<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>

Indiana University-Purdue University Indianapolis (IUPUI) / In this thesis, we present novel computational methods and frameworks to address the challenges associated with the determination of free energy profiles for condensed-phase chemical reactions using combined quantum mechanical and molecular mechanical (QM/MM) approaches. We focus on overcoming issues related to force matching, molecular polarizability, and convergence of free energy profiles. First, we introduce a method called Reaction Path-Force Matching in Collective Variables (RP-FM-CV) that efficiently carries out ab initio QM/MM free energy simulations through mean force fitting. This method provides accurate and robust simulations of solution-phase chemical reactions by significantly reducing deviations on the collective variables forces, thereby bringing simulated free energy profiles closer to experimental and benchmark AI/MM results. Second, we explore the role of pairwise repulsive correcting potentials in generating converged free energy profiles for chemical reactions using QM/MM simulations. We develop a free energy correcting model that sheds light on the behavior of repulsive pairwise potentials with large force deviations in collective variables. Our findings contribute to a deeper understanding of force matching models, paving the way for more accurate predictions of free energy profiles in chemical reactions. Next, we address the underpolarization problem in semiempirical (SE) molecular orbital methods by introducing a hybrid framework called doubly polarized QM/MM (dp-QM/MM). This framework improves the response property of SE/MM methods through high-level molecular polarizability fitting using machine learning (ML)-derived corrective polarizabilities, referred to as chaperone polarizabilities. We demonstrate the effectiveness of the dp-QM/MM method in simulating the Menshutkin reaction in water, showing that ML chaperones significantly reduce the error in solute molecular polarizability, bringing simulated free energy profiles closer to experimental results. In summary, this thesis presents a series of novel methods and frameworks that improve the accuracy and reliability of free energy profile estimations in condensed-phase chemical reactions using QM/MM simulations. By addressing the challenges of force matching, molecular polarizability, and convergence, these advancements have the potential to impact various fields, including computational chemistry, materials science, and drug design.

<p>Fibre suspensions in the fluid medium are common in industry, biology, and the environment. Industrial examples of concentrated suspensions include fresh concrete, uncured solid rocket fuel, and biomass slurries; natural examples include silt transfer in rivers and red blood cells in the blood.  These suspensions often include a Newtonian fluid as their suspending medium; still, these suspensions exhibit a plethora of non-Newtonian properties, such as yield stresses, rate-dependent rheology, and normal stresses, to name a few. Other than volume fraction, the type of fiber material, the presence of fluid-fiber or fiber-fiber interactions such as hydrodynamic, Brownian, colloidal, frictional, chemical, and/or electrostatic determine the rheological behavior of suspension. The average inter-fiber gaps between the neighboring fibers decrease significantly as the suspension volume fraction move towards a concentrated regime. As a result, in this regime, inter-fiber interactions become dominant.  Moreover, the surface asperities are present on the fiber surface even in the case of so-called smooth fibers, as fibers in real suspensions are not perfectly smooth. Hence, contact forces arising from the direct touching of the fibers become one of the essential factors in determining the rheology of suspensions.</p> <p>We first describe the causes of yield stress, shear thinning, and normal stress differences in fibre suspensions. We model the fibers as inextensible continuous flexible slender bodies with the Euler-Bernoulli beam equation governing their dynamics suspended in an incompressible Newtonian fluid. The fiber dynamics and fluid flow coupling is achieved using the immersed boundary method (IBM). In addition, the fiber surface roughness lead to inter-fiber contacts resulting in normal and tangential forces between the fibers, which follow Coulomb’s law of<br> friction. The surface roughness is modeled as hemispherical protrusions on the fiber surfaces. In addition to the comparison of the computational model to the experimental results, we demonstrate that attractive interactions lead to yield stress and shear thinning rheology.</p> <p>Furthermore, we investigate the effects of fiber aspect ratio, roughness, flexibility, and volume fraction on the rheology of concentrated suspensions. We find that the suspension viscosity increases with increasing the volume fraction, roughness, fiber rigidity, and aspect ratio. The increase in relative viscosity is the macroscopic manifestation of a similar increase  in the microscopic contact contribution with these parameters. In addition, we observe positive and negative first and second normal stress differences, respectively, in agreement with previous experiments. Lastly, we propose a modified Maron-Pierce law to quantify the the jamming volume fraction with varying fiber aspect ratio and roughness. Additionally, we provide a constitutive model to calculate the viscosity at various volume fractions, aspect ratios, and shear rates.</p>

