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Category# Fluid mechanics

Summary

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.
It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach. , an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow.
History of fluid mechanics
The study of fluid mechanics goes back at least to the days of ancient Greece, when Archimedes investigated fluid statics and buoyancy and formulated his famous law known now as the Archimedes' principle, which was published in his work On Floating Bodies—generally considered to be the first major work on fluid mechanics. Iranian scholar Abu Rayhan Biruni and later Al-Khazini applied experimental scientific methods to fluid mechanics. Rapid advancement in fluid mechanics began with Leonardo da Vinci (observations and experiments), Evangelista Torricelli (invented the barometer), Isaac Newton (investigated viscosity) and Blaise Pascal (researched hydrostatics, formulated Pascal's law), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in Hydrodynamica (1739).

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ME-280: Fluid mechanics (for GM)

Basic lecture in fluid mechanics

ME-341: Heat and mass transfer

This course covers fundamentals of heat transfer and applications to practical problems. Emphasis will be on developing a physical and analytical understanding of conductive, convective, and radiative

ME-474: Numerical flow simulation

This course provides practical experience in the numerical simulation of fluid flows. Numerical methods are presented in the framework of the finite volume method. A simple solver is developed with Ma

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Applications

Learn about plasma applications from nuclear fusion powering the sun, to making integrated circuits, to generating electricity.

Burgers' equation

Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. For a given field and diffusion coefficient (or kinematic viscosity, as in the original fluid mechanical context) , the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system: When the diffusion term is absent (i.

Particle image velocimetry

Particle image velocimetry (PIV) is an optical method of flow visualization used in education and research. It is used to obtain instantaneous velocity measurements and related properties in fluids. The fluid is seeded with tracer particles which, for sufficiently small particles, are assumed to faithfully follow the flow dynamics (the degree to which the particles faithfully follow the flow is represented by the Stokes number). The fluid with entrained particles is illuminated so that particles are visible.

Laser Doppler velocimetry

Laser Doppler velocimetry, also known as laser Doppler anemometry, is the technique of using the Doppler shift in a laser beam to measure the velocity in transparent or semi-transparent fluid flows or the linear or vibratory motion of opaque, reflecting surfaces. The measurement with laser Doppler anemometry is absolute and linear with velocity and requires no pre-calibration. The development of the helium–neon laser (He-Ne) in 1962 at the Bell Telephone Laboratories provided the optics community with a continuous wave electromagnetic radiation source that was highly concentrated at a wavelength of 632.

AEDS

Active in engineering, consulting and numerical simulations. AEDS is a consulting firm specializing in scientific engineering services related to numerical simulations, with a focus on fluid dynamics, acoustics, and heat transfer.

Online Control

Active in control engineering, optimization and automation. Online Control specializes in innovative control engineering solutions for optimizing and automating processes in various industries.

CFS Engineering

Active in numerical simulation, fluid mechanics and structural mechanics. CFS Engineering specializes in Numerical Simulation of Fluid Mechanics and Structural Mechanics Engineering Problems, collaborating with clients to enhance product design and performance.

Turbulence: Numerical Flow SimulationME-474: Numerical flow simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Continuity Equation, Newton's 2nd Law in Eulerian ConceptPHYS-201(d): General physics: electromagnetism

Covers the continuity equation for steady laminar flow and Newton's 2nd law.

Inviscid Flows: Understanding Fluid DynamicsME-280: Fluid mechanics (for GM)

Explores inviscid flows, Reynolds number importance, linear deformations, and volume change in fluid dynamics.

Aerodynamics

Aerodynamics (ἀήρ aero (air) + δυναμική (dynamics)) is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an important domain of study in aeronautics. The term aerodynamics is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air.

Deformation of materials

In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve.

Topics in physical quantities

A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Following ISO 80000-1, any value or magnitude of a physical quantity is expressed as a comparison to a unit of that quantity.

The presence of aerodynamic vortices is widespread in nature. They can be found at small scales near the wing tip of flying insects or at bigger scale in the form of hurricanes, cyclones or even galaxies. They are identified as coherent regions of high vorticity where the flow is locally dominated by rotation over strain. A better comprehension of vortex dynamics has a great potential to increase aerodynamic performances of moving vehicles, such as drones or autonomous underwater vehicles. An accelerated flat plate, a pitching airfoil or a jet flow ejected from a nozzle give rise to the formation of a primary vortex, followed by the shedding of smaller secondary vortices. We experimentally study the growth, timing and trajectory of primary and secondary vortices generated from a rectangular flat plate that is rotated around its centre location in a quiescent fluid. We systematically vary the rotational speed of the plate to get a chord based Reynolds number \Rey that ranges from 800 to 12000. We identify the critical \Rey for the occurrence of secondary vortices to be at 2500. The timing of the formation of the primary vortex is \Rey independent but is affected by the plate's dimensions. The circulation of the primary vortex increases with the angular position $\alpha$ of the plate, until the plate reaches 30°. Increasing the thickness and decreasing the chord lead to a longer growth of the primary vortex. Therefore, the primary vortex reaches a higher dimensionless limit strength. We define a new dimensionless time $T^*$ based on the thickness of the plate to scale the age of the primary vortex. The primary vortex stops growing when $T^* \approx 10$, regardless of the dimensions of the plate. We consider this value to be the vortex formation number of the primary vortex generated from a rotating rectangular flat plate in a Reynolds number range that goes from 800 to 12000. When $\alpha$ > 30°, the circulation released in the flow is entrained into secondary vortices for $\Rey > 2500$. The circulation of all secondary vortices is approximately 4 to 5 times smaller than the circulation of the primary vortex. We present a modified version of the Kaden spiral that accurately predicts the shear layer evolution and the trajectory of primary and secondary vortices during the entire rotation of the plate.We model the timing dynamics of secondary vortices with a power law equation that depends on two distinct parameter: $\chi$ and $\alpha_{0}$.The parameter $\chi$ indicates the relative increase in the time interval between the release of successive secondary vortices.The parameter $\alpha_{0}$ indicates the angular position at which the primary vortex stops growing and pinches-off from the plate.We also observe that the total circulation released in the flow is proportional to $\alpha^{1/3}$, as predicted by the inviscid theory.The combination of the power law equation with the total circulation computed from inviscid theory predict the strength of primary and secondary vortices, based purely on the plate's geometry and kinematics.The strength prediction is confirmed by experimental measurements.In this thesis we provided a valuable insight into the growth, timing and trajectory of primary and secondary vortices generated by a rotating flat plate. Future work should be directed towards more complex object geometries and kinematics, to confirm the validity of the modified Kaden spiral and explore the influence on the formation number.

