This dissertation presents useful nonlinear models for fluid forcing on a moving body in two distinct contexts, and methods for analyzing the geometric structure within those and other mathematical models. This manuscript style dissertation presents three works within the theme of understanding fluid forcing and geometric structure. When a bluff body is free to move in the presence of an incoming bluff body wake, the average forcing on the body is dependent on its position relative to the upstream bluff body. This position-dependent forcing can be conceptualized as a stiffness, much like a spring. This work presents an updated model for the quasi-steady fluid forcing of a wake and extends the notion of wake stiffness to consider a nonlinear spring. These results are compared with kinematic experimental results to provide an example of the application of this framework. Fluid force models also play a role in understanding the behavior of passive aerodynamic gliders, such as gliding animals or plant material. The forces a glider experiences depend on the angle that its body makes with respect to its direction of motion. Modeling the glider as capable of pitch control, this work considers a glider with a fixed angle with respect to the ground. Within this model, all trajectories in velocity space collapse to a 1-dimensional invariant manifold known as the terminal velocity manifold. This work presents methods to identify the terminal velocity manifold, investigates its properties, and extends it to a 2-dimensional invariant manifold in a 3-dimensional space. Finally, in the search for manifolds such as the terminal velocity manifold, this dissertation introduces a new diagnostic for identifying the low dimensional geometric structure of models. The trajectory divergence rate uses instantaneous vector field information to identify regions of large normal stretching and strong normal convergence between nearby invariant manifolds. This work lays out the mathematical basis of the trajectory divergence rate and shows its application to approximate a variety of structures including slow manifolds and Lagrangian coherent structures. This dissertation applies nonlinear theoretical and numerical techniques to analyze models of fluid forcing and their geometric structure. The tools developed in this dissertation lay the groundwork for future research in the fields of flow-induced vibration, plant and animal biomechanics, and dynamical systems. / Ph. D. / When an object moves through a fluid such as air or water, the motion of the surrounding fluid generates forces on the moving object, affecting its motion. The moving object, in turn, affects the motion of the surrounding fluid. This interaction is complicated, nonlinear, and hard to even simulate numerically. This dissertation aims to analyze simplified models for these interactions in a way that gives a deeper understanding of the physics of the interaction between an object and a surrounding fluid. In order to understand these interactions, this dissertation looks at the geometric structure of the models. Very often, there are low-dimensional points, curves, or surfaces which have a very strong effect on the behavior of the system. The search for these geometric structures is another key theme of this dissertation. This dissertation presents three independent studies, with an introduction and conclusion to discuss the overall themes. The first work focuses on the forces acting on a cylinder in the wake of another cylinder. These forces are important to understand, because the vibrations that arise from wake forcing are important to consider when designing bridges, power cables, or pipes to carry oil from the ocean floor to offshore oil platforms. Previous studies have shown that the wake of a circular cylinder acts like a spring, pulling harder on the downstream cylinder the more it is moved from the center of the wake. In this work, I extend this idea of the wake as a spring to consider a nonlinear spring, which keeps the same idea, but provides a more accurate representation of the forces involved. The second work considers a simple model of gliding flight, relevant to understanding the behavior of gliding animals, falling leaves, or passive engineered gliders. Within this model, a key geometric feature exists on which the majority of the motion of the glider occurs, representing a 2-dimensional analogy to terminal velocity. In this work, I study the properties of this influential curve, show several ways to identify it, and extend the idea to a surface in a 3-dimensional model. The third study of this dissertation introduces a new mathematical quantity for studying models of systems, for fluid-body interaction problems, ocean flows, chemical reactions, or any other system that can be modeled as a vector field. This quantity, the trajectory divergence rate, provides an easily computed measurement of highly attracting or repelling regions of the states of a model, which can be used to identify influential geometric structures. This work introduces the quantity, discusses its properties, and shows its application to a variety of systems.

