Effects of Aspect Ratio on Rolling and Twisting Foils

TL;DR

This paper investigates how the aspect ratio of flapping foils affects flow features and forces, revealing the importance of spanwise flow and proposing a correction to improve strip theory for finite AR foils.

Contribution

It introduces an aspect-ratio correction for strip theory applicable to finite AR flapping foils, supported by flow analysis and force comparisons.

Findings

Finite AR induces spanwise flow stabilizing vortex structures.

Spanwise flow enhances dynamics at the foil root.

Proposed correction enables better analysis of finite AR foils.

Abstract

Flapping flight and swimming are increasingly studied both due to their intrinsic scientific richness and their applicability to novel robotic systems. Strip theory is often applied to flapping wings, but such modeling is only rigorously applicable in the limit of infinite aspect ratio (AR) where the geometry and kinematics are effectively uniform. This work compares the flow features and forces of strip theory and three-dimensional flapping foils, maintaining similitude in the rolling and twisting kinematics while varying the foil AR. We find the key influence of finite AR and spanwise varying kinematics is the generation of a time-periodic spanwise flow which stabilizes the vortex structures and enhances the dynamics at the foil root. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in analysis and design of finite aspect ratio flapping foils.