The thesis presents a fluid-structure interaction studies on the hemodynamics of blood flow in the left ventricle and through the mitral valve. The virtual model consists of a mathematical model of the left ventricle coupled with a complex and structurally flexible bi-leaflet valve representing the mitral opening. The mitral valve is a bicuspid valve with anterior and posterior leaflets and it regulates unidirectional blood flow from the left atrium to the left ventricle in the diastole phase. The leaflets are made of chordae, annulus and papillary muscles. The goal of this study is to provide biomedical engineers and clinical physicians with a virtual laboratory tool to understand the dynamics of blood flow in a diseased heart and aid in the design of novel artificial heart valves. To this end, the simulation studies present an increasingly complex model of the heart to evaluate the vortex ring formation and evolution of the diastole phase in the left ventricle; and to characterize the septal-anterior motion in a diseased heart with obstructive hypertrophic cardiomyopathy. Finally, in collaboration with an industrial partner, the fluid-structure modeling framework was used to evaluate the performance of a new accelerated artificial valve tester. / Graduate

Motivated by the physiological phenomena of collapse and flow limitation for a serial pulmonary artery stenosis, we investigated the three-dimensional influence of spatial configuration on the wall motion and hemodynamic. Our numerical study focused on the effect of two geometrical parameters: the relative distance and the angular orientation between the two stenoses. The collapse of a compliant arterial stenosis may cause flow choking, which would limit the flow reserve to major vital vascular beds such as the lungs, potentially leading to a lethal ventilation-perfusion mismatch. Flow through a stenotic vessel is known to produce flow separation downstream of the throat. The eccentricity of a stenosis leads to asymmetric flow where the high velocity jets impinge on the sidewall, thereby inducing significant dissipation. The additional viscous dissipation causes a higher pressure drop for a flow through a stenotic vessel, than in a straight compliant vessel. It is likely that some particular morphology would have a higher vulnerability to the fluid induced instability of buckling (divergence), under physiological pulsatile flow. It was found that fluid pressure distribution have substantial implication for the downstream wall motion, under conditions of strong coupling between nonlinear vessel geometries, and their corresponding asymmetric flow. The three-dimensional fluid structure interaction problem is solved numerically by a finite element method based on the Arbitrary Lagrangian Eulerian formulation, a natural approach to deal with the moving interface between the flow and vessel. The findings of this investigation reveal that the closeness between stenoses is a substantial indication of wall collapse at the downstream end. Moreover, the results suggest a close link between the initial angular orientation of the distal stenosis (i.e. the constriction direction) and the subsequent wall motion at the downstream end. For cases showing evidence of preferential direction of wall motion, it was found that the constricted side underwent greater cumulative displacement than the straight side, suggestive of significant wall collapse.

In this dissertation we study multiscale methods for slowly varying porous media, fluid and solid coupling, and application to geomechanics. The thesis consists of three closely connected results. We outline them and their relation. First, we derive a homogenization result for Stokes flow in slowly varying porous media. These results are important for homogenization in deformable porous media. Traditionally, these techniques are applied to periodic media, however, in the case of Fluid-Structure Interaction (FSI) slowly varying domains occur naturally. We then develop a computational methodology to compute effective quantities to construct homogenized equations for such media. Next, to extend traditional geomechanics models based primarily on the Biot equations, we use formal two-scale asymptotic techniques to homogenize the fully coupled FSI model. Prior models have assumed trivial pore scale deformation. Using the FSI model as a fine-scale model, we are able to incorporate non-trivial pore scale deformation into the macroscopic equations. The primary challenge here being the fluid and solid equations are represented in different coordinate frames. We reformulate the fluid equation in the fixed undeformed frame. This unified domain formulation is known as the Arbitrary Lagrange-Eulerian (ALE). Finally, we utilize the ALE formulation of the Stokes equations to develop an efficient multiscale finite element method. We use this method to compute the permeability tensor with much less computational cost. We build a dense hierarchy of macro-grids and a corresponding collection of nested approximation spaces. We solve local cell problems at dense macro-grids with low accuracy and use neighboring high accuracy solves to correct. With this method we obtain the same order of accuracy as we would if we computed all the local problems with highest accuracy.

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 54-55). Also available on the World Wide Web.

Thesis (M.S.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (leaves 93-96).

Thesis (M.S.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaves 68-71).

Thesis (M.S.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaves 90-92).

Thesis (Ph. D.)--University of Alabama at Birmingham, 2006. / Description based on contents viewed Jan. 26, 2007; title from title screen. Includes bibliographical references (p. 112-126).

