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.

Two-dimensional oscillation of convection roll in a finite liquid metal layer under a horizontal magnetic field

2021 ◽  
Vol 911 ◽  
Author(s):  
Y. Tasaka ◽  
T. Yanagisawa ◽  
K. Fujita ◽  
T. Miyagoshi ◽  
A. Sakuraba
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Layer ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Convection Roll

Abstract

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

scholarly journals Linear and Nonlinear Convection with an Aligned Magnetic Field

1990 ◽  
Vol 142 ◽  
pp. 135-136
Author(s):  
N. Rudraiah ◽  
I S Shivakumara ◽  
P Geetavani
Keyword(s):  
Magnetic Field ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Nonlinear Convection ◽  
Linear And Nonlinear ◽  
Horizontal Fluid Layer ◽  
Aligned Magnetic Field

The effect of horizontal magnetic field on the onset of three-dimensional convection in a horizontal fluid layer is studied. It is found that the two-dimensional solutions are unstable to three-dimensional disturbances. A detailed bifurcation study is reported.

Rayleigh–Bénard convection in liquid metal layers under the influence of a horizontal magnetic field

2002 ◽  
Vol 453 ◽  
pp. 345-369 ◽  
Author(s):  
ULRICH BURR ◽  
ULRICH MÜLLER
Keyword(s):  
Magnetic Field ◽  
Heat Transport ◽  
Convective Heat ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Horizontal Magnetic Field ◽  
Two Dimensional Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

This article presents an analytical and experimental study of magnetohydrodynamic Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103< Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.When a horizontal magnetic field is imposed on a heated liquid metal layer, the electromagnetic forces give rise to a transition of the three-dimensional convective roll pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls become more and more aligned with the magnetic field. A linear stability analysis based on two-dimensional model equations shows that the critical Rayleigh number for the onset of convection of quasi-two-dimensional flow is shifted to significantly higher values due to Hartmann braking at walls perpendicular to the magnetic field. This finding is experimentally confirmed by measured Nusselt numbers. Moreover, the experiments show that the convective heat transport at supercritical conditions is clearly diminished. Adjacent to the onset of convection there is a significant region of stationary convection with significant convective heat transfer before the flow proceeds to time-dependent convection. However, in spite of the Joule dissipation effect there is a certain range of magnetic field intensities where an enhanced heat transfer is observed. Estimates of the local isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport is accompanied by the formation of strong non-isotropic time-dependent flow in the form of large-scale convective rolls aligned with the magnetic field which exhibit a simpler temporal structure compared to ordinary hydrodynamic flow and which are very effective for the convective heat transport.

scholarly journals Transport and instability in driven two-dimensional magnetohydrodynamic flows

2016 ◽  
Vol 799 ◽  
pp. 541-578 ◽  
Author(s):  
Sam Durston ◽  
Andrew D. Gilbert
Keyword(s):  
Magnetic Field ◽  
Time Scale ◽  
Large Scale ◽  
Body Force ◽  
Passive Scalar ◽  
Fast Time ◽  
Two Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Background Shear

This paper concerns the generation of large-scale flows in forced two-dimensional systems. A Kolmogorov flow with a sinusoidal profile in one direction (driven by a body force) is known to become unstable to a large-scale flow in the perpendicular direction at a critical Reynolds number. This can occur in the presence of a ${\it\beta}$-effect and has important implications for flows observed in geophysical and astrophysical systems. It has recently been termed ‘zonostrophic instability’ and studied in a variety of settings, both numerically and analytically. The goal of the present paper is to determine the effect of magnetic field on such instabilities using the quasi-linear approximation, in which the full fluid system is decoupled into a mean flow and waves of one scale. The waves are driven externally by a given random body force and move on a fast time scale, while their stress on the mean flow causes this to evolve on a slow time scale. Spatial scale separation between waves and mean flow is also assumed, to allow analytical progress. The paper first discusses purely hydrodynamic transport of vorticity including zonostrophic instability, the effect of uniform background shear and calculation of equilibrium profiles in which the effective viscosity varies spatially, through the mean flow. After brief consideration of passive scalar transport or equivalently kinematic magnetic field evolution, the paper then proceeds to study the full magnetohydrodynamic system and to determine effective diffusivities and other transport coefficients using a mixture of analytical and numerical methods. This leads to results on the effect of magnetic field, background shear and ${\it\beta}$-effect on zonostrophic instability and magnetically driven instabilities.

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.

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