The purpose of this thesis is to explore the performance of a bio-inspired plate undergoing oscillatory heave motions and active shape change. The shape change will be achieved using a panel embedded with Fluidic Flexible Matrix Composite (F2MC) tubes for actuation. A beam, or plate strip, model is presented as a means of verifying that F2MC tubes can effectively serve as a means of actuation. This model was actuated in air and water at several internal tube pressures. The static experimental deflections were compared to two beam models relying on Euler-Bernoulli and Timoshenko beam theories with concentrated tip moments and a distributed moment. It was found that the Euler-Bernoulli model with a concentrated tip moment best approximated the static experimental deflections. Following the success of the plate strip, and panel with 10 embedded F2MC tubes was manufactured. The plate panel was constructed with Dragon Skin Silicone and embedded with two rows of five F2MC tubes which provide the means of shape actuation. Experimental results from actuating the panel in static conditions showed that F2MC tubes are an effective means of prescribing a repeatable shape change to a silicone panel. Then, Classical Plate Theory and First-Order Shear Deformation Plate Theory were used with a concentrated tip moment at the free edge to provide a means of modeling the full panel. When comparing the static experimental results to the numerical models, it was found that the deflected plate shape could be most accurately predicted at lower pressures for upward deflection and higher pressures for downward deflections. When tested in unsteady conditions in a heaving experiment (0.5 Hz to 2.3 Hz), the force measured at frequencies above 1.5 Hz were up to 3.6 times greater than those measured for frequencies below 1.5 Hz. Additionally, the phase difference between the tip deflection and force with respect to the keel position decreased for force as frequency increased, while the opposite was true for the tip deflection. At 1.5 Hz, the tip deflection and force were equally out of phase with the keel. When the panel was subjected to an oscillatory heaving motion while asymmetrically actuated, it was found that faster heaving frequencies resulted in higher maximum force values for all actuation pressures, actuation directions, and depths below the free surface. However, when subjected to dual actuation by pressurizing the top and bottom tubes at the same pressure, the tip amplitude was highly dependent on specific combinations of heaving frequency, actuation pressure, and depth below the free surface. This indicates that the actuation pressure must be tuned to the depth and frequency of operation to obtain the desired tip amplitude for a given application. These findings further the knowledge of shape-changing F2MC panels operating near a free surface and lay a groundwork for developing flapping propulsors that mimic marine animals. / Master of Science / The purpose of this thesis is to explore the performance of a bio-inspired plate undergoing oscillatory (up and down) heave motions and active shape change. The active shape change is achieved using Fluidic Flexible Matrix Composite (F2MC) tubes, which act as an artificial muscles to deflect the panel. To verify that F2MC tubes are capable of prescribing a repeatable deflection, a simple beam model with two embedded tubes was manufactured and tested statically in air and water. It was found that the F2MC tubes were able to prescribe a repeatable deflection, and when comparing to two beam models, Euler-Bernoulli and Timoshenko, it was found that the Euler Bernoulli model with a concentrated tip moment best approximated the static experimental deflections. Following the success of the beam model with 2 embedded tubes, a panel was made with 10 embedded F2MC tubes, 5 along the bottom and 5 along the top, was created. This panel was tested statically and dynamically. Static results showed strong deflection repeatability. When subjected to heaving motions, it was found that the force in the system increased with increasing heaving frequency. The phase difference measured between the tip deflection and force with respect to the keel position decreased for force as frequency increased, while the opposite was true for the tip deflection. It was also observed that there exists a point where the tip deflection and force were equally out of phase with the keel. When the panel was subjected to dual actuation by pressurizing the top and bottom tubes at the same pressure, the tip amplitude was highly dependent on specific combinations of heaving frequency, actuation pressure, and depth below the free surface. This indicates that the actuation pressure must be tuned to the depth and frequency of operation to obtain the desired tip amplitude for a given application. These findings further the knowledge of shape-changing F2MC panels operating near a free surface and lay a groundwork for developing flapping propulsors that mimic marine animals.

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. / Many natural and man-made systems exhibit behavior which is a combination of the structural elastic response, such as bending or twisting, and aerodynamic or fluid response, such as pressure; for example, flow of blood in arteries, flapping of a bird’s wings, fluttering of a flag, and flight of a hot-air balloon. Such a coupled fluid-structure response is defined as aeroelastic response. Flight of an aircraft through turbulent weather is another example of an aeroelastic response. In this work, a novel method is proposed for calculating the sensitivity of an aircraft’s aeroelastic response to changes in the shape of the aircraft. These sensitivities are numbers that indicate how sensitive the aircraft’s responses are to changes in the shape of the aircraft. Such sensitivities are essential for aircraft design. The method presented in this work is called Continuum Sensitivity Analysis (CSA). The main goal is to accurately and efficiently calculate the sensitivities which are used by optimization tools to compute the best aircraft shape that suits the customers needs. The key advantages of CSA, as compared to the other methods, are that it is more efficient and it can be used effectively with commercially available (nonintrusive) tools. A unique contribution is that the proposed method can be used to calculate sensitivities with respect to a few or many shape design variables, without much effort. Integration of structural and fluid sensitivities is carried out first by applying CSA individually for structural and fluid systems, followed by connecting these together to obtain the coupled aeroelastic sensitivity. We present the first application of local formulation of CSA for nonintrusive implementation of high-fidelity aeroelastic sensitivities. The following challenging tasks are tackled in this research: (a) deriving the sensitivity equations and boundary conditions, (b) developing and linking computer codes written in different languages (C++, MATLAB, FORTRAN) for solving these equations, and (c) implementing CSA using commercially available tools such as NASTRAN, FLUENT, and SU2. CSA can improve the design process of complex aircraft and spacecraft. Owing to its modularity, CSA is also applicable to multidisciplinary areas such as biomedical, automotive, ocean engineering, space science, etc.

