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.

This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure-interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, geometrically non-linear deformations, which has a major interest in, amongst others, the aerospace and biomedical industries. The first part of this work investigates improving the efficiency with which a stable and robust in-house code, Elemental, models thin structures undergoing dynamic fluid-induced bending deformations. Variations of the existing finite volume formulation as well as linear and higher-order finite element formulations are implemented. The governing equations for the solid domain are formulated in a total Lagrangian or undeformed conguration and large geometrically non-linear deformations are accounted for. The set of equations is solved via a single-step Jacobi iterative scheme which is implemented such as to ensure a matrix-free and robust solution. Second-order accurate temporal discretisation is achieved via dual-timestepping, with both consistent and lumped mass matrices and with a Jacobi pseudo-time iteration method employed for solution purposes. The matrix-free approach makes the scheme particularly well-suited for distributed memory parallel hardware architectures. Three key outcomes, not well documented in literature, are highlighted: the issue of shear locking or sensitivity to element aspect ratio, which is a common problem with the linear Q4 finite element formulation when subjected to bending, is evaluated on the finite volume formulations; a rigorous comparison of finite element vs. finite volume methods on geometrically non-linear structures is done; a higher-order finite volume solid mechanics procedure is developed and evaluated. The second part of this work is concerned with fluid-structure interaction (FSI) modelling. It considers the implementation and coupling of a higher order finite element structural solver with the existing finite volume fluid-flow solver in Elemental. To the author’s knowledge, this is the first instance in which a strongly-coupled hybrid finite element–finite volume FSI formulation is developed. The coupling between the fluid and structural components with non-matching nodes is rigorously assessed. A new partitioned fluid-solid interface coupling methodology is also developed, which ensures stable partitioned solution for strongly-coupled problems without any additional computational overhead. The solver is parallelised for distributed memory parallel hardware architectures. The developed technology is successfully validated through rigorous temporal and mesh independent studies of representative two-dimensional strongly-coupled large-displacement FSI test problems for which analytical or benchmark solutions exist. / Dissertation (MEng)--University of Pretoria, 2012. / Mechanical and Aeronautical Engineering / unrestricted

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

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<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.

Porosity is known to be one of the primary detrimental factors controlling fatigue life and total elongation of several cast alloy components. The two main aims of this work are to examine pore nucleation and growth effects for predicting gas microporosity and to study the physics of bifilm dynamics to gain understanding in the role of bifilms in producing defects and the mechanisms of defect creation. In the second chapter of this thesis, an innovative technique, based on the combination of a set of conservation equations that solves the transport phenomena during solidification at the macro-scale and the hydrogen diffusion into the pores at the micro-scale, was used to quantify the amount of gas microporosity in A356 alloy castings. The results were compared with published experimental data. In the reminder of this work, the Immersed Element-Free Galerkin method (IEFGM) is presented and it was used to study the physics of bifilm dynamics. The IEFGM is an extension of the Immersed Finite Element method (IFEM) developed by Zhang et al. [50] and it is an attractive technique for simulating FSI problems involving highly deformable bifilm-like solids.

No description available.

The long-term operational safety of nuclear power plants is of utmost importance. Seismic isolation has been shown to be effective in reducing the demands on structures in many applications, including nuclear power plants (NPP). Many designs for Generation III+ NPP include a large passive cooling tank as a measure of safety that can be used during power failure. In a large seismic event, the fluid in the tank may be excited, and while the phenomenon of fluid-structure interaction (FSI) has also been studied in the context of base isolated liquid storage tanks, the effect on seismically isolated NPP has not yet been explored. This thesis presents a two-part study on a base isolated NPP with friction pendulum bearings. The first part of the study compares the usage of a linear fluid model to a nonlinear fluid model in determining tank and structural demand parameters. The linear fluid model was found to represent the nonlinear fluid model well for preliminary analysis apart from peak sloshing height, which it consistently underestimated. The second part of the study uses a linear fluid model, an empty tank model and a rigid fluid model to investigate the influence of FSI on the structural response of an isolated NPP compared to a fixed base NPP. In general, the response of a fixed base NPP considering FSI using a linear fluid model can typically be bound by the results assuming an empty tank and assuming a full tank with rigid fluid mass. However, this does not hold for the base isolated NPP, as the peak isolation displacement for an NPP with a linear fluid model at design depth is greater than the peak isolation displacement than the same NPP with an empty tank and with a rigid fluid model. / Thesis / Master of Applied Science (MASc)