scholarly journals A non-conventional discontinuous Lagrangian for viscous flow

2017 ◽  
Vol 4 (2) ◽  
pp. 160447 ◽  
Author(s):  
M. Scholle ◽  
F. Marner
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Navier Stokes Equations ◽  
New Formalism ◽  
Limiting Case ◽  
Physical Phenomena

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

Numerical Investigation of the Coulter Principle in a Microfluidic Device

2013 ◽  
Author(s):  
Muheng Zhang ◽  
Yongsheng Lian
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Working Mechanism ◽  
Navier Stokes Equations ◽  
Sheath Flow ◽  
Coulter Counters ◽  
Pass Through ◽  
Cell Motion

Coulter counters are analytical microfluidic instrument used to measure the size and concentration of biological cells or colloid particles suspended in electrolyte. The underlying working mechanism of Coulter counters is the Coulter principle which relies on the fact that when low-conductive cells pass through an electric field these cells cause disturbances in the measurement (current or voltage). Useful information about these cells can be obtained by analyzing these disturbances if an accurate correlation between the measured disturbances and cell characteristics. In this paper we use computational fluid dynamics method to investigate this correlation. The flow field is described by solving the Navier-Stokes equations, the electric field is represented by a Laplace’s equation in which the conductivity is calculated from the Navier-Stokes equations, and the cell motion is calculated by solving the equations of motion. The accuracy of the code is validated by comparing with analytical solutions. The study is based on a coplanar Coulter counter with three inlets that consist of two sheath flow inlet and one conductive flow inlet. The effects of diffusivity, cell size, sheath flow rate, and cell geometry are discussed in details. The impacts of electrode size, gap between electrodes and electrode location on the measured distribution are also studied.

Aerodynamic and Aeroacoustic Analyses of a Regenerative Blower

2015 ◽  
Author(s):  
Man-Woong Heo ◽  
Tae-Wan Seo ◽  
Chung-Suk Lee ◽  
Kwang-Yong Kim
Keyword(s):  
Shear Stress ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Side Channel ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Unsteady Flow Analysis

This paper presents a parametric study to investigate the aerodynamic and aeroacoustic characteristics of a side channel regenerative blower. Flow analysis in the side channel blower was carried out by solving three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence closure. Aeroacoustic analysis was conducted by solving the variational formulation of Lighthill’s analogy on the basis of the aerodynamic sources extracted from the unsteady flow analysis. The height and width of the blade and the angle between inlet and outlet ports were selected as three geometric parameters, and their effects on the aerodynamic and aeroacoustic performances of the blower have been investigated. The results showed that the aerodynamic and aeroacoustic performances were enhanced by decreasing height and width of blade. It was found that angle between inlet and outlet ports significantly influences the aerodynamic and aeroacoustic performances of the blower due to the stripper leakage flow.

scholarly journals Vortex motion of a continuous medium depending on the pressure change

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Alexander Braginsky
Keyword(s):  
Angular Velocity ◽  
Continuous Medium ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Vortex Motion ◽  
Pressure Change ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Least Action ◽  
Force Components

Abstract In this paper, we study the vortex motion of a continuous medium, which is described by forces obtained from the principle of least action. It is shown that in a continuous medium the vortex force components are proportional to the velocity and pressure gradient components. This article gives a description of the 2D vortex motion of air in zones of high and low pressure. If the pressure decreases, the angular velocity of rotation of the continuous medium increases, whereas if the pressure increases, the angular velocity fades. The lifting force is obtained due to the vortex movement of air in the form of a funnel. It is shown that the vortex force contains a vortex term of the Euler hydrodynamic equations with a relative factor equal to the velocity of the continuous medium squared divided by the sound velocity squared. To describe the motion of a continuous medium correctly it is necessary to replace the forces obtained by Euler with the forces obtained from the minimum of action in the equations of motion. It is concluded that vortex motions and turbulence are described by the obtained equations of motion, and not by the Navier–Stokes equations. Most likely, this is related to the Problem of the Millennium description of turbulence announced at the International Congress of Mathematics in 2000.

