The Scientific Legacy of George Gabriel Stokes

2019 ◽  
pp. 197-216
Author(s):  
Andrew Fowler
Keyword(s):  
Stokes Equations ◽  
Research Work ◽  
Rogue Waves ◽  
Navier Stokes ◽  
Contact Lines ◽  
Nls Equation ◽  
Navier Stokes Equations ◽  
Scientific Legacy ◽  
Moving Contact ◽  
Moving Contact Lines

The scientific legacy of George Gabriel Stokes is considered. Certain aspects of Stokes’s research work are reviewed and related to more recent fields of research. These include the Navier–Stokes equations and other approaches to rational continuum mechanics, the issue of existence of solutions, the boundary no-slip condition; Stokes flow and the issue of pendulum drag; the Hele-Shaw cell, viscous fingering, wavelength selection in pattern formation; moving contact lines; the highest water wave, rogue waves, the NLS equation; Stokes lines, exponential asymptotics, dendrite growth, slow manifods, and diffraction.

Modeling and analysis of solar air channels with attachments of different shapes

2019 ◽  
Vol 29 (5) ◽  
pp. 1815-1845 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Research Work ◽  
Convection Heat Transfer ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Modeling And Analysis ◽  
Air Channels

Purpose This paper aims to report the results of numerical analysis of turbulent fluid flow and forced-convection heat transfer in solar air channels with baffle-type attachments of various shapes. The effect of reconfiguring baffle geometry on the local and average heat transfer coefficients and pressure drop measurements in the whole domain investigated at constant surface temperature condition along the top and bottom channels’ walls is studied by comparing 15 forms of the baffle, which are simple (flat rectangular), triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, double V (or W), Z, T, G and epsilon (or e)-shaped, with the Reynolds number changing from 12,000 to 32,000. Design/methodology/approach The baffled channel flow model is controlled by the Reynolds-averaged Navier–Stokes equations, besides the k-epsilon (or k-e) turbulence model and the energy equation. The finite volume method, by means of commercial computational fluid dynamics software FLUENT is used in this research work. Findings Over the range investigated, the Z-shaped baffle gives a higher thermal enhancement factor than with simple, triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, W, T, G and e-shaped baffles by about 3.569-20.809; 3.696-20.127; 3.916-20.498; 1.834-12.154; 1.758-12.107; 7.272-23.333; 6.509-22.965; 8.917-26.463; 8.257-23.759; 5.513-18.960; 8.331-27.016; 7.520-26.592; 6.452-24.324; and 0.637-17.139 per cent, respectively. Thus, the baffle of Z-geometry is considered as the best modern model of obstacles to significantly improve the dynamic and thermal performance of the turbulent airflow within the solar channel. Originality/value This analysis reports an interesting strategy to enhance thermal transfer in solar air channels by use of attachments with various shapes

Study of the 3D Flows in the Forward-Curved Blades Centrifugal Fans

2002 ◽  
Author(s):  
Thomas Bouquet ◽  
Farid Bakir ◽  
Smai¨ne Kouidri ◽  
Robert Rey
Keyword(s):  
Test Bench ◽  
Stokes Equations ◽  
Research Work ◽  
Internal Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Acoustic Performance ◽  
Commercial Code ◽  
Centrifugal Fans ◽  
3D Flows

The study presented in this paper is part of the research work on forward-curved blades centrifugal fans carried out the last years by the « Laboratoire d’Energe´tique et de Me´canique des Fluides Interne » (Lemfi – Site Paris). The objective of this study is to better understand the internal flow in this type of machine in order to be able to correlate the aeraulic and acoustic behavior with the geometrical characteristics of the machine. Two impellers with different profiles were manufactured and tested. The aeraulic and acoustic tests were carried out on a test bench standardized ISO 5801. The 3D CFD of the flow was carried out with a commercial code based on the resolution of the Navier-Stokes equations in finite volumes. The analysis of these results confirms that a more organized flow field leads to a better acoustic performance.

The dynamics of three-dimensional liquid bridges with pinned and moving contact lines

2012 ◽  
Vol 707 ◽  
pp. 521-540 ◽  
Author(s):  
Shawn Dodds ◽  
Marcio S. Carvalho ◽  
Satish Kumar
Keyword(s):  
Contact Line ◽  
Liquid Bridge ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Liquid Bridges ◽  
Contact Lines ◽  
Flat Surfaces ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Contact Line Friction

