Corrosion Protection of a Ship Hull

Impressed current cathodic protection (ICCP) is a commonly employed strategy to mitigate ship hull corrosion, by which an external current is applied to the hull surface, polarizing it to a lower potential. Although there are various parameters such as salinity, temperature, hull surface coating that contribute to the demand for current, the area of bare metal (mainly propeller) is the most governing parameter.

This model example simulates the effect of propeller coating on the current demand and is based on a paper by Huber and Wang (Ref. 1, however using slightly different geometry and polarization data). Two different cases are investigated; a coated and an uncoated propeller.

Model Definition

The CAD built geometry of the ship hull considered in this example is shown in Figure 1. The model geometry is created by adding rectangular block outside the hull geometry to represent the ocean.

Figure 1: The geometry of the ship hull surface, which is exposed to the sea water.

The zoomed-in model geometry highlighting the propeller features is shown Figure 2 where the anode, shaft and propeller surfaces and the electrolyte domain are highlighted.

Figure 2: The zoomed-in model geometry of the ship hull surface highlighting anode, shaft, propeller surfaces and electrolyte domain.

Use the Secondary Current Distribution interface to solve for the electrolyte potential,

(SI unit: V), over the electrolyte domain according to:

where il (SI unit: A/m2) is the electrolyte current density vector and σl (SI unit: S/m) is the electrolyte conductivity of the sea water which is assumed to be a constant at 4 S/m.

Use the Electrode Surface boundary node at the shaft electrode surfaces to add electrode reactions and set the boundary condition for the electrolyte potential to

where iloc (SI unit: A/m2) is the local individual electrode reaction current density.

The propeller and the shaft are considered to be made up of nickel aluminum bronze (NAB) alloy and Alloy 625, respectively.

Use the Electrode Surface boundary node at the shaft surface to add electrode reaction. The electrode kinetics at the shaft, ikin, is set using the experimental polarization data for Alloy 625 which is available in corrosion material library (Ref. 2).

In case of uncoated propeller, use the Electrode Surface boundary node at the propeller base surfaces and use the Thin Electrode Surface boundary node at the propeller blades surfaces to add electrode reactions. Note that the Thin Electrode Surface boundary feature allows to prescribe the electrode kinetics at both the upside and downside of the propeller blades. The electrode kinetics at the propeller base and blades, ikin, is set using the experimental polarization data for NAB alloy which is available in corrosion material library (Ref. 2).

The electrode reaction considered on the metal surfaces is oxygen reduction. Also enable a limiting current density of 5 A/m2 to the electrode kinetics expressions, since oxygen transport in the seawater is limited by the rate of transport to the surface. This will result in the following local current density expression

The ICCP system controls the hull potential versus the reference electrode. Describe this in the model by adding a Reference Electrode node, and then setting the electrode phase potential,

, of the Electrode Surface nodes to −850 mV versus the potential of the Reference Electrode.

Since the anode kinetics of this model is not known (and of minor interest for this analysis), use an Electrolyte Potential node for the anode surface and set the potential to 0 V. Note that the choice of potential level is at this boundary arbitrary and only serves to “bootstrap” (ground) the potentials of the model.

Use the default Insulation condition for all boundaries of the ship hull surfaces:

where n is the normal vector, pointing out of the domain.

Use an Infinite Electrolyte condition on the external boundaries to the Electrolyte domain to describe the infinite extension of the ocean. Specify the ocean surface and mid ship plane as symmetry planes. This models the current conduction outside the drawn geometry, using the boundary element method.

The mesh used in the model is shown in Figure 3, with a close-up of the propeller shown in Figure 4.

Figure 3: The mesh used in model.

Figure 4: The mesh used in model, zoomed-in around propeller.

Results and Discussion

A surface plot of the hull potential for the case with a coated propeller is shown in Figure 5. It can be seen that the potential distribution across the ship hull surface is quite uniform, except in the region close to the anode surface and the propeller and shaft surfaces. The potential is higher near the shaft compared to the rest of the ship hull surface, indicating that this part of the hull is less protected compared to the other parts.

Figure 5: A surface plot of the hull potential for the case with a coated propeller.

