Three-Dimensional Flow in a Driven Cavity Subjected to an External Magnetic Field

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
K. Jin ◽  
S. P. Vanka ◽  
B. G. Thomas
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Graphics Processing Unit ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Processing Unit ◽  
Field Equations ◽  
Driven Cavity ◽  
Electrically Conducting ◽  
The Magnetic Field

In this paper, we study the three-dimensional (3D) flow of an electrically conducting fluid in a cubic cavity with the top wall moving and subjected to an external magnetic field. The governing flow and electromagnetic field equations are integrated by a second-order space and time accurate numerical scheme, implemented on a graphics processing unit (GPU) with high parallel efficiency. Solutions for several Reynolds and Stuart numbers have been obtained on sufficiently fine grids to achieve grid independent solutions. As expected, the magnetic field significantly influences the circulation in the cavity and modifies the shape and locations of the primary and secondary eddies. The observed flow patterns are illustrated graphically as well as through selected line plots and tabulated data. With increasing magnetic field strength, the center of the primary eddy is seen to shift to the top right corner. Further, situations where the flow is unsteady in the absence of the magnetic field have become steady after a certain value of the magnetic interaction parameter.

scholarly journals Three-Dimensional Magnetic Fluid Boundary Layer Flow Over a Linearly Stretching Sheet

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
E. E. Tzirtzilakis ◽  
N. G. Kafoussias
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Magnetic Fluid ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Layer Flow ◽  
The Magnetic Field

The three-dimensional laminar and steady boundary layer flow of an electrically nonconducting and incompressible magnetic fluid, with low Curie temperature and moderate saturation magnetization, over an elastic stretching sheet, is numerically studied. The fluid is subject to the magnetic field generated by an infinitely long, straight wire, carrying an electric current. The magnetic fluid far from the surface is at rest and at temperature greater of that of the sheet. It is also assumed that the magnetization of the fluid varies with the magnetic field strength H and the temperature T. The numerical solution of the coupled and nonlinear system of ordinary differential equations, resulting after the introduction of appropriate nondimensional variables, with its boundary conditions, describing the problem under consideration, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the case of a representative water-based magnetic fluid and for specific values of the dimensionless parameters entering into the problem, and the obtained results are presented graphically for these values of the parameters. The analysis of these results showed that there is an interaction between the motions of the fluid, which are induced by the stretching surface and by the action of the magnetic field, and the flow field is noticeably affected by the variations in the magnetic interaction parameter β. The important results of the present analysis are summarized in Sec. 6.

Transition from two-dimensional to three-dimensional magnetohydrodynamic turbulence

2007 ◽  
Vol 579 ◽  
pp. 383-412 ◽  
Author(s):  
ANDRÉ THESS ◽  
OLEG ZIKANOV
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Vortex Sheet ◽  
Triaxial Ellipsoid ◽  
Two Dimensional ◽  
Vortex Sheets ◽  
Mhd Flows ◽  
Open Question ◽  
The Magnetic Field

We report a theoretical investigation of the robustness of two-dimensional inviscid magnetohydrodynamic (MHD) flows at low magnetic Reynolds numbers with respect to three-dimensional perturbations. We use a combination of linear stability analysis and direct numerical simulations to analyse three problems, namely the flow in the interior of a triaxial ellipsoid, and two unbounded flows: a vortex with elliptical streamlines and a vortex sheet parallel to the magnetic field. The flow in a triaxial ellipsoid is found to present an exact analytical model which demonstrates both the existence of inviscid unstable three-dimensional modes and the stabilizing role of the magnetic field. The nonlinear evolution of the flow is characterized by intermittency typical of other MHD flows with long periods of nearly two-dimensional behaviour interrupted by violent three-dimensional transients triggered by the instability. We demonstrate, using the second model, that motion with elliptical streamlines perpendicular to the magnetic field becomes unstable with respect to the elliptical instability once the magnetic interaction parameter falls below a critical magnitude whose value tends to infinity as the eccentricity of the streamlines increases. Furthermore, the third model indicates that vortex sheets parallel to the magnetic field, which are unstable for any velocity and any magnetic field, emit eddies with vorticity perpendicular to the magnetic field. Whether the investigated instabilities persist in the presence of small but finite viscosity, in which case two-dimensional turbulence would represent a singular state of MHD flows, remains an open question.

scholarly journals The effect of an external magnetic field on the entropy generation in three-dimensional natural convection

