Transonic flutter prediction and aeroelastic tailoring for next-generation transport aircraft

Novel commercial transport aircra concepts feature large wing spans to increase their fuel e ciency; these wings are more exible, leading to more potential aeroelastic problems. Furthermore, these aircra y in the transonic ow regime, where utter prediction is di cult. ¿e goals for this thesis are to devise a method to reduce the computational burden of including transonic utter constraints in conceptual design tools, and to o er a potential solution for mitigating utter problems through the use of additive manufacturing techniques, speci cally focusing on a design methodology for lattice structures. To reduce the computational expense of considering transonic utter in conceptual aircra design, a physics-based low-order method for transonic utter prediction is developed, which is based on small unsteady disturbances about a known steady ow solution. ¿e states of the model are the circulation and doublet perturbations, and their evolution equation coe cients are calibrated using o -line unsteady two-dimensional ow simulations. ¿e model is formulated for swept high-aspect ratio wings through strip theory and 3D corrections. ¿e resulting low-order unsteady ow model is coupled to a typical-section structural model (for airfoils) or a beam model (for wings) to accurately predict utter of airfoils and wings. ¿e method is fast enough to permit incorporation of transonic utter constraints in conceptual aircra design calculations, as it only involves solving for the eigenvalues of small state-space systems. ¿is model is used to describe the in uence of transonic utter on nextgeneration aircra con gurations, where it was found that transonic utter constraints can limit the e ciency gains seen by better material technology.

[1]  E. Dowell A simplified theory of oscillating airfoils in transonic flow - Review and extension , 1977 .

[2]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[3]  Dan Mateescu,et al.  Theoretical solutions for unsteady compressible subsonic flows past oscillating rigid and flexible airfoils , 2011 .

[4]  Bret Stanford,et al.  Coupled aerostructural topology optimization using a level set method for 3D aircraft wings , 2015 .

[5]  Esan Mandal,et al.  Solidifying Wireframes , 2005 .

[6]  R. K. Amiet,et al.  Compressibility Effects in Unsteady Thin-Airfoil Theory , 1974 .

[7]  R. Hague,et al.  The design of impact absorbing structures for additive manufacture , 2012 .

[8]  Frédéric Alauzet,et al.  Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error , 2011, SIAM J. Numer. Anal..

[9]  Vojislav Petrovic,et al.  Additive layered manufacturing: sectors of industrial application shown through case studies , 2011 .

[10]  David Walker,et al.  Wing design utilizing topology optimization and additive manufacturing , 2016 .

[11]  M. Giles,et al.  Viscous-inviscid analysis of transonic and low Reynolds number airfoils , 1986 .

[12]  Egbert Torenbeek,et al.  Advanced Aircraft Design: Conceptual Design, Analysis and Optimization of Subsonic Civil Airplanes , 2013 .

[13]  S. Osher,et al.  Level Set Methods for Optimization Problems Involving Geometry and Constraints I. Frequencies of a T , 2001 .

[14]  Matthijs Langelaar,et al.  Topology optimization of 3D self-supporting structures for additive manufacturing , 2016 .

[15]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[16]  Bernardo Cockburn,et al.  An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems , 2009, SIAM J. Numer. Anal..

[17]  S. Rajeev,et al.  Discrete Optimization of Structures Using Genetic Algorithms , 1992 .

[18]  Dan M. Frangopol,et al.  Effects of Damage and Redundancy on Structural Reliability , 1987 .

[19]  Jonathan E. Cooper,et al.  Improved aeroelastic tailoring using tow-steered composites , 2013 .

[20]  Adrien Loseille,et al.  Anisotropic Adaptive Simulations in Aerodynamics , 2010 .

[21]  Kristian Ejlebjerg Jensen Anisotropic Mesh Adaptation and Topology Optimization in Three Dimensions , 2016 .

[22]  Juan J. Alonso,et al.  SUAVE: An Open-Source Environment for Multi-Fidelity Conceptual Vehicle Design , 2015 .

