Bei der Rektifikation werden heute zunehmend Füllkörperkolonnen mit geordneten Packungen eingesetzt. Die Maldistribution, ein bislang ungelöstes Problem in Füllkörperkolonnen, wirkt sich negativ auf die Stoffaustauschleistung aus. Zur Verringerung der Maldistribution wird zwischen den Packungssektionen mehrfach die Rücklaufflüssigkeit gesammelt und erneut gleichmäßig über den Kolonnenquerschnitt verteilt. Diese Neuverteilung realisieren Zwischenverteiler, die somit einen Großteil der Kolonnenhöhe beanspruchen und damit die Investitions- und Betriebskosten erheblich erhöhen. Hauptursache für die Bauhöhe der Zwischenverteiler ist der Wunsch nach einem vollständigen Konzentrationsausgleich vor der Neuverteilung. Um die Kolonnenhöhe zu verringern und dennoch die gleiche Trennleistung zu erreichen, mangelt es den Anlagenbauern bislang an einer praktikablen Lösung. Entgegen der bisherigen Lehrbuchmeinung wird in dieser Arbeit die Bedeutung des vollständigen Konzentrationsausgleich grundsätzlich in Frage gestellt. Es erfolgen deshalb theoretische und experimentelle Untersuchungen für ein besseres Verständnis der Neuverteilung der Rücklaufflüssigkeit und deren Auswirkung auf die Trennleistung. Durch Modifizierung des klassischen Zwei-Kolonnen-Modells gelingt es, den Einfluss der Maldistribution, der Dampfquervermischung und der hydraulisch gleichmäßigen Flüssigkeitsneuverteilung mit und ohne vollständigen Konzentrationsausgleich numerisch zu simulieren. Die Überprüfung der Simulationsmodelle erfolgt an einer Pilotkolonne mit einem inneren Durchmesser von 1 m. Die Kolonne ist mit Sulzer MellapakPlus 752.Y ausgerüstet und als Testgemisch dient trans-/cis-Dekalin. Im Ergebnis zeigt sich, dass vor allem der hydraulische Ausgleich erforderlich ist und es praktisch keinen Unterschied zwischen vollständigen und unvollständigen Konzentrationsausgleich bei sonst gleichen Betriebsbedingungen gibt. Überlegungen für deutlich flachere Verteilerkonstruktionen werden vorgestellt.

<p>  </p> <p>With the recent advancement of computation and imaging technology, Image-based computational fluid dynamics (ICFD) has emerged as a great non-invasive capability to study biomedical flows. These modern technologies increase the potential of computation-aided diagnostics and therapeutics in a patient-specific environment. I studied three components of this image-based computational fluid dynamics process in this work.</p> <p>To ensure accurate medical assessment, realistic computational analysis is needed, for which patient-specific image segmentation of the diseased vessel is of paramount importance. In this work, image segmentation of several human arteries, veins, capillaries, and organs was conducted to use them for further hemodynamic simulations. To accomplish these, several open-source and commercial software packages were implemented. </p> <p>This study incorporates a new computational platform, called <em>InVascular</em>, to quantify the 4D velocity field in image-based pulsatile flows using the Volumetric Lattice Boltzmann Method (VLBM). We also conducted several parametric studies on an idealized case of a 3-D pipe with the dimensions of a human renal artery. We investigated the relationship between stenosis severity and Resistive index (RI). We also explored how pulsatile parameters like heart rate or pulsatile pressure gradient affect RI.</p> <p>As the process of ICFD analysis is based on imaging and other hemodynamic data, it is often time-consuming due to the extensive data processing time. For clinicians to make fast medical decisions regarding their patients, we need rapid and accurate ICFD results. To achieve that, we also developed surrogate models to show the potential of supervised machine learning methods in constructing efficient and precise surrogate models for Hagen-Poiseuille and Womersley flows.</p>

<p>Two studies incorporated providing the groundwork for a blueprint to design sodium sulfur cells from electrode fabrication to choices in electrolyte such as DME, DEGDME, TEGDME and two different salts NaClO4 and NaPF6. First study describes role of the binder within the system comparing carboxymethyl cellulose and carboxymethyl cellulose with a styrene butadiene elastomer addition. The second study focuses on methods to prevent polysulfide shuttling within room temperature sodium sulfur system</p>

