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Modeling Approach for Galvanic Corrosion Protection of Multi-material Aircraft Structures

Siva PALANI1, Theo HACK2, Andres PERATTA3, Robert ADEY4, John

BAYNHAM5, Hubertus LOHNER6

1 EADS, Germany, siva.palani@eads.net 2 EADS, Germany, theo.hack@eads.net 3CM BEASY, UK, aperatta@beasy.com 4 CM BEASY, UK, r.adey@beasy.com

5 CM BEASY, UK, jbaynham@beasy.com 6AIRBUS, Germany, hubertus.lohner@airbus.com

Abstract: The paper gives an overview of the development and experimental validation of a computational model for simulating galvanic corrosion in specific application case scenarios appearing in an aircraft environment. The numerical approach is based on solving the electro-neutrality equation with a three dimensional Boundary/Finite Element Method. Amongst the inputs of the problem are: geometrical description and physical properties of the electrolyte, as well as macroscopic polarization curves of the active electrodes. The main outcomes of the model are electric current density and potential distribution on the surface. The focus of the study is thin electrolyte conditions that could occur in the upper part of A/C structure. A model considering a co-planar unpainted bi-material combination composed exemplarily of Aluminum AA2024 and carbon fibre reinforced polymer (CFRP) has been developed. An experimental set-up has been established for validation of the computational results. The validation approach is explained and the results obtained are presented. Good agreement has been obtained between observed and simulated data. This conceptual model can be applied to different multi-material combinations relevant for aircraft structures. In particular variations in the environmental condition are considered, including for example different thicknesses of electrolyte film, and different aggressiveness of electrolytes. Further parameter studies are discussed to show the effect of different physical properties of the electrolyte on corrosion rates and total current changes in the materials involved. Keywords: Galvanic corrosion, AA2024, CFRP, Boundary/Finite Element Method, Aircraft

1. Introduction Corrosion protection plays a very important role in the design and maintenance of the aircraft. The alloys currently used are the compromise of high specific strength and corrosion resistance. The extreme long aircraft design life requires durable protection systems to ensure acceptable operational cost during in-service. Current maintenance concepts require corrosion flaws found during inspection to be repaired. This philosophy causes high repair and maintenance costs for the airliner. Reduction in maintenance costs of new aircraft structures can be achieved by

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extension of the inspection intervals. New maintenance requirements have to be defined and the protection against corrosion has to be very effective. In addition, at the same time the corrosion protection should also be adequately optimized in order to reduce design and manufacturing cost of the aircraft. Therefore, a tailored corrosion protection system is required. In the aircraft industry, because of the recent demand for better fuel-efficiency, more lightweight materials such as aluminum, magnesium, titanium and CFRP (Carbon Fiber Reinforced Plastics) are utilized and particularly combinations thereof. The application of this increasing “mixed materials” enhances the risk for galvanic corrosion. Galvanic corrosion (GC) is one type of corrosion and can occur when two different materials with different electrochemical properties are coupled in the presence of a corrosive electrolyte. Therefore, galvanic corrosion is the undesirable result of this “mixed materials” usage. New aircraft designs contain a high degree of CFRP materials which are in contact with Aluminum in specific areas. Galvanic corrosion can be induced, since the carbon fibers behave electrochemically like a noble metal where cathodic corrosion reaction will take place and the aluminium alloy is preferentially corroded. The basic principles of GC are quite well established and generally understood, but the general understanding gained so far has not yet been exploited enough to narrow down the difference between scientific research and reality. On the other hand, the progressive advance of computational resources in the last few decades has today made possible to model a variety of complex corroding systems, thus representing a leading edge technology not only for research in the subject, but also for direct application in engineering design [1]. At present, a computational modelling approach is one of the most effective tools for design and optimization purposes, as well as for failure detection, monitoring, and quality performance assessment. In addition, recent advances in numerical methods have allowed the solution of increasingly larger and more complicated structures [2]. One of the general objectives of modeling GC is to tailor the corrosion protection measures in order to avoid GC for hybrid structures without performing a huge amount of laboratory testing. A crucial aspect of computational modeling for GC is its connection with reality, and its reliability as a predictive tool, and for this reason the validation step of any model is as important as any other aspect of the model. This work generally describes the status of the development of a conceptual galvanic corrosion model based on Boundary/ Finite Element Method in order to optimize the protection of the mixed structures against galvanic corrosion under thin electrolyte layers occurring in aircraft environments. The validation approach consists of comparing experimental measurements of electrolyte potential and corrosion rates obtained from a corroding sample with the predictions coming from the equivalent computational model. The materials involved in the experiment are unpainted aluminum alloy AA2024 unclad and Carbon Fiber Reinforced Plastics (CFRP) acting as anode and cathode, respectively.

