Exact solutions for ground effect

TL;DR

This paper derives exact, versatile solutions for the ground effect phenomenon in aerodynamics, covering a wide range of flow conditions without restrictive assumptions, and compares these solutions with experimental data to identify missing physics.

Contribution

It introduces a novel method using a special function to obtain exact solutions for ground effect across various flow regimes, surpassing previous analytic limitations.

Findings

Solutions valid for point vortices, unsteady flows, and more

Comparison with experiments reveals boundary layer separation effects

Provides new mathematical insights into ground effect phenomena

Abstract

"Ground effect" refers to the enhanced performance enjoyed by fliers or swimmers operating close to the ground. We derive a number of exact solutions for this phenomenon, thereby elucidating the underlying physical mechanisms involved in ground effect. Unlike previous analytic studies, our solutions are not restricted to particular parameter regimes such as "weak" or "extreme" ground effect, and do not even require thin aerofoil theory. Moreover, the solutions are valid for a hitherto intractable range of flow phenomena including point vortices, uniform and straining flows, unsteady motions of the wing, and the Kutta condition. We model the ground effect as the potential flow past a wing inclined above a flat wall. The solution of the model requires two steps: firstly, a coordinate transformation between the physical domain and a concentric annulus, and secondly, the solution of the potential flow problem inside the annulus. We show that both steps can be solved by introducing a new special function which is straightforward to compute. Moreover, the ensuing solutions are simple to express and offer new insight into the mathematical structure of ground effect. In order to identify the missing physics in our potential flow model, we compare our solutions against new experimental data. The experiments show that boundary layer separation on the wing and wall occurs at small angles of attack, and we suggest ways in which our model could be extended to account for these effects.