# Browsing by Subject "Computational fluid dynamics"

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Item Open Access A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications(2016) Lee, CurtisThe computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Item Open Access Aeroelasticity and Enforced Motion Frequency Lock-in Associated with Non-Synchronous Vibrations in Turbomachinery(2022) Hollenbach III, Richard LeeOne of the most complex challenges in our world today is the interaction between fluids and structures. This complicated meeting is one of the focal points in the design and manufacturing of turbomachinery, whether in jet engines, steam turbines, or rocket pumps. When an unsteady aerodynamic instability interacts with the natural modes of vibration of a rigid body, a phenomenon known as Non-Synchronous Vibrations (NSV) occurs, also referred to in other parts of the world as Vortex-Induced Vibrations (VIV). These vibrations cause blade fracture and ultimately failure in jet engines; however, the underlying flow physics are much less understood than other aeroelastic phenomenon such as flutter or forced response. When the buffeting frequency of the flow around a bluff body nears one of its natural frequencies, the former frequency “locks in” to the latter. Within this “lock in” region there is only one main frequency, while outside of it there are two. Although this phenomenon has been documented both experimentally and computationally, the unsteady pressures associated with this phenomenon have not been accurately measured. In a comprehensive three-fold approach, the spectra of unsteady pressure amplitudes are collected around a few different, increasingly complex, configurations. 1. a circular cylinder 2. a symmetric NACA 0012 airfoil 3. a three-stage turbine All three exhibit NSV in wind tunnel experiments as well as computationally using fluid dynamics simulations. For all cases, the time domain unsteady lift and pressure data is Fast Fourier Transformed to provide frequency domain data. Then, the data is analyzed to understand the underlying flow physics; to do so, the unsteady pressures are separated into contributions due to the enforced motion of the body and those due to vortex shedding. Finally, the unlocked pressure spectrum is linearly combined to reconstruct the lock-in responses. These additional insights into NSV will pave the way towards a design tool for engine manufacturers. In addition, many attempts have been made to model this lock-in behavior, comparing it against experimental and computational fluid dynamics data. A reduced-order model (ROM) utilizes a Van der Pol oscillator model to capture the wake of vortices. This model has been expanded and improved to model NSV in cylinders, airfoils, and turbomachinery blades; the model proved to match experimental data better than its predecessors. This notional model will provide further insight into the phenomenon of NSV and will assist in creating a tool to design safe and efficient jet engines and steam turbines in the future. While this work focuses on Non-Synchronous Vibrations, some time was devoted to the design and manufacturing of another experimental test rig. The seven bladed linear cascade (aptly named “LASCADE”) will be used for flutter tests. The center blade oscillates about its mid-chord at an enforced frequency and amplitude, while the center three titanium printed blades contain pressure taps located at the midspan. Over the course of four years, the author has served as a design consultant, research mentor, manufacturing instructor, and project manager for this cascade. Ultimately, this work furthers the understanding of the underlying flow physics of enforced motion frequency lock-in associated with Non-Synchronous Vibrations and Flutter. The solitary experiments and simulations set the groundwork for additional studies on turbomachinery specific geometry. The three-stage turbine study is just the beginning of a full NSV study to be done in conjunction with experiments. Finally, the ROMs open the door for a full design tool to be constructed for use by turbomachinery designers and manufacturers, saving time, energy, and money in the end.

Item Open Access Anaerobic Digestion Pasteurization Latrine – Self-sustaining onsite fecal sludge treatment for developing countries(2017) ForbisStokes, Aaron AnthonyDespite significant advances in public health and engineering over the last 100 years, diarrheal disease remains one of the highest global burdens of disease, particularly for children under 5 years of age. Access to clean water, sanitation, and hygiene greatly reduces this risk, but access to improved sanitation remains a challenge for a large percentage of the world. Due to the lack of access to safely managed sanitation and rapid urbanization, sustainable onsite fecal sludge treatment systems need to be developed and deployed to reduce the burden of diarrheal disease.

The Anaerobic Digestion Pasteurization Latrine (ADPL) is a concept that was developed by Professor Marc Deshusses to meet this need. The goal of the ADPL was to produce a pathogen-free effluent through pasteurization powered by biogas produced from anaerobic digestion of fecal sludge. The concept was supported through laboratory studies on the anaerobic digestion of a simulant fecal sludge and inactivation of E. coli in a pasteurization system using a heater maintained at 65-75 °C and a tube-in-shell counter-flow heat exchanger for heat recovery.

