COMSOL 6.4 - Atmospheric Corrosion of a Busbar

In this model example, the Atmospheric Corrosion model is extended to a busbar, which is a metallic strip typically used for high current power distribution. The busbar geometry considered here consists of a copper (Cu) flange, an aluminum (Al) flange and a zinc nut and bolt and is exposed to humidified air.

This tutorial model example solves for both the electric potential in the electrode domain and the electrolyte potential in the thin electrolyte layer. A high current is applied at the Cu terminal whereas the Al terminal is grounded while solving for the electric potential. The electrolyte potential variation is solved only over the exterior surfaces of the busbar geometry. The electrolyte film thickness and conductivity depend on the relative humidity of the surrounding air. The limiting oxygen reduction current density depends on the oxygen diffusivity and solubility.

The example uses parameter data from Ref. 1, Ref. 2, and Ref. 3.

Model Definition

The model setup is shown in Figure 1.

Figure 1: Model setup. The busbar geometry consists of a copper flange, an aluminum flange and a zinc nut and bolt.

The busbar model geometry consists of a copper flange, an aluminum flange, and a zinc nut and bolt. Use the Secondary Current Distribution interface to solve for the electric potential, ϕs (SI unit: V), over the metal electrode domains of aluminum, copper, and zinc according to

where is (SI unit: A/m2) is the electrode current density vector and σs (SI unit: S/m) is the electrical conductivity, which is assumed to be a constant for all three domains.

The aluminum terminal is grounded whereas a total current of 100 A is applied at the copper terminal.

Use the Current Distribution, Shell interface to solve for the electrolyte potential, ϕl (SI unit: V), over the thin electrolyte domain (over the exterior surfaces of the busbar geometry) according to

where il (SI unit: A/m2) is the electrolyte current density vector, s (SI unit: m) the electrolyte film thickness and σl (SI unit: S/m) is the electrolyte conductivity, which depends on relative humidity.

The thickness of the electrolyte film depends on both the salt load density and the relative humidity. The oxygen solubility and the electrolyte conductivity also depend on the relative humidity. The same expressions as used in the Atmospheric Corrosion model are used here for the electrolyte film thickness, oxygen solubility and electrolyte conductivity to account for the relative humidity dependence. The oxygen diffusivity is assumed to be constant in this model.

Electrochemical Reactions

The aluminum, copper, and zinc surfaces account for both the metal dissolution reaction and the oxygen reduction reaction. The metal dissolution electrode reaction kinetics are described by an Anodic Tafel expression whereas the oxygen reduction electrode kinetics are described by a Cathodic Tafel expression.

The oxygen reduction reaction is limited by oxygen transport through the film. The limiting current density, ilim, O2 (SI unit: A/m2), depends on the film thickness, the oxygen solubility and the oxygen diffusivity according to:

where F (96,485 C/mol) is Faraday’s constant, D (SI unit: m2/s) is the diffusivity of oxygen in the film, csol (SI unit: mol/m3) is the solubility of oxygen, and dfilm (SI unit: m) is the film thickness.

By assuming a first order dependency of the oxygen reduction kinetics on the local current density of the oxygen concentration, the following expression for the current density, ilim,O2 (SI unit: A/m2), can be derived:

where iexpr is the local current density of the electrode reaction in absence of mass transport limitations.

Results and Discussion

Figure 2 shows the electric potential variation in the metal. It can be seen that the applied current of 100 A causes a potential drop of about 2.5 mV over the busbar.

Figure 2: The electric potential in the metal.

Figure 3 shows the variation in electrode potential versus adjacent reference, which is the difference between the electric potential in the metal and the electrolyte film potential. The electrode potential versus adjacent reference is positive over the copper flange and negative over the zinc nut and bolt and aluminum flange surfaces.

Figure 3: The electrode potential vs. adjacent reference.

Figure 4 shows the electrolyte potential variation in the electrolyte film.

Figure 4: The electrolyte potential obtained in the electrolyte film covering the busbar.