Hydrodynamics at the nanoscale involves both fundamental study and application of fluid and mass transport phenomena in nanometer-sized confinements. Nanopores in single-layer graphene can be highly attractive for exploring the molecular transport of gas and water molecules and hydrated ions at the ultimate scales of pore size and pore length. However, the experimental data is limited, and the state-of-the-art artificial nanopores still underperform compared to biological channels in cellular membranes. This dissertation focuses on developing ultimate graphene nanopore devices to study mass transport phenomena under controlled spatial confinement. We first investigated the kinetics of liquidâvapor transport from nanoscale confinements which is attractive for novel evaporation and separation applications; however, it is not explored at the ultimate confinement limit, i.e., at the atomic-thick and Ã-scale nanopore placed at the liquidâvapor interface. We show that the evaporation flux from such nanopores increases with decreasing pore size by up to one order of magnitude relative to the bare liquidâvapor interface. Molecular dynamics simulations reveal that oxygen-functionalized nanopores render rapid rotational and translational dynamics to water molecules by reducing and shortening the lifetime of waterâwater hydrogen bonds. Graphene nanopores also enable the study of ion transport across sub-nanometer-scale 2D confinements. We produce tailor-made nanopores approaching the size of hydrated ions by decoupling the pore nucleation and expansion. Monovalent metal ions are efficiently sieved from divalent ions, with K+/Mg2+ selectivity up to 70 and Li+/Mg2+ selectivity up to 50, corresponding to a sieving resolution of 1 Ã. Mitigating the non-selective pore formation further enhance the ion-sieving performance, reaching K+/Mg2+ selectivity up to 350 and Li+/Mg2+ selectivity up to 260. The pore size and structure allow adjusting the diffusion of ions across the nanopores, suggesting that the sterically induced partial dehydration process may play an important role in the observed cation selectivities. These selectivities were realized from centimeter-scale suspended graphene membranes, prepared in crack-free fashion by using dual layer reinforcement strategy where the first layer is 200-nm-thick nanoporous carbon (NPC) film hosting 20 nm pores which ensures a conformal contact and reinforcement of the graphene film and the second (top) layer is Nafion.Finally, a dual layer reinforcement is also demonstrated for preparing crack-free centimeter-scale gas separation membranes to utilize the full potential of graphene nanopores for energy-efficient applications. The bottom layer of the composite film is NPC film while the top layer is made of a 500-nm thick multi-walled carbon nanotube (MWNT) film with a pore size ranging from 200 to 300 nm. The obtained selectivities from crack-free centimeter-scale graphene membranes for H2/CH4 and H2/CO2 are 11â23 and 5â8, respectively, which is significantly higher than the corresponding Knudsen selectivities. Overall, this dissertation presents a graphene nanopore toolkit for studying fluid mechanics at the ultimate scales. The findings of enhanced water evaporation rate and ion selectivity using the nanopore platform could enrich our understanding of mass transport under extreme confinement and open new opportunities for a range of separation applications.

Fernando Porté Agel, Dara Vahidi

Analytical wind turbine wake models are widely used to predict the wake velocity deficit. In these models, the wake growth rate is a key parameter specified mainly with empirical formulations. In this study, a new physics-based model is proposed and validated to predict the wake expansion downstream of a turbine based on the incoming ambient turbulence and turbine operating conditions. The new model utilises Taylor diffusion theory, the Gaussian wake model, turbulent mixing layer theory and the analogy between wind turbine wake expansion and scalar diffusion. These components ensure that the model conserves mass and momentum in the far wake and accounts for the ambient turbulence and turbine-induced turbulence effects on the wake expansion. To account for the turbulence relevant scales that contribute to the wake expansion, the model uses the root-mean-square of the low-pass filtered radial velocity component. A simplified version that only requires the unfiltered velocity standard deviation and turbulence integral scale is also proposed. In addition, a new relation for the near-wake length is derived. The model performance is validated using large-eddy simulation data of a wind turbine wake under neutral atmospheric conditions with a wide range of incoming turbulence levels. The results show that the proposed model yields reasonable predictions of the wake width, maximum velocity deficit and near-wake length. In the case with a relatively low incoming streamwise turbulence intensity of 0.05, the ambient and turbine-induced terms in the model contribute almost equally to the wake width, rendering them both crucial for reasonable wake predictions.

2022