The goal of this research was to build upon initial laboratory-based research on the ADPL and demonstrate the feasibility of the ADPL concept at full-scale in field conditions, simulate improved digester designs to increase digestion efficiency, evaluate digester effluent post-treatment for residual organic and nutrient removal, and develop a remote data acquisition and controls system to improve system understanding and operation of the pasteurization system. The desired outcome of this work is a complete, self-sustaining system that efficiently digests fecal sludge for maximum biogas production, produces a polished effluent that can be reused, and pasteurizes the effluent efficiently and reliably, all while being low-cost with minimal operation and maintenance requirements.

Two ADPL systems were installed on residential plots with 15-35 residents in a peri-urban area outside of Eldoret, Kenya. Each system was comprised of 3 toilets built above a floating dome digester and heat pasteurization system. The ADPLs are simple systems, with no moving parts and relying on gravity-induced flows. Adoption at two sites was successful, and residents reported that the systems had little to no odor or flies, and the residents were interested in the possibility of excess biogas and effluent reuse. The ADPLs were monitored daily for biogas production and temperatures in the pasteurization system. The ADPL serving 35 residents produced on average 350 Lbiogas d-1, and the temperature in the heating tank was greater than 65 °C on 87% of sampling days. The treated effluent was analyzed periodically for chemical oxygen demand (COD), biochemical oxygen demand (BOD), total ammonia nitrogen (TAN), and pH. On average, the effluent contained 4,500-5,600 mg COD L-1 (an 87-89% reduction of the estimated input), 2,000-3,900 mg BOD L-1, 2,400-4,800 mg NH3-N, and had a pH of 7.4-7.7. Results from this field study show that anaerobic digestion of minimally diluted fecal sludge can provide enough energy to pasteurize the effluent, and that the ADPL can be a suitable option for onsite fecal sludge treatment.

Three variations of a 2 m3 anaerobic digester were simulated with a flow of 120 Lwater d-1 – a reactor with no internal baffle walls (CSTR), a reactor with baffle walls that forced flow to wind in the xy-direction (HABR), and a reactor with baffle walls that forced flow to wind in the xz-direction (ABR). Results showed that increasing the number of baffle walls significantly improved the hydraulic performance of the reactor in terms of residence time, dead space, and Morrill Index. Adding angled portions to the end of baffle walls and adjusting the D:U ratio in the ABR had minimal impact while a variable inflow had a moderate impact on performance. Overall, these results suggest that adding 3-5 baffle walls inside of an anaerobic digester would greatly improve the digester’s hydraulic efficiency and better utilize the reactor volume. These adjustments would thus cause enhanced solids removal and digestion efficiency, resulting in higher biogas production and a cleaner effluent. However, simulation work including solids and biological reactions would be beneficial to future reactor design considerations.

The biological filter study analyzed the treatment of high-strength anaerobic digester effluent using trickling filters for nitrification and then submerged attached growth filters for denitrification. Five media types were tested in the trickling filters (8 L volume): biochar, granular activated carbon (GAC), zeolite (clinoptilolite), Pall rings, and gravel. Five columns were tested for denitrifying filters (4 L volume) using sand, bamboo wood chips, eucalyptus wood chips, bamboo with sand, and eucalyptus with sand. Wood chips were used in denitrifying filters as a supplemental carbon source for denitrification. From six months of operation, biochar, GAC, zeolite, Pall rings, and gravel media had turbidity removal efficiencies of 90, 91, 77, 74, and 74%, respectively, and NH3-N removal efficiencies of 83, 87, 85, 30, and 80%, respectively. The primary mechanism for ammonia removal was nitrification to nitrate, but some adsorption was seen in biochar, GAC, and zeolite filters. From four months of operation, sand, bamboo, bamboo with sand, eucalyptus, and eucalyptus with sand filters had NO3-N removal efficiencies of 30, 59, 51, 31, and 30%, respectively, and turbidity removal efficiencies of 88, 89, 84, 89, and 88%, respectively. Bamboo had the greatest NO3-N removal rate at 0.054 kg N m-3 d-1 and released more COD than eucalyptus (0.076-0.120 gCOD gbamboo-1 compared to 0.012-0.043 gCOD geucalyptus-1). Biochar and bamboo were selected as the best media types from this study for the nitrification and denitrification filters, respectively, due to their low-cost and sustainable supply. Based on an average initial influent of 600 mg NH3-N L-1 and 980 NTU, the biochar filter’s expected effluent would be 97 mg NH3-N L-1, 450 mg NO3-N L-1, and 120 NTU. The bamboo filter would then produce an effluent of 82 mg NH3-N L-1, 180 mg NO3-N L-1, and 13 NTU. This theoretical combined performance would thus result in 56% removal of total N and 98.7% removal of turbidity. Based on nitrate removal rate, full denitrification could be achieved by doubling reactor volume. Total nitrogen removal efficiency of 80-90% could thus be achievable. These filter media were successful in treating high-strength digester effluent and present an alternative for sustainable, low-cost, and low-maintenance post-treatment options for nitrogen management.

