N pax Passenger count p fuel Price of aviation fuel ($/gal) p oil Price of lubrication oil ($/lb) R Aircraft mission range R req Required mission range RF Range factor S Stratford concavity parameter s Airfoil surface coordinate S h Horizontal tail area S u Upper surface Stratford concavity parameter S ref Trapezoidal wing reference area t(x) Airfoil thickness distribution T 0 Sea-level static engine thrust T m Air and ground maneuver time t s Wing box skin gauge thickness t w Wing box web gauge thickness t ce Labor man-hours per flight hour T cl Climb time t he Labor man-hours per flight cycle t inv Airfoil thickness distribution from the inverse solution TSFC Thrust specific fuel consumption U a Annual utilization u e External velocity u r Velocity at the start of recovery 4 U ds 1–Cosine design gust amplitude U ref Gust reference vertical design velocity u te Velocity at trailing edge V Cruise velocity V block Block speed W e Engine dry weight W f Final cruise weight w g Gust vertical velocity W i Initial cruise weight W MLW Maximum landing weight (lb) W MTOW Maximum takeo weight W MZFW Maximum zero-fuel weight x Eective boundary layer length x a Longitudinal position of aft spar in the airfoil system x e Longitudinal position of elastic axis in the airfoil system x f Longitudinal position of forward spar in the airfoil system x t Longitudinal location of transition in aircraft system x mg Longitudinal position of main landing gear x ng Longitudinal position of the nose gear x root Longitudinal position of wing root x TE Airfoil trailing edge z(x) Airfoil camber distribution z f Final cruise altitude z i Initial cruise altitude z max Maximum operational altitude (ft) Re x Eective local Reynolds number ◊ te Momentum thickness at trailing edge C Lh Horizontal tail lift coecient C linv Airfoil C l from the inverse C lmax Section maximum lift coecient C Mac Pitching moment about aerodynamic center 5 L e” 4 Elastic wing pitch moment due to aileron deflection L r” 4 Rigid wing pitch moment due to aileron deflection Re x Local Reynolds number Re exp 9 Local transition Reynolds number as predicted by e 9 fits Re e 9 Transition Re x as predicted by e 9 fits. RF f Final cruise range factor RF i Initial cruise range factor R L Labor rate $/hr t ha Labor man-hours per flight hour C Lhmax Maximum horizontal tail lift coecient C p LEl Lower surface airfoil leading edge C p C p LEu Upper surface airfoil leading edge C p AIC Aerodynamic influence coecient matrix TSFC 0 Sea-level static TSFC – 0 Zero-lift angle of attack – i Local angle of attack at panel i — Prandtl-Glauert correction factor ” Flap deflections in between breakpoints ” i Control surface deflection for channel i c Wing trailing edge extension ratio ” s Slat deflection ÷ Dimensionless span ÷ = y/(b/2) d” i dt Control surface deflection rate for channel i i Circulation at panel i ⁄ Trapezoidal wing taper ratio 1/4 Trapezoidal wing quarter-chord sweep ‹ Kinematic viscosity Ê Wing natural frequency fl Element mass density ‡ Bending stress · Shear stress 6 ◊ Wing jig twist ˜ · ” 4 Wing torque due to aileron deflection ’ Damping ratio ” land Landing flap deflection ” to Takeo flap deflection ‡ a Allowable bending stress · a Allowable shear stress Chapter 1 Introduction 1.1 Motivation The classical Breguet Range equation decomposes aircraft range and hence, cruise eciency into propulsive (TSFC), structural (W i /W f ) and aerodynamic (L/D) com- ponents: R = 3 L D 4 V TSFC ln A W i W f B (1.1) One can certainly improve the individual terms in the range equation: Historically, the most significant improvements in jet aircraft eciency have come from improvements in the propulsive term associated with the development of high-bypass turbofan engines. The expanding use of high-strength composites can increase the weight fraction. And configuration changes such as increased wingspan can lead to improved L/D. However, the integrated nature of the aircraft design means that few substantive configuration changes can be made without incurring some multidisciplinary trade-os. Increasing the wingspan for example also increases the wing weight. Yet the same integrated nature of aircraft design is also an opportunity: significant improvements can come from configurations that can simultaneously exploit aerody- namic, control and structural advances to improve eciency. The Boeing/NASA Sugar 7 CHAPTER 1. INTRODUCTION 8 Volt pictured in fig. 1.1 is one such multidisciplinary design concept. Developed as part of the NASA N+3 studies to envision future airliners, the Sugar Volt deploy a slew of advanced technologies from hybrid-electric open rotor engines to truss-braced wings (TBW) to greatly improve cruise eciency and enviromental performance. 1 Figure 1.1. The Boeing Sugar Volt – part of the NASA N+3 advanced subsonic transport study. 1 The focus of this thesis is on the Sugar Volt’s combination of extreme span and extensive natural laminar flow (NLF) – all made possible by the aggressive application of maneuver (MLA) and gust load alleviation (GLA). The combination of these technologies holds the potential to greatly improve both the weight and aerodynamic terms in the Breguet equation. However, the potential gains from a complex and highly coupled design like the Sugar Volt can be dicult to quantify. Conceptual design tools typically reduce laminar flow and active load alleviation to empirical technology factors applied on weight and drag. 1,3,4 The Sugar Volt design for example assumes that a properly designed active load alleviation system can reduce the wing weight by 25%. It also assumes that the wing transition Reynolds number lies somewhere between 15 to 17 million irrespective of the pressure distribution over the wing. 1 An empirical approach however can miss important trade-os and constraints that drive the design: the eectiveness of load alleviation systems can be constrained by maximum lift, wing aeroelastic response and control power. And the design of a transonic NLF wing is driven by a balancing act to control profile drag, structural CHAPTER 1. INTRODUCTION 9 weight and compressibility eects. The objective of this research is to develop a new design framework that leverage physic-based methods to incorporate active load alleviation and natural laminar flow into conceptual design. 1.2 Natural Laminar Flow Viscous drag accounts for upwards of half of the total aircraft drag in cruise. Achieving extensive laminar flow over the wings net significant drag reductions. One way to maintain laminar flow at high Reynolds numbers is to employ active laminar flow control (LFC) to reshape the pressure distribution, re-energize the boundary layer and delay flow transition. The notional geometry and pressure distribution of an active laminar flow control airfoil is shown in fig. 1.2. Active flow control systems however can incur significant weight, maintenance and power penalties. An alternative to active LFC is to design the wing pressure distribution to passively stabilize the boundary layer, which gives rise to natural laminar flow (NLF). There is a substantial body of literature that aims to solve the NLF wing design problem using high fidelity tools. 5–9 However, these methods often require detailed definitions of the wing geometry, which may not be practical in the early stages of design. This has led aircraft designers to use empirical, design-oriented fits of flow transition in aircraft design problems. 4,10 Yet the impact of laminar flow can be fundamental. And laminar flow wing design should be formally integrated into conceptual design. The potential fuel savings from airliners designed with NLF wings have been variously quoted as somewhere between 5-12%. 11–13 The extent of the fuel savings is subject to complex multidisciplinary trade-os. The most important of which involves wing sweep. In two dimensions an NLF airfoil can be designed with extended regions of flow acceleration to suppress streamwise Tollmien-Schlichting (TS) instabilities. In the CHAPTER 1. INTRODUCTION 10 (a) Turbulent -C p Suclion x l x l (b) Active laminar flow control (c) Natural laminar flow (NLF) Figure 1.2. Representative airfoil geometries and C p distributions. 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 S w e e p ( D e g ) Transition Reynolds Number (Million) NLF Region Figure 1.3. A plot of NLF transition as a function of wing sweep based on the results of historical laminar flow experiments. 2 CHAPTER 1. INTRODUCTION 11 case of swept wings there exists a fundamental trade-o between the need to stabilize the streamwise and crossflow (CF) boundary layers: while flow acceleration stabilizes the streamwise boundary layer, it has the opposite, destabilizing eect on crossflow. The implication is that extensive natural laminar flow becomes progressively more dicult to maintain at higher wing sweep. Indeed flight tests demonstrate that at a sweep of 10 ¶ laminar flow can be reasonably achieved over 50% of a NLF wing. However, if sweep is increased to 25 ¶ then the laminar region is reduced to just 20% of the wing area. 11 The trend of reduced laminar flow with increasing sweep is also demonstrated by the complication of four decades of NLF flight test results in fig. 1.3. 2 0.06 0.07 0.08 0.09 0.1 0 5 10 15 20 Mach=0.78, C l =0.4 Airfoil t/c C o m p r e s s i b i l i t y D r a g ( C o u n t s ) Λ = 25 deg Λ = 10 deg Figure 1.4. An illustration of typical compressibility drag rise trend as a function of streamwise t/c and wing sweep. One could certainly reduce the sweep to render wings more compatible with NLF. However, unsweeping the wing at transonic speed carries steep penalties. 14–16 A typical plot of transonic drag rise as a function of sweep and thickness in fig. 1.4 shows that an unswept wing has to be made much thinner than its swept counterpart to prevent drag divergence. The structural consequences of reducing wing sweep and thickness CHAPTER 1. INTRODUCTION 12 can be illustrated with the simple wing weight relationship of Cleveland: 17 W wing s à ⁄ M x t dy à b 3 (t/c) cos 2 S ref The equation shows that although unsweeping the wing may have a small, positive eect on structural eciency, the eect of the cos 2 () term is easily overshadowed by the linear weight increase with reduced t/c. A thin, unswept NLF wing can therefore weigh substantially more than its turbulent counterpart. And the weight penalties can wipe out the drag savings. One way to cope with the aerostructural consequences of unsweep is to simply slow down. Indeed, most NLF design concepts are designed to cruise at Mach 0.70 to 0.75. The Sugar Volt for example is designed to cruise at Mach 0.71. However, in the absence of variable cycle technology, reduced cruise speed can negatively impact engine eciency. And at today’s fuel prices, slowing down can incur utilization and cost penalties. Moreover, air trac control (ATC) could also be complicated by the presence of slower aircraft. The alternative to slowing down is to reduce the weight penalties from a thin wing. Active load alleviation is one such technology that can tilt the balance of the Mach- sweep-thickness (MT) trade in favor of low-sweep NLF wings. 1.3 Maneuver Load Alleviation Maneuver load alleviation systems respond to pseudo-static maneuvers commanded by the pilot. Figure 1.5 shows two aircraft undergoing symmetric maneuver at the same load factor. The dierence is that the MLA-equipped aircraft can use coordinated control deflections to concentrate lift inboard and reduce the wing bending moment. This allows the wing of the MLA-equipped aircraft to be made lighter, or longer and thinner at the same weight. CHAPTER 1. INTRODUCTION 13 (a) Conventional (b) MLA Figure 1.5. Lift distribution for conventional and MLA aircraft at the same maneu- ver load factor. MLA has been the subject of numerous studies. Results suggest that MLA can achieve span increases of 10-15% and drag savings of 8-13% at fixed wing weight. 3,18–21 Experimental MLA systems have been flight tested under the NASA Mission Adaptive Wing (MAW) and Active Flexible Wing (AFW) programs. And production MLA systems have been integrated into commercial aircraft like the Airbus A320, A330. 22,23 However, the full benefit from load control can only be realized by incorporating the technology early on in the design process. The goal of the present research is to formally incorporate MLA into conceptual design. 1.4 Gust Load Alleviation As MLA relaxes the structural design constraints imposed by maneuver loads, dynamic gust loads can becomes critical design conditions. 