Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation

Abstract

An efficient approach is presented to search for transonic aeroelastic instability of realistic aircraft structures in multidimensional parameter spaces. Aeroelastic instability is predicted by a small nonlinear eigenvalue problem for the structural equations which is corrected by the aerodynamic influence. The approximation of this computationally expensive interaction term, simulated by nonlinear high fidelity computational fluid dynamics, is formulated to allow both the blind search for aeroelastic instability and the update of lower order predictions with available better information. The approximation is based on a kriging interpolation of exact numerical samples covering the parameter space. The approach is presented for the Goland and MDO wing configurations and the open source fighter.

Lyapunov Inverse Iteration for Stability Analysis using Computational Fluid Dynamics

“…The eigenvalue estimate µ j (and also the eigenvector x j ) are found as solution from Eq. (11). The expression r j 2 gives the norm of the residual of Eq.…”

“…Once the Schur complement formulation was presented, the step of approximating the aerodynamic influence matrix became obvious. 10,11 Using the aerodynamic influence matrix interpolated from numerical samples, stability analyses in multidimensional parameter spaces can be accomplished at the cost of several steady state simulations (provided an efficient algorithm for linear system solves is available and smart a posteriori sampling of the parameter space is performed). More importantly, the Schur complement variation of the aeroelastic eigenvalue problem made the approach equivalent to using linear aerodynamic models, such as the doublet lattice method, and work-processes long established in industrial flutter analyses can easily be adapted for the use of CFD methods.…”

Updating Computational Aeroelastic Models using Flight Flutter Test Data

“…Mach number and angle of attack) and the structural model due to structural parameters generally influencing the mode shapes required to compute the matrix (A f η + λA fη ). In [7,8] an approximation of the aerodynamic influence term was devised which enables the stability analysis in larger parameter spaces efficiently. Two approximations were applied.…”

“…The original Nissim and Gilyard method made two important assumptions. First, the assumed simplified aerodynamics challenge the method's applicability in the transonic flight regime where significant variation of the aerodynamic influence can be expected [7,8]. Indeed, we are dealing with a strictly nonlinear problem and the aerodynamic coupling matrix cannot be assumed to be constant with respect to any parameter variation.…”

“…In previous work [7,8,10] a small nonlinear eigenvalue problem, consisting of the structural equations corrected for the fluid/structural coupling, was solved to predict the stability of the aeroelastic system. Computational fluid dynamics methods were used to compute the aerodynamic correction term, the evaluation of which significantly influences the accuracy and efficiency of the numerical scheme, particularly in the transonic flight regime with nonlinear flow features (like shock waves and separation) where linear aerodynamics fail.…”