Skip to main content
SpringerLink
Log in

Efficient aerodynamic shape optimization by structure exploitation

  • Published:
Optimization and Engineering Aims and scope Submit manuscript

Abstract

In this paper, we consider an optimization problem for the complete design chain of an airfoil. Starting with a parameter vector, one has to perform a three step procedure to evaluate the desired objective: Generate a grid around the airfoil, compute the flow around the airfoil, and compute the objective. Applying a gradient-based optimization method, one has to provide derivatives for this complex process. In the present paper, we propose the advanced use of automatic differentiation to compute the required gradient information. We report numerical results together with a mesh independency study and an analysis of the optimization process for an inviscid RAE2822 airfoil under transonic flight conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Barttfeld M, Alleborn N, Durst F (2006) Dynamic optimization of multiple-zone air impingement drying processes. Comput Chem Eng 30:467–489

    Article  Google Scholar 

  • Biegler LT, Zavala VM (2009) Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization. Comput Chem Eng 33:575–582

    Article  Google Scholar 

  • Bücker M, Corliss G, Hovland P, Norris B, Naumann U (eds) (2005) Automatic differentiation: applications, theory, and tools. Springer, Berlin

    Google Scholar 

  • Christianson B (1994) Reverse accumulation and attractive fixed points. Optim Methods Softw 3:311–326

    Article  Google Scholar 

  • Corliss G, Faure C, Griewank A, Hascoët L, Naumann U (eds) (2001) Automatic differentiation: from simulation to optimization. Springer, New York

    Google Scholar 

  • Giering R, Kaminski T (1998) Recipes for adjoint code construction. ACM Trans Math Softw 24:437–474

    Article  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  • Griewank A, Juedes D, Utke J (1996) ADOL-C: a package for the automatic differentiation of algorithms written in C/C++. ACM Trans Math Softw 22:131–167

    Article  MATH  Google Scholar 

  • Hascoët L, Pascual V (2004) Tapenade 2.1 user’s guide. Technical report 300, INRIA

  • Heinrich R (2006) Implementation and usage of structured algorithms within an unstructured CFD-code. Notes on numerical fluid mechanics and multidisciplinary design, vol 92

    Google Scholar 

  • Hounjet MHL, Prananta BB, Zwaan R (1995) A thin layer Navier-Stokes solver and its application for aeroelastic analysis of an airfoil in transonic flow. In: Proceedings international forum on aeroelasticity and structural dynamics, pp 1.1–1.9

    Google Scholar 

  • Jameson A (1988) Aerodynamic design via control theory. J Sci Comput 3(3):233–261

    Article  MATH  Google Scholar 

  • Jameson A, Reuther J (1994) Control theory based on airfoil design using the Euler equations. In: AIAA proceedings 94-4272-CP

    Google Scholar 

  • Jameson A, Martinelli L, Pierce NA (1998) Optimum aerodynamic design using the Navier-Stokes equations. Theor Comput Fluid Dyn 10(1–4):213–237

    Article  MATH  Google Scholar 

  • Kroll N, Gerhold Th et al. (2001) Parallel large scale computations for aerodynamic aircraft design with the German CFD system MEGAFLOW. In: Proceedings of ‘Parallel CFD 2001’, Egmond aan Zee

    Google Scholar 

  • Kroll N, Rossow CC, Becker K, Thiele F (2000) The MEGAFLOW project. Aerosp Sci Technol 4:223–237

    Article  MATH  Google Scholar 

  • Oyama A, Liou M-S, Obayashi S (2004) Transonic axial-flow blade optimization: Evolutionary algorithms/three-dimensional Navier-Stoke solver. J Propuls Power 20(4):612–619

    Article  Google Scholar 

  • Periaux J, Deconinck H (eds) (2006) Introduction to optimization and multidisciplinary design. Lecture series, vol. 2006-03. von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode. ISBN 2-930389-65-6

    Google Scholar 

  • Rossow C-C (2000) A flux splitting scheme for compressible and incompressible flows. J Comput Phys 164:104–122

    Article  MATH  Google Scholar 

  • Schlenkrich S, Walther A, Gauger NR, Heinrich R (2008) Differentiating fixed point iterations with ADOL-C: Gradient calculation for fluid dynamics. In: Bock HG, Kostina E, Phu HX, Rannacher R (eds) Modeling, simulation and optimization of complex processes—proceedings of the third international conference on high performance scientific computing 2006, pp 499–508

    Google Scholar 

  • Swanson RC, Turkel E (1997) Multistage scheme with multigrid for Euler and Navier-Stokes equations (components and analysis). Technical Report 3631, NASA

  • Wächter A, Biegler L (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JF, Periaux J, Sefrioui M (2002) Parallel evolutionary algorithms for optimization problems in aerospace engineering. J Comput Appl Math 149(1):155–169

    Article  MATH  Google Scholar 

  • Widhalm M, Rossow C-C (2004) Improvement of upwind schemes with the least square method in the DLR TAU code. Notes Numer Fluid Mech 87

Download references

Acknowledgement

The authors gratefully acknowledge the support of the DFG Priority Program 1253 entitled Optimization with Partial Differential Equations.

Author information

Authors and Affiliations

  1. Computational Mathematics Group, CCES, RWTH Aachen University, Aachen, Germany

    Nicolas Gauger & Emre Özkaya

  2. Institute of Mathematics, Paderborn University, Paderborn, Germany

    Andrea Walther

  3. Institute of Computer Sciences, Humboldt University Berlin, Berlin, Germany

    Carsten Moldenhauer

Authors
  1. Nicolas Gauger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Walther
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Emre Özkaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Carsten Moldenhauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicolas Gauger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gauger, N., Walther, A., Özkaya, E. et al. Efficient aerodynamic shape optimization by structure exploitation. Optim Eng 13, 563–578 (2012). https://doi.org/10.1007/s11081-011-9184-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11081-011-9184-9

Keywords

Search

Navigation