Optimizing Aerodynamic Efficiency in Subsonic Flows: A Parametric Analysis of Bio-Inspired Flaps using Asymptotic Methods

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Abstract
This research is focused on optimizing aircraft performance by harnessing the principles of avian covert feathers, specifically through the passive control of subsonic laminar incompressible boundary layers on airfoils. The exigency of this study is rooted in the growing need for more aerodynamically efficient aircraft, especially in light of increasing fuel costs and environmental concerns. To achieve this, the study employs a robust mathematical framework that amalgamates asymptotic methods, perturbation techniques, and triple-deck boundary layer theory, aiming for a rigorous quantification of aerodynamic behavior under various flight conditions. Three key parameters are meticulously scrutinized: the corrective parameter b, the flap position s0, and the flap angle β. These parameters are analysed for their impact on the lift (Cl) and drag (Cd) coefficients over a range of angles of attack (α). A notable outcome of this research is the identification of b as a pivotal variable that plays a stabilizing role in the aerodynamic system. Through extensive asymptotical modelling and non-linear stability analysis, it was deduced that b is indispensable for managing lift-to-drag ratios effectively across fluctuating flight conditions. To translate these theoretical findings into practical applications, the study introduces a comprehensive parametric landscape. This landscape serves as a decision-making tool by outlining how the parameters s0 and β behave across varying α scenarios, thereby providing actionable insights for airfoil configuration. Importantly, these results bear significant implications for the aerospace industry. They offer a pathway for the development of more efficient airfoils that promise reduced drag and, consequently, diminished fuel consumption.

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