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Comparing free-form deformation and harmonic coordinates for the concurrent geometry and computation grid deformation in aerodynamic shape optimization

Tavla Sofia

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Summary

In the field of aerodynamics, shape optimization aims to obtain high performance aerodynamic configurations by the optimization of an objective function, subject to specific geometrical constraints. Such problems include the maximization and minimization of the lift and drag forces, which act on an airfoil, respectively. Initially, the proper selection of the deformation technique, which later on will produce the candidate geometries, is of paramount importance in the optimization process. Specifically, during shape optimization, it is crucial for the computational grid – on which nodes the flow equations (Euler & Navier-Stokes) are solved – to continuously adapt to the new geometrical entities. To this end, in recent decades several grid and shape parameterization techniques have been developed, with the common goal of minimizing both the computational cost and time required for the deformation, and at the same time, handle intricate geometries. In the present dissertation, two of the most prevalent methods of deformation are examined; the Free Form Deformation (FFD) and the Harmonic Function-based deformation techniques. Initially, an extensive literature review of Free Form Deformation and Harmonic Functions-based deformation methodologies, used for shape parameterization and grid adaptation, is conducted. Furthermore, a modified Harmonic functions-based methodology – developed in the Turbomachinery and Fluid Dynamics Laboratory of the Technical University of Crete (TUC) – is presented in detail and tested.Finally, a grid interpolation algorithm is developed and presented in the context of the present work. The purpose of the aforementioned algorithm is to enable data interpolation between two computational grids with different densities, during the aerodynamic shape optimization procedure. The mesh interpolation algorithm was implemented in FORTRAN 90 programming language.

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