Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping

Eirikur Jonsson, Leifur Leifsson, Slawomir Koziel

Abstract

This paper presents an efficient aerodynamic design optimization methodology for wings in transonic flow. The approach replaces the computationally expensive high-fidelity CFD model in an iterative optimization process with a corrected polynomial approximation model constructed by a cheap low-fidelity CFD model. The output space mapping technique is used to correct the approximation model to yield an accurate predictor of the high-fidelity one. Both CFD models employ the RANS equations with the Spalart-Allmaras turbulence model, but the low-fidelity one uses a coarse mesh resolution and relaxed convergence criteria. Our method is applied to a constrained lift maximization of a rectangular wing at transonic conditions with 3 design variables. The optimized designs are obtained by using 50 low-fidelity CFD model evaluations to set up the approximation model and 7 to 8 high-fidelity model evaluations, equivalent to around 10 high-fidelity CFD model evaluations.

References

  1. Abbott, I. and Von Doenhoff, A. (1959). Theory of wing sections: including a summary of airfoil data. Dover.
  2. Alexandrov, N. and Lewis, R. (2001). An overview of firstorder model management for engineering optimization. Optimization and Engineering, 2(4):413-430.
  3. ANSYS (2010). ANSYS FLUENT Theory Guide. ANSYS, Southpointe 275 Thecnology Drive Canonburg PA 15317, release 13.0 edition.
  4. Bandler, J., Cheng, Q., Dakroury, S., Mohamed, A., Bakr, M., Madsen, K., and Sondergaard, J. (2004). Space mapping: the state of the art. Microwave Theory and Techniques, IEEE Transactions on, 52(1):337-361.
  5. Echeverria, D. and Hemker, P. (2005). Space mapping and defect correction. Computational Methods in Applied Mathematics, 5(2):107-136.
  6. Forrester, A. and Keane, A. (2009). Recent advances in surrogate-based optimization. Progress in Aerospace Sciences, 45(1-3):50-79.
  7. Haikin, S. (1998). Neural Networks: A Comprehensive Foundation. Prentice Hall.
  8. Journel, A. and Huijbregts, C. (1978). Mining geostatistics. Academic press.
  9. Koziel, S., Cheng, Q., and Bandler, J. (2008). Space mapping. Microwave Magazine, IEEE, 9(6):105-122.
  10. Koziel, S., Ciaurri, D. E., and Leifsson, L. (2011). Surrogate-based methods. In Computational optimization and applications in engineering and industry, volume 359. Springer.
  11. Koziel, S. and Leifsson, L. (2012). Knowlegde-based airfoil shape optimization using space mapping. In 30th AIAA Applied Aerodynamics Conference.
  12. Leifsson, L. and Koziel, S. (2011a). Airfoil shape optimization using variable-fidelity modeling and shapepreserving response prediction. In Comp. Opt., Methods and Algorithms, volume 356. Springer.
  13. Leifsson, L. and Koziel, S. (2011b). Variable-fidelity aerodynamic shape optimization. In Comp. Opt., Methods and Algorithms, volume 356. Springer.
  14. Minsky, M. and Papert, S. (1969). Perceptrons: An introduction to computational geometry. The MIT Press, Cambridge, MA.
  15. NASA (2008). Onera-m6-wing validation case. In http://www.grc.nasa.gov.
  16. O'Hagan, A. and Kingman, J. (1978). Curve fitting and optimal design for prediction. Journal of the Royal Statistical Society. Series B (Methodological).
  17. Queipo, N., Haftka, R., Shyy, W., Goel, T., Vaidyanathan, R., and Kevin Tucker, P. (2005). Surrogate-based analysis and optimization. Progress in Aerospace Sciences, 41(1):1-28.
  18. Raymer, D. (2006). Aircraft design: a conceptual approach. American Institute of Aeronautics and Astronautics.
  19. Robinson, T., Willcox, K., Eldred, M., and Haimes, R. (2006). Multifidelity optimization for variablecomplexity design. In Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA.
  20. Schmitt, V. and Charpin, F. (1979). Pressure distributions on the onera-m6-wing at transonic mach numbers. Experimental Data Base for Computer Program Assessment, Report of the Fluid Dynamics Panel Working Group 04, AGARD AR 138, May 1979.
  21. Simpson, T., Poplinski, J., Koch, P., and Allen, J. (July 2001). Metamodels for computer-based engineering design: survey and recommendations. Engineering with computers, 17(2):129-150.
  22. Smola, A. and Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and computing, 14(3):199-222.
  23. Søndergaard, J. (2003). Optimization using surrogate models by the space mapping technique. PhD thesis, PhD. Thesis, Technical University of Denmark, Informatics and mathematical modelling.
  24. Tannehill, J., Anderson, D., and Pletcher, R. (1997). Computational fluid mechanics and heat transfer. Taylor & Francis Group.
  25. Wild, S., Regis, R., and Shoemaker, C. (2008). Orbit: Optimization by radial basis function interpolation in trust-regions. SIAM Journal on Scientific Computing, 30(6):3197-3219.
  26. Zhu, J., Bandler, J., Nikolova, N., and Koziel, S. (2007). Antenna optimization through space mapping. Antennas and Propagation, IEEE Transactions on, 55(3):651-658.
Download


Paper Citation


in Harvard Style

Jonsson E., Leifsson L. and Koziel S. (2012). Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping . In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012) ISBN 978-989-8565-20-4, pages 489-498. DOI: 10.5220/0004164004890498


in Bibtex Style

@conference{sddom12,
author={Eirikur Jonsson and Leifur Leifsson and Slawomir Koziel},
title={Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping},
booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)},
year={2012},
pages={489-498},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004164004890498},
isbn={978-989-8565-20-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)
TI - Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping
SN - 978-989-8565-20-4
AU - Jonsson E.
AU - Leifsson L.
AU - Koziel S.
PY - 2012
SP - 489
EP - 498
DO - 10.5220/0004164004890498