Water hammer represents a complex hydraulic phenomenon with significant consequences on the proper functioning and safety of operation for pipe and conduit systems. The complexity and intricate physics of water hammer translated into significant difficulties associated firstly, with finding a proper solution for understanding the mechanism of its occurrence and, secondly, relating to proposing technically and economically viable design methods and devices that would help reduce and mitigate water hammer effects. In this context, the present thesis deals with the numerical modeling of the transient behaviour of water pipe segments. Following an extensive literature review of the state-of-the-art on the water hammer mechanisms and past work on experimental, analytical and numerical analysis of this phenomenon, a three dimensional numerical model of the water hammer in a pipe which considers the fluid-structure interaction (FSI) is developed using a Finite Element Method – Finite Volume Method (FEM-FVM) technique. Structural and fluid computational results based on rapid and slow gate closure scenarios are compared with existing closed-form solutions of the water hammer. A parametric study is also performed on a simply supported pipe segment to determine the influence of various design parameter. A systematic sensitivity analysis was conducted and a ranking mechanism was established for the importance of each parameter on the fluid fields and structural response. A first comparative analysis is conducted on horizontally and vertically bent elevated pipe segments to quantify the influence of the bend angle on the results. A second comparative analysis is performed on a horizontally bent segment buried in soil to determine the influence of the pipe interaction with the soil on the response. It is observed that the thickness, span, initial velocity and bend angle had a significant impact on the pressure and structural response. The presence of soil was observed to have a significant benefit in decreasing the von-Mises stresses.

In this dissertation, a continuum sensitivity method is developed for efficient and accurate computation of design derivatives for nonlinear aeroelastic structures subject to transient<br />aerodynamic loads. The continuum sensitivity equations (CSE) are a set of linear partial<br />differential equations (PDEs) obtained by differentiating the original governing equations of<br />the physical system. The linear CSEs may be solved by using the same numerical method<br />used for the original analysis problem. The material (total) derivative, the local (partial)<br />derivative, and their relationship is introduced for shape sensitivity analysis. The CSEs are<br />often posed in terms of local derivatives (local form) for fluid applications and in terms of total<br />derivatives (total form) for structural applications. The local form CSE avoids computing<br />mesh sensitivity throughout the domain, as required by discrete analytic sensitivity methods.<br />The application of local form CSEs to built-up structures is investigated. The difficulty<br />of implementing local form CSEs for built-up structures due to the discontinuity of local<br />sensitivity variables is pointed out and a special treatment is introduced. The application<br />of the local form and the total form CSE methods to aeroelastic problems are compared.<br />Their advantages and disadvantages are discussed, based on their derivations, efficiency,<br />and accuracy. Under certain conditions, the total form continuum method is shown to be<br />equivalent to the analytic discrete method, after discretization, for systems governed by a<br />general second-order PDE. The advantage of the continuum sensitivity method is that less<br />information of the source code of the analysis solver is required. Verification examples are<br />solved for shape sensitivity of elastic, fluid and aeroelastic problems. / Ph. D.

Please read the abstract (Summary) in the 00front part of this document / Dissertation (M Eng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

<p>In this thesis, a theory of fluid--structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit is developed for  canonical geometries consisting of a 2D channel with a deformable top wall and an axisymmetric deformable tube. Focusing on hydrodynamics, a linear relationship between wall displacement and  hydrodynamic pressure is employed, due to its suitability for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, which is used to relate flow rate  to the pressure gradient (and the tube/wall deformation) via the classical solutions for oscillatory flow in a channel and in a tube (attributed to Womersley). Then, by two-way coupling the oscillatory flow and the wall deformation via the continuity equation, a one-dimensional nonlinear partial differential equation (PDE) governing the instantaneous pressure distribution along the conduit is obtained, without \textit{a priori} assumptions on the magnitude of the oscillation frequency (i.e., at arbitrary Womersley number).The PDE is solved numerically to evaluate the pressure distribution as well as the cycle-averaged pressure at several points along the length of the channel and the tube. It is found  that the cycle-averaged pressure (for harmonic pressure-controlled conditions) deviates from the expected steady pressure distribution, suggesting the presence of a streaming flow. An analytical perturbative solution for a weakly deformable conduit is also obtained to rationalize how FSI induces such streaming. In the case of a compliant tube, the results obtained from the proposed reduced-order PDE and its perturbative solutions are validated against three-dimensional, two-way-coupled direct numerical simulations. A good agreement is shown  between theory and simulations for a range of dimensionless parameters characterizing the oscillatory flow and the FSI, demonstrating the validity of the proposed theory of oscillatory flows in compliant conduits at arbitrary Womersley number.</p>