2010 ◽  
Vol 14 (2) ◽  
pp. 341-352 ◽  
Author(s):  
Lioua Kolsi ◽  
Awatef Abidi ◽  
Naceur Borjini ◽  
Ben Aïssia
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
External Magnetic Field ◽  
Liquid Metal ◽  
Entropy Generation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Laminar Natural Convection ◽  
The Magnetic Field

A 3-D original numerical study of entropy generation in the case of liquid metal laminar natural convection in a differentially heated cubic cavity and in the presence of an external magnetic field orthogonal to the isothermal walls is carried out. The effect of this field on the various types of irreversibilities is analyzed. It was observed that in the presence of a magnetic field the generated entropy is distributed on the entire cavity and that the magnetic field limits the 3-D character of the distribution of the generated entropy.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

Characterization of the flow past a truncated square cylinder in a duct under a spanwise magnetic field

2011 ◽  
Vol 691 ◽  
pp. 341-367 ◽  
Author(s):  
Vincent Dousset ◽  
Alban Pothérat
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Homogeneous Magnetic Field ◽  
Steady Flows ◽  
Square Cylinder ◽  
Electrically Conducting ◽  
Truncated Cylinder ◽  
The Magnetic Field

AbstractWe study the flow of an electrically conducting fluid past a truncated square cylinder in a rectangular duct under the influence of an externally applied homogeneous magnetic field oriented along the cylinder axis. Our aim is to bridge the gap between the non-magnetic regime, where we previously found a complex set of three-dimensional recirculations behind the cylinder (Dousset & Pothérat, J. Fluid Mech., vol. 653, 2010, pp. 519–536) and the asymptotic regime of dominating Lorentz force analysed by Hunt & Ludford (J. Fluid. Mech., vol. 33, 1968, pp. 693–714). The latter regime is characterized by a remarkable structure known as Hunt’s wake in the magnetohydrodynamics community, where the flow is deflected on either side of a stagnant zone, right above the truncated cylinder as if the latter would span the full height of the duct. In steady flows dominated by the Lorentz force, with negligible inertia, we provide the first numerical flow visualization of Hunt’s wake. In regimes of finite inertia, a thorough topological analysis of the steady flow regimes reveals how the Lorentz force gradually reorganizes the flow structures in the hydrodynamic wake of the cylinder as the Hartmann number $\mathit{Ha}$ (which gives a non-dimensional measure of the magnetic field) is increased. The nature of the vortex shedding follows from this rearrangement of the steady structures by the magnetic field. As $\mathit{Ha}$ is increased, we observe that the vortex street changes from a strongly symmetric one to the alternate procession of counter-rotating vortices typical of the non-truncated cylinder wakes.

Particle Transport and Deposition in a Turbulent Square Duct Flow With an Imposed Magnetic Field

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Rui Liu ◽  
Surya P. Vanka ◽  
Brian G. Thomas
Keyword(s):  
Magnetic Field ◽  
Particle Transport ◽  
Graphics Processing Unit ◽  
Solution Procedure ◽  
Mhd Equations ◽  
Navier Stokes ◽  
Processing Unit ◽  
Duct Flow ◽  
Square Duct ◽  
The Magnetic Field

In this paper, we study particle transport and deposition in a turbulent square duct flow with an imposed magnetic field using direct numerical simulations (DNS) of the continuous flow and Lagrangian tracking of particles. The magnetic field and the velocity induce a current and the interaction of this current with the magnetic field generates a Lorentz force that brakes the flow and modifies the flow structure. A second-order accurate finite volume method is used to integrate the coupled Navier–Stokes and magnetohydrodynamic (MHD) equations and the solution procedure is implemented on a graphics processing unit (GPU). Magnetically nonconducting particles of different Stokes numbers are continuously injected at random locations in the inlet cross section of the duct and their rates of deposition on the duct walls are studied with and without a magnetic field. Because of the modified instantaneous turbulent flow structures as a result of the magnetic field, the deposition rates and patterns on the walls perpendicular to the magnetic field are lower than those on the walls parallel to the magnetic field.

