A simple vortex-loop-based model for unsteady rotating wings

Abstract

An analytical model is developed for the lift force produced by unsteady rotating wings; this configuration is a simple representation of a flapping wing. Modelling this is important for the aerodynamic and control-system design for bio-inspired drones. Such efforts have often been limited to being two-dimensional, semi-empirical, sometimes computationally expensive, or quasi-steady. The current model is unsteady and three-dimensional, yet simple to implement, requiring knowledge of only the wing kinematics and geometry. Rotating wings produce a vortex loop consisting of the root vortex, leading-edge vortex, tip vortex and trailing-edge vortex, which grows with time. This is modelled as a tilted planar loop, geometrically specified by the wing size, orientation and motion. By equating the angular impulse of the vortex loop to that of the fluid volume driven by the wing, the circulatory lift force is derived. Potential flow theory gives the fluid-inertial lift. Adding these two contributions yields the total lift formula. The model shows good agreement with a range of experimental and computational cases. Also, a steady-state lift model is developed that compares well with previous work for various angles of attack.

The force generation mechanism of lifting surfaces with flow separation

“…However, in this paper we do not consider these numerical methods and we focus on how this theory can be used to interpret the observed flow fields. Interpreting the force generation mechanism can, in turn, underpin low-order models to predict the forces (Babinsky et al, 2016;Stevens et al, 2016;Corkery and Babinsky, 2018;Chowdhury and Ringuette, 2019). Hence, whilst the proposed paradigm is not a predictive model per se, it is envisaged that it will underpin low order models for lifting surfaces experiencing separated flow in different applications.…”

A numerical study on the aerodynamic effects of dynamic twisting on forward flight flapping wings

“…In equation (5), the undetermined coefficients a, b, c, d, e, f and g are determined by applying constraints on α eff , αeff , and αeff . Specifically, the transition phase form the downstroke to upstroke in flapping motion by several key features:…”

“…However, relying solely on flapping motion leads to low efficiency, and achieving a thrust coefficient of 0.1 becomes challenging. In recent years, there is a growing interest among researchers, including Jiao et al [4] and Chowdhury and Ringuette [5], in studying the correlation between combined flapping and pitching motions and the generation of thrust. By parameterizing the geometry and kinematics of flapping wings, researchers are exploring a series of design possibilities, and have made great progress in realizing wing designs that can generate high thrust.…”