arXiv subjects

Oleg Zikanov

Publications and source records attributed to Oleg Zikanov.

At least 19 recordsLinked to original sources

arXiv2026

Oscillatory liquid-metal flow in a channel under rapidly decaying applied magnetic field

The channel flow of a liquid metal driven by a rapidly varying applied magnetic field is analyzed. The flow configuration, physical properties, and parameters correspond to a duct within a liquid-metal blanket of a nuclear fusion reactor under off-normal plasma conditions, such as plasma disruptions. The problem is solved numerically using a one-dimensional flow approximation. The longitudinal magnetic field, decaying at a typical rate on the order of 100 T/s, induces eddy currents that interact with a steady wall-normal magnetic field, generating the Lorentz force that drives the flow. Standing Alfvén waves are identified as the key mechanism controlling the liquid metal's response. These waves manifest as large-amplitude, gradually decaying oscillations of velocity, the induced magnetic field, and eddy currents. A parametric study predicts a severe response developing within the first few milliseconds of the event, with maximum flow velocities reaching several meters per second and Lorentz forces exceeding $10^9 \text{ N/m}^3$. Power-law approximations for the dependencies of the response characteristics on the flow parameters are developed. Finally, the effects of fluid compressibility and pressure waves are analyzed and found not to lead to a major modification of the flow evolution.

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arXiv2025

Inflection point instability in Hartmann channel flow with variable electric conductivity

The stability of a flow of an electrically conducting, incompressible fluid in a channel with an imposed uniform wall-normal magnetic field and electrically insulating walls is studied using linear stability analysis and direct numerical simulations. The novelty of the system, which differentiates it from the classical Hartmann channel flow, is that, as in some technological applications of liquid metals, the electric conductivity and viscosity of the fluid vary across the channel. This variation is found to have a strong influence on the stability characteristics of the flow. Specifically, a linear variation in electric conductivity significantly alters the base velocity profile, leading to pronounced asymmetry and the development of inflection points. When this transformation is sufficiently strong, the flow becomes linearly unstable at Reynolds numbers much lower than the threshold for the linear instability of the Hartmann channel flow. The instability exhibits distinct features: a large typical axial wavelength and the localization of perturbation growth in the channel core. The characteristics of this instability suggest a mechanism similar to the classical inviscid inflection-point instability of one-dimensional velocity profiles. The resulting transition to turbulence is demonstrated in direct numerical simulations.

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arXiv2025

Exploratory study of liquid metal response to rapid variation of applied magnetic field

Transient plasma events, such as plasma disruptions, are anticipated in the future magnetic-confinement nuclear fusion reactors. The events are accompanied by a rapid change in the magnetic field generated by the plasma current and, accordingly, induction of strong eddy currents and Lorentz forces within the reactor structure. This work targets processes within liquid-metal components of the reactor's breeding blankets. Order-of-magnitude analysis and {exploratory} numerical simulations are performed to understand the response of liquid metal to a rapidly changing magnetic field and to evaluate the accuracy of commonly used simplifying model assumptions. The response is found to consist of two stages: an initial brief stage ($\sim 1$ ms) characterized by a rapid increase in the induced currents, forces, and fluid velocity; and a subsequent stage, which is triggered by the growing velocity of the metal and marked by reversals of Lorentz force, and oscillations and decreases in the amplitude of the induced fields. The transition to the second stage sets the upper limit of the velocity ($\sim 0.5$ m/s in our tests), to which an initially quiescent metal can be accelerated during the event. The simulations indicate that many widely used model assumptions, such as the negligible role of Joule dissipation in the heat balance and the constancy of physical property coefficients, remain valid during the response. However, the assumption of liquid metal incompressibility is found to be questionable due to the potential significant effects of pressure waves.

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arXiv2024

Magnetoconvection in a Long Vertical Enclosure With Walls of Finite Electrical Conductivity

Magnetoconvection in a tall vertical box with vertical hot and cold walls, and an imposed steady uniform magnetic field perpendicular to the temperature gradient, is analyzed numerically. The geometry and the values of the non-dimensional parameters - the Prandtl number of 0.025, the Rayleigh number of $7.5 \times 10^5$, and the Hartmann number between 0 and 798 - match those of an earlier experiment. A parametric study of the effect of wall electric conductivity, across a wide range of conductance ratio values, on flow properties is performed. Two configurations of electric boundary conditions are explored. In one configuration, all walls have finite electric conductivity, while in the other, only the walls with constant temperature are electrically conducting. The flows are analyzed using their integral properties and distributions of velocity, temperature, and electric currents. It is found that, in general, the convection flow is suppressed by the magnetic field. However, this effect is strongly modified by the wall's electric conductivity and is markedly different for the two wall configurations. The associated changes in flow structure, rate of heat transfer, and flow's kinetic energy are revealed. It is also shown that the assumption of quasi-two-dimensionality may not be valid under some conditions, even at high Hartmann numbers.

