A New Mathematical Model for the Performance of Axial Magnetic Filters

H K Collan,O E Toikka,M A Kokkala

doi:10.1155/1984/48016

H K Collan, O E Toikka + Show 1 more

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https://doi.org/10.1155/1984/48016

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Abstract

A mathematical model to describe the macroscopic behaviour of an axial magnetic filter is developed. The model takes into account the long range of absorption forces. Partial mixing of the particles in the fluid is included by introducing the concept of “mixing length”. Behaviour of an axial filter under different conditions is numerically simulated. Experiments with colloidal ferrite particles indicate that for an axial filter composed of 12 μm steel wires with a packing factor of 4.8% the mixing length is of the order of 4 mm.

Highlights

Magnetic filters are divided into longitudinal, transverse and axial filters accordin@ to the mutual orientation of the fibers, the flow velocity vo’ and the magnetic field Bo All the filters have Bo perpendicular to the fibres
An axial filter is rather different, because the flow velocity is parallel to the fibers
In an axial filter the particles travel along the fibres, interacting with it all the time they are inside the filter

Summary

INTRODUCTION

Magnetic filters are divided into longitudinal, transverse and axial filters accordin@ to the mutual orientation of the fibers, the flow velocity vo’ and the magnetic field Bo All the filters have Bo perpendicular to the fibres. In an axial filter the particles travel along the fibres, interacting with it all the time they are inside the filter We call xra the "mixing length", because it is physically reasonable to assume that inside the filter the range of the absorption phenomenon is longitudinally limited by a gradual mixing of particles in the fluid. Fig. depicts the calculated concentration of solids, C(x)/Cin inside an axial filter at time T --O, as a function of the distance x from the inlet. The measured saturation concentrations Cs were found to be about three times those measured for longitudinal filters made of the same fibers An explanation for this might be the mechanical instabilities of the deposition of particles onto the fibers when the flow is perpendicular to the fibers. The result of the fit, x m 4 ram, is physically reasonable

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A CKNOWLE DGEMENT