Figure 5 shows the local current density variation for the anodic metal dissolution reaction. It can be seen that the metal dissolution electrode reaction predominantly occurs near the intersection region between the copper flange and the zinc bolt, at the zinc surface. (Zooming and rotating the plot in the model file also reveals metal dissolution occurring between the copper flange and aluminum flange at the aluminum surface.)

Figure 5: The local current density for metal dissolution electrode reaction over the exterior busbar surfaces.

Finally, Figure 6 shows the local current density variation for the oxygen reduction electrode reaction over the exterior surfaces of the busbar. It can be seen that the oxygen reduction electrode reaction predominantly occurs on the aluminum and zinc surfaces. The magnitude of local oxygen reduction current density is close to the limiting current density, indicating that transport of oxygen is limiting the corrosion process.

Figure 6: The local current density for oxygen reduction electrode reaction over the exterior surfaces of the busbar.

Notes About the COMSOL Implementation

The model is implemented using the Secondary Current Distribution interface to solve for the electric potential and the Current Distribution, Shell interface to solve for the electrolyte potential in the thin electrolyte film. Note that the Current Distribution, Shell interface is only applicable to the exterior boundary selections of the busbar domain.

References

1. Z.Y. Chen, F. Cui, and R.G. Kelly, “Calculations of the Cathodic Current Delivery Capacity and Stability of Crevice Corrosion under Atmospheric Environments,” J. Electrochem. Soc., vol. 155, no. 7, pp. C360–368, 2008.

2. D. Mizuno and R.G. Kelly, “Galvanically Induced Intergranular Corrosion of AA5083-H131 Under Atmospheric Exposure Conditions — Part II — Modeling of the Damage Distribution,” Corrosion, vol. 69, no. 6, pp. 580–592, 2013.

3. D. Mizuno, Y. Shi, and R.G. Kelly, “Modeling of Galvanic Interactions between AA5083 and Steel under Atmospheric Conditions,” Excerpt from the Proceedings of the 2011 COMSOL Conference in Boston.

Corrosion_Module/Atmospheric_Corrosion/atmospheric_corrosion_busbar

Modeling Instructions

Begin by loading the model geometry file which also includes customized selections.

Application Libraries

From the menu, choose .

In the window, select > > in the tree.

Click

Add Physics

In the toolbar, click

to open the window.

Add physics interfaces to solve for the electric potential and to solve for the electrolyte potential.

Go to the window.

In the tree, select > > .

Click the button in the window toolbar.

In the tree, select > > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Global Definitions

Parameters 1

Load the model parameters.

In the window for , locate the section.

Click

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

Secondary Current Distribution (cd)

Start setting up the model for electric potential by first adding Electrode domain. Then, set electric ground at aluminum terminal boundary, set electrode current at copper terminal boundary and set the electrode current density at all other exterior boundaries.

Current Conductor 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Electric Ground 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Electrode Current 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Is,total text field, type 100[A].

Electrode Current Density 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the in,s text field, type -cdsh.itot.

Note that the variable cdsh.itot appears in orange color since it is not yet defined. This variable will be available after adding Electrode Surface nodes in Current Distribution, Shell interface in the next step.

Add Material

Now, add material properties.

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the tree, select > .

Click the button in the window toolbar.

Materials

Aluminum 3003-H18 (mat1)

In the window for , locate the section.

From the list, choose .

Copper (mat2)

In the window, click .

In the window for , locate the section.

From the list, choose .

Zinc

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	1.66e7[S/m]	S/m	Basic

In the text field, type Zinc.

In the toolbar, click

to close the window.

Current Distribution, Shell (cdsh)

Now, set up the model for the electrolyte potential. Note that the interface is applied on all boundaries by default. Set the boundary selection for the interface to exterior boundaries of a busbar geometry. Set the electrolyte thickness and conductivity at the Electrolyte node first and then set the electrode kinetics appropriately.

In the window for , locate the section.

From the list, choose .

Electrolyte 1

In the window, under > click .

In the window for , locate the section.

In the s text field, type d_film.