24 The implications are twofold: 1) gust loads should be considered when evaluating the eectiveness of MLA systems and 2) a gust load alleviation system is likely needed to realize the full benefits of MLA. GLA responds to dynamic, unanticipated atmospheric turbulence. Unlike the MLA system, eectiveness of GLA systems may be fundamentally constrained by sensor and actuator bandwidths. The close interdependence between aircraft configuration and gust response complicates the process of GLA control law design. Previous studies have sought to address components of the integrated GLA design problem: 1) how to CHAPTER 1. INTRODUCTION 14 find the worst-case gust for a given airplane, 25–29 2) how to design aircraft structure to sustain a given gust 30–33 and 3) how to design a GLA control systems for a given airplane. 34–36 The more recent work of Fidkowski et al. 37 surveys stochastic gust design criteria and assesses the sensitivities of gust load to modeling assumptions. The present work extends these previous research and address the integrated problem of how to simultaneously design an aircraft with its GLA control system. 1.5 Organization In chapter 2 we introduce the design framework, which extends our previous work on MLA and gust load alleviation. 38 In chapters 3 and 4 we develop new aerodynamic and structure analysis tools to incorporate laminar flow and active load alleviation into conceptual design. Next, the aeroservoelastic design framework is applied to a series of design studies in chapter 5. This is followed by a discussion of the results in chapter 6. Finally, we examine the performance sensitivities of the optimized aircraft to changes in critical design assumptions in chapter 7. Chapter 2 Design Framework The aeroservoelastic design framework developed in this thesis is based on the Program for Aircraft Synthesis Studies (PASS). 39 PASS in its basic form leverages fast, semi- empirical models to capture aircraft performance sensitivities to configuration and mission variables. In this chapter we introduce the components of the PASS mission analysis framework that are most relevant to load alleviation and NLF design. A more detailed discussion of the basic PASS framework can be found in Kroo. 39 2.1 Aircraft Parameterization The design framework is geared toward the analysis of "conventional" aircraft configu- rations characterized discrete fuselage, empennage and wing components. The wing parameterization and design are detailed in the next chapter. The aircraft fuselage dimensions are dictated by the seating arrangement and passenger count, which are fixed for a given optimization. The horizontal tail is parameterized by its area ratio relative to the wing S h /S ref . The longitudinal position of the wing root x root is an important parameter for trim, stability and landing gear integration. 15 CHAPTER 2. DESIGN FRAMEWORK 16 The set of aircraft optimization variables can be summarized as: x aircraft = C S h S ref , x root , W MTOW , W MZFW , T 0 , x mg D The engine weight and dimensions are sized by the sea level static thrust variable T 0 . The thrust and fuel consumption at a given flight condition are computed using a rubberized PW-2037 engine deck. 39 The sea-level static thrust-to-weight ratio and fuel consumption (TSFC) are scaled to match the more modern CFM-56-7B27 turbofan used on the comparable Boeing 737-800. The characteristics of the reference PW- 2037 engine and the CFM-56-7B27 used in the engine scaling are summarized in table 2.1. Engine TSFC 0 (lb/lb-hr) W e (lb) T 0 (lb) PW-2037 0.326 7,160 34,250 CFM-56-7B27 0.380 5,216 24,000 Table 2.1. Engine parameters for the PW-2037 (reference engine deck) and CFM- 56-7B27 turbofans. A number of aircraft parameters are included as design variables to eliminate internal iterations. For example, the values of the maximum takeo and zero fuel weights W MOTW and W MZFW are both needed before they can be evaluated in the analysis. Rather than relying on iterations to converge the weights, we simply include W MOTW and W MZFW as design variables and use compatibility constraints to enforce conver- gence. Similarly, the longitudinal placement of the landing gear x mg is a function of the aircraft center-of-gravity (CG), which is itself dependent on the landing gear position. The aircraft-level compatibility constraints can be summarized as follows: x mg = max (x CG ) ≠0.08x ng 0.92 W MTOW = W MZWF +W fuel +W res Z _ _ ^ _ _ \ Aircraft Compatibility Constraints The weight constraint ensures that the sum of the empty weight, fuel weight and fuel reserves W res adds up to the takeo weight. The landing gear compatibility constraint CHAPTER 2. DESIGN FRAMEWORK 17 ensures that the nose carries at least 8% of the aircraft weight for traction. 2.2 Mission Analysis We evaluate aircraft performance in the context of the representative short-haul mission profile illustrated in fig. 2.1. The mission includes takeo, climb, cruise and approach segments. Not shown is a standard diversion reserve. The mission also includes representative gust encounters and limit maneuvers that combine to size the wing structure. The choice of the maneuver and gust flight conditions are detailed in chapter 4. The important mission parameters such as the initial and final cruise altitudes and the takeo and landing Mach numbers and flap schedules are optimized concurrently with the aircraft: x mission = [z i , z f , M to , M land , ” to , ” land ] The aircraft is designed to meet the range, field length, engine-out climb gradient and cruise thrust margin constraints summarized in eq. (2.1). The field performance requirements are based on published payload-range diagrams for the Boeing 737-800. The climb gradient constraint follows from the Federal Aviation Regulations (FAR). The cruise stage drag-to-thrust constraints ensure that the aircraft has sucient thrust at altitude to sustain operational climb. l to < 7,900ft, l land < 5,500ft, h c > 0.024 D T i < 0.88, D T f < 0.88, R > 2,000nm Z _ _ ^ _ _ \ Performance Constraints (2.1) The computation of the climb gradient, cruise stage drag-to-thrust ratios and cruise range require the aircraft drag and thrust at dierent flight conditions. The available thrust comes from the rubberized engine deck discussed in section 2.1. 39 We compute CHAPTER 2. DESIGN FRAMEWORK 18 Finul Ciuiso, h f , V f 2.ó-g Munouvoi 20,000 fl, V c Socono Sognonl ClinL 400 fl, 1.2V s 1ukool Iolulion S.L. V i Appiouch S.L. ,1.8V s Iniliul Ciuiso, h i , V i 1.8-g Munouvoi 40,000 fl, V c 2,000-nn nission plus slunouio iosoivos Gusl Lncounloi 10,000 fl, V c Gusl Lncounloi, h i , V c Gusl Lncounloi, h f , V c Figure 2.1. The design mission profile and flight conditions. the fuselage and empennage parasite drag using equivalent plate area methods and empirical shape factors. 39 We assume that the wave drag of the fuselage and tail are negligible compared to the wing. The more wing drag build-up is discussed in detail in chapter 3. To approximate the eects of step-climbs we assume a linear variation in aircraft weight, drag and TSFC from an initial to a final cruise state.The aircraft range R can then be integrated as follows: R = RF i ≠RF f + A RF f ≠W f RF f ≠RF i W f ≠W i B ln A W i W f B (2.2) The aerodynamic and propulsion contributions to range are captured in the range factor: RF = v TSFC 3 L D 4 The aircraft is subject to trim, stability and maximum lift constraints at each of the flight conditions in fig. 2.1. The trim constraints consists of lift matching and tail maximum lift components: C Lh < C Lhmax , nW = flv 2 S ref C L 2 < Trim Constraints CHAPTER 2. DESIGN FRAMEWORK 19 A conservative static stability margin of 10% is imposed at all flight conditions to account for aeroelastic washout in cruise, which tends to move the aerodynamic center forward and thereby diminish the stability margin: ≠ dC Mac dC L > 0.10c J Stability Constraints In addition to the flight conditions outlined in the mission profile we also include a stability constraint for cruise at operational empty weight (OEW). For conventional configurations the empty aircraft typically has the aft-most center of gravity and is critical in stability. The lift-matching constraint enforces force balance in each equilibrium flight condition. The tail maximum lift coecient prevents tail stall. The wing C L and the horizontal tail C Lh needed to trim the aircraft are solved from the force and moment balance: C mac ≠ C Lw c (x acw ≠x cg ) ≠ C Lh c (x ach ≠x cg ) S h S w = 0 C L = C Lw +C Lh S h S w The wing aerodynamic center x ac and stability derivatives such as the pitch moment coecient C mac are evaluated using the Weissinger panel method. The pitch moment includes contributions from wing twist, control surface deflections and the zero-lift airfoil pitch moment, which is integrated from the inverse airfoil design discussed in more detail in section 3.5.1. Also included are the aeroelastic wing twist induced by control surface deflection. Chapter 3 Wing Design The multitude of new design sensitivities and constraints introduced by load alleviation and NLF call for physics-based wing design tools. The analysis is grounded on a detailed parameterization of the wing and structure box. A Weissinger panel method with compressibility corrections is used to solve the aerodynamic loads and stability derivatives. Finally, we develop a hybrid-inverse viscous design tool to incorporate NLF into aircraft design. 3.1 Geometry The wing parametrization begins with the definition of the trapezoidal planform. The reference area S ref , aspect ratio AR, taper ratio ⁄ and quarter-chord sweep 1/4 are all design variables. The vector of wing jig twists ◊ at the exposed breakpoints are also subject to optimization. The trapezoidal wing is modified by trailing edge extensions defined at wing breakpoints. The extensions c are defined as fractions of the trapezoidal chord. All intermediate planform geometries and twists are linearly interpolated. While the design framework can accommodate an arbitrary number of wing breaks, we 20 CHAPTER 3. WING DESIGN 21 choose the six sections highlighted in fig. 3.1 to define the planform. The breakpoint positions as fractions of the semispan are held constant in the optimization. y=y](b]2) Fuselage WidLh y=0.3 y=0.5 y=0.1 y=0.7 y=0 y=1 Figure 3.1. The wing break sections that define the planform and twist. The inner- most section (÷ = 0) corresponds to the wing root. The next section defines the wing-fuselage intersection. Figure 3.2. The wing structure box configuration. The wing structural box in fig. 3.2 extends from 20 to 65% of the chord. The hexagonal wing box geometry is defined by the elastic axis and forward and aft spar heights at each breakpoint section. The skin and web thicknesses t s and t w at the breakpoints are also optimization variables. The intermediate wing box geometries are again interpolated. The wing load-bearing weight follows directly from the wing box geometry and material density. However, the weight of the spars and webs represents only a portion of the total wing weight. We establish the relationship between wing load-bearing and total weight using the empirical fit developed by Gallman, 40 which accounts for minimum gauge eects and non-structural weight. The wing geometry CHAPTER 3. WING DESIGN 22 Figure 3.3. The parameterization of the wing box cross section. design variables x wing can be summarized as follows: x wing = Ë S ref , AR, ⁄, 1/4 , c, ◊, t(x e ), t(x f ), t(x a ), t s , t w È The wingbox geometry is fully defined by the optimization variables. The winbox is sized by the spanwise static and dynamic stress constraints in the optimization. The resolution of the aerodynamic loads are discussed in detail in chapter 4. 3.2 Aerodynamics We compute the wing lift distribution and stability derivatives using a modified Weissinger method, which is a vortex lattice method (VLM) with only one chord-wise panel. 