scholarly journals An analytical solution to electromagnetically coupled duct flow in MHD

2015 ◽  
Vol 771 ◽  
pp. 595-623 ◽  
Author(s):  
Michael J. Bluck ◽  
Michael J. Wolfendale
Keyword(s):  
Magnetic Field ◽  
Analytical Solution ◽  
Applied Magnetic Field ◽  
Homogeneous Solution ◽  
Duct Flow ◽  
Mean Flow ◽  
Validation Data ◽  
Electrically Conducting ◽  
Fusion Applications ◽  
Fusion Blankets

The flow of an electrically conducting fluid in an array of square ducts, separated by arbitrary thickness conducting walls, subject to an applied magnetic field is studied. The analytical solution presented here is valid for thick walls and is based on the homogeneous solution obtained by Shercliff (Math. Proc. Camb. Phil. Soc., vol. 49 (01), 1953, pp. 136–144). Arrangements of ducts arise in a number of applications, most notably in fusion blankets, where liquid metal is used both as coolant and for tritium generation purposes. Analytical solutions, such as those presented here, provide insight into the physics and important benchmarking and validation data for computational magnetohydrodynamics (MHD), as well as providing approximate flow parameters for 1D systems codes. It is well known that arrays of such ducts with conducting walls exhibit varying degrees of coupling, significantly affecting the flow. An important practical example is the so-called Madarame problem (Madarame et al., Fusion Technol., vol. 8, 1985, pp. 264–269). In this work analytical results are derived for the relevant hydrodynamic and magnetic parameters for a single duct with thick walls analogous to the Hunt II case. These results are then extended to an array of such ducts stacked in the direction of the applied magnetic field. It is seen that there is a significant coupling affect, resulting in modifications to pressure drop and velocity profile. In certain circumstances, counter-current flow can occur as a result of the MHD effects, even to the point where the mean flow is reversed. Such phenomena are likely to have significant detrimental effects on both heat and mass transfer in fusion applications. The dependence of this coupling on parameters such as conductivities, wall thickness and Hartmann number is studied.

scholarly journals Generation of Reverse Meniscus Flow by Applying An Electromagnetic Brake

2021 ◽  
Author(s):  
Alexander Vakhrushev ◽  
Abdellah Kharicha ◽  
Ebrahim Karimi-Sibaki ◽  
Menghuai Wu ◽  
Andreas Ludwig ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Applied Magnetic Field ◽  
Numerical Study ◽  
Flow Direction ◽  
Experimental Studies ◽  
Submerged Entry Nozzle ◽  
Mean Flow ◽  
Slab Caster ◽  
The Mean

AbstractA numerical study is presented that deals with the flow in the mold of a continuous slab caster under the influence of a DC magnetic field (electromagnetic brakes (EMBrs)). The arrangement and geometry investigated here is based on a series of previous experimental studies carried out at the mini-LIMMCAST facility at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). The magnetic field models a ruler-type EMBr and is installed in the region of the ports of the submerged entry nozzle (SEN). The current article considers magnet field strengths up to 441 mT, corresponding to a Hartmann number of about 600, and takes the electrical conductivity of the solidified shell into account. The numerical model of the turbulent flow under the applied magnetic field is implemented using the open-source CFD package OpenFOAM®. Our numerical results reveal that a growing magnitude of the applied magnetic field may cause a reversal of the flow direction at the meniscus surface, which is related the formation of a “multiroll” flow pattern in the mold. This phenomenon can be explained as a classical magnetohydrodynamics (MHD) effect: (1) the closure of the induced electric current results not primarily in a braking Lorentz force inside the jet but in an acceleration in regions of previously weak velocities, which initiates the formation of an opposite vortex (OV) close to the mean jet; (2) this vortex develops in size at the expense of the main vortex until it reaches the meniscus surface, where it becomes clearly visible. We also show that an acceleration of the meniscus flow must be expected when the applied magnetic field is smaller than a critical value. This acceleration is due to the transfer of kinetic energy from smaller turbulent structures into the mean flow. A further increase in the EMBr intensity leads to the expected damping of the mean flow and, consequently, to a reduction in the size of the upper roll. These investigations show that the Lorentz force cannot be reduced to a simple damping effect; depending on the field strength, its action is found to be topologically complex.

scholarly journals Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers

2021 ◽  
Vol 931 ◽  
Author(s):  
R. Akhmedagaev ◽  
O. Zikanov ◽  
Y. Listratov
Keyword(s):  
Magnetic Field ◽  
Magnetic Field Effect ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Duct Flow ◽  
Mean Flow ◽  
Horizontal Magnetic Field ◽  
Nuclear Fusion Reactor ◽  
Dimensional Approximation ◽  
Very High

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and an imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of a very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behaviour in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann numbers up to $10^4$ and Grashof numbers up to $10^{10}$ ). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. It is also demonstrated that quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.

scholarly journals Modified boundary integral method for pressure driven MHD duct flow

1989 ◽  
Vol 12 (1) ◽  
pp. 159-174
Author(s):  
B. D. Aggarwala ◽  
P. D. Ariel
Keyword(s):  
Magnetic Field ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Computationally Efficient ◽  
Electrically Conducting ◽  
Flow Through ◽  
The Magnetic Field

In this paper, we investigate the flow of a viscous, Incompressible, electrically conducting fluid through a rectangular duct in the presence of a magnetic field, when one of the boundaries perpedicular to the magnetic field is partly conducting and partly Insulating, by a modified Boundary Integral Method.Three problems are considered (i) flow through an infinite channel, (ii) flow through a rectangular duct when the conducting part is symmetrically situated, and (iii) flow through a rectangular duct when the conducting part is arbltrarily positioned.Such problems have been studied before by asymptotic means for large values of M, the Hartmann number. Hoverer, the present modification of the Boundary Integral Method renders the problem computationally efficient and provides a reliable numerical solution for all values of M. For large M, our coputation time decreases significantly.

The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

1971 ◽  
Vol 69 (2) ◽  
pp. 337-351 ◽  
Author(s):  
D. J. Temperley ◽  
L. Todd
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Classical Model ◽  
Critical Discussion ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Wall Conductivity ◽  
Expansion Procedure

AbstractLaminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

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.

Semiconductor Crystal Growth by the Vertical Bridgman Process With Transverse Rotating Magnetic Fields

2006 ◽  
Vol 129 (2) ◽  
pp. 241-243 ◽  
Author(s):  
X. Wang ◽  
N. Ma
Keyword(s):  
Magnetic Field ◽  
Crystal Growth ◽  
Magnetic Fields ◽  
Applied Magnetic Field ◽  
Rotating Magnetic Field ◽  
Semiconductor Crystal ◽  
Rotating Magnetic Fields ◽  
Electrically Conducting ◽  
Vertical Bridgman ◽  
Bridgman Process

During the vertical Bridgman process, a single semiconductor crystal is grown by the solidification of an initially molten semiconductor contained in an ampoule. The motion of the electrically conducting molten semiconductor can be controlled with an externally applied magnetic field. This paper treats the flow of a molten semiconductor and the dopant transport during the vertical Bridgman process with a periodic transverse or rotating magnetic field. The frequency of the externally applied magnetic field is sufficiently low that this field penetrates throughout the molten semiconductor. Dopant distributions in the crystal are presented.

A note on magnetohydrodynamic duct flow

1969 ◽  
Vol 66 (3) ◽  
pp. 655-662 ◽  
Author(s):  
G. F. Butler
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Conducting Fluid ◽  
Thin Wall ◽  
Duct Flow ◽  
Electrically Conducting ◽  
Thin Walls ◽  
Electrically Conducting Fluid

AbstractThis paper is concerned with the problem of the flow of an incompressible electrically conducting fluid along a rectangular duet under a transverse magnetic field. The case in which the walls perpendicular to the field are perfectly conducting and those parallel to the field are non-conducting has been considered by Hunt (1), who derives the solution in two ways; as the limiting cases of the flows with (a) non-conducting walls parallel and thin walls of arbitrary conductivity perpendicular to the field, and (b) thin walls of arbitrary conductivity parallel and perfectly conducting walls perpendicular to the field. We show that these two limiting solutions derived by Hunt are in fact equivalent. In addition, we extend the solution of case (b) above by removing the thin wall restriction.

Generation of magnetic fields by convection

1973 ◽  
Vol 57 (3) ◽  
pp. 529-544 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Magnetic Field ◽  
Longitudinal Direction ◽  
Two Dimensional ◽  
Mean Flow ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Magnetic Prandtl Number ◽  
Hydromagnetic Dynamo ◽  
Convection Rolls ◽  
The Magnetic Field

The nonlinear hydromagnetic dynamo problem is investigated for the case of convection in a layer of an electrically conducting fluid heated from below. It is shown that two-dimensional convection rolls in conjunction with a longitudinal mean flow are capable of amplifying a magnetic field in the form of a wave propagating in the longitudinal direction. The action of the Lorentz forces causes a reduction of the amplitude of convection with the consequence that the energy of the magnetic field cannot grow beyond an equilibrium value which is determined as a function of the parameters of the problem. The analysis is based on an expansion in powers of the longitudinal wavenumber β of the magnetic field and applies in the case of large values of the magnetic Prandtl number.

Magnetohydrodynamic Squeeze Films

1964 ◽  
Vol 86 (3) ◽  
pp. 441-444 ◽  
Author(s):  
D. C. Kuzma
Keyword(s):  
Magnetic Field ◽  
Film Thickness ◽  
Applied Magnetic Field ◽  
Conducting Fluid ◽  
Squeeze Film ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Fluid Film Thickness

An analysis of hydrodynamic squeeze films is presented for the case of an electrically conducting fluid in the presence of a magnetic field. Circular plates and infinitely long rectangular plates are considered with a uniformly applied magnetic field. The relationships between fluid-film thickness and time are determined analytically and compared with the ordinary hydrostatic squeeze films. It is shown that the application of a magnetic field improves the squeeze-film action.

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