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2. General Approach

The model under consideration consists of two co-planar electrodes composed of anode (AA2024 unclad) and cathode (CFRP) separated by a small non conductive gap (~0.1 cm wide) to avoid direct electrical contact between the electrodes, see Figure 1. The electrolyte consists of a saline solution (NaCl) with varying chloride concentration. The electrolyte is enclosed in a parallelepiped of dimensions (26 x 9.7 x he) cm, in x, y and z directions, respectively. The model height (he) of the electrolyte is variable.

To establish the galvanic effect, an electrical return path connection is made between anode and cathode. In the experiment this is achieved using an Ammeter.

Figure 1: Schematic representation of galvanic corrosion in the presence of thin film electrolytes, where w << L

The analysis is based on the polarization curves obtained experimentally for the different chloride concentrations and conductivities as shown in Table 1. The polarization curves correspond to milled Aluminum (AA 2024 unclad) and ground CFRP. The validation work consists of experimental determination of electrochemical data which can be compared with the results of the computational modeling (Figure 2). These electrochemical data are: • Potentio-dynamic polarization curves of the AA2024 and CFRP under the

conditions shown in Table 1. • Total current flowing between anode and cathode in the case of thin film

electrolytes. Once the experimental setup has been designed and established, the experimental part of the validation involves monitoring of the total current flowing between anode and cathode in the external circuit at the external electric short cut while recording the electrolyte thickness of the thin film deposited over the samples. In this work, two case scenarios with different chloride contents (electrolyte conductivity) have been selected as shown in Table 1.

Table 1: Aggressiveness of the electrolyte

Conductivity Chloride concentration 4980 µS/cm 0.05 mol/l 9600 µS/cm 0.10 mol/l

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Figure 2: Validation approach

3. Numerical Modeling Approach for Thin Films In general terms, the problem formulation for the electrolyte is based on the charge conservation equation in the bulk of the electrolyte under steady state, homogeneous conditions. The mathematical description of the problem is based on the 3D Poisson equation for the electrolyte potential with non-linear boundary conditions imposed by the prescribed polarization curves on the active electrodes. The physical and mathematical background for the modeling can be followed from [1-5]. In the steady state case, the governing equation for the electrolyte becomes1:

0=⋅∇ j ; (1)

where j is the current density given by: )(xj eV∇−= σ , σ represents the electrolyte

conductivity, and )(xeV is the electric potential in the electrolyte at point 3R∈x . The

integration domain Ω of this problem is the electrolyte, and the boundaries Ω∂=Γ are defined by all the surfaces surrounding it, including the anode, cathode and the insulating walls. The boundary conditions applied to the active electrodes are of the generic form:

)(

ˆVf

Vj en ∆=

∂

∂−=

nσ (2)

where nj is the current density flowing throughout the surface in normal direction ( n ),

and V∆ is the polarization potential across the interface metal/electrolyte given by

me VVV −=∆ , where Vm is the potential of the metal.

This boundary condition is actually given by the corresponding polarization curves which result from the representative polarization curves characterization of the material. The function f, usually containing exponential factors of V∆ as prescribed by Butler-Volmer type equations, is in general non-linear and considered as an assembly of linear functions.

1 ( )321 ,, xxx ∂∂∂∂∂∂=∇ represents the 3D gradient operator.

Validation experiment 1. Measurement of polarisation

curves of the electrodes involved

2. Measurement of total current between anode and cathode

Numerical modelling 1. Geometry definition (3D CAD) 2. Definition of

physical/electrochemical properties

3. Mesh generation 4. Numerical calculation 5. Post-processing and results

interpretation

1. Results comparison 2. Sensitivity analysis

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This relationship must be known prior to solving the model. The software BEASY-Thin Film used for the simulation needs to know the representative polarization data as an input in order to assign this type of non-linear boundary condition to the corresponding electrode. In this particular model, all other surfaces in contact with electrolyte apart from the interfaces with the AA2024 and CFRP samples are considered as insulating, i.e.

0=nj .

The computer code BEASY for solving problems of galvanic corrosion where the electrolyte is considered to be a thin film is used. By “thin” we refer to the situation in which the depth of the electrolyte (w) is much smaller than its other dimensions, e.g. the thickness (w) is much smaller than the characteristic lateral length of the assembly (L), as illustrated in Figure 1. The computational cost for solving a thin film electrolyte model with a standard three dimensional code can be very high, since the electrolyte is treated as a three dimensional object and the mesh discretization needs to have element sizes of a fraction of the thickness. However, it has been observed that when the electrolyte thickness becomes negligible in comparison with its other dimensions, quantities such as the electric potential in the electrolyte remain constant along the coordinate associated with the thickness, i.e. Z coordinate in Figure 1, but not with respect of the other two coordinates X and Y. This behavior allows us to consider a two dimensional approach for solving eq.(1), where the z component of the gradient of the z component of the current density in

the electrolyte (z

j z

∂∂

) can be directly integrated along the z coordinate and therefore

excluded from the mathematical formulation of the problem. In this way, the electro-neutrality equation (1) becomes:

( ) )(22 VfVw eDD ∆−=∇−⋅∇ σ (3)

Where represents the two dimensional “grad” operator acting on x and y coordinates, w is the electrolyte thickness, and )( Vf ∆ is the current density coming

from the active electrodes, or zero if the surface underneath the thin film electrolyte is perfectly coated which acts as an insulator. Solving (3) in two dimensional (2-D) space rather than equation (1) in the three dimensional (3-D) space helps to reduce substantially the complexity of the calculation for large structures with thin layers of electrolyte. Any case of a thin film of electrolyte covering arbitrarily complex 3-D electrodes can be reduced to a 2-D problem “warped” in 3-D space where the physical 3-D space is mapped onto a 2-D computational space.

Note also that by reducing the dimensionality from three to two, the effect of the charge exchange between the electrolyte and active electrodes enters into the formulation as a source term, rather than as a boundary condition.

For an active electrode )( Vf ∆ represents the polarization curve of the material,

which is required as input data for the model. A key feature of the model is that polarization data obtained from standard polarization tests can be used as input data thus enabling a database of polarization properties to be created. Note that only eq. (3) which considers homogenous electrolyte is solved by the model and no attempt is made to simulate the details of the diffusion layer or any

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other physical process apart from electrical neutrality of the electrolyte such as diffusion, migration, chemical reactions, etc, which are more suitable for localized models. Instead, the goal of this formulation is to solve macroscopic engineering scale problems such as aircraft structures and joints where galvanic corrosion occurs due to the presence of a thin film of electrolyte on the surface of the structure. The ability to simulate the general behavior of complex and large geometries provides information about the risk of corrosion due to current flow through the electrolyte film and the effectiveness of surface protection systems such as coatings. Note a model for considering deep electrolyte pools or films has been presented in [1]. The numerical approach for solving eq (3) is based on the Finite Element Method (FEM) [6]. The main objective of this paper is to demonstrate how the results obtained with this approach compare against the corresponding experimental results. The FEM discretization of the model solved in this paper is shown in Figure 3. In order to obtain good accuracy for the steep gradient of electric potential near the gap between anode and cathode a finer mesh discretization was locally assigned to that area.

