Effect of Three-Dimensional Geometry on Harmonic Gust–Airfoil Interaction

Abstract

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

Unsteady gust interaction with tidal rotors: Importance of 3D wake effects and implications for turbine load modelling

“…3D effects were most significant near the blade tips, at low reduced frequencies and at low aspect ratios. Smyth et al [11] arrived at similar conclusions after carrying out a parametric study of 3D geometry effects in unsteady flow, using an inviscid 3D vortex lattice model. They found that aspect ratio effects largely determined the degree of 3D response, including for a rotor geometry.…”

“…For steady or quasi-steady flow, the impact of streamwise tip vortices on tidal turbines can be accounted for by tip-loss corrections (e.g., the commonly used Prandtl correction [12]). However, Smyth et al [11] demonstrated that the influence of the streamwise wake vortices changes substantially in unsteady flow conditions. As such, due to both the finite nature of the spanwise wake vorticity and the unsteady nature of the streamwise wake vorticity, the applicability of the Theodorsen function to tidal turbines is called into question.…”

“…Building on the work presented in Smyth et al [11], the aims of this study are: (1) to evaluate the extent of 3D effects in tidal turbine load response, (2) to identify the nondimensional groups that govern the unsteady load response, and (3) to explore the implications for turbine modelling and operation. These aims are achieved through a numerical parametric study of a turbine in idealised unsteady flow conditions, using unsteady Reynolds-Averaged Navier Stokes (URANS) simulations of a fully-resolved model tidal turbine blade and also an inviscid 3D vortex lattice model (VLM).…”

An unsteady aerodynamic model for three-dimensional wing based on augmented lifting-line method

“…Studies in references [16,29] have shown that when aspect ratio or reduction frequency is large enough, 2D and 3D results will tend to be consistent. Therefore, the expression of the circulation correction factor in this paper is given as follows:…”

“…In theory, the wake vorticity of a wing with finite span can be divided into the streamwise vorticity and the spanwise vorticity [16]. For steady flow, the spanwise wake vorticity doesn't exist and the streamwise vorticity remains unchanged.…”