<div>Gerotor units are widely used in low-pressure (up to 30 bar) </div><div>fluid power applications, injection and lubrication systems, due to their compact package and low cost. Their performance in terms of volumetric efficiency, flow pulsations, internal pressure peaks or localized cavitation depends on many parameters, such as the rotors profiles and the manufacturing tolerances. In this work, a multi-domain simulation approach for the numerical analysis of the performance of Gerotor units is proposed. The model can be used for analysis and virtual prototyping of units considering the actual geometry of the rotors, their geometrical tolerances and the properties of the working fluid and materials.</div><div><br></div><div><div>The approach is based on the coupling of different models: a numerical geometric model evaluating the instantaneous volumes and flow areas inside the unit; a lumped parameter fluid dynamic model describing the displacing process of the tooth space volumes; and a mechanical model evaluating the internal micro-motions of the rotors axes according to their tolerances. In this way, the model determines the actual loading of the rotors, considering also the actual location of the points of contact. Advanced 2D CFD models for the analysis of lubricated interfaces have been developed to study the axial and the radial gaps. This approach allows an accurate prediction of the power losses and radial micro-motion of the rotors taking into account fluidstructure interaction effects. A line contact model is used to describe the contact interface using an elastohydrodynamic approach and non-Newtonian fluid behavior for the prediction of the friction between the rotors.</div></div><div><br></div><div><div>Specic experiments were performed by connecting the pump outlet to a variable loading orifice and by measuring the delivered flow, pressure ripple and required torque under dfferent operating conditions of speed and outlet pressure. These experiments allowed a detailed model validation through the comparisons with simulation data in terms of signicant steady-state as well as transient pressure, flow and torque features. After the model validation, gaps compensation solutions to minimize the volumetric losses are developed and studied showing the potential improvements on the performances of a prototype unit by reaching up to 55% volumetric effciency at high pressure (pmax > 100bar).</div><div><br></div><div>The approach used in the current work along with its proven accuracy through experiments can be considered a valuable tool when studying the impact of real-life technological clearances and gears geometry on the fluid-dynamic performance of the pump.</div></div>

<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>

<div>The atomization of jets and droplets undergoing breakup in high-speed flows has been experimentally measured and theoretically modeled. Systems for producing individual droplet breakup and full jet breakup were designed, and a wide range of diagnostics were developed and adapted to measure the results with reduced uncertainty.</div><div><br></div><div>A detailed methodology for investigating high-speed sprays in the Purdue Experimental Turbine Aerothermal Lab is presented. Optical diagnostic techniques were carefully selected and optimized for the test section geometries and flow features, such that images could be collected at high frequencies of 20 kHz with high resolutions. Developed image processing routines are outlined to demonstrate how backlit imaging with specialized lenses allowed for more accurate spray depth measurements in supersonic conditions, which were then used in regression modeling routines to derive empirical correlations that factored in test section geometry, flow conditions, and injector design. A Mie scattering imaging technique was used for quantitative analysis of the supersonic spray plume profile and measurement of the spray width. 20 kHz shadowgraphy provided sufficient gradients for analysis of the unsteadiness of the spray and surrounding supersonic flow at the point of injection. Droplet sizes and velocities were measured in subsonic conditions using digital in-line holography, in which recent advancements to the reconstruction algorithm were implemented to reduce out-of-plane measurement uncertainty, and phase Doppler particle analysis.</div><div><br></div><div>The breakup of a single drop undergoing multi-mode breakup was analytically characterized, with the proposal of a new breakup criterion in the Taylor analogy breakup model. Hill vortices within the drop were proposed as a new flow mechanism promoting multi-mode breakup. Product drop sizes from the ring breakup were predicted and compared with experimental results.</div>

<p>This work utilized Pointwise and Fluent to generate a two-dimensional axisymmetric model a Mk 48 torpedo, with the intention of informing methods to reduce the turbulence, and therefore hydrodynamic noise, of the torpedo’s wake. However, this work was unable to gather data on the unsteady nature of the turbulence expected around the torpedo due to Fluent providing unrealistic results when run using a transient solver. This work shows that the transient solver computed boundary layers greater than one order of magnitude smaller than expected, and in some cases there was no change in boundary layer thickness over the torpedo’s body. The work does contain steady state solutions that were validated by first performing a grid convergence study for a flat plate. The steady state results for the flat plate and torpedo both showed the expected growth for a turbulent boundary layer. Additionally, there was a high level of convergence with the Log-Law showing that the steady state data is valid. Future work should use a transient solver to determine the characteristics of the turbulence to resolve unsteady flow from vortex shedding, wake characteristics, and any broadband or narrowband noise to develop solutions to reduce the noise made by the Mk 48.</p>

