Accelerated loosely-coupled CFD/CSD method for nonlinear static aeroelasticity analysis

Abstract The flexible high-aspect-ratio wings of high-altitude long-endurance unmanned aerial vehicles experience large geometrical deformations. The nonlinear aeroelastic analysis for such a wing is carried out by using a loosely-coupled CFD/CSD method, which treats the fluid and structure as two separate modules and updates the CFD and CSD variables separately with a transfer of variables at the fluid–structure interface. In the loosely-coupled method employed here, an unsteady Euler solver and a nonlinear CSD solver are joined together by a fully three-dimensional integral constant volume tetrahedron (CVT) interfacing technique. The computation process is very time-consuming when the computed incremental displacements of every aerodynamic node on the wing surface are fully added to the previously computed deformed wing configuration. For a maximum deflection of approximately 8.7 mm (0.54% of semi-span length), the coupled computation scheme takes 20 coupling iteration steps with about 72 hours to converge on an HP XW6400 workstation with a 3 GHz Xeon5160 CPU. To reduce the computational expense of this loosely-coupled method, the golden section technique with an empirical parameter is introduced to speed up convergence. The deflections relaxed by using this technique are assimilated, and the wing bends up monotonically to its static equilibrium position with a maximum deflection 44.9 mm. The convergence history shows that, this accelerated algorithm takes just 6 coupling iteration steps with about 24 hours to monotonically converge to its static equilibrium position, although the maximum deflection 44.9 mm is 5 times larger than the maximum deflection 8.7 mm of the above test case with aeroelastic deflections fully assimilated. So, it is employed in the following nonlinear fluid–structure interaction (FSI) computations. After this nonlinear aeroelastic system has reached its static equilibrium position, the aerodynamic loads on wing surface are extracted and then applied onto the linear wing structure to calculate its deformation. In present paper, if the geometric nonlinear effects are taken into account for wing deflection calculation, the wing structure model is named as “nonlinear wing structure”; otherwise, the wing structure model is named as “linear wing structure”. The role of geometric nonlinearity on aeroelastic deformation is analyzed by comparing the deformations of linear and nonlinear wing structures. It is shown that, geometric nonlinearity plays an important role for large static aeroelastic deformation and should be accounted for in aeroelastic analyses for such high-aspect-ratio flexible wings.