<p>Subcutaneous administration has become a common approach for drug delivery of biotherapeutics, such as monoclonal antibodies, which is achieved mainly by absorption through the lymphatic system. This dissertation focuses on the computational modeling of the fluid flow and solute transport in the skin tissue and the quantitative investigation of lymphatic uptake. First, the various mechanisms governing drug transport and lymphatic uptake of biotherapeutics through subcutaneous injection are investigated quantitatively through high-fidelity numerical simulations, including lymphatic drainage, blood perfusion, binding, and metabolism. The tissue is modeled as a homogeneous porous medium using both a single-layered domain and a multi-layered domain, which includes the epidermis, dermis, hypodermis (subcutaneous tissue), and muscle layers. A systematic parameter study is conducted to understand the roles of different properties of the tissue in terms of permeability, porosity, and vascular permeability. The role of binding and metabolism on drug absorption is studied by varying the binding parameters for different macromolecules after coupling the transport equation with a pharmacokinetic equation. The interstitial pressure plays an essential role in regulating the absorption of unbound drug proteins during the injection, while the binding and metabolism of drug molecules reduce the total free drugs. </p> <p>  </p> <p>The lymphatic vessel network is essential to achieve the functions of the lymphatic system. Thus, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. The explicit heterogeneous vessel network is embedded into the continuum model to investigate the role of explicit heterogeneous vessel network in drug transport and absorption. The solute transport across the vessel wall is investigated under various transport conditions. The diffusion of the drug solutes through the explicit vessel wall affects the drug absorption after the injection, while the convection under large interstitial pressure dominates the drug absorption during the injection. The effect of diffusion cannot be captured by the previously developed continuum model. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. The injection volume significantly affects lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence. At last, the binding and metabolism of drug molecules are studied to bridge the simulation to the experimentally measured drug clearance. </p> <p><br></p> <p>Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection.  An approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. </p> <p><br></p> <p>At last, an improved Kedem-Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. The effect of different drug solutes with different Stokes radii and different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. The drug solute with a small size has a larger partition coefficient and diffusivity across the openings of the lymphatic vessel wall, which favors drug absorption. The Voronoi structure is found to be more efficient in lymphatic uptake. </p> <p><br></p> <p>The systematic and quantitative investigation of subcutaneous absorption based on high-fidelity numerical simulations can provide guidance on the optimization of drug delivery systems and is valuable for the translation of bioavailability from the pre-clinical species to humans. We provide a novel approach to studying the diffusion and convection of drug molecules into the lymphatic system by developing the hybrid discrete-continuum vessel network. The study of the solute transport across the discrete lymphatic vessel walls further improves our understanding of lymphatic uptake. The novel and time-efficient computational model for solute transport across the lymphatic vasculature connects the microscopic properties of the lymphatic vessel membrane to macroscopic drug absorption. The comprehensive hybrid vessel network model developed here can be further used to improve our understanding of the diseases caused by the disturbed lymphatic system, such as lymphedema, and provide insights into the treatment of diseases caused by the malfunction of lymphatics.</p>

<p>Gaussian Process Regression (GPR) is a widely used surrogate model in efficient global optimization (EGO) due to its capability to provide uncertainty estimates in the prediction. The cost of creating a GPR model for large data sets is high. On the other hand, neural network (NN) models scale better compared to GPR as the number of samples increase. Unfortunately, the uncertainty estimates for NN prediction are not readily available. In this work, a scalable algorithm is developed for EGO using NN-based prediction and uncertainty (EGONN). Initially, two different NNs are created using two different data sets. The first NN models the output based on the input values in the first data set while the second NN models the prediction error of the first NN using the second data set. The next infill point is added to the first data set based on criteria like expected improvement or prediction uncertainty. EGONN is demonstrated on the optimization of the Forrester function and a constrained Branin function and is compared with EGO. The convergence criteria is based on the maximum number of infill points in both cases. The algorithm is able to reach the optimum point within the given budget. The EGONN is extended to handle constraints explicitly and is utilized for aerodynamic shape optimization of the RAE 2822 airfoil in transonic viscous flow at a free-stream Mach number of 0.734 and a Reynolds number of 6.5 million. The results obtained from EGONN are compared with the results from gradient-based optimization (GBO) using adjoints. The optimum shape obtained from EGONN is comparable to the shape obtained from GBO and is able to eliminate the shock. The drag coefficient is reduced from 200 drag counts to 114 and is close to 110 drag counts obtained from GBO. The EGONN is also extended to handle uncertainty quantification (uqEGONN) using prediction uncertainty as an infill method. The convergence criteria is based on the relative change of summary statistics such as mean and standard deviation of an uncertain quantity. The uqEGONN is tested on Ishigami function with an initial sample size of 100 samples and the algorithm terminates after 70 infill points. The statistics obtained from uqEGONN (using only 170 function evaluations) are close to the values obtained from directly evaluating the function one million times. uqEGONN is demonstrated on to quantifying the uncertainty in the airfoil performance due to geometric variations. The algorithm terminates within 100 computational fluid dynamics (CFD) analyses and the statistics obtained from the algorithm are close to the one obtained from 1000 direct CFD based evaluations.</p>

<p>Two-phase modeling and simulation capabilities are strongly dependent on the accuracy of flow regime identification methods. Flow regimes have traditionally been determined through visual observation, resulting in subjective classifications that are susceptible to inconsistencies and disagreements between researchers. Since the majority of two-phase flow studies have been concentrated around vertical and horizontal pipe orientations, flow patterns in inclined pipes are not well-understood. Moreover, they may not be adequately described by conventional flow regimes which were conceptualized for vertical and horizontal flows. Recent work has explored applying machine learning methods to vertical and horizontal flow regime identification to help remedy the subjectivity of classification. Such methods have not, however, been successfully applied to inclined flow orientations. In this study, two novel unsupervised machine learning methods are proposed: a modular configuration of multiple machine learning algorithms that is adaptable to different pipe orientations, and a second universal approach consisting of several layered algorithms which is capable of performing flow regime classification for data spanning multiple orientations. To support this endeavor, an experimental database is established using a dual-ring impedance meter. The signals obtained by the impedance meter are capable of conveying distinct features of the various flow patterns observed in vertical, horizontal, and inclined pipes. Inputs to the unsupervised learning algorithms consist of statistical measures computed from these signals. A novel conceptualization for flow pattern classification is developed, which maps three statistical parameters from the data to red, green, and blue primary color intensities. By combining the three components, a flow pattern map can be developed wherein similar colors are produced by flow conditions with like statistics, transforming the way flow regimes are represented on a flow regime map. The resulting dynamic RGB flow pattern map provides a physical representation of gradual changes in flow patterns as they transition from one regime to another. By replacing the static transition boundaries with physically informed, dynamic gradients between flow patterns, transitional flow patterns may be described with far greater accuracy. This study demonstrates the effectiveness of the proposed method in generating objective flow regime maps, providing a basis for further research on the characterization of two-phase flow patterns in inclined pipes. The three proposed methods are compared and evaluated against flow regime maps found in literature.</p>

<p>Uncertainty analysis is of great use both for calculating outputs that are more akin to real<br> flight, and for optimization to more robust shapes. However, implementation of uncertainty<br> has been a longstanding challenge in the field of aerodynamics due to the computational cost<br> of simulations. Geometric uncertainty in particular is often left unexplored in favor of uncer-<br> tainties in freestream parameters, turbulence models, or computational error. Therefore, this<br> work proposes a method of geometric uncertainty analysis for aerodynamic shapes that miti-<br> gates the barriers to its feasible computation. The process takes a two- or three-dimensional<br> shape and utilizes a combination of multifidelity meshes and Gaussian process regression<br> (GPR) surrogates in a multifidelity Monte Carlo (MFMC) algorithm. Multifidelity meshes<br> allow for