<div>Advances in modern research have unveiled numerous fundamental and practical benefits of studying the hydrodynamics of microorganisms. Many microorganisms, especially bacteria, actively search for nutrients via a process called chemotaxis. The physical constraints posed by hydrodynamics in the locomotion of microorganisms can combine with their chemotactic ability to significantly affect functions like colonization of nutrient sources. In this thesis, we investigate the interplay between hydrodynamics and chemotaxis toward dictating bacterial distribution around fluid-fluid interfaces, which often act as a source of nutrition. We approach our problem statements using mathematical models and numerical and/or semi-analytical tools. Our studies are particularly relevant in the context of hydrocarbon degradation after oil-spills.</div><div><br></div><div>We begin by showing that the flow generated by rising oil drops delocalizes dissolved nutrient patches in the ocean, and aids chemotactic bacteria in improving their nutrition (over non-chemotactic bacteria) by 45%. We then move from studying colonization of soluble nutrient patches to colonization around nutrient sources, e.g., oil drops, marine snow. Towards this, we first demonstrate the phenomenon of hydrodynamics-mediated 'trapping' of bacteria around oil drops and show that a surfactant-laden drop can retain an approaching bacterium on its surface for approximately 35% longer times than a clean drop. We also analyze hydrodynamic trapping of bacteria around settling marine snow particles and show how bacteria can collide with and colonize the marine snow, even when the latter moves 10 times faster than the former. In all the cases above, we show how the hydrodynamic interactions are complemented by chemotaxis to enable extremely effective bacterial foraging. We next explore how propulsion mechanisms of microorganisms affect their ability to form biofilms on fluid-fluid interfaces and unveil the hydrodynamic origins behind the tendency of flagellated bacteria to swim parallel to plane surfactant-laden interfaces. Finally, we summarize our results, identify further avenues of research and propose problem statements related to them.</div>

<div>Particle Image Velocimetry (PIV) is a non-invasive measurement technique which resolves the flow velocity by taking instantaneous snapshots of tracer particle motion in the flow and uses digital image cross-correlation to estimate the particle shift up to subpixel accuracy. The measurement chain incorporates numerous sets of parameters, such as the particle displacements, the particle image size, the flow shear rate, the out-of-plane motion for planar PIV and image noise to name a few, and these parameters are interrelated and influence the final velocity estimate in a complicated way. In the last few decades, PIV has become widely popular by virtue of developments in both the hardware capabilities and correlation algorithms, especially with the scope of 3-component (3C) and 3-dimensional (3D) velocity measurements using stereo-PIV and tomographic-PIV techniques, respectively. The velocity field measurement not only leads to other quantities of interest such as Pressure, Reynold stresses, vorticity or even diffusion coefficient, but also provides a reference field for validating numerical simulations of complex flows. However, such a comparison with CFD or applicability of the measurement to industrial design requires one to quantify the uncertainty in the PIV estimated velocity field. Even though the PIV community had a strong impetus in minimizing the measurement error over the years, the problem of uncertainty estimation in local instantaneous PIV velocity vectors have been rather unnoticed. A typical norm had been to assign an uncertainty of 0.1 pixels for the whole field irrespective of local flow features and any variation in measurement noise. The first article on this subject was published in 2012 and since then there has been a concentrated effort to address this gap. The current dissertation is motivated by such a requirement and aims to compare the existing 2D PIV uncertainty methods, propose a new method to directly estimate the planar PIV uncertainty from the correlation plane and subsequently propose the first comprehensive methods to quantify the measurement uncertainty in stereo-PIV and 3D Particle Tracking Velocimetry (PTV) measurements.</div><div>The uncertainty quantification in a PIV measurement is, however, non-trivial due to the presence of multitude of error sources and their non-linear coupling through the measurement chain transfer function. In addition, the advanced algorithms apply iterative correction process to minimize the residual which increases the complexity of the process and hence, a simple data-reduction equation for uncertainty propagation does not exist. Furthermore, the calibration or a reconstruction process in a stereo or volumetric measurement makes the uncertainty estimation more challenging. Thus, current uncertainty quantification methods develop a-posterior models utilizing the evaluated displacement information and combine it with either image information, correlation plane information or even calibration “disparity map” information to find the desired uncertainties in the velocity estimates.</div><div><br></div>

Finite amplitude perturbations in compressible media are ubiquitous in scientific and engineering applications such as gas-turbine engines, rocket propulsion systems, combustion instabilities, inhomogeneous solids, and traffic flow prediction models, to name a few. Small amplitude waves in compressible fluids propagate as sound and are very well described by linear theory. On the other hand, the theory of nonlinear acoustics, concerning high-amplitude wave propagation (Mach<2) is relatively underdeveloped. Most of the theoretical development in nonlinear acoustics has focused on wave steepening and has been centered around the Burgers' equation, which can be extended to nonlinear acoustics only for purely one-way traveling waves. In this dissertation, theoretical and computational developments are discussed with the objective of advancing the multi-fidelity modeling of nonlinear acoustics, ranging from quasi one-dimensional high-amplitude waves to combustion-induced detonation waves. <br> <br> We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order in perturbation variables is derived. The exact energy corollary of such second-order system of equations is then formulated and used to elucidate the spectral energy dynamics of nonlinear acoustic waves. We then extend this analysis to thermoacoustically unstable waves -- i.e. amplified as a result of thermoacoustic instability. We drive such instability up until the generation of shock waves. We further study the nonlinear wave propagation in geometrically complex case of waves induced by the spark plasma between the electrodes. This case adds the geometrical complexity of a curved, three-dimensional shock, yielding vorticity production due to baroclinic torque. Finally, detonation waves are simulated by using a low-order approach, in a periodic setup subjected to high pressure inlet and exhaust of combustible gaseous mixture. An order adaptive fully compressible and unstructured Navier Stokes solver is currently under development to enable higher fidelity studies of both the spark plasma and detonation wave problem in the future. <br>

The study is focused on study of surface and interfacial properties of oil at high temperatures, to understand the mechanisms of heat transfer and oil absorption during frying

<p>A droplet subjected to external aerodynamic disturbances disintegrates into smaller droplets and is known as secondary atomization. Droplet breakup has been studied for low Ohnesorge (<b><i>Oh < </i></b>0.1) numbers and good agreement has been seen amongst researchers. However, when it comes to cases with high the <b><i>Oh</i></b> number, i.e. atomization where the influence of viscosity is significant, very little data is available in the literature and poor agreement is seen amongst researchers. </p> <p> </p> <p>This thesis presents a complete analysis of the modes of deformation and breakup exhibited by a droplet subjected to continuous air flow. New modes of breakup have been introduced and an intermediate case with no droplet fragmentation has been discovered. Further, results are presented for droplet size-velocity distributions. In addition, Digital in-line holography (DIH) was utilized to quantify the size-velocity pdfs using a hybrid algorithm. Finally, particle image velocimetry (PIV) was employed to characterize the air flow in the unique cases where drops exhibited no breakup and cases with multiple bag formation. </p> <p> </p> <p>A droplet subjected to external aerodynamic disturbances disintegrates into smaller droplets and is known as secondary atomization. Secondary breakup finds relevance is almost every industry that utilizes sprays for their application. </p> <p> </p>

<p>Hydraulic systems have many applications in the construction, transportation, and manufacturing sectors. Recent design trends involve systems with higher working pressures and more compact systems, which are advantageous because of power density increase. However, these trends imply higher forces and larger vibration amplitudes while having lesser mass and damping, leading to higher noise levels. Meanwhile, hydraulic machinery started prospecting new applications with tighter noise regulations, a trend which was also pushed by the electrification tendency in several fields of transportation and agriculture. One method to attain noise mitigation is passive-noise canceling techniques have the advantage of not introducing energy to the system. This approach arranges pressure ripple waves in a destructive pattern by projecting a hydraulic circuit's geometry, configuration, and features.</p> <p> </p> <p>This dissertation aims to predict fluid-borne noise sources and investigate passive noise-canceling solutions for multiple operations conditions targeting to impact many hydraulic systems and a broad range of operating conditions. Primarily a coupled system model strategy that includes a one-dimensional line finite element model is developed. The line model predicts pressure wave generation and propagation. The model features versatility since parameters like line diameter and material can be discretized node by node. Simulations are compared to measured data in a realistic novel hydraulic hybrid transmission for validation. </p> <p> </p> <p>Subsequently, an extensive numerical investigation is performed by setting fixed parameters along the hydraulic lines' length and comparing several isolated geometric properties in simulation. The developed line model is also used to study the influence of line features such as diameter and extent of the conduit. Cost-effective and simple passive solution solutions such as Quincke tubes (parallel lines), expansion chambers, and closed branches are selected and investigated on simulation. Four target pressure ripples are chosen as indicators for summarizing passive line elements behavior. The frequency-domain behavior of the pressure ripple peaks regarding the line's length is identified and isolated in simulation at the 50-5000Hz frequency spectrum. An experiment test rig is designed to implement these solutions and the experiments show three developed passive elements as practical and effective solutions for reducing fluid borne noise sources. The selected designs yielded noise source attenuation over most of the frequency spectrum measured with piezoelectric pressure variation sensors and accelerometers in different positions in the hydraulic circuit. Sound pressure measurements detected reductions over 3dB in the best cases. </p> <p> </p> <p>Also, a passive interference approach based on the principle of secondary source flow ripple cancellation was conceptualized, modeled, and implemented in a tandem axial-piston unit. The strategy consists of setting the phase between the two synchronous units to accomplish destructive interference in targeted unit harmonics. Two indexing strategies are investigated first analytically and then on simulation. One of the indexing strategies was implemented in a pre-existent commercial axial-piston tandem unit. Experiment results confirmed effectiveness for the first and third unit’s harmonics, where reductions over 15dB on pressure ripple were measured.</p> <p> </p> <p>Finally, a fluid-structure interaction based on the poison coupling principle is developed using the method of characteristics. Transfer functions of the pipeline accelerations versus the pressure ripples on lines calculated on simulation and later obtained experimentally to highlight ta critical vibration band from 2000Hz to 3000Hz with high acceleration response.</p> <p> </p><br>