Fluid-structure interaction (FSI) is an important physical phenomenon in many applications and across various disciplines including aerospace, civil and bio-engineering. In civil engineering, applications include the design of wind turbines, pipelines, suspension bridges and offshore platforms. Ocean structures such as drilling risers, mooring lines, cables, undersea piping and tension-leg platforms can be subject to strong ocean currents, and such structures may suffer from Vortex-Induced Vibrations (VIV's), where vortex shedding of the flow interacts with the structural properties, leading to large amplitude vibrations in both in-line and cross-flow directions. Over the past years, many experimental and numerical studies have been conducted to comprehend the underlying physical mechanisms. However, to date there is still limited understanding of the effect of oscillatory interactions between fluid flow and structural behavior though such interactions can cause large deformations. This research proposes a mathematical framework to accurately predict FSI for elastically supported rigid structures. The numerical method developed solves the Navier-Stokes (NS) equations for the fluid and the Equation of Motion (EOM) for the structure. The proposed method employs Finite Differences (FD) on Cartesian grids together with an improved, efficient and oscillation-free Immersed Boundary Method (IBM), the accuracy of which is verified for several test cases of increasing complexity. A variety of two and three dimensional FSI simulations are performed to demonstrate the accuracy and applicability of the method. In particular, forced and a free vibration of a rigid cylinder including Vortex-Induced Vibration (VIV) of an elastically supported cylinder are presented and compared with reference simulations and experiments. Then, the interference between two cylinders in tandem arrangement at two different spacing is investigated. In terms of VIV, three different scenarios were studied for each cylinder arrangement to compare resonance regime to a single cylinder. Finally, the IBM is implemented into a three-dimensional Large-Eddy Simulation (LES) method and two high Reynolds number (Re) flows are studied for a stationary and transversely oscillating cylinder. The robustness, accuracy and applicability of the method for high Re number flow is demonstrated by comparing the turbulence statistics of the two cases and discussing differences in the mean and instantaneous flows.

Fluid-structure interaction (FSI) is an interesting and challenging interdisciplinary area comprised of fields such as engineering- fluids/structures/solids, computational science, and mathematics. FSI has several practical engineering applications such as the design of coastal infrastructure (such as bridges, levees) subjected to harsh environments from natural forces such as tsunamis, storm surges, etc. Development of accurate input conditions to more detailed and complex models involving flexible structures in a fluid domain is an important requirement for the solution of such problems. FSI researchers often employ methods that use results from physical wave basin experiments to assess the wave forces on structures. These experiments, while closer to the physical phenomena, often tend to be time-consuming and expensive. Experiments are also not easily accessible for conducting parametric studies. Alternatively, numerical models when developed with similar capabilities will complement the experiments very well because of the lower costs and the ability to study phenomena that are not feasible in the laboratory. This dissertation is aimed at contributing to the solution of a significant component of the FSI problem with respect to engineering applications, covering accurate input to detailed models and a numerical wave basin to complement large-scale laboratory experiments. To this end, this work contains a description of a three-dimensional numerical wave tank (3D-NWT), its enhancements including the piston wavemaker for generation of waves such as solitary, periodic, and focused waves, and validation using large-scale experiments in the 3D wave basin at Oregon State University. Performing simulations involving fluid dynamics is computational-intensive and the complexity is magnified by the presence of the flexible structure(s) in the fluid domain. The models are also required to take care of large-scale domains such as a wave basin in order to be applicable to practical problems. Therefore, undertaking these efforts requires access to high-performance computing (HPC) platforms and development of parallel codes. With these objectives in mind, parallelization of the 3D-NWT is carried out and discussed in this dissertation. / Graduation date: 2011

Indiana University-Purdue University Indianapolis (IUPUI) / LBM-IB method is useful and popular simulation technique that is adopted ubiquitously to solve Fluid-Structure interaction problems in computational fluid dynamics. These problems are known for utilizing computing resources intensively while solving mathematical equations involved in simulations. Problems involving such interactions are omnipresent, therefore, it is eminent that a faster and accurate algorithm exists for solving these equations, to reproduce a real-life model of such complex analytical problems in a shorter time period. LBM-IB being inherently parallel, proves to be an ideal candidate for developing a parallel software. This research focuses on developing a parallel software library, LBM-IB based on the algorithm proposed by [1] which is first of its kind that utilizes the high performance computing abilities of supercomputers procurable today. An initial sequential version of LBM-IB is developed that is used as a benchmark for correctness and performance evaluation of shared memory parallel versions. Two shared memory parallel versions of LBM-IB have been developed using OpenMP and Pthread library respectively. The OpenMP version is able to scale well enough, as good as 83% speedup on multicore machines for <=8 cores. Based on the profiling and instrumentation done on this version, to improve the data-locality and increase the degree of parallelism, Pthread based data centric version is developed which is able to outperform the OpenMP version by 53% on manycore machines. A distributed version using the MPI interfaces on top of the cube based Pthread version has also been designed to be used by extreme scale distributed memory manycore systems.