<p>  </p> <p>Water scarcity is a global problem impacting a majority of the world population. A significant proportion of the global population is deprived of clean drinking water, an impact felt by the rural as well as urban population. Saltwater desalination provides an attractive option to produce clean water. Some technologies to generate potable water include reverse osmosis (RO), multi-stage flash distillation (MSF), vapor compression distillation and multi-effect distillation (MED). Distillation plants such as those in MED often have falling-film evaporators operating at low energy conversion efficiency and hence distillation is performed over multiple stages (or effects). Porous materials can be utilized as evaporators in such plants with the objective of leveraging their superior efficiency. This can potentially decrease the number of effects over which distillation occurs. However, evaporation of high-salinity salt solution eventually results in salt precipitation which can cause fouling and induce structural damages, especially if the precipitates appear within the porous medium. Crystallization-induced structural damages are also of significant concern to building materials and for their role in weathering of historical monuments. It is thus crucial to understand the mechanisms governing salt precipitation in a porous medium.</p> <p>Transport of solute in such a medium is either driven by flow of the solution (advection) or by concentration gradients (diffusion). The dynamics of solute transport is further complicated due to the involvement of a reaction term accounting for any salt precipitation. The relative strengths of these driving forces determine the solute transport behavior during an evaporation-driven process. The wide-scale applications of solute transport and its complicated nature warrant investigation, both experimental and theoretical, of the dependence of solute transport and the subsequent precipitation on the operating conditions and the properties of the porous medium.</p> <p>This dissertation first focuses on developing a novel modeling framework for evaluating the transient behavior of the solute mass fraction profile within the domain of a one-dimensional porous medium, and extending its capability to predict the formation of salt precipitate in the medium.  Experimental investigations are then performed to study the formation of precipitate on sintered porous copper wicks of different particle-size compositions, and developing a mechanistic understanding of the governing principles.</p> <p>A numerical modeling framework is developed to analyze evaporation-driven solute transport. Transient advection-diffusion equations govern the salt mass fraction profile of the solution inside the porous medium. These governing equations are solved to obtain the solute mass fraction profile within the porous medium as well as the effloresced salt crust. Further accounting for precipitation allows a study of the formation and growth of efflorescence and subflorescence. Crystallization experiments are performed by allowing a NaCl solution to evaporate from a porous medium of copper particles and the subflorescence trends predicted by the model are validated. The modeling framework offers a comprehensive tool for predicting the spatio-temporal solute mass fraction profiles and subsequent precipitation in a porous medium.</p> <p>The dependence of efflorescence pattern on the properties of a porous medium is also investigated. Efflorescence patterns are visually observed and characterized on sintered copper particle wicks with spatially unimodal and bimodal compositions of different particle sizes. Efflorescence is found to form earlier and spread readily over a wick made from smaller particles, owing to their lower porosity, while it is limited to certain areas of the surface for wicks composed of the larger particles. A scaling analysis explains the observed efflorescence patterns in the bimodal wicks caused by particle size-induced non-uniform porosity and permeability. The non-uniformity reduces the advective flux in a high-permeability region by diverting flow towards a low-permeability region. This reduction in advective flux manifests as an exclusion distance surrounding a crystallization site where efflorescence is not expected to occur. The dependence of this exclusion distance on the porosity and permeability of the porous medium and the operating conditions is investigated. A large exclusion distance associated with the regions with bigger particles in the bimodal wicks explains preferential efflorescence over the regions with smaller particles. This novel scaling analysis coupled with the introduction of the exclusion distance provides guidelines for designing heterogeneous porous media that can localize efflorescence.</p> <p>Additionally, droplet interactions with microstructured superhydrophobic surfaces as well as soft surfaces were investigated during the course of this dissertation, separate from the above investigations. These investigations involve the interplay of surface energies with electrical or elastic energies and are studied both experimentally and through theoretical models, and therefore are retained as additional chapters in the thesis as being of relevant interest.  Electrowetting experiments are performed on superhydrophobic surfaces with re-entrant structures to study their resilience to the Cassie-to-Wenzel transition. The deformation of soft surfaces caused by forces exerted by microscale droplets is studied and the resulting interaction between multiple droplets is explored. </p>

