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In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

<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>

The influence of symmetry breaking on the flow induced oscillations of bluff bodies in the steamwise direction is studied. First, a series of experiments is conducted on a one-degree-of-freedom circular cylinder allowed to exhibit pure translational motion in the streamwise direction over a range of reduced velocities, 1.4 < U* < 4.4, corresponding to a Reynolds number range of 970 < Re < 3370. Two distinct regions of displacements were observed in reduced velocity ranges of 1.6 < U* < 2.5 and 2.75 < U* < 3.85. Measured force coefficients in the drag and lift direction were examined, along with the wake visualization, through the range of reduced velocities, to infer the resulting wake modes. A new Alternating Symmetric (AS) mode was found. This transition from symmetric to AS shedding occurred near the end of the first region of response. Similar tests were run with a square prism in the parameter space of 2.4 < U* < 5.8 and 757 < Re < 1900 over angles of incidence of 0° ≤ α ≤ 45°. A distinct region of lock-in is observed for α = 0°, 2.5°, 5°, 7.5° over 3.2 < U* < 5.4 for α = 0°, and decreasing with increasing α. The wake structures were found to be roughly symmetric for α = 0°, but transitioned towards asymmetry with increasing α. For α = 0° and 2.5° a gradual increase in the asymmetry of the fluid forcing was observed with increasing U*, similar to the circular cylinder.

A hot isostatic press (HIP) is a system which utilises high temperatures and pressure in order to densifyand enhance the material properties of components in the aerospace, automotive and additive manufacturingindustries, to mention a few. Quintus is a world leading manufacturer of HIP systems, and this master’s thesiswork has been written in collaboration with them. A HIP consists of a cylinder which gets filled with an inert gas, a gas which is then pressurised using compressors.Inside of the cylinder are heaters which ensure that the gas and load reach the desired temperature. Quintus’HIP construction has a wire wound cylinder. This means that a pre-stressed wire is wound around the cylinderfor a number of laps, resulting in the cylinder always being in a compressive stress state, thus ensuring a safeconstruction if a crack were to propagate in the material. This construction also allows for a more slim design ofthe cylinder which is beneficial when the gas is to be cooled, as the heat gets transported through the cylinder.An alternative design to this wire wound cylinder is a so called monoblock cylinder. This is a solid, thicker,cylinder, not wound by any wire. Quintus does not manufacture the monoblock HIP system, but these HIPs areon the market and therefore Quintus is keen to learn more about them. In this work, differences in the cooling capabilities with respect to the cylinders’ strength has been investigated,regarding the wire wound and monoblock cylinders. This has been done by the means of CFD and FEM(ANSYS CFX and ANSYS Mechanical), where a simplified 2D axisymmetric model of each HIP version wasused. In CFX, both a steady state and transient simulation was run for each model in order to capture the coolingof the gas. The resulting temperature load on the cylinder was then exported to the Mechanical setup to solvefor the arising stresses of the cylinders. The results of the work showed that the wire wound HIP does indeed exceed the monoblock cylinder when itcomes to the cooling rate, especially after some time when the gas has cooled off. Neither one of the cylinderswere at risk of yielding, and the monoblock cylinder was calculated to withstand &gt;20 000 cycles, which is alsothe fatigue life of the wire in Quintus’ HIPs. The models and boundary conditions used in this work weresubjected to approximations, but the results obtained have still brought a lot of new insights to the monoblockconstruction, and have provided a good foundation for further analyses.

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.

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

Sensor technology has played an essential role in improving the observability in manufacturing processes and providing input to enabling more effective and efficient product and process design. To analyze an injection molding process, pressure and temperature variations have shown to be the most critical factors that affect quality in the molded parts. The state of sensing in the industry utilizes separate and wired sensors placed away from the mold cavity to measure these parameters, and holes have to be drilled through the mold steel to accommodate the wires. To minimize mold structural modification, which is time consuming and expensive, it is desired to design a miniaturized sensor module that can be structurally embedded into the molding cavity and simultaneously measures the two parameters (i.e. a dual-parameter sensor) in real time, during the molding process. This thesis presents the structural optimization of the sensor and development of a new Fluid-Structure algorithm to analyze the performance of the sensor as in an actual injection molding cycle. Thus, research involves three key tasks. Given a required mold steel thickness, an optimization problem was solved analytically with outer diameter, thickness and number of rings as variables under the maximum allowable pressure and minimum required energy constraints to achieve a minimum volume of the piezo stack. As it is infeasible to test the sensor with different dimensions under the flow to understand its behavior under high pressure and temperature polymer melt, the development of a numerical model is required. A mold-melt interaction algorithm is developed to have a mold-melt interface using finite element analysis, analogous to an injection molding process. The model showed the change in state of polymer melt and its effect on cavity due to change in viscosity with the change in temperature. The model validated the energy output of the optimized sensor when the temperature and pressure of polymer changes and the effect of these parameters on mold and sensor. The voltage output and temperature results were compared with analytical solution. The numerical results of voltage output matched within 0.1% and temperature results matched within 3% of the analytical solutions. Finally a test bed was fabricated to simulate and reconstruct the pressure profile obtained from the numerical model to study the actual output from a fabricated sensor. The aim of the test bed was to reconstruct pressure profiles obtained from numerical simulations to investigate the sensor output from the fabricated injection molding sensor. The test bed evaluated the output from sensor as can be observed in actual injection molding machine. Comparison of the injection molding sensor with a piezo-resistive sensor showed good agreement.

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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.