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Articles 8851 - 8880 of 30042
Full-Text Articles in Mechanical Engineering
A Study Of The Design And Manufacturing Of An Elevated Dog Feeder, Lena Turner
A Study Of The Design And Manufacturing Of An Elevated Dog Feeder, Lena Turner
Honors Theses
ABSTRACT
The senior capstone which students in the Center for Manufacturing Excellence program partake in was the basis for project. The Dog Box is an elevated dog feeder with an internal food storage compartment. It was designed for medium to large dogs, and can hold over 40 lbs of dog food. The internal storage compartment has drawer access and contains a plastic tote that will hold the food. The purpose of the design was to create an aesthetically pleasing elevated dog feeder that would double as a storage device, and elevated feeding can help prevent health issues in large dog …
Urban Cargo Transport Uav Final Design Review, Niko Giannakakos, Rafael Barreto Gutierrez, Tejas Bhavsar
Urban Cargo Transport Uav Final Design Review, Niko Giannakakos, Rafael Barreto Gutierrez, Tejas Bhavsar
Senior Design Project For Engineers
Delivery of goods to homes and offices over the last decades has seen a significant increase as more people and businesses need or want items sent directly to them. With the increase in demand, technology has also experienced a rapid growth, specifically in the field of unmanned aerial vehicles (UAVs). Many major companies are currently researching UAVs as the future of their delivery operations. With this ever-growing demand, NASA has issued a design competition of a UAV developed for urban deliveries. This unmanned aircraft system (UAS) would need to be able to deliver small packages, in a timely manner, within …
Aerial Screw Vtol Rotorcraft, Macale Rielly, Alexa Culp, Thomas Osteen, Adeline Perry
Aerial Screw Vtol Rotorcraft, Macale Rielly, Alexa Culp, Thomas Osteen, Adeline Perry
Senior Design Project For Engineers
Known as the “Renaissance Man,” DaVinci’s impressive knowledge of mechanics and inventive prowess would influence engineers and innovators hundreds of years later to make human flight a reality. However, due to the limited capacity of engineering and manufacturing at the time, his invention had been shallowly investigated in a production setting. This project strove to properly acknowledge DaVinci’s invention by thorough examination and critical analysis of his concept with the hopes of gaining a better understanding of why it is considered the “foundation of vertical flight”.
An iterative design approach was employed, utilizing faculty and university resources, team knowledge from …
Faculty Instruction Face Shield Project, David Holden, John Schneiderhan
Faculty Instruction Face Shield Project, David Holden, John Schneiderhan
Michigan Tech 3D Designs
Early in the spring of 2020 project contributors David Holden and John Schneiderhan began test printing a variety of open source Personal Protective Equipment (PPE)/Covid related items that could help protect or prevent the spread of the emerging virus. With assistance from Pete Baril of the Western Upper Peninsula Health Department (WUPHD) approval was obtained for the face shields to be used in the health care and nursing homes in the area. With the support and approval from university and library administration efforts were coordinated with Dr. Joshua Pearce and the students from the MOST lab to concentrate on the …
A Numerical Investigation Of Microgravity Evaporation, Daniel Peter Ringle
A Numerical Investigation Of Microgravity Evaporation, Daniel Peter Ringle
Dissertations and Theses
Evaporation is important to myriad engineering processes such as cooling, distillation, thin film deposition, and others. In fact, NASA has renewed interest in using cabin air pressure evaporation as a means to recycle waste water in space. As one example, NASA recently conducted experiments aboard the International Space Station (ISS) to measure evaporation rates in microgravity and to determine the impacts of porous structure on the process. It has long been assumed that differences in evaporation rates between 1-g0 and microgravity are small. However, discrepancies by as much as 40% have been observed in practice. The assumption now …
Thermal Modeling Of Additive Manufacturing Using Graph Theory: Validation With Directed Energy Deposition, Jordan Severson
Thermal Modeling Of Additive Manufacturing Using Graph Theory: Validation With Directed Energy Deposition, Jordan Severson
Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research
Metal additive manufacturing (AM/3D printing) offers unparalleled advantages over conventional manufacturing, including greater design freedom and a lower lead time. However, the use of AM parts in safety-critical industries, such as aerospace and biomedical, is limited by the tendency of the process to create flaws that can lead to sudden failure during use. The root cause of flaw formation in metal AM parts, such as porosity and deformation, is linked to the temperature inside the part during the process, called the thermal history. The thermal history is a function of the process parameters and part design.