A low-cost data acquisition and controls system with remote, real-time data access was developed using the Particle Electron. This device records temperature and liquid flow data while controlling a gas valve and igniter as part of pasteurization system. The device was tested in lab and field conditions. The power consumption is low, 34 Wh per day, and data acquisition matched the results of standard laboratory devices. The field deployment (Eldoret, Kenya) successfully operated the pasteurization system in its target range while reporting real-time data. This low-cost and low-power device has improved the operation of the onsite pasteurization system, and adaptations of the device would be valuable in many other onsite fecal sludge treatment systems.

Together, these objectives have demonstrated the ADPL concept works in field conditions, digester performance can be improved with simple modifications, digester effluent can be further treated to encourage reuse or for safe disposal with biological filters using sustainable media that have low operational requirements, and low-cost controls can improve the pasteurization system efficiency and reliability while generating more data to expand understanding of the system.

Item Open Access Analyzing Hydrodynamic Properties of the North Atlantic Right Whales with Computer Solutions(2020) Wu, Chen-YiAnimals experience hydrodynamic forces (lift, drag, and side) and moments (pitching, yawing, and rolling) as a result of motion in an aqueous medium. Under selective pressure, most cetaceans, including porpoises, dolphins, and whales, developed a streamlined body shape and modified limbs, which delay the separation of flow, create lower drag when they swim, and therefore decrease their locomotor cost. In order to calculate the locomotor cost and propulsive efficiency of cetaceans, accurate estimates of drag on marine animals are required. However, extra momentum imparted into the fluid from lift and side forces as well as pitching, rolling, and yawing moments (here, the parasitic loads) results in extra drag force on the animal. Therefore, in addition to streaming and delaying flow separation, animals must also minimize excess fluid momentum resulting from parasitic loads. Given the endangered status of the North Atlantic right whale (Eubalaena glacialis; hereafter NARW), analyzing the hydrodynamic characteristics of the NARWs was the focus of this work. Additionally, previous studies showed that body shape of NARWs changes with life stages, reproduction status, nutritive conditions or prey abundance, and the effects of entanglement in fishing gear. Therefore, in this study, computational fluid dynamics (CFD) analysis was performed on multiple 10 m three-dimensional NARW models with different body shapes (e.g., normal condition, emaciated, and pregnant) to measure baseline measurements of flow regimes and hydrodynamic loads on the animal. Swimming speeds covering known right whale speed range (0.125 m/s to 8 m/s) were simulated in most scenarios. In addition to the hydrodynamic effects of different body shapes, drag was also considered a function of parasitic loads. The NARW models were embedded with bone segments that allowed one to manipulate the body pose of the model via adjusting the flippers or the spine of the animal before measuring hydrodynamic drag. By doing so, momentum from parasitic loads was expected to be eliminated. CFD simulations revealed that drag on NARWs is dictated by its irregular outline and that the drag coefficient (0.0071-0.0059; or dimensionless drag) of on NARWs is approximately twice that of many previous estimates for large cetaceans. It was also found that pregnant NARW model encounters the lowest drag coefficient due to delayed flow separation resulting from enlarged abdomen, whereas the emaciated NARW model experiences the highest drag coefficient possibly due to the concavity at the post-nuchal region. These results suggested that drag on NARWs and their thrust power requirements were indeed affected by its body shape but the differences between the three NARW models tested were small. Lastly, minimum drag, which corresponds to the elimination of the parasitic loads, can be obtained by adjusting the pose of the animal. Thus, minimum drag occurs at the neutral trim pose. For the static, normo-nourished NARW model, simulations revealed that by changing the angle of attack of the flippers by 4.03° (relative to the free-stream flow) and pitching the spine downward by 5° while maintaining fluke angle, the drag was lowered by approximately 11% across the flow speeds tested. This drag reduction was relative to the drag study conducted on the same animal model but without body pose adjustments. Together the studies included in the present work explored and highlighted the capability of numerical methods in investigating the hydrodynamics and energetics of cetaceans. Future studies should address how computer solutions can be used to solve problems from a wider aspect. For instance, extra parasitic loads caused by attached gear as well as possible injuries due to the encounter with fishing gear should also be considered while evaluating the energy budget of the North Atlantic right whales.

