Applying inviscid linear unsteady lifting-line theory to viscous large-amplitude problems

Abstract

Unsteady Lifting-Line Theory (ULLT) is a low order method capable of modeling interacting unsteady and finite wing effects at low computational cost. Most formulations of the method assume inviscid flow and small amplitudes. Whilst these assumptions might be suitable for small-amplitude aeroelastic problems at high Reynolds numbers, modern engineering applications increasingly involve lower Reynolds numbers, large amplitude kinematics and vortex structures that lead to aerodynamic non-linearities. This paper establishes that ULLT still provides a good solution for low Reynolds number, large-amplitude kinematics problems, by comparing ULLT results against those of experimentally validated computational fluid dynamics simulations at Re=10000. Three-dimensional (3D) effects stabilize Leading Edge Vortex (LEV) structures, resulting in a good prediction of whole wing force coefficients by ULLT. Whilst the inviscid spanwise force distributions are accurate for small-amplitude kinematics, the ULLT cannot model 3D vortical structures, and thus it cannot correctly predict the force distribution due the LEV. It can however predict the shedding of LEVs to a limited extent via the leading edge suction parameter criterion. This can then be used as an indicator of the usefulness of the force distribution results.