scholarly journals Thermal relaxation of a two-dimensional plasma in a dc magnetic field. Part II. Numerical simulation

1974 ◽  
Author(s):  
J.Y. Hsu ◽  
D. Montgomery ◽  
G. Joyce
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Thermal Relaxation ◽  
Two Dimensional ◽  
Dc Magnetic Field

Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number

1998 ◽  
Vol 358 ◽  
pp. 299-333 ◽  
Author(s):  
OLEG ZIKANOV ◽  
ANDRE THESS
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Boundary Conditions ◽  
Interaction Parameter ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetic Interaction Parameter

The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.

scholarly journals Induction Heating of Aluminum Billets With Linear Motion in a Strong DC Magnetic Field: Magnetothermal Analysis in Two-Dimensional

2011 ◽  
Vol 21 (4) ◽  
pp. 3479-3487 ◽  
Author(s):  
Hakim Bensaidane ◽  
Youcef Ouazir ◽  
Thierry Lubin ◽  
Smail Mezani ◽  
Abderrezak Rezzoug
Keyword(s):  
Magnetic Field ◽  
Induction Heating ◽  
Linear Motion ◽  
Two Dimensional ◽  
Dc Magnetic Field

Three-dimensional MHD flows in rectangular ducts with internal obstacles

2000 ◽  
Vol 418 ◽  
pp. 265-295 ◽  
Author(s):  
B. MÜCK ◽  
C. GÜNTHER ◽  
U. MÜLLER ◽  
L. BÜHLER
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Magnetic Fields ◽  
Interaction Parameter ◽  
Hartmann Number ◽  
Three Dimensional ◽  
Side Length ◽  
Two Dimensional ◽  
The Magnetic Field

This paper presents a numerical simulation of the magnetohydrodynamic (MHD) liquid metal flow around a square cylinder placed in a rectangular duct. In the hydrodynamic case, for a certain parameter range the well-known Kármán vortex street with three-dimensional flow patterns is observed, similar to the flow around a circular cylinder. In this study a uniform magnetic field aligned with the cylinder is applied and its influence on the formation and downstream transport of vortices is investigated. The relevant key parameters for the MHD flow are the Hartmann number M, the interaction parameter N and the hydrodynamic Reynolds number, all based on the side length of the cylinder. The Hartmann number M was varied in the range 0 [les ] M [les ] 85 and the interaction parameter N in the range 0 [les ] N [les ] 36. Results are presented for two fixed Reynolds numbers Re = 200 and Re = 250. The magnetic Reynolds number is assumed to be very small. The results of the numerical simulation are compared with known experimental and theoretical results. The hydrodynamic simulation shows characteristic intermittent pulsations of the drag and lift force on the cylinder. At Re = 200 a mix of secondary spanwise three-dimensional instabilities (A and B mode, rib vortices) could be observed. The spanwise wavelength of the rib vortices was found to be about 2–3 cylinder side lengths in the near wake. At Re = 250 the flow appears more organized showing a regular B mode pattern and a spanwise wavelength of about 1 cylinder side length. With an applied magnetic field a quasi-two-dimensional flow can be obtained at low N ≈ 1 due to the strong non-isotropic character of the electromagnetic forces. The remaining vortices have their axes aligned with the magnetic field. With increasing magnetic fields these vortices are further damped due to Hartmann braking. The result that the ‘quasi-two-dimensional’ vortices have a curvature in the direction of the magnetic field can be explained by means of an asymptotic analysis of the governing equations. With very high magnetic fields the time-dependent vortex shedding can be almost completely suppressed. By three-dimensional visualization it was possible to show characteristic paths of the electric current for this kind of flow, explaining the action of the Lorentz forces.

Thermal relaxation of a two-dimensional plasma in a d.c. magnetic field. Part 1. Theory

1974 ◽  
Vol 12 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Jang-Yu Hsu ◽  
David Montgomery ◽  
Glenn Joyce
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Plasma Frequency ◽  
Thermal Relaxation ◽  
Collision Term ◽  
Dimensionless Time ◽  
Two Dimensional ◽  
Kinetic Description ◽  
Off Time ◽  
Number Of Particles

A theory is presented for the rate of thermal relaxation of a two-dimensional plasma in a strong uniform d.c. magnetic field. The Vahala—Montgomery kinetic description is completed by providing a cut-off time for the time of interaction of two particles which contribute to the collision term. The kinetic equation preclicts that thermal relaxation occurs as a function of the dimensionless time (ωpt) (ωp/Ω) (n0λ2D)−½, where ωp, is the plasma frequency, Ω is the gyrofrequency, and n0 λ2D is the number of particles per Debye square. By contrast, in the absence of an external magnetic field, a two-dimensional plasma relaxes as a function of (ωpt) (n0λ2D)−1.

scholarly journals Isotropy restoration toward high-beta space plasmas

2014 ◽  
Vol 1 (2) ◽  
pp. 1313-1330
Author(s):  
H. Comişel ◽  
Y. Narita ◽  
U. Motschmann
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Scaling Law ◽  
Field Measurements ◽  
Plasma Turbulence ◽  
Space Plasmas ◽  
Two Dimensional ◽  
Magnetic Field Measurements ◽  
Spacecraft Mission ◽  
High Beta

Abstract. Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of beta. Two complementary methods are used. One is multi-point measurements of magnetic field in the near-Earth solar wind as provided by the Cluster spacecraft mission, and the other is hybrid numerical simulation of two-dimensional plasma turbulence. The both methods provide evidence of wavevector anisotropy as a function of beta such that isotropy is gradually restored toward higher values of beta. Furthermore, the numerical simulation study demonstrates the existence of scaling law between plasma beta and wavevector anisotropy. This fact can be used to construct a diagnostic tool to determine or to constrain plasma beta using multi-point magnetic field measurements in space.

Discretization of the magnetic field in MPD thrusters

2004 ◽  
Vol 14 (4) ◽  
pp. 559-572 ◽  
Author(s):  
Jörg Heiermann ◽  
Monika Auweter‐Kurtz
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Numerical Simulation ◽  
Stream Function ◽  
Maxwell Equations ◽  
Two Dimensional ◽  
Adaptive Meshes ◽  
Faraday’S Law ◽  
Mpd Thrusters ◽  
The Magnetic Field

For the numerical simulation of magnetoplasmadynamic (MPD) self‐field thruster flow, the solution of one of the two dynamical Maxwell equations – Faraday's law – is required. The Maxwell equations and Ohm's law for plasmas can be summarized in one equation for the stream function so that the two‐dimensional, axisymmetric magnetic field can be calculated. The finite volume (FV) discretization of the equation on unstructured, adaptive meshes is presented in detail and solutions for different thruster currents are shown. The calculated thrust is compared with the experimental data.

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