scholarly journals Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 77 ◽  
Author(s):  
Tagawa ◽  
Song
Keyword(s):  
Magnetic Field ◽  
Velocity Profile ◽  
Stokes Equation ◽  
Hartmann Number ◽  
Metal Flow ◽  
Basic Flow ◽  
Rotating Magnetic Field ◽  
Navier Stokes ◽  
Force Term ◽  
Navier Stokes Equation

The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of the basic flow for the case of an infinitely long cylinder depends on the number of pole-pairs and the Hartmann number. A set of linearized disturbance equations to obtain a neutral state was successfully solved using the highly simplified marker and cell (HSMAC) method together with a Newton–Raphson method. For various cases of the basic flow, depending on both the number of pole-pairs and the Hartmann number, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The linear stability analyses reveal that the critical Reynolds number takes its minimum at a certain value of the Hartmann number. On the other hand, the velocity profile for cases of a finite length cylinder having a no-slip condition at the flat walls generates the Bödewadt boundary layers and such flows need to be computed including the non-linear terms of the Navier-Stokes equation.

scholarly journals Nonlinear Dynamos

2010 ◽  
Vol 6 (S271) ◽  
pp. 297-303
Author(s):  
David Galloway
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Stokes Equation ◽  
Lorentz Force ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Direct Competition ◽  
Astrophysical Objects ◽  
Flow Domain ◽  
The Magnetic Field

AbstractThis paper discusses nonlinear dynamos where the nonlinearity arises directly via the Lorentz force in the Navier-Stokes equation, and leads to a situation where the Lorentz force and the velocity and the magnetic field are in direct competition over substantial regions of the flow domain. Filamentary and non-filamentary dynamos are contrasted, and the concept of Alfvénic dynamos with almost equal magnetic and kinetic energies is reviewed via examples. So far these remain in the category of toy models; the paper concludes with a discussion of whether similar dynamos are likely to exist in astrophysical objects, and whether they can model the solar cycle.

Liquid Metal Flow in the Annular Passage of an Electromagnetic Pump

2009 ◽  
Author(s):  
Jeong-Tae Kwon ◽  
Taek-Hoon Nahm ◽  
Seo-Hyun Kim ◽  
Hyo-Jae Lim ◽  
Chang-Eob Kim
Keyword(s):  
Liquid Metal ◽  
Stokes Equation ◽  
Lorentz Force ◽  
Metal Flow ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Electromagnetic Pump ◽  
Liquid Metal Flow ◽  
Constant Source

An electromagnetic pump using tubular induction motor (TLIM) has been proposed to pump liquid metal fluids. TLIM has been designed for the liquid metal flow system with motor thrust force of about 40∼77 N. The flow characteristics have been investigated by solving Navier-Stokes equation. The Lorentz force effect was included simply by considering it as a constant source term in the Navier-Stokes equation. A wood-metal was chosen for the simulation of liquid metal. The effect of Lorentz force on the flow rate was investigated. Also, in order to verify the analysis results, an experiment was conducted and the experimental results were compared with those of the simulation. The simulation results showed over-estimation of about 10% compared with the experimental ones.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

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