Wang, Zi
(2021)
Aeroelastic modelling and analyses of a short wing-propeller configuration.
PhD thesis, University of Nottingham.
Abstract
Rotorcraft designs with the ability to fly as an aircraft but take off and land vertically as helicopters were first introduced in the early 1950s. However, the development of such concept stopped after a few failed attempts. Similar configurations, in which wings are equipped with additional propulsive propellers, has re-emerged in the past ten years for the compound helicopter and tilt-rotor aircraft. Those designs are aimed at introducing a new way of providing propulsive thrust, increasing the cruise speed, while retaining hovering advantages. However, the still open issue of high level of vibration resulting from fluid-structure interaction is exacerbated in the case of those rotorcrafts, with even more critical effects on the fatigue life, maintenance costs, on-board instrumental efficiency and comfort. Being able to model and predict the complex aeroelastic behaviour associated with the wing-propeller system is extremely important for achieving an optimised design. This project is an initial attempt to apply comprehensive analysis onto such compound aero-structures. Aiming at providing sufficient information of dynamic responses in the time-domain for the preliminary design stages, low-fidelity aeroelastic models are reviewed and basic structural and aerodynamic theories are introduced as basic building blocks.
With this intention, a numerical computational approach is developed for characterising aeroelastic behaviour of a short-wing/propeller configuration on small rotorcrafts. The computational tool consists of many components and the integration of them. Firstly, a two-dimensional aerodynamic model is developed based on thin aerofoil theories, including Wagner's, K\"{u}ssner's, Theodorsen's and Sears' unsteady models. The combinations of those theories are investigated for different output. The Wagner's and K\"{u}ssner's theories are found to be the most suitable approach for obtaining time-domain dynamic responses, which is one of the main objective outcomes for this thesis. Theodorsen's model, formulated in the frequency domain, is better suited for instability analyses and Sears' model is ideal for dynamic steady-state response solutions. At the same time, propeller inflow is simplified as several velocity components in its axial and vertical directions based on the general characteristic of propeller slipstream. Hence, the propeller effects on the wing structure can be taken into account by the two-dimensional aerodynamic model.
As for the mathematical representation of a short wing structure, beam theories are reviewed. Considering flapping, torsion and lead-lag motion, governing equations based on different beam theories are derived. In order to evaluate different structural effects and form a simple, yet realistic, representation, modal analyses based on different theories are compared. To perform efficient modal analyses, a numerical tool based on the transfer matrix method is introduced and validated. Structural coupling between flapping and torsion is examined and coupled modes are introduced. With the aid of modal analyses results, structural coupling, rotary inertia and shear deformation are found to contribute the most towards the structural modal behaviour. Hence, coupled flapping-torsion motion characterised by Euler-Bernoulli beam theory and separate lead-lag motion defined as a Timoshenko beam are found to be the most appropriate.
The integration of aerodynamic and structural models allows further investigation of aeroelastic stability boundary and time-domain dynamic responses under forced conditions. A numerical procedure is developed, featuring coupled modes, which has been proved to be accurate enough when validated against experimental results. Instability, both statically and dynamically, is then studied and flight condition defined. To obtain solutions of aeroelastic response under a defined flight condition, solution strategy and procedures for convergence analyses are specified. A case study on the short wing under propeller inflow is presented and time-domain dynamic responses are obtained. Collecting all modular solvers developed for the aeroelastic model, the tool was further exploited to demonstrate its capability in analysing phenomena involving different structural, flight and propeller conditions in preliminary design stages. It was found that, apart from the aeroelastic instability, the wingspan and propeller operational speed needs to be designed carefully in order to keep deformation at a minimal level.
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