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arXiv2021

Experimental study of submerged liquid metal jet in transverse magnetic field

A liquid metal flow in the form of a submerged round jet entering a square duct in the presence of a transverse magnetic field is studied experimentally. A range of high Reynolds and Hartmann numbers is considered. Flow velocity is measured using electric potential difference probes. A detailed study of the flow in the duct's cross-section about seven jet's diameters downstream of the inlet reveals the dynamics, which is unsteady and dominated by high-amplitude fluctuations resulting from instability of the jet. The flow structure and fluctuation properties are largely determined by the value of the Stuart number N. At moderate N, the mean velocity profile retains a central jet with three-dimensional perturbations increasingly suppressed by the magnetic field as N grows. At higher values of N, the flow becomes quasi-two-dimensional and acquires the form of an asymmetric macrovortex, with high-amplitude velocity fluctuations reemerging.

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arXiv2021

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

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 imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of 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.

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arXiv2020

Rayleigh-Bénard Convection in Strong Vertical Magnetic Field: Flow Structure and Verification of Numerical Method

Direct numerical simulations are performed to study turbulent Rayleigh-Bénard convection in a vertical cylindrical cavity with uniform axial magnetic field. Flows at high Hartmann and Rayleigh numbers are considered. The calculations reveal that, similarly to the behavior observed in Rayleigh-Bénard convection with strong rotation, flows at strong magnetic field develop a central vortex, while the heat transfer is suppressed.

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arXiv2020

Turbulent Rayleigh-Bénard convection in a strong vertical magnetic field

Direct numerical simulations are carried out to study flow structure and transport properties in turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number 0.025 and the Rayleigh and Hartmann numbers up to $10^9$ and 1400 are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by strong magnetic field. At the same time, their growth with the Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in the Rayleigh-Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. Detailed analysis of the spatial structure of the flows and its effect of global transport properties is reported.

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arXiv2019

Numerical simulation of rolling pad instability in cuboid liquid metal batteries

The rolling pad instability is caused by electromagnetic interactions in systems of horizontal layers with strongly different electric conductivities. We analyze the instability for a simplified model of a liquid metal battery (LMB), a promising device for large-scale stationary energy storage. Numerical simulations of the flow and the dynamics of electromagnetically coupled interfacial waves are performed using OpenFOAM. The work confirms the earlier conclusions that the instability is a significant factor affecting battery's operation. The critical role played by the ratio between the density differences across the two interfaces is elucidated. It is found that the ratio determines the stability characteristics and the type (symmetrically or antisymmetrically coupled) of dominant interfacial waves.

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arXiv2019

Decay of turbulence in a liquid metal duct flow with transverse magnetic field

Decay of honeycomb-generated turbulence in a duct with a static transverse magnetic field is studied via direct numerical simulations. The simulations follow the revealing experimental study of Sukoriansky et al. (1986), in particular the paradoxical observation of high-amplitude velocity fluctuations, which exist in the downstream portion of the flow when the strong transverse magnetic field is imposed in the entire duct including the honeycomb exit, but not in other configurations. It is shown that the fluctuations are caused by the large-scale quasi-two-dimensional structures forming in the flow at the initial stages of the decay and surviving the magnetic suppression. Statistical turbulence properties, such as the energy decay curves, two-point correlations and typical length scales are computed. The study demonstrates that turbulence decay in the presence of a magnetic field is a complex phenomenon critically depending on the state of the flow at the moment the field is introduced.

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arXiv2018

Instabilities in extreme magnetoconvection

Thermal convection in an electrically conducting fluid (for example, a liquid metal) in the presence of a static magnetic field is considered in this chapter. The focus is on the extreme states of the flow, in which both buoyancy and Lorentz forces are very strong. It is argued that the instabilities occurring in such flows are often of unique and counter-intuitive nature due to the action of the magnetic field, which suppresses conventional turbulence and gives preference to two-dimensional instability modes not appearing in more conventional convection systems. Tools of numerical analysis suitable for such flows are discussed.

