A coupled fluid-structure interaction solver capability is developed and validated. A high fidelity fluids solver, Loci-Chem, is coupled with a finite-element structural dynamics toolkit, MAST. The coupled solver is validated for the prediction of several panel instability cases in uniform flows and in the presence of an impinging shock for a range of subsonic and supersonic Mach numbers, dynamic pressures, and pressure ratios. The panel deflections and limit-cycle oscillation amplitudes, frequencies, and bifurcation point predictions compare very well with benchmark results for 2D simulations. The same procedures outlined in the validation study have been applied to simulations of varying dynamic pressures at M = 2 for an impinging oblique shockwave. The influence of inviscid, laminar and turbulent boundary layer profiles on the development of flow field characteristics has been analyzed, and laminar predictions characterized by a large flow separation results in vastly different behavior than that of traditional flutter.

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Corrugated pipes are widely used in offshore gas and oil fields for their flexibility while offering local rigidity. However, self-sustained pressure pulsations associated with the flow in corrugated pipes results in a noisy environment, high running costs and eventually structure fatigue failure upon long exposure. Recent literature has addressed either the flow over a single cavity or the global oscillations. The current research aims at understanding the flow over multiple cavities as a first step to correlate the rich single cavity literature and the actual corrugated pipe problem with the ultimate goal of predicting oscillations amplitude in corrugate pipes. The standing wave method (SWM), which is an efficient experimental tool, has been successfully adapted in the first phase of the project to measure the source of multiple cavity configurations. One, two and three-cavity configurations have been investigated by means of the SWM. The source non-linearly becomes more pronounced as the number of cavities increases. The cavity length (L) is still found to be the appropriate length scale to define the oscillation dimensionless frequency (the Strouhal number). The measured source data have been successfully employed in a semi-empirical model to predict the amplitude of the self-excited oscillations. Accurate model performance is achieved for the single, double and triple cavity configurations. Including the absorption losses at the cavity corners has been found to be crucial for the model prediction accuracy. The separation distance (Lp) effect on the generated source is investigated for two and three-cavity configurations using the SWM over a practical range of spacing ratios. At extremum spacing ratios of (Lp/L) 0.5 and 1.375, constructive hydrodynamic interference associated with strong sources has been observed. At high excitation levels the source consistently becomes weaker upon increasing the spacing ratio. The reported trends are consistent for both the double and triple cavity configurations. However, the destructive interference spacing ratio is found to depend on the number of cavities indicating a relatively more complicated interaction mechanism. The different interaction patterns have been analytically interpreted based on the synchronization of the hydrodynamic cycle of the cavity shear layer and the disturbance convection along the pipe spacing between the cavities. Moreover, the three-cavity constructive interference cases have been visualized using Particle Image Velocimetry (PIV). The source evaluated based on the PIV data and applying Howe’s analogy revealed each cavity share of the global source, which fairly agrees with the SWM measured source. The source contribution due to gradually increasing the number of cavities is investigated using the SWM up to a six-cavity configuration. The source contribution reaches asymptotically a consistent value starting from the fourth cavity. This persistent contribution defines a building unit cavity source which is representative of a general cavity in a long corrugated pipe. The building unit source fairly agrees with the ninth-cavity source in a twelve-cavity configuration extracted by means of the PIV technique. Finally, a predication model, based on the building unit source, successfully predicts the oscillations amplitude of a twelve-cavity configuration, which serves as a model for a corrugated pipe section. / Thesis / Doctor of Philosophy (PhD)

Recently, numerous flexible structures have been employed in various fields of industry. Loading conditions sustained by these flexible structures are often not described well enough for engineering analyses even though these conditions are important. Here, a flexible tent with an interior Collective Protection System, which is subjected to an explosion, is analyzed. The tent protects personnel from biological and chemical agents with a pressurized liner inside the tent as an environmental barrier. Field tests showed unexpected damage to the liner, and most of the damage occurred on tent's leeward side. To solve this problem, various tests and analyses have been performed, involving material characteristics of the liner, canvas, and zip seals, modeling of the blast loading over the tent and inside the tent, and structural response of the tent to the blast loading as collaborative research works with others. It was found that the blast loading and the structural response can not be analyzed separately due to the interaction between the flexible structure and the dynamic pressure loading. In this dissertation, the dynamic loadings imposed on both the interior and the exterior sides of the tent structure due to the airblasts and the resulting dynamic responses were studied. First, the blast loadings were obtained by a newly proposed theoretical method of analytical/empirical models which was developed into a FORTRAN program. Then, a numerical method of an iterative Fluid-Structure Interaction using Computational Fluid Dynamics and Computational Structural Dynamics was employed to simulate the blast wave propagation inside and outside the flexible structure and to calculate the dynamic loads on it. All the results were compared with the field test data conducted by the Air Force Research Laboratory. The experimental pressure data were gathered from pressure gauges attached to the tent surfaces at different locations. The comparison showed that the proposed methods can be a good design tool to analyze the loading conditions for rigid or flexible structures under explosive loads. In particular, the causes of the failure of the liner on the leeward were explained. Also, the results showed that the effect of fluid-structure interaction should be considered in the pressure load calculation on the structure where the structural deflection rate can influence the solution of the flow field surrounding the structure. / Ph. D.

Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-sensors, micro-actuators, and micro-valves. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability, and the pull-in instability of bi-stable arch shaped MEMS under steady and transient electric loads. We analyze transient finite electroelastodynamic deformations of perfect electrically conducting clamped-clamped beams and arches suspended over a flat rigid semi-infinite perfect conductor. The coupled nonlinear partial differential equations (PDEs) for mechanical deformations are solved numerically by the finite element method (FEM) and those for the electrical problem by the boundary element method. The coupled nonlinear PDE governing transient deformations of the arch based on the Euler-Bernoulli beam theory is solved numerically using the Galerkin method, mode shapes for a beam as basis functions, and integrated numerically with respect to time. For the static problem, the displacement control and the pseudo-arc length continuation (PALC) methods are used to obtain the bifurcation curve of arch's deflection versus the electric potential. The displacement control method fails to compute arch's asymmetric deformations that are found by the PALC method. For the dynamic problem, two distinct mechanisms of the snap-through instability are found. It is shown that critical loads and geometric parameters for instabilities of an arch with and without the consideration of mechanical inertia effects are quite different. A phase diagram between a critical load parameter and the arch height is constructed to delineate different regions of instabilities. The local water slamming refers to the impact of a part of a ship hull on stationary water for a short duration during which high local pressures occur. We simulate slamming impact of rigid and deformable hull bottom panels by using the coupled Lagrangian and Eulerian formulation in the commercial FE software LS-DYNA. The Lagrangian formulation is used to describe planestrain deformations of the wedge and the Eulerian description of motion for deformations of the water. A penalty contact algorithm couples the wedge with the water surface. Damage and delamination induced, respectively, in a fiber reinforced composite panel and a sandwich composite panel and due to hydroelastic pressure are studied. / Ph. D.

The vulnerability of a ship to the impact of underwater explosions (UNDEX) and how to incorporate this factor into early-stage ship design is an important aspect in the ship survivability study. In this dissertation, attention is focused on the cost-efficient simulation of the ship response to a far-field UNDEX which involves fluid shock waves, cavitation, and fluid-structural interaction. Traditional fluid numerical simulation approaches using the Finite Element Method to track wave propagation and cavitation requires a high-level of mesh refinement to prevent numerical dispersion from discontinuities. Computation also becomes quite expensive for full ship-related problems due to the large fluid domain necessary to envelop the ship. The burden is aggravated by the need to generate a fluid mesh around the irregular ship hull geometry, which typically requires significant manual intervention. To accelerate the design process and enable the consideration of far-field UNDEX vulnerability, several contributions are made in this dissertation to make the simulation more efficient. First, a Cavitating Acoustic Spectral Element approach which has shown computational advantages in UNDEX problems, but not systematically assessed in total ship application, is used to model the fluid. The use of spectral elements shows greater structural response accuracy and lower computational cost than the traditional FEM. Second, a novel fully automatic all-hexahedral mesh generation scheme is applied to generate the fluid mesh. Along with the spectral element, the all-hex mesh shows greater accuracy than the all-tetrahedral finite element mesh which is typically used. This new meshing approach significantly saves time for mesh generation and allows the spectral element, which is confined to the hexahedral element, to be applied in practical ship problems. A further contribution of this dissertation is the development of a surrogate non-numerical approach to predict structural peak responses based on the shock factor concept. The regression analysis reveals a reasonably strong linear relationship between the structural peak response and the shock factor. The shock factor can be conveniently employed in the design aspects where the peak response is sufficient, using much less computational resources than numerical solvers. / Doctor