Design-Oriented Computational Fluid Dynamics-Based Unsteady Aerodynamics for Flight-Vehicle Aeroelastic Shape Optimization

A design-oriented computational fluid dynamics-based unsteady aerodynamic capability has been developed for the generation of shape sensitivities and approximations of aeroelastic constraints for integration into general flight-vehicle multidisciplinary-design-optimization systems. Complex-variable differentiation was used to convert an Euler unsteady solver with boundary-layer coupling into a design-oriented capability. The resulting shape-sensitivity results have been validated using finite difference method sensitivities on selected lifting surfaces: the AGARD wing, the Cohen wing, and the F-5 wing. Because the complex-variable-differentiation technique is numerically exact, the accuracy of the sensitivity computed by the new capability is step-size independent, whereas that of finite difference methods is highly step-size dependent. The resulting capability is computationally efficient. It covers all flight Mach numbers, including the transonic regime. It is accurate and robust, and interfaces seamles...

[1]  Manav Bhatia,et al.  Design-Oriented Thermostructural Analysis with External and Internal Radiation, Part 2: Transient Response , 2009 .

[2]  Robert Thomas Jones,et al.  High speed wing theory , 1960 .

[3]  Eli Livne,et al.  Finite Element-Based Analytic Shape Sensitivities of Local and Global Airframe Buckling Constraints , 1999 .

[4]  D. Liu,et al.  Unsteady supersonic computations of arbitrary wing-body configurations including external stores , 1988 .

[5]  Eli Livne,et al.  Unsteady-Aerodynamic Shape Sensitivities for Airplane Aeroservoelastic Configuration Optimization , 2006 .

[6]  Eli Livne,et al.  Analytic Sensitivities and Approximations in Supersonic and Subsonic Wing/Control Surface Unsteady Aerodynamics , 1997 .

[7]  Eric J. Nielsen,et al.  Sensitivity analysis for the Navier-Stokes equations on unstructured meshes using complex variables , 1999 .

[8]  Jeffrey P. Thomas,et al.  Discrete Adjoint Method for Nonlinear Aeroelastic Sensitivities for Compressible and Viscous Flows , 2013 .

[9]  Joaquim R. R. A. Martins,et al.  AN AUTOMATED METHOD FOR SENSITIVITY ANALYSIS USING COMPLEX VARIABLES , 2000 .

[10]  B. Prasad,et al.  Novel Concepts for Constraint Treatments and Approximations in Efficient Structural Synthesis , 1983 .

[11]  Manav Bhatia,et al.  Design-Oriented Thermostructural Analysis with Internal and External Radiation, Part 1: Steady State , 2008 .

[12]  Walter A. Silva,et al.  Simultaneous Excitation of Multiple-Input Multiple-Output CFD-Based Unsteady Aerodynamic Systems , 2007 .

[13]  J. Alonso,et al.  A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design , 2005 .

[14]  Daniella E. Raveh,et al.  Identification of computational-fluid-dynamics based unsteady aerodynamic models for aeroelastic analysis , 2004 .

[15]  Y. K. Shyy,et al.  An integrated approach to topology, sizing, and shape optimization , 2004 .

[16]  Eli Livne,et al.  Minimum State Unsteady Aerodynamic Shape Sensitivities Using Sensitivity of Optimal Solutions to Problem Parameters , 2007 .

[17]  J. N. Lyness,et al.  Numerical Differentiation of Analytic Functions , 1967 .

[18]  David M. Schuster,et al.  An E-cient Euler Method on Non-Moving Cartesian Grids with Boundary-Layer Correction for Wing Flutter Simulations , 2006 .

[19]  Satyajit S. Ghoman,et al.  ModelCenter-Integrated Reduced Order Multi-fidelity Optimization Scheme for NASA MDAO Framework , 2013 .

[20]  Danny D. Liu,et al.  Unsteady subsonic aerodynamics for bodies and wings with external stores including wake effect , 1993 .

[21]  Layne T. Watson,et al.  Multidisciplinary Design Optimization , 2009, Encyclopedia of Optimization.

[22]  John T. Hwang,et al.  Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models , 2013 .

