On the applicability of the actuator line method for unsteady aerodynamics

TL;DR

This paper develops and validates a linear theory for the actuator line method (ALM) in unsteady aerodynamics, comparing it with classical theories and providing practical guidelines for its application.

Contribution

The study introduces a linear theoretical framework for ALM in unsteady flows and identifies optimal Gaussian width parameters for accurate simulations across frequencies.

Findings

ALM results align well with Theodorsen's theory at low reduced frequencies.

Optimal Gaussian width ratio for ALM is between 0.33 and 0.4.

Proper angle of attack definition is crucial for accurate unsteady aerodynamics simulations.

Abstract

A linear theory for unsteady aerodynamic effects of the actuator line method (ALM) was developed. This theory is validated using two-dimensional ALM simulations, where we compute the unsteady lift generated by the plunging and pitching motion of a thin airfoil in uniform flow, comparing the results with Theodorsen's theory. This comparison elucidates the underlying characteristics and limitations of ALM when applied to unsteady aerodynamics. Numerical simulations were conducted across a range of chord lengths and oscillation frequencies. Comparison of ALM results with theoretical predictions shows consistent accuracy, with all Gaussian parameter choices yielding accurate results at low reduced frequencies. Furthermore, the study indicates that selecting a width parameter ratio of $\varepsilon/c$ (the Gaussian width parameter over the chord length) between 0.33 and 0.4 in ALM yields the closest alignment with analytical results across a broader frequency range. Additionally, a proper definition of angle of attack for a pitching airfoil is shown to be important for accurate computations. These findings offer valuable guidance for the application of ALM in unsteady aerodynamics and aeroelasticity.