Reconstruction of the velocity distribution in conducting melts from induced magnetic field measurements

Abstract

A possibility to reconstruct the velocity field in a conducting melt without using tracer particles or any mechanical contact to the melt is presented. To recover the flow distribution the liquid under study is placed in an external magnetic field and the induced magnetic field due to the currents appearing in such a liquid is measured. The problem of velocity field reconstruction from these measurement data is closely related to inverse problems of potential theory. It is shown that in contrast to the latter problem the reconstruction of the velocity field can be performed uniquely if there exists a possibility to measure the induced field for different applied field configurations. A stable solution of the corresponding integral equation (arising from a Poisson equation for the induced magnetic field), which is known as an ill-conditioned problem, is obtained by means of the method of singular value analysis. Demonstration results for the case of a two-dimensional flow pattern in an infinitely long pipe are presented.