finer sampling with a given budget, making the surrogates more accurate. GPR<br> surrogates are made practical to use by parameterizing major factors in geometric uncer-<br> tainty with only four variables in 2-D and five in 3-D. In both cases, two parameters control<br> the heights of steps that occur on the top and bottom of airfoils where leading and trailing<br> edge devices are attached. Two more parameters control the height and length of waves<br> that can occur in an ideally smooth shape during manufacturing. A fifth parameter controls<br> the depth of span-wise skin buckling waves along a 3-D wing. Parameters are defined to<br> be uniformly distributed with a maximum size of 0.4 mm and 0.15 mm for steps and waves<br> to remain within common manufacturing tolerances. The analysis chain is demonstrated<br> with two test cases. The first, the RAE2822 airfoil, uses transonic freestream parameters<br> set by the ADODG Benchmark Case 2. The results show a mean drag of nearly 10 counts<br> above the deterministic case with fixed lift, and a 2 count increase for a fixed angle of attack<br> version of the case. Each case also has small variations in lift and angle of attack of about<br> 0.5 counts and 0.08◦, respectively. Variances for each of the three tracked outputs show that<br> more variability is possible, and even likely. The ONERA M6 transonic wing, popular due<br> to the extensive experimental data available for computational validation, is the second test<br> case. Variation is found to be less substantial here, with a mean drag increase of 0.5 counts,<br> and a mean lift increase of 0.1 counts. Furthermore, the MFMC algorithm enables accurate<br> results with only a few hours of wall time in addition to GPR training. </p>

<p>Free surface flows, characterized by a deformable interface between two immiscible fluids or between a liquid and a gas, play a pivotal role in numerous natural phenomena and industrial processes. The fluid-fluid interface dynamics, governed by the complex interplay of forces such as inertia, capillary force, viscous force, and possibly elastic force, significantly influence the behavior of the fluids involved. Examples of free surface flows can be observed in everyday situations, such as droplet formation from a faucet, propagation and breaking of ocean waves, and tear films that coat the eye. An in-depth understanding of free surface flows and fluid-fluid interface dynamics has extensive implications for optimizing applications like inkjet printing, coating, spraying, and droplet formation while providing insights into the intricate behavior of natural fluid systems. Most of these applications, except for coating, involve abrupt and catastrophic topological changes of interfaces present in processes such as drop breakup, sheet rupture, and drop impact, where small droplets form from liquid sheets or filaments.</p> <p>This thesis examines the dynamics of contracting liquid filaments through computational means. Previous computational simulations have assumed that initially the fluid within the filament is quiescent which, however, may not typically be the case in practical applications. Here, the effect of a realistic, non-zero initial velocity profile is considered with the hypothesis that the fact that the fluid is already in motion when it starts to contract may result in significant alterations in the filament’s final fate vis-a-vis whether it breaks up into multiple small droplets or contracts into a sphere as its ends retract toward each other. The transient system of governing equations, the three-dimensional but axisymmetric (3DA) Navier-Stokes and continuity equations subjected to interfacial boundary conditions, are solved using rigorous and robust numerical algorithms in both fully 3DA and one-dimensional (1D) settings using the Galerkin finite element (GFEM) method. The simulation results are then used to construct comprehensive phase diagrams to delineate regions where filaments break up into smaller droplets from those where filaments contract to spheres without breakup.</p> <p>Polymer additives are often present in practical applications involving filament contraction and breakup. The presence of polymer molecules in an otherwise Newtonian solvent gives rise to non-Newtonian rheology. In this thesis, the dynamics of filaments containing polymer additives are analyzed using a 1D algorithm that is developed specifically for simulating viscoelastic free surface flows where the fluid’s rheology is described by the oft-used Oldroyd-B model. In real-world applications, filaments produced from nozzles are expected to be prestressed at the instant when they are created and begin to contract. It is demonstrated that the retraction velocity of tips of highly viscous, prestressed filaments is significantly increased compared to filaments in which the polymer molecules are initially relaxed and Newtonian filaments. This enhancement is explained by examining the value of f σ: D (σ: Elastic stress; D: Rate-of-strain tensor), which can be positive or negative. This quantity is positive when the flow does work on the polymer molecules but negative when the molecules do work on the flow, i.e., when elastic recoiling or unloading takes place. In prestressed filaments, elastic unloading takes place because σ: D < 0. The elastic stresses work by pulling the fluid in axially and pushing it out radially, thereby drastically increasing the tip velocity.  