Solver Development for Three-Dimensional Magnetohydrodynamic Flow on a Collocated Structured Grid System Based on SIMPLE Method

2014 ◽  
Vol 525 ◽  
pp. 247-250
Author(s):  
Jie Mao ◽  
Ke Liu ◽  
Hua Chen Pan
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Velocity Vector ◽  
Hartmann Number ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Grid System ◽  
Simple Method ◽  
Conservative Scheme ◽  
Structured Grid

A steady state magnetohydrodynamic laminar solver with low magnetic Reynolds number has been developed in OpenFOAM platform. SIMPLE method has been used to solve the velocity vector and pressure. The induced electric potential and induced electric current has been solved according to a consistent and conservative scheme on a collocated structure grid. The solver has been validated by simulating Shercliff's case with medium Hartmann number. The results show that the numerical solution results match the analytical solutions well.

A magneto-hydrodynamic Stokes flow

1961 ◽  
Vol 260 (1300) ◽  
pp. 79-90 ◽  
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Hartmann Number ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Slow Flow ◽  
Magnetic Pole ◽  
Total Drag ◽  
Conducting Sphere ◽  
Stokes Drag

This paper considers the slow flow of a viscous, conducting fluid past a non-conducting sphere at whose centre is a magnetic pole. The magnetic Reynolds number is assumed to be small, and the modifications to the classical Stokes flow and the free magnetic pole field are obtained for an arbitrary Hartmann number. The total drag D on the sphere has been calculated, and the ratio D / D s determined as a function of the Hartmann number M , where D s is the Stokes drag. In particular ( D — D s )/ D s = 37/210 M 2 + O ( M 4 ) for small M and ( D — D s )/ Ds ~ 0·7205 M - 1 as M → ∞.

MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field

1980 ◽  
Vol 96 (2) ◽  
pp. 335-353 ◽  
Author(s):  
Richard J. Holroyd
Keyword(s):  
Magnetic Field ◽  
Experimental Study ◽  
Reynolds Number ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Mhd Flow ◽  
Magnetic Reynolds Number ◽  
Rectangular Duct ◽  
Mean Velocity ◽  
Side Walls

A theoretical and experimental study has been carried out on the flow of a liquid metal along a straight rectangular duct, whose pairs of opposite walls are highly conducting and insulating, situated in a planar non-uniform magnetic field parallel to the conducting walls. Magnitudes of the flux density and mean velocity are taken to be such that the Hartmann numberMand interaction parameterNhave very large values and the magnetic Reynolds number is extremely small.The theory qualitatively predicts the integral features of the flow, namely the distributions along the duct of the potential difference between the conducting walls and the pressure. The experimental results indicate that the velocity profile is severely distorted by regions of non-uniform magnetic field with fluid moving towards the conducting walls; even though these walls are very good conductors the flow behaves more like that in a non-conducting duct than that predicted for a duct with perfectly conducting side walls.

A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop

2000 ◽  
Vol 411 ◽  
pp. 325-350 ◽  
Author(s):  
SAEED MORTAZAVI ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Poiseuille Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Lateral Position ◽  
Physical Parameters ◽  
Computational Domain ◽  
Two Dimensional ◽  
Lateral Migration

The cross-stream migration of a deformable drop in two-dimensional Hagen–Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (< 1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For viscosity ratio 0.125 a drop moves toward the centre of the channel, while for ratio 1.0 it moves away from the centre until halted by wall repulsion. The rate of migration increases with the deformability of the drop. At higher Reynolds numbers (5–50), the drop either moves to an equilibrium lateral position about halfway between the centreline and the wall – according to the so-called Segre–Silberberg effect or it undergoes oscillatory motion. The steady-state position depends only weakly on the various physical parameters of the flow, but the length of the transient oscillations increases as the Reynolds number is raised, or the density of the drop is increased, or the viscosity of the drop is decreased. Once the Reynolds number is high enough, the oscillations appear to persist forever and no steady state is observed. The numerical results are in good agreement with experimental observations, especially for drops that reach a steady-state lateral position. Most of the simulations assume that the flow is two-dimensional. A few simulations of three-dimensional flows for a modest Reynolds number (Re = 10), and a small computational domain, confirm the behaviour seen in two dimensions. The equilibrium position of the three-dimensional drop is close to that predicted in the simulations of two-dimensional flow.

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 Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field

2015 ◽  
Vol 773 ◽  
pp. 154-177 ◽  
Author(s):  
Basile Gallet ◽  
Charles R. Doering
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Threshold Value ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Static Approximation ◽  
Long Time

We investigate the behaviour of flows, including turbulent flows, driven by a horizontal body force and subject to a vertical magnetic field, with the following question in mind: for a very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2-D, with no dependence along the vertical direction? We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number, $\mathit{Rm}\ll 1$: we prove that the flow becomes exactly 2-D asymptotically in time, regardless of the initial condition and provided that the interaction parameter $N$ is larger than a threshold value. We call this property absolute two-dimensionalization: the attractor of the system is necessarily a (possibly turbulent) 2-D flow. We then consider the full magnetohydrodynamic (MHD) equations and prove that, for low enough $\mathit{Rm}$ and large enough $N$, the flow becomes exactly 2-D in the long-time limit provided the initial vertically dependent perturbations are infinitesimal. We call this phenomenon linear two-dimensionalization: the (possibly turbulent) 2-D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3-D attractors may also exist and be attained for strong enough initial 3-D perturbations. These results shed some light on the existence of a dissipation anomaly for MHD flows subject to a strong external magnetic field.

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