Item Open Access Development of an Efficient Design Method for Non-synchronous Vibrations(2008-04-24) Spiker, Meredith AnneThis research presents a detailed study of non-synchronous vibration (NSV) and the development of an efficient design method for NSV. NSV occurs as a result of the complex interaction of an aerodynamic instability with blade vibrations. Two NSV design methods are considered and applied to three test cases: 2-D circular cylinder, 2-D airfoil cascade tip section of a modern compressor, and 3-D high pressure compressor cascade that encountered NSV in rig testing. The current industry analysis method is to search directly for the frequency of the instability using CFD analysis and then compare it with a fundamental blade mode frequency computed from a structural analysis code. The main disadvantage of this method is that the blades' motion is not considered and therefore, the maximum response is assumed to be when the blade natural frequency and fluid frequency are coincident. An alternate approach, the enforced motion method, is also presented. In this case, enforced blade motion is used to promote lock-in of the blade frequency to the fluid natural frequency at a specified critical amplitude for a range of interblade phase angles (IBPAs). For the IBPAs that are locked-on, the unsteady modal forces are determined. This mode is acceptable if the equivalent damping is greater than zero for all IBPAs. A method for blade re-design is also proposed to determine the maximum blade response by finding the limit cycle oscillation (LCO) amplitude. It is assumed that outside of the lock-in region is an off-resonant, low amplitude condition. A significant result of this research is that for all cases studied herein, the maximum blade response is not at the natural fluid frequency as is assumed by the direct frequency search approach. This has significant implications for NSV design analysis because it demonstrates the requirement to include blade motion. Hence, an enforced motion design method is recommended for industry and the current approach is of little value.Item Open Access Influence of Outlet Boundary Conditions on Cerebrovascular Aneurysm Hemodynamics(2016) Adrianzen Alvarez, Daniel RobertoComputational fluid dynamic (CFD) studies of blood flow in cerebrovascular aneurysms have potential to improve patient treatment planning by enabling clinicians and engineers to model patient-specific geometries and compute predictors and risks prior to neurovascular intervention. However, the use of patient-specific computational models in clinical settings is unfeasible due to their complexity, computationally intensive and time-consuming nature. An important factor contributing to this challenge is the choice of outlet boundary conditions, which often involves a trade-off between physiological accuracy, patient-specificity, simplicity and speed. In this study, we analyze how resistance and impedance outlet boundary conditions affect blood flow velocities, wall shear stresses and pressure distributions in a patient-specific model of a cerebrovascular aneurysm. We also use geometrical manipulation techniques to obtain a model of the patient’s vasculature prior to aneurysm development, and study how forces and stresses may have been involved in the initiation of aneurysm growth. Our CFD results show that the nature of the prescribed outlet boundary conditions is not as important as the relative distributions of blood flow through each outlet branch. As long as the appropriate parameters are chosen to keep these flow distributions consistent with physiology, resistance boundary conditions, which are simpler, easier to use and more practical than their impedance counterparts, are sufficient to study aneurysm pathophysiology, since they predict very similar wall shear stresses, time-averaged wall shear stresses, time-averaged pressures, and blood flow patterns and velocities. The only situations where the use of impedance boundary conditions should be prioritized is if pressure waveforms are being analyzed, or if local pressure distributions are being evaluated at specific time points, especially at peak systole, where the use of resistance boundary conditions leads to unnaturally large pressure pulses. In addition, we show that in this specific patient, the region of the blood vessel where the neck of the aneurysm developed was subject to abnormally high wall shear stresses, and that regions surrounding blebs on the aneurysmal surface were subject to low, oscillatory wall shear stresses. Computational models using resistance outlet boundary conditions may be suitable to study patient-specific aneurysm progression in a clinical setting, although several other challenges must be addressed before these tools can be applied clinically.

