<div>This thesis examines the problem of low Reynolds number viscous fluid–structure interactions (FSIs) at the microscale. A myriad of examples of such phenomena exist, both in nature (blood flow in arteries, air flow in lungs), as well as in the laboratory (microfluidics devices, soft robotics). For this thesis, we restrict to internal flows in conduits with deformable walls. Specifically, two types of conduits of different cross-sectional shapes are considered: microchannels and microtubes. Both of these geometries are slender and thin.</div><div>Different types of material behavior are considered, via constitutive laws, in the solid domain, namely linearly elastic, hyperelastic and viscoelastic; and in the fluid domain, namely Newtonian and power-law fluids with shear-dependent viscosity. Similarly, the geometry and dimensions of the structures allow us to use shell and plate theories in the solid domain, and the lubrication approximation of low Reynolds number flow in the fluid domain.</div><div>First, we study a rectangular microchannel with a deformable top wall of moderate thickness, conveying a power-law fluid at steady conditions. We obtain a nonlinear differential equation for pressure as a function of imposed steady flow rate, consisting of infinite expansions of hypergeometric functions. We also conduct simulations of FSI using the commercial computer-aided engineering (CAE) software ANSYS, to both benchmark our perturbative theory and to establish the limits of its applicability.</div><div>Next, we study fluid–structure interactions in a thin microtube constituted of a linearly elastic material conveying a generalized Newtonian fluid. Here, we employ the Donnell shell theory to model the deformation field in the structure of the tube. As a novel contribution, we formulate an analytical expression for the (radial) deformation of the tube using the method of matched asymptotic expansions, taking into account the bending boundary layers near the clamped ends. Using our perturbative theory, we also improve certain classical but partial results, like Fung’s model and the law of Laplace, to match with direct numerical simulations in ANSYS.</div><div>Subsequently, we explore FSI in hyperelastic tubes via the Mooney–Rivlin model. In a thin-walled vessel, we formulate a novel nonlinear relationship between (local) deformation and (local) pressure A similar approach for the thick-walled tube, yields a nonlinear ODE to be solved numerically. Due to strain hardening, the hyperelastic tube appears stiffer and supports higher pressure drops than a linearly elastic tube.</div><div>Finally, we study transient compressible flow being conveyed in a linearly viscoelastic tube. By employing a double perturbation expansion (for weak compressibility and weak FSI), a predictive relationship between the deformed radius, the flow rate and the (local) pressure is obtained. We find that, due to FSI, the Stokes flow takes a finite time to adjust to any changes emanating from the boundary motion. In the case of oscillatory pressure imposed at the inlet, acoustic streaming is shown to arise due to FSI in this compressible flow. Fundamentally, the goal of the research in this thesis is to generate a catalog of flow rate–pressure drop relationships for different types of fluid–structure interactions, depending on the combinations of fluid mechanics and structural mechanics models (behaviors). These relationships can then be used to solve practical problems. We formulate a theory of hydrodynamic bulge testing, through which the elastic modulus is estimated from the pressure drop and flow rate measurements in a microchannel with a (thick and pre-stressed) compliant top wall, without measuring the deformation. A sensitivity analysis, via Monte Carlo simulation, shows that the hydrodynamic bulge test is only a slightly less accurate</div><div>than the traditional bulge test, but is less susceptible to uncertainty emanating from the noise in measurements.</div>

Includes bibliographical references / In this thesis, the development of a strongly coupled, partitioned fluid-structure interactions (FSI) solver is outlined. Well established methods are analysed and new methods are proposed to provide robust, accurate and efficient FSI solutions. All the methods introduced and analysed are primarily geared towards the solution of incompressible, transient FSI problems, which facilitate the use of black-box sub-domain field solvers. In the first part of the thesis, radial basis function (RBF) interpolation is introduced for interface information transfer. RBF interpolation requires no grid connectivity information, and therefore presents an elegant means by which to transfer information across a non-matching and non-conforming interface to couple finite element to finite volume based discretisation schemes. The transfer scheme is analysed, with particular emphasis on a comparison between consistent and conservative formulations. The primary aim is to demonstrate that the widely used conservative formulation is a zero order method. Furthermore, while the consistent formulation is not provably conservative, it yields errors well within acceptable levels and converges within the limit of mesh refinement. A newly developed multi-vector update quasi-Newton (MVQN) method for implicit coupling of black-box partitioned solvers is proposed. The new coupling scheme, under certain conditions, can be demonstrated to provide near Newton-like convergence behaviour. The superior convergence properties and robust nature of the MVQN method are shown in comparison to other well-known quasi-Newton coupling schemes, including the least squares reduced order modelling (IBQN-LS) scheme, the classical rank-1 update Broyden's method, and fixed point iterations with dynamic relaxation. Partitioned, incompressible FSI, based on Dirichlet-Neumann domain decomposition solution schemes, cannot be applied to problems where the fluid domain is fully enclosed. A simple example often provided in the literature is that of balloon inflation with a prescribed inflow velocity. In this context, artificial compressibility (AC) will be shown to be a useful method to relax the incompressibility constraint, by including a source term within the fluid continuity equation. The attractiveness of AC stems from the fact that this source term can readily be added to almost any fluid field solver, including most commercial solvers. AC/FSI is however limited in the range of problems it can effectively be applied to. To this end, the combination of the newly developed MVQN method with AC/FSI is proposed. In so doing, the AC modified fluid field solver can continue to be treated as a black-box solver, while the overall robustness and performance are significantly improved. The study concludes with a demonstration of the modularity offered by partitioned FSI solvers. The analysis of the coupled environment is extended to include steady state FSI, FSI with free surfaces and an FSI problem with solid-body contact.