of Philosophy / The vulnerability of a ship to the impact of underwater explosions (UNDEX) and how to incorporate this factor into early-stage ship design is an important aspect in the ship survivability study. In this dissertation, attention is focused on the cost-efficient simulation of the ship response to a far-field UNDEX which involves fluid shock waves, cavitation, and fluid-structural interaction. Traditional fluid numerical simulation approaches using the Finite Element Method to track wave propagation and cavitation requires a highly refined mesh to deal with large numerical errors. Computation also becomes quite expensive for full ship-related problems due to the large fluid domain necessary to envelop the ship. The burden is aggravated by the need to generate a fluid mesh around the irregular ship hull geometry, which typically requires significant manual intervention. To accelerate the design process and enable the consideration of far-field UNDEX vulnerability, several contributions are made in this dissertation to make the simulation more efficient. First, a Cavitating Acoustic Spectral Element approach, which has shown computational advantages in UNDEX problems but not systematically assessed in total ship application, is used to model the fluid. The use of spectral elements shows greater structural response accuracy and lower computational cost than the traditional FEM. Second, a novel fully automatic all-hexahedral mesh generation scheme is applied to generate the fluid mesh. Along with the spectral element, the all-hex mesh shows greater accuracy than the all-tetrahedral finite element mesh which is typically used. A further contribution of this dissertation is the development of a non-numerical approach which can approximate peak structural responses comparable to the numerical solution with far less computational effort.

A time spectral and coupled adjoint based sensitivity analysis of rotor blade is carried out in this study. The time spectral method is an efficient technique to solve unsteady periodic problems by transforming unsteady equation of motion to a steady state one. Due to the availability of the governing equations in the steady form, the steady form of the adjoint equations can be applied for the sensitivity analysis of the coupled fluid-structure system. An expensive computational time and memory requirement for the unsteady adjoint sensitivity analysis is thus avoided. A coupled analysis of fluid, structural, and flight dynamics is carried out through a CFD/CSD/CA coupling procedure that combines FSI analysis with enforced trim condition. Coupled sensitivity analysis results and their validations are presented and compared with aerodynamics only sensitivity analysis results. The fluid-structure coupled adjoint based sensitivity analysis will be applied to the shape optimization of a rotor blade in the future work. Minimization of required power is the objective of the optimization problem with constraints on thrust and drag of the rotor. The bump functions are considered as the design variables. Rotor blade shape changes are obtained by using the bump function on the surface of the airfoil sections along the span. / Doctor of Philosophy / The work in this dissertation is motivated by the reducing the computational cost at the early design stage with guaranteed accuracy. In the research, the author proposes that the goal can be achieve through coupled adjoint based sensitivity analysis using a fluid structure interaction in time spectral form. Adjoint based sensitivity analysis is very efficient for solving design problems with a large number of design variables. The time spectral approach is used to overcome inefficient calculation of rotor flows by expressing flow and structural state variables as Fourier series with small number of harmonics. The accuracy and the efficiency of flow solver are examined by simulating UH-60A forward flight condition. A significant reduction in the computational cost is achieved by its Fourier series form of the periodic time response and the assumption of periodic steady state. A good agreement between time accurate and time spectral analysis is noted for the high speed forward flight condition of UH-60A configuration. Prediction from both methods also agree quite well with the experimental data. The adjoint based sensitivity analysis results are compared with the finite difference sensitivity analysis results. Even with presence of small discrepancies, these two results show a good agreement to each other. Coupled sensitivity analysis includes not only the effect of fluid state changes but also the contribution of structural deformation.