Item Open Access Investigating the Influence of Red Blood Cell Interactions on Large-Scale Cancer Cell Transport: Bridging the Gap through Advances in Computational Techniques(2023) Roychowdhury, SayanMetastatic cancer, the leading cause of cancer mortality, involves the complex process of circulating tumor cells (CTCs) spreading through the bloodstream and forming secondary tumors far away from the primary mass, which often travel a distance many thousand times its size. The interactions between CTCs and their neighboring red blood cells (RBCs), as well as the local hemodynamics in vessels, play a crucial role in determining these cells' fate; however, the mechanisms guiding their transit are still unclear. Predicting secondary tumor sites remains challenging due to the intricate dynamics of CTC migration. Thus, there remains a need to understand the interplay between the fluid dynamics, intercellular interactions, and vessel topology which can determine the fate of the CTC and subsequent likelihood of cancer progression.

Investigating CTC transport has involved a range of \textit{in vivo} and \textit{in vitro} studies to unravel the intricate mechanisms that dictate cellular outcomes. However, the process of tracking an individual CTC's trajectory through the massive vascular system is still not possible today \textit{in vivo}. The integration of \textit{in silico} models has proven instrumental, complementing traditional experimental approaches. In this work, we utilize our advanced fluid dynamics solver HARVEY to perform high-fidelity hemodynamic simulations to capture CTC dissemination. We outline several key contributions, including the addition of new physics interactions models and software optimizations, to enable these simulations to better capture biological phenomena and run to completion within a reasonable timeframe.

Numerical optimizations for \textit{in silico} models are still necessary: the drastic difference in length scales of CTC size versus distance traveled hinders current simulation models. To accurately capture intercellular dynamics, interactions must be modeled with sub-micrometer precision; meanwhile, the characteristic length scale of CTC traversal through the blood stream can be on the order of hundreds of millimeters, over 5 orders of magnitude larger. Numerically modeling hundreds of millions of individual cells at a sub-micron resolution over this timescale would require the entirety of multiple leadership-class supercomputers over the course of several weeks, if not months. Therefore, there still exists a disparity between these two ranges that needs to be addressed to make simulations of CTC transport with the presence of neighboring RBCs tractable.

We also address one of the pillars of the inherent variability in cell transport: the fate of a single CTC can exhibit significant variations due to its interactions with neighboring RBCs in the context of an \textit{in vivo} experiment,. A single simulation of a CTC may not encompass the range of outcomes, necessitating the consideration of many simulations with different RBC distributions. Multiplying the number of simulations required to capture this variability by the computational workload of a single simulation results in a computationally intractable workload, making it essential to optimize the number of simulations required for proper results. The number of potential cell configurations is vast, which makes it essential to identify representative configurations that encompass the full range of possible outcomes while optimizing computational feasibility.

This dissertation explores the influence of several hemodynamic and geometric parameters, microvasculature interactions, and the impact of RBCs on CTC movement, including the presence of RBC aggregation, RBC volume fraction, microvessel size, and shear rate. Furthermore, it discusses the enhancement of adaptive physics refinement methods to model cellular transport phenomena and highlights the capabilities of fluid-structure interaction models in capturing the dynamics of CTCs and RBCs across the system-scale. The dissertation concludes by discussing the development of a novel framework to account for the range of outcomes in CTC transport due to the variability in neighboring RBCs; it addresses the importance of generating representative configurations using quantitative metrics such as the Jaccard index applied to sets of sphere and RBC data sets. By integrating these advances, we further reduce the gap towards biologically accurate computational models of cancer cell transport, which holds promise for improving our understanding of cancer metastasis and developing effective strategies for cancer treatment.

Item Open Access Multi-Row Aerodynamic Interactions and Mistuned Forced Response of an Embedded Compressor Rotor(2016) Li, JingThis research investigates the forced response of mistuned rotor blades that can lead to excessive vibration, noise, and high cycle fatigue failure in a turbomachine. In particular, an embedded rotor in the Purdue Three-Stage Axial Compressor Research Facility is considered. The prediction of the rotor forced response contains three key elements: the prediction of forcing function, damping, and the effect of frequency mistuning. These computational results are compared with experimental aerodynamic and vibratory response measurements to understand the accuracy of each prediction.

A state-of-the-art time-marching computational fluid dynamic (CFD) code is used to predict the rotor forcing function. A highly-efficient nonlinear frequency-domain Harmonic Balance CFD code is employed for the prediction of aerodynamic damping. These allow the compressor aerodynamics to be depicted and the tuned rotor response amplitude to be predicted. Frequency mistuning is considered by using two reduced-order models of different levels of fidelity, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM) methods. This allows a cost-effective method to be identified for mistuning analysis, especially for probabilistic mistuning analysis.

