Volume 4 Preprint 3
Computational Modeling of Shipboard ICCP Systems
V. G. DeGiorgi, E. Hogan, K. E. Lucas, S. A. Wimmer
Keywords: Boundary Element, Cathodic Protection, Computational Modeling, Physical Scale Modeling
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Volume 4 Preprint
Computational Modeling of Shipboard ICCP
V. G. DeