Reproducing Existing Nacelle Geometries with the Free-Form Deformation Parametrization

Abstract

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. In this paper we present a method that is able to create a G2 continuous approximation of existing reference nacelles with the B-spline based FFD, which is a generalization of the classical FFD. The basic principle of our 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. We derive a method 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 - we regularize the inverse problem with the Tikhonov approach. For the reference geometries we selected the NASA CRM model and the IAE V2500 engine. Both resemble nacelles that are typically found on common aircraft models and both deviate sufficiently from the rotational symmetry. We demonstrate that the mean error of our approximation decreases with an increase of the number of FFD grid points and how the regularization affects these results. Finally, we compare the B-spline based FFD with the classical Bernstein based FFD for both models.