Evaluation of linear, inviscid, viscous, and reduced-order modelling aeroelastic solutions of the AGARD 445.6 wing using root locus analysis

Abstract

Reduced-order modelling (ROM) methods are applied to the Computational Fluid Dynamics (CFD)-based aeroelastic analysis of the AGARD 445.6 wing in order to gain insight regarding well-known discrepancies between the aeroelastic analyses and the experimental results. The results presented include aeroelastic solutions using the inviscid Computational Aeroelasticity Programme-Transonic Small Disturbance (CAP-TSD) code and the FUN3D code (Euler and Navier-Stokes). Full CFD aeroelastic solutions and ROM aeroelastic solutions, computed at several Mach numbers, are presented in the form of root locus plots in order to better reveal the aeroelastic root migrations with increasing dynamic pressure. Important conclusions are drawn from these results including the ability of the linear CAP-TSD code to accurately predict the entire experimental flutter boundary (repeat of analyses performed in the 1980s), that the Euler solutions at supersonic conditions indicate that the third mode is always unstable, and that the FUN3D Navier-Stokes solutions stabilize the unstable third mode seen in the Euler solutions. IntroductionClassical linear aeroelastic analyses typically produce velocity-damping-frequency (V-g-f) plots and/or root locus plots. The use of these plots has enabled the aeroelastician to view the nature of the flutter mechanism(s) in addition to identifying the condition(s) at which flutter occurs. The rapid creation of these plots was facilitated by the use of linear unsteady aerodynamics and linear aeroelastic equations of motion (Adams and Hoadley 1993).During the last few years, higher order CFD-based methods have become an important method for the computation of nonlinear unsteady aerodynamics for use in aeroelastic analyses. The use of these higher order methods provides valuable insight regarding complex flow physics at conditions where linear methods are not theoretically valid. However, the increased computational cost associated with the computation of unsteady aerodynamics and aeroelastic responses using higher order methods has resulted in a subtle change in the manner in which the aeroelastician evaluates and interprets these analyses. First, the increased computational cost of these analyses has tended to dictate a 'snapshot' approach to aeroelastic analyses whereby the aeroelastic response at a handful of dynamic pressures is all that is computed. This 'snapshot' approach is used to identify the flutter dynamic pressure but the actual flutter mechanism is not easily discernible. Second, due to the complexity of the computational methods, methods that could

Neurofuzzy-Model-Based Unsteady Aerodynamic Computations Across Varying Freestream Conditions

“…In contrast, the results for three considered modes show a different behavior, since the values for both the FSI and the FR are much smaller than the experimental values and the respective quantities at N 2. This is due to the fact that the third mode becomes unstable, as was already noted by Silva et al [40]. Therefore, it is confirmed that the inviscid AER-Eu solver also leads to this instability for the AGARD 445.6 wing at supersonic conditions.…”

“…If the inflow becomes supersonic, the flutter speed index and the frequency ratio are increased substantially for N 2, while the overprediction of those indicators in terms of the experimental results was already noted by Lee-Rausch and Batina [39], as well as numerous other publications for Euler-equations-based flutter computations (see also [40]). In contrast, the results for three considered modes show a different behavior, since the values for both the FSI and the FR are much smaller than the experimental values and the respective quantities at N 2.…”

“…The aeroelastic characteristics of this wing have been investigated in wind-tunnel flutter tests at the NASA Langley Transonic Dynamics Tunnel [29], as well as in several numerical studies for a variety of freestream conditions; see the work of Lee-Rausch and Batina [39] and Silva et al [40] for instance. In the following, the general modeling approach is highlighted, while the focus is on the ROM training and application.…”

“…This change in the flowfield affects the pressure distribution and, as a consequence, the integral forces. Although the flow across the thin AGARD 445.6 wing is not governed by strong transonic effects [40], neither the steady nor the unsteady aerodynamic loads are linearly related to the freestream Mach number due to the influence of compressibility. Above a freestream Mach number of approximately Ma ∞ 1.07, the flow can be considered as entirely supersonic, except of some negligibly small regions near the leading and the trailing edge where still subsonic conditions are observed.…”

“…To address the question about the flutter mechanism at supersonic inflow conditions raised by Silva et al [40], the frequency-domain flutter equation is solved, on the one hand, by considering two structural modes (N 2) and, on the other hand, by taking three modes into account (N 3). The aim is to clarify whether generalized aerodynamic forces computed by an inviscid solver lead to instabilities in the third mode for Ma ∞ 1.072; 1.141.…”