In the world of electromagnetism, changing magnetic fields are generated by alternating electric currents, which result in induced electric current in conducting materials. In some situations the induced current is an undesirable product which generates heats and implies a loss of energy.
Atkins encountered a problem of this nature on an oil pipeline when two adjacent copper tubes carrying deionised water were energised with alternative currents (AC). IDAC was contracted to evaluate the induced current density and the joule heating in the pipe using ANSYS EMAG.
A simple two dimensional (2D) geometry was prepared from the drawing. Apart from the main steel pipe, the two copper pipes and the lamination, the geometry also included the surrounding air and the fluids within the pipes, which were assumed to have properties of air. The geometry was meshed using 2D axisymmetric, higher order quadrilateral elements. Infinite boundary elements were generated around the domain to represent far field effects.
The mesh on the surface of the pipes was refined to resolve the high current density and heating due to skin effects. Nonlinear BH curves were specified for the lamination material and the steel pipe.
AC currents with magnitudes of 2,107A and 2,550A at 2,040Hz were applied to the two copper pipes. A harmonic analysis was performed to give solutions expressed in real (in phase) and imaginary (out of phase) parts.
The redistribution of current in the current carrying copper pipes and the induced eddy current were evident in the contour plot of total current density.
The resulting eddy current or Joule heating (RMS value) along the pipe at a depth of 0.0978mm was plotted in a graph. The graph of joule heating through the thickness of the main steel showed the heating near the surface, rapidly decreasing below the skin depth.
The study carried by IDAC enabled Atkins to quickly evaluate the significant eddy current and joule heating in the main steel pipe, without resorting to cumbersome and complex instrumentation. The skin depth was found to be very shallow, around 0.1mm, which would again have caused difficulty if measured directly. The skin effects however were effectively and accurately depicted with the refined mesh at the surface of the pipe.