Ce travail de thèse est une contribution à l’analyse de bifurcation des écoulements fluides avec prise en compte des interactions fluide-structure. Les phénomènes d’instabilité en interaction fluide-structure apparaissent dans de nombreux domaines de la vie courante ou industriels comme, par exemple : le flottement d’un drapeau dans le vent ou bien l’écoulement au sein d’échangeurs thermiques sur les sites de production d’énergie, l’écoulement autour des câbles sous-marins pour l’extraction de matières premières ou la fixation des plateformes off-shore, l’écoulement autour des structures aéronautiques ou navales. Dans ces situations, un phénomène complexe de vibration des structures induite par vortex peut se produire. L’objectif de la thèse est de proposer un algorithme permettant l’analyse de stabilité de tels systèmes. Ainsi, le couplage original d’une méthode de perturbation d’ordre élevé (Méthode Asymptotique Numérique - MAN) à une discrétisation spatiale permettant la prise en compte des interactions fluide-structure est proposée. À cet effet, une description purement eulérienne du mouvement est retenue. L’interaction fluide- structure est décrite au moyen d’une méthode de frontières immergées (MFI) à forçage continu (méthode de pénalisation) et discret (méthode Ghost-Cell). La présence d’obstacles au sein de l’écoulement est obtenue au moyen de la méthode de Level-Set. En complément, un intégrateur temporel des équations du mouvement associant la MAN, la MFI et une technique d’homotopie est proposé. L’ensemble de ces algorithmes est appliqué à des problèmes d’écoulement incompressible, à faible nombre de Reynolds, d’un fluide visqueux newtonien en présence d’obstacles solides rigides (fixes ou mobiles). L’analyse de stabilité d’un écoulement dans une conduite avec expansion/contraction soudaine (bifurcation stationnaire), et autour d’un cylindre (bifurcation de Hopf) est traitée. L’analyse transitoire d’un écoulement autour d’un cylindre rigide et mobile est également proposée. Les résultats obtenus permettent d’évaluer la précision et la performance des algorithmes proposés. Ainsi, les résultats de cette thèse permettent de conclure sur le bien-fondé de l’approche et constituent une première étape vers l’analyse de stabilité d’écoulements en présence de structures complexes, représentatifs de situations réelles / This thesis is a first contribution to the bifurcation analysis of fluid flows by taking into account fluid-structure interactions. Instability with fluid-structure interactions appears in many areas of everyday life or industry such as, for example: flag floating in the wind, flow within heat exchangers for energy production, flow around submarine cables for the extraction of raw materials or the fixing of off-shore platforms, flow around aeronautical or naval structures. In these situations, complex vortex-induced vibrations of the structures can occur. The aim of the thesis is to propose an algorithm allowing stability analysis of such systems. Thus, an original coupling of a high order perturbation method (Asymptotic Numerical Method - ANM) to a spatial discretization which takes into account fluid-structure interactions is proposed. For this purpose, a purely Eulerian description of the motion is retained. Fluid-structure interaction is described using an immersed boundary method (IBM) with continuous forcing (penalization method) and discrete (Ghost-Cell method) forcing. The presence of bodies within the flow is obtained by means of the Level-Set method. In addition, a time integrator of the governing equations associating ANM, IBM and homotopy technique is proposed. All these algorithms are applied to analyse incompressible flows, at low Reynolds number, of a Newtonian viscous fluid in the presence of rigid solids (fixed or moving). Bifurcation analysis of flows in a channel with sudden expansion / contraction (stationary bifurcation), or around a cylinder (Hopf bifurcation) are carried out. Transient analysis of a flow around a moving rigid cylinder is also proposed. Our results make it possible to evaluate accuracy and performance of the proposed algorithms. Thus, thesis results allow to conclude on the validity of the proposed approach. Finally, this thesis work constitutes a first step towards flow stability analysis in the presence of complex structures, representative of real situations.

High-mast light poles are used frequently to illuminate large areas such as motorways and parking lots. These poles are extremely tall with respect to their cross-section, reaching heights of more than 40 meters. These structures undergo a strong aeroelastic response due to wind, oftentimes resulting in fatigue cracking at the base. The purpose of the research is to better understand the effects of wind-induced vibrations of tall flexible structures using a combination of computational fluid dynamics and structural finite element codes. Field results of existing high-mast poles will be used to calibrate and verify the theoretical modeling.Periodic vortex shedding is observed to occur on these structures at certain wind velocities. The shedding of vortices causes pressure differences across the pole, resulting in a net driving force perpendicular to the direction of the wind. When the frequency of shedding, and thus the driving force, matches the natural frequency of the pole, excitation of the structure can be significant. This phenomenon is called lock-in. Poles that are repeatedly subjected to wind at lock-in velocity may suffer excessive deformation and fatigue damage. The aeroelastic response is especially significant, since the damping of the structural system is so small.In order to model the fluid-structure interaction, OpenFOAM libraries were compiled into a single application that combined a structural dynamic finite element code along with a mesh movement algorithm. The loosely coupled system applies the driving forces (integrated pressures) to the structure in a conventional serial staggered procedure. The coupling of the two domains and the mesh deformation calculationswere software written by the author. The 3-field solution formulation is implemented using a mesh movement algorithm based on a pseudo-elastic approach. Incompressible flow is assumed, as the lock-in velocities for the first three natural frequency modes ofthe pole are relatively low. Large Eddy Simulation is used for turbulence modeling.In conjunction with the University of Wyoming, two existing steel hexadecagonal high-mast poles in Wyoming, USA, were instrumented with accelerometers and anemometers. These data were used to calibrate and verify the structural, stiffness, damping, and response characteristics.A series of 14 simulations were run that increased in the difficulty of the domain being simulated. Different aspects of the pole aparatus were investigated individually, such as the taper and angle of incidence of flow. An atmospheric boundary layer model was incorporated. The final case resulted in the simulation of a 16-sided tapered pole subject to flow from an atmospheric boundary layer inlet, incorporating large eddy simulation turbulence modeling. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished