Reproducing Existing Nacelle Geometries With the Free-Form Deformation Parametrization

In the conceptual and preliminary aircraft design phase the Free-Form Deformation (FFD) is one of various parametrization schemes to define the geometry of an engine’s nacelle. This paper presents a method that is able to create a C2 continuous periodic approximation of existing reference nacelles with the B-spline based FFD, which is a generalization of the classical FFD. The basic principle of this method is to start with a rotational symmetric B-spline approximation of the reference nacelle, which is subsequently deformed with a FFD grid that is placed around the initial geometry. A method is derived that computes the displacement of the FFD grid points, such that the deformed nacelle approximates the reference nacelle with minimal deviations. As this turns out to be a linear inverse problem, it can be solved with a linear least squares fit. To avoid overfitting effects — like degenerative FFD grids which imply excessive local deformations — the inverse problem is regularized with the Tikhonov approach. The NASA CRM model and the IAE V2500 engine have been selected as reference geometries. Both resemble nacelles that are typically found on common aircraft models and both deviate sufficiently from the rotational symmetry. It is demonstrated that the mean error of the approximation decreases with an increase of the number of FFD grid points and how the regularization affects these results. Finally, the B-spline based FFD with the classical Bernstein based FFD are compared for both models. The results conceptually prove the usability of the FFD approach for the construction of nacelle geometries in the preliminary aircraft design phase.