41 Each semispan is modeled using 31 skewed bound vortices centered along the quarter chord line. The flow tangency boundary conditions are enforced at control points along the three-quarter-chord line. The control point arrangement is illustrated in fig. 3.4. The linear system for the vortex strengths i can be written in terms of the aerody- namic influence coecient matrix and the local angle of attack – i : [AIC] i = U Œ – i Where element AIC ij relates the induced downwash at control point i to the vortex CHAPTER 3. WING DESIGN 23 C l (y) 0.525 The required aileron eciency of 53% at V c is rather conservative. The aileron reversal limit is an operational parameter and should be investigated in more detail. The rigid wing roll moment due to a unit aileron deflection can be readily solved using the Weissinger method. To obtain the elastic wing roll moment we add the aeroelastic twist ◊ e to the panel method boundary conditions. The aileron-induced twist about the elastic axis can be integrated as follows: ˜ · ” 4 = q ⁄ b/2 ˜ y cos 3 e c(›) 2 C m” 4 (›)d› ˜ ◊ e = ⁄ ˜ y 0 ˜ · ” 4 (›) GJ(›) d› We transform the twist into the spanwise direction to obtain the modifications to the aerodynamic boundary conditions. CHAPTER 3. WING DESIGN 29 3.5 Inverse Design The extent of attainable wing natural laminar flow is a strong function of the pressure distribution. We develop a hybrid-inverse viscous design tool to link flow transition and profile drag to the wing geometry and lift distribution. In the inverse approach, we first define the pressure distribution and then solve for the corresponding geometry. The pressure distribution and geometry are then combined with integral methods to solve for the boundary layer development, transition location and ultimately, the profile drag. The method is inspired by the work of Liebeck. 45 It can also be understood as a smooth, 2-D analogue of the more involved 3-D viscous design system of Allison el. al. 13 3.5.1 Pressure Distribution The pressure variables define the compressible streamwise C p distributions at the ex- posed wing stations highlighted in fig. 3.10. The wing-fuselage intersection highlighted in red is always assumed to be turbulent to reflect the dominant eects of attachment line instabilities at the intersection. Fuselage WidLh y=0.3 y=0.5 y=0.1 y=0.7 y=0 y=1 Figure 3.10. The wing breakpoints with inverse design sections highlighted. The blue sections can be designed for NLF while the red wing-fuselage inter- section is always assumed to be turbulent to account for the dominant role of attachment line instabilities. CHAPTER 3. WING DESIGN 30 Slialfoio-lypo iocovoiy Linoai iooflop Slail of Iocovoiy Figure 3.11. An illustration of the airfoil C p parameterization with important pres- sure features labeled. x i oC p ,ox(u) M i (u) C I LL (u) C I LL (l) oC p ,ox(l) S(u) M i (l) Figure 3.12. The inverse deisgn C p parametrization with the pressure variables labeled in blue. CHAPTER 3. WING DESIGN 31 The motivation for an inverse approach stems chiefly from the commonality of NLF airfoil pressure distributions. Figure 3.11 illustrates the features of a representative NLF pressure distribution: 1) an extended region of accelerating, 2) a short transition ramp, 3) a weak shock and 4) a rapid recovery to the trailing edge. The pressure features can be even more succinctly described using the parameterization illustrated in fig. 3.12. Here the C p distribution is parameterized by a linear ramp followed by a Stratford-type recovery. 46 The pressure variables are defined in eq. (3.3). x pressure = C x r , C p LEl , C p LEu , A dC p dx B u , A dC p dx B l , S u D (3.3) The most important variable for laminar flow is the rooftop pressure gradient dCp dx – a "favorable" pressure gradient can stabilize the streamwise boundary layer. The start of recovery x r determines both the extent of the rooftop and the balance of aft loading. In the present analysis the value of x r controls the start of recovery on both the upper and lower airfoil surfaces. This is done to reduce discretization and numerical integration errors. The Stratford criteria in section 3.5.1 defines a rapid recovery that is everywhere on the verge of separation. By minimizing the recovery distance the Stratford recovery can maximize the length of the laminar rooftop. An added computational benefit of the Stratford recovery is its simplicity: the shape of the recovery can be defined using only the flow conditions at x r and the concavity parameter S: S = C p Ú x dCp dx (10 ≠6 Re x ) 0.1 Here the canonical pressure coecient C p and eective Reynolds number Re x are defined in terms of the flow properties at the start of recovery: Re x = xu r ‹ C p = 1 ≠ 3 u u r 4 2 CHAPTER 3. WING DESIGN 32 The classical Stratford criteria is formulated with a concave recovery at S = 0.39. However, a flow that is everywhere on the edge of separation cannot be used for practical design. We derive therefore the solution to the Stratford criteria for an arbitrary S in section 3.5.1 and use a more conservative S of 0.35 to define the recovery. C p = Y _ _ ] _ _ [ 5 C p m 3 + 0.1893Re x 1/5 ln 1 x xm 2 S 2 6 1/3 C p < 4/7 1 ≠ ka Ô k b + x xm C p Ø 4/7 Here the free parameters k a and k b are solved numerically to match the canonical pressure C p and its derivative at the inflection point where C p exceeds 4/7. Pressure Constraints The pressure distribution generated using the current parameterization scheme are not guaranteed to be realistic. We use constraints to ensure that the design pressure distributions are consistent with the spanwise lift distribution and produce acceptable high-speed performance: ⁄ c 0 Ë C p l (x) ≠C p u (x) È dx > C l (÷) M ru‹ < 1.1, M rl‹ < 0.95 Z _ ^ _ \ Pressure Constraints (3.4) The section lift coecient integrated from the chord-wise pressure distribution must match the spanwise C l from the Weissinger solution. We specify the lift-matching constraint as an inequality because the optimized pressure distribution should always reach the C l upper bound. A useful design heuristic for supercritical airfoils is to limit the pre-shock Mach number on the suction side M ru‹ to less than 1.1. Stronger shocks may lead to drag divergence and flow separation. We apply the sweep-taper transformation of Lock 47 to obtain M ru‹ from the design pressure distribution. For a given C l and thickness the pressure gradient is restricted only by the pre-shock CHAPTER 3. WING DESIGN 33 Mach number. The inverse design method captures therefore a fundamental trade-o between high speed performance and natural laminar flow. The restriction on the shock Mach number is conservative. Indeed, a recent study by Jameson, Vassberg and Shankaran 48 suggests that low sweep transonic wings may be attainable with modern CFD design tools. This would a significant eect on the extent of realizable laminar flow. Sensitivity studies show that even an increase from a limit pre-shock Mach number of 1.1 to 1.15 can lead to significant increases in the laminar run. The compressibility drag is estimated using an assumed quartic drag rise profile. We assume 15 counts of compressibility drag for a top wing surface shock Mach number of 1.1. This is in line with the performance of well-designed supercritical sections. A single-parameter empirical model of C dc is admittedly quite limited. However, by restricting the maximum recovery Mach number above and below the airfoil we ensure that the airfoil designs are reasonable. And by making the compressibility drag sensitive to the peak Mach number, we link the compressibility drag evaluation to NLF and structural design: the optimizer can trade C dc against C dp and structural eciency. The compressibility drag is referenced to the sweep of the x-position of the start of pressure recovery (x r ) to better match the isobar ahead of the moderate shock. Implicit is the assumption that the compressible aerodynamics of the section is better related to the wing sweep incident of the shock. C dc‹ à M xr ‹ C dc = C dc‹ cos 3 ( xr ) 3.5.2 Airfoil Geometry We use thin airfoil theory to map a defined pressure distribution to its associated airfoil geometry. Classical thin airfoil theory holds for incompressible flow. It is necessary then to apply both the sweep-taper and inverse Kármán-Tsien transformations to convert the compressible streamwise C p to the equivelent incompressible pressure distribution ˜ C p normal to the local isobars. We map the incompressible pressure CHAPTER 3. WING DESIGN 34 distribution to airfoil thickness t(x) and camber z(x) distributions using the following integral equations: ˜ u u (x) + ˜ u l (x) 2 = 1 fi ⁄ c 0 dt(›) d› d› x ≠› – ≠ dz dx = 1 4fi ⁄ c 0 Ë ˜ C p l (›) ≠ ˜ C p u (›) È d› › ≠x The induced velocity at the chord line are specified by the pressure distribution: ˜ u(x) = Ò 1 ≠ ˜ C p (x) We discretize the airfoil and solve the integral equations using a panel method. Thick- ness constraints defined in the chordwise direction ensure that the inverse airfoil geometry can accommodate the previously defined wing box: t inv (x e ) > t e , t inv (x f ) > t f t inv (x a ) > t a , t inv (x te ) = 0 Z _ ^ _ \ Wing Box Compatibility Constraints The inverse thicknesses solution at the forward spar, elastic axis and aft spar must match the wingbox geometry defined in x wing . The trailing edge thickness is con- strained to close the airfoil. An example of optimized wing section C p distributions and their corresponding geometries can be found in figs. 3.13 and 3.14. The first section at ÷ = 0.1 corresponds to the wing root. The root section is forced to be turbulent to reflect the impact of attachment line boundary layer instabilities. The optimizer sees little incentive to design a favorable pressure gradient in that case. The outboard sections are designed for NLF and all show various degrees of favorable pressure gradient. CHAPTER 3. WING DESIGN 35 0 0.5 1 −0.5 0 0.5 − C p (a) ÷ = 0.1 0 0.5 1 −0.5 0 0.5 − C p (b) ÷ = 0.3 0 0.5 1 −0.5 0 0.5 − C p (c) ÷ = 0.5 0 0.5 1 −0.5 0 0.5 − C p (d) ÷ = 0.7 Figure 3.13. Example wing section pressure distributions at selected spanwise loca- tions. 0 0.5 1 −0.1 0 0.1 x/c z / c (a) ÷ = 0.1 0 0.5 1 −0.1 0 0.1 x/c z / c (b) ÷ = 0.3 0 0.5 1 −0.1 0 0.1 x/c z / c (c) ÷ = 0.5 0 0.5 1 −0.1 0 0.1 x/c z / c (d) ÷ = 0.7 Figure 3.14. Example wing section geometry at selected spanwise locations. 3.5.3 Boundary Layer Solution We employ the integral methods of Thwaites and Head to solve the laminar and turbulent boundary layers. 49 Compressible boundary layer solutions can certainly increase accuracy. However, since compressibility tends to stabilize the streamwise boundary layer, 14,50,51 an incompressible analysis is at least conservative. We do however, apply compressibility corrections to the turbulent surface friction coecient C f . 14 Laminar Boundary Layer The Thwaites solution for the laminar momentum thickness ◊ is given by equation section 3.5.3. The equation can be exactly integrated if the pressure distribution is analytic with respect to the surface coordinate s. However, the laminar ramp in the CHAPTER 3. WING DESIGN 36 present analysis is only linear in x; a numerical solution is still required. ◊ 2 = 0.45‹ u e 6 ⁄ s 0 u e 5 ds Transition To simulate turbulent sections we force flow transition near 3% chord. For NLF sections we allow the flow to transition freely. Transition prediction remains an area of active research. An often used engineering transition criteria is the method of Michel. 