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Adjoint-Based Aerodynamic Optimisation of Wing Shape Using Non-uniform Rational B-Splines

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Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 49))

Abstract

Numerical shape optimisation with adjoint CFD is applied using the NURBS-based parametrisation method with continuity constraints (NSPCC) for aerodynamically optimising three dimensional surfaces. The ONERA M6 wing is re-parametrised with NURBS surfaces including weight adjustments to represent the three dimensional wing accurately, resulting in fewer control points and smoother variation of curvature. The NSPCC CAD kernel is coupled with the in-house flow and adjoint solver STAMPS and a gradient-based optimiser to minimise the drag of the ONERA M6 wing in transonic Euler flow conditions. Optimisation results are presented for the B-Spline and NURBS parametrisations.

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References

  • Auriemma S, Banovic M, Mykhaskiv O, Legrand H, Müller JD, Walther A (2016) Optimisation of a U-bend using CAD-based adjoint method with differentiated cad kernel. In: ECCOMAS Congress

    Google Scholar 

  • Bartholomew-Biggs M (2008) Nonlinear optimization with engineering applications, vol 19. Springer, Berlin

    Google Scholar 

  • Christakopoulos F, Jones D, Müller J-D (2011) Pseudo-timestepping and validation for automatic differentiation derived code. Comput Fluids 46(1):174–179

    Article  MathSciNet  Google Scholar 

  • Giles MB, Duta MC, Müller J-D, Pierce NA (2003) Algorithm developments for discrete adjoint methods. AIAA J 41(2):198–205

    Article  Google Scholar 

  • Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation. PA, 2nd edn, SIAM, Philadelphia

    Google Scholar 

  • Gugala M (2017) Output-based mesh adaptation using geometric multi-grid for error estimation. PhD thesis, Queen Mary University of London

    Google Scholar 

  • Gugala M, Xu S, Mueller J-D (2014) Node-based vs CAD-based Approach in CFD Adjoint- based Shape Optimisation. In: International Conference on Engineering and Applied Sciences Optimization, Kos, Greece

    Google Scholar 

  • Hascoët L, Pascual V (2004) Tapenade 2.1 user’s guide. Technical Report 0300, INRIA

    Google Scholar 

  • Hascoët L, Pascual V (2013) The Tapenade Automatic Differentiation tool: principles, Model, and Specification. ACM Trans Math Softw 39(3):

    Google Scholar 

  • Jakobsson S, Amoignon O (2007) Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization. Comput Fluids 36(6):1119–1136

    Article  Google Scholar 

  • Jameson A (1988) Aerodynamic design via control theory. J Sci Comput 3:233–260

    Article  Google Scholar 

  • Jameson A (1995) Optimum aerodynamic design using CFD and control theory. AIAA paper 1729:124–131

    Google Scholar 

  • Jameson A, Vassberg A (2000) Studies of alternative numerical optimization methods applied to the Brachistochrone problem. Comput Fluid Dyn J 9(3):

    Google Scholar 

  • Jaworski A, Müller J-D (2008) Toward modular multigrid design optimisation. In: Bischof C, Utke J (eds) Lecture notes in computational science and engineering, vol 64. Springer, New York, pp 281–291

    Google Scholar 

  • Jesudasan R, Zhang X, Gugala M, Mueller JD (2016) CAD-free vs CAD-based parametrisation method in adjoint-based aerodynamic shape optimization. In: ECCOMAS Congress 2016

    Google Scholar 

  • Jones D, Christakopoulos F, Müller J-D (2011) Preparation and assembly of adjoint CFD codes. Comput Fluids 46(1):282–286

    Article  Google Scholar 

  • Lépine J, Guibault F, Trépanier J-Y, Pépin F (2001) Optimized nonuniform rational B-spline geometrical representation for aerodynamic design of wings. AIAA J 39(11):2033–2041

    Article  Google Scholar 

  • Liu D, Nocedal J (1989) On the limited memory bfgs method for large scale optimization. Math Program 45(1):503–528

    Article  MathSciNet  Google Scholar 

  • Müller J-D, Gugala M, Xu S, Hüchelheim J, Mohanamuraly P, Imam-Lawal OR (2016) Introducing STAMPS: an open-source discrete adjoint CFD solver using source-transformation ad. In: 11th ASMO UK/ISSMO/NOED2016: International Conference on Numerical Optimisation Methods for Engineering Design

    Google Scholar 

  • Naumann U (2011) The art of differentiating computer programs: an introduction to algorithmic differentiation. SIAM

    Google Scholar 

  • Nocedal J (1980) Updating quasi-Newton matrices with limited storage. Math Comput 35(151):773–782