Consequently, the first step …
Simulation And Verification Of Phase Change Materials For Thermal Energy Storage, Marwan Mosubah Belaed
Simulation And Verification Of Phase Change Materials For Thermal Energy Storage, Marwan Mosubah Belaed
USF Tampa Graduate Theses and Dissertations
Greenhouse gas (GHG) emissions have a global impact on world economies and the ecosystem. Scientific assessment of GHG emissions is an issue that requires immediate action from key decision-makers and influencers. A comprehensive review of the impact of climate change and its dire consequences on daily life is illustrated in this dissertation. The most common technique to lower GHG emissions in the atmosphere is by switching GHG emission sources to zero-emission sources such as solar energy, wind energy, bioenergy, and geothermal power. Recently, all these technologies have made significant progress in lowering capital operation costs and their cycle efficiencies. This …
Laser Micropatterning Effects On Corrosion Resistance Of Pure Magnesium Surfaces, Yahya Efe Yayoglu
Laser Micropatterning Effects On Corrosion Resistance Of Pure Magnesium Surfaces, Yahya Efe Yayoglu
USF Tampa Graduate Theses and Dissertations
Magnesium and its alloys are good candidates to manufacture medical implants. They have excellent biocompatibility and because they biodegrade secondary surgical operation to remove the implant could be eliminated. However, in aqueous environments, magnesium alloys rapidly corrode, resulting in premature degradation of the implant along with biologically intolerable hydrogen gas generation. In literature, there are multiple studies focused on creating water repelling hydrophobic magnesium surfaces in order to decrease corrosion rates. Hydrophobic properties can be achieved by creation of a roughness profile on an initially smooth surface combined with a treatment that reduces the free surface energy. In theory, hydrophobic …
Investigation Of Navigation Systems For Size, Cost, And Mass Constrained Satellites, Omar Awad
Investigation Of Navigation Systems For Size, Cost, And Mass Constrained Satellites, Omar Awad
USF Tampa Graduate Theses and Dissertations
The feasibility of using radically inexpensive micro-electromechanical system (MEMS) technology for navigation of a nanosatellite is investigated with a focus on attitude estimation. Typically, larger satellites are equipped with star cameras, sun sensors, or Earth horizon sensors for attitude estimation. These sensors can provide very accurate attitude measurements. A nanosatellite is highly size, power, and cost constrained and cannot readily accommodate these sensors. Our mission is to design, build, and operate a radically inexpensive nanosatellite system. While there is no consensus on what constitutes a "radically inexpensive" satellite, our goal is a maximum cost of $10,000 per unit. This precludes …
Using The Chloride Penetration Depth Obtained From Rcpt To Assess The Permeability Of Concrete, Kang-Shiun Huang, Chung-Chia Yang
Using The Chloride Penetration Depth Obtained From Rcpt To Assess The Permeability Of Concrete, Kang-Shiun Huang, Chung-Chia Yang
Journal of Marine Science and Technology–Taiwan
A review of the literature on the rapid chloride permeability test (RCPT; ASTM C1202) indicates that RCPT has a few shortcomings, namely complex anions in concrete and Joule heating. The charge passed through concrete is affected by chloride ions because of the complex anions in concrete. Moreover, Joule heating influences the experimental temperature and causes an abnormal increase in the charge passed. Engineers have focused on the advance of the critical chloride front toward steel, but the charge passed in RCPT experiments has a poor relationship with the chloride penetration depth in fly ash concrete. Thus, it is risky to …
Evaluation Of Migration Characteristics Of Opc And Slag Concrete From The Rapid Chloride Migration Test, Rues-Wen Shiu, Chung-Chia Yang
Evaluation Of Migration Characteristics Of Opc And Slag Concrete From The Rapid Chloride Migration Test, Rues-Wen Shiu, Chung-Chia Yang
Journal of Marine Science and Technology–Taiwan
In this study, the non-steady state chloride migration coefficient in concrete was measured using the rapid chloride migration (RCM) test. After completing the test, we established the specimen’s chloride profile by collecting concrete powder samples at predetermined, controlled depths. In order to investigate whether the RCM (NT BUILD 492) can be applied to slag concrete, we made ordinary Portland cement (OPC) concrete and slag concrete with different water binder (w/b) ratios. The combined results from the concrete chloride profile and regression analysis demonstrated that the NT BUILD 492 RCM method can be successfully applied to slag concrete. In summary, a …
Fuzzy-Sliding-Mode-Based Robust Tracking Control Of Autonomous Underwater Vehicles, Qiaomei Sun, Jinguo Chen, Wan Yu, Huashan Su
Fuzzy-Sliding-Mode-Based Robust Tracking Control Of Autonomous Underwater Vehicles, Qiaomei Sun, Jinguo Chen, Wan Yu, Huashan Su
Journal of Marine Science and Technology–Taiwan
Control of an autonomous underwater vehicle (AUV) is difficult due to its nonlinear and coupled characteristics, parameter uncertainties, and unknown disturbances. This paper presents a motion control system based on an adaptive fuzzy sliding mode control (FSMC) method for trajectory tracking of an AUV. The proposed FSMC method is primarily based on a combination of sliding mode control (SMC) strategy with an adaptive fuzzy algorithm to estimate external disturbances and weaken the chattering effect. A waypoint guidance law based on a line-of-sight (LOS) algorithm is applied to the guidance system. Simulation studies confirm a good performance of the proposed controller. …
Quantifying Wicking In Functionlized Surfaces, Maureen Winter, Ryan Regan, Alfred Tsubaki, Craig Zuhlke, Dennis Alexander, George Gogos
Quantifying Wicking In Functionlized Surfaces, Maureen Winter, Ryan Regan, Alfred Tsubaki, Craig Zuhlke, Dennis Alexander, George Gogos
UCARE: Research Products
Wicking remains the enigmatic key factor in many research areas. From boiling in power plants, to anti-icing on plane wings, to medical instruments, to heat pipes, efficiency and safety depend on how quickly a surface becomes wet. Yet wicking remains difficult to quantify and define as a property of the surface. This experiment strives to measure the wicking property by examining the rate that a liquid can be pulled out of a container. A superhydrophilic surface is placed in contact with the liquid at the bottom of a tube so that the volume flow rate across the surface can be …
Manipulation And Patterning Of Mammalian Cells Using Vibrations And Acoustic Forces, Joel Cooper
Manipulation And Patterning Of Mammalian Cells Using Vibrations And Acoustic Forces, Joel Cooper
USF Tampa Graduate Theses and Dissertations
Recently, there has been a surge in researchers and scientists investigating different methods which move, manipulate, and pattern biological cells. Multiple different mechanisms can be used for cellular manipulation, microfluidics, biochemical queues, and even optics, just to name a few. However, all techniques have their downsides. A majority of these methods require expensive equipment or reagents and can only manipulate a small number of cells at a time.
