<p>Fluids conveyed in deformable conduits are often encountered in  microfluidic applications, which makes fluid--structure interactions (FSIs) an unavoidable phenomenon. In particular, experiments reported the existence of FSI instabilities in compliant microchannels at low Reynolds numbers, Re, well below the established values for rigid conduits. This observation has significant implications for new strategies for mixing at the microscale, which might harness FSI instabilities in the absence of  turbulence. In this thesis, we conduct research on the modeling and stability of microscale FSIs. Understanding the steady response, the dynamics and the stability of these FSIs are the three major objectives. This thesis begins with the analysis of the steady-state scalings and the linear stability of a previously derived mathematical model, through which we emphasize the power of reduced modeling in making the FSI problems tractable. Next, we turn to a more realistic problem regarding FSIs in a common configuration of low-Re flows through long, shallow rectangular three-dimensional microchannels. Through a scaling analysis, which takes advantage of the geometric separation of scales, we find that the flow can be simplified under the lubrication approximation, while the wall deforms like a variable-stiffness Winkler foundation at the leading order. Coupling these dominant effects, we obtain a new fitting-parameter-free flow rate--pressure drop relation for a thick-walled microchannel, which rationalizes previous experiments. Then, we derive a one-dimensional (1D) steady model, at both vanishing and finite Re, by coupling the reduced flow and deformation models. To satisfy the displacement constraints along the channel edges, weak tension is introduced to regularize the underlying Winkler-foundation-like mechanism. This model is then made dynamic by introducing flow unsteadiness and the elastic wall's inertia. We conduct a global stability analysis of this system by perturbing the non-flat steady state with infinitesimal perturbations. We identify the existence of globally unstable modes, typically in the weakly inertial flow regime, whose features are consistent with experimental observations. The unstable eigenmodes oscillate at frequencies close to the natural frequency of the wall, suggesting that the instabilities are resonance phenomena. We also capture the transient energy amplification of perturbations through a linear non-normality analysis of the proposed reduced 1D FSI model.</p>

M. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / Fault diagnosis of a rotor system operating in a fluid is one of the most difficult aspects of rotating machinery. Fluid in machinery plays a significant role in concealing the allowable rubbing stress limit during the impact generated from the rotor-stator rub which may progressively deteriorate the rotating system. Therefore, a numerical and experimental investigation was performed to analyse the influence of the fluid during the rotor-stator contact of a vertical rotor system partially submerged in an incompressible inviscid fluid with a focus on detecting rubbing fault in the presence of axial load. The theoretical model of lateral-torsional rotor consists of a 3-D rub-impact induced parametric excitation, which was assimilated to operate as elastic vertical rotor system by considering the transient vibration of a flexible axial force and energy of the vertical shaft system. The model was established based on Jeffcott rotor, time-varying stiffness and the rotor-stator fluid interaction. The Lagrangian principle was used to establish the governing equation of motion. The hydrodynamic forces acting on the vertical rotor were established and introduced into the system based on the Laplace form of the linearized Navier–Stokes equations under lateral excitation yielding a highly nonlinear 5-DOF system. To evaluate the dynamic response and ensure the accurate acquisition of rubbing features in a fluid, the classical Fast Fourier Transform (FFT) and the vibration waveform have been discretised and illustrated through the frequency components. Furthermore, for effective extraction of some hidden features of rub, the nonlinear features embedded in the vibration waveform have been discretised and illustrated through to the lateral deformation of the rotor and the orbit patterns of the shaft. Qualitative numerical analysis suitable for highly nonlinear and non-stationary signal Time-Frequency strategies, Wavelet Synchrosqueezed Transform (WSST) and Instantaneous Frequency (IF) technique were employed to successfully extract the frequency of oscillating modes and the periodic frequency response of the faulted rotor system. It is demonstrated that the coupled lateral-torsional vibration of the submerged vertical rotor system has the potential to enhance the much-unwanted hidden frequencies of vibration that leads to significant instability of the rotor system. In particular, the responses revealed the existence of unstable regimes with respect to the lateral-torsional deflection as well as the angular velocity. High harmonic peaks were also identified at the critical speed, which can be considered as a monitoring index to detect the rubbing in rotating shafts in a fluid. It was found that even at relatively slow rotating speed fluid elastic forces induced by the co-rotating flow surrounding the shaft significantly affect the transverse natural modes of vibration of the shaft. Despite the interaction between the fluid and the rotor generates self-excitation of low frequencies, obtained results indicated that the fluid-rotor interaction reduces the dynamic vibration response of the faulted system running below the second critical speed. It has been analytically demonstrated that the time-varying stiffness induced is the principal cause of the frequency-modification feature of the dynamic response of an unbalance-rub rotor system at the contact region. The model investigated in this study has potential application for drill string-borehole shaft system used in the oil industry.

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Fluid structure interactions occur to some extent in nearly every type of fluid flow. Understanding how structures interact with fluids and visa-versa is of vital importance in many engineering applications. The purpose of this research is to explore how fluids interact with flexible and rigid structures. A computational model was used to model the fluid structure interactions of vibrating synthetic vocal folds. The model simulated the coupling of the fluid and solid domains using a fluid-structure interface boundary condition. The fluid domain used a slightly compressible flow solver to allow for the possibility of acoustic coupling with the subglottal geometry and vibration of the vocal fold model. As the subglottis lengthened, the frequency of vibration decreased until a new acoustic mode could form in the subglottis. Synthetic aperture particle image velocimetry (SAPIV) is a three-dimensional particle tracking technique. SAPIV was used to image the jet of air that emerges from vibrating human vocal folds (glottal jet) during phonation. The three-dimensional reconstruction of the glottal jet found faint evidence of flow characteristics seen in previous research, such as axis-switching, but did not have sufficient resolution to detect small features. SAPIV was further applied to reconstruct the smaller flow characteristics of the glottal jet of vibrating synthetic vocal folds. Two- and four-layer synthetic vocal fold models were used to determine how the glottal jet from the synthetic models compared to the glottal jet from excised human vocal folds. The two- and four-layer models clearly exhibited axis-switching which has been seen in other 3D analyses of the glottal jet. Cavitation in a quiescent fluid can break a rigid structure such as a glass bottle. A new cavitation number was derived to include acceleration and pressure head at cavitation onset. A cavitation stick was used to validate the cavitation number by filling it with different depths and hitting the stick to cause fluid cavitation. Acceleration was measured using an accelerometer and cavitation bubbles were detected using a high-speed camera. Cavitation in an accelerating fluid occurred at a cavitation number of 1.

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The onset of fluid-elastic instability in cylinder arrays is usually thought to depend primarily on the mean flow velocity, the Scruton number and the natural frequency of the cylinders. Currently, there is considerable evidence from experimental measurements and computational fluid dynamic (CFD) simulations that the Reynolds number is also an important parameter. However, the available data are not sufficient to understand or quantify this effect. In this study we use a high resolution pseudo-spectral scheme to solve 2-D penalized Navier-Stokes equations in order to accurately model turbulent flow past cylinder array. To uncover the Reynolds number effect we perform simulations that vary Reynolds number independent of flow velocity at a fixed Scruton number, and then analyze the cylinder responses. The computational complexity of our algorithm is a function of Reynolds number. Therefore, we developed a high performance parallel code which allows us to simulate high Reynolds numbers at a reasonable computational cost. The simulations reveal that increasing Reynolds number has a strong de-stabilizing effect for staggered arrays. On the other hand, for the in-line array case Reynolds number still affects the instability threshold, but the effect is not monotonic with increasing Reynolds number. In addition, our findings suggest that geometry is also an important factor since at low Reynolds numbers critical flow velocity in the staggered array is considerably higher than the in-line case. This study helps to better predict how the onset of fluid-elastic instability depends on Reynolds number and reduces uncertainties in the experimental data which usually do not consider the effect of Reynolds number. / Thesis / Master of Science (MSc)

