Non-Linear Lifting Line Implementation and Validation for Aerodynamic and Stability Analysis
Carvalho, A. R. D.1; Brito, P. P. C.1
1 Universidade Federal de Uberlândia
doi:10.20906/CPS/CILAMCE2017-1307
Resumo
The well-known Prandtl's Lifting-Line Theory, elaborated in 1922, was the first well-succeded mathematical model able to describe the flow along the span of a wing. Since then, several modifications in the original linear formulation were proposed, aiming to extend its applications. The most popular modification, based on Gaussian quadrature, was presented by Multhopp. Most recently, Philips deduced a formulation in which it is possible to analyze wings with sweep and dihedral. Anderson also provided a non-linear algorithm that uses viscous airfoil data to feed the tridimensional model and predict the stall region. Compared to other potential flow based methods, such as Vortex Lattice and Panel Method, Lifting-Line has the advantage of the lowest computational cost and easier implementation, with comparable results, making it suitable for fast aerodynamic optimization codes. Furthermore, Anderson's method has the convenience of incorporating both, numerical or experimental, bi-dimensional viscous data. These facts explain why Lifting-Line is still being used in early simple aircraft and UAV designs. In this paper, we will describe the implementation and numerical modifications made in the algorithm proposed by (Anderson, 2010), in order to simulate the flow over a wing under angles of attack near the stall region. A big concern of this work is to show, with enough details, the effects of the boundary conditions adopted over the results accuracy and the computational time required. Different numerical differentiation, interpolation, and discretization schemes were tested to achieve the right values of circulation at the wing tip inside the iterative process of the method. Further, force and moment coefficients, as well as stability derivatives due to symmetric and asymmetric movement of control surfaces, was added to Anderson's formulation, allowing it to predict stability parameters due to the aileron actuation, for instance. The results were compared with classical and Philips's Lifting Line formulat
Palavras-chave: Nonlinear Lifting-Line; Aerodynamics; Aircraft stability; Potencial flow methods; Numerical methods