Figure 6 shows a streamline plot of electrolyte current density and a surface plot of absolute value of the total current density over the shaft surface for the case with the coated propeller. The ionic current flow from the anode surface to the shaft surface can be seen in Figure 6.

Figure 6: A surface plot of the total current density for the case with a coated propeller.

Figure 7 shows the potential for the case with an uncoated propeller. It can be seen that the potential distribution across the ship hull surface is less uniform compared to the coated propeller case.

Figure 7: A surface plot of the hull potential for the case of an uncoated propeller.

A streamline plot of electrolyte current density and a surface plot of absolute value of the total current density over the shaft and propeller surfaces for the case of the uncoated propeller is shown in Figure 8. The ionic current flow from the anode surface to the shaft and propeller surfaces can be seen in Figure 8. The total current demand is found to be higher in case of the uncoated propeller compared to the coated propeller case, which could be attributed to the higher cathode surface area in case of the uncoated propeller.

Figure 8: A surface plot of the total current density for the case of an uncoated propeller.

Figure 9 shows the electrode potential (vs an adjacent reference electrode) along the keel of the ship for both coated and uncoated propellers. It can be seen that, for the case of the uncoated propeller, the potential in the regions closer to the anode and the propeller surfaces deviates significantly from the rest of the ship hull surface. This deviation is less significant in the case of a coated propeller. Thus, the potential distribution across the length of ship hull surface is found to be considerably uniform in the case with the coated propeller, and more non-uniform for the uncoated propeller.

Figure 9: The electrode potential variation along the keel of the ship for both coated and uncoated propellers.

Finally, the integrated anode current is evaluated for the two cases. For the coated case the current is 0.84 A, and for the uncoated case the current is 6.5 A.

References

1. T. Huber and Y. Wang, “Effect of propeller coating on cathodic protection current demand: Sea trial and modeling studies,” Corrosion, vol. 68, pp 441–448, 2012.

2. H.P. Hack, “Atlas of polarization diagrams for naval materials in seawater,” Naval Surface Warfare Centre Technical Report, CARDIVNSWC-TR-61-94/44, April 1995.

Corrosion_Module/Cathodic_Protection/ship_hull

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Geometry 1

Import the geometry of the ship hull from a geometry file.

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file ship_hull_geometry.mphbin.

Click

Mesh Control Faces 1 (mcf1)

The geometry is divided into two domains, use a mesh control face to remove this split when setting up the physics. This will reduce the number of geometry entities that can be selected when setting up the physics.

In the toolbar, click

and choose .

On the object , select Boundaries 8–11 and 14 only.

It might be easier to select the boundaries by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)

In the toolbar, click

Click the

button in the toolbar.

Click the

button in the toolbar.

The geometry should now look like Figure 1.

Select and a region closer to propeller. The zoomed in geometry should now look like Figure 2.

Global Definitions

Load the model parameters.

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file ship_hull_parameters.txt.

Definitions

Create explicit selections for the propeller base, propeller blades, shaft, anode, reference electrode and hull surfaces. Then create a selection for the ship hull surface by using a union. The selections will be used later on when specifying the physics, setting up the mesh and when plotting and evaluating the results.

Propeller base

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog box, type 20-22 in the text field.

Click .

In the window for , type Propeller base in the text field.

Propeller blades

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog box, type 14,16,17,40,41 in the text field.

Click .

In the window for , type Propeller blades in the text field.

Shaft

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog box, type 29,39 in the text field.

Click .

In the window for , type Shaft in the text field.

Anode

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog box, type 19 in the text field.

Click .

In the window for , type Anode in the text field.

Reference electrode

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog box, type 18 in the text field.

Click .

In the window for , type Reference electrode in the text field.

Hull surface

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog box, type 6-13, 15, 20-28, 30-38, 42-47 in the text field.

Click .

In the window for , type Hull surface in the text field.

Ship surface

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. Under , click

In the dialog box, in the list, choose , , , , and .

Click .

In the window for , type Ship surface in the text field.

Propeller and Shaft

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. Under , click

In the dialog box, in the list, choose , , and .

Click .

In the window for , type Propeller and Shaft in the text field.

Propeller

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. Under , click

In the dialog box, in the list, choose and .

