Fast Reconstruction Algorithm for Contactless Inductive Flow Tomography

The contactless inductive flow tomography is a measurement technique for the determination of the flow structure of an electrically conducting liquid. The procedure is based on the measurement of the magnetic field and can potentially be applied for visualisation and online-monitoring of industrial processes as, for example, continuous steel casting or the production of mono-crystalline silicon using the Czochralski crystal growth method. With the aid of the measured field values, the velocity field is reconstructed by solving a linear inverse problem that is described by a system of coupled integral equations. The frame rate of the field measurement is typically in the order of one frame per second, whereas the inversion of the integral equations usually takes about twenty times as long, since a regularisation parameter needs to be determined for each reconstruction. In order to reduce this discrepancy, a new algorithm is introduced in this article. The algorithm relies on the pre-computation of inverted matrices, so that the inversion can be determined solely by performing matrix-vector products. This technique reduces the time required for the inversion process at each reconstruction to same length of time a measurement cycle takes, i.e. about one second. The efficiency of the method will be demonstrated using a modified Rayleigh-Bénard experiment with liquid metal at room temperature.