scholarly journals Magnetohydrodynamic Simulations of Hypersonic Flow over a Cylinder Using Axial- and Transverse-Oriented Magnetic Dipoles

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Andrew N. Guarendi ◽  
Abhilash J. Chandy
Keyword(s):  
Magnetic Field ◽  
Hypersonic Flow ◽  
Magnetic Reynolds Number ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Magnetic Dipoles ◽  
Quasistatic Approximation ◽  
Magnetohydrodynamic Simulations ◽  
Energy Equations ◽  
The Magnetic Field

Numerical simulations of magnetohydrodynamic (MHD) hypersonic flow over a cylinder are presented for axial- and transverse-oriented dipoles with different strengths. ANSYS CFX is used to carry out calculations for steady, laminar flows at a Mach number of 6.1, with a model for electrical conductivity as a function of temperature and pressure. The low magnetic Reynolds number (≪1) calculated based on the velocity and length scales in this problem justifies the quasistatic approximation, which assumes negligible effect of velocity on magnetic fields. Therefore, the governing equations employed in the simulations are the compressible Navier-Stokes and the energy equations with MHD-related source terms such as Lorentz force and Joule dissipation. The results demonstrate the ability of the magnetic field to affect the flowfield around the cylinder, which results in an increase in shock stand-off distance and reduction in overall temperature. Also, it is observed that there is a noticeable decrease in drag with the addition of the magnetic field.

Static magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Problem Solving ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Scalar Potential ◽  
Multipole Expansion ◽  
Magnetic Vector Potential ◽  
Magnetic Dipoles ◽  
Static Magnetic Fields ◽  
The Magnetic Field

Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.

scholarly journals Filaments and striations: anisotropies in observed, supersonic, highly magnetized turbulent clouds

2019 ◽  
Vol 492 (1) ◽  
pp. 668-685 ◽  
Author(s):  
James R Beattie ◽  
Christoph Federrath
Keyword(s):  
Magnetic Field ◽  
Column Density ◽  
Three Dimensional ◽  
High Density ◽  
Systematic Analysis ◽  
Guide Field ◽  
Degree Of Anisotropy ◽  
Mach Numbers ◽  
Magnetohydrodynamic Simulations ◽  
The Magnetic Field

ABSTRACT Stars form in highly magnetized, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields and magnetosonic striations introduce anisotropies into the cloud. In this study, we use the two-dimensional power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\operatorname{\mathcal {M}_{\text{A}}}=0.1{\!-\!10}$) and turbulent Mach numbers ($\operatorname{\mathcal {M}}=2{\!-\!20}$), with 20 high-resolution, three-dimensional turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to $\operatorname{\mathcal {M}_{\text{A}}}\lt 1$, and $\operatorname{\mathcal {M}}\lesssim 4$, the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for $\operatorname{\mathcal {M}}\gtrsim 4$ the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by $\operatorname{\mathcal {M}}$ that determine which kind of anisotropy dominates the morphology of a cloud.

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.

Optimal Growth and Transition to Turbulence in Magnetohydrodynamic Duct Flow

2010 ◽  
Author(s):  
Dmitry Krasnov ◽  
Oleg Zikanov ◽  
Maurice Rossi ◽  
Thomas Boeck
Keyword(s):  
Magnetic Field ◽  
Optimal Growth ◽  
Transition Process ◽  
Finite Amplitude ◽  
Magnetic Reynolds Number ◽  
Transition To Turbulence ◽  
Duct Flow ◽  
Electrically Conducting ◽  
Nonlinear Mechanism ◽  
The Magnetic Field

We consider the flow of an electrically conducting fluid in a duct in the presence of a constant magnetic field perpendicular to the flow. The technologically relevant approximation of small magnetic Reynolds number is adopted. The focus of investigation is on the nonlinear mechanism of transition consisting of transient growth and subsequent breakdown of finite amplitude perturbations. Numerical analysis demonstrates that the strongest growth is experienced by perturbations localized in the sidewall boundary layers parallel to the imposed magnetic field. This result and the direct numerical simulations of the transition process indicate that the commonly accepted picture of the transition in MHD duct based on the numerical and theoretical analysis of the flow in the Hartmann channel is misleading. The flow may become turbulent within the sidewall layers long before the Hartmann layers on the walls perpendicular to the magnetic field are able to sustain nonlinear transition.

