  The three-dimensional velocity field of a propeller driven liquid metal flow
is reconstructed by a contactless inductive flow tomography (CIFT). The
underlying theory is presented within the framework of an integral equation
system that governs the magnetic field distribution in a moving electrically
conducting fluid. For small magnetic Reynolds numbers this integral equation
system can be cast into a linear inverse problem for the determination of the
velocity field from externally measured magnetic fields. A robust
reconstruction of the large scale velocity field is already achieved by
applying the external magnetic field alternately in two orthogonal directions
and measuring the corresponding sets of induced magnetic fields. Kelvin's
theorem is exploited to regularize the resulting velocity field by using the
kinetic energy of the flow as a regularizing functional. The results of the new
technique are shown to be in satisfactory agreement with ultrasonic
measurements.
