In this thesis we use a diffeo-geometric framework based on manifolds hat are locally modeled on ``convenient'' vector spaces to study the geometry of some infinite dimensional spaces. Given a finite dimensional symplectic manifold M, we construct a weak symplectic structure on each leaf I_w of a foliation of the space of compact oriented isotropic submanifolds in M equipped with top degree forms of total measure 1. These forms are called weightings and such manifolds are said to be weighted. We show that this symplectic structure on the particular leaves consisting of weighted Lagrangians is equivalent to a heuristic weak symplectic structure of Weinstein. When the weightings are positive, these symplectic spaces are symplectomorphic to reductions of a weak symplectic structure of Donaldson on the space of embeddings of a fixed compact oriented manifold into M. When M is compact, by generalizing a moment map of Weinstein we construct a symplectomorphism of each leaf I_w consisting of positive weighted isotropics onto a coadjoint orbit of the group of Hamiltonian symplectomorphisms of M equipped with the Kirillov-Kostant-Souriau symplectic structure. After defining notions of Poisson algebras and Poisson manifolds, we prove that each space I_w can also be identified with a symplectic leaf of a Poisson structure. Finally, we discuss a kinematic description of spaces of weighted submanifolds.

Thesis (M.S. in Astronautical Engineering)--Naval Postgraduate School, March 2004. / Thesis advisor(s): I. Michael Ross, Don Danielson. Includes bibliographical references (p. 39-40). Also available online.

Thesis--M. Phil., University of Hong Kong. / Mimeographed.

In this thesis we use a diffeo-geometric framework based on manifolds hat are locally modeled on ``convenient'' vector spaces to study the geometry of some infinite dimensional spaces. Given a finite dimensional symplectic manifold M, we construct a weak symplectic structure on each leaf I_w of a foliation of the space of compact oriented isotropic submanifolds in M equipped with top degree forms of total measure 1. These forms are called weightings and such manifolds are said to be weighted. We show that this symplectic structure on the particular leaves consisting of weighted Lagrangians is equivalent to a heuristic weak symplectic structure of Weinstein. When the weightings are positive, these symplectic spaces are symplectomorphic to reductions of a weak symplectic structure of Donaldson on the space of embeddings of a fixed compact oriented manifold into M. When M is compact, by generalizing a moment map of Weinstein we construct a symplectomorphism of each leaf I_w consisting of positive weighted isotropics onto a coadjoint orbit of the group of Hamiltonian symplectomorphisms of M equipped with the Kirillov-Kostant-Souriau symplectic structure. After defining notions of Poisson algebras and Poisson manifolds, we prove that each space I_w can also be identified with a symplectic leaf of a Poisson structure. Finally, we discuss a kinematic description of spaces of weighted submanifolds.

Thesis (Ph. D.)--Oregon State University, 1990. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (2005)--University of Western Australia, 2005.

Thesis (M.S.)--Naval Postgraduate School, 1995. / "September, 1995." Includes bibliographical references (p. 83-85).

No description available.