Figure 3: Mesh discretization of the bi-metallic GC model, viewed from below the electrodes. 6. Experiment 6.1 Electrochemical Input

The electrode behavior of AA2024 unclad and CFRP are described by the polarization curves which serve as an input for the active electrodes in the model. Throughout this investigation for the anode, aluminum sheet alloy AA2024 unclad with milled surface was used. As for the cathode, a ground CFRP plate where the outer resin layer was removed by grinding down into the first carbon ply (~100 µm) to achieve an almost pure carbon surface. All carbon fibers were electrically connected by silver glue at the cut edges. Figure 4 shows a completed electrode arrangement.

9.7 11.2

Gap = 0.2

CFRP AA2024

12.3 12.3

26.2

Top View:

All dimensions in centimetres

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Top View:

Figure 4: Arrangement of a completed bi-electrode coplanar sample for galvanic corrosion test under thin film electrolytes.

The experimental work consists of two stages. The first stage involves obtaining the electrochemical properties of the AA2024 and CFRP, by means of an electrochemical cell which is a standard three electrode cell. Figure 5 shows polarization curves obtained through experiment for AA2024 unclad immersed in air purged and near neutral electrolytes with different Chloride concentrations and conductivities. The different conductivities are corresponding with varying of the Chloride (Cl-) content: Conductivity Chloride concentration

5000 µS/cm ~ 0.05 M 10000 µS/cm ~ 0.10 M

A representative polarisation curve measurement of CFRP (cathode) is shown (exemplarily 0.05 mol/l) in Figure 5 since here the curve is not sensitive to the electrolyte composition in the investigated range.

1,00E-07

1,00E-06

1,00E-05

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

-1 -0,9 -0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0

Potential [V vs SCE]

log

i[A

/cm

2]

CFRP-0.05M_5080 µS/cm

AA2024-0.05M_5000 µS/cm

AA2024-0.1M_10000 µS/cm

Figure 5: Polarization curves of the CFRP and AA2024 samples used for the validation test. The potential is referred to the standard calomel electrode (SCE) [7]

Interface

CFRP ground

AA2024 unclad

milled

CFRP

ground

AA2024 unclad milled

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6.2 Experimental Validation 6.2.1 Theoretical Background The experimental approach for the validation consists of measuring the total current flowing between the two co-planar plates acting as electrodes. The anode consists of milled AA2024 unclad and the cathode of a ground plate of CFRP. The challenge here was to generate thin homogeneous electrolyte films with different but known thickness on various known relevant substrate surfaces i.e. AA2024 and CFRP in this case. Basically, the formation of homogeneous film is based on theory of Nusselt falling film-wise condensation on a vertical flat plate. Laminar film condensation has first been successfully treated by Nusselt [8] in 1916, who provided an analysis for laminar film condensation on an isothermal vertical plate and applied it also to horizontal plain tubes [9-12]. It depicts the process of laminar film condensation on a vertical plate from a quiescent vapor. In general, the film condensate begins at the top and flows downwards under the force of gravity, adding additional new condensate as it flows and the flow is laminar. Other assumptions according to the Nusselt analysis and which were also assumed during this experiment are as follows:

• The vapor temperature is uniform and is at its saturation temperature;

• Gravity is the only external force acting on the film (momentum is neglected so there is a static force balance);

• Fluid properties are constant i.e. homogeneous electrolyte condition;

• The adjoining vapor is stagnant and does not exert drag on the film;

The Figure 6 shows the schematics of the experimental setup designed to produce the thin electrolyte film and also for the fulfilment of numerical model validation.