Some of the most common cell manipulation devices utilize acoustic pressure waves to move the cells to desired locations. Currently, it is unknown what level of force from these types of devices …
Design Of A Carbon Fiber Composite Monocoque Chassis For A Formula-Style Vehicle, Alexander Carline
Design Of A Carbon Fiber Composite Monocoque Chassis For A Formula-Style Vehicle, Alexander Carline
Honors Theses
Western Michigan University’s Formula SAE team, Bronco Racing, designs and manufactures a formula-style vehicle to compete annually at an international collegiate design and racing competition. In order to remain competitive, Bronco Racing required a lighter chassis for the 2021 vehicle. To achieve this, the full 2020 carbon fiber monocoque chassis system was redesigned to be lightweight while considering packaging constraints, the Formula SAE rules, and design parameters set by Bronco Racing. The monocoque geometry was modeled using SolidWorks and the carbon composite was simulated, tested, and verified using ANSYS and quasi-static load frame testing. The newly designed 2021 monocoque chassis …
Design Of A Carbon Fiber Composite Monocoque Chassis For A Formula Style Vehicle, Mitchell Hiller
Design Of A Carbon Fiber Composite Monocoque Chassis For A Formula Style Vehicle, Mitchell Hiller
Honors Theses
Western Michigan University’s Formula SAE team, Bronco Racing, designs and manufactures a formula-style vehicle to compete annually at an international collegiate design and racing competition. In order to remain competitive, Bronco Racing required a lighter chassis for the 2021 vehicle. To achieve this, the full 2020 carbon fiber monocoque chassis system was redesigned to be lightweight while considering packaging constraints, the Formula SAE rules, and design parameters set by Bronco Racing. The monocoque geometry was modeled using SolidWorks and the carbon composite was simulated, tested, and verified using ANSYS and quasi-static load frame testing. The newly designed 2021 monocoque chassis …
Energy Storage Power And Energy Sizing And Specification Using Hsspfc, Mehrzad M. Bijaieh, Wayne Weaver, Rush D. Robinett Iii
Energy Storage Power And Energy Sizing And Specification Using Hsspfc, Mehrzad M. Bijaieh, Wayne Weaver, Rush D. Robinett Iii
Michigan Tech Publications, Part 1
The intermittent nature of renewable sources requires the integration of Energy Storage Systems (ESSs) with appropriate power and energy densities. One of the applications of Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) is to size ESSs for power and energy densities by employing them as sole actuators of Microgrid (MG) systems. This Article provides a comprehensive yet simplified example of utilization of HSSPFC to size ESSs of inverter-based three-phase MG systems under hierarchical control. Here, the distributed Hamiltonian controller is expanded for control of parallel ESSs and power sharing metrics are defined to distribute power between hybrid storage systems …
Nytrox As “Drop-In” Replacement For Gaseous Oxygen In Smallsat Hybrid Propulsion Systems, Stephen A. Whitmore
Nytrox As “Drop-In” Replacement For Gaseous Oxygen In Smallsat Hybrid Propulsion Systems, Stephen A. Whitmore
Mechanical and Aerospace Engineering Faculty Publications
A medical grade nitrous oxide (N2O) and gaseous oxygen (GOX) “Nytrox” blend is investigated as a volumetrically-efficient replacement for GOX in SmallSat-scale hybrid propulsion systems. Combined with 3-D printed acrylonitrile butadiene styrene (ABS), the propellants represent a significantly safer, but superior performing, alternative to environmentally-unsustainable spacecraft propellants like hydrazine. In a manner analogous to the creation of soda-water using dissolved carbon dioxide, Nytrox is created by bubbling GOX under pressure into N2O until the solution reaches saturation. Oxygen in the ullage dilutes N2O vapor and increases the required decomposition energy barrier by several orders …
Qualitative Investigation Of Gaseous Hydrodynamic Mixing Model Efficacy And Associated Sensitivity, Caleb White
Qualitative Investigation Of Gaseous Hydrodynamic Mixing Model Efficacy And Associated Sensitivity, Caleb White
Mechanical Engineering ETDs
A mixing model analyzes the mixing of helium (He) and sulfur hexafluoride (SF6) according to two classical gaseous equations of state (EOS), namely, Amagat’s Law and Dalton’s Law, undergoing planar traveling shocks in three dimensions (3D). Numerical simulations utilize the Sandia National Laboratories (SNL) shock hydrodynamic code CTH and other codes including the SNL thermochemical equilibrium code TIGER and the uncertainty qualification (UQ) and sensitivity analysis code DAKOTA. Comparison with experimental results show that none of the equations of state are able to accurately predict the properties of the shocked mixture; similar discrepancies have been observed in previous …
Predictive Models For Pulmonary Artery Size In Fontan Patients, Akash Gupta, Chris Gillett, Patrick Gerard, Michael M.H. Cheung, Jonathan P. Mynard, Ethan Kung
Predictive Models For Pulmonary Artery Size In Fontan Patients, Akash Gupta, Chris Gillett, Patrick Gerard, Michael M.H. Cheung, Jonathan P. Mynard, Ethan Kung
Publications
We developed models of pulmonary artery (PA) size in Fontan patients as a function of age and body surface area (BSA) using linear regression and breakpoint analyses based on data from 43 Fontan patients divided into two groups: the extracardiac conduit (ECC) group (n = 24) and the non-ECC group (n = 19). Model predictions were compared against those of a non-Fontan control group (n = 18) and published literature. We observed strong positive correlations of the mean PA diameter with BSA (r = 0.9, p < 0.05) and age (r = 0.88, p < 0.05) in the ECC group. The absolute percentage differences between our BSA and age model predictions against published literature were less than 16% and 20%, respectively. Predicted PA size for Fontan patients was consistently smaller than the control group. These models may serve as useful references for clinicians and be utilized to construct 3D anatomic models that correspond to patient body size or age.
Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-Asam) Applied To A Subcritical Experimental Reactor Physics Benchmark. Vi: Overall Impact Of 1st- And 2nd-Order Sensitivities On Response Uncertainties, Dan Gabriel Cacuci, Ruixian Fang, Jeffrey A. Favorite
Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-Asam) Applied To A Subcritical Experimental Reactor Physics Benchmark. Vi: Overall Impact Of 1st- And 2nd-Order Sensitivities On Response Uncertainties, Dan Gabriel Cacuci, Ruixian Fang, Jeffrey A. Favorite
Faculty Publications
: This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the 1st-order and unmixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity to the isotopic number densities for the two fissionable isotopes have large values, which are comparable to, or larger than, the corresponding sensitivities for the total cross sections. Furthermore, several 2nd-order unmixed sensitivities for the isotopic number densities are significantly larger than the corresponding 1st-order ones. This work also presents …
Loading Orientation Dependence On The Compressive Response Of Ice-Templated Ceramic-Polymer Composites, Sashanka Akurati, Justine Marin, Dipankar Ghosh
Loading Orientation Dependence On The Compressive Response Of Ice-Templated Ceramic-Polymer Composites, Sashanka Akurati, Justine Marin, Dipankar Ghosh
College of Engineering & Technology (Batten) Posters
Natural materials are made from weak constituents, yet exhibit an excellent synergy of high stiffness, strength, and damage-tolerance. They consist of alternate layers of the hard and soft phases with a complex hierarchical structural organization. The ice-templating technique provides an approach to fabricate multilayered architectures for engineering applications. In this technique, an aqueous ceramic suspension is solidified unidirectionally leading to phase separation into alternating layers of ice-crystals and ceramic particles. Ice-crystals are sublimated by freeze-drying process and resultant ceramic foams are sintered to impart strength. The fabricated sintered ceramic foams contain alternate layers of oriented ceramic lamella walls and pores. …
Team Creation Methods In Practice: Understanding The Potential Effects Of Nonverbal Communication In The Leadership Of Team Formation, Troy Allen Robertson
Team Creation Methods In Practice: Understanding The Potential Effects Of Nonverbal Communication In The Leadership Of Team Formation, Troy Allen Robertson
Dissertations
Teams require leadership, even if they are self-managed. The group of individuals who make up a team must be gathered in some form or another. For self managed teams to function successfully, the first step is the process of creating the team. Many aspects may factor into the creation process. Often time is of the essence and methods to quickly assess and form teams show merit. First impressions in general are based largely on nonverbal communication. The focus of this mixed-methods concurrent embedded study is to analyze the potential effects of nonverbal communication on influencing team creation. A group of …
The Application Of Evolutionary Algorithms In Multi-Objective Design And Optimization Of Air Cooled Heatsinks, Younis Osama Abdelsalam, Sajad Alimohammadi, Tim Persoons
The Application Of Evolutionary Algorithms In Multi-Objective Design And Optimization Of Air Cooled Heatsinks, Younis Osama Abdelsalam, Sajad Alimohammadi, Tim Persoons
Articles
Genetic algorithms (GAs) are considered to be one of the main types of evolutionary algorithms (EAs) and are being increasingly used in various engineering design applications. To a large extent, plate-fin heatsinks are used in the thermal management of compact electronic equipment and data centers. The shape optimization of the heatsinks is not rigorously investigated during the design process of high power electronics. Any improvements in the effectiveness of the heatsinks impact the energy consumed by large-scale information communication technology (ICT) facilities including data centers and telecommunication systems and promote a more sustainable use of raw materials. This paper investigates …
Computational Approach To Correcting Joint Instability In Patients With Recurrent Patellar Dislocation, Oliver Alvarez, Robert N. Steensen, Paul J. Rullkoetter, Clare K. Fitzpatrick
Computational Approach To Correcting Joint Instability In Patients With Recurrent Patellar Dislocation, Oliver Alvarez, Robert N. Steensen, Paul J. Rullkoetter, Clare K. Fitzpatrick
