Applying frequency-domain unsteady lifting-line theory to time-domain problems

TL;DR

This paper presents a method to leverage frequency-domain unsteady lifting-line theory for solving time-domain problems involving finite wings with arbitrary motion, by transforming kinematics to the frequency domain, performing convolutions, and converting back.

Contribution

It introduces a novel approach to apply frequency-domain unsteady lifting-line theory to time-domain problems through a transformation-convolution-inversion process.

Findings

Effective prediction of forces and moments on finite wings with arbitrary kinematics.

Demonstrates the practicality of frequency-domain methods for time-domain unsteady aerodynamics.

Simplifies complex unsteady flow calculations by leveraging frequency-domain techniques.

Abstract

Frequency-domain unsteady lifting-line theory is better developed than its time-domain counterpart. To take advantage of this, this paper transforms time-domain kinematics to the frequency domain, performs a convolution and then returns the results back to the time-domain. It demonstrates how well-developed frequency-domain methods can be easily applied to time-domain problems, enabling prediction of forces and moments on finite wings undergoing arbitrary kinematics.