Figure 6: Schematics of thin film validation experimental setup

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As Nusselt analysis is valid for vertical plates, it is also applicable to inclined plate as long as the angle of inclination is sufficient for drainage of the condensate. The local thickness of film formed can be calculated analytically based on following relation:

41

LGGLL

wsatLL

)ghρ(ρρ

)Tz(Tk4µδ

−

−= (4)

where:

δ = local film thickness;

T = temperature (saturated: water);

ρ = mass density (liquid; gas);

µ = viscosity (liquid);

g = gravity acceleration

k = thermal conductivity (liquid);

z = z-coordinate point from top of the plate

h = latent heat

For an inclined plate, the force of gravity g on the film in the above expression is replaced with g sin α, where α is the angle of the plate relative to horizontal. However, analytical solutions for the film thicknesses are not covered within this investigation since the thicknesses were measured experimentally. The details on the first Nusselt’s analysis for condensation on a plate before arriving to equation (4) can be followed at Thome [9]. Figure 7 depicts the process of laminar film condensation on a vertical plate from a quiescent vapor. Thus, the temperature profile across the film is linear and heat transfer is by one-dimensional heat conduction across the film to the wall.

Figure 7: Film condensation on flat vertical electrode surface

Inclination

angle

z

δ

α

Electrode

Water Film

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The details on the thermodynamic properties of the condensate being formed in this experimental setup i.e. the temperature profile across the film, the temperature profile from top to bottom of the flow and temperature gradient within the tested sample or plate will not be discussed in detail here since:

• The temperature gradient for the points mentioned above are found to be small in-relative to the working temperature i.e. room temperature

• Small changes in temperature (< 10%) is not expected to influence the final result within the measured domain

• Change of thickness of the film, ∆δ from top to bottom (z-direction) is much smaller than the length of the plate in z-direction besides the measured thickness for each experiment in this investigation were averaged from top to bottom.

6.2.2 Experimental Procedures

The electrolyte of interest, which are 0.3% and 0.6% NaCl in this case are prepared and filled into a container. In the electrolyte a non ionic surfactant is mixed which helps to lower the interfacial tension between liquid and the surface and therefore supporting the wettability and formation of a homogeneous film without affecting the conductivity of the electrolyte and the flow. A fog consisting of this type of electrolyte is generated by piezo atomizers. The electrolyte container and the specimen are setup in an enclosed chamber in order to assure an undisrupted homogeneous and laminar flow of the fog out of the container onto the surface of the specimen. The film properties are defined by the electrolyte composition of the bath, inclination of the electrodes and flow rate of the fog. The flow-rate of the fog out of the container can be controlled though a variable opening size. The continuous flow of fog of such properties creates thin electrolyte film of interest where the thickness of the film is stabilized through time. The electrolyte film is in equilibrium state with the continuously flowing fog and not directly exposed to the ambient atmosphere. Therefore evaporation of the film can be prohibited. Besides, the film deposition is almost independent of the thermal conductivity of the substrate.

Different thickness of the electrolyte film is achieved by changing the angle of the inclination, α of the electrode plane. The film thickness is measured online by optical spectroscopy technique. The thickness of the achieved thickness at certain inclination can be measured at different locations on the specimen during the experiment. In this investigation, the thickness of the film is varied between 13-45 µm. At the same time the corresponding or correlating total current (coupling current) required for the validation of the computational results is measured via potentiostat and recorded.

7. Results The present work is restricted to the study of four different case scenarios as listed in Table 2. Two more cases corresponding to high chloride concentration will be considered for future work. The case number matches the notation adopted for the experimental part. The surface area ratio between cathode and anode is fixed as 1:1 throughout the investigation.

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Table 2: List of parameters considered for modelling and experimental work

Electrolyte Aggressiveness

Case Cl- Content [mol/L]

Electrolyte Temperature

[oC]

pH Conductivity, σ

[µS/cm]

Electrolyte thickness, he

[µm]

C/A Ratio

1 0.05 23 7.1 4980 13 1 Low Cl- Concentration

2 0.05 23 7.1 4980 45 1

3 0.1 24 6.9 9600 13 1 Medium Cl- Concentration

4 0.1 24 6.9 9600 44 1

7.1 Total Current

Total Current vs Time (0.05 M NaCl; 4980 µS/cm)

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,1

0 200 400 600 800 1000

Time [s]

To

tal C

urr

en

t [m

A]

13 µm

45 µm

Total Current vs Time (0.1 M NaCl ; 9600 µS/cm)

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0 200 400 600 800 1000

Time [s]

To

tal

Cu

rre

nt

[mA

]

13 µm

44 µm

Figure 8: (a) Experimental total current measurement for Case 1 and 2 – (b) Experimental total current measurement for Case 3 and 4.