Stationary waves at the interface between a plasma stream and magnetic field

1982 ◽  
Vol 28 (1) ◽  
pp. 13-17 ◽  
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Magnetic Field ◽  
Plasma Stream ◽  
Stationary Waves ◽  
Transform Method ◽  
Magnetic Dipoles ◽  
Shallow Water Approximation ◽  
Supersonic Plasma ◽  
Gravity Effects ◽  
The Magnetic Field ◽  
Effect Of Surface

A uniformly-streaming compressible and infinitely-conducting plasma is confined by a magnetic field aligned with the stream. The system is disturbed by introducing magnetic dipoles into the field. A Fourier-transform method is used to determine the displacement of the interface between the streaming plasma and the magnetic field within the framework of a ‘shallow-water’ approximation. For the case of a subsonic plasma stream, stationary waves appear on the interface upstream of the dipoles, and it is found that (i) these stationary waves are possible only if the gravity effects on the plasma are weak enough; (ii) the effect of surface tension at the interface is to reduce the amplitude and increase the wavelength of these waves. For the case of a supersonic plasma stream, however, stationary waves at the interface are not possible.

scholarly journals Magnetic field dependent viscous fluid-flow between squeezing plates with homogeneous and heterogeneous reactions

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 423-431
Author(s):  
Wajid Jan ◽  
Muhammad Farooq ◽  
Jamel Baili ◽  
Rehan Ali Shah ◽  
Aamir Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Tangential Velocity ◽  
Magnetic Reynolds Number ◽  
Heterogeneous Reactions ◽  
Navier Stokes ◽  
Fluid Temperature ◽  
Field Equations ◽  
Homogeneous And Heterogeneous Reactions ◽  
Field Dependent

The impacts of magnetic field dependent viscous fluid is explored between squeezing plates in the presence of homogeneous and heterogeneous reactions. The unsteady constitutive equations of heat and mass transfers, modified Navier-Stokes, magnetic field and homogeneous and heterogeneous reactions are coupled as an system of ODE. The appropriate solutions are established for the vertical and axial induced magnetic field equations for the transformed and momentum as well as for the MHD pressure and torque exerted on the upper plate, and are in details. In the case of a smooth plate, the self-similar equation with acceptable starting assumptions and auxiliary parameters is solved by utilising a homotopy analytics method, to generate an algorithm with fast and guaranteed convergence. By comparing homotopy analytics method solutions with BVP4c numerical solver packaging, the validity and correctness of the homotopy analytics method findings are demonstrated. Magnetic Reynolds number have been shown to cause to decrease the distribution of magnetic field, fluid temperature, axial and tangential velocity. The magnetic field also has vertical and axial components with increasing viscosity. The applications of the investigation include car magneto-rheological shock absorbers, modern aircraft landing gear systems, procedures for heating or cooling, biological sensor systems, and bio-prothesis, etc.

Dimensionality of Anisotropic Homogeneous Turbulence With Distortions: Compared Effects Between the Coriolis Force and the Lorentz Force

2014 ◽  
Author(s):  
Fabien Godeferd ◽  
Claude Cambon ◽  
Alexandre Delache
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Coriolis Force ◽  
Magnetic Reynolds Number ◽  
Homogeneous Turbulence ◽  
Spectral Space ◽  
Structure And Dynamics ◽  
Induction Equation ◽  
The Magnetic Field

We consider initially isotropic homogeneous turbulence which is submitted to an external force, in statistically axisymmetric configurations. First, we study hydrodynamical turbulence in a rotating frame, in which case the Coriolis force modifies the structure and dynamics of the flow, thus creating elongated structures along the axis of rotation, corresponding to an accumulation of energy in the neighbourhood of the equatorial spectral plane. Secondly, a very similar configuration is that of magnetohydrodynamics (MHD) of a conducting fluid within an externally applied space uniform magnetic field, in which case the Lorentz force also concentrates energy to the same spectral equatorial manifold, but creates axially extending current sheets, along the magnetic field. We more specifically consider the quasi-static limit at small magnetic Reynolds number, in which the induction equation is analytically solved. We study the anisotropy of each turbulent flow using progressively refined statistics applied to results of direct numerical simulations, and we show that an accurate characterization of the flow structure requires advanced two-point statistics, which are available easily only in spectral space.