Modelling of a plasma column sustained by a travelling circularly polarized electromagnetic wave (m = 1 mode) in the presence of a constant axial magnetic field

1992 ◽  
Vol 48 (1) ◽  
pp. 37-57 ◽  
Author(s):  
E. Benova ◽  
P. Staikov ◽  
I. Zhelyazkov
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
External Magnetic Field ◽  
Plasma Column ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Wave Structure ◽  
Gas Discharge ◽  
Surface Mode ◽  
The Magnetic Field

We present a set of equations modelling a low-pressure plasma column sustained by a travelling electromagnetic wave in the dipolar mode in the presence of a constant external magnetic field. It is shown that, from a practical point of view, only the m = 1 mode (the right-hand-polarized wave) can sustain plasma columns in a wide region of gas-discharge conditions: plasma radius R, wave frequency ωo, magnetic field Bo and low pressures, irrespective of the nature of the gas. We have examined two gas-discharge regimes: freefall/diffusion and recombination respectively. For a given gas-discharge regime the axial column structure and wave-field characteristics are specified by two numerical parameters: σ = ωR/c and ω = ωc/ω, where c is the speed of light and ωc the electron-cyclotron frequency. The main result of our study is that the magnetic field-makes it possible to sustain a plasma column for values of σ smaller than σcr = 0.3726, below which, in the absence of a magnetic field, the dipolar wave cannot produce a plasma. Moreover, at a fixed wave power, the magnetic field – in contrast with the case of plasma columns sustained by azimuthally symmetric waves – increases the plasma density and its axial gradient. The limit of an infinite external magnetic field (Ω → ∞) is also considered. A three-dimensional wave structure is obtained, and it indicates that the wave can be a generalized surface mode, a pure surface or a pseudosurface one.

scholarly journals Magnetohydrodynamic entry flow for a plane channel in an axial magnetic field

1977 ◽  
Vol 80 (2) ◽  
pp. 209-221 ◽  
Author(s):  
Gerald P. D'Arcy ◽  
Philip S. Schmidt
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Plane Channel ◽  
Magnetic Interaction ◽  
Wall Region ◽  
Mean Flow ◽  
Entry Length ◽  
Electrically Conducting ◽  
Lorentz Forces ◽  
The Magnetic Field

An integral solution is described for flow of an electrically conducting fluid in a plane channel in a magnetic field which is aligned with the direction of the mean flow. It is shown that the presence of the magnetic field retards the development of the velocity profile by producing Lorentz forces which oppose the movement of fluid from the viscous wall region to the core. Solutions are presented for the entry length as a function of the magnetic interaction parameter. Solutions are also given for the dependence of the frictional component of the pressure drop on the magnetic field strength. The transverse pressure gradient produced by Lorentz forces is discussed for a typical case.

scholarly journals Path integrals for mean-field equations in nonlinear dynamos

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
Dmitry Sokoloff ◽  
Nobumitsu Yokoi
Keyword(s):  
Magnetic Field ◽  
Path Integrals ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean ◽  
Path Integral Method ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Mean-field dynamo equations are addressed with the aid of the path integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener integrals taken over all the trajectories of the fluid particles. The form of the equations is just the same as the conventional mean-field equations, but here the equations are derived with the velocity field realisation affected by the force exerted by the magnetic field. In this sense, we derive nonlinear dynamo equations.

Effect of strength and direction of external magnetic field on dynamics of vortices in a square lid-driven cavity flow

2021 ◽  
pp. 095440892110059
Author(s):  
Amin Hadidi
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Vortex Formation ◽  
Cavity Flow ◽  
Bottom Surface ◽  
Field Equations ◽  
Driven Cavity ◽  
Driven Cavity Flow ◽  
The Magnetic Field

In this study, the effect of magnetic field strength and its direction are considered on square lid-driven cavity flow. The whole range of applicable magnetic field strength which is used in practice up to now (0 to 10 Tesla) is accomplished in this research. The governing equations, including non-linear conservative equations of continuity, momentum and magnetic field equations are solved numerically. Continuity and momentum equations are solved by the finite volume method using SIMPLE algorithm, where the finite difference method is used in the magnetic field equation solving. In this research the effect of magnetic field on the velocity distribution, streamlines and vortex flow show that the vortices of the cavity shrink (decreases) up to 0.01 T where the uniform and vertical magnetic field applied from the bottom surface of the square cavity. For the magnetic field of 0.01 T, vortices in the cavity flow disappear. Higher values of the magnetic field create larger vortices. It was also concluded that the magnetic field has a strong effect on vortex formation, its size and location; therefore it can be used to control the vortex dynamics in a contactless way.

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