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.

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.

scholarly journals Stationary and axisymmetric magnetized equilibria of stars and winds

2010 ◽  
Vol 6 (S274) ◽  
pp. 437-440
Author(s):  
Shin Yoshida ◽  
Kotaro Fujisawa ◽  
Yoshiharu Eriguchi ◽  
Shijun Yoshida ◽  
Rohta Takahashi
Keyword(s):  
Magnetic Field ◽  
Stream Function ◽  
Maxwell Equations ◽  
Bernoulli Equation ◽  
Integral Conditions ◽  
Basic Variable ◽  
Ideal Mhd ◽  
Basic Equations ◽  
New Formulation ◽  
The Magnetic Field

AbstractWe present a new formulation to compute numerically stationary and axisymmetric equilibria of magnetized and self-gravitating astrophysical fluids. Under the assumption of ideal MHD, the stream function for the flow can be chosen as a basic variable with which the Euler-Maxwell equations are cast into a set of basic equations, i.e. a generalized Bernoulli equation and a Grad-Shafranov-like equation by employing various integral conditions. A novel feature of this formulation is that systems with stars, disks and winds are treated in a simple unified picture and the magnetic field structures can contain both poloidal and toroidal components.

Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Unstructured Adaptive Meshes

AIAA Journal ◽  
2002 ◽  
Vol 40 (3) ◽  
pp. 474-480 ◽  
Author(s):  
Woo Seop Oh ◽  
Joo Sung Kim ◽  
Oh Joon Kwon
Keyword(s):  
Numerical Simulation ◽  
Two Dimensional ◽  
Adaptive Meshes ◽  
Vortex Interactions

HEXAGON-STRIPE TRANSITION AT THE MAGNETIC FIELD INDUCED PHASE TRANSFORMATIONS OF THE MAGNETORHEOLOGICAL SUSPENSIONS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2345-2351 ◽  
Author(s):  
A. CEBERS
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Physical Parameters ◽  
Phase Boundaries ◽  
Modulated Phases ◽  
Magnetorheological Suspensions ◽  
Perturbed State ◽  
Magnetorheological Suspension ◽  
The Magnetic Field ◽  
Hele Shaw Cell

The phase diagram of the magnetorheological suspension allowing for the modulated phases in the Hele-Shaw cell under the action of the normal field is calculated. The phase boundaries between the stripe, the hexagonal and the unmodulated phases in dependence on the layer thickness and the magnetic field strength are found. The existence of the transitions between the stripe and the hexagonal phases at the corresponding variation of the physical parameters is illustrated by the numerical simulation of the concentration dynamics in the Hele-Shaw cell. It is remarked that those transitions in the case of the magnetorheological suspensions can be caused by the compression or the expansion of the layer. Among the features noticed at the numerical simulation of the concentration dynamics in the Hele-Shaw cell are: the stripe patterns formed from the preexisting hexagonal structures are more ordered than arising from the initial randomly perturbed state; at the slightly perturbed boundary between the concentrated and diluted phases the hexagonal and the inverted hexagonal phases are formed and others.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

Numerical Simulation of High-Aspect-Ratio Micro-Hole Electroforming with External Magnetic Field

2010 ◽  
Vol 42 ◽  
pp. 13-16
Author(s):  
Wei Li ◽  
Ping Mei Ming ◽  
Wu Ji Jiang ◽  
Yin Ding Lv
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Flow State ◽  
Cathode Electrode ◽  
Micro Hole ◽  
Fluent Software ◽  
The Magnetic Field ◽  
Enhance Mass

In this paper, the influences of applied magnetic field on flow state during electroforming of the high-aspect-ratio (HAR) blind micro-hole were numerically analyzed using the Fluent software. The results showed that, when microelectroforming of nickel without external agitation, three vortexes could form due to the magnetohydrodynamic (MHD) effect within the HAR micro-hole with magnetic field in parallel to cathode-electrode surface, and the flow rate in the micro-hole increased with the increase of the magnetic field and current density. The MHD effect helped to enhance mass transfer during the microelectroforming of HAR microstructures.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

scholarly journals Numerical simulation of induction heating thick-walled tubes

2018 ◽  
Vol 168 ◽  
pp. 02004
Author(s):  
Richard Lenhard ◽  
Milan Malcho ◽  
Katarína Kaduchová
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Field Distribution ◽  
Induction Heating ◽  
Electromagnetic Induction ◽  
Magnetic Field Distribution ◽  
The Magnetic Field ◽  
Heated Material ◽  
Ansys Workbench

In the paper is shown the connection of two toolboxes in an Ansys Workbench solution for induction heating. In Ansys Workbench, Maxwell electromagnetism programs and Fluent have been linked. In Maxwell, a simulation of electromagnetic induction was performed, where data on the magnetic field distribution in the heated material was obtained and then transformed into the Fluent program in which the induction heating simulation was performed.

Sign in / Sign up

Export Citation Format

Share Document