An approach for unsteady lifting-line time-marching numerical computation

Abstract

This paper presents the basis of a computational time-marching approach, for large-aspect ratio lifting systems submitted to unsteady motions, using the lifting-line concept. When engineering requires such an approach, quasi-steady ones are currently encountered, which are based on Prandtl's lifting-line approach for steady flows. The results of recent theoretical works on the unsteady lifting-line, based on the matched asymptotic expansion technique, allow one to improve, on sound theoretical foundations, this quasi-steady approach. The proposed approach solves a first-order approximation of the unsteady outer problem for the time-evolution of the spanwise circulation distribution along the lifting-line. It introduces, in the same kind of process as Prandtl's one, for each span section, an unsteady two-dimensional description of the aerofoil behaviour together with a formulation for the three-dimensional unsteady induced velocity on the lifting-line. The approach's validity is examined through a simple numerical implementation for three wing motion cases. Considering the numerical results it produces, it can be stated that the unsteady lifting-line model implementation can be considered as time-consistent, whereas the quasi-steady one cannot. Furthermore, the approach presented here allows large time steps, even for very unsteady wing motions, and compares favourably with some classical results of R. T. Jones. © 1998 John Wiley & Sons, Ltd.