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Gradient-free aerodynamic shape optimization using Large Eddy Simulation. (English) Zbl 1521.76221

Summary: 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.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence

Software:

PyFR; DAFoam; OpenFOAM; elsA
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Full Text: DOI

References:

[1] Skinner, S. N.; Zare-Behtash, H., State-of-the-art in aerodynamic shape optimisation methods, Appl Soft Comput, 62, 933-962 (2018)
[2] Slotnick, J.; Khodadoust, A.; Alonso, J.; Darmofal, D.; Gropp, W.; Lurie, E.; Mavriplis, D., CFD vision 2030 study: A path to revolutionary computational aerosciences (2014)
[3] Zingg, D. W.; Nemec, M.; Pulliam, T. H., A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization, Eur J Comput Mech, 17, 1-2, 103-126 (2008) · Zbl 1292.76062
[4] Wakayama, S.; Kroo, I., Subsonic wing planform design using multidisciplinary optimization, J Aircr, 32, 4, 746-753 (1995)
[5] Ning, S. A.; Kroo, I., Multidisciplinary considerations in the design of wings and wing tip devices, J Aircr, 47, 2, 534-543 (2010)
[6] Sobieszczanski-Sobieski, J.; Haftka, R. T., Multidisciplinary aerospace design optimization: Survey of recent developments, Struct Optim, 14, 1, 1-23 (1997)
[7] Wunderlich, T. F., Multidisciplinary wing optimization of commercial aircraft with consideration of static aeroelasticity, CEAS Aeronaut J, 6, 3, 407-427 (2015)
[8] Goldberg, D. E., Genetic algorithms (2006), Pearson Education India
[9] Schmitt, L. M., 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, Theoret Comput Sci, 310, 1-3, 181-231 (2004) · Zbl 1071.68100
[10] Streuber, G. M.; Zingg, D. W., Evaluating the risk of local optima in aerodynamic shape optimization, AIAA J, 1-13 (2020)
[11] Poole, D. J.; Allen, C. B.; Rendall, T., Comparison of local and global constrained aerodynamic shape optimization, (32nd AIAA applied aerodynamics conference (2014)), 3223
[12] Pandya, M. J.; Baysal, O., Gradient-based aerodynamic shape optimization using alternating direction implicit method, J Aircr, 34, 3, 346-352 (1997)
[13] Jameson, A.; Kim, S., Reduction of the adjoint gradient formula for aerodynamic shape optimization problems, AIAA J, 41, 11, 2114-2129 (2003)
[14] Carrier, G.; Destarac, D.; Dumont, A.; Meheut, M.; Salah El Din, I.; Peter, J.; Ben Khelil, S.; Brezillon, J.; Pestana, M., Gradient-based aerodynamic optimization with the elsa software, (52nd aerospace sciences meeting (2014)), 0568
[15] Lyu, Z.; Kenway, G. K.; Martins, J. R., Aerodynamic shape optimization investigations of the common research model wing benchmark, AIAA J, 53, 4, 968-985 (2015)
[16] Martins, J. R.; Alonso, J. J.; Reuther, J. J., A coupled-adjoint sensitivity analysis method for high-fidelity aero-structural design, Opt Eng, 6, 1, 33-62 (2005) · Zbl 1145.76418
[17] Xu, Z.; Xia, J., Aerodynamic optimization based on continuous adjoint method for a flexible wing, Int J Aerosp Eng, 2016 (2016)
[18] Pironneau, O., On optimum design in fluid mechanics, J Fluid Mech, 64, 1, 97-110 (1974) · Zbl 0281.76020
[19] Gauger, N.; Brezillon, J., The continuous adjoint approach in aerodynamic shape optimization, (MEGAFLOW-Numerical flow simulation for aircraft design (2005), Springer), 181-193 · Zbl 1273.76312
[20] Luo, J.; Xiong, J.; Liu, F., Aerodynamic design optimization by using a continuous adjoint method, Sci China Phys Mech Astron, 57, 7, 1363-1375 (2014)
[21] Sivanandam, S.; Deepa, S., Genetic algorithms, (Introduction to genetic algorithms (2008), Springer), 15-37 · Zbl 1129.90001
[22] Praveen, C.; Duvigneau, R., Low cost PSO using metamodels and inexact pre-evaluation: Application to aerodynamic shape design, Comput Methods Appl Mech Engrg, 198, 9-12, 1087-1096 (2009) · Zbl 1229.74112
[23] Wang, Y. Y.; Zhang, B. Q.; Chen, Y. C., Robust airfoil optimization based on improved particle swarm optimization method, Appl Math Mech, 32, 10, 1245 (2011) · Zbl 1329.76306
[24] Zhang, Y.; Wang, S.; Ji, G., A comprehensive survey on Particle Swarm Optimization algorithm and its applications, Math Probl Eng, 2015 (2015) · Zbl 1394.90588
[25] Hassan, R.; Cohanim, B.; De Weck, O.; Venter, G., A comparison of particle swarm optimization and the genetic algorithm, (46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference (2005)), 1897
[26] Grosan, C.; Abraham, A.; Nicoara, M., Search optimization using hybrid particle sub-swarms and evolutionary algorithms, Int J Simul Syst Sci Technol, 6, 10, 60-79 (2005)