However, this enhancement in contraction velocity is not observed in low to intermediate viscosity prestressed filaments and whose Newtonian counterparts typically experience end-pinching. It has been established by others that end-pinching can be precluded in either filaments of intermediate viscosity or surfactant-laden filaments of low viscosity through a process known as escape from end-pinching. In this study, we demonstrate that a similar escape can also occur in prestressed viscoelastic filaments of low-to-intermediate viscosity, as revealed by one-dimensional numerical simulations and rationalized by examining when and where the elastic recoil takes place.</p> <p>Beyond cylindrical filaments, thin liquid films or planar liquid sheets are also prevalent in atomization, curtain coating, and other processes where liquid sheet stability has been a subject of extensive research. Numerous authors have examined wave formation and growth leading to sheet breakup. Free liquid films or sheets without edges or caps at their two ends, which typically have two free surfaces and are surrounded by air or sometimes another liquid, can destabilize and rupture due to intermolecular van der Waals attractive forces, despite the stabilizing influence of surface tension. In this thesis, the dynamics of contracting free films or sheets with caps---two-dimensional (2D) drops---of Newtonian fluids is examined without considering van der Waals forces to confirm or refute the hypothesis that such systems can rupture due to finite-amplitude perturbations even in the absence of intermolecular forces. In particular, both two-dimensional and one-dimensional high-accuracy simulations are employed to demonstrate that unlike inviscid 2D drops that can rupture in the absence of van der Waals forces, 2D drops or sheets can escape from pinch-off due to the action of viscous forces which are present in real systems no matter how small their viscosity. The reopening of the interface and escape from pinch-off in 2D drops and sheets are explained by demonstrating the key role played by vorticity. New power-law relations or scaling laws are obtained as a function of Ohnesorge number (ratio of viscous to the square root of the product of inertial and capillary forces) for the value of the minimum film thickness for which 2D drops or sheets stop thinning and after which the interface begins to reopen. Simple yet powerful arguments are presented rationalizing these scaling laws. It is expected that these power-law relations should be of great interest to experimentalists who study such phenomena by high-speed visualization experiments.</p> <p>Some of the motivation for this thesis research comes from crop spraying applications in which achieving zero or negligible drift is highly desirable. To further the understanding of fluid mechanics underpinning current and future drift reduction technologies, a simplified experimental setup is adopted to generate liquid sheets and analyze their disintegration into droplets. This new setup is both simpler and more universal than commonly utilized experimental systems that use single or multiple nozzles to generate liquid sheets and spray droplets from the disintegration of free liquid films. In the current experiments, droplets of test fluids are made to collide with or impact the top planar surface of a solid cylinder or rod. A series of MATLAB codes are developed and employed to extract droplet size distributions from images that are obtained from high-speed visualization experiments. The experimental setup and the means of data analysis are then used to probe the effect of fluid properties on the dynamics of sheet disintegration and droplet size distributions. It is hoped that future researchers will be able to combine what has been done in this thesis by simulations and in this chapter via experimental observations to develop an improved mechanistic understanding of spray formation.</p>