[23]  B. Oskam,et al.  Transonic panel method for the full potential equation applied to multicomponent airfoils , 1985 .

[24]  E Dansberry Bryan,et al.  Physical Properties of the Benchmark Models Program Supercritical Wing , 2003 .

[25]  Bong Wie,et al.  Space Vehicle Dynamics and Control , 1998 .

[26]  Kurt Maute,et al.  An Aeroelastic Topology Optimization Approach for Adaptive Wing Design , 2004 .

[27]  Chi-Wang Shu,et al.  Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems , 2001, J. Sci. Comput..

[28]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[29]  Bernardo Cockburn Discontinuous Galerkin methods , 2003 .

[30]  Earl H. Dowell,et al.  Improved Understanding of Transonic Flutter: A Three-Parameter Flutter Surface , 2004 .

[31]  Gershon Elber,et al.  Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition , 2018, Comput. Aided Des..

[32]  Zahra Zamani,et al.  Curvilinear fiber optimization tools for aeroelastic design of composite wings , 2012 .

[33]  Duc Truong Pham,et al.  Rapid prototyping and rapid tooling—the key enablers for rapid manufacturing , 2003 .

[34]  Earl H. Dowell,et al.  Modeling Viscous Transonic Limit Cycle Oscillation Behavior Using a Harmonic Balance Approach , 2002 .

[35]  A. Michell LVIII. The limits of economy of material in frame-structures , 1904 .

[36]  REDUCED-ORDER AEROELASTIC MODELING USING PROPER-ORTHOGONAL DECOMPOSTIONS , .

[37]  Xiaoping Qian,et al.  Undercut and overhang angle control in topology optimization: A density gradient based integral approach , 2017 .

[38]  Earl H. Dowell,et al.  Parametric Study of Flutter for an Airfoil in Inviscid Transonic Flow , 2003 .

[39]  James K. Guest,et al.  Achieving minimum length scale in topology optimization using nodal design variables and projection functions , 2004 .

[40]  Earl H. Dowell A Modern Course in Aeroelasticity , 1999 .

[41]  E. C. Yates,et al.  Modified-strip-analysis method for predicting wing flutter at subsonic to hypersonic speeds. , 1966 .

[42]  O. Rehme Cellular Design for Laser Freeform Fabrication , 2022 .

[43]  Jennifer Heeg,et al.  FUN3D Analyses in Support of the Second Aeroelastic Prediction Workshop , 2016 .

[44]  Rakesh K. Kapania,et al.  Effect of Flutter on the Multidisciplinary Design Optimization of Truss-Braced-Wing Aircraft , 2015 .

[45]  Harvey J. Greenberg,et al.  Automatic design of optimal structures , 1964 .

[46]  Jennifer Heeg,et al.  Overview and Lessons Learned from the Aeroelastic Prediction Workshop , 2013 .

[47]  Frédéric Vignat,et al.  Evaluating Current CAD Tools Performances in the Context of Design for Additive Manufacturing , 2014 .

[48]  Mark Drela,et al.  Development of the D8 Transport Configuration , 2011 .

[49]  M. Wolcott Cellular solids: Structure and properties , 1990 .

[50]  Feng Wang,et al.  Manufacture of the die of an automobile deck part based on rapid prototyping and rapid tooling technology , 2002 .

[51]  Harry Bikas,et al.  Additive manufacturing methods and modelling approaches: a critical review , 2015, The International Journal of Advanced Manufacturing Technology.

[52]  Frédéric Hecht,et al.  Mesh adaption by metric control for multi-scale phenomena and turbulence , 1997 .

[53]  Frédéric Alauzet,et al.  Continuous Mesh Framework Part II: Validations and Applications , 2011, SIAM J. Numer. Anal..

[54]  Ulf Ringertz,et al.  Design and construction of aeroelastic wind tunnel models , 2015, The Aeronautical Journal.

