The development of modern unmanned aerial vehicles, high-altitude long-endurance drones, wind turbines, energy harvesting devices and micro air vehicles all require the consideration of unsteady aerodynamics. Unsteady flow simulation is not only more computationally expensive than steady simulations, but the unsteadiness expands the range of relevant parameters to be considered. This makes the use of traditional unsteady computational fluid dynamics methods too computationally expensive for many applications.
Low-order methods provide an alternative. By neglecting less important aspects of the problem being solved, the cost of obtaining a solution can be greatly reduced. However, currently available low-order methods are limited by being either too narrow in the phenomena they model, still too computationally expensive, or not sufficiently well understood to be used with confidence. In this dissertation, low-order methods for the unsteady aerodynamics of finite wings are investigated. Uncertainties around Unsteady Lifting-Line Theory (ULLT) are resolved and new methods are derived where existing methods are either too slow or do not exist.
This thesis primarily studies ULLT. ULLT allows a problem to be modelled as interacting two-dimensional problems, reducing the cost of obtaining a solution. This approach is applied to Euler cases and low Reynolds number (Re = 10 000) cases for both sinusoidal oscillation kinematics and arbitrary kinematics. Small and large amplitude kinematics are investigated, with large amplitudes introducing additional complications including leading-edge vortex structures.
Frequency-domain problems are initially considered in the Euler regime using frequency domain ULLT. It is shown that existing methods produce good solutions when the assumptions made in their derivation are satisfied. For low Reynolds number cases, where their assumptions are violated, they still provide reasonable accuracy, even in the presence of aerodynamic non-linearities. Frequency-domain methods are then applied to time-domain
problems using a new, low-computational-cost method. It is shown how Fourier transforms can be used to obtain solutions for arbitrary input kinematics. Some of the limitations of this method are then alleviated with a new time-marching geometrically non-linear ULLT. However, this method cannot model the leading-edge vortex. For that, another new method is obtained, based on the 3D vortex particle method