Unsteady Multicellular Natural Convection in a Narrow Horizontal Cylindrical Annulus

1990 ◽  
Vol 112 (2) ◽  
pp. 379-387 ◽  
Author(s):  
D. B. Fant ◽  
J. Prusa ◽  
A. P. Rothmayer
Keyword(s):  
Chaotic Systems ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Cylindrical Annulus ◽  
Gap Spacing ◽  
Limiting Case

Numerical and analytical solutions are presented for multicellular flow instability and the subsequent nonlinear development in a horizontal cylindrical annulus. The Boussinesq approximated Navier–Stokes equations are simplified to Cartesian-like boundary layer equations by means of a high Rayleigh number small gap asymptotic expansion. The full numerical problem is explored for the limiting case of zero Prandtl number. At a finite scaled gap spacing, an instability sets in, which results in periodic multicellular flow. The numerical solutions are found to progress through an increasingly complex sequence of periodic solutions, culminating in a very complex unsteady solution that has features normally associated with chaotic systems.

Hierarchical Divergence-Free Bases and Their Application to Particulate Flows

2003 ◽  
Vol 70 (1) ◽  
pp. 44-49 ◽  
Author(s):  
V. Sarin ◽  
A. H. Sameh
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Particulate Flow ◽  
Particulate Flows ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Rigid Particles ◽  
The Matrix ◽  
Divergence Free

The paper presents an algebraic scheme to construct hierarchical divergence-free basis for velocity in incompressible fluids. A reduced system of equations is solved in the corresponding subspace by an appropriate iterative method. The basis is constructed from the matrix representing the incompressibility constraints by computing algebraic decompositions of local constraint matrices. A recursive strategy leads to a hierarchical basis with desirable properties such as fast matrix-vector products, a well-conditioned reduced system, and efficient parallelization of the computation. The scheme has been extended to particulate flow problems in which the Navier-Stokes equations for fluid are coupled with equations of motion for rigid particles suspended in the fluid. Experimental results of particulate flow simulations have been reported for the SGI Origin 2000.

Mechanics of thermohaline interleaving: beyond the empirical flux laws

2011 ◽  
Vol 675 ◽  
pp. 117-140 ◽  
Author(s):  
TIMOUR RADKO
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Field Measurements ◽  
Navier Stokes ◽  
Homogeneous Field ◽  
Spontaneous Generation ◽  
Navier Stokes Equations ◽  
Salt Fingers ◽  
Stratified Ocean

An analytical theory is developed which illustrates the dynamics of the spontaneous generation of thermohaline intrusions in the stratified ocean with density compensated lateral temperature and salinity gradients. Intrusions in the model are driven by the interaction with the initially homogeneous field of salt fingers, whose amplitude and spatial orientation is weakly modulated by the long wavelength perturbations introduced into the system. The asymptotic multiscale analysis makes it possible to identify intrusive instabilities resulting from the positive feedback of salt fingers on large-scale perturbations and analyse the resulting patterns. The novelty of the proposed analysis is related to our ability to avoid using empirical double-diffusive flux laws – an approach taken by earlier models. Instead, we base our analytical explorations directly on the governing (Navier–Stokes) equations of motion. The model predictions of the growth rates and preferred slopes of intrusions are in general agreement with the laboratory and field measurements.

scholarly journals Classical Solvability of a Free Boundary Problem for an Incompressible Viscous Fluid with a Surface Density Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yoshiaki Kusaka
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Mass ◽  
A Free Boundary Problem ◽  
Physical Phenomena ◽  
Density Equation

We investigate a mathematical model introduced by Shikhmurzaev to remove singularities that arise when classical hydrodynamic models are applied to certain physical phenomena. The model is described as a free boundary problem consisting of the Navier-Stokes equations and a surface mass balance equation. We prove the local-in-time solvability in Hölder spaces.

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