The first topic of this work concerns the prediction of the forcing function of the embedded rotor due to the periodic passing of the neighboring stators that have the same vane counts. Superposition and decomposition methods are introduced under a linearity assumption, which states that the rotor forcing function comprises of two components that are induced by each neighboring stator, and that these components stay unchanged with only a phase shift with respect to a change in the stator-stator clocking position. It is found that this assumption captures the first-order linear relation, but neglects the secondary nonlinear effect which alters each stator-induced forcing functions with respect to a change in the clocking position.

The second part of this work presents a comprehensive mistuned forced response prediction of the embedded rotor at a high-frequency (higher-order) mode. Three steady loading conditions are considered. The predicted aerodynamics are in good agreement with experimental measurements in terms of the compressor performance, rotor tip leakage flow, and circumferential distributions of the stator wake and potential fields. Mistuning analyses using FMM and CMM models show that the extremely low-cost FMM model produces very similar predictions to those of CMM. The predicted response is in good agreement with the measured response, especially after taking the uncertainty in the experimentally-determined frequency mistuning into consideration. Experimentally, the characteristics of the mistuned response change considerably with respect to loading. This is not very well predicted, and is attributed to un-identified and un-modeled effects. A significant amplification factor over 1.5 is observed both experimentally and computationally for this higher-order mode.

Item Open Access Probabilistic Modeling of Decompression Sickness, Comparative Hydrodynamics of Cetacean Flippers, Optimization of CT/MRI Protocols and Evaluation of Modified Angiocatheters: Engineering Methods Applied to a Diverse Assemblage of Projects(2010) Weber, Paul WilliamThe intent of the work discussed in this dissertation is to apply the engineering methods of theory/modeling, numerics/computation, and experimentation to a diverse assemblage of projects. Several projects are discussed: probabilistic modeling of decompression sickness, comparative hydrodynamics of cetacean flippers, optimization of CT/MRI protocols, evaluation of modified catheters, rudder cavitation, and modeling of mass transfer in amphibian cone outer segments.

The first project discussed is the probabilistic modeling of decompression sickness (DCS). This project involved developing a system for evaluating the success of decompression models in predicting DCS probability from empirical data. Model parameters were estimated using maximum likelihood techniques, and exact integrals of risk functions and tissue kinetics transition times were derived. Agreement with previously published results was excellent including maximum likelihood values within one log-likelihood unit of previous results and improvements by re-optimization, mean predicted DCS incidents within 1.4% of observed DCS, and time of DCS occurrence prediction. Alternative optimization and homogeneous parallel processing techniques yielded faster model optimization times. The next portion of this project involved investigating the nature and utility of marginal decompression sickness (DCS) events in fitting probabilistic decompression models to experimental dive trial data. Three null models were developed and compared to a known decompression model that was optimized on dive trial data containing only marginal DCS and no-DCS events. It was found that although marginal DCS events are related to exposure to decompression, empirical dive data containing marginal and full DCS outcomes are not combinable under a single DCS model; therefore, marginal DCS should be counted as no-DCS events when optimizing probabilistic DCS models with binomial likelihood functions. The final portion of this project involved the exploration of a multinomial DCS model. Two separate models based on the exponential-exponential/linear-exponential framework were developed: a trinomial model, which is able to predict the probabilities of mild, serious and no-DCS simultaneously, and a tetranomial model, which is able to predict the probabilities of mild, serious, marginal and no-DCS simultaneously. The trinomial DCS model was found to be qualitatively better than the tetranomial model, for reasons found earlier concerning the utility of marginal DCS events in DCS modeling.

The next project discussed is comparative hydrodynamics of cetacean flippers. Cetacean flippers may be viewed as being analogous to modern engineered hydrofoils, which have hydrodynamic properties such as lift coefficient, drag coefficient and associated efficiency. The hydrodynamics of cetacean flippers have not previously been rigorously examined and thus their performance properties are unknown. By conducting water tunnel testing using scale models of cetacean flippers derived via computed tomography (CT) scans, as well as computational fluid dynamic (CFD) simulations, a baseline work is presented to describe the hydrodynamic properties of several cetacean flippers. It was found that flippers of similar planform shape had similar hydrodynamic performance properties. Furthermore, one group of flippers of planform shape similar to modern swept wings was found to have lift coefficients that increased with angle of attack nonlinearly, which was caused by the onset of vortex-dominated lift. Drag coefficient versus angle of attack curves were found to be less dependent on planform shape. Larger cetacean flippers were found to have degraded performance at a Re of 250,000 compared to flippers of smaller odontocetes, while performance of larger and smaller cetacean flippers was similar at a swim speed of 2 m/s. Idealization of the planforms of cetacean flippers was found to capture the relevant hydrodynamic effects of the real flippers, although unintended consequences such as the lift curve slope changing from linear to nonlinear were sometimes observed. A numerical study of an idealized model of the humpback whale flipper showed that the leading-edge tubercles delay stall compared to a baseline (no tubercle) flipper because larger portions of the flow remaining attached at higher angles of attack.

