Inverse Design of Transonic Airfoils Using Variable-Resolution Modeling and Pressure Distribution Alignment

Abstract The paper presents a computationally efficient and robust methodology for the inverse design of transonic airfoils. The approach replaces the direct optimization of an accurate, but computationally expensive, high-fidelity airfoil model by an iterative reoptimization of a corrected low-fidelity 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. The shape-preserving response prediction technique is utilized to align the pressure distribution of the low-fidelity model with that of the high-fidelity model. This alignment process is particularly suitable since a target pressure distribution is specified in the inverse design problem. The method is applied to constrained inverse airfoil design in inviscid transonic flow. The results show that the proposed method is able to match the target pressure distributions closely and requiring over 90 percent lower computational cost than when using only the high-fidelity model.

[1]  P. A. Henne.  Subsonic Airfoil Design , 1990 .

[2]  J. Anderson,et al.  Modern Compressible Flow: With Historical Perspective , 1982 .

[3]  Andy J. Keane,et al.  Airfoil shape design and optimization using multifidelity analysis and embedded inverse design , 2006 .

[4]  Theresa Dawn Robinson,et al.  Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping , 2008 .

[5]  Kevin A. Lane,et al.  Inverse Airfoil Design Utilizing CST Parameterization , 2010 .

[6]  S. Koziel,et al.  Space mapping , 2008, IEEE Microwave Magazine.

[7]  Slawomir Koziel,et al.  Multi-Fidelity Multi-Grid Design Optimization of Planar Microwave Structures with Sonnet , 2010 .

[8]  René Van den Braembussche,et al.  Numerical Optimization for Advanced Turbomachinery Design , 2008 .

[9]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[10]  Slawomir Koziel,et al.  Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction , 2010, J. Comput. Sci..

[11]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[12]  R. M. Hicks,et al.  Wing Design by Numerical Optimization , 1977 .

[13]  A. Jameson,et al.  Design Optimization of High-Lift Configurations Using a Viscous Continuous Adjoint Method , 2002 .

[14]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[15]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[16]  I. H. Abbott,et al.  Theory of Wing Sections , 1959 .

[17]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[18]  S. Koziel,et al.  Space-mapping-based interpolation for engineering optimization , 2006, IEEE Transactions on Microwave Theory and Techniques.

[19]  S Koziel,et al.  Shape-Preserving Response Prediction for Microwave Design Optimization , 2010, IEEE Transactions on Microwave Theory and Techniques.

[20]  George S. Dulikravich,et al.  Aerodynamic shape design and optimization , 1991 .

[21]  Hyoung-Jin Kim,et al.  Aerodynamic Design of Transonic Wings Using the Target Pressure Optimization Approach , 1998 .

[22]  Christian B Allen,et al.  48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition , 2010 .

[23]  Antony Jameson,et al.  Viscous Aerodynamic Shape Optimization of Wings including Planform Variables , 2003 .

[24]  J. W. Slooff,et al.  COMPUTATIONAL METHODS FOR THE AERODYNAMIC DESIGN OF AIRCRAFT COMPONENTS , 1993 .

[25]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[26]  Marian Nemec,et al.  Optimization of High-Lift Configurations Using a Newton-Krylov Algorithm , 2003 .