The shock buffet phenomenon (SB) is a well-known large-scale flow instability occurring at high angles of attack and moderate transonic Mach numbers around airfoils and wings. It is characterized by the interaction of a suction-side lambda shock system with the turbulent boundary layer. Beyond a critical angle of attack the shock starts to oscillate and large fluctuations of the air loads due to cyclic flow separation and re-attachment are the result. The SB instability manifests itself already far below the actual SB onset by the emerging of a typical resonance peaks in the linearized frequency response functions of the unsteady airloads. These resonance peaks can result in non-classical 1-degree-of-freedom aileron and torsion flutter depending on the location of the flexural axis and corresponding structural eigenfrequencies.

The SB stability boundary can be reliably reproduced with numerical RANS models. The same does not hold for the prediction of the shock oscillation amplitudes itself once the buffet boundary is exceeded. Different RANS and RANS-LES models will produce a large variety of periodic solutions. The situation gets worse when the structural response that cannot be avoided in most practical situations (traditionally termed “buffeting”) is taken into account and the task is, for instance, to predict response amplitudes with and without lock-in. A large portion of that uncertainty originates from the limited understanding of the flow physics behind SB oscillations. Still no testable theory exists to explain the phenomenon. Early attempts that proclaimed a crucial role of a hypothetical acoustic feed-back loop between the shock and the trailing edge collide with the observation of SB over wall-bounded bumps utterly without trailing edges.

Although being a pure 2-D flow phenomenon SB and buffeting are of high relevance for the outer-envelope behavior of modern 3-D transport aircraft wings (cf. Figure 6). Recently, a growing interest of the aircraft industry can be stated in more reliable modelling of the flow physics at high-speed off-design conditions.

Fig. 6: Relation of wing loads and buffet boundaries

In order to make substantial progress in reducing the environmental impact of aircraft, one of the key research axes is the reduction of aircraft weight to contribute to providing a step-change in fuel consumption levels. This challenge is based on the development of innovative configurations or disruptive technologies. It requires especially the development and the assessment of new technologies and methodologies for both structural design and load control. In the specific domain of fluid structure interaction, aeroelastic wind tunnel testing and numerical simulations take as their main objective to improve the understanding of the classical physical phenomena involved in fluid structure interaction such as Flutter, Gust Response, Buffet, Limit Cycle Oscillation etc. The acquisition of comprehensive and relevant experimental databases allows to validate numerical capabilities and tools such as high fidelity tools of Computational Fluid Dynamic (CFD) and Computational Structure Mechanics (CSM). In the process, precious new insights can be gained into innovative configurations involving complex or nonlinear aeroelastic phenomena (High Aspect ratio wing, Truss Braced Wing, etc.), as well as in the efficiency assessment of control strategies of aeroelastic phenomena: Buffet control by active flow control, Gust Load alleviation based on advanced control functions, Flutter margin increase through closed loop approaches etc.

To date, on the numerical and modelling side of these studies, the standard approach classically considers a linear behavior for the structure. The structural model is in this case restricted to a small- displacements small- strains formulation. The structural model may then be handled in the aeroelastic simulation directly using a finite element model (FEM), or via a modal projection of the static/dynamic structural equations. Regarding the fluid model, large efforts has been made during the last decades to move from a linear description of the fluid behavior in aeroelastic simulations (via integral formulations, such the one used in the so-called Doublet Lattice method) to a non-linear one, gradually including compressibility, viscous and turbulent effects, in order to reach a high level of maturity of aeroelastic static and dynamic simulation implementing RANS and URANS fluid models. Attempts are now made to include even higher fidelity aerodynamic models in aeroelastic models using LES or DES formulations, which is still out of reach for complex configurations.

However, only few efforts have yet been made to implement fully non-linear models for both fluid and structure in the aeroelastic modelling. In the static case, accounting of large displacements in the formulation is now possible via the coupling of non-linear fluid solvers and structural solvers such as NASTRAN. However this leads to rather high computing costs, but may still be necessary in the case of non-linear large displacements structural behaviors, such those observed for high aspect ratio flexible wings or rotating blading’s of turbomachines. In the dynamic case, the challenge is even more severe, because of the need of a robust fluid-structure CFD/CSM coupling algorithm in the time-domain, and that of both individually efficient non-linear fluid and structural solvers. Reduced order models may also be used to couple aerodynamic solvers to a non-linear structural model.

Fig. 7: Aeroelastic gust response of a 2DoFs suspended airfoil in transonic flow – (CleanSky SFWA - CleanSky2 NACOR)

At ONERA and DLR, numerical activities have been conducted for years in the development of numerical solution strategies for the modelling of aeroelastic linear and non-linear stability and response problems. These activities are now mainly oriented towards the development of aeroelastic simulation environments complementing the CFD solvers elsA and TAU, widely used in the European aeronautics industry. The purpose of these simulations is the prediction of the in-flight static or dynamic behavior of flexible aerodynamic structures and their aeroelastic stability. The available simulations include non-linear and linearized harmonic forced motion computations, static coupling and consistent dynamic coupling simulations in the time-domain. Harmonic balance method is also implemented for periodic forced motion simulations. A linear behavior of the structure is assumed, but external coupling capabilities have been developed in the last few years, which allow for the coupling of the elsA and TAU solver with a structural solver, potentially implementing non-linear capabilities. These aeroelastic numerical tools have been implemented in a number of internally, nationally or European funded projects (e.g. CleanSky SFWA, CleanSky GRA, CleanSky2 NACOR), see Fig. 7. In the scope of the HOMER project, one may also cite the ONERA-DLR collaborations in the NLAS, NLAS2 and HIFAS common research projects, in particular dealing with LCO aeroelastic phenomena numerical prediction.