49 Michel’s method is simple to use but does not direct account for the eects of the pressure gradient. More importantly, the method is not smooth and therefore incompatible with gradient-based optimiza- tion. The e 9 transition envelope fits of Drela and Giles 52 and those of Arnal, Habiballah and Delcourt 53 are smooth and are sensitive to the pressure gradient. However, these methods also require the numerical solution of both a point of critical stability and a point of transition. The two-point solution presents diculties for surface discretization and numerical integration. To minimize numerical error we use the simpler, single-step H ≠R x transition criteria: 54 log[Re e 9] = ≠40.4557 + 64.8066H ≠26.7538H 2 + 3.3819H 3 The H≠R x criteria defines the transition Reynolds number at all points on the airfoil as a function of the local shape factor of the boundary layer. Re e 9 is the local Reynolds number Re x where the fits to the e 9 envelope predict flow transition. Transition occurs when the local Reynolds number exceeds the local transition Reynolds number: Re x (x) > Re e 9(x) CHAPTER 3. WING DESIGN 37 At this point one could use interpolation on iterative solvers to solve the H ≠ R x criteria. However, while an interpolation scheme may be suciently accurate for purposes of boundary layer analysis, it is not accurate enough for gradient-based optimization. The numerical problems becomes intractable at high Reynolds numbers where the transition location x t is sensitive to even small changes in the pressure gradient. One way around this numerical problem is specify x t as an optimization variable: x transition = x t Of course the optimizer cannot be allowed to freely pick a transition point. That would be too easy. It is necessary to further apply a compatibility constraint to enforce laminar flow before x t : Re x (x t ) < Re e 9(x t ) The application of optimizer-based decomposition leverages the non-linear solver already present in the optimizer to converge the transition location. This eliminates the costly internal iterations that would otherwise be needed to solve the transition problem. The decomposition also reduces the laminar boundary layer evaluation to just one point at x t . Turbulent Boundary Layer We solve the turbulent boundary layer using the Heads method. The boundary layer solution is advanced to the trailing edge using the fourth-order Runge-Kutta scheme. The section profile drag of each surface is solved using the Squire-Young momentum equation: C dp = 2 ◊ te c 3 u te u Œ 4 H te +5 2 The total wing profile drag in cruise is integrated from the C dp solutions at the break sections. Chapter 4 Active Load Alleviation An important goal of this thesis is to find a way to develop the aircraft load control system concurrently with the configuration. The design framework includes therefore detailed parameterization of the MLA control schedule and the GLA control law. The dynamic loads in gust encounters are resolved using a combination of aircraft dynamics simulations and modal solutions of the wing structural response. The individual components of the structural dynamics solver are validated against standard beam test cases. 4.1 MLA and GLA Parameterization Active load alleviation systems use coordinated control surface deflections to minimize wing stress. In principle any combination of control surfaces can be utilized. For simplicity we restrict the MLA and GLA control surfaces to the ailerons and flaps. This includes all of the trailing edge control surfaces in shown in fig. 4.1. The sensitivity of the aircraft design to control allocation is examined in more detail in chapter 7. Figure 4.1 illustrates the trailing edge control surface arrangement and parameteri- zation. Each exposed trailing edge section bounded by successive wing breakpoints 38 CHAPTER 4. ACTIVE LOAD ALLEVIATION 39         Figure 4.1. The wing control surfaces are defined by the wing break sections. represents an independent control surface. The inboard sections simulate flap de- flections; outboard sections simulate ailerons. Both the aileron and flap surfaces are assumed to extend over 25% of the chord. The chord ratio is somewhat lower than the typical extended chord of flaps. A conservative parameterization of the flap chord is however consistent with the need for lightweight, high-bandwidth control surfaces to achieve eective dynamic load alleviation. The control surface deflection schedules and dynamic gains are optimized with the aircraft. 4.2 Maneuver Load Alleviation A first-order question in the design of the MLA system is the definition of the limit maneuvers. The aircraft should ideally be designed for the entire V–n envelope. An exhaustive search for the worst loads may not, however, be practical or indeed necessary for conceptual design. An alternative is to identify representative maneuvers that can eciently capture the key aerostructural trade-os and inform design. The Federal Aviation Regulations (FAR) require commercial aircraft structures to be designed to withstand a 2.5-g maneuver at a structural safety factor of 1.5. For a conventional aircraft the speed and altitude of the limit maneuver flight condition are not particularly important – the stress is determined by the load factor. Defining representative maneuvers becomes more complicated for aircraft designed with MLA. CHAPTER 4. ACTIVE LOAD ALLEVIATION 40 Here the wing stress state is fundamentally dependent on the eectiveness of load alleviation, which can in turn be dictated by aerodynamic constraints such as the wing maximum lift. We design the aircraft for a 2.5-g symmetric pull-up at an altitude of 30,000 feet and the structural design velocity V c . The maneuver altitude is justified by two observations. First, drastic maneuvers at altitudes higher than 30,000 feet are likely constrained by available engine thrust and maximum lift. The flight control system of commercial aircraft typically restrict the maneuver envelope at altitude to prevent stall. 22,23 Second, drastic maneuvers for obstacle avoidance and stall recovery are far more likely at lower altitudes. We also design the aircraft for a 1.3-g pull-up at 40,000 feet and the cruise velocity. The maximum-lift constraints help to ensure that the wing remains buet-free in cruise-stage maneuvers at high altitude. The MLA design variables are the vector of trailing edge control deflections ” for each of the design maneuver conditions: x MLA = ” The range of trailing edge deflections are limited by hinge moment, control reversal and flow separation considerations. We impose a generous absolute MLA deflection limit of 10 ¶ on each of the control surface: ≠10 ¶ < ” i < 10 ¶ The deflection limit is consistent with the published parameters of the load allevia- tion systems on the Airbus A320, A330 and A340, which share a maximum control deflection of 11 ¶ . 22,23 The limit is further supported by experiments, which show that high-speed trailing edge deflections on the order of 8 ¶ can be sustained without significant flow separation. 18 And since limit maneuvers need not be performed at constant altitude, drag penalties from the control surface deflections do not mean- ingfully impact the design. The sensitivity of the optimized aircraft to the allowable range of control surface deflections is examined in more detail in chapter 7. CHAPTER 4. ACTIVE LOAD ALLEVIATION 41 4.3 Gust Load Alleviation The wing structure is also sized by time-dependent gust load constraints in eq. (4.1). The gust load constraints are imposed at the three dierent gust encounter flight conditions discussed in section 2.2: at 10,000 ft and the initial and final cruise alti- tudes. The y-positions of the gust-induced stress constraints are collocated with the aerodynamic control points. {‡(÷, t)} < ‡ a , {·(÷, t)} < · a Ô Dynamic Stress Constraints (4.1) o(y,L) 0.024 D T i < 0.88, D T f < 0.88, R > 2,000nm Trim C Lh < C Lhmax , nW = flv 2 S ref C L 2 Stability ≠ dC Mac dC L > 0.10c Maximum Lift C l (÷) < I C lmax (÷) if ÷ < 0.75 C lmax (÷) ≠0.2 otherwise Pressure ⁄ c 0 # C p l (x) ≠C p u (x) $ dx > C l (÷) M ru‹ < 1.1, M rl‹ < 0.95 Wing Box t inv (x e ) > t e , t inv (x f ) > t f t inv (x a ) > t a , t inv (x te ) = 0 Transition Re x (x t ) < Re e 9(x t ) Static Stress {‡(÷)} < ‡ a , {·(÷)} < · a Dynamic Stress {‡(÷, t)} < ‡ a , {·(÷, t)} < · a Aileron Reversal L e”4 L r”4 - - - - Vc > 0.525 Table 5.3. Summary of all optimization constraints. Chapter 6 Results This chapter details the results of a number of design studies meant to demonstrate the workings of the aeroservoelastic conceptual design framework. We first present a series of optimized turbulent aircraft with varying degrees of active load alleviation: no load alleviation, MLA-only, GLA-only and finally both MLA and GLA (MLA+GLA). This is followed by an analogous series of laminar aircraft with dierent load alleviation systems. Finally, we compare the turbulent and laminar MLA+GLA designs in detail to highlight the potential synergy between active load alleviation and laminar flow. The results include both "point optimizations" at a cruise Mach number of 0.78 and optimization sweeps with cruise Mach numbers ranging from 0.70 to 0.82. We treat the Mach 0.78 turbulent aircraft designed without load alleviation as the baseline against which all other data are normalized. 60 CHAPTER 6. RESULTS 61 6.1 Turbulent Designs 6.1.1 Point Optimizations The four optimized turbulent aircraft are compared in fig. 6.1. In each design we force flow transition near the leading edge to ensure turbulent flow over the wing. The transition lines are highlighted in green. (a) Turbulent (b) Turbulent MLA (c) Turbulent GLA (d) Turbulent MLA+GLA Figure 6.1. The optimized Mach 0.78 turbulent aircraft with dierent levels of active load alleviation. The details of the aircraft and wing configuration are tabulated in table 6.1. The optimized Mach 0.78 turbulent aircraft in fig. 6.1a represents a conventional CHAPTER 6. RESULTS 62 Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA W MTOW (lb) 158,065 153,146 158,547 148,139 W fuel (lb) 25,916 25,030 25,779 23,520 W wing (lb) 19,200 16,582 19,720 14,637 T 0 (lb) 21,367 20,607 21,267 18,963 S ref (ft 2 ) 1,652 1,512 1,678 1,497 b (ft) 136 140 137 151 AR 11.2 13.0 11.2 15.3 1/4 (Deg) 26.6 21.7 26.6 17.6 t/c 0.096 0.089 0.096 0.091 L/D 18.2 18.3 18.4 19.0 z i 30,095 30,535 30,178 30,951 z f 41,514 41,496 41,554 41,190 Table 6.1. Summary of optimized Mach 0.78 turbulent aircraft design parameters. short-haul design in the same class as the Boeing 737 and the Airbus A320. In fact, the optimized maximum takeo weight matches well with the published figure of the Boeing 737-800 at 155,500 lb. The wing sweep of 26.6 ¶ and average cruise L/D of 18 are also in line with the 737. The optimized span at 136 feet is on the other hand substantially greater than the span of both the 737-800 at 117 feet and the Airbus A320 at 111 feet. The dierence is in part attributable to the absence of gate compatibility constraints in the optimization. We examine the sensitivity of the aircraft design to gate constraints in the next chapter. Compared with the baseline, the Turbulent MLA aircraft in fig. 6.1b shows a modest increase in span from 136 to 140 feet. The introduction of MLA decreases the optimum wing sweep by 5 ¶ . A simultaneous decrease in the area-weighted average thickness-to- chord t/c from 9.6 to 8.9% compensates for the compressibility penalties of reduced sweep. The MLA wing is both thinner and longer than the baseline wing but still manages to be some 3,000 lb lighter. Load alleviation clearly leads to tangible gains in structural eciency. The eectiveness of the MLA system acting alone also suggests that maneuver loads likely size a substantial portion of the baseline wing. CHAPTER 6. RESULTS 63 Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA Wing Weight 1.000 0.864 1.027 0.762 Fuel Weight 1.000 0.966 0.995 0.908 Sea Level Thrust 1.000 0.964 0.995 0.888 L/D 1.000 1.006 1.011 1.045 Cost 1.000 0.987 0.999 0.966 Figure 6.2. A comparison of the optimized turbulent aircraft. The performance metrics and configuration parameters are normalized against the corre- sponding values of the Mach 0.78 turbulent baseline. CHAPTER 6. RESULTS 64 The GLA design shown in fig. 6.1c on the other hand, is nearly identical to the baseline. The only dierence is the formers slightly larger wing. The other planform parameters are all within 1% of their baseline values. Gust loads then are clearly not sizing the baseline wing in any significant way. This result is not surprising because high wing sweep leads to significant aerodynamic stiness and damping in gust encounters. Figure 6.1d shows that the application of both MLA and GLA significantly alters the optimized configuration. Compared to the baseline the MLA+GLA wing is not only 15 feet longer but also 25% lighter. The sweep is reduced to 18 ¶ . The gain in L/D is modest in part because the ATA cost model used in the present analysis scales the aircraft manufacturing cost against the zero-fuel weight. Under this model the light aircraft is not only more ecient in lift but also costs less. It should be emphasized that the results in this chapter are all based on a fuel price of $2.5/gal. The balance between weight and fuel savings is fundamentally dependent on fuel prices. In certain cases it is convenient to examine the relative changes in performance metrics and design parameters. The parameters in fig. 6.2 are normalized to their baseline values in the Mach 0.78 turbulent design. We observe that the independent application of MLA has led to a modest but tangible 3.4% reduction in fuel burn and 1.3% reduction in cost. The independent application of GLA on the other hand produces only negligible gains. The combination of MLA and GLA has led to a significant 10% reduction in fuel burn and 3.4% reduction in cost. The exposed wing planforms of the turbulent aircraft are compared in fig. 6.3. Once again we normalize the relevant parameters by their baseline values. The figure highlight visually the similarity between the baseline and GLA wing and a clear trend towards increased span and decreased wing sweep with the successive addition of load alleviation technologies. Figure 6.4 compares the turbulent wing and skin thickness distributions. The in- creased structural eciency of the MLA and MLA+GLA aircraft leads to reduced wing and skin thicknesses. As load alleviation reduces the stress constraints, aeroe- lasticity can become dominant considerations. The optimizer chooses therefore to CHAPTER 6. RESULTS 65 Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA S ref 1.00 0.92 1.02 0.91 b 1.00 1.03 1.01 1.11 1.00 0.82 1.00 0.66 t/c 1.00 0.93 1.00 0.95 AR 1.00 1.16 1.00 1.36 Figure 6.3. A comparison of the optimized turbulent wing planforms. All parameters are normalized by their values in the Mach 0.78 turbulent baseline. 