The third project discussed is optimization of CT/MRI protocols. In order to optimize contrast material administration protocols for Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), a custom-built physiologic flow phantom was constructed to model flow in the human body. This flow phantom was used to evaluate the effect of varying volumes, rates, and types of contrast material, use of a saline chase, and cardiac output on aortic enhancement characteristics. For CT, reducing the volume of contrast material decreased duration peak enhancement and reduced the maximum value of peak enhancement. Increasing the rate of contrast media administration increased peak enhancement and decreased duration of peak enhancement. Use of a saline chase resulted in an increase in peak enhancement. Peak aortic enhancement increased when reduced cardiac output was simulated. For MRI, when the same volume of contrast material was injected at the same rate, the type of contrast material used has a significant effect on the greatest peak signal intensity and duration peak signal intensity. A higher injection rate of saline chaser is more advantageous than a larger volume of saline chaser to increase the peak aortic signal intensity using low contrast material doses. Furthermore, for higher volumes of contrast material, the effect of increasing the volume of saline chaser makes almost no difference while increasing the rate of injection makes a significant difference. When a saline chaser with a high injection rate is used, the dose of the contrast material may be reduced by 25-50% and more than 86% of the non-reduced dose peak aortic enhancement will be attained.

The next project discussed is evaluation of modified angiocatheters. In this study, a standard peripheral end hole angiocatheter was compared to those modified with side holes or side slits by using experimental techniques to qualitatively compare the contrast material exit jets, and by using numeric techniques to provide flow visualization and quantitative comparisons. A Schlieren imaging system was used to visualize the angiocatheter exit jet fluid dynamics at two different flow rates, and a commercial computational fluid dynamics (CFD) package was used to calculate numeric results for various catheter orientations and vessel diameters. Experimental images showed that modifying standard peripheral intravenous angiocatheters with side holes or side slits qualitatively changed the overall flow field and caused the exiting jet to become less well-defined. Numeric calculations showed that the addition of side holes or slits resulted in a 9-30% reduction of the velocity of contrast material exiting the end hole of the angiocatheter. With the catheter tip directed obliquely to the wall, the maximum wall shear stress was always highest for the unmodified catheter and always lowest for the 4 side slit catheter. Modified angiocatheters may have the potential to reduce extravasation events in patients by reducing vessel wall shear stress.

The next project discussed involves studying the effect of leading-edge tubercles on cavitation characteristics for marine rudders. Three different rudders were constructed and tested in a water tunnel: baseline, 3-tubercle leading edge, and 5-tubercle leading edge. In the linear (non-stall) regime, tubercled rudders performed equally to the smooth rudder. Hydrodynamic stall occurred at smaller angles of attack for the tubercled rudders than for the smooth rudder. When stall did occur, it was more gradual for the tubercled rudders, whereas the smooth rudder demonstrated a more dramatic loss of lift. At lower Re, the tubercled rudders also maintained a higher value of lift post-stall than the smooth rudder. Cavitation onset for the tubercled rudders occurred at lower angles of attack and higher values of cavitation number than for the smooth rudder, but cavities on the tubercled rudders were localized in the slots as opposed to the smooth rudder where the cavity spread across the entire leading edge.

In the final project discussed, modeling of mass transfer in amphibian cone outer segments, a detailed derivation of a simplified (continuum, one-dimensional) mathematical model for the radio-labeled opsin density profile in the amphibian cone outer segment is presented. This model relies on only one free parameter, which was the mass transfer coefficient between the plasmalemma and disc region. The descriptive equations were nondimensionalized, and scale analysis showed that advective effects could be neglected as a first approximation for early times so that a simplified system could be obtained. Through numeric computation the solution behavior was found to have three distinct stages. The first stage was marked by diffusion in the plasmalemma and no mass transfer in the disc region. The second stage first involved the plasmalemma reaching a metastable state whereas the disc region density increased, then involved both the plasmalemma and disc regions increasing in density with their distributions being qualitatively the same. The final stage involved a slow relaxation to the steady-state solution.