Developing lifelike vocal fold models is challenging due to various associatedbiomechanical complexities. Nevertheless, the development and analysis of improved vocal foldmodels is worthwhile since they are valuable tools for gaining insight into human vocal foldvibratory, aerodynamic, and acoustic response characteristics. This thesis seeks to contribute tothe development of computational and physical vocal fold modeling in two ways. First is byintroducing a method of obtaining internal deformation fields within vibrating synthetic vocal foldmodels; second is by presenting an optimization algorithm coupled with a computational vocalfold model to optimize geometry and stiffness of a synthetic vocal fold model to achieve morerealistic vibration patterns.The method for tracking the internal deformation of self-oscillating vocal fold models isbased on MR imaging. Silicone models scaled to four times life-size to lower the flow-inducedvibration frequency were imbedded with fiducial markers in a coronal plane. Candidate markermaterials were tested using static specimens, and two materials, cupric sulfate and glass, werechosen for testing in the vibrating VF models. The vibrating models were imaged using a gatedMRI protocol wherein MRI acquisition was triggered using the subglottal pressure signal. Twodimensionalimage slices at different phases during self-oscillation were captured, and in eachphase the fiducial markers were clearly visible. The process was also demonstrated using a threedimensionalscan at two phases. The benefit of averaging to increase signal-to-noise ratio wasexplored. The results demonstrate the ability to use MRI to acquire quantitative deformation datathat could be used, for example, to validate computational models of flow-induced VF vibrationand quantify deformation fields encountered by cells in bioreactor studies.A low fidelity, two-dimensional, finite element model of VF flow-induced vibration wascoupled with a custom MATLAB-based genetic algorithm optimizer. The objective was to achievea closed quotient within the normal human physiological range. The results showed that changesin geometry and stiffness would lead to a model that exhibited the desired characteristics. Aphysical model based on optimized parameters was then fabricated and the closed quotient wastested. The physical model successfully vibrated with nonzero closed quotient as predicted by thecomputational model.

This thesis deals with dynamic behavior of swirl turbine vibrating in a liquid. Primarily is studied decrease of natural frequencies of rotor due the interaction with fluid environment, namely for different levels of submerged rotor in fluid. After that follows the detection of natural frequencies of swirl turbine in operating speed. The problem is solved by computational modeling in ANSYS system. For this solution is used acoustic elements method. The results are compared with experiment.

This master thesis is focused on usage of monitoring pulse wave propagation in aortic system in a field of diagnostic abdominal aortic aneurysm (AAA). There is a description of cardio-vascular system and its pathology in a form of AAA. A summarization of temporary diagnostic method was created and some new methods were proposed. This new methods presume monitoring of pulse wave propagation. Fluid structure interaction (FSI) analyses of pulse wave propagation were performed on simplified models of geometry which representing specific sections of aorta. The goal of these analyses was to prove usage of FSI method in a future development of proposed diagnostic methods.

In this thesis we introduce a new fluid-structure interaction model in the Eulerian description. This model is developed for blood flow in viscoelastic artery. For the fluid part a non-Newtonian model Oldroyd-B is used and for the structure part Kelvin-Voigt model is employed. Kelvin-Voigt model will be reached by a limiting process of the Oldroyd-B model. Interface between these two materials is guaranteed by conservative level-set method. Numerical tests of this model is performed by finite element method. This model is used for a simulation of two problems: a two dimensional channel with viscoelastic walls and pulsating inflow and Turek-Hron FSI benchmark. 1

The cylinder block/valve plate interface is a critical design element of axial piston machines. In the past, extensive work has been done at Maha Fluid Power Research center to model this interface were a novel fluid structure thermal interaction model was developed which accounts for thermal and elasto-hydrodynamic effects and has been proven to give an accurate prediction of the fluid film thickness. This paper presents an in-depth investigation of the impact of the elastic deformation due to pressure and thermal loadings of the end case/housing on the performance of the cylinder block/valve plate interface. This research seeks to understand in a systematic manner the sensitivity of the cylinder block/valve plate interface to the structural design and material properties. A comparison between simulations results is done by utilizing different end case designs and material compositions, both in the valveplate and end case solids.