0 0.5 1 0 0.05 0.1 0.15 0.2 Spanwise Position η t / c Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA (a) Wing t/c 0 0.5 1 0 0.5 1 1.5 Spanwise Position η t s ( i n c h ) Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA (b) Skin Thickness (inch) Figure 6.4. Turbulent wing and skin thickness distributions. CHAPTER 6. RESULTS 66 increase the outboard stiness to prevent aileron reversal and increase MLA control authority. 0 0.5 1 0 0.5 1 1.5 2 2.5 Spanwise Position η C l a n d C l m a x Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA (a) 2.5-g at 30,000 ft 0 0.5 1 0 0.5 1 1.5 2 2.5 Spanwise Position η C l a n d C l m a x Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA (b) 1.3-g at 40,000 ft Figure 6.5. Comparisons of the turbulent maneuver C l (solid lines) and C lmax (dashed lines) distributions. We compare the maneuver C l distributions of the turbulent aircraft in fig. 6.5. The C l distributions show that the MLA system has concentrated load inboard to reduce bending and shear stresses. In the MLA design for example the wing tips are actually negatively loaded in the 2.5-g maneuvers. In this case the lift penalties are more than oset by the greatly increased load alleviation inboard. The drag penalties from the negatively loaded tips do not directly aect the design because the maneuvers do not have to be performed at constant altitude. The dashed lines in fig. 6.5 corresponds to the section C lmax . A discontinuous change in the section maximum lift indicates a change in the trailing edge controls surface deflection. The actions of the MLA system on the turbulent designs, which gave relatively thick wings enabled by sweep, are not constrained by the lift limit. We examine the structure design in more detail in fig. 6.6, which overlays the maneuver and gust-induced wing stresses to highlight which load is sizing each section of the CHAPTER 6. RESULTS 67 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (a) Turbulent 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (b) MLA 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (c) GLA 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (d) MLA+GLA Figure 6.6. Maneuver and gust bending stresses for the optimized turbulent designs at Mach 0.78. The wing bending stresses ‡ are normalized by the allowable stress ‡ a . The gust stresses represent the maximum values encounter by each wing section at all gust gradient lengths. CHAPTER 6. RESULTS 68 wing. The maneuver loads at 1.3 and 2.5-g are shown as solid lines. The dashed lines are formed by the maximum stresses at each wing section for all of the time-domain gust simulations at a given altitude. The maximum stresses are normalized by the allowable stresses ‡ a . fig. 6.6 is therefore a visual representation of both the optimized state of the static and dynamic stress constraints discussed in chapter 4. A wing section is deemed stress-critical if the local stress ratio ‡/‡ a reaches their limit values of 1 or -1. The plot of stress constraints confirms that the turbulent baseline wing structure is essentially sized by maneuver loads. Much of the inboard wing is fully-stressed in maneuver. The outboard sections are designed by minimum gauge. The MLA system significantly reduces the maneuver load but leaves the wing to be designed by gust. Figure 6.6b shows that the Turbulent MLA wing is designed by low-altitude gusts inboard and cruise stage gusts outboard. So while the MLA system has diminished the role of maneuver loads in structural sizing, the gust loads remain to undercut the potential structural savings. The opposite is true in the case of the GLA wing stresses shown in fig. 6.6b. Here the wing is designed almost exclusively by maneuver loads. Finally, fig. 6.6d demonstrates that the MLA+GLA wing is designed by both maneuver and gust loads. We also observe that the outboard portions of the wing are far from being fully-stressed; they are instead sized by the aforementioned aeroelastic and minimum gauge considerations. 6.1.2 Mach Number Sweeps The aircraft presented thus far are all designed to cruise at Mach 0.78. We now present the cost and fuel burn trends of the four turbulent aircraft as functions of the cruise Mach number. The cost and fuel burn metrics shown in figs. 6.7 and 6.8 are normalized by the cost and fuel weight of the baseline design at Mach 0.78. The results in Figure 6.7 demonstrate that at a fuel price of $2.5 per gallon the CHAPTER 6. RESULTS 69 0.7 0.72 0.74 0.76 0.78 0.8 0.92 0.94 0.96 0.98 1 1.02 1.04 Cruise Mach Number R e l a t i v e C o s t Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA Figure 6.7. A plot of the relative operating cost of optimized turbulent designs as functions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. minimum-cost objective continues to favor speed over fuel savings. Cost continues to fall with increasing Mach number. Only the MLA+GLA design flat-lines near Mach 0.82. So while the turbulent designs can slow down to reduce fuel burn, they can only do so at higher costs. Figures 6.7 and 6.8 show that the relative savings from the independent application of MLA and GLA are constant across the range of Mach numbers. The savings from the MLA+GLA are however dependent on the Mach number. We reason that aileron reversal constraints, which become more critical with increased speed, diminish the savings from load alleviation. CHAPTER 6. RESULTS 70 0.7 0.72 0.74 0.76 0.78 0.8 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Cruise Mach Number R e l a t i v e F u e l B u r n Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA Figure 6.8. A plot of the relative fuel burn of optimized turbulent designs as func- tions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. 6.2 Laminar Designs 6.2.1 Point Optimizations The optimized NLF aircraft with dierent levels of load alleviation are compared in fig. 6.9. The wing sweeps of the NLF designs are restricted to less than 10 ¶ – a limit that is inevitably reached. The upper wing surfaces are designed for laminar flow while the lower surfaces are assumed to be turbulent. We observe that in all but the MLA+GLA aircraft, the region of extensive laminar flow is restricted to the outboard portions of the wings. This result underscores the severe structural penalties faced by a low-sweep NLF design at transonic speed. The optimizer favors weight savings from improved structural eciency than aerodynamic benefits from extensive laminar flow. The data in table 6.2 show that all of the laminar designs reach their maximum wing sweep of 10 ¶ . This result is also consistent with the strong aerodynamic and aeroelastic incentives to increase wing sweep. Moreover, since the boundary layer analysis does not include crossflow, there is no viscous penalty against high wing sweep. CHAPTER 6. RESULTS 71 (a) Laminar (b) Laminar MLA (c) Laminar GLA (d) Laminar MLA+GLA Figure 6.9. The optimized Mach 0.78 turbulent aircraft with dierent levels of active load alleviation. CHAPTER 6. RESULTS 72 Laminar Laminar MLA Laminar GLA Laminar MLA+GLA W MTOW (lb) 160,904 157,382 158,961 148,897 W fuel (lb) 25,780 25,036 25,032 21,833 W wing (lb) 21,701 20,295 20,783 17,437 T 0 (lb) 21,569 20,756 20,638 17,845 S ref (ft 2 ) 1,503 1,376 1,647 1,489 b (ft) 145 155 141 169 AR 14.0 17.4 12.0 19.1 1/4 (Deg) 10.0 10.0 10.0 10.0 t/c 0.088 0.091 0.091 0.090 L/D 18.7 18.9 19.1 20.9 z i 29,531 30,310 30,191 30,019 z f 41,998 41,784 41,604 42,000 Table 6.2. Summary of Mach 0.78 high sweep NLF aircraft parameters. Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Laminar Laminar MLA Laminar GLA Laminar MLA+GLA Laminar Laminar MLA Laminar GLA Laminar MLA+GLA Wing Weight 1.130 1.057 1.082 0.908 Fuel Weight 0.995 0.966 0.966 0.842 Sea Level Thrust 1.009 0.971 0.966 0.835 L/D 1.027 1.039 1.052 1.148 Cost 1.002 0.991 0.993 0.951 Figure 6.10. A comparison of the optimized laminar aircraft. The performance metrics and configuration parameters are normalized by those of the Mach 0.78 turbulent baseline. CHAPTER 6. RESULTS 73 Figure 6.10 compares the key design parameters of the dierent laminar aircraft. The thrust, L/D, weight and costs are all normalized by the corresponding turbulent baseline values. The NLF aircraft achieves only a negligible 0.5% gain in fuel savings and also costs more to operate. The thin, NLF wing contributes to a 2% improvement in aircraft L/D but weighs 13% more than the baseline. The lackluster performance of the NLF design is therefore directly attributable to the penalties associated with unsweep. The results from the independent application of MLA and GLA to the NLF wing are comparable: both produce less than 1% improvements in cost and more than 3% improvements in fuel burn. While the turbulent designs benefit more from MLA than GLA. The laminar design with its gust-sensitive low-sweep wing stands to benefit more from GLA. As in the case of the turbulent designs, the greatest performance gains come from the coordinated application of both MLA and GLA. The Laminar MLA+GLA aircraft sees an impressive 15% reduction in fuel burn and a 5% reduction in cost relative to the baseline. The improvement comes from both aerodynamics and structural improvements: a 15% increase in average cruise L/D coupled with a 5% reduction in wing weight. The planforms of the optimized NLF laminar aircraft are overlaid in fig. 6.11. The combination of MLA and GLA leads to a 24% increase optimized wingspan. Aircraft designed without GLA have smaller wing areas. This is expected as gust load intensity scales linearly with wing area. In the absence of GLA the optimum wing loading increases. The wing thickness and t/c distributions are compared in fig. 6.12. The significant increases in the outboard t/c in the MLA+GLA wing are once again motivated by the need to increase wing torsional rigidity and improve control authority. Figure 6.13 shows the wing C l and C lmax distributions in maneuver. Unlike its turbu- lent counterpart the laminar MLA+GLA aircraft is lift-critical in a 2.5-g maneuver. CHAPTER 6. RESULTS 74 Laminar Laminar MLA Laminar GLA Laminar MLA+GLA Laminar Laminar MLA Laminar GLA Laminar MLA+GLA S ref 0.91 0.83 1.00 0.90 b 1.06 1.14 1.03 1.24 0.38 0.38 0.38 0.38 t/c 0.92 0.95 0.94 0.94 AR 1.25 1.55 1.07 1.70 Figure 6.11. A comparison of the optimized laminar wing planforms. All parameters are normalized by their values in the Mach 0.78 turbulent baseline. 