Click .

In the window for , type Propeller in the text field.

Materials

Use the Corrosion Material Library to set up the material properties for the electrode kinetics at the shaft and propeller electrode surfaces.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Alloy 625 in seawater at 30 C (mat1)

In the window for , locate the section.

From the list, choose .

In the window, expand the node.

Interpolation 1 (iloc_exp)

In the window, expand the node, then click .

In the window for , click

The function plot should look like this:

Add Material

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

NAB in seawater at 30 C (mat2)

In the window for , locate the section.

From the list, choose .

In the window, expand the node.

Interpolation 1 (iloc_exp)

In the window, expand the node, then click .

In the window for , click

The function plot should look like this:

In the toolbar, click

to close the window.

Cathodic Protection (cp)

Now, set up the Cathodic Protection interface for the case of a coated propeller.

Electrolyte 1

Set up the user defined electrolyte conductivity.

In the window for , locate the section.

From the σl list, choose . In the associated text field, type sigma.

Reference Electrode 1

The ICCP system will control the potential of the ship hull versus a reference electrode, located at midship. In this model we set all Equilibrium potential with reference to Ag/AgCl. The equilibrium potential of this reference is hence 0.

In the window, right-click and choose .

Select Point 35 only.

Impressed Current Surface 1

In this model we will not explicitly define the anode reaction kinetics. Instead we will use a potential (primary) condition for the anode potential.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Eimpr text field, type E_control.

From the φs,ref list, choose .

Electrode Surface 1

Now specify the electrode potential and the kinetics for the shaft surface.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Electrode Reaction 1

In the window, click .

In the window for , locate the section.

From the iloc,expr list, choose .

Select the check box.

In the ilim text field, type ilim.

Passive Metal Surface 1

Next set the insulation condition for the ship surface.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Thin Passive Metal Surface 1

Next set the insulation condition for the propeller blade surface.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Add an Infinite Electrolyte to describe an infinite extension of the electrolyte. Use symmetry planes to describe the ocean surface and the midship symmetry planes.

Infinite Electrolyte 1

In the toolbar, click

and choose .

Select Boundaries 1–3 and 5 only.

In the window for , locate the section.

In the σl text field, type sigma.

Click to expand the section. Select the check box.

Select the check box.

No more boundary conditions are needed for study with the coated propeller since Insulation condition is applied by default, including the coated propeller surfaces.

Initial Values 1

Provide an initial value for the electrolyte potential to reduce the computational time.

In the window, click .

In the window for , locate the section.

In the phil text field, type 0.5.

Mesh 1

Build a mesh with a finer resolution at the propeller, shaft and hull surface. Mesh the domain around the propeller first.

Free Tetrahedral 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domain 2 only.

Size 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Click the button.

Locate the section.

Select the check box. In the associated text field, type 1.5.

Select the check box. In the associated text field, type 0.01.

Size 2

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Size 3

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Click

Free Tetrahedral 2

In the toolbar, click

Size 1

Right-click and choose .

Free Tetrahedral 2

In the window, right-click and choose .

The mesh should look like Figure 3 (You may want to toggle the transparency button in order to see the mesh better).

Study : Coated Propeller

Now, solve the model for the coated propeller case.

In the window, click .

In the window for , type Study : Coated Propeller in the text field.

In the toolbar, click

Results

Several plots are added by default. Now, add a surface plot for hull potential to the electrode potential versus adjacent reference plot.

Electrode Potential vs. Adjacent Reference (cp)

In the window, under click .

In the window for , locate the section.

Clear the check box.

Locate the section. From the list, choose .

In the toolbar, click

The surface plot of the potential for the ship surface with the coated propeller should look like Figure 5.

Surface 1

In the window, expand the node, then click .

Selection 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Electrolyte Current Density (cp)

Select and a region closer to propeller. The surface plot of the total current density for the zoomed in region near the coated propeller should look like Figure 6.

Cathodic Protection (cp)

Now, set up the problem for an uncoated propeller case by describing the electrode kinetics at the propeller base surfaces using the Electrode Surface boundary feature and at the propeller blade surfaces using the Thin Electrode Surface boundary feature.

Electrode Surface 2

In the toolbar, click