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

  • Mladen BanovićEmail author
  • Ilias Vasilopoulos
  • Andrea Walther
  • Marcus Meyer
Research Article


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.


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



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.


  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. CrossRefGoogle 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.
  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. MathSciNetCrossRefzbMATHGoogle 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, LondonGoogle Scholar
  5. Dannenhoffer J, Haimes R (2015) Design sensitivity calculations directly on CAD-based geometry. In: 53rd AIAA aerospace sciences meeting, AIAA SciTech Forum. AIAA 2015-1370Google Scholar
  6. Giles M (2002) On the iterative solution of adjoint equations. In: Automatic differentiation of algorithms. Springer, New York, pp 145–151CrossRefGoogle Scholar
  7. Giles MB, Duta MC, Müller JD, Pierce NA (2003) Algorithm developments for discrete adjoint methods. AIAA J 41(2):198–205CrossRefGoogle Scholar
  8. Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation, 2nd edn. Society for Industrial MathematicsGoogle Scholar
  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. MathSciNetCrossRefzbMATHGoogle 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. CrossRefGoogle Scholar
  11. Lapworth L (2004) Hydra-CFD: a framework for collaborative CFD development. In: International conference on scientific and engineering computation (IC-SEC)Google Scholar
  12. Müller JD (2018) AboutFlow benchmark test-case: TU Berlin TurboLab stator. 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. CrossRefzbMATHGoogle Scholar
  14. Nethercote N, Seward J (2007) Valgrind: a framework for heavyweight dynamic binary instrumentation. ACM SIGPLAN Not 42(6):89–100. CrossRefGoogle Scholar
  15. Pascual V, Hascoët L (2018) Mixed-language automatic differentiation. Optim Methods Softw 33(4–6):1192–1206. MathSciNetCrossRefzbMATHGoogle Scholar
  16. Pironneau O (1974) On optimum design in fluid mechanics. J Fluid Mech 64(1):97–110MathSciNetCrossRefGoogle 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):20CrossRefGoogle Scholar
  18. Shahpar S, Lapworth L (2003) PADRAM: parametric design and rapid meshing system for turbomachinery optimisation. In: ASME Turbo ExpoGoogle Scholar
  19. Vandevender WH, Haskell KH (1982) The SLATEC mathematical subroutine library. SIGNUM Newsl 17(3):16–21. CrossRefGoogle 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 ExpoGoogle Scholar
  21. Walther A, Griewank A (2012) Getting started with ADOL-C. Dagstuhl seminar proceedings 09061, pp 181–202Google Scholar
  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):153–68MathSciNetCrossRefGoogle 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: TurbomachineryGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Mladen Banović
    • 1
    Email author
  • Ilias Vasilopoulos
    • 3
  • Andrea Walther
    • 2
  • Marcus Meyer
    • 3
  1. 1.Paderborn UniversityPaderbornGermany
  2. 2.Humboldt University of BerlinBerlinGermany
  3. 3.Rolls-Royce Deutschland Ltd & Co KGBlankenfelde-MahlowGermany

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