(b)

(a)

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Figure 8 shows the total current measurement as a function of time for Case 1 to 4 at variable electrolyte film thicknesses, He and chloride concentration. It is seen that that increase in electrolyte film thickness translates into the increase of total current. The increase in chloride concentration from 0.05 M to 0.1 M also reflects into increase of total current. 7.2 Simulation Results The outcomes of the simulation are essentially potential distribution and the three dimensional components of the current density anywhere on the model, as well as its integral over selected surfaces, i.e. total current flowing to each electrode. The potential and normal current density obtained from the simulation for the case of a 30 µm thick electrolyte with 0.1M NaCl, 9600 µS/cm2 are shown in Figure 9 and Figure 10, respectively. The AA2024 presents a very steep gradient of current density near the gap, whereas the distribution on the CFRP is more uniform.

Figure 9: Showing the potential (“+” symbol) and normal current density (“x” symbol) along the X coordinate of the sample on the CFRP electrode for the case of a 30 µm thick electrolyte with 0.1M NaCl, 9600 µS/cm2

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Figure 10: Showing the potential (“+” symbol) and normal current density (“x” symbol) along the X coordinate of the sample on the AA2024 electrode for the case of a 30 µm thick electrolyte with 0.1M NaCl, 9600 µS/cm2 7.3 Validation

The results are based on three case scenarios, one for each chloride concentration value shown in Table 1. Figure 11 shows a comparison between experimental and numerical modeling results for the three case scenarios. The vertical axis represents total current flowing between anode and cathode while the horizontal axis represents the electrolyte thickness in µm. The curves with continuous lines and markers represent experimental results; where each marker corresponds to one case scenario in the experiment. The curves without marker symbols represent results coming from the numerical modeling. The agreement for all the test cases in the 4980 µS/cm and 9600 µS/cm is good.

Total Current vs Electrolyte Thickness

0

50

100

150

200

250

0 5 10 15 20 25 30 35 40 45 50

Electrolyte Thickness [µm]

Ave

rage T

ota

l C

urr

en

t [µ

A]

0,05M NaCl-Experiment

0,1M NaCl-Experiment

0.05 M NaCl-Model

0.1 M NaCl-Model

Figure 11: Comparison between experimental and modeling results for two case scenarios of conductivity, including 4980 µS/cm and 9600 µS/cm.

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8. Discussion For all scenarios, the trend observed in the experiments can be reproduced with

the numerical simulation. Besides, the rate of change of total current with respect to changes of electrolyte thickness can always be reproduced.

Note that the underpinning theory of the thin film approximation is no longer valid for cases where the potential distribution in the electrolyte presents a non-zero gradient with respect to the Z direction, being Z the coordinate along the thickness of the film. In this case, a full three dimensional approach should be used. The stability of the total current in each measurement could be further improved if the electrolyte pooling/accumulation at the sample edges especially close to the interface could be reduced. This is due the fact that during the experiment, it was found generally all the corrosion activity takes place near the edge/interface where the anode and the cathode converge especially in electrolyte of lower conductivity. Hence, the regions of the samples far away enough from the joint can become nearly inactive in the sense that no significant current density will be observed. Therefore, these results give us an overview of the galvanic corrosion phenomenon under thin film for a simple structure in controlled environment in-terms of total current. 9. Conclusion

