Study of the model-order reduction of the aerolastic behavior of a wing

Abstract

The ultimate goal of this project is to construct a reduced-order model capable of providing real-time predictions of the aeroelastic behavior of a wing. The approach for carrying out such a task is, firstly, in the spirit of classic modal analysis, to project the full-order, governing equations of the wing (finite element equations, for instance) onto the low-dimensional subspace spanned by a few global displacement modes. Such displacement modes, in turn, are obtained by applying data compression algorithms to a representative set of full-order simulations. Once these dominant displacement modes have been identified, the next step in the approach is to choose, among all points of the underlying finite element mesh, a set of sampling points so that the integrals appearing in the weak form of the balance equation can be accurately evaluated by monitoring the strains and stresses only at such key points.

The main objective of this paper is to apply the model-order reduction technique to an airplane’s wing in order to speed up development of aircrafts or to get real-time results of a plane structural state. However, this case is especially complex since the wings are an aeroelastic problem where both fluid and structure must be computed in order to get realistic results. In order to improve the overall airplane design speed -in addition to the usage of MOR techniques- a complementary software has been developed. This is a parametric software capable of quickly generating a geometry and exporting it to simulate both the fluid and the structure with a FE software like Kratos. This software will be open sourced. The usage of the custom software helps to generate geometries that differ only on a single design parameter (the angle of attack in this paper). These different geometries are then processed with Kratos to obtain the high-fidelity result from each one of them. Once the high-fidelity snapshots have been obtained (five are used in this paper), the reduced order models are generated using a discrete version of the Proper Orthogonal Decomposition (POD) called Single Value Decomposition (SVD). Finally, using the discrete empirical interpolation method (DEIM), it is possible to interpolate between the simulations and obtain the results of any intermediate state in less than a second without having to perform the full simulation. No physical model has been constructed to compute the fluid and only statistical methods are employed for that part. The results turned out to be very precise regarding the structure ROM; all the same, the only statistical approach to the fluid proved to be not ideal and the accuracy error remained around 15% for this part.