0 0.5 1 0 0.05 0.1 0.15 0.2 Spanwise Position η t / c Laminar Laminar MLA Laminar GLA Laminar MLA+GLA (a) Wing t/c 0 0.5 1 0 0.5 1 1.5 Spanwise Position η t s ( i n c h ) Laminar Laminar MLA Laminar GLA Laminar MLA+GLA (b) Skin Thickness Figure 6.12. Laminar wing and skin thickness distributions. CHAPTER 6. RESULTS 75 0 0.5 1 0 0.5 1 1.5 2 2.5 Spanwise Position η C l a n d C l m a x Laminar Laminar MLA Laminar GLA Laminar MLA+GLA (a) 2.5-g Maneuver 0 0.5 1 0 0.5 1 1.5 2 2.5 Spanwise Position η C l a n d C l m a x Laminar Laminar MLA Laminar GLA Laminar MLA+GLA (b) 1.3-g Maneuver Figure 6.13. Laminar wing C l and C lmax distributions. The maximum lift constraints limit then the eectiveness of the MLA system. Al- though the reduction in wing sweep has a small, positive eect on maximum lift, the thinner wings need to cope with increased compressibility drag produce a more significant reduction in C Lmax The normalized maneuver and gust-induced wing stresses are overlaid in fig. 6.14. Solid lines correspond to maneuver loads; dashed lines to the maximum gust loads. Figure 6.14a shows that absent any load alleviation the wing of the laminar aircraft is designed by gust loads inboard and by maneuver loads outboard. When comparing the laminar wing stress distribution to its turbulent counterpart in fig. 6.6a it is clear that a greater portion of the laminar wing is sized by gust. The result is attributable to the low aerodynamic damping associated with the nearly unswept wing. The stress distributions in fig. 6.14b show that while the MLA system is successfully suppresses the maneuver stresses, gusts continue to size the wing. Similarly, while the GLA system can eliminate the eects of intermediate and long-wave gusts, the maneuvers emerge to become critical design conditions. The simultaneous application CHAPTER 6. RESULTS 76 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (a) Laminar 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (b) Laminar MLA 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (c) Laminar GLA 0 0.5 1 −1 −0.5 0 0.5 1 B e n d i n g S t r e s s σ / σ a Spanwise Position η 2.5−g (30,000 ft) 1.3−g (40,000 ft) gust (initial cruise) gust (final cruise) gust (10,000 ft) (d) Laminar MLA+GLA Figure 6.14. Maneuver and gust bending stresses for the optimized laminar designs at Mach 0.78. The wing bending stresses ‡ are normalized by the allowable stress ‡ a . The gust stresses represent the maximum values encounter by each wing section at all gust gradient lengths. CHAPTER 6. RESULTS 77 of both load alleviation systems lead to a MLA+GLA design that balances the need to suppress both gust and maneuver loads. The outboard portions of the MLA+GLA wing are once again designed by elastic constraints. 6.2.2 Mach Number Sweeps The variation in cost and fuel burn performance for the laminar aircraft as a function of the cruise Mach number are shown in figs. 6.15 and 6.16. We observe that the perfor- mance of the MLA aircraft is progressively diminished by the need to sustain stronger gust loads at high speed. The more important observation is that the combination of the two load alleviations has unlocked much of the potential of NLF. 0.7 0.72 0.74 0.76 0.78 0.8 0.92 0.94 0.96 0.98 1 1.02 1.04 Cruise Mach Number R e l a t i v e C o s t Laminar Laminar MLA Laminar GLA Laminar MLA+GLA Figure 6.15. A plot of the relative cost of optimized laminar designs as functions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. CHAPTER 6. RESULTS 78 0.7 0.72 0.74 0.76 0.78 0.8 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Cruise Mach Number R e l a t i v e F u e l B u r n Laminar Laminar MLA Laminar GLA Laminar MLA+GLA Figure 6.16. A plot of the relative fuel burn of optimized laminar designs as functions of Mach number. Each point represents an optimized aircraft. The performance metrics are normalized to the Mach 0.78 baseline. 6.3 Turbulent and Laminar Comparison We compare the turbulent and laminar MLA+GLA designs side-by-side in fig. 6.17. In the turbulent design the eciency gains come primarily from increased structural eciency though active control. The Laminar MLA+GLA design on the other hand invests a portion of the weight savings from load alleviation to enable extensive laminar flow. So while the Turbulent MLA+GLA wing manages to be 24% lighter than the baseline, the corresponding wing weight reduction in the laminar wing is only 9.2%. But the addition of laminar flow has led to a 14.8% improvement in aircraft L/D relative to the baseline while the improvement in the turbulent aircraft L/D is limited to 4.5%. An inspection of the Laminar MLA+GLA design shows extensive laminar flow even in the inboard portions of the wing. Figures 6.18 and 6.19 show the trends in cost and fuel burn as we change the cruise Mach number. We compare the aircraft designed without any load alleviation with the respective MLA+GLA designs. The results demonstrate that active load alleviation increases the Mach number at which NLF can be eciently exploited. Without load alleviation, the NLF aircraft has to be designed to cruise at Mach 0.74 or less to realize CHAPTER 6. RESULTS 79 Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Turbulent MLA+GLA Laminar MLA+GLA Turbulent MLA+GLA Laminar MLA+GLA Wing Weight 0.762 0.908 Fuel Weight 0.908 0.842 Sea Level Thrust 0.888 0.835 L/D 1.045 1.148 Cost 0.966 0.951 Figure 6.17. A comparison of the optimized MLA+GLA aircraft parameters. The displayed parameters are normalized by the value of the Mach 0.78 turbulent baseline. 0.7 0.72 0.74 0.76 0.78 0.8 0.92 0.94 0.96 0.98 1 1.02 1.04 Cruise Mach Number R e l a t i v e C o s t Turbulent Turbulent MLA+GLA Laminar Laminar MLA+GLA Figure 6.18. Relative cost of turbulent and laminar designs as functions of Mach number. CHAPTER 6. RESULTS 80 0.7 0.72 0.74 0.76 0.78 0.8 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Cruise Mach Number R e l a t i v e F u e l B u r n Turbulent Turbulent MLA+GLA Laminar Laminar MLA+GLA Figure 6.19. Relative fuel burn of turbulent and laminar designs as functions of Mach number. tangible fuel and cost savings over the turbulent baseline. The Laminar MLA+GLA aircraft on the other hand can achieve savings over turbulent MLA+GLA counterpart at up to Mach 0.80, which match the cruise Mach number of typical airliners. The combination of MLA and GLA therefore alters the terms of the transonic MT trade in favor of a low-sweep, natural laminar flow wing. The results presented in this chapter assume conventional aluminum structures and in-service engines. The gains in eciency are realized through laminar flow, active control and configuration changes. The incorporation of advanced engines and composites would compound the savings. Chapter 7 Sensitivity Studies The results presented in chapter 6 are based on a number of important assumptions: 1) the NLF wing sweep are less than 10 ¶ , 2) the bottom surface of NLF wings are turbulent, 3) all trailing edge control surfaces are available for load alleviation, 4) the maximum load alleviation control surface deflections and rates are restricted to 10 ¶ and 25 ¶ /s respectively and 5) there are no gate compatibility constraints on wingspan. Many of these assumptions are operational and dicult to set in conceptual design. Yet changes in these assumptions can have profound impacts on the optimized design. It is instructive therefore to examine the sensitivities of the design studies to changes in our assumptions. 7.1 NLF Wing Sweep A number of recent studies 11,13 suggest that the 10 ¶ limit on the maximum NLF wing sweep is likely conservative. It is not surprising then that the NLF aircraft without load alleviation should compare unfavorably against its turbulent counterpart. The results in the previous chapter demonstrate that a low-sweep transonic NLF wing only becomes viable after the introduction of aggressive load alleviation technologies. 81 CHAPTER 7. SENSITIVITY STUDIES 82 But unsweeping the wing is not the only way to maintain laminar flow. One can certainly tailor the 3-D wing pressure distribution to suppress both T-S and crossflow instabilities. 12,13 For completeness, the performance of a low-sweep NLF wing should be compared to its high-sweep counterpart. However, the design of a 3-D NLF wing is a non-trivial problem that requires so- phisticated flow solvers and transition prediction tools. In this section we use the 2-D inverse design tools at hand to give an optimistic estimate of 3-D NLF wing performance. We design the Laminar-25 and Laminar-25 MLA+GLA aircraft in fig. 7.1 with a maximum wing sweep of up to 25 ¶ . We assume that the wings of these aircraft are designed with tailored 3-D pressure distributions and/or hybrid laminar flow control (HLFC) technologies to suppress crossflow instabilities without compromising streamwise boundary layer stability. By neglecting all-together the design trade-os associated with stabilizing the crossflow, we arrive by definition at an optimistic projection of what 3-D boundary layer control can achieve. (a) Laminar-25 (b) Laminar-25 MLA+GLA Figure 7.1. Optimized high-sweep NLF design at Mach 0.78. Not surprisingly, fig. 7.1a shows that the sweep of the optimized Laminar-25 wing reaches its upper bound of 25 ¶ . Without the eect of crossflow the optimizer has every incentive to increase sweep to moderate compressibility drag and increase aerodynamic damping. The wing sweep of the Laminar-25 MLA+GLA design is only 18 ¶ – a consequence of the increased eective structural eciency from load alleviation. The CHAPTER 7. SENSITIVITY STUDIES 83 fact that the load alleviation drives the optimum sweep closer to the low sweep NLF wing is important. Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Laminar Laminar−25 Laminar Laminar-25 Wing Weight 1.130 1.088 Fuel Weight 0.995 0.953 Sea Level Thrust 1.009 0.965 L/D 1.027 1.065 Cost 1.002 0.990 Figure 7.2. Comparison of high-sweep laminar-25 aircraft. We compare the Laminar-25 design with its low-sweep counterpart in fig. 7.2. The table shows that the high sweep NLF wing has a higher L/D and lower wing weight, which combine to produce a 1% reduction in cost and a more than 4% reduction in fuel burn. The Laminar-25 MLA+GLA design in fig. 7.3 on the other hand oers only negligible benefits over its low sweep counterpart. The cost is virtually unchanged and the fuel burn savings amounts to less than 1%. The results confirm that as the load alleviation systems moderate the transonic MT trade, the low-sweep NLF wing becomes more and more attractive. This result is of course a function of the Mach number. The performance of the unswept wing is still constrained at high Mach numbers. Figures 7.4 and 7.5 show the variation of the optimized cost and fuel burn metrics as functions of the cruise Mach numbers. As expected the Laminar-25 designs outperform the low-sweep designs at all Mach numbers. After all the additional wing sweep is "free". However, in CHAPTER 7. SENSITIVITY STUDIES 84 Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Laminar MLA+GLA Laminar−25 MLA+GLA Laminar MLA+GLA Laminar-25 MLA+GLA Wing Weight 0.908 0.832 Fuel Weight 0.842 0.833 Sea Level Thrust 0.835 0.835 L/D 1.148 1.156 Cost 0.951 0.948 Figure 7.3. Comparison of high-sweep laminar-25 MLA+GLA aircraft. 0.7 0.72 0.74 0.76 0.78 0.8 0.92 0.94 0.96 0.98 1 1.02 1.04 Cruise Mach Number R e l a t i v e C o s t Laminar Laminar−25 Laminar MLA+GLA Laminar−25 MLA+GLA Figure 7.4. Optimized aircraft cost as functions of Mach number. CHAPTER 7. SENSITIVITY STUDIES 85 0.7 0.72 0.74 0.76 0.78 0.8 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Cruise Mach Number R e l a t i v e F u e l B u r n Laminar Laminar−25 Laminar MLA+GLA Laminar−25 MLA+GLA Figure 7.5. Optimized aircraft fuel burn as functions of Mach number. the MLA+GLA designs the benefits of increased wing sweep are negligible at Mach numbers below 0.78. The results suggest that the combination of active load control and low-sweep NLF wing can be a potential alternative to more sophisticated 3-D NLF wing design and complex active laminar flow control systems. 7.2 MLA and GLA Control Surface Deflection The eectiveness of the load alleviations systems can be a strong function of the practical range of high speed control surface deflections max ”. Yet determining the rational bounds on these control deflections is complex problem – one that involves detailed considerations of hinge moment, reserve control authority, aeroelasticity and actuator design and integration. It is instructive therefore to examine the aircraft design sensitivities to changes in max ”. Figures 7.6 and 7.7 show the variation in optimized MLA+GLA aircraft cost and fuel burn as functions of the maximum allowable high-speed control surface deflections. The cost and fuel burn trends both flatten beyond a deflection of 10 ¶ . The combina- tion of maximum lift constraints, elastic constraints and minimum gauge thickness combine to eliminate further gains from increased deflection bounds. The results CHAPTER 7. SENSITIVITY STUDIES 86 0 5 10 15 0.92 0.94 0.96 0.98 1 1.02 1.04 Allowable Load Control Deflection (Deg) R e l a t i v e C o s t Turbulent MLA+GLA Laminar MLA+GLA Figure 7.6. Optimized MLA+GLA aircraft costs as functions of maximum load alleviation control surface deflections. 0 5 10 15 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Allowable Load Control Deflection (Deg) R e l a t i v e F u e l B u r n Turbulent MLA+GLA Laminar MLA+GLA Figure 7.7. Optimized MLA+GLA aircraft fuel burns as functions of maximum load alleviation control surface deflections. CHAPTER 7. SENSITIVITY STUDIES 87 also demonstrate that our assumed MLA and GLA control surface deflection ranges – based on published parameters of existing load alleviation systems – are sucient to achieve eective load control. 