Algorithmic differentiation of an industrial airfoil design tool coupled with the adjoint CFD method

Abstract

Computer Aided Design (CAD) systems and tools are considered essential for industrial design. They construct and manipulate the geometry of a certain component with an arbitrary set of design parameters. However, it is a challenging task to incorporate the parametric definition in a gradient-based shape optimization loop, since the CAD libraries usually do not provide shape sensitivities w.r.t. the design parameters of the model to be optimized. Typically, these derivatives are evaluated with inaccurate finite differences. On the contrary, to obtain the exact derivative information, algorithmic differentiation (AD) can be applied if the CAD sources are available. In this study, the Rolls-Royce in-house airfoil design and blade generation tool Parablading is differentiated using the AD software tools ADOL-C and Tapenade. The differentiated CAD tool is coupled with a discrete adjoint CFD solver that is part of the Rolls-Royce in-house HYDRA suite of codes, also produced by algorithmic differentiation. This differentiated design chain is used to perform gradient-based shape optimization of the TU Berlin TurboLab stator test-case w.r.t.  minimize the total pressure loss and exit angle deviation objectives.

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References

  1. Agarwal D, Robinson TT, Armstrong CG, Marques S, Vasilopoulos I, Meyer M (2018) Parametric design velocity computation for CAD-based design optimization using adjoint methods. Eng Comput 34(2):225–239. https://doi.org/10.1007/s00366-017-0534-x

    Article  Google Scholar 

  2. Auriemma S, Banović M, Walther A, Mykhaskiv O, Müller JD (2018) Applications of differentiated CAD kernel in gradient-based aerodynamic shape optimisation. In: 2018 joint propulsion conference. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2018-4828

  3. Banović M, Mykhaskiv O, Auriemma S, Walther A, Legrand H, Müller JD (2018) Algorithmic differentiation of the open CASCADE technology CAD kernel and its coupling with an adjoint CFD solver. Optim Methods Softw. https://doi.org/10.1080/10556788.2018.1431235

    MathSciNet  Article  MATH  Google Scholar 

  4. Bestle D, Flassig P (2010) Optimal aerodynamic compressor blade design considering manufacturing noise. In: 8th Association for Structural and Multidisciplinary Optimization in the UK/International Society for Structural and Multidisciplinary Optimization (ASMO-UK/ISSMO) conference on engineering design optimization, London

  5. Dannenhoffer J, Haimes R (2015) Design sensitivity calculations directly on CAD-based geometry. In: 53rd AIAA aerospace sciences meeting, AIAA SciTech Forum. AIAA 2015-1370

  6. Giles M (2002) On the iterative solution of adjoint equations. In: Automatic differentiation of algorithms. Springer, New York, pp 145–151

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

    Article  Google Scholar 

  8. Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation, 2nd edn. Society for Industrial Mathematics

  9. Hascoët L, Pascual V (2013) The Tapenade automatic differentiation tool: principles, model, and specification. ACM Trans Math Softw 39(3):20:1–20:43. https://doi.org/10.1145/2450153.2450158

    MathSciNet  Article  MATH  Google Scholar 

  10. Jameson A (1989) Aerodynamic design via control theory. In: Chao CC, Orszag SA, Shyy W (eds) Recent advances in computational fluid dynamics, pp 377–401. Springer, Berlin. https://doi.org/10.1007/978-3-642-83733-3_14

    Google Scholar 

  11. Lapworth L (2004) Hydra-CFD: a framework for collaborative CFD development. In: International conference on scientific and engineering computation (IC-SEC)

  12. Müller JD (2018) AboutFlow benchmark test-case: TU Berlin TurboLab stator. http://aboutflow.sems.qmul.ac.uk/events/munich2016/benchmark/testcase3/. Accessed 23 Oct 2018

  13. Mykhaskiv O, Banović M, Auriemma S, Mohanamuraly P, Walther A, Legrand H, Müller JD (2018) NURBS-based and parametric-based shape optimization with differentiated CAD kernel. Comput Aided Design Appl. https://doi.org/10.1080/16864360.2018.1462881

    Article  MATH  Google Scholar 

  14. Nethercote N, Seward J (2007) Valgrind: a framework for heavyweight dynamic binary instrumentation. ACM SIGPLAN Not 42(6):89–100. https://doi.org/10.1145/1273442.1250746

    Article  Google Scholar 

  15. Pascual V, Hascoët L (2018) Mixed-language automatic differentiation. Optim Methods Softw 33(4–6):1192–1206. https://doi.org/10.1080/10556788.2018.1435650

    MathSciNet  Article  MATH  Google Scholar 

  16. Pironneau O (1974) On optimum design in fluid mechanics. J Fluid Mech 64(1):97–110

    MathSciNet  Article  Google Scholar 

  17. Sanchez Torreguitart I, Verstraete T, Mueller L (2018) Optimization of the LS89 axial turbine profile using a CAD and adjoint based approach. Int J Turbomach Propuls Power 3(3):20

    Article  Google Scholar 

  18. Shahpar S, Lapworth L (2003) PADRAM: parametric design and rapid meshing system for turbomachinery optimisation. In: ASME Turbo Expo

  19. Vandevender WH, Haskell KH (1982) The SLATEC mathematical subroutine library. SIGNUM Newsl 17(3):16–21. https://doi.org/10.1145/1057594.1057595

    Article  Google Scholar 

  20. Vasilopoulos I, Flassig P, Meyer M (2017) CAD-based aerodynamic optimization of a compressor stator using conventional and adjoint-driven approaches. In: ASME Turbo Expo

  21. Walther A, Griewank A (2012) Getting started with ADOL-C. Dagstuhl seminar proceedings 09061, pp 181–202

  22. Xu S, Jahn W, Müller JD (2013) CAD-based shape optimisation with CFD using a discrete adjoint. Int J Numer Meth Fluids 74(3):153–68

    MathSciNet  Article  Google Scholar 

  23. Xu S, Radford D, Meyer M, Müller JD (2015) CAD-based adjoint shape optimisation of a one-stage turbine with geometric constraints. In: ASME Turbo Expo 2015 2C: Turbomachinery

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Acknowledgements

The authors are very thankful to Dr.-Ing. Peter Flassig and Dr.-Ing. André Huppertz (Rolls-Royce Deutschland) for their support related to the Parablading tool and its parametrization principles. This research is part of the IODA Project—Industrial Optimal Design using Adjoint CFD. IODA is Marie Skłodowska-Curie Innovative Training Network funded by the European Union’s Horizon 2020 research and innovation programme under the Grant Agreement No. 642959.

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Correspondence to Mladen Banović.

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Banović, M., Vasilopoulos, I., Walther, A. et al. Algorithmic differentiation of an industrial airfoil design tool coupled with the adjoint CFD method. Optim Eng 21, 1221–1242 (2020). https://doi.org/10.1007/s11081-019-09474-x

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Keywords

  • Algorithmic differentiation
  • Industrial CAD tool
  • Adjoint CFD method
  • Gradient-based optimization