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arXiv2018

Mixed convection in a downward flow in a vertical duct with strong transverse magnetic field

The downward flow in a vertical duct with one heated and three thermally insulated walls is analyzed numerically using the two-dimensional approximation valid in the asymptotic limit of an imposed strong transverse magnetic field. The work is motivated by the design of liquid metal blankets with poloidal ducts for future nuclear fusion reactors, in which the main component of the magnetic field is perpendicular to the flow direction and very strong heating is applied at the wall facing the reaction chamber. The flow is found to be steady-state or oscillating depending on the strengths of the heating and magnetic field. A parametric study of the instability leading to the oscillations is performed. It is found among other results that the flow is unstable and develops high-amplitude temperature oscillations at the conditions typical for a fusion reactor blanket.

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arXiv2017

Shallow water modeling of rolling pad instability in liquid metal batteries

Magnetohydrodynamically induced interface instability in liquid metal batteries is analyzed. The batteries are represented by a simplified system in the form of a rectangular cell, in which strong vertical electric current flows through three horizontal layers: the layer of a heavy metal at the bottom, the layer of a light metal at the top, and the layer of electrolyte in the middle. A new two-dimensional nonlinear model based on the conservative shallow water approximation is derived and utilized in a numerical study. It is found that in the case of small density difference between the electrolyte and one of the metals, the instability closely resembles the rolling pad instability observed earlier in the aluminum reduction cells. When the two electrolyte-metal density differences are comparable, the dynamics of unstable systems is more complex and characterized by interaction between two nearly symmetric or antisymmetric interfacial waves.

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arXiv2017

Subcritical convection in an internally heated layer

Thermal convection in a horizontal layer with uniform internal heating and stress-free constant-temperature boundaries is analyzed numerically. The work is motivated by the questions arising in development of liquid metal batteries, in which convection is induced by the Joule heating of electrolyte. It is demonstrated that three-dimensional convection cells exist at subcritical Rayleigh numbers.

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arXiv2015

Metal pad instabilities in liquid metal batteries

A mechanical analogy is used to analyze the interaction between the magnetic field, electric current and deformation of interfaces in liquid metal batteries. It is found that, during charging or discharging, a sufficiently large battery is prone to instabilities of two types. One is similar to the metal pad instability known for aluminum reduction cells. Another type is new. It is related to the destabilizing effect of the Lorentz force formed by the azimuthal magnetic field induced by the base current and the current perturbations caused by the local variations of the thickness of the electrolyte layer.

physics.flu-dyn↗

arXiv2015

Thermal convection in a liquid metal battery

Generation of thermal convection flow in the liquid metal battery, a device recently proposed as a promising solution for the problem of the short-term energy storage, is analyzed using a numerical model. It is found that convection caused by Joule heating of electrolyte during charging or discharging is virtually unavoidable. It exists in laboratory prototypes larger than a few cm in size and should become much stronger in larger-scale batteries. The phenomenon needs further investigation in view of its positive (enhanced mixing of reactants) and negative (loss of efficiency and possible disruption of operation due to the flow-induced deformation of the electrolyte layer) effects.

physics.flu-dyn↗

arXiv2009

Energy dissipation rates in low-$\Re_m$ MHD turbulence with mean shear: Results for channel flow with spanwise field

We examine the changes in kinetic energy dissipation of a turbulent channel flow caused by a spanwise magnetic field. The numerical study is based on our simulation data from [Krasnov, Zikanov, Schumacher, Boeck, Phys. Fluids 20, 095105 (2008)] obtained by direct and large eddy simulations. We find that the Joule dissipation can exceed the viscous dissipation in the weakly dissipative bulk region, but remains comparatively small in the turbulence-generating near-wall region.

physics.flu-dyn↗

arXiv2008

Large-scale intermittency of liquid-metal channel flow in a magnetic field

We predict a novel flow regime in liquid metals under the influence of a magnetic field. It is characterised by long periods of nearly steady, two-dimensional flow interrupted by violent three-dimensional bursts. Our prediction has been obtained from direct numerical simulations in a channel geometry at low magnetic Reynolds number and translates into physical parameters which are amenable to experimental verification under laboratory conditions. The new regime occurs in a wide range of parameters and may have implications for metallurgical applications.

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