Interpolation Parameters of the FIE Method for Beam Models

The interpolation parameters of the FIE method are the angular limit of the interpol­ation area in the vicinity of beam kinks внтіь the limit ratio of projection distances in the vicinity of beam kinks dlimit, and the width of the intersection region between assemblies alimit. They are varied and their respective influence on the shape of the deformed wetted surface is assessed. The test case is the HIRENASD configura­tion with a dummy fuselage, which constitutes a second assembly next to the wing. The CFD surface mesh sketched in the top left of Fig. 11 has 46919 points and the structural beam model has 654 nodes. These components are subjected to forces and moments which resulted from a previous aeroelastic simulation. These are kept constant during the parameter study. The deformed wetted surface acting as a ref­erence for the deviations was obtained with the default settings of the ACM, which are elimit = 0.08rad, dljmit = 1.2 and alimit = 0.1 m. This last value amounts to ap­proximately 8% of the model half-span of 1.29 m. As the parameters dlimit and eljmit both relate to the interpolation in the vicinity of kinks, these parameters are studied together. The RMS deviation of the surface point coordinates eS is determined by analogy to eu as defined in Eq. (19). Also in this case only the differences in the flap-wise deflection are considered.

In the top right diagram of Fig. 11 the RMS deviations of the normalised de­flection are plotted over the investigated parameter combinations. Whereas the minimum valid values of ^limit and dljmit are defined inside the ACM, the upper values were chosen arbitrarily. The choice of dljmit has a more profound effect on the shape of the wetted surface than ftimit. There is a weak interdependence visible between the two parameters. The indication of a global RMS value is somewhat misleading here, as both parameters lead to highly localised deviations. This can be seen in the bottom right image. The distributed values are displayed as bars over the configuration’s planform for combinations of the maximum and the default set­tings of ftimit and dljmit. Distinct peaks close to the leading edge are apparent for the maximum value of dljmit, whereas for the maximum value of elimit there are dif­ferences visible in the wedge-shaped areas of non-unique projection mentioned in Chap. 3.2. The choice of the width of the intersection region between fuselage and wing not only has a more widespread influence. It also produces deviations an order of magnitude higher and it thus gives far higher RMS errors. To put the given norm­alised distributed values into perspective: Assuming a bending deflection of 5% of the model half-span of 1.29 m, the peak deviation for parameter combination 0 is less than 0.5 mm, but for setting 0 with alimit = 1.0 m it exceeds 3 mm.