Item Open Access Statistical Learning of Particle Dispersion in Turbulence and Modeling Turbulence via Deep Learning Techniques(2021) Momenifar, RezaTurbulence is a complex dynamical system that is strongly high-dimensional, non-linear, non-local and chaotic with a broad range of interacting scales that vary over space and time. It is a common characteristic of fluid flows and appears in a wide range of applications, both in nature and industry. Moreover, many of these flows contain suspended particles. Motivated by this, the research presented here aims at (i) studying particle motion in turbulence and (ii) modeling turbulent flows using modern machine learning techniques.

In the first research objective, we conduct a parametric study using numerical experiments (direct numerical simulations) to examine accelerations, velocities and clustering of small inertial settling particles in statistically stationary isotropic turbulent flow under different values of the system control parameters (Taylor Reynolds number $Re_\lambda$, particle Stokes number $St$ and settling velocity $Sv$). To accomplish our research goals, we leveraged a wide variety of tools from applied mathematics, statistical physics and computer science such as constructing the probability density function (PDF) of quantities of interest, radial distributionfunction (RDF), and three-dimensional Vorono\text{\"i} analysis. Findings of this study have already been published in two journal papers (PhysRevFluids.4.054301 and PhysRevFluids.5.034306), both of which received editors' suggestion awards. In the following paragraphs, some of the important results are highlighted.

The results for the probability density function (PDF) of the particle relative velocities show that even when the particles are settling very fast, turbulence continues to play a key role in their vertical relative velocities, and increasingly so as $Re_\lambda$ is increased. Thisoccurs because although the settling velocity may be much larger than typical velocities of the turbulence, due to intermittency, there are significant regions of the flow where the contribution to the particle motion from turbulence is of the same order as that from gravitational settling.

In agreement with previous results using global measures of particle clustering, such as the RDF, we find that for small Vorono\text{\"i} volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon $St$ and $Sv$, but only weakly dependent upon $Re_\lambda$, unless $St>1$. However, larger Vorono\text{\"i} volumes (void regions) exhibit a much stronger dependence on $Re_\lambda$, even when $St\leq 1$, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Vorono\text{\"i} volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Vorono\text{\"i} volumes as $Sv$ is increased.

Our local analysis of the acceleration statistics of settling inertial particles shows that clustered particles experience a net acceleration in the direction of gravity, while particles in void regions experience the opposite. The particle acceleration variance, however, is a convex function of the Vorono\text{\"i} volumes, with or without gravity, which seems to indicate a non-trivial relationship between the Vorono\text{\"i} volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle positions are of the order of the square of the Kolmogorov acceleration and depend only weakly on Vorono\text{\"i} volumes. These results call into question the ``sweep-stick'' mechanism for particle clustering in turbulence which would lead one to expect that clustered particles reside in regions where the fluid acceleration is zero (or at least very small).

In the second research objective, we propose two cutting-edge, data-driven, deep learning simulation frameworks, with the capability of embedding physical constraints corresponding to properties of three-dimensional turbulence. The first framework aims to reduce the dimensionality of data resulting from large-scale turbulent flow simulations (static mapping), while the second framework is designed to emulate the spatio-temporal dynamics of a three-dimensional turbulent flow (dynamic mapping).

In the static framework, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients.A detailed analysis of the performance of this lossy data compression scheme, with evaluations based on multiple sets of data having different characteristics to that of the training data, show that this framework can faithfully reproduce the statistics of the flow, except at the very smallest scales, while offering 85 times compression. %Compared to the recent study of Glaws. et. al. (Physical Review Fluids, 5(11):114602, 2020), which was based on a conventional autoencoder (where compression is performed in a continuous space), our model improves the CR by more than $30$ percent, and reduces the MSE by an order of magnitude. Our compression model is an attractive solution for situations where fast, high quality and low-overhead encoding and decoding of large data are required. Our proposed framework for dynamic mapping consists of two deep learning models, one for dimension reduction and the other for sequence learning. In the model, we first generate a low-dimensional representation of the velocity data and then pass it to a sequence prediction network that learns the spatio-temporal correlations of the underlying data. For the sequence forecasting, the idea of Transformer architecture is used and its performance compared against a standard Recurrent Network, Convolutional LSTM. These architectures are designed to perform a sequence to sequence multi-class classification task, which is attractive for modeling turbulence. The diagnostic tests show that our Transformer based framework can perform short-term predictions that retain important characteristics of large and inertial scales of flow across all the predicted snapshots.