Cedric Liauzun, Christophe Blondeau
DOI Number: N/A
Conference number: IFASD-2024-034
Several typical aeroelastic phenomena and instabilities, like flutter, induce periodic oscillations of the structure and of the aerodynamic forces. Numerical methods based on
the harmonic balance technique or the Time Spectral Method (TSM) with a projection on the Fourier space has proven to be very efficient to predict the oscillatory phenomena by resolving the established regime without solving for the transient one. Such formulations lead however to critical numerical difficulties especially with a fine time sampling. A modular parallel TSM solver is implemented in a high level abstraction Python layer in order to perform aeroelastic analyses and optimizations of wings. This solver is in charge of performing all the operations regarding the temporal discretization and the time resolution. An interface with the CFD code elsA extracts all the needed information related to the spatial discretization. An Approximate Newton algorithm is used to solve the TSM problem. Both a Block-Jacobi method and a pre-conditioned GMRES are implemented to solve the implicit linear system. Such a modular approach makes the evaluation of resolution algorithms easier to improve the computational robustness and efficiency. A ”block-circulant” preconditioner is thus assessed for its capability to provide convergence profiles independent of the number of harmonics. An adjoint solver is also developed in order to perform aeroelastic optimizations with dynamic objective functions and constraints. This TSM solver is evaluated for the NACA64A010 airfoil in transonic inviscid flows. Responses to harmonic pitching motions and to gusts are first computed and compared to unsteady simulations for both rigid and deforming meshes. The computation of the gradient of the unsteady pressure drag with respect to shape parameters is then validated against finite differences.