On Weak Solutions And The Navier-Stokes Equations, 2024 University of Arkansas, Fayetteville

#### On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

*Mathematical Sciences Undergraduate Honors Theses*

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

Thermal Hydraulic Analysis For Different Subchannels Of Generic Vver-1200, 2024 Military Institute of Science and Technology, Bangladesh

#### Thermal Hydraulic Analysis For Different Subchannels Of Generic Vver-1200, Mosaddak Ahamed Zahid, Md. Imam Mehedi, Shamsul Arefin Shibly, A. S. Mollah

*International Journal of Nuclear Security*

The demand for nuclear energy is steadily increasing all over the world. Most nuclear power is used for peaceful applications such as power generation, healthcare, agriculture, food security, industry, and research. One of the primary applications of nuclear energy is the generation of electricity through nuclear power plants based on nuclear reactors. Many developing countries around the world (such as Bangladesh) are moving toward nuclear power plants because they have huge advantages, including low-cost energy, reliable energy sources, zero carbon emissions, and high energy concentration. As a result, the demand for nuclear reactor protection and operational protection of nuclear power …

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, 2024 The Graduate Center, City University of New York

#### Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

*Dissertations, Theses, and Capstone Projects*

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Aspects Of Parity Breaking In Classical And Quantum Fluids, 2024 The Graduate Center, City University of New York

#### Aspects Of Parity Breaking In Classical And Quantum Fluids, Dylan J. Reynolds

*Dissertations, Theses, and Capstone Projects*

Parity-breaking is ubiquitous across many scales of physics, from the rotation of galaxies at the largest of scales, to the cyclotron orbits of electrons at the microscopic scale. In describing the collective dynamics of many particle systems, parity breaking effects typically originate from some form of chirality, such as angular momentum, at the level of the constituent particles. External forces can also induce chiral motion, with the primary examples being the Lorentz and Coriolis forces.

The effects of parity breaking are perhaps most strikingly seen in active matter, systems of complex particles that tend to convert energy into some directed …

On The Ubiquity, Properties And Evolution Of Small-Scale Magnetic Flux Ropes In The Heliosphere, 2024 New Jersey Institute of Technology

#### On The Ubiquity, Properties And Evolution Of Small-Scale Magnetic Flux Ropes In The Heliosphere, Hameedullah Farooki

*Dissertations*

The solar wind is a plasma constantly blowing out from the Sun with a large-scale magnetic field having significant local complexity at small scales. Small-scale magnetic flux ropes (SMFRs), plasma structures with twisted field lines, are an important element of this complexity. This dissertation contributes several studies that further our understanding of SMFRs. The first study applies machine learning to measurements from Wind labeled by the presence of SMFRs and magnetic clouds (MCs). MCs were distinguished from non-MFRs with an AUC of 94% and SMFRs with an AUC of 89% and had distinctive plasma properties, whereas SMFRs appeared to be …

Effects Of Ti Addition On The Characteristics Of Al-10zn-6mg-2si/Zro2 Composites Produced By Squeeze Casting, 2024 Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, 16424, Indonesia

#### Effects Of Ti Addition On The Characteristics Of Al-10zn-6mg-2si/Zro2 Composites Produced By Squeeze Casting, Qesha Diva Prameshvara, Pipin Indah Lestari, Bondan Tiara Sofyan

*Journal of Materials Exploration and Findings*

Metal matrix composite (MMC) with 7xxx aluminum matrix is potential for ballistic applications due to the combination of strength, toughness, and light weight. Previous study successfully produced aluminum-based composites with SiC particles which were able to stop type III bullet, however cracks remained on back of the plate. Therefore, in this research, SiC was replaced by zirconia (ZrO_{2}) due to its high fracture toughness. Ti-B grain refiner was added to further improve toughness through grain boundary strengthening mechanism. This research developed 5 vol.% ZrO_{2} strengthened Al-10Zn-6Mg-2Si composite with addition of Al-5Ti-1B grain refiner produced through squeeze casting …

Analysis Of The Effect Of Different Surface Preparation Methods On Corrosion Resistance And Adhesion Strength Of Astm A36 Steel Substrate With Surface Tolerant Epoxy Paint As Coating Material, 2024 Department of Metallurgical and Materials Engineering, Faculty of Engineering, Universitas Indonesia, Depok, 16424, Indonesia

#### Analysis Of The Effect Of Different Surface Preparation Methods On Corrosion Resistance And Adhesion Strength Of Astm A36 Steel Substrate With Surface Tolerant Epoxy Paint As Coating Material, Irwan Wijaya Santoso, Daffa Aqila, Rini Riastuti, Rizal Tresna Ramadhani

*Journal of Materials Exploration and Findings*

In the industrial world, to extend the service life of materials, protection methods are carried out to slow down the material's corrosion rate. The protection method that is often used is the coating method. The coating method is a protection method by coating the substrate material using a coating material to prevent contact between the substrate material and the environment. In this research, the substrate material used is ASTM A36 steel and the coating material used is Surface Tolerant Epoxy paint. The independent variable used in this study lies in the surface preparation method which consists of: solvent cleaning, hand …

Simulating Cross-Scale Solid-Fluid Interaction Phenomena, 2024 Dartmouth College

#### Simulating Cross-Scale Solid-Fluid Interaction Phenomena, Jinyuan Liu

*Dartmouth College Ph.D Dissertations*

Solid-fluid interactions are ubiquitous in nature, and accurate simulation methods are essential for realistic animation, industrial design, and engineering analysis. Com- pared to large-scale coupling phenomena, simulating fine-scale interactions poses extra challenges due to factors such as surface tension, material wettability, and geometric complexity. In this thesis, we pursue novel methodologies to accurately model in- terfacial dynamics between surface-tension fluids and codimensional solids, involving capillary interactions, controllable wettability, and robust contact behaviors. Our ini- tial approach involves developing a novel three-way coupling method, which utilizes a thin liquid membrane, modelled as a simplicial mesh, to facilitate accurate momen- tum transfer, …

Blade Design And Validation Of Hydrokinetic Turbine To Harvest Water Current Energy, 2024 University of New Orleans

#### Blade Design And Validation Of Hydrokinetic Turbine To Harvest Water Current Energy, Setare Sadeqi

*University of New Orleans Theses and Dissertations*

The innovative aspect of this research lies in the careful integration of cutting-edge technologies throughout the entire process of designing, fabricating, and testing the carbon fiber propeller for the 3-bladed horizontal axis ocean current turbine (OCT). SolidWorks software played a pivotal role in the initial design phase, enabling a meticulous and precise modeling of the propeller's geometry. The utilization of SolidWorks allowed for a detailed exploration of various design parameters, ensuring that the propeller's structure and form were optimized for performance in ocean current conditions. Moving beyond the realm of virtual design, the choice of carbon fiber as the fabrication …

Towing Tank Trials Of Hydrokinetic Turbine Scale Model To Support Marine Energy System Verification, 2024 University of New Orleans

#### Towing Tank Trials Of Hydrokinetic Turbine Scale Model To Support Marine Energy System Verification, Shahab Rouhi

*University of New Orleans Theses and Dissertations*

In response to the escalating demand for sustainable energy solutions and the critical reevaluation of conventional fossil fuels due to environmental concerns, this dissertation embarks on a comprehensive exploration of hydrokinetic energy as a promising alternative. The study delves into the underexplored domain of hydrokinetic energy, leveraging innovative methodologies for effective utilization and harnessing, particularly through the development and investigation of hydrokinetic turbines.

In the realm of hydrokinetic energy conversion, our research has exclusively concentrated on horizontal-axis turbines, distinct from other turbine configurations. Noteworthy is the adaptation of a conventional horizontal-axis wind turbine for water currents, revealing enhanced performance through …

Oscillations Of Capillary Surfaces With Volume And Edge Effects, 2024 Clemson University

#### Oscillations Of Capillary Surfaces With Volume And Edge Effects, Dingqian Ding

*All Dissertations*

Capillary surfaces are defined by an interface endowed with surface tension that is partially supported by a solid substrate and are susceptible to oscillations reflecting a balance between fluid inertia and the restorative force of surface tension. The wave dynamics strongly depend upon volume change within the domain and edge effects through the boundary conditions applied at the contact-line formed at the liquid-gas-solid interface, while the spatial wave structure conforms to the geometry of the capillary surface. This dissertation develops mathematical models to address these effects for several canonical capillary surfaces, which are organized into two parts that are focused …

Dispersion Of Artificial Tracers In Ventilated Caves, 2024 Swiss Institute for Speleology and Karst Studies (SISKA), La Chaux-de-Fonds, Switzerland

#### Dispersion Of Artificial Tracers In Ventilated Caves, Claudio Pastore, Eric Weber, Frédéric Doumenc, Pierre-Yves Jeannin, Marc Lütscher

*International Journal of Speleology*

Artificial CO_{2} was used as a tracer along ventilated karst conduits to infer airflow and investigate tracer dispersion. In the karst vadose zone, cave ventilation is an efficient mode of transport for heat, gases and aerosols and thus drives the spatial distribution of airborne particles. Modelling this airborne transport requires geometrical and physical parameters of the conduit system, including the cross-sectional areas, the airflow and average air speed, as well as the longitudinal dispersion coefficient which describes the spreading of a solute. Four gauging tests were carried out in one mine (artificial conduit) and two ventilated caves (natural conduits). …

Development Of On-The-Fly Quasi-Steady State Approximation For Chemical Kinetics In Cfd, 2024 Embry-Riddle Aeronautical University

#### Development Of On-The-Fly Quasi-Steady State Approximation For Chemical Kinetics In Cfd, Abhinav Balamurugan

*Doctoral Dissertations and Master's Theses*

This study analyzes the feasibility of On-The-Fly Quasi-Steady-State Approximation (OTF-QSSA) application for solving chemical kinetics within Computational Fluid Dynamics (CFD) simulations, aiming to reduce the computational demand of detailed mechanisms. An algorithm that dynamically identifies and designates Quasi-Steady-State (QSS) species at specific grid locations and instances during the simulation was developed. With this information, our method pseudo-delays the advancement of concentrations for these QSS species—effectively setting their rate of concentration change to zero for a set number iteration before updating using the detailed mechanism and thereby omitting the computationally intensive processes typically required for their calculation during those skipped iteration. …

Investigation Of Gas Dynamics In Water And Oil-Based Muds Using Das, Dts, And Dss Measurements, 2024 Louisiana State University at Baton Rouge

#### Investigation Of Gas Dynamics In Water And Oil-Based Muds Using Das, Dts, And Dss Measurements, Temitayo S. Adeyemi

*LSU Master's Theses*

Reliable prediction of gas migration velocity, void fraction, and length of gas-affected region in water and oil-based muds is essential for effective planning, control, and optimization of drilling operations. However, there is a gap in our understanding of gas behavior and dynamics in water and oil-based muds. This is a consequence of the use of experimental systems that are not representative of field-scale conditions. This study seeks to bridge the gap via the well-scale deployment of distributed fiber-optic sensors for real-time monitoring of gas behavior and dynamics in water and oil-based mud. The aforementioned parameters were estimated in real-time using …

Modeling Thermosyphon And Heat Pipe Performance For Mold Cooling Applications, 2024 Western University

#### Modeling Thermosyphon And Heat Pipe Performance For Mold Cooling Applications, Dwaipayan Sarkar

*Electronic Thesis and Dissertation Repository*

Thermosyphons are enhanced heat transfer devices that can continuously transfer very large amounts of heat rapidly over long distances with small temperature differences. The high heat transfer rate is achieved through simultaneous boiling and condensation of the working fluid and the continuous heat transfer is achieved through recirculation of the working fluid in its liquid and vapor phase. A potentially important application of the thermosyphons has been towards reducing the cycle times of the mold cooling processes which would provide economic incentives to the automotive industry.

Different operational and geometrical parameters such as the input heating power, fill ratio (FR), …

Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, 2024 University of Tennessee, Knoxville

#### Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw

*Faculty Publications and Other Works -- Mathematics*

In this second progress report we expand upon our previous report and preliminary work. Specifically, we review some work on the numerical solution of single- and multi-species BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for each species for accurate simulation. …

Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, 2024 Michigan Technological University

#### Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert

*Dissertations, Master's Theses and Master's Reports*

In the first chapter of this dissertation, we give some background on the Navier-Stokes equations and turbulence modeling. The next two chapters in this dissertation focus on two important numerical difficulties arising in fluid flow modeling: poor mass-conservation and nonphysical oscillations. We investigate two different formulations of the Crank-Nicolson method for the Navier-Stokes equations. The most attractive implementation, second order accurate for both velocity and pressure, is shown to introduce non-physical oscillations. We then propose two options which are shown to avoid the poor behavior. Next, we show that grad-div stabilization, previously assumed to have no effect on the target …

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, 2024 North Carolina State University

#### Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

*Mathematics & Statistics Faculty Publications*

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Numerical Study Of Owls' Leading-Edge Serrations, 2023 Coastal Carolina University

#### Numerical Study Of Owls' Leading-Edge Serrations, Asif Shahriar Nafi, Nikolaos Beratlis, Elias Balaras, Roi Gurka

*Physics and Engineering Science*

Owls' silent flight is commonly attributed to their special wing morphology combined with wingbeat kinematics. One of these special morphological features is known as the leading-edge serrations: rigid miniature hook-like patterns found at the primaries of the wings' leading-edge. It has been hypothesized that leading-edge serrations function as a passive flow control mechanism, impacting the aerodynamic performance. To elucidate the flow physics associated with owls' leading-edge serrations, we investigate the flow-field characteristic around a barn owl wing with serrated leading-edge geometry positioned at 20° angle of attack for a Reynolds number of 40 000. We use direct numerical simulations, where …

Combined Risk Based Inspection And Fault Tree Analysis For Repetitive 3-Phase Line Piping Leakage At West Java Offshore Topside Facility, 2023 Universitas Indonesia

#### Combined Risk Based Inspection And Fault Tree Analysis For Repetitive 3-Phase Line Piping Leakage At West Java Offshore Topside Facility, Dona Yuliati, Akhmad Herman Yuwono, Datu Rizal Asral, Donanta Dhaneswara

*Journal of Materials Exploration and Findings*

Hydrocarbon releases might result in serious consequences in various aspects. In addition to the contribution to environmental pollution, repetitive leakages need high repair costs. This study aim is to minimize potential repetitive leakage for other typical 3-phase piping systems. We conducted the risk assessment by adopting Risk Based Inspection (RBI) API 581 to identify risk level, calculating piping lifetime, recommended inspection plan and mitigations. The most relevant root causes can be obtained through quantitative Fault Tree Analysis (FTA). Observation and investigation was taken from eight 3-phase piping systems that experienced repetitive leakages. It has been found that the risk level …