A computational model was developed to predict galvanic corrosion for multi-material structures exposed to thin aqueous layer of NaCl electrolytes in specific application case scenarios appearing in an aircraft environment. A model considering a co-planar unpainted bi-material combination composed exemplarily of Aluminum AA2024 unclad and carbon fiber reinforced polymer (CFRP) has been developed. An experimental set-up has been established for validation of the computational results. The results predicted by the developed computational model for galvanic corrosion have been compared against experimental measurements on the corresponding model. The experimental work was performed on a macroscopic co-planar bi-metallic corrosion cell. The modeling approach is based on the finite element method. This approach has allowed a rapid prototyping and computational implementation of the underpinning theory. In general the trends and results obtained from the model in terms of the galvanic coupling current flowing between electrodes are in good agreement with the observed experimental results. The absolute total current values predicted by the model are also in good agreement with the experimental measurements. The galvanic current found to be sensitively dependent on the concentration of the electrolyte and the thickness of the layer where as the concentration and the thickness of the electrolyte layer decreases, the galvanic current over the AA2024 unclad was concentrated at narrow edge closest to the cathode i.e. CFRP, resulting in a very steep current density distribution. Besides, it was observed from both experiment and computation that the surface of CFRP and AA2024 unclad was becoming less active as it gets further from the interface. It is important to note that the total corrosion current between anode and cathode are not sensitive to small variations in the electrolyte conductivity. The polarization data of the participating electrodes, obtained usually from the material characterization,

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must be provided as accurately as possible in order to obtain results of good quality, i.e. good matching between experimental and modeling results. Note that the modeling approach does not keep into account the detailed description of the transport process of the different ionic species participating in the corrosion. Instead it is focused on solving the electro-neutrality equation at a macroscopic level. This is to avoid having excessive computational costs which could deter the simulation of large scale practical applications often necessary in productive environments. For example, the effect of oxygen concentration is dictated by the polarization curves which are entered as input data (not internally simulated), i.e. the modeling approach does not aim at solving oxygen diffusion. It is important to note that after all the crude assumptions done to the general theory of galvanic corrosion in the presence of thin film layers of electrolyte have lead to a simplified theory which produces quite adequate modeling results. The capability of modeling detailed ionic transport processes for individual species are considered as a further improvement to the existing model which is in progress and will be implemented in the future. 10. Acknowledgement This work is supported by the Six Framework Programme for Research and Development of the European Commission in the Specific Targeted Project “SICOM”, Priority 4, Aeronautic and Space ; Project No.: AST5-CT-2006-030804 SICOM. 11. References

[1] A.Peratta, T.Hack, R.Adey, J. Baynham, H.Lohner, Galvanic Corrosion Modelling for Aircraft Environments, Eurocorr (2009). [2] K. Amaya, S. Aoki. Effective boundary element methods in corrosion analysis. Engineering Analysis with Boundary Elements 27 (2003) 507–519 [3] Robert A. Adey and Seyyed Niku. Computer Modelling of Galvanic Corrosion, in “Galvanic Corrosion”. Harvey P. Hack, editor. ASTM Committee G-1 on Corrosion of Metals. ASTM International, (1988). [4] Pierre R. Roberge. “Corrosion Engineering. Principles and Practice”. McGraw-Hill (2008). [5] BEASY software user guide, Computational Mechanics BEASY. Version 10. Southampton, UK, (2009). Available at: http://www.beasy.com. [6] O. C. Zienkiewicz. The Finite Element Method. Mc Graw Hill. 3rd Edition. ISBN. 0070840725 </search/books/isbn/0070840725>, 1977. [7] S.Palani: “Modelling and Simulation of Impact of Surface Protection on Galvanic Corrosion of Al/CFC Combinations”, MSc. Thesis, Munich, (2009). [8] Nusselt, W., Die Oberflächenkondesation des Wasserdampfes, Z. Ver.Dt. Ing., 60(27), pp. 541–546 (1916).

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[9] John R.Thome. “Engineering Data Handbook III” Wolverine Tube, Inc (2010). [10] Chen, M. M. “An Analytical Study of Laminar Film Condensation, II: Single and Multiple Horizontal Tubes”, J. Heat Transfer, 83, 55–60 (1961). [11] Chen, S. L., Gerner, F. M., and Tien, C. L. “General Film Condensation Correlations”,Exp. Heat Transfer, 1, 93–107 (1987). [12] L.Phan, A.Narain. “Nonlinear stability of the classical Nusselt Problem of Film Condensation and wave Effects”. ASME Journal of Applied Mechanics (2007).