AbstractLiquid bridges with moving contact lines are relevant in a variety of natural and industrial settings, ranging from printing processes to the feeding of birds. While it is often assumed that the liquid bridge is two-dimensional in nature, there are many applications where either the stretching motion or the presence of a feature on a bounding surface lead to three-dimensional effects. To investigate this we solve Stokes equations using the finite-element method for the stretching of a three-dimensional liquid bridge between two flat surfaces, one stationary and one moving. We first consider an initially cylindrical liquid bridge that is stretched using either a combination of extension and shear or extension and rotation, while keeping the contact lines pinned in place. We find that whereas a shearing motion does not alter the distribution of liquid between the two plates, rotation leads to an increase in the amount of liquid resting on the stationary plate as breakup is approached. This suggests that a relative rotation of one surface can be used to improve liquid transfer to the other surface. We then consider the extension of non-cylindrical bridges with moving contact lines. We find that dynamic wetting, characterized through a contact line friction parameter, plays a key role in preventing the contact line from deviating significantly from its original shape as breakup is approached. By adjusting the friction on both plates it is possible to drastically improve the amount of liquid transferred to one surface while maintaining the fidelity of the liquid pattern.

scholarly journals Evidence of Landau Damping in a Fluid Coupled with an Anharmonic Lattice

2018 ◽  
Author(s):  
Andrei Ludu ◽  
Eric Padilla ◽  
M. A. Qaayum Mazumder
Keyword(s):  
Drag Force ◽  
Water Waves ◽  
Stokes Equations ◽  
Collisionless Plasma ◽  
Rogue Waves ◽  
Landau Damping ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Anharmonic Lattice ◽  
Specific Frequency

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

Modeling of Atmospheric Processes Based on the Averaged Navier-Stokes Equations

2014 ◽  
Vol 565 ◽  
pp. 74-79
Author(s):  
Bakytzhan Zhumagulov ◽  
Dauren Zhakebaev ◽  
Aigerim Abdibekova
Keyword(s):  
Stokes Equations ◽  
Research Work ◽  
Navier Stokes ◽  
Problem Solution ◽  
Navier Stokes Equations ◽  
Atmospheric Processes ◽  
Eddy Simulation ◽  
Scientific Research Work ◽  
Large Eddy ◽  
The Mathematical Model

This work is devoted to the mathematical and numerical modeling of atmospheric processes based on the ensemble-averaged Navier-Stokes equations with the implementation of large eddy simulation. Within the real scientific research work are shown features of modeling atmospheric processes, the mathematical model of dynamic processes was developed in the average atmosphere, the numerical scheme and algorithm of the problem solution were developed, and realization of the problem characterized by instability of Rayleigh-Taylor about convective mass substances transfer with various densities was made.

scholarly journals Numerical investigation on combustion and NOx emissions of a CH4 / kerosene afterburner

2021 ◽  
Vol 286 ◽  
pp. 01002
Author(s):  
Andreea Cristina Mangra ◽  
Ene Barbu
Keyword(s):  
Natural Gas ◽  
Gas Turbines ◽  
Alternative Fuels ◽  
Stokes Equations ◽  
Research Work ◽  
Spray Angle ◽  
Navier Stokes ◽  
Future Research ◽  
Nox Emissions ◽  
Navier Stokes Equations

Cogeneration groups equipped with gas turbines usually operate with natural gas. The new requirements regarding the flexibility of functioning both with conventional and alternative fuels have led to the development of new solutions. An afterburning installation facilities, on the one hand, the combustion of fuels which can not normally be used in gas turbines, and on the other hand, allows a rapid adaptation of the cogeneration group to the user's variable thermal energy requirements. In some cases, an afterburning installation may contribute to the reduction of NOx emissions. It also increases the group's adaptability to changing environmental conditions, especially during the summer. Having in mind these tendencies and starting from the data collected from the 2xST 18 – Suplacu de Barcau cogeneration plant, this paper presents a numerical analysis of an afterburner in order to switch from natural gas to natural gas / kerosene functioning, with minimal modifications to the existing solution. A 3D steady RANS numerical integration of the Navier-Stokes equations has been carried out using the commercial software ANSYS CFX. For future research work, it will be taken into consideration the use of more complex reaction mechanisms and the variation of the spray angle will be considered. Also, in order to validate the CFD results a combustion experiments campaign will be conducted.

scholarly journals Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bo You
Keyword(s):  
Stokes System ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Time Behavior ◽  
Contact Lines ◽  
Trajectory Attractor ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Long Time ◽  
Statistical Solutions

<p style='text-indent:20px;'>The objective of this paper is to consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. As we know, it is very difficult to obtain the uniqueness of an energy solution for this system even in two dimensions caused by the presence of the strong coupling at the boundary. Thus, we first prove the existence of a trajectory attractor for such system, which is a minimal compact trajectory attracting set for the natural translation semigroup defined on the trajectory space. Furthermore, based on the abstract results (trajectory attractor approach) developed in [<xref ref-type="bibr" rid="b38">38</xref>], we construct trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines.</p>

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