This dissertation focuses on the development and application of numerical algorithms for solving compressible multiphase fluid-material interaction problems. The first part of this dissertation is motivated by the extraordinary shock-resisting ability of elastomer coating materials (e.g., polyurea) under explosive loading conditions. Their performance, however, highly depends on their dynamic interaction with the substrate (e.g., metal) and ambient fluid (e.g., air or liquid); and the detailed interaction process is still unclear. Therefore, to certify the application of these materials, a fluid-structure coupled computational framework is needed. The first part of this dissertation developes such a framework. In particualr, the hyper-viscoelastic constitutive relation of polyurea is incorporated into a high-fidelity computational framework which couples a finite volume compressible multiphase fluid dynamics solver and a nonlinear finite element structural dynamics solver. Within this framework, the fluid-structure and liquid-gas interfaces are tracked using embedded boundary and level set methods. Then, the developed computational framework is applied to study the behavior a bilayer coating–substrate (i.e., polyurea-aluminum) system under various loading conditions. The observed two-way coupling between the structure and the bubble generated in a near-field underwater explosion motivates the next part of this dissertation. The second part of this dissertation investigates the yielding and collapse of an underwater thin-walled aluminum cylinder in near-field explosions. As the explosion intensity varies by two orders of magnitude, three different modes of collapse are discovered, including one that appears counterintuitive (i.e., one lobe extending towards the explosive charge), yet has been observed in previous laboratory experiments. Because of the transition of modes, the time it takes for the structure to reach self-contact does not decrease monotonically as the explosion intensity increases. Detailed analysis of the bubble-structure interaction suggests that, in addition to the incident shock wave, the second pressure pulse resulting from the contraction of the explosion bubble also has a significant effect on the structure's collapse. The phase difference between the structural vibration and the bubble's expansion and contraction strongly influences the structure's mode of collapse. The third part focuses on the development of efficient solution algorithms for compressible multi-material flow simulations. In these simulations, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular class of methods in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation, such as the one used in the preceding parts of the dissertation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. This dissertation accelerates the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed. The performance of these acceleration methods is assessed using four example problems that exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times. / Doctor of Philosophy / This dissertation focuses on the development and application of numerical methods for solving multiphase fluid-material interaction problems. The first part of this dissertation is motivated by the extraordinary shock-resisting ability of elastomer coating materials (e.g., polyurea) under explosive loading conditions. Their performance, however, highly depends on their dynamic interaction with the underlying structure and the ambient water or air; and the detailed interaction process is still unclear. Therefore, the first part of this dissertation developes a fluid-structure coupled computational framework to certify the application of these materials. In particular, the special material property of the coating material is incorparated into a state-of-the-art fluid-structure coupled computational framework that is able to model large deformation under extreme physical conditions. Then, the developed computational framework is applied to study how a thin-walled aluminum cylinder with polyurea coating responds to various loading conditions. The observed two-way coupling between the structure and the bubble generated in a near-field underwater explosion motivates the next part of this dissertation. The second part of this dissertation investigates the failure (i.e., yielding and collapse) of an underwater thin-walled aluminum cylinder in near-field explosions. As the explosion intensity varies by two orders of magnitude, three different modes of collapse are discovered, including one that appears counterintuitive (i.e., one lobe extending towards the explosive charge), yet has been observed in previous laboratory experiments. Via a detailed analysis of the interaction between the explosion gas bubble, the aluminum cylinder, and the ambient liquid water, this dissertation elucidated the role of bubble dynamics in the structure's different failure behaviors and revealed the transition mechanism between these behaviors. The third part of this dissertation presents efficient solution algorithms for the simulations of compressible multi-material flows. Many problems involving bubbles, droplets, phase transitions, and chemical reactions fall into this category. In these problems, discontinuities in fluid state variables (e.g., density) and material properties arise across the material interfaces, challenging numerical schemes' accuracy and robustness. In this regard, a promising class of methods that emerges in the recent decade is to resolve the exact wave structure at material interfaces, such as the one used in the preceding parts of the dissertation. However, the computational cost of these methods is prohibitive due to the nested loops invoked at every mesh edge along the material interface. To address this issue, the dissertation develops four efficient solution methods, following the idea of exploiting special properties of governing equations and recycling previous solutions. Then, the acceleration effect of these methods is assessed using various challenging multi-material flow problems. In different test cases, significant reduction in computational cost (acceleration of 18 to 81 times) is achieved, without sacrificing solver robustness and solution accuracy.

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