# TRANSONIC AIRFOIL DESIGN BY THE INVERSE METHOD USING VARIABLE-FIDELITY MODELLING

### Slawomir Koziel, Leifur Leifsson, Stanislav Ogurtsov

#### Abstract

The paper presents an improved optimization algorithm for the inverse design of transonic airfoils. Our approach replaces the direct optimization of an accurate, but computationally expensive, high-fidelity airfoil model by an iterative re-optimization of two different surrogate models. Initially, for a few design iterations, a corrected physics-based low-fidelity model is employed, which is subsequently replaced by a response surface approximation model. The low-fidelity model is based on the same governing fluid flow equations as the high-fidelity one, but uses coarser discretization and relaxed convergence criteria. A shape-preserving response prediction technique is utilized to align the pressure distribution of the low-fidelity model with that of the high-fidelity one. This alignment process is particularly suitable since the inverse design aims at matching a given target pressure distribution. Our algorithm is applied to constrained inverse airfoil design in inviscid transonic flow. A comparison with the basic version of the optimization algorithm, exploiting only a physics-based low-fidelity model, is also carried out. While the performance of both versions is similar with respect to their ability to match the target pressure distribution, the improved algorithm offers substantial design cost savings, from 25 to 72 percent, depending on the test case.

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#### Paper Citation

#### in Harvard Style

Koziel S., Leifsson L. and Ogurtsov S. (2011). **TRANSONIC AIRFOIL DESIGN BY THE INVERSE METHOD USING VARIABLE-FIDELITY MODELLING** . In *Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2011)* ISBN 978-989-8425-78-2, pages 474-482. DOI: 10.5220/0003646204740482

#### in Bibtex Style

@conference{sddom11,

author={Slawomir Koziel and Leifur Leifsson and Stanislav Ogurtsov},

title={TRANSONIC AIRFOIL DESIGN BY THE INVERSE METHOD USING VARIABLE-FIDELITY MODELLING},

booktitle={Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2011)},

year={2011},

pages={474-482},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003646204740482},

isbn={978-989-8425-78-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2011)

TI - TRANSONIC AIRFOIL DESIGN BY THE INVERSE METHOD USING VARIABLE-FIDELITY MODELLING

SN - 978-989-8425-78-2

AU - Koziel S.

AU - Leifsson L.

AU - Ogurtsov S.

PY - 2011

SP - 474

EP - 482

DO - 10.5220/0003646204740482