Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Unsteady time-domain analysis of finite wings using the lifting-line theory via a finite element approach
Submission Author:
Guilherme Bueno , SP
Co-Authors:
Guilherme Bueno, Felipe Liorbano, Ricardo Afonso Angélico
Presenter: Guilherme Bueno
doi://10.26678/ABCM.COBEM2021.COB2021-0685
Abstract
Over the past few years, aeronautical entities have been dedicating themselves to reduce the carbon footprint of aircraft operations, production, and maintenance. Among the advances in design concepts, it is possible to highlight some technologies that achieved drag and weight reductions. The combination of high aspect ratio wings with advanced materials used on modern aircraft leads to structural systems susceptible to large displacements when subjected to loads. This behavior must be considered in the aircraft dynamic response and in its performance evaluations. The analysis of these complex phenomena in the time domain requires an unsteady aerodynamic model to predict spanwise wing loading history. Therefore, this article aims to develop a method to compute the unsteady lift and pitch moment of a rigid thin finite wing undergoing step or oscillatory motions in plunge or pitch. Since Wagner's function describes the airfoil's non-stationary behavior, its solution can be extended to finite wings when combined with the lifting-line theory. This combination leads to a second kind Volterra-Fredholm integrodifferential equation with a singular kernel. Herein, the model is written on its weak form and is applied an approach based on the finite element method framework. Hence, the problem is described by a set of equations that one can differentiate with respect to time using the Leibniz integral rule yielding an initial value problem. Runge-Kutta algorithm applies to time integration. A Python routine was implemented using an object-oriented paradigm. The developed code is applied to investigate the aerodynamic behavior of a finite wing for four cases: (i) a step in pitch, (ii) a step in plunge; (iii) an oscillating pitch motion; and (iv) an oscillating plunge motion. The results are compared with reported literature data presenting a good agreement.
Keywords
Unsteady Aerodynamics, lifting-line, Wagner function, Finite Element Method
