Dynamic derivatives are used to represent the influence of the aircraft motion rates on the aerodynamic forces and moments needed for studies of flight dynamics. The use of computational fluid dynamics has potential to supplement costly wind-tunnel testing. The paper considers the problem of the fast computation of forced periodic motions using the Euler equations. Three methods are evaluated. The first is computation in the time domain, which provides the benchmark solution in the sense that the time-accurate solution is obtained. Two acceleration techniques in the frequency domain are compared. The first uses a harmonic solution of the linearized problem, referred to as the linear frequency-domain approach. The second uses the harmonic balance method, which approximates the nonlinear problem using a number of Fourier modes. These approaches are compared for the ability to predict dynamic derivatives and for computational cost. The NACA 0012 aerofoil and the DLR-F12 passenger jet wind-tunnel model are the test cases. Compared to time-domain simulations, an order of magnitude reduction in computational costs is achieved and satisfactory predictions are obtained for cases with a narrow frequency spectrum and moderate amplitudes using the frequency-domain methods

Starting from a comparative study of various methods for uncertainty propagation, this paper presents a novel reduced quadrature technique to be used in gradient-based robust design optimization of aerodynamic shapes. The accuracy and computational efficiency of the method are investigated by means of mathematical analyses and numerical examples. The method is then applied to the robust design of airfoils under probabilistic uncertainty. It is shown that the solutions obtained through the proposed method can outperform those obtained through linearization, without any significant increase in computational cost

The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest The solution procedure of the linear harmonic Euler/Navier-Stokes solver of the HYDRA suite of codes consists of a preconditioned fixed-point iteration, which in some circumstances becomes numerically unstable. Previous work had already highlighted the physical origin of these numerical instabilities and demonstrated the code stabilization achieved by wrapping the core part of the linear code with a Generalized Minimal Residual (GMRES) solver. The implementation and the use of an alternative algorithm, namely, the Recursive Projection Method, is summarized. This solver is shown to be well suited for both stabilizing the fixed-point iteration and improving its convergence rate in the absence of numerical instabilities. In the framework of the linear analysis of turbomachinery aeroelasticity, this method can be computationally competitive with the GMRES approach