The role of the leading edge vortex in lift augmentation of steadily revolving wings: a change in perspective

Abstract

The presence of a stable leading edge vortex (LEV) on steadily revolving wings increases the maximum lift coefficient that can be generated from the wing and its role is important to understanding natural flyers and flapping wing vehicles. In this paper, the role of LEV in lift augmentation is discussed under two hypotheses referred to as 'additional lift' and 'absence of stall'. The 'additional lift' hypothesis represents the traditional view. It presumes that an additional suction/circulation from the LEV increases the lift above that of a potential flow solution. This behaviour may be represented through either the 'Polhamus leading edge suction' model or the so-called 'trapped vortex' model. The 'absence of stall' hypothesis is a more recent contender that presumes that the LEV prevents stall at high angles of attack where flow separation would normally occur. This behaviour is represented through the so-called 'normal force' model. We show that all three models can be written in the form of the same potential flow kernel with modifiers to account for the presence of a LEV. The modelling is built on previous work on quasi-steady models for hovering wings such that model parameters are determined from first principles, which allows a fair comparison between the models themselves, and the models and experimental data. We show that the two models which directly include the LEV as a lift generating component are built on a physical picture that does not represent the available experimental data. The simpler 'normal force' model, which does not explicitly model the LEV, performs best against data in the literature. We conclude that under steady conditions the LEV as an 'absence of stall' model/mechanism is the most satisfying explanation for observed aerodynamic behaviour.

Keywords: absence of stall; aerodynamics; flapping flight; insect flight; leading edge vortex; revolving wings.

Figure 1.

(a) Schematic showing the simplest valid LEV structure for a cylindrical vortex—cross-section view. The LEV is stable at high angles of attack with flow reattachment on the upper surface and satisfaction of the Kutta condition at the trailing edge. The black dots represent stagnation points. (b) An idealized top view schematic illustrating a conical LEV topology for a steadily revolving wing with a focus at the root. This topology has been observed at Reynolds numbers of O(10³–10⁴) [2,3]. (Online version in colour.)

Figure 2.

Comparison of the mathematical structure and graphical representation for the models discussed in this study over the first quadrant of angle of attack (potential flow (yellow), normal force (black), leading edge suction (blue) and trapped vortex with C_Lfree,3D > 0 (red)). All models contain the potential flow model as a component. We choose to show the potential flow model results only up to 45° because this model is known to be non-physical as it approaches 90° angle of attack. Gray band represents typical angle of attack values within the mid-half-strokes of normal hovering insect flight. A nominal experimental representation of a classical stalled translating wing (dashed line) is added for reference.

Figure 3.

Comparison of aerodynamic model predictions against experimental and CFD data. Lift coefficient data are plotted against geometric angle of attack. Models are compared with available data for (a) hawkmoth-1; experimental data digitized from fig. 6 of [15], (b) hawkmoth-2; experimental data digitized from fig. 5 of [21], (c) hawkmoth-3; CFD data digitized from fig. 5 of [22], (d) bumblebee; experimental data digitized from fig. 7 of [16], (e) mayfly; experimental data digitized from fig. 8 of [16], (f) fruitfly; experimental data digitized from fig. 7 of [19], (g) pigeon; experimental data digitized from fig. 3 of [17] and (h) hummingbird; experimental data digitized from fig. 6 of [20].