[55]  Koji Isogai,et al.  On the Transonic-Dip Mechanism of Flutter of a Sweptback Wing , 1979 .

[56]  G. Paulino,et al.  GRAND3 — Ground structure based topology optimization for arbitrary 3D domains using MATLAB , 2015, Structural and Multidisciplinary Optimization.

[57]  D. Rosen Design for Additive Manufacturing: A Method to Explore Unexplored Regions of the Design Space , 2007 .

[58]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[59]  David Nixon,et al.  Perturbation of a Discontinuous Transonic Flow , 1977 .

[60]  L. Sirovich TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I : COHERENT STRUCTURES , 2016 .

[61]  Charbel Farhat,et al.  Adaptation of Aeroelastic Reduced-Order Models and Application to an F-16 Configuration , 2007 .

[62]  P. Schmid,et al.  Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.

[63]  Joaquim R. R. A. Martins,et al.  Towards gradient-based design optimization of flexible transport aircraft with flutter constraints , 2014 .

[64]  Zafer Gürdal,et al.  Stiffness Optimization of Composite Wings with Aeroelastic Constraints , 2013 .

[65]  J. Giannatsis,et al.  Additive fabrication technologies applied to medicine and health care: a review , 2009 .

[66]  Frédéric Alauzet,et al.  Connectivity-change moving mesh methods for high-order meshes: Toward closed advancing-layer high-order boundary layer mesh generation , 2018, 2018 Fluid Dynamics Conference.

[67]  Thomas A. Poulsen A new scheme for imposing a minimum length scale in topology optimization , 2003 .

[68]  Frédéric Hecht,et al.  Anisotropic unstructured mesh adaption for flow simulations , 1997 .

[69]  Mark Drela,et al.  Design Drivers of Energy-Efficient Transport Aircraft , 2011 .

[70]  J. Leishman,et al.  State-space representation of unsteady airfoil behavior , 1990 .

[71]  Ole Sigmund,et al.  Giga-voxel computational morphogenesis for structural design , 2017, Nature.

[72]  Robert A. Canfield,et al.  Joined-Wing Aeroelastic Design with Geometric Nonlinearity , 2005 .

[73]  David W. Rosen,et al.  Synthesis Methods for Lightweight Lattice Structures , 2009 .

[74]  Bryan Glaz,et al.  Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight , 2006 .

[75]  Ulf Ringertz,et al.  On structural optimization with aeroelasticity constraints , 1994 .

[76]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[77]  Peter D. Dunning,et al.  Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads , 2014 .

[78]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[79]  Krzysztof J. Fidkowski,et al.  Output-based space-time mesh adaptation for the compressible Navier-Stokes equations , 2011, J. Comput. Phys..

[80]  Thiemo Kier,et al.  Comparison of Unsteady Aerodynamic Modelling Methodologies with Respect to Flight Loads Analysis , 2005 .

[81]  Joaquim R. R. A. Martins,et al.  High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet , 2002 .

[82]  Scott Townsend,et al.  Aeroelastic Level Set Topology Optimization for a 3D Wing , 2018 .

[83]  Robert Haimes,et al.  On The Construction of Aircraft Conceptual Geometry for High-Fidelity Analysis and Design , 2012 .

[84]  Claus Emmelmann,et al.  Process and Mechanical Properties: Applicability of a Scandium modified Al-alloy for Laser Additive Manufacturing , 2011 .

[85]  H. Ashley,et al.  Aerodynamics of Wings and Bodies , 1965 .

[86]  Satchi Venkataraman,et al.  Investigating Alternate Load Paths and Damage Tolerance of Structures Optimized for Multiple Load Cases , 2009 .

[87]  Steven L. Brunton,et al.  Dynamic Mode Decomposition with Control , 2014, SIAM J. Appl. Dyn. Syst..

[88]  Adrien Loseille,et al.  Metric-orthogonal Anisotropic Mesh Generation☆ , 2014 .

