Gradient-free aerodynamic shape optimization using Large Eddy Simulation

Abstract In this paper we demonstrate the ability to perform gradient-free aerodynamic shape optimization using Large Eddy Simulation (LES) with the Mesh Adaptive Direct Search (MADS) optimization algorithm. We first outline the challenges associated with performing gradient-based optimization using LES, specifically chaotic divergence of the adjoint. We then introduce a Dynamic Polynomial Approximation (DPA) procedure, which allows the high-order solution polynomial representation used by the flow solver to be increased, or decreased, depending on the poll size being used by MADS. This allows rapid convergence towards the optimal design space using lower-fidelity simulations, followed by automatic transition to higher-fidelity simulations when close to the optimal design point. We demonstrate the utility of MADS for optimization of simple chaotic problems, specifically the Lorenz system. We then demonstrate the utility of DPA for aerodynamic optimization of a low Reynolds SD7003 airfoil, highlighting the benefits of the binary DPA approach. Finally, we perform aerodynamic optimization of a turbulent SD7003 airfoil with a final design that increases the mean lift to drag ratio by 32% relative to experimental data, demonstrating that shape optimization using LES and MADS is feasible for aerodynamic design.

[1]  Yuan-yuan Wang,et al.  Robust airfoil optimization based on improved particle swarm optimization method , 2011 .

[2]  Freddie D. Witherden,et al.  PyFR: An open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach , 2013, Comput. Phys. Commun..

[3]  Ilan Kroo,et al.  Subsonic wing planform design using multidisciplinary optimization , 1995 .

[4]  C. J. Price,et al.  On the Convergence of Grid-Based Methods for Unconstrained Optimization , 2000, SIAM J. Optim..

[5]  Freddie D. Witherden,et al.  On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools , 2017, J. Comput. Phys..

[6]  T Haftka Raphael,et al.  Multidisciplinary aerospace design optimization: survey of recent developments , 1996 .

[7]  Yudong Zhang,et al.  A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications , 2015 .

[8]  O. Weck,et al.  A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM , 2005 .

[9]  O. Pironneau.  On optimum design in fluid mechanics , 1974 .

[10]  Qiqi Wang,et al.  Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil , 2016 .

[11]  Paul G. Tucker,et al.  Implicit large eddy simulation using the high‐order correction procedure via reconstruction scheme , 2016 .

[12]  R. Haftka,et al.  Multidisciplinary aerospace design optimization: survey of recent developments , 1997 .

[13]  Joaquim R. R. A. Martins,et al.  Natural Laminar-Flow Airfoil Optimization Design Using a Discrete Adjoint Approach , 2020, AIAA Journal.

[14]  Weiguang Yang.  Surgical design for the Fontan procedure using computational fluid dynamics and derivative-free optimization , 2012 .

[15]  Tobias Wunderlich,et al.  Multidisciplinary wing optimization of commercial aircraft with consideration of static aeroelasticity , 2015 .

[16]  Régis Duvigneau,et al.  Low cost PSO using metamodels and inexact pre-evaluation: Application to aerodynamic shape design , 2009 .

[17]  François Guibault,et al.  Multi-fidelity design optimization of Francis turbine runner blades , 2014 .

[18]  M. Selig.  Summary of low speed airfoil data , 1995 .

[19]  Charles Audet,et al.  Derivative-Free and Blackbox Optimization , 2017 .

[20]  Daniel J Poole,et al.  Application of Control Point-Based Aerodynamic Shape Optimization to Two-Dimensional Drag Minimization , 2014 .

[21]  Charles Audet,et al.  A mesh adaptive direct search algorithm for multiobjective optimization , 2009, Eur. J. Oper. Res..

[22]  Qiqi Wang,et al.  Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations , 2012, J. Comput. Phys..

[23]  Joel Brezillon,et al.  The Continuous Adjoint Approach in Aerodynamic Shape Optimization , 2005 .

[24]  Lothar M. Schmitt,et al.  Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling , 2004, Theor. Comput. Sci..

[25]  J. Dennis,et al.  Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation , 2007, Journal of Fluid Mechanics.

[26]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[27]  Oktay Baysal,et al.  Gradient-based aerodynamic shape optimization using alternating direction implicit method , 1997 .

[28]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[29]  Jacques Peter,et al.  Gradient-Based Aerodynamic Optimization with the elsA Software , 2014 .

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

[31]  William Gropp,et al.  CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences , 2014 .

[32]  Scott M. Murman,et al.  Toward a chaotic adjoint for LES , 2017, 1702.06809.

[33]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[34]  Ping He,et al.  DAFoam: An Open-Source Adjoint Framework for Multidisciplinary Design Optimization with OpenFOAM , 2020 .

[35]  Hossein Zare-Behtash,et al.  State-of-the-art in aerodynamic shape optimisation methods , 2018, Appl. Soft Comput..

[36]  J. Xia,et al.  Aerodynamic Optimization Based on Continuous Adjoint Method for a Flexible Wing , 2016 .

[37]  David W. Zingg,et al.  Evaluating the Risk of Local Optima in Aerodynamic Shape Optimization , 2020 .

[38]  Antony Jameson,et al.  Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems , 2003 .

[39]  Brian C. Vermeire,et al.  On the properties of energy stable flux reconstruction schemes for implicit large eddy simulation , 2016, J. Comput. Phys..

[40]  Joaquim R. R. A. Martins,et al.  Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark , 2015 .

[41]  A. U.S.,et al.  Implicit Large Eddy Simulation of Transitional Flows Over Airfoils and Wings , 2009 .

[42]  Feng Liu,et al.  Aerodynamic design optimization by using a continuous adjoint method , 2014 .

[43]  H. T. Huynh,et al.  A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods , 2007 .

[44]  T. Pulliam,et al.  A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization , 2008 .

[45]  Brian C. Vermeire,et al.  Spectral Properties of High-Order Element Types for Implicit Large Eddy Simulation , 2020, Journal of Scientific Computing.

[46]  Christophe Tribes,et al.  Multi-fidelity shape optimization of hydraulic turbine runner blades using a multi-objective mesh adaptive direct search algorithm , 2016 .

[47]  Daniel J Poole,et al.  Comparison of Local and Global Constrained Aerodynamic Shape Optimization , 2014 .

[48]  Qiqi Wang,et al.  Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization , 2016, J. Comput. Phys..

[49]  Ilan Kroo,et al.  Multidisciplinary Considerations in the Design of Wings and Wing Tip Devices , 2010 .

[50]  Claus-Dieter Munz,et al.  High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations , 2014 .

[51]  Patrice Castonguay,et al.  Cross Validation of Aerodynamic Shape Optimization Methodologies for Aircraft Wing-Body Optimization , 2020, AIAA Journal.

[52]  Ajith Abraham,et al.  SEARCH OPTIMIZATION USING HYBRID PARTICLE SUB- SWARMS AND EVOLUTIONARY ALGORITHMS , 2005 .