<p>  </p> <p>The study of two-phase flow in different orientations can allow for greater understanding of the fundamentals of two-phase flow dynamics. While a large amount of work has been performed for vertical flows and recent work has been done for horizontal flows, limited research has been done studying inclined upward two-phase flows between those two orientations. Studying two-phase flows at various inclinations is important for developing physical models and simulations of two-phase flow systems and understanding the changes between what is observed for symmetric vertical flows and asymmetric horizontal flows. The present work seeks to systematically characterize the effects of inclination on adiabatic concurrent air-water two-phase flows in straight pipes. An experimental database is established for local and global two-phase flow parameters in a novel inclinable 25.4 mm inner diameter test facility using four-sensor conductivity probes, high speed video capabilities, a ring-type impedance meter, a pressure transducer, and a gamma densitometer. Rotatable measurement ports are employed to allow for local conductivity probe measurements across the flow profile to capture asymmetric parameter distributions during experiments without stopping the flow. Some of the major effects of inclination are investigated, including the effects on flow regime transition, bubble distribution, frictional pressure loss, and relative motion between the two phases. Flow visualization and machine-learning methods are employed to identify the transitions between flow regimes for inclined orientations, and these transitions are compared against existing theoretical flow regime transition criteria proposed in literature. The theoretical transitions in literature agree well with both methods for vertical flow, but additional work is necessary for angles between 0 degrees and 60 degrees. The effect of inclination on two-phase frictional pressure drop is explored, and a novel adaption of the Lockhart-Martinelli pressure drop correlation is proposed, which is able to predict the pressure drop for the conditions investigated with an absolute percent difference of 2.6%. To explore the relationships between orientation, void fraction, and relative motion, one-dimensional drift flux analyses are performed for the data at each angle investigated. It is observed that the relative velocity between phases decreases as the angle is reduced, with a relative velocity near zero at some intermediate angles and a negative relative velocity for near-horizontal orientations.  Existing modeling capabilities that have been developed for vertical and horizontal flows are evaluated based on the local two-phase parameters collected at multiple orientations. The performance of the one-dimensional interfacial area transport equation for vertical and horizontal flows is tested against experimental data and a novel model for horizontal and inclined-upward bubbly flows is proposed. Finally, an evaluation of existing momentum transfer relations is performed for the two-fluid model using three-dimensional computational fluid dynamics tools for horizontal and inclined. The prediction of the void fraction distribution and gas velocity profiles are compared against experimental data, and improvements to the lift force model are identified based on changes in the relative velocity between phases. </p>

<p> Wire-wrapped rod bundles are often used in nuclear reactors operating in a fast neutron spectrum, as designers seek to minimize neutron scattering by packing the fuel pins into a hexagonal lattice. Bundles with many rods have extensively been studied as representative of large fuel assemblies, however far fewer experiments have investigated bundles with 7 rods (7-pin bundles). The large difference in subchannel number between these bundles leads to 7-pin bundles having different pressure drop characteristics. The Versatile Test Reactor (VTR) sodium cartridge loop proposes to use a 7-pin bundle as its experimental core region, highlighting the need for additional data and models. The current work seeks to establish a better understanding of the pressure drop in 7-pin wire-wrapped rod bundles through scaled experiments and a novel pressure drop model. A scaling analysis is first performed to demonstrate the applicability of water experiments to the VTR sodium cartridge loop, before an experimental test facility is designed and constructed. Experiments are then performed at a range of Reynolds numbers to determine the pressure drop. Current models are able to predict the data well, but are complex and can be difficult to use. A comparatively simpler model is developed, based on exact laminar solutions of a simplified rod bundle, which also offers a theoretical lower bound for the pressure drop in wire-wrapped bundles. The proposed model compares well with the existing experimental database, able to predict bundle friction factor with an average absolute percent difference of 10.8%. This accuracy is also similar to existing correlations, while relying on fewer empirical coefficients. The theoretical lower bound is also used to identify several datasets in literature that may feature data that is systemically lower than the true pressure drop, which agrees with previous observations in literature. </p>