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

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.