This dissertation investigates the development of numerical algorithms for coupling computational fluid dynamics (CFD) and computational solid dynamics (CSD) solvers, and the use of these solvers for simulating fluid-solid interaction (FSI) problems involving large deformation, shock waves, and multiphase flow. The dissertation consists of two parts. The first part investigates the use of Robin interface conditions to resolve the well-known numerical added-mass instability, which affects partitioned coupling procedures for solving problems with incompressible flow and strong added-mass effect. First, a one-parameter Robin interface condition is developed by linearly combining the conventional Dirichlet and Neumann interface conditions. Next, a numerical algorithm is developed to implement the Robin interface condition in an embedded boundary method for coupling a parallel, projection-based incompressible viscous flow solver with a nonlinear finite element solid solver. Both an analytical study and a numerical study reveal that the new algorithm can clearly outperform conventional Dirichlet-Neumann procedures in terms of both stability and accuracy, when the parameter value is carefully selected. Moreover, the studies also indicate that the optimal parameter value depends on the materials and geometry of the problem. Therefore, to efficiently solve FSI problems involving non-uniform structures, a generalized Robin interface condition is presented, in which the constant parameter is replaced by a spatially varying function that depends on the local material and geometric properties of the structure. Numerical experiments using two benchmark problems show that the spatially varying Robin interface condition can clearly improve numerical accuracy compared to the constant- parameter version with the same computational cost. The second part of this dissertation focuses on simulating complex FSI problems featuring shock waves, multiphase flow (e.g., bubbles), and shock-induced material damage and fracture. A recently developed three-dimensional computational framework is employed, which couples a multiphase, compressible CFD solver and a nonlinear finite element CSD solver using an embedded boundary method and a partitioned procedure. In particular, the CFD solver applies a level-set method to capture the evolution of the bubble surface, and the CSD solver utilizes a continuum damage mechanics model and an element erosion method to simulate the dynamic fracture of the material. Two computational studies are presented. The first one investigates the dynamic response and failure of a brittle material exposed to a prescribed shock wave. The predictive capability of the computational framework is first demonstrated by simulating a series of laboratory experiments in the context of shock wave lithotripsy. Then, a parametric study is conducted to elucidate the significant effects of the shock wave's profile on material damage. In the second study, the computational framework is applied to simulate shock-induced bubble collapse near various solid and soft materials. The reciprocal effect of the material's properties (e.g., acoustic impedance, Young's modulus) on bubble dynamics is discussed in detail. / Doctor of Philosophy / Numerical simulations that couple computational fluid dynamics (CFD) solvers and computational solid dynamics (CSD) solvers have been widely used in the solution of nonlinear fluid-solid interaction (FSI) problems underlying many engineering applications. This is primarily because they are based on partitioned solutions of fluid and solid subsystems, which facilitates the use of existing numerical methods and computational codes developed for each subsystem. The first part of this dissertation focuses on developing advanced numerical algorithms for coupling the two subsystems. The aim is to resolve a major numerical instability issue that occurs when solving problems involving incompressible, heavy fluids and thin, lightweight structures. Specifically, this work first presents a new coupling algorithm based on a one-parameter Robin interface condition. An embedded boundary method is developed to enforce the Robin interface condition, which can be advantageous in solving problems involving complex geometry and large deformation. The new coupling algorithm has been shown to significantly improve numerical stability when the constant parameter is carefully selected. Next, the constant parameter is generalized into a spatially varying function whose local value is determined by the local material and geometric properties of the structure. Numerical studies show that when solving FSI problems involving non-uniform structures, using this spatially varying Robin interface condition can outperform the constant-parameter version in both stability and accuracy under the same computational cost. In the second part of this dissertation, a recently developed three-dimensional multiphase CFD - CSD coupled solver is extended to simulate complex FSI problems featuring shock wave, bubbles, and material damage and fracture. The aim is to understand the material’s response to loading induced by a shock wave and the collapse of nearby bubbles, which is important for advancing the beneficial use of shock wave and bubble collapse for material modification. Two computational studies are presented. The first one investigates the dynamic response and failure of a brittle material exposed to a prescribed shock wave. The causal relationship between shock loading and material failure, and the effects of the shock wave’s profile on material damage are discussed. The second study investigates the shock-induced bubble collapse near various solid and soft materials. The two-way interaction between bubble dynamics and materials response, and the reciprocal effects of the material’s properties are discussed in detail.