Milko Kuilekov

Interface reconstruction between two conducting fluids applying genetic algorithms

In magnetic fluid dynamics, there appears the problem of reconstruction of free boundary between conducting fluids, e.g., in aluminum electrolysis cells. We have investigated how the interface between two fluids of different conductivity of a highly simplified model of an aluminum electrolysis cell could be reconstructed by means of external magnetic field measurements using a simple genetic algorithm.

Forward simulations for free boundary reconstruction in magnetic fluid dynamics

In many industrial applications of magnetic fluid dynamics it is important to control the motion of the surface of liquids. In aluminium electrolysis cells, large surface deformations of the molten aluminium are undesired, and it would be useful to have the possibility to recognize the surface deviation. This includes the problem of reconstructing a free boundary between the conducting fluids. We have investigated how the interface between two fluids of different conductivity assumed in a highly simplified model of an aluminium electrolysis cell could be reconstructed by means of external magnetic field measurements. Forward simulations of the magnetic field generated by the impressed current are done by applying the FEM software code FEMLAB. Several interface shapes which can be realized in experiments are investigated and a strategy for identifying the main interface characteristics using magnetic field measurements as an initial guess to the solution of the inverse problem is proposed.

Magnetic field tomography on two electrically conducting fluids

A cylindrical cell containing GaInSn alloy and aqueous solution of KOH, a highly simplified aluminium reduction cell, is constructed. A direct current is applied to the cylindrical cell to generate the magnetic field. In a range of amplitude and frequency of vertical vibration, a stable, non-axisymmetric wave pattern is produced, and the displacement of the oscillating interface is measured by a digital camcorder. The perturbation of the magnetic field caused by the non-axisymmetric interface is measured by fluxgate sensors and processed by fast Fourier transforms. The measurements are consistent with forward calculations, and have been exploited to reconstruct the deformed interface by solving an inverse problem so as to develop magnetic field tomography to reconstruct an unknown interface between two electrically conducting fluids.

Surface current reconstruction using magnetic field tomography

The identification of characteristics or shape reconstruction of boundary surfaces are inverse problems arising in industrial applications, e.g., in magnetic fluid dynamics. We have investigated the identification of the interface between two conducting fluids using multichannel magnetic field measurements (magnetic field tomography). We considered a highly simplified model of an aluminum electrolysis cell consisting of a cylinder containing two compartments with different conductivities. Numerical simulations using the finite element method (FEM) have been evaluated. Additionally, magnetic field measurements taken from an experimental setup of this cylindrical object have been used as a reference for comparison. We propose a new test problem for the evaluation of inverse methods which consists in the estimation of the interface shape characteristics based on the current density distribution in the vicinity of the deformed interface using magnetic field measurements.

Identification of dominant modes in the interface between two conducting fluids

There are several applications in magnetic fluid dynamics where it is important to know the behavior of separation surfaces between fluids. Our magnetic field tomography system enables to reconstruct interface shapes between two conducting fluids on the basis of magnetic field measurements. A simple direct searching strategy for an identification of dominant modes of the interface in a cylindrical two-fluid system is presented

Measurement of magnetic flux density on a rotating distorted electrolyte-metal interface

A novel experiment for characterization of liquid–solid interface deformation by measurement of magnetic flux density has been carried out. A single-axis fluxgate sensor is used to measure the distribution of radial- and z-components of magnetic field around a rotating cylindrical cell containing a solid copper cylinder with a sinusoidal surface and KOH solution above it. The signal from the magnetic sensor is collected by a data acquisition board and processed by fast Fourier transformation. The experimental results agree well with the theoretical predictions calculated by the finite element method, which reveals that the set-up is applicable to develop magnetic field tomography for reconstruction of interface deformation.

An improved technique for interface shape identification in magnetic fluid dynamics

Purpose – The interface between two conducting fluids in a magnetic fluid dynamics (MFD) problem was identified by means of external magnetic field measurements. Genetic algorithms (GA) were applied to solve the inverse problem.The principal component analysis (PCA) was used to speed up the process of interface reconstruction.Design/methodology/approach – With respect to the experimental results we have designed a general technique for mode identification and/or interface reconstruction. Two main procedures are available to solve the inverse problem, the full interface reconstruction and the principle component analysis (PCA) mode. In the case of full reconstruction, it can be decided whether an algorithm for fast identification of the dominant modes applying a FFT module should be performed or not. The full interface reconstruction applies stochastic optimization methods ((GA) or evolution strategies (ES)) for the estimation of the interface shape characteristics. The main goal of the PCA mode is to find...

Reconstruction of the Interface Between two Conducting Fluids with Modified Genetic Algorithms

In magnetic fluid dynamics appears the problem of reconstruction of free boundary between conducting fluids. The reconstruction problem of the interface between two conducting fluids with different conductivities using external magnetic field measurements in the case of a highly simplified model of an aluminium electrolysis cell has been investigated. In the paper, the comparison of two reconstruction procedures based on modified and simple genetic algorithms has been presented.

Comparison of semi‐analytical and FEM solutions in a certain magnetic fluid dynamics problem

Purpose – To provide a new semi‐analytical procedure which is much faster than FEM and for this reason can be applied in a reconstruction of an interface between two conducting fluids (magnetic fluid dynamics problem) by means of magnetic field tomography.Design/methodology/approach – Three approaches are compared: a simple analytical solution (AS1), a modified semi‐analytical solution (AS2), and the finite element method solution. The modified semi‐analytical approach takes into account an information about azimuthal spatial harmonics received from the Fourier analysis of magnetic flux density distributions calculated by FEM. AS1 and AS2 have been compared for different modes of the interface using FEM solution as a reference.Findings – It is shown that for small perturbations the AS2 in every case provides smaller errors than AS1 although for some modes (14,24) the quality of the solution is still not satisfactory.Originality/value – This paper describes a new technique for the analysis of electromagnet...