A finite element-based unsteady lifting line method using the attached-flow Leishman-Beddoes model

State-space aerodynamic models are of interest for preliminary aircraft design, particularly
in the context of a multi-disciplinary optimization framework. Such models can be used in order to estimate aeroelastic and aeroservoelastic performance at low computational cost. The Wagner-Lifting Line (WLL) method was developed to fill this role but it is incompressible. This work presents an alternative that seeks to extend the applicability the WLL approach
to low compressible airspeeds. Instead of coupling the lifting line method to theWagner
function, the present model couples the lifting line approach to the attached-flow components of the Leishman-Beddoes model. The 3D solution is obtained using a finite element discretization in an object-oriented programming framework written in Python and using a Runge-Kutta scheme for the time integration. A mesh analysis is carried out and a good accuracy is obtained even using a low number of finite elements. Comparisons with higher-fidelity incompressible and compressible models are carried out, showing a satisfactory agreement in the first case with some differences due to the fact that these models are of distinct natures. In the compressible case, the comparison is made in the frequency domain. It shows a good agreement for the oscillatory lift amplitude mainly for low reduced frequencies.