<p dir="ltr">Positive displacement machines are used in various industries spanning the power spectrum, from industrial robotics to heavy construction equipment to aviation. These machines should be highly efficient, compact, and reliable. It is very advantageous for designers to use virtual simulations to design and improve the performance of these units as they significantly reduce cost and downtime. The recent trends of electrification and the goal to increase power density force these units to work at higher pressures and higher rotational speeds while maintaining their efficiencies and reliability. This push means that the simulation models need to advance to account for various aspects during the operation of these machines. </p><p dir="ltr">These machines typically have several bodies in relative motion with each other. Quantifying these motions and solving for their effect on the fluid enclosed are vital as they influence the machine's performance. The push towards higher rotational speeds introduces unwanted cavitation and aeration in these units. To model these effects, keeping the design evaluation time low is key for a designer. The lumped parameter approach offers the benefit of computational speed, but a major drawback that comes along with it is that it typically assumes fluid inertia to be negligible. These effects cannot be ignored, as quantifying and making design considerations to negate these effects can be beneficial. Therefore, this thesis addresses these key challenges of cavitation dynamics, body dynamics, and accounting for fluid inertia effects using a lumped parameter formulation.</p><p dir="ltr">To account for dynamics features related to cavitation, this thesis proposes a novel approach combining the two types of cavitation, i.e., gaseous and vaporous, by considering that both vapor and undissolved gas co-occupy a spherical bubble. The size of the spherical bubble is solved using the Rayleigh-Plesset equation, and the transfer of gas through the bubble interface is solved using Henry's Law and diffusion of the dissolved gas in the liquid. These equations are coupled with a novel pressure derivative equation. To account for body dynamics, this thesis introduces a novel approach for solving the positions of the bodies of a hydraulic machine while introducing new methods to solve contact dynamics and the application of Elasto Hydrodynamic Lubrication (EHL) friction at those contact locations. This thesis also proposes strategies to account for fluid inertia effects in a lumped parameter-based approach, taking as a reference an External Gear Machine. This thesis proposes a method to study the effects of fluid inertia on the pressurization and depressurization of the tooth space volumes of these units. The approach is based on considering the fluid inertia in the pressurization grooves and inside the control volumes with a peculiar sub-division. Further, frequency-dependent friction is also modeled to provide realistic damping of the fluid inside these channels.</p><p dir="ltr">To show the validity of the proposed dynamic cavitation model, the instantaneous pressure of a closed fluid volume undergoing expansion/compression is compared with multiple experimental sources, showing an improvement in accuracy compared to existing models. This modeling is then further applied to a gerotor machine and validated with experiments. Integrating this modeling technique with current displacement chamber simulation can further improve the understanding of cavitation in hydraulic systems. Formulations for body dynamics are tested on a prototype Gerotor and Vane unit. For both gerotor and vane units, comparisons of simulation results to experimental results for various dynamic quantities, such as pressure ripple, volumetric, and hydromechanical efficiency for multiple operating conditions, have been done. Extensive validation is performed for the case of gerotors where shaft torque ripple and the motion of the outer gear is experimentally validated. The thesis also comments on the distribution of the different torque loss contributions. The model for fluid inertia effects has been validated by comparing the lumped parameter model with a full three-dimensional Navier Stokes solver. The quantities compared, such as tooth space volume pressures and outlet volumetric flow rate, show a good match between the two approaches for varying operating speeds. A comparison with the experiments supports the modeling approach as well. The thesis also discusses which operating conditions and geometries play a significant role that governs the necessity to model such fluid inertia effects in the first place.</p>

The work of this thesis was focused on the development of high-performance algorithms for a new generation of molecular descriptors, with many advantages with respect to its predecessors, suitable for diverse applications in the field of drug design, as well as its implementation in commercial grade scientific software (Pentacle). As a first step, we developed a new algorithm (AMANDA) for discretizing molecular interaction fields which allows extracting from them the most interesting regions in an efficient way. This algorithm was incorporated into a new generation of alignmentindependent molecular descriptors, named GRIND-2. The computing speed and efficiency of the new algorithm allow the application of these descriptors in virtual screening. In addition, we developed a new alignment-independent encoding algorithm (CLACC) producing quantitative structure-activity relationship models which have better predictive ability and are easier to interpret than those obtained with other methods. / El trabajo que se presenta en esta tesis se ha centrado en el desarrollo de algoritmos de altas prestaciones para la obtención de una nueva generación de descriptores moleculares, con numerosas ventajas con respecto a sus predecesores, adecuados para diversas aplicaciones en el área del diseño de fármacos, y en su implementación en un programa científico de calidad comercial (Pentacle). Inicialmente se desarrolló un nuevo algoritmo de discretización de campos de interacción molecular (AMANDA) que permite extraer eficientemente las regiones de máximo interés. Este algoritmo fue incorporado en una nueva generación de descriptores moleculares independientes del alineamiento, denominados GRIND-2. La rapidez y eficiencia del nuevo algoritmo permitieron aplicar estos descriptores en cribados virtuales. Por último, se puso a punto un nuevo algoritmo de codificación independiente de alineamiento (CLACC) que permite obtener modelos cuantitativos de relación estructura-actividad con mejor capacidad predictiva y mucho más fáciles de interpretar que los obtenidos con otros métodos.