The primary motivation for this dissertation is to address the problem of aircraft engine degradation due to ingestion of non-aqueous particulates such as sand, dust, and ash. This dissertation introduces high fidelity Lagrangian particle models to account for the rotational effects of particles in complex turbulent flows. Part of the focus of the research is to provide novel techniques to model particle-surface collision induced rotation as well as develop correlations for forces and torques on non-spherical particles. Particulates in nature have a tendency to damage turbomachinery components through a number of mechanisms which include erosion and adhesion and will lead to engine failure. The trajectory, size, velocity, chemical composition and shape of the particles play an important role in predicting the damage occurring in the engine. An aircraft engine consists of a cold section, comprising of an inlet and compressor, and a hot section consisting of the combustion chamber and turbine. The particulates enter through the inlet and impact against the components within the compressor eroding away the surfaces as well as causing the particles to fracture into smaller sizes. On entering the hot section, the particles encounter drastic phase changes leading to change in their intrinsic properties. Some of these particles may also adhere to the blade surfaces blocking cooling ports. In this report we focus on particle interaction with the cold sections of aviation gas turbine engines, and so we do not study any of the phenomena that occur due to the heating of particles. To predict how particles will interact with the engine components it is first important to understand the trajectory of particles. For flow into the inlets and early stages of the compressor, particle trajectory is dominated by a two factors: particle aerodynamics and rebounds from surface collisions. Near-wall aerodynamics also play an important role in particle impact and surface erosion. The particle trajectories show the adverse effects of the near wall aerodynamic effects just before collision. The particle velocities are influenced significantly by these effects, and in order to predict particle rebound properties and erosion accurately, these effects have to be taken into account. One important, but often neglected aspect of particle trajectory is accurate prediction of particle rotation. The primary source of the angular velocity of the particles is through particle collisions with walls. However, few models of particle-wall impact introduce rotation. Several studies indicate that the particle angular velocity plays a significant role on their trajectories even in simple geometries such as curved pipes. The research in this dissertation introduces a collision-induced particle rotation model that improves the prediction of particle trajectories after rebound. The improved collision model compares well to experimental data provided in literature and its importance is demonstrated in a simple pipe bend. There have been several experimental studies from past literature, that have developed lift and drag correlations for rotating particles. However, from the literature we also see that these correlations are very specific to the particle shape, Reynolds Number and their orientation relative to the oncoming flow. Real particles are non-spherical, and almost all existing models for particles consider only spheres. Non-spherical particles have different values of aerodynamic lift, drag, and torque compared to their spherical counterparts. As a means to explore and quantify the effect of particle shape, and orientation on the aerodynamic forces and torques on non-spherical particles, we developed a CFD framework that has the ability to measure the lift and drag on arbitrarily shaped non-spherical particles by rotating a single particle in space in an airstream. On changing parameters such as the air velocity, rotation rate, orientation we can tabulate the lift and drag forces and torques on the particle. These correlations can be implemented into Lagrangian particle models to improve the predictions of particle trajectories due to rotation induced lift and drag. The importance of particle rotation is demonstrated by injecting particles into a high pressure compressor section of a gas turbine engine and comparing erosion profiles and impact locations between particles with and without the rotation models. The research presented in this dissertation aims to improve the prediction of particle trajectories by considering non-ideal parameters such as the aerodynamic effects on non-spherical particles and the influence of rotation on particle motion. Particle-surface collisions play a significant role in particle trajectories and so the first step in improving these predictions is to gain a better understanding of particle rebound phenomena. / Doctor of Philosophy / Aircraft engines suffer significant damage due to ingestion of solid particles such as sand, dust, and ash. The primary motivation for this dissertation is to investigate these phenomena and provide a better understanding of particle physics. These particles have a tendency to damage turbomachinery components through a number of mechanisms which include erosion and adhesion which will lead to engine failure. The trajectory, size, velocity, chemical composition and shape of the particles play an important role in predicting the damage occurring in the engine. An aircraft engine consists of a cold section, comprising of an inlet and compressor, and a hot section consisting of the combustion chamber and turbine. The particles enter through the inlet and impact against the components within the compressor eroding away the surfaces as well as causing the particles to fracture into smaller sizes. On entering the hot section, the particles encounter drastic phase changes leading to change in their intrinsic properties. Some of these particles may also adhere to the blade surfaces blocking cooling ports. In this report we focus on particle interaction with the cold sections of aviation gas turbine engines, and so we do not study any of the phenomena that occur due to the heating of particles. To predict how particles will damage the engine components it is first important to understand the trajectory of particles. For flow into the inlets and early stages of the compressor, particle trajectory is dominated by two factors: particle aerodynamics and rebounds from surface collisions. One important, but often neglected aspect of particle trajectory is accurate prediction of particle rotation. The primary source of particle rotation is through particle collisions with walls. However, few models of particle-wall impact introduce rotation and so the research in this dissertation introduces a collision-induced particle rotation model that improves the prediction of particle trajectories after rebound. The improved collision model compares well to experimental data provided. Real sand particles are oddly shaped particles and not perfect spheres. These non-spherical particles behave differently in air when compared to their spherical counterparts. The aerodynamic lift, drag, and torque are the driving factors for this difference in behavior. As a means to explore and quantify the effect of particle shape, and orientation on the aerodynamic forces and torques on non-spherical particles, we developed a CFD framework that has the ability to measure the lift and drag on arbitrarily shaped non-spherical particles by rotating a single particle in space in an airstream. On changing parameters such as the air velocity, particle rotation rate, and orientation we can tabulate the lift and drag forces and torques on the particle. These correlations can be implemented into to improve the predictions of particle motion in an aircraft engine. The importance of particle rotation is demonstrated by injecting particles into a high pressure compressor section of a gas turbine engine and comparing erosion profiles and impact locations between particles with and without the rotation models.

No description available.