The purpose of this study was to develop a robust fluid-structure-interaction (FSI) technology that can accurately model non-linear flutter responses for sub- and transonic fluid flow. The Euler equation set governs the fluid domain, which was spatially discretised by a vertex-centred edge-based finite volume method. A dual-timestepping method was employed for the purpose of temporal discretisation. Three upwind schemes were compared in terms of accuracy, efficiency and robustness, viz. Roe, HLLC (Harten-Lax-Van Leer with contact) and AUSM+-up Advection Up-stream Splitting Method). For this purpose, a second order unstructured MUSCL (Monotonic Upstream-centred Scheme for Conservation Laws) scheme, with van Albada limiter, was employed. The non-linear solid domain was resolved by a quadratic modal reduced order model (ROM), which was compared to a semi-analytical and linear modal ROM. The ROM equations were solved by a fourth order Runge-Kutta method. The fluid and solid were strongly coupled in a partitioned fashion with the information being passed at solver sub-iteration level. The developed FSI technology was verified and validated by applying it to test cases found in literature. It was demonstrated that accurate results may be obtained, with the HLLC upwind scheme offering the best balance between accuracy and robustness. Further, the quadratic ROM offered significantly improved accuracy when compared to the linear method. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

We have developed a third-order shear and normal deformable plate/shell theory (TSNDT) incorporating all geometric nonlinearities and used it to analyze, by the finite element method (FEM), transient finite deformations of a sandwich beam with two face sheets and the core made of St. Venant-Kirchhoff materials.  A triangular cohesive zone model with stress based criterion for delamination initiation and energy based relation for complete separation is used to analyze delamination failure in a beam under mixed-mode loading. We have studied transient post-buckling deformations and delamination progression in an axially compressed and initially delaminated clamped-clamped sandwich beam.  The buckling load for transient deformations exceeds that for static deformations and the increase depends upon the loading rate.  This FE software for analyzing deformations of sandwich beam is coupled with that based on the boundary element method (BEM) for studying time-dependent deformations of water and the coupled software is used to analyze deformations of flexible curved hulls due to water slamming loads.  The water is assumed to be inviscid and incompressible and undergo irrotational deformations.  The Laplace equation for the velocity potential is numerically solved by the BEM with normal velocity and pressure assumed to be continuous across the interface between the hull and the water.  Challenging issues resolved in this work include finding the wetted surface of the hull, nonlinear deformations of the fluid due to convective part of acceleration, effects of geometric nonlinearities on hull\'s deformations, resolution of the jet tip, as well as the initiation and propagation of delamination between the face sheets and the core.  It is found that both delamination and geometric nonlinearities significantly affect the hydrodynamic pressure acting on the hull, and transverse shear deformations contribute more to the strain energy absorbed by the core than its transverse normal deformations.  <br />We have used the discontinuous basis functions to derive the Galerkin formulation of a nonlinear problem involving simple shearing deformations of a homogeneous and isotropic thermo-elasto-visco-plastic body with uniform deformations perturbed to simulate the effect of a defect.  The resulting coupled nonlinear ordinary differential equations are integrated with respect to time by using the package, LSODE (Livermore Solver for Ordinary Differential Equations).  Computed results showing localization of deformations into narrow regions are found to agree well with those found by the FEM, and spatial variations of the shear stress are smoother than those obtained by the FEM.<br /><br /> / Ph. D.

Interaction of fluctuating vortex shedding with blade vibration can lead to a new class of aeromechanical instability referred as Non-synchronous vibrations. Investigating a well-known case that shows similar NSV features such as a circular cylinder can develop the understanding of physics behind NSV. A common approach to further investigating the vortex induced vibration is to control the motion of the cylinder and allowing the response of the wake to the motion to be studied in isolation. It has been found very important to carefully match the experimental conditions between free and controlled vibration. Many of research in the field of vortex induced vibration apply a rigid cylinder mounted horizontally and moving transversely to the flow stream as a paradigm for understanding the physics behind this phenomenon. Regarding the difficulties of implementation of vertically moving cylinder in experimental study, vortex dynamic and lock-in behavior of eccentrically rotating cylinder is studied in this M.Sc. Thesis. The main focus of this research is to understand to what extend a general feature of free vortex-induced vibration can be observed in the case of eccentrically rotating cylinder. If the present case captures the essential characteristics of freely oscillating cylinder the results of the forced motion via eccentrically rotating cylinder can be applied to predict the motion of an elastically mounted body. To do so a CFD model is established to predict the response, vorticity structure in near wake, timing of vortex shedding and the range of lock-in region over specific parameter space of the introduced alternative case. A commercial CFD code, Ansys/CFX, was implemented to perform this numerical study. Existences of synchronization region, striking similarity in lift force coefficient and wake mode have been observed in the current study.