<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)

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.

Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating and steering. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Before using a full-scale tire model, interactions of the tread block with a specific surface is studied. To do so, several mechanical tests such as uniaxial, biaxial, planar (shear), and DMA are conducted to predict the hyper-viscoelastic properties of the rubber. Using multi-scale modeling techniques, the friction coefficient between the tire and pavement, for wet conditions, is characterized via developing 2D and 3D model representing the rubber tread interacting with the rough surface. Using a tire model that is validated based on results found in the literature as well as in-house experimental data, fluid-structure interaction (FSI) between the tire-water-road surfaces are investigated through two approaches. In the first approach, the coupled Eulerian-Lagrangian (CEL) formulation was used. The drawback associated with the CEL method is the laminar assumption that the behavior of the fluid at length scales smaller than the smallest element size is not captured. To improve the simulation results, in the second approach, an FSI model incorporating finite-element methods and the Navier-Stokes equations for a two-phase flow of water and air, and the shear stress transport k-ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. The improved FSI model was applied to hydroplaning speed and cornering force scenarios. In addition, tire contact patch length was calculated using the developed FSI model and was compared to the results obtained from the intelligent tire. / Doctor of Philosophy / Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating and steering. Hydroplaning as well as low skid resistance are considered as the main factors leading to traffic accidents. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Different factors involve in the hydroplaning phenomenon such as water film thickness, tire pressure, tire tread pattern, tire tread depth, vehicle speed and pavement texture. Before using a full-scale tire model, interactions of the tire tread with a specific surface is studied. To do so, several mechanical tests are conducted to predict the hyper-viscoelastic properties of the rubber. Using a single scale methodology is not capable to obtain the sufficient information regarding the effect of roughness on the friction. As a result, using multi-scale modeling techniques, the friction coefficient between the tire and pavement, for wet conditions, is characterized via developing 2D and 3D model representing the rubber tread interacting with the rough surface. Since in the hydroplaning problem, a solid structure and a fluid domain are in interaction, such a problem considered as a fluid-structure interaction (FSI) problem. In this work, the FSI between the tire-water-road surfaces are investigated through two approaches. To improve the simulation results, an FSI model incorporating finite-element methods and the Navier-Stokes equations for a two-phase flow of water and air, and the shear stress transport k-ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. In addition, tire contact patch length was calculated using the developed FSI model and was compared to the results obtained from the intelligent tire.

The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the derivation of local CSA with SGR for obtaining flow derivatives using finite volume formulation and its nonintrusive implementation (i.e. without accessing the analysis source code). Examples of a NACA0012 airfoil and a lid-driven cavity highlight the effect of the accuracy of the sensitivity boundary conditions on the flow derivatives. It is shown that the spatial gradients of flow velocities, calculated using SGR, contribute significantly to the sensitivity transpiration boundary condition and affect the accuracy of flow derivatives. The effect of using an inconsistent flow solution and Jacobian matrix during the nonintrusive sensitivity analysis is also studied. Another novel contribution is derivation of a hybrid adjoint formulation of CSA, which enables efficient calculation of design derivatives of a few performance functions with respect to many design variables. This method is demonstrated with applications to 1-D, 2-D and 3-D structural problems. The hybrid adjoint CSA method computes the same values for shape derivatives as direct CSA. Therefore accuracy and convergence properties are the same as for the direct local CSA. Finally, we demonstrate implementation of CSA for computing aeroelastic response shape derivatives. We derive the sensitivity equations for the structural and fluid systems, identify the sources of the coupling between the structural and fluid derivatives, and implement CSA nonintrusively to obtain the aeroelastic response derivatives. Particularly for the example of a flexible airfoil, the interface that separates the fluid and structural domains is chosen to be flexible. This leads to coupling terms in the sensitivity analysis which are highlighted. The integration of the geometric sensitivity with the aeroelastic response for obtaining shape derivatives using CSA is demonstrated. / Ph. D.

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.