Thèse : Sciences : Lausanne : 1923. / Bibliographie, p. 107.

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Thesis--University of Adelaide, 1957 (presented for Angas Engineering Scholarship). / Typewritten.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 91-95). Also available via the Internet.

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During the two last decades, topology optimization has grown to be an accepted and used method to produce conceptual designs. Topology optimization is traditionally carried out on a component level, but in this project, the possibility to apply it to airframe design on a full scale aeroplane model is evaluated. The project features a conceptual flying-wing design on which the study is to be carried out. Inertia Relief is used to constrain the aeroplane instead of traditional single point constraints with rigid body motion being suppressed by the application of accelerations instead of traditional forces and moments. The inertia relief method utilized the inertia of the aeroplane to achieve a state of quasi-equilibrium such that static finite element analysis can be carried out. Two load cases are used: a steep pitch-up manoeuvre and a landing scenario. Aerodynamic forces are calculated for the pitch-up load case via an in-house solver, with the pressure being mapped to the finite element mesh via a Matlab-script to account for different mesh sizes. Increased gravitational loads are used in the landing load case to simulate the dynamic loading caused in a real landing scenario, which is unable to be accounted for directly in the topology optimization. It can be concluded that the optimization is unable to account for one of the major design limitations: buckling of the outer skin. Approaches to account for the buckling of the outer skin are introduced and analysed, with a focus on local compression constraints throughout the wing. The compression constraints produce some promising results but are not without major drawbacks and complications. In general, a one-step topology optimization to produce a mature conceptual airframe design is not possible with optimization algorithms today. It may be possible to adopt a multiple-step optimization approach utilizing topology optimization with following size and shape optimization to achieve a design, which could be expanded on in a future project.

The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance for the circulation of the atmosphere and oceans, mainly because of the momentum and energy they transport and because of the mixing they create upon breaking. So far the study of inertia-gravity waves has answered a number of questions about their propagation and dissipation, but many aspects of their generation remain poorly understood. The interactions that take place between the slow motion, termed balanced or vortical motion, and the fast inertia-gravity wave modes provide mechanisms for inertia-gravity wave generation. One of these is the instability of balanced flows to gravity-wave-like perturbations; another is the so-called spontaneous generation in which a slowly evolving solution has a small gravity-wave component intrinsically coupled to it. In this thesis, we derive and study a simple model of inertia-gravity wave generation which considers the evolution of a small-scale, small amplitude perturbation superimposed on a large-scale, possibly time-dependent °ow. The assumed spatial-scale separation makes it possible to apply a WKB approach which models the perturbation to the flow as a wavepacket. The evolution of this wavepacket is governed by a set of ordinary differential equations for its position, wavevector and its three amplitudes. In the case of a uniform flow (and only in this case) the three amplitudes can be identifed with the amplitudes of the vortical mode and the two inertia-gravity wave modes. The approach makes no assumption on the Rossby number, which measures the time-scale separation between the balanced motion and the inertia-gravity waves. The model that we derive is first used to examine simple time-independent flows, then flows that are generated by point vortices, including a point-vortex dipole and more complicated flows generated by several point vortices. Particular attention is also paid to a flow with uniform vorticity and elliptical streamlines which is the standard model of elliptic instability. In this case, the amplitude of the perturbation obeys a Hill equation. We solve the corresponding Floquet problem asymptotically in the limit of small Rossby number and conclude that the inertia-gravity wave perturbation grows with a growth rate that is exponentially small in the Rossby number. Finally, we apply the WKB approach to a flow obtained in a baroclinic lifecycle simulation. The analysis highlights the importance of the Lagrangian time dependence for inertia-gravity wave generation: rapid changes in the strain field experienced along wavepacket trajectories (which coincide with fluid-particle trajectories in our model) are shown to lead to substantial wave generation.

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