7.3 GLA Control Surface Bandwidth The eectiveness of the GLA systems is a function of actuator bandwidth. In this section we examine the sensitivity of the aircraft design to changes in actuator band- widths. 0 10 20 30 40 0.92 0.94 0.96 0.98 1 1.02 1.04 Load Control Deflection Rate (Deg/s) R e l a t i v e C o s t Turbulent MLA+GLA Laminar MLA+GLA Figure 7.8. MLA+GLA aircraft cost trends as functions of maximum allowable load alleviation control surface deflection rates. Figures 7.8 and 7.9 show the variation in the optimized MLA+GLA aircraft cost and fuel burn as functions of the maximum control surface deflection rate max (d”/dt). The results confirm that slow actuators can indeed restrict the eectiveness of the GLA system. However, the trends for both the laminar and turbulent aircraft flatten out beyond a rate of 20 ¶ /s – a rate that is well within the operating parameters of commercial aircraft ailerons at 35-40 ¶ /s. 55 The diminishing returns can mean one of two things: 1) typical aileron actuators are powerful enough to cope with the high frequency gusts specified by the 1–Cosine criteria or 2) if a gust is fast enough to saturate high-speed aileron actuators then it is also probably too fast to substantially CHAPTER 7. SENSITIVITY STUDIES 88 0 10 20 30 40 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Load Control Deflection Rate (Deg/s) R e l a t i v e F u e l B u r n Turbulent MLA+GLA Laminar MLA+GLA Figure 7.9. MLA+GLA aircraft fuel burn trends as functions of maximum allowable load alleviation control surface deflection rates. excite the wing structure modes. The consistent rate-saturation of the GLA actuators in the dynamic simulations suggests that the second explanation is likely correct. 7.4 GLA with Only Ailerons We assume that all trailing edge control surfaces can be used for both MLA and GLA and that all control surfaces can sustain the same deflection rate. However, aircraft flaps are not typically sized as control surfaces. In fact, most flap actuators on commercial aircraft tend to be quite slow – a deflection rate of less than 2 ¶ /s is typical for complex, multi-slotted flaps 55 . So while flaps can be reasonably allocated to the MLA system to work with anticipated, pseudo-static loads, their utilities in gust encounters are questionable at best. An conservative approach is to simply remove the flaps from the GLA control system and see how the design might change. To this end we set the two inboard GLA control channel gains to 0. This leaves the outboard control surface deflections ” 3 and ” 4 shown in fig. 7.10 for GLA. The MLA system remains unchanged and can schedule all trailing edge control channels. The control arrangement represents a GLA system CHAPTER 7. SENSITIVITY STUDIES 89     Figure 7.10. GLA using only outboard control surfaces. that uses only ailerons. 0.7 0.72 0.74 0.76 0.78 0.8 0.92 0.94 0.96 0.98 1 1.02 1.04 Cruise Mach Number R e l a t i v e C o s t Laminar MLA+GLA GLA with aileron Figure 7.11. Laminar MLA+GLA aircraft cost trends with dierent GLA control allocations. The results in figs. 7.11 and 7.12 demonstrate that most of the savings from the GLA can be achieved with the outboard aileron control channels. This result suggests that the control arrangements found on typical airliners should be adaquate for eective GLA. CHAPTER 7. SENSITIVITY STUDIES 90 0.7 0.72 0.74 0.76 0.78 0.8 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Cruise Mach Number R e l a t i v e F u e l B u r n Laminar MLA+GLA GLA with aileron Figure 7.12. Laminar MLA+GLA aircraft fuel burn trends with dierent GLA control allocations. 7.5 Lower Surface Laminar Flow We study the sensitivities of the aircraft design to laminar flow on the bottom surface. We add the lower surface transition locations x tl as design variables and impose compatibility constraints to ensure laminar flow up to x tl : Re x (x tl ) < Re e 9(x tl ) The optimized MLA+GLA aircraft with turbulent and laminar bottom surfaces are compared in fig. 7.13. The similarity between the two aircraft suggests that only modest changes to the pressure distributions are needed to stabilize the lower surface boundary layer. The normalized aircraft parameters and performance metrics in fig. 7.14 show that maintaining laminar flow on both the upper and lower surfaces nets a tangible 1% improvement in cost and 5% improvement in fuel burn. The total fuel burn reduction over the baseline turbulent design now stands at 20%. The fuel and cost trends plotted in sections 7.5 and 7.5 confirm that the improvement from lower surface laminar flow are consistent across a wide range of cruise Mach CHAPTER 7. SENSITIVITY STUDIES 91 (a) Laminar MLA+GLA (b) Laminar Bottom Surface Figure 7.13. Comparison of the MLA+GLA aircraft designed with turbulent and laminar bottom surfaces. Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Laminar MLA+GLA Bottom Surface NLF Laminar MLA+GLA Bottom Surface NLF Wing Weight 0.908 0.897 Fuel Weight 0.842 0.796 Sea Level Thrust 0.835 0.803 L/D 1.148 1.213 Cost 0.951 0.939 Figure 7.14. Comparison of the MLA+GLA aircraft designed with turbulent and laminar bottom surfaces. CHAPTER 7. SENSITIVITY STUDIES 92 0.7 0.72 0.74 0.76 0.78 0.8 0.92 0.94 0.96 0.98 1 1.02 1.04 Cruise Mach Number R e l a t i v e C o s t Turbulent MLA+GLA Laminar MLA+GLA Laminar Bottom Surface Figure 7.15. Cost trends for the Laminar MLA+GLA aircraft with turbulent and laminar bottom surfaces. The results of the Turbulent MLA+GLA are included for reference. 0.7 0.72 0.74 0.76 0.78 0.8 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Cruise Mach Number R e l a t i v e F u e l B u r n Turbulent MLA+GLA Laminar MLA+GLA Laminar Bottom Surface Figure 7.16. Duel burn trends for the Laminar MLA+GLA aircraft with turbulent and laminar bottom surfaces. The results of the Turbulent MLA+GLA are included for reference. CHAPTER 7. SENSITIVITY STUDIES 93 numbers. The plots also demonstrate that achieving laminar flow on the upper surface still accounts for the bulk of the fuel savings. 7.6 Gate Constraints Active load alleviation systems can greatly increase the wingspan and reduce drag. However, the wingspans of commercial aircraft are limited by more than just stress and aeroelastic constraints. Gate and runway compatibility requirements can restrict the wingspan and pose indirect operational constraints on MLA and GLA eectiveness. Figure 7.17 shows the Mach 0.78 Turbulent, Turbulent MLA+GLA and Laminar MLA+GLA aircraft designed with a 120 feet limit on wingspan. (a) Turbulent (b) Turbulent MLA+GLA (c) Laminar MLA+GLA Figure 7.17. A comparison of gate-constrained aircraft.(b<120 ft) We first ground the analysis with a comparison of the baseline turbulent aircraft designed with and without gate constraints in fig. 7.18. The results, not surprisingly, demonstrate that the baseline is insensitive to the gate constraint.The span restrictions produce only a negligible increase in cost and a modest 2% increase in fuel burn. While the gate constraint reduces the span, the dierence is made up in part by reduced wing weight. The results in figs. 7.19 and 7.20 show that the addition of gate constraints halves CHAPTER 7. SENSITIVITY STUDIES 94 Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Turbulent Gate−constrained Turbulent Gate-constrained Wing Weight 1.000 0.864 Fuel Weight 1.000 1.022 Sea Level Thrust 1.000 1.054 L/D 1.000 0.958 Cost 1.000 1.005 Figure 7.18. A comparison of the turbulent aircraft designed with and without gate constraints. CHAPTER 7. SENSITIVITY STUDIES 95 Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Turbulent MLA+GLA Gate−constrained Turbulent MLA+GLA Gate-constrained Wing Weight 0.762 0.616 Fuel Weight 0.908 0.957 Sea Level Thrust 0.888 0.978 L/D 1.045 0.968 Cost 0.966 0.979 Figure 7.19. A comparison of the Turbulent MLA+GLA aircraft designed with and without gate constraints. CHAPTER 7. SENSITIVITY STUDIES 96 Wing Weight Fuel Weight Sea Level Thrust L/D Cost 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R e l a t i v e V a l u e Laminar MLA+GLA Gate−constrained Laminar MLA+GLA Gate-constrained Wing Weight 0.908 0.718 Fuel Weight 0.842 0.923 Sea Level Thrust 0.835 0.980 L/D 1.148 1.026 Cost 0.951 0.975 Figure 7.20. A comparison of the Laminar MLA+GLA aircraft designed with and without gate constraints. CHAPTER 7. SENSITIVITY STUDIES 97 the fuel savings in both the Turbulent and Laminar MLA+GLA aircraft. Unable to increase the span, the optimizer reduces the wing weight to take advantage of load alleviation. Hence gate-constrained wing is 40% lighter than the baseline. But the weight savings cannot match the benefits from increased span. An aggressive load alleviation system may be hard to justify if aircraft remain constrained by existing airport footprints. However, experience show that gate constraints can evolve with new operational realities. The potentials of load alleviation and other new technologies can motivate re-evaluations of aircraft gate constraints. Chapter 8 Conclusions and Future Work In this thesis we develop a conceptual aircraft design framework that formally in- corporates active load alleviation and natural laminar flow. We design the aircraft concurrently with its load control system. The design framework incorporates both aircraft dynamic simulations and modal solutions of the wing structural dynamics to obtain gust loads. A hybrid-inverse viscous design tool is used to incorporate laminar flow into aircraft design. By directly operating on the wing pressure distribution, we capture the trade-o between structure eciency, compressibility drag and natural laminar flow. A series of design studies demonstrates two important results: first, the gains from the independent application of MLA and GLA control are modest. This is intuitive: as MLA or GLA reduces one type of stress, other loads can emerge as critical design conditions. Only by combining MLA and GLA can we realize significant improvements in eciency. Second, active load alleviation can tilt the balance of the transonic aerostructural trade in favor of high-span, low-sweep laminar flow wings. Without load alleviation, a low-sweep NLF wing oers little real advantage over its turbulent counterpart at high transonic speeds. Active load alleviation can increase the Mach number at which NLF can be eciently exploited. The combination of MLA, GLA and NLF represents therefore a potential alternative to the long-established transonic 98 CHAPTER 8. CONCLUSIONS AND FUTURE WORK 99 paradigm of high-sweep turbulent wing. The results demonstrate that a minimum cost turbulent aircraft designed concurrently with MLA and GLA control systems can a achieve a significant 10% reduction in fuel burn and 3.4% reduction in cost relative to a baseline design without load control. The eciency gains come primarily from reduced weight and increased span though active load control. The corresponding NLF aircraft invests the weight savings from load alleviation to enable extensive laminar flow and reduce drag. In this case the fuel and cost savings grow to 15% and 5% respectively. Sensitivity studies demonstrate that the control requirements for eective active load control are within the parameters of today’s aircraft control actuators. We demonstrate that a GLA system that utilizes only aileron to aect load control can be eective. Comparisons with idealized high-sweep NLF wing also suggest that the combination of active load control and low-sweep NLF wing is a potential alternative to more sophisticated 3-D NLF wing design or complex active laminar flow control (LFC) systems. The design framework developed in this thesis represents only the first step toward the design of more intelligent and responsive wings and their associated load control systems. There is certainly room for improvement. The development and integration of higher fidelity boundary layer solvers that account for compressibility and crossflow would complete the viscous design. Flutter and its suppression are also important considerations for the high span, flexible wings enabled by load alleviation. Finally, while the application of quasi-steady aerodynamics in the gust simulations is likely conservative, 37 this assumption should be validated. The most important area of improvement is in the GLA design process. In this thesis we consider only reactive GLA control laws. Future research examine in more detail the performance of dierent GLA control policies. Detailed exploration of controller design also raises interesting questions of sensor selection and emplacement. Equally important is the needs to account for measurement uncertainties and time delay in CHAPTER 8. CONCLUSIONS AND FUTURE WORK 100 the dynamic simulations. Sophisticated GLA controller design also requires a more physical description of the gust. The 1–Cosine gust may be the FAR specified design criteria, but it does not reflect the stochastic nature of atmospheric gust, nor does it produce the worst-case gust. 37 And since the 1–Cosine gust is fully characterized by the gust gradient length, it can be anticipated by a sophisticated controller. The matched filter technique (MFT) 26 and statistical discrete gust (SDG) 28 represent two attempts to address the shortfalls of the 1–Cosine gust in the context of controller design. For linear systems the MFT method exploits superposition to directly solve for the worst-case gust. 26,27,61 The SDG method on the other hand is an extension of the 1–Cosine gust description with stochastic elements. 