[23]  C. Mader,et al.  Derivatives for Time-Spectral Computational Fluid Dynamics Using an Automatic Differentiation Adjoint , 2012 .

[24]  Graeme J. Kennedy,et al.  Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations , 2014 .

[25]  P. Chen Damping Perturbation Method for Flutter Solution: The g-Method , 2000 .

[26]  Jaroslaw Sobieszczanskisobieski,et al.  On the sensitivity of complex, internally coupled systems , 1988 .

[27]  W. K. Anderson,et al.  Step-Size Independent Approach for Multidisciplinary Sensitivity Analysis , 2003 .

[28]  Earl H. Dowell,et al.  Doublet-Point Method for Supersonic Unsteady Lifting Surfaces. , 1984 .

[29]  Prabhat Hajela,et al.  A root locus-based flutter synthesis procedure , 1983 .

[30]  Kumar G. Bhatia,et al.  Optimization of complex structures to satisfy flutter requirements , 1971 .

[31]  Peretz P. Friedmann,et al.  Towards integrated multidisciplinary synthesis of actively controlled fiber composite wings , 1990 .

[32]  Kenneth C. Hall,et al.  Sensitivity Analysis of Unsteady Inviscid Flow Through Turbomachinery Cascades , 2001 .

[33]  L. A. Schmit,et al.  Structural synthesis - Its genesis and development , 1981 .

[34]  C. Farhat,et al.  Coupled Analytical Sensitivity Analysis and Optimization of Three-Dimensional Nonlinear Aeroelastic Systems , 2001 .

[35]  Eli Livne,et al.  Analytic sensitivities for shape optimization in equivalent plate structural wing models , 1994 .

[36]  Eli Livne,et al.  ZEUS-DO: Design Oriented CFD-Based Unsteady Aerodynamics for Flight Vehicle Shape Optimization , 2010 .

[37]  Eli Livne,et al.  Design-Oriented Leading-Edge Thrust Force Prediction for Supersonic Lifting Surfaces , 1997 .

[38]  Eli Livne,et al.  Minimum-state unsteady aerodynamics for aeroservoelastic configuration shape optimization of flight vehicles , 2004 .

[39]  E. Livne,et al.  Aeroservoelastic aspects of wing/control surface planform shape optimization , 1995 .

[40]  Raphael T. Haftka,et al.  On repetitive flutter calculations in structural design , 1974 .

[41]  Jeffrey P. Thomas,et al.  Discrete Adjoint Approach for Modeling Unsteady Aerodynamic Design Sensitivities , 2005 .

[42]  Zhichao Zhang,et al.  Overset Euler/Boundary-Layer Solver with Panel-Based Aerodynamic Modeling for Aeroelastic Applications , 2009 .

[43]  Eli Livne,et al.  Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis , 1995 .

[44]  Eli Livne,et al.  Panel Flutter Constraints: Analytic Sensitivities and Approximations Including Planform Shape Design Variables , 1997 .

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

[46]  Garret N. Vanderplaats,et al.  Structural Shape Optimization with MSC/NASTRAN , 1990 .

[47]  J. Martins A coupled-adjoint method for high-fidelity aero-structural optimization , 2002 .

[48]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[49]  D. J. Neill,et al.  ASTROS - A multidisciplinary automated structural design tool , 1987 .

[50]  M. Karpel Sensitivity derivatives of flutter characteristics and stability margins for aeroservoelastic design , 1990 .

[51]  George Trapp,et al.  Using Complex Variables to Estimate Derivatives of Real Functions , 1998, SIAM Rev..

[52]  K. G. Mahmoud,et al.  Structural shape optimization using msc/nastran and sequential quadratic programming , 1999 .

[53]  J. Samareh Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization , 2001 .

[54]  Alexander I. J. Forrester,et al.  Aircraft Aerodynamic Design: Geometry and Optimization , 2014 .

[55]  Eli Livne,et al.  Integrated Aeroservoelastic Optimization: Status and Direction , 1999 .

[56]  Eli Livne,et al.  Sensitivities and Approximations for Aeroservoelastic Shape Optimization with Gust Response Constraints , 2006 .

[57]  Jack W. Langelaan,et al.  Analytic sensitivities and design oriented structural analysis for airplane fuselage shape synthesis , 1997 .