This work details the development and implementation of a numerical model capable of solving strongly-coupled fluid-structure interaction problems involving long thin structures, which are common multi-physics problems encountered in many applications. In most fluid-structure interaction problems the deformation of the slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal decomposition technique for linear structural analysis, the governing equations and boundary conditions are updated to account for the leading-order non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. Two computational fluid-structure interaction approaches are then implemented in a partitioned manner: a finite volume method for discretisation of both the fluid and solid domains and the quadratic modal formulation for the structure coupled with a finite volume fluid solver. Strong-coupling is achieved by means of a fixed-point solver with dynamic relaxation. The fluid-structure interaction approaches are validated and compared on benchmark problems of increasing complexity and strength of coupling between the fluid and solid domains. Fluid-structure interaction systems may become unstable due to the interaction between the fluid-induced pressure and structural rigidity. A thorough stability analysis of finite elastic plates in uniform flow is conducted by varying the structural length and flow velocity showing that these are critical parameters. Validation of the results with those from analytical methods is done. An analysis of the dynamic interactions between multiple finite plates in various configurations is also conducted.

A study of the interaction of one-sided flow over a compliant surface is presented. When fluid passes over a flexible surface the simultaneous interaction between the flow and structure gives rise to vibrations and instabilities on the surface as well as in the fluid. The fluid-structure interaction (FSI) has potential to be used in the control of boundary layer dynamics to achieve drag reduction through transition delay. The modelling and control of FSI systems apply to many fields of engineering beyond drag reduction, for example: the modelling and analysis of biomechanical systems; natural environmental systems; aero-elastics; and other areas where flow interacts moving or compliant boundaries. The investigation is performed through numerical simulation. This returns more detail than could be resolved through experiments, while also permitting the study of finite compliant surfaces that are prohibitively difficult, or impossible, to study with analytical techniques. In the present work, novel numerical modelling methods are developed from linear system analysis through to nonlinear disturbances and viscous effects. / Two numerical modelling techniques are adopted to approach the analysis of the FSI system. A potential-flow method is used for the modelling of flows in the limit of infinite Reynolds numbers, while a grid-free Discrete Vortex Method (DVM) is used for the modelling of the rotational boundary-layer flow at moderate Reynolds numbers. In both inviscid and viscous studies, significant contributions are made to the numerical modelling techniques. The application of these methods to the study of flow over compliant panels gives new insight to the nature of the FSI system. In the linear inviscid model, a novel hybrid computational/theoretical method is developed that evaluates the eigenvalues and eigenmodes from a discretised FSI system. The results from the non-linear inviscid model revealed that the steady-state of the non-linear wall motion is independent of initial excitation. For the viscous case, the first application of a DVM to model the interaction of a viscous, rotational flow with a compliant surface is developed. This DVM is successfully applied to model boundary-layer flow over a finite compliant surface.

The development of a numerical model of a two-stroke engine is undertaken to study the scavenging characteristics of the engine. The engine design is unique in its use of 16 passive intake valves in the cylinder head which, along with the exhaust ports located at bottom centre (BC), give the engine a top-down uniflow-scavenged configuration. Each valve constitutes a small stainless steel platelet within a cavity in the cylinder head which reacts to the pressure difference across the cylinder head. The principle focus of this study is the transient simulation of the scavenging flow using dynamic meshing to model the piston motion and the response of the passive intake valves to the scavenging flow for varied engine speed and peak pressure. A flowbench study of the steady flow through the cylinder head into a duct is incorporated as a step in the development of the transient numerical model. Validation of the numerical predictions is undertaken by comparing results from an experimental flowbench for the steady case and using a cold-flow scavenging rig for the transient simulations. Both the steady flow through the cylinder head and the unsteady flow within the cylinder indicate the presence of a recirculation region on the cylinder axis. As a result, short-circuiting of scavenging gas becomes considerable and leads to scavenging characteristics comparable to Hopkinson’s perfect mixing one-dimensional scavenging model. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2008-09-26 18:38:53.375

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.

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).