Coherent vortex-dominated structures in the wake are ubiquitous in natural and engineered flows. The well-known 'von Karman street', in which two rows of counter-rotating vortices develop on the leeward side of a solid body immersed in a fluid, is only one such vortex-based structure in the wake. Recent work on fluid-structure interaction has shown that several other types of vortex structures can arise in natural and engineered systems. The production of these vortex structures downstream often mark the onset of qualitative and/or quantitative changes in the forces exerted on the vortex-shedding body upstream, and can be used as diagnostic tools for engineering structures undergoing Vortex-Induced Vibrations. This dissertation presents a two-part study of vortex dynamics in the laminar wakes of bluff bodies. The first part consists of a series of experiments on a transversely oscillating circular cylinder in a uniform flow field at Re≲250. These experiments were carried out in a gravity-driven soap film channel, which provides a `two-dimensional laboratory' for hydrodynamics experiments under certain conditions. In these experiments, we generated a `map' of the vortex patterns that arise in the wake as a function of the (nondimensional) frequency and amplitude of the cylinder's motion. Our results show that the '2P mode' of vortex shedding can robustly occur in the two-dimensional wake of an oscillating cylinder, contrary to what has been reported in the literature. By making small changes to the meniscus region of the soap film, we have explored possible mechanisms that can explain why the `P+S mode' of vortex shedding is usually reported to be more prevalent than the '2P mode' at low Reynolds number, when the flow is two-dimensional. In doing so, we have found that small modifications to the cylinder on the order of the boundary layer thickness can make a significant difference to the vortex shedding process. In the second part, we develop a generalized form of von Karman's drag law for N-vortex streets: periodic wakes in which the vortices are arranged in regularly-repeating patterns with N>2 vortices per period. The original form of von Karman's drag law then reduces to a special case of this generalized form, which has the potential to model several kinds of vortex-dominated wakes that have been reported in the literature. In this work, we show how this generalized drag law can be used to model '2P' and 'P+S' wakes in both `drag' and `thrust' form. As a contribution to the study of three-dimensional wakes, we also studied a periodic array of vortex rings, which are often used to represent the wakes of marine organisms like jellyfish and squid. We described the problem mathematically using a newly-developed Green's function, and comprehensively examine the fluid physics of such an array of vortex rings as a function of the non-dimensional parameters that govern this phenomenon. In the process, we have discovered a new type of topology that arises in this flow, which may have connections with the `optimal vortex formation length' of vortex rings. / Doctor of Philosophy / The interaction of solid objects with fluids such as water and air, often termed Fluid-Structure Interaction (FSI), gives rise to a wide variety of natural phenomena. Understanding FSI is important as an avenue of scientific interest as well as for engineering applications. In this dissertation, we are interested in the subset of FSI phenomena known as wakes: the fluid flow that is left behind when a solid moves rapidly through quiescent fluid, or when water or air flows rapidly past a stationary obstacle. In such situations, the flow is often rapidly rotating, taking the form of vortices or eddies, i.e., concentrated regions of rotating fluid. These eddies, or vortices, can be described mathematically using simple differential equations, and are the subject of the field of vortex dynamics, which is a branch of fluid mechanics. In the first part of this thesis, we have made contributions to the experimental study of FSI and wakes by making use of an experimental technique known as a gravity-driven soap film channel. In these experiments, a 'soap film', i.e., the surface of a soap bubble, is stretched out over a longitudinal channel formed by nylon wires and held taut in a rectangular shape. This rectangular film of soap is only a few micrometers thick, and is continuously fed by soap solution from the top and drained at the bottom, resulting in a steadily-flowing 'channel' of two-dimensional flow. In this experimental setup, we introduce a circular acrylic cylinder to serve as the archetypal 'obstacle' to fluid flow and oscillate it at a range of frequencies and amplitudes while using a high-speed camera to visualize the flow. This gives rise to a fascinating set of qualitatively distinct vortex patterns in the wake, with the structure depending on the selected frequency and amplitude of cylinder oscillation. In the second part of this thesis, we have developed mathematical models of two-dimensional wakes using a system of point vortices and of three-dimensional wakes using a system of circular vortex rings. We show how these idealized mathematical models of rotating flow, i.e., point vortices and vortex rings, can be used as building blocks for physically-plausible models of actually-occurring wakes, including those which were observed in the first part of this work. For two-dimensional wakes, we use Newton's laws applied to a fluid to determine the forces being exerted on a solid body, immersed in a fluid, whose wake takes the form of regularly-repeating vortices known as 'vortex streets'. This allows us to give, for the first time, theoretical predictions of the drag or thrust force associated with vortex streets such as those observed in our experiments.

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In this dissertation, we examine mechanics of rhythmic tracheal compression (RTC) in the darkling beetle, Zophobas morio. In Chapter 2, we studied the relationship between hemolymph pressure and tracheal collapse to test the hypothesis that pressure is a driving mechanism for RTC. We found that tracheae collapse as pressure increases, but other physiological factors in the body may be affecting tracheal compression in live beetles. Additionally, as the tracheae compress, they do so in varying spatial patterns across the insect body. In chapter 3, we examined spatial variations in the taenidial spacing, stiffness, and tracheal thickness along the length of the tracheae. We related variations in Young's modulus and taenidial spacing with measurements of collapse dimples and found that spatial patterns of Young's modulus correlate with dimensions of collapse dimples. This correlation suggests an intuitive link between tracheal stiffness variations and the unique patterns observed in compressing tracheae. Lastly, in chapter 4, we studied the non-uniform collapse patterns in 3-D. By manually pressurizing the hemocoel and imaging using synchrotron microcomputed tomography (SR-µCT), we reconstructed the tracheal system in its compressed state. While previous studies used 2-D x-ray images to examine collapse morphology, ours is the first to quantify collapse patterns in 3-D and compare with previous 2-D quantification methods. Our method is also the first to make a direct measure of tracheal volume as the tracheal system compresses, similar to the phenomenon that occurs during rhythmic tracheal compression. / Doctor of Philosophy / Insects have long been a source of curiosity and inspiration for scientists and engineers. The insect respiratory system stands as an example of a seemingly complex oxygen delivery system that operates with relative simplicity. As opposed to mammals and other vertebrates, the insect respiratory system does not deliver oxygen using blood. Instead, insects possess a massive network of hollow tracheal tubes that are distributed throughout the body. Air enters spiracular valves along the length of the insect body, travels through the tracheal tube network, and is delivered directly to the tissues. In some insects, the tracheae compress and expand, driving flow of respiratory gasses. However, unlike vertebrate lungs, there are no muscles directly associated with the tracheal system that would drive this tracheal compression, and exactly how this behavior occurs is not fully understood. In this dissertation, we examined pulsatory increases in blood pressure as a possible mechanism that underlies these tracheal compressions in the darkling beetle, Zophobas morio. Additionally, as the tracheae compress, they do so with varying spatial patterns across the insect body. Because tracheae are complex and non-uniform composite tubes, we examined spatial variations in the microstructure, stiffness, and tracheal thickness along the length of the trachea. Lastly, we visualized the variable collapse patterns in three dimensions using synchrotron micro-computed tomography combined with manual pressurization of the hemocoel. While previous studies used two-dimensional x-ray images to quantify tracheal collapse patterns, this work represents the first three-dimensional study. Understanding tracheal collapse mechanics, material properties, and their relationships with the circulatory system can help to gain an understanding of how insects create complex fluid flows within the body using relatively simple mechanisms.

