Sectional Leading Edge Vortex Lift and Drag Coefficients of Autorotating Samaras

Abstract

Autorotating samaras such as Sycamore seeds are capable of descending at exceptionally slow speeds and the secret behind this characteristic is attributed to a flow mechanism known as the leading edge vortex (LEV). A stable LEV is known to increase the maximum lift coefficient attainable at high angles of attack and recent studies of revolving and flapping wings have proposed suitable lift and drag coefficient models to characterise the aerodynamic forces of the LEV. For the samara, however, little has been explored to properly test the suitability of these low-order lift and drag coefficient models in describing the aerodynamic forces produced by the samara. Thus, in this paper, we aim to analyse the use of two proposed aerodynamic models, namely, the normal force and Polhamus models, in describing the sectional aerodynamic lift of a samara that is producing a LEV. Additionally, we aim to quantify the aerodynamic parameters that can describe the lift and drag of the samara for a range of wind speed conditions. To achieve this, the study first examined the samara flight data available in the literature, and from it, the profiles of the lift coefficient curves were investigated. Subsequently, a numerical Blade Element-Momentum model (BEM) of the autorotating samara encompassing different lift profiles was developed and validated against a comprehensive set of samara flight data, which were measured from wind tunnel experiments conducted at the University of Bristol for three different Sycamores. The results indicated that both the normal force and Polhamus lift models combined with the normal force drag can be used to describe the two-dimensional lift characteristics of a samara exhibiting an LEV. However, the normal force model appeared to be more suitable, since the Polhamus relied on many assumptions. The results also revealed that the aerodynamic force parameters can vary with windspeed and with the samara wing characteristics, as well as along the span of the samara wing. Values of the lift curve slope, zero-lift drag coefficient, and maximum lift coefficient are predicted and presented for different samaras. The study also showed that the low-order BEM model was able to generate a good agreement with the experimental measurements in the prediction of both rotational speed and thrust. Such a validated BEM model can be used for the initial design of bio-inspired rotors for micro-air vehicles.