This work is focused on the 3D simulation of CP systems for ships. The paper is divided into two sections, the first applies detailed representation of the ICCP circuit and geometry of the propellers in order to better predict the actual performance of the individual anodes and therefore improve the accuracy of the Underwater Electric Potential (UEP) and the Corrosion Related Magnetic (CRM) field. The second introduces an improved model which simplifies in the prediction of the electric field in electrolytes in which the conductivity varies rapidly with depth or is stratified.

In the model each transformer-rectifier unit in the ICCP system is represented in a circuit which includes the TRU, supply cabling connecting the TRU to one or more anodes, and return cabling connecting the hull to the return of the TRU. The cable resistances and any connection resistances may be included in the circuit, for example between the propeller shaft and the ship hull. The output of the TRU is defined either as a voltage difference (supply to return) or as current supplied by the TRU.

The electrical circuit equations are solved to determine current flow and electrical potential throughout. Current flow from the surfaces of the anodes into the surrounding electrolyte is described using a polarisation curve. Current flowing through the electrolyte is determined by solving the Laplacian equation, using the boundary element method (BEM). Dual elements are used to represent each side of thin structures, such as the propeller blades. The entire solution process is non-linear, and is solved iteratively.

The results of the mathematical modelling include current flowing from each ICCP anode, current density and protection potentials on all wetted parts of the ship; potentials at reference electrodes; power loss, current and potential throughout the circuit; and potential, electric field and magnetic field at any number of positions in the electrolyte.

For a given ICCP system, the aims of the simulation are to predict the level of protection against corrosion on the ship, and to identify the resulting electric and magnetic signatures.

The detailed representation of the ICCP circuit allows investigation into the effects of deficiencies in the system for example failure of an anode, or into effects of variable resistance in a shaft grounding system.

The use of dual elements to represent the propeller allows use of the real (thin) geometry of the blades. This in turn makes it meaningful to investigate the effects on signatures of movement (or at least changed position) of the blades as the shaft rotates.

Examples are presented which investigate these effects. Where appropriate, comparisons are made with the more simplified approaches normally used, and benefits are discussed.

A new BEM method is also described which encapsulates solutions for the multi-layered Laplacian equation. Because the stratified nature of the electrolyte is included in the mathematics, it is not necessary to create a mesh on interfaces between regions with different conductivity, such as the sea-bed.

The use of the new method makes it possible to solve a ship model using elements only on the wetted surfaces of the hull. This and other benefits of the new approach are investigated and discussed, and where appropriate comparisons are made with the alternative multi-domain method.

Keywords: Simulation, ICCP, supply and return circuit, TRU, UEP, CRM, anode failure, multi-layered BEM.

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