Novel aircraft configurations tend to be sized by physical phenomena that are largely neglected during conventional fixed wing aircraft design. High-fidelity fluid-structure interaction that accurately models geometric nonlinerity during a transient aeroelastic gust response is critical for sizing the aircraft configuration early in the design process. The primary motivation of this research is to develop a continuum shape sensitivity method that can support gradient-based design optimization of practical and multidisciplinary high-fidelity analyses. A local continuum sensitivity analysis (CSA) that utilizes spatial gradient reconstruction (SGR) and avoids mesh sensitivities is presented for shape design derivative calculations. Current design sensitivity analysis (DSA) methods have shortcomings regarding accuracy, efficiency, and ease of implementation. The local CSA method with SGR is a nonintrusive and element agnostic method that can be used with black box analysis tools, making it relatively easy to implement. Furthermore, it overcomes many of the accuracy issues documented in the current literature. The method is developed to compute design derivatives for a variety of applications, including linear and nonlinear static beam bending, linear and nonlinear transient gust analysis of a 2-D beam structure, linear and nonlinear static bending of rectangular plates, linear and nonlinear static bending of a beam-stiffened plate, and two-dimensional potential flow. The analyses are conducted using general purpose codes. For each example the design derivatives are validated with either analytic or finite difference solutions and practical numerical and modeling considerations are discussed. The local continuum shape sensitivity method with spatial gradient reconstruction is an accurate analytic design sensitivity method that is amenable to general purpose codes and black box tools. / Ph. D.

This work presents a partitioned approach to simulating free-surface flow interaction with hyper-elastic structures in which a smoothed particle hydrodynamics (SPH) solver is coupled with a finite-element (FEM) solver. SPH is a mesh-free, Lagrangian numerical technique frequently employed to study physical phenomena involving large deformations, such as fragmentation or breaking waves. As a mesh-free Lagrangian method, SPH makes an attractive alternative to traditional grid-based methods for modeling free-surface flows and/or problems with rapid deformations where frequent re-meshing and additional free-surface tracking algorithms are non-trivial. This work continues and extends the earlier coupled 2D SPH-FEM approach of Yang et al. [1,2] by linking a double-precision GPU implementation of a 3D weakly compressible SPH formulation [3] with the open source finite element software Code_Aster [4]. Using this approach, the fluid domain is evolved on the GPU, while the CPU updates the structural domain. Finally, the partitioned solutions are coupled using a traditional staggered algorithm. / Ph. D.

Current Federal Aviation Regulations require costly and time consuming crashworthiness testing to certify aircraft. These tests are only capable of a limited assessment of progressive damage and all crash configurations and scenarios cannot be physically evaluated. Advancements in technology have led to accurate and effective developments in numerical modeling that have the possibility of replacing these rigorous physical experiments. Through finite element analysis, an in-depth investigation of an aircraft equipped with a fabricated composite undercarriage was evaluated during water ditching. The severe impact of aircraft ditching is dynamic and nonlinear in nature; the goal of this work to develop a methodology that not only captures the structural response of the aircraft, but also the fluidic behavior of the water. Fundamental studies were first conducted on a well-researched fluid-solid interaction problem, the water entry of a wedge. Typical modeling strategies did not capture the desired detail of the event. An advanced meshing scheme combining meshed and meshless Lagrangian techniques was developed and multiple wedge angles were tested and compared to analytic and qualitative results. The meshing technique proved valid, as the difficult to model phenomena of splashing was captured and the maximum impact force was within five percent of analytical calculations for the 20° and 30° deadrise wedge. Physical small scale aircraft ditching experiments were then performed with an innovative testing platform capable of producing varied aircraft approach configurations. The model was outfitted with an instrumented composite undercarriage to record data throughout the impact while a high-speed camera recorded the event. Numerical simulations of the model aircraft were then compared to experimental results with a strong correlation. This methodology was then ultimately tested on a deformable model of a fuselage section of a full-size aircraft. / Master of Science