[89]  Jonathan Richard Shewchuk,et al.  Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates , 1997, Discret. Comput. Geom..

[90]  James K. Guest,et al.  Imposing maximum length scale in topology optimization , 2009 .

[91]  Alan Edelman,et al.  Julia: A Fresh Approach to Numerical Computing , 2014, SIAM Rev..

[92]  Andreas Kahlow The History of the Theory of Structures: from Arch Analysis to Computational Mechanics , 2011 .

[93]  G. Rozvany On design-dependent constraints and singular topologies , 2001 .

[94]  M. Giles Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation , 2008 .

[95]  Andreas Schäfer,et al.  Historical and future trends in aircraft performance, cost, and emissions , 2001 .

[96]  Juan J. Alonso,et al.  Fully-implicit time-marching aeroelastic solutions , 1994 .

[97]  Moses Farmer,et al.  Comparison of supercritical and conventional wing flutter characteristics , 1976 .

[98]  Mark Drela,et al.  INTEGRATED SIMULATION MODEL FOR PRELIMINARY AERODYNAMIC, STRUCTURAL, AND CONTROL-LAW DESIGN OF AIRCRAFT , 1999 .

[99]  W. Rodden,et al.  A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows. , 1969 .

[100]  Neil Hopkinson,et al.  Rapid manufacturing : an industrial revolution for the digital age , 2006 .

[101]  Joseba Murua,et al.  Applications of the unsteady vortex-lattice method in aircraft aeroelasticity and flight dynamics , 2012 .

[102]  Martin Leary,et al.  Just-in-time Design and Additive Manufacture of Patient-specific Medical Implants , 2016 .

[103]  Her Mann Tsai,et al.  Calculation of Wing Flutter by a Coupled Fluid-Structure Method , 2001 .

[104]  P. S. Dwyer,et al.  Symbolic Matrix Derivatives , 1948 .

[105]  Thomas P. Kicher,et al.  Optimum Design — Minimum Weight Versus Fully Stressed , 1966 .

[106]  A. Jirásek,et al.  Computational Fluid Dynamics Study of Benchmark Supercritical Wing at Flutter Condition , 2017 .

[107]  Gene F. Franklin,et al.  Model reduction via balanced realizations: an extension and frequency weighting techniques , 1988 .

[108]  Sujit Das,et al.  Energy and emissions saving potential of additive manufacturing: the case of lightweight aircraft components , 2016 .

[109]  Rakesh Srivastava,et al.  The effects of rotational flow, viscosity, thickness, and shape on transonic flutter dip phenomena , 1988 .

[110]  Rakesh K. Kapania,et al.  Wing-Box Weight Optimization Using Curvilinear Spars and Ribs (SpaRibs) , 2011 .

[111]  John W. Miles,et al.  On the Compressibility Correction for Subsonic Unsteady Flow , 1950 .

[112]  Inderjit Chopra,et al.  Aeroelastic Tailoring of Composite Couplings and Blade Geometry of a Helicopter Rotor Using Optimization Methods , 1997 .

[113]  Walter A. Silva,et al.  Application of nonlinear systems theory to transonic unsteady aerodynamic responses , 1993 .

[114]  Uri Kirsch,et al.  Structural Optimization: Fundamentals and Applications , 1993 .

[115]  Earl H. Dowell,et al.  Modeling of Fluid-Structure Interaction , 2001 .

[116]  Adam Jirasek,et al.  Overview and Data Comparisons from the 2ndAeroelastic Prediction Workshop , 2016 .

[117]  Bret Stanford,et al.  Trim and Structural Optimization of Subsonic Transport Wings using Nonconventional Aeroelastic Tailoring , 2014 .

[118]  Krzysztof J. Fidkowski,et al.  Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains , 2013, J. Comput. Phys..

[119]  Ole Sigmund,et al.  Exploiting Additive Manufacturing Infill in Topology Optimization for Improved Buckling Load , 2016 .