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.

A monolithic approach to aero-structural analysis and optimization has been developed and implemented. In contrast to a partitioned approach which uses individual fluid and structural solvers to solve their respective systems separately, the monolithic approach solves a fully-coupled system simultaneously, enforcing solution compatibility across the sub-system interfaces at each iteration. In this work, a three-field formulation is used, consisting of fluid, structural, and fluid mesh-movement sub-systems. The performance of the monolithic approach is characterized using 1-D unsteady and 2-D steady analysis problems, and compared with a partitioned approach. Four steady model aero-structural optimization problems are also investigated. Gradients of the objective function are computed using the discrete-adjoint and flow-sensitivity (direct) methods. In each case, the monolithic approach is shown to be a promising option for efficient aero-structural analysis and optimization, though the implementation requires additional development of coupling sub-matrices when compared to a partitioned approach.

Mechanical ventilation has been a major therapy used by physicians in support of surgery as well as for treating patients with reduced lung function. Despite its many positive outcomes and ability to maintain life, in many cases, it has also led to increased injury of the lungs, further exacerbating the diseased state. Numerous studies have investigated the effects of long term ventilation with respect to lungs, however, the connection between the global deformation of the whole organ and the strains reaching the alveolar walls remains unclear. The walls of lung alveoli also called the alveolar septum are characterized as a multilayer heterogeneous biological tissue. In cases where damage to this parenchymal structure insist, alveolar overdistension occurs. Therefore, damage is most profound at the alveolar level and the deformation as a result of such mechanical forces must be investigated thoroughly. This study investigates a three-dimensional lung alveolar model from generations 22 (alveolar ducts) through 24 (alveoli sacs) in order to estimate the strain/stress levels under mechanical ventilation conditions. Additionally, a multilayer alveolar tissue model was generated to investigate localized damage at the alveolar wall. Using ANSYS, a commercial finite element software package, a fluid-structure interaction analysis (FSI) was performed on both models. Various cases were simulated that included a normal healthy lung, normal lung with structural changes to model disease and normal lung with mechanical property changes to model aging. In the alveolar tissue analysis, strains obtained from the aged lung alveolar analysis were applied as a boundary condition and used to obtain the mechanical forces exerted as a result. This work seeks to give both a qualitative and quantitative description of the stress/strain fields exerted at the alveolar region of the lungs. Regions of stress/strain concentration will be identified in order to gain perspective on where excess damage may occur. Such damage can lead to overdistension and possible collapse of a single alveolus. Furthermore, such regions of intensified stress/strain are translated to the cellular level and offset a signaling cascade. Hence, this work will provide distributions of mechanical forces across alveolar and tissue models as well as significant quantifications of damaging stresses and strains.

La prédiction des instabilités fluide-élastique qui se développent dans un faisceau de tubes est importante pour la conception des générateurs de vapeur dans les centrales nucléaires, afin de prévenir les accidents liés à ces instabilités. En effet, ces instabilités fluide-élastique, ou flottements, conduisent à une fatigue vibratoire des matériaux, voire à des chocs entre les tubes, et par la suite, à des dégâts importants. Ces aspects sont d'une grande complexité pour les applications scientifiques impliquant l'industrie nucléaire. Le présent travail est issu d'une collaboration entre l'EDF, le CEA et l'IMFT. Elle vise à améliorer la simulation numérique de cette interaction fluide- structure dans le faisceau de tubes, en particulier dans la gamme de paramètres critiques favorisant l'apparition d'un amortissement négatif du système et de l'instabilité fluide-élastique. / The prediction of fluid-elastic instabilities that develop in a tube bundle is of major importance for the design of modern heat exchangers in nuclear reactors, to prevent accidents associated with such instabilities. The fluid-elastic instabilities, or flutter, cause material fatigue, shocks between beams and damage to the solid walls. These issues are very complex for scientific applications involving the nuclear industry. This work is a collaboration between EDF, CEA and IMFT. It aims to improve the numerical simulation of the fluid-structure interaction in the tube bundle, in particular in the range of critical parameters contribute to the onset of damping negative system and the fluid-elastic instability.