62 A logical next step is to incorporate SDG or MFT gusts into the design framework and understand their impact on total aircraft design. However, as the gust description becomes more complex, the combinatorial growth in the number of possible gust waveforms may require a completely dierent optimization strategy. Finally, aerodynamic load alleviation is by no means the only way to increase the wing structural eciency. Pfenninger first proposed the strut-braced wing (SBW) in the 1960s as a means to enable wings of very high span or thin wings that are compatible with transonic laminar flow. 63–66 SBW and aerodynamic load alleviation represent therefore two dierent ways to exploit the same aerostructural synergy. The current design framework can be readily extended to study the relative merits of the dierent load alleviation schemes and their combined eect on natural laminar flow and aircraft design. Appendix A Airfoil Inverse Design In this appendix we present the results of a series of airfoil optimizations to illustrate the workings of the hybrid-inverse airfoil design tool. The objective in each case is to minimize the sum of the section profile and compressibility drag with respect to the pressure variables. We first presents the results of a point airfoil optimization at a chord Reynolds number of 20 million, a wing sweep of 10 ¶ and a freestream Mach number of 0.75. The elastic axis x e is assumed to be at 43% of the chord. The optimization is subject to pressure distribution, boundary layer and airfoil geometry constraints: Pressure Distribution M xm < 1.1 C l > 0.4 C m0 > ≠0.2 Transition Re x (x t ) < Re E9 (x t ) 101 APPENDIX A. AIRFOIL INVERSE DESIGN 102 Geometry t inv (x e ) > 0.09c t inv (x TE ) = 0 The optimized airfoil geometry, pressure distributions and boundary layer properties are shown in fig. A.1. The airfoil designed at the reference condition has 42 counts of parasite drag with upper surface transition at 60% chord. 0 0.5 1 −0.1 0 0.1 z / c x/c (a) Airfoil 0 0.5 1 −1 −0.5 0 0.5 1 x/c C p (b) C p 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 x 10 −3 θ / c x/c (c) Momentum Thickness Figure A.1. Example airfoil optimization geometry, C p and boundary layer momen- tum thickness results. In the example optimization we force transition on the bottom surface near the leading edge. There are two reasons for this simplification: 1) the lower surface of an airfoil is responsible for only about 1/3 of the total parasite drag 12 and 2) slat gaps, track APPENDIX A. AIRFOIL INVERSE DESIGN 103 fairings and contaminants can lead to early transition on the bottom surface despite the presence of favorable pressure gradients. Hence only the upper surface transition x tu point is subject to optimization and the transition compatibility is also only imposed on the upper surface. Finally, the constraint on C m0 is added to impose a trim penalty on severely aft-loaded airfoil designs. 0.72 0.73 0.74 0.75 0.76 0 0.2 0.4 0.6 0.8 1 Mach x t / c C l = 0.35 C l = 0.4 C l = 0.45 (a) x transition 0.72 0.73 0.74 0.75 0.76 0 20 40 60 80 100 Mach C d p ( c o u n t s ) C l = 0.35 C l = 0.4 C l = 0.45 (b) C dp Figure A.2. Optimized airfoil transition and C dp as a function of C l and Mach Œ . The section t/c and Re c are fixed at 9% and 20 million respectively. Figures A.2 and A.3 show the optimized airfoil C dp and x t as a function of variations in C l , t/c and M Œ . Each point corresponds to the results of an optimized airfoil. The performance of the low-sweep NLF section is constrained by compressibility: once the maximum M xm is reached, any increase in M Œ , C l or t/c has to be compensated by re- duced flow acceleration. The result could well be earlier transition and increased drag. The inverse method captures therefore the fundamental tradeo among structural eciency, compressibility and laminar flow. APPENDIX A. AIRFOIL INVERSE DESIGN 104 0.72 0.73 0.74 0.75 0.76 0 0.2 0.4 0.6 0.8 1 Mach x t / c t/c = 0.085 t/c = 0.09 t/c = 0.095 (a) x transition 0.72 0.73 0.74 0.75 0.76 0 20 40 60 80 100 Mach C d p ( c o u n t s ) t/c = 0.085 t/c = 0.09 t/c = 0.095 (b) C dp Figure A.3. Optimized airfoil transition and drag as a function of t/c and Mach Œ . The C l and Re c are fixed at 0.4 and 20 million respectively. 0.72 0.73 0.74 0.75 0.76 0 0.2 0.4 0.6 0.8 1 Mach x t / c Re c = 20 Re c = 30 Re c = 40 (a) x transition 0.72 0.73 0.74 0.75 0.76 0 20 40 60 80 100 Mach C d p ( c o u n t s ) Re c = 20 Re c = 30 Re c = 40 (b) C dp Figure A.4. Optimized airfoil transition and drag as a function of Re c and Mach Œ . The C l and t/c are fixed at 0.4 and 9% respectively. Appendix B Numerical Solution of Second-Order ODEs Modal decomposition can be used to decouple a system of ODEs into scalar inhomo- geneous second-order ODEs: ¨ y i (t) + 2’ i Ê i ˙ y i (t) + Ê i 2 y i (t) = ¯ f i (t) The transient forced response of each mode i can be solved by the superposition of piece-wise impulse responses at discrete timesteps. The time-marching integration 105 APPENDIX B. NUMERICAL SOLUTION OF SECOND-ORDER ODES 106 scheme used in the structural dynamics solver is as follows: 59 A 0 = a Ê i 2 ≠ 2’ i b Ê i 3 A 1 = b Ê i 2 A 2 = y i (t 0 ) ≠A 0 A 3 = ˙ y i (t 0 ) + Ê i ’ i A 2 ≠A 1 Ê di B 1 = e ≠Ê i ’ i t cos(Ê di t) B 2 = e ≠Ê i ’ i t sin(Ê di t) y(t 1 ) = A 0 +A 1 t +A 2 B 1 +A 3 B 2 ˙ y(t 1 ) = A 1 + (Ê di A 3 ≠Ê i ’ i A 2 )B 1 ≠(Ê di A 2 + Ê i ’ i A 3 )B 2 Here the solution y(t) is propagated from step 0 to 1. If the timestep t is constant then only the A 2 and A 3 coecients need to be evaluated at every time step. Appendix C Cost Model In this appendix we detail the methods contained in the extended Air Transport Association (ATA) cost model. 60 The cost objective used in the analysis in the previous chapters is the estimated ticket price c tic ($/pax) in eq. (C.1). In chapters 6 and 7 the ticket price are presented in relative terms against the Mach 0.78 turbulent baseline aircraft. The application reflects the fact that the simple cost model is at best very approximate measure of relative economic performance. The methods detailed in this section are heavy on empiricism. They represent a preliminary attempt to inject cost-sensitivity into the design process. c tic = 1.1 A DOC 100 N seat N pax R +IOC B (C.1) The distinction between N seat and N pax is that the former refers to the number of seats in a one-class configuration while the latter is the number of passengers in the typical 3-class arrangement. The ticket price can be decomposed into direct and indirect operating component. The next section discusses the buildup of the aircraft direct operating cost (DOC). This is followed by the discussion of the indirect operating cost (IOC). 107 APPENDIX C. COST MODEL 108 C.1 Direct Operating Cost The DOC includes all of the cost items that are associated with the flight operations of the aircraft. This includes the cost of fuel, the pilot (which is deemed essential for flight) and maintenance. Also included in the DOC estimates are the cost to insure the aircraft and the cost of depreciation, which are strong functions of the acquisition cost of the aircraft and the utilization rate. The DOC in cents per seat-mile can be written as: DOC = (c fuel +c pilot +c depreciation +c insurance +c maintenance ) 100 N seat C.1.1 Fuel Cost We estimate the combined cost of fuel and lubrication oil as a function of thrust, the price aviation fuel p fuel and the price of lubricants p oil : c fuel = 1.02(p fuel W fuel + 0.135p oil N e T 0 ) R Unless otherwise specified, the assumed fuel and oil prices are $2.5/gal and $20/lb respectively. C.1.2 Pilot Cost The pilot cost is correlated to the number and types of engines mounted on the aircraft. For the twin turbofan configuration in this study the following equation is used: c pilot = Ÿ if 0.05(W MTOW /1000) + 100 V block APPENDIX C. COST MODEL 109 Where the block speed – an important utilization parameter – is estimated as follows: V block = R T m +T cl +T cr Here the climb time T cl and ground and air maneuver time T m are based on historical data. The cruise time in turn represents a small increase in the flight time. T cr = 1.02R + 20 V The estimate of the block time is based on the assumption that the climb and descend segments adds no additional distance to the mission. The descent is assumed to incur no additional flight time. C.1.3 Depreciation and Insurance Costs The depreciation of the capital value of an airplane is dependent to a large degree on the individual airline and the world economic and competitive conditions as the airplane is maintained in a fully airworthy condition throughout its life. c depr = c t + 0.10(c a ) + 0.40N e c t D a U a V b The insurance rate is roughly a function of the aircraft total cost and the utilization rate. A typical insurance rate I ra is in the neighborhood of 0.2%. The insurance cost is estimated using the following relationship: c insurance = I ra (c t ) U a V b APPENDIX C. COST MODEL 110 C.1.4 Maintenance Cost The aircraft maintenance cost includes both labor and material components. The airframe and engine maintenance costs are computed separately to reflect the dierent operational cost sensitivities of the dierent aircraft components. The total aircraft maintenance cost can be written as a sum of the engine and airframe maintenance labor and material costs: c maintenance = 1.8 Ë c (af,labor) +c (af,mat) +c (en,labor) +c (en,mat) È The material costs are dependent on the engine c e and the airframe costs c a . We estimate the engine cost based on a fit of published engine cost to engine T/W. The total aircraft cost is estimated using the per-lb cost of aircraft subsystem collected in Thomas. 60 The weight data of the various components comes from historical data and the PASS aircraft sizing modules. The total aircraft cost is as follows: c t = (c a +c e n e ) Labor Cost The aircraft maintenance labor costs is composed of per-flight-cycle (landing and takeo) and per-flight-hour components. The labor man-hours per flight cycle t ca and per flight hour t ha are extrapolated using historical data: c (af,labor) = [t ha (t block ≠0.25) +t ca ] R L R t ca = 0.05 W a ≠W e 1000 + 6 ≠ 630 Wa 1000 + 120 t ha = 0.59l ca The labor rate R L is a user input and reflects the prevailing wage of aircraft mainte- nance personal. No inflation factor is applied to the labor cost if up-to-date labor rates APPENDIX C. COST MODEL 111 are used. W a refers to the aircraft empty weight excluding the engine weight. The engine labor cost is also described by per-flight-hour and per-cycle components: c (en,labor) = (t he t f +t ce )R L R t ce = (0.6 + 0.027T 0 10,000 )N e t he = (0.3 + 0.03T 0 10,000 )N e Material Cost The aircraft material cost c (af,mat) is correlated to the estimated aircraft cost: c (af,mat) = Ÿ if 3.08c a t f + 6.24c a 10 6 R The engine material cost c (en,mat) is broken down into per flight hour and per flight cycle components: c (en,mat) = Ÿ if c he t f +c ce R c he = 2.5n e c e 10 5 c ce = 2.0n e c e 10 5 C.2 Indirect Operating Cost Indirect operating costs (IOC) as the name may suggest include airline-specific costs that are not directly connected with the flight of the aircraft. They can include the cost of the cabin crew, landing fees, ground handling labor and even advertising. Indirect costs are operational by nature and can be dicult to define. The IOC is APPENDIX C. 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