[120]  Wei Xu,et al.  Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review. , 2016, Biomaterials.

[121]  Yaoyao Fiona Zhao,et al.  Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing , 2015, Comput. Aided Des..

[122]  Mark Drela,et al.  Design and optimization method for multi-element airfoils , 1993 .

[123]  J. Alonso,et al.  SU2: An Open-Source Suite for Multiphysics Simulation and Design , 2016 .

[124]  Frédéric Alauzet,et al.  Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries , 2017, J. Comput. Phys..

[125]  Damiano Pasini,et al.  Analysis and design of lattice materials for large cord and curvature variations in skin panels of morphing wings , 2015 .

[126]  Ole Sigmund,et al.  On the (non-)optimality of Michell structures , 2016, Structural and Multidisciplinary Optimization.

[127]  Donald L. Kunz,et al.  Analysis of Proprotor Whirl Flutter: Review and Update , 2005 .

[128]  Charbel Farhat,et al.  Sensitivity analysis and design optimization of three‐dimensional non‐linear aeroelastic systems by the adjoint method , 2003 .

[129]  Shijun Guo,et al.  Aeroelastic tailoring of composite wing structures by laminate layup optimization , 2006 .

[130]  David L. Darmofal,et al.  An optimization-based framework for anisotropic simplex mesh adaptation , 2012, J. Comput. Phys..

[131]  Raphael T. Haftka,et al.  Topology optimization of transport wing internal structure , 1996 .

[132]  Martin L. Dunn,et al.  Isogeometric collocation for nonlinear dynamic analysis of Cosserat rods with frictional contact , 2018 .

[133]  Paul F. Jacobs,et al.  Rapid Prototyping & Manufacturing: Fundamentals of Stereolithography , 1992 .

[134]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 2019, Wiley Series in Probability and Statistics.

[135]  James K. Guest,et al.  Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design , 2016 .

[136]  Askin T. Isikveren,et al.  Preliminary Aerostructural Optimization of a Large Business Jet , 2007 .

[137]  David M. Stubbs,et al.  Optomechanical performance of 3D-printed mirrors with embedded cooling channels and substructures , 2015, SPIE Optical Engineering + Applications.

[138]  Martin Leary,et al.  Programmatic Lattice Generation for Additive Manufacture , 2015 .

[139]  Bret Stanford,et al.  Structural Optimization of Platelike Aircraft Wings Under Flutter and Divergence Constraints , 2018, AIAA Journal.

[140]  Rakesh K. Kapania,et al.  Multidisciplinary Design Optimization of Medium-Range Transonic Truss-Braced Wing Aircraft with Flutter Constraint , 2013 .

[141]  Jun Hee Kim,et al.  Fragility Assessment of Light-Frame Wood Construction Subjected to Wind and Earthquake Hazards , 2004 .

[142]  O. Bendiksen Review of unsteady transonic aerodynamics: Theory and applications , 2011 .

[143]  A. Jameson Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[144]  Joaquim R. R. A. Martins,et al.  Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration , 2014 .

[145]  P. Holmes,et al.  The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .

[146]  David W. Rosen,et al.  A HYBRID GEOMETRIC MODELING METHOD FOR LARGE SCALE CONFORMAL CELLULAR STRUCTURES , 2005 .

[147]  J. Katz,et al.  Low-Speed Aerodynamics , 1991 .

[148]  J. Sethian,et al.  Structural Boundary Design via Level Set and Immersed Interface Methods , 2000 .

[149]  Charles L. Thomas,et al.  Rapid prototyping of large scale aerospace structures , 1996, 1996 IEEE Aerospace Applications Conference. Proceedings.

[150]  Bernardo Cockburn,et al.  A hybridizable discontinuous Galerkin method for linear elasticity , 2009 .

[151]  Joaquim R. R. A. Martins,et al.  Aerostructural optimization of the D8 wing with varying cruise mach numbers , 2017 .