[27] He, P.; Mader, C. A.; Martins, J. R.; Maki, K. J., DAfoam: An open-source adjoint framework for multidisciplinary design optimization with openFOAM, AIAA J, 58, 3, 1304-1319 (2020)
[28] Shi, Y.; Mader, C. A.; He, S.; Halila, G. L.; Martins, J. R., Natural laminar-flow airfoil optimization design using a discrete adjoint approach, AIAA J, 58, 11, 4702-4722 (2020)
[29] Blonigan, P. J.; Wang, Q.; Nielsen, E. J.; Diskin, B., Least-squares shadowing sensitivity analysis of chaotic flow around a two-dimensional airfoil, AIAA J, 56, 2, 658-672 (2018)
[30] Wang, Q.; Hu, R.; Blonigan, P., Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations, J Comput Phys, 267, 210-224 (2014) · Zbl 1349.37082
[31] Blonigan, P. J.; Fernandez, P.; Murman, S. M.; Wang, Q.; Rigas, G.; Magri, L., Toward a chaotic adjoint for LES (2017), arXiv preprint arXiv:1702.06809
[32] Bahrami, S.; Tribes, C.; von Fellenberg, S.; Vu, T.; Guibault, F., Multi-fidelity design optimization of Francis turbine runner blades, (IOP conference series: Earth and environmental science, Vol. 22 (2014), IOP Publishing), Article 012029 pp.
[33] Bahrami, S.; Tribes, C.; Devals, C.; Vu, T.; Guibault, F., Multi-fidelity shape optimization of hydraulic turbine runner blades using a multi-objective mesh adaptive direct search algorithm, Appl Math Model, 40, 2, 1650-1668 (2016) · Zbl 1446.76009
[34] Yang, W., Surgical design for the Fontan procedure using computational fluid dynamics and derivative-free optimization (2012), UC San Diego, (Ph.D. thesis)
[35] Marsden, A. L.; Wang, M.; Dennis, J.; Moin, P., Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation, Journal of Fluid Mechanics, 572, 13-36 (2007) · Zbl 1145.76044
[36] Marsden, A. L.; Wang, M.; Mohammadi, B.; Moin, P., Shape optimization for aerodynamic noise control, Center for Turbulence Research Annual Brief (2001), 241-47
[37] Witherden, F. D.; Farrington, A. M.; Vincent, P. E., PyFR: An open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach, Comput Phys Comm, 185, 11, 3028-3040 (2014) · Zbl 1348.65005
[38] Huynh, H. T., A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods, (18th AIAA computational fluid dynamics conference (2007)), 4079
[39] Vermeire, B. C.; Witherden, F. D.; Vincent, P. E., On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools, J Comput Phys, 334, 497-521 (2017)
[40] Vermeire, B. C.; Nadarajah, S.; Tucker, P. G., Implicit large eddy simulation using the high-order correction procedure via reconstruction scheme, Internat J Numer Methods Fluids, 82, 5, 231-260 (2016)
[41] Pereira, C. A.; Vermeire, B. C., Spectral properties of high-order element types for implicit large eddy simulation, J Sci Comput, 85, 2, 1-38 (2020) · Zbl 1457.65236
[42] Vermeire, B. C.; Vincent, P. E., On the properties of energy stable flux reconstruction schemes for implicit large eddy simulation, J Comput Phys, 327, 368-388 (2016) · Zbl 1373.76066
[43] Audet, C.; Dennis, J. E., Mesh adaptive direct search algorithms for constrained optimization, SIAM J Optim, 17, 1, 188-217 (2006) · Zbl 1112.90078
[44] Coope, I. D.; Price, C. J., On the convergence of grid-based methods for unconstrained optimization, SIAM J Optim, 11, 4, 859-869 (2001) · Zbl 1035.90107
[45] Audet, C.; Savard, G.; Zghal, W., A mesh adaptive direct search algorithm for multiobjective optimization, European J Oper Res, 204, 3, 545-556 (2010) · Zbl 1181.90137
[46] Audet, C.; Hare, W., Derivative-free and blackbox optimization (2017), Springer · Zbl 1391.90001
[47] Uranga, A.; Persson, P.-O.; Drela, M.; Peraire, J., Implicit large eddy simulation of transitional flows over airfoils and wings, (19th AIAA computational fluid dynamics (2009), American Institute of Aeronautics and Astronautics), 4131
[48] Fernandez, P.; Wang, Q., Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization, J Comput Phys, 350, 453-469 (2017) · Zbl 1380.76014
[49] Beck, A. D.; Bolemann, T.; Flad, D.; Frank, H.; Gassner, G. J.; Hindenlang, F.; Munz, C.-D., High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations, Internat J Numer Methods Fluids, 76, 8, 522-548 (2014)
[50] Selig, M. S., Summary of low speed airfoil data (1995), SOARTECH publications
[51] Reist, T. A.; Koo, D.; Zingg, D. W.; Bochud, P.; Castonguay, P.; Leblond, D., Cross validation of aerodynamic shape optimization methodologies for aircraft wing-body optimization, AIAA J, 58, 6, 2581-2595 (2020)
[52] Poole, D. J.; Allen, C. B.; Rendall, T., Application of control point-based aerodynamic shape optimization to two-dimensional drag minimization, (52nd aerospace sciences meeting (2014)), 0413
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