    Article  MathSciNet  Google Scholar 

  • Painchaud-Ouellet Simon, Tribes Christophe, Trépanier Jean-Yves, Pelletier Dominique (2006) Airfoil shape optimization using a nonuniform rational B-splines parametrization under thickness constraint. AIAA J 44(10):2170–2178

    Article  Google Scholar 

  • Piegl L, Tiller W (1997) The NURBS Book. 2nd edn

    Google Scholar 

  • Pironneau O (1974) On optimum design in fluid mechanics. J Fluid Mech 64:97–110

    Article  MathSciNet  Google Scholar 

  • Pratt MJ (2001) Introduction to ISO 10303–the STEP standard for product data exchange. J Comput Inf Sci Eng 1(1):102

    Article  Google Scholar 

  • Robinson TT, Armstrong CG, Chua HS, Othmer C, Grahs T (2009) Sensitivity-based optimization of parameterised CAD geometries. In: 8th World Congress on Structural and Multidisciplinary Optimisation, Lisbon

    Google Scholar 

  • Samareh JA (2004) Aerodynamic shape optimization based on free-form deformation. AIAA, paper 4630:1–13. https://doi.org/10.2514/6.2004-4630

    Article  Google Scholar 

  • Schmidt S, Ilic C, Gauger N, Schulz V (2008) Shape gradients and their smoothness for practical aerodynamic design optimization. DFG SFB 1253 Preprint-Number SPP1253-10-03, Universität Erlangen

    Google Scholar 

  • Schmitt V, Charpin F (1979) Pressure distributions on the Onera-M6-wing at transonic mach numbers. Experimental data base for computer program assessment, 4

    Google Scholar 

  • Spivak M (1999) A comprehensive introduction to differential geometry. Publish or perish, Houston

    MATH  Google Scholar 

  • Squire W, Trapp G (1998) Using complex variables to estimate derivatives of real functions. SIAM-Review 10(1):110–112

    Article  MathSciNet  Google Scholar 

  • Witteveen JAS, Bijl H (2009) Explicit mesh deformation using inverse distance weighting interpolation. In: 19th AIAA Computational Fluid Dynamics, p 3996

    Google Scholar 

  • Xu S, Jahn W, Müller J-D (2014) CAD-based shape optimisation with CFD using a discrete adjoint. Int J Numer Methods Fluids 74(3):153–168

    Article  MathSciNet  Google Scholar 

  • Xu S, Radford D, Meyer M, Müller J-D (2015) CAD-based adjoint shape optimisation of a one-stage turbine with geometric constraints. ASME Turbo Expo 2015, GT2015-42237

    Google Scholar 

  • Zhang X, Wang Y, Gugala M, Müller J-D (2016) Geometric continuity constraints for adjacent NURBS patches in shape optimisation. In: ECCOMAS Congress 2

    Google Scholar 

Download references

Acknowledgements

The first author would like to thank the China Scholarship Council (No. 201306230097) and Queen Mary University of London for funding this research. The second author acknowledges the support from the IODA project (http://ioda.sems.qmul.ac.uk), funded by the European Union HORIZON 2020 Framework Programme for Research and Innovation under Grant Agreement No. 642959.

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Authors and Affiliations

  1. School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Xingchen Zhang, Rejish Jesudasan & Jens-Dominik Müller

Authors
  1. Xingchen Zhang
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  2. Rejish Jesudasan
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  3. Jens-Dominik Müller
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Corresponding author

Correspondence to Xingchen Zhang .

Editor information

Editors and Affiliations

  1. ISDEFE , Madrid, Spain

    Esther Andrés-Pérez

  2. Fluid Mechanics and Propulsion Department, Universidad Politécnica de Madrid, Madrid, Spain

    Leo M. González

  3. International Center for Numerical Methods in Engineering (CIMNE), Barcelone, Spain

    Jacques Periaux

  4. Chair for Scientific Computing, Technische Universität Kaiserslautern, Kaiserslautern, Rheinland-Pfalz, Germany

    Nicolas Gauger

  5. Department of Fluid Mechanics, Italian Aerospace Research Center, Capua, Italy

    Domenico Quagliarella

  6. School of Mechanical Engineering, National Technical University of Athens, Athens, Greece

    Kyriakos Giannakoglou

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Zhang, X., Jesudasan, R., Müller, JD. (2019). Adjoint-Based Aerodynamic Optimisation of Wing Shape Using Non-uniform Rational B-Splines. In: Andrés-Pérez, E., González, L., Periaux, J., Gauger, N., Quagliarella, D., Giannakoglou, K. (eds) Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems. Computational Methods in Applied Sciences, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-89890-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-89890-2_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-89889-6

  • Online ISBN: 978-3-319-89890-2

  • eBook Packages: EngineeringEngineering (R0)

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