Abstract
This work reviews different analytical formulations for the time-dependent aerodynamic load of a thin aerofoil and clarifies numerical flutter results available in the literature for the typical section of a flexible wing; inviscid, two-dimensional, incompressible, potential flow is considered in all test cases. The latter are investigated using the exact theory for small airflow perturbations, which involves both circulatory and non-circulatory effects of different nature, complemented by the p-k flutter analysis. Starting from unsteady aerodynamics and ending with steady aerodynamics, quasi-unsteady and quasi-steady aerodynamic models are systematically derived by successive simplifications within a unified approach. The influence of the aerodynamic approximations on the aeroelastic stability boundary is then rigorously assessed from both physical and mathematical perspectives. All aerodynamic models are critically discussed and compared in the light of the numerical results as well, within a comprehensive theoretical framework in practice. In all cases, results accuracy depends on the aero-structural arrangement of the flexible wing; however, simplified unsteady and simplified quasi-unsteady aerodynamic approximations are suggested for robust flutter analysis whenever the wing’s elastic axis lies ahead of the aerofoil’s control point.
Highlights
Models for Flutter Analysis: ASemi-analytical formulations of the aerodynamic loads for the flutter analysis of thin wing sections in subsonic potential flow have been available for a long time [1]; some definitions are not universal and the relative models are still under discussion [2]: this is the case of quasi-steady aerodynamics
Numerical flutter test cases found in the literature for the typical section of a flexible wing are analysed and clarified, specifying the input data and critically assessing the influence of different aerodynamic approximations on the aeroelastic stability boundary, from both physical and mathematical perspectives
The results from degenerate unsteady (DU) and SS models are not plotted since they are less relevant, as anticipated in the dedicated sections: those from the former model are questionable from a physical standpoint, while those from the latter model are already available in the references and provide no realistic evolution of modal damping
Summary
Semi-analytical formulations of the aerodynamic loads for the flutter analysis of thin wing sections in subsonic potential flow have been available for a long time [1]; some definitions are not universal and the relative models are still under discussion [2]: this is the case of quasi-steady aerodynamics. In this respect, it is immediately clarified that, at least in the present work, the attributes “unsteady”, “quasi-unsteady”, “quasi-steady” and “steady” refer to the type of flow, which is generally time-dependent (as required for aeroelastic flutter calculations) [3]. Aeroelastic flutter calculations are performed using all presented aerodynamic models and critically compared with numerical results already available in the literature for the typical section of a flexible wing [18], which are explained and clarified in light of the proposed theoretical derivation within a comprehensive assessment
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