scholarly journals A MAGNETOHYDRODYNAMIC STUDY OF BEHAVIOR IN AN ELECTROLYTE FLUID USING NUMERICAL AND EXPERIMENTAL SOLUTIONS

2012 ◽  
Vol 11 (1-2) ◽  
pp. 53
Author(s):  
L. P. Aoki ◽  
M. G. Maunsell ◽  
H. E. Schulz
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Fluid Velocity ◽  
Flow Analysis ◽  
Test Chamber ◽  
Cross Product ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Vector Density ◽  
The Magnetic Field

This article examines a rectangular closed circuit filled with an electrolyte fluid, known as macro pumps, where a permanent magnet generates a magnetic field and electrodes generate the electric field in the flow. The fluid conductor moves inside the circuit under magnetohydrodynamic effect (MHD). The MHD model has been derived from the Navier Stokes equation and coupled with the Maxwell equations for Newtonian incompressible fluid. Electric and magnetic components engaged in the test chamber assist in creating the propulsion of the electrolyte fluid. The electromagnetic forces that arise are due to the cross product between the vector density of induced current and the vector density of magnetic field applied. This is the Lorentz force. Results are present of 3D numerical MHD simulation for newtonian fluid as well as experimental data. The goal is to relate the magnetic field with the electric field and the amounts of movement produced, and calculate de current density and fluid velocity. An u-shaped and m-shaped velocity profile is expected in the flows. The flow analysis is performed with the magnetic field fixed, while the electric field is changed. Observing the interaction between the fields strengths, and density of the electrolyte fluid, an optimal configuration for the flow velocity isdetermined and compared with others publications.

scholarly journals Zur Begrenzung der radialen Ausdehnung des Lichtbogenstromes durch ein axiales Magnetfeld

1970 ◽  
Vol 25 (11) ◽  
pp. 1583-1600
Author(s):  
O. Klüber
Keyword(s):  
Magnetic Field ◽  
Hall Current ◽  
Axial Magnetic Field ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Plasma Radius ◽  
Arc Current ◽  
Field Lines ◽  
The Magnetic Field ◽  
Generally True

Abstract In an arc without external magnetic field the current carrying region is identical with the conducting plasma column. This is no longer generally true if the arc is in an axial magnetic field and if the electrode radius is much smaller than the plasma radius. Radial current components then produce a rotational motion of the plasma and an azimuthal Hall current, and hence electromotive forces which try to suppress the current perpendicular to the magnetic field. In a plasma with finite viscosity the rotation is determined by the Navier-Stokes equation, which is solved here for a homogeneous plasma simultaneously with generalized Ohm's law. The results show that the plasma rotation is always an essential, and often the dominant, mechanism for guiding the arc current parallel to the magnetic field lines.

Hiemenz magnetic flow of a non-Newtonian fluid of second grade with heat transfer

2000 ◽  
Vol 78 (9) ◽  
pp. 875-882 ◽  
Author(s):  
H A Attia
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Newtonian Fluid ◽  
Second Grade ◽  
Magnetic Flow ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Energy Equations ◽  
The Magnetic Field ◽  
Steady Laminar

The steady laminar flow of an incompressible viscous electrically conducting non-Newtonian fluid of second grade impinging normal to a plane wall with heat transfer is investigated. An externally applied uniform magnetic field is applied normal to the wall, which is maintained at a constant temperature. A numerical solution for the governing momentum and energy equations is obtained. The effect of the characteristics of the non-Newtonian fluid and the magnetic field on both the flow and heat transfer is outlined. PACS Nos.: 47.50 and 47.15

Sign in / Sign up

Export Citation Format

Share Document