Two-dimensional (2D) strip-theory modelling of unsteady gust-aerofoil interaction is standard practice in many industrial applications, but the limits of applicability of 2D unsteady flow modelling on 3D wing and rotor geometries are not well understood. This paper investigates the effects of 3D geometry features, such as finite span, taper, sweep and rotation, on the unsteady lift response to gusts, and the flow-physical differences between 2D and 3D geometries in unsteady flow. A frequency-domain inviscid vortex lattice model is validated and used for the 3D analysis. The results are compared to unsteady transfer functions from 2D linear analytic theory (e.g. Theodorsen and Sears functions). The study agrees with previous research findings that 3D effects are most significant at low reduced frequencies and low aspect ratios, as well as near the wing tips. The driving cause of 3D response is shown to be the wake vorticity: both streamwise and spanwise components of unsteady wake vorticity must be modelled. The study concludes by investigating whether unsteady response of more complex 3D wing and rotor geometries can be represented by the response of a rectangular wing. The results indicate that this is possible for tapered wings and rotating blades, but not for swept wings. Nomenclature Influence matrix Semi-chord (m) c Chord (m) Cl Local lift coefficient CL Total lift coefficient Force (N) Reduced frequency Lift (N) Number of chordwise lattice panels Surface normal vector Number of blades Radius

No abstract

The unsteady load response of an aerofoil encountering a gust is often modelled using analytical transfer functions, which assume idealised behaviour of both the flow and the aerofoil.One such transfer function is the Sears function, which models a pure transverse gust interacting with a flat-plate aerofoil at zero mean incidence. The function was extended by Goldstein and Atassi to account for camber and incidence as well as the presence of a streamwise gust component. Atassi showed that the effects of camber and incidence (i.e. non-zero mean aerofoil loading) are not negligible when there is a streamwise gust component. In this work, new

Unsteady flow response is an important consideration for a range of engineering applications, from unmanned air vehicles, where it has implications for control, to tidal turbines, where the accurate calculation of fatigue load is vital. Designers often use 2D strip-theory predictions for both steady and unsteady performance, applying Theodorsens unsteady transfer function for uniform gusts at each blade section to estimate the unsteady bending moments on the turbine blades. The purpose of this investigation is to explore the limits of the applicability of this 2D classical unsteady aerofoil theory to aerofoils with significant 3D geometry features. Using a harmonic vortex lattice model, this study shows that there are significant 3D features in the unsteady flow response, which increase with decreasing reduced frequency and with decreasing aspect ratio. The response near the blade tips is strongly 3D, and does not reach the 2D characteristic, even at high frequencies. The phase response also varies strongly along the span, leading to different blade sections responding out of phase with each other even with no spanwise gust variation. This has significant implications for bending moment calculations, with require integration of the load along the span. The observed 3D effects are shown to be caused by changes to the spanwise component of the unsteady wake, and by the presence and behaviour of a streamwise unsteady wake. The results for a model tidal turbine geometry show that the Loewy function does not capture returning wake effects adequately, but that it does model the mid-span response characteristic well at reduced frequencies over 0.8. The study concludes that using transfer functions from 2D classical aerofoil theory provides a conservative estimate of the blade loads affecting a tidal turbine, but only if no steady tip-loss corrections have been applied to the unsteady response. If tip-loss corrections are applied to the quasi-steady lift response before unsteady transfer functions are used, the resulting load amplitude will be significantly under-predicted.

No abstract