Unsteady lifting-line theory and the influence of wake vorticity on aerodynamic loads

TL;DR

This paper evaluates the effectiveness of unsteady lifting-line theory (ULLT) in predicting aerodynamic loads on oscillating rectangular wings, comparing different models to high-fidelity CFD results to identify their accuracy regimes.

Contribution

It introduces a complete ULLT based on Sclavounos's work, along with simplified models, and assesses their accuracy against CFD for various wing aspect ratios and oscillation frequencies.

Findings

ULLT is a low-cost model effective for certain aspect ratios and frequencies.

Simplified ULLT considering only streamwise vorticity performs well in specific regimes.

The study identifies the regimes where each ULLT variant provides accurate predictions.

Abstract

Frequency domain Unsteady Lifting-Line Theory (ULLT) provides a means by which the aerodynamics of oscillating wings may be studied at low computational cost without neglecting the interacting effects of aspect ratio and oscillation frequency. Renewed interest in the method has drawn attention to several uncertainties however. Firstly, to what extent is ULLT practically useful for rectangular wings, despite theoretical limitations? And secondly, to what extent is a complicated wake model needed in the outer solution for good accuracy? This paper aims to answer these questions by presenting a complete ULLT based on the work of Sclavounos, along with a novel ULLT that considers only the streamwise vorticity and a Prandtl-like pseudosteady ULLT. These are compared to high fidelity Euler CFD for cases of rectangular wings at multiple aspect ratios and oscillation frequencies. The results of this work establish ULLT as a low computational cost model capable of accounting for interacting finite-wing and oscillation frequency effects, and identify the aspect ratio and frequency regimes where the three ULLTs are most accurate. This research paves the way towards the construction of time-domain or numerical ULLTs which may be augmented to account for non-linearities such as flow separation.