Mechanical and Biomedical Engineering Faculty Publications and Presentations
Patellar dislocation is a debilitating injury common in active adolescents and young adults. Conservative treatment after initial dislocation is often recommended, but almost half of these patients continue to suffer from recurrent dislocation. The objective of this study was to compare preoperative patellofemoral joint stability with stability after a series of simulated procedures, including restorative surgery to correct to pre-injury state, generic tibial tubercle osteotomy, patient-specific reconstructive surgery to correct anatomic abnormality, less invasive patient-specific surgery, and equivalent healthy controls. Three-dimensional, subject-specific finite element models of the patellofemoral joint were developed for 28 patients with recurrent patellar dislocation. A …
Advanced Mechatronics, Hao Su
Advanced Mechatronics, Hao Su
Open Educational Resources
Project-based course on the design of mechatronic devices to address needs identified by hospital-based clinicians and industry. Students work in teams to develop a mechatronic prototype. The lectures will cover the design of medical devices and robotics including sensors, actuators, and robots. The students will communicate with customers to understand design needs, then conduct study on prior art, intellectual property, due diligence, and idea conceptualization. Students will present ideas in class and to a broad audience from local industry. Students will also write a publication-quality final report, which they will be encouraged for publication submission.
Engineering Design I, Hao Su
Pool Boiling Inversion On Femtosecond Laser Surface Processed 304 Stainless Steel And Its Impact On Steady-State Time Constants, Justin Costa-Greger, Alfred Tsubaki, Josh Gerdes, Mark Anderson, Craig Zuhlke, Dennis Alexander, Jeff Shield, George Gogos
Pool Boiling Inversion On Femtosecond Laser Surface Processed 304 Stainless Steel And Its Impact On Steady-State Time Constants, Justin Costa-Greger, Alfred Tsubaki, Josh Gerdes, Mark Anderson, Craig Zuhlke, Dennis Alexander, Jeff Shield, George Gogos
UCARE: Research Products
FLSP surfaces resulting in boiling inversion require longer times to reach steady-state once inversion has occurred Boiling inversion has been shown to be the result of changing nucleation dynamics in which a large number of nucleation sites activate Increased time required to reach steady-state is linked to the rate at which these nucleation sites activate. Heat fluxes above the boiling inversion point can require up to an additional 3 hours to reach steady-state, compared to the typical 15-20 minutes reported in the literature
Fluid Power Vehicle Challenge, Jacob Torrey, Kayla Londono, Bryson Chan, Aaron Trujillo
Fluid Power Vehicle Challenge, Jacob Torrey, Kayla Londono, Bryson Chan, Aaron Trujillo
Mechanical Engineering
The FPVC combines mechanical engineering disciplines to design and manufacture a vehicle that utilizes hydraulic power. The FDR covers the final manufacturing process and verification processes developed during the front end of research and analysis built upon the Critical Design Review (CDR) and the PDR (Preliminary Design Review). This report showcases the design decisions and extensive research that supports the continuing efforts by the Team Pump My Ride, to build upon the accomplishments of Cal Poly’s previous team, The Incompressibles. The FDR presents how Team Pump My Ride produced the design changes from the CDR and PDR to achieve improvements …
Critical Point Identification In 3d Velocity Fields, Mohammadreza Zharfa
Critical Point Identification In 3d Velocity Fields, Mohammadreza Zharfa
Mechanical Engineering Research Theses and Dissertations
Classification of flow fields involving strong vortices such as those from bluff body wakes and animal locomotion can provide important insight to their hydrodynamic behavior. Previous work has successfully classified 2D flow fields based on critical points of the velocity field and the structure of an associated weighted graph using the critical points as vertices. The present work focuses on extension of this approach to 3D flows. To this end, we have used the Gauss-Bonnet theorem to find critical points and their indices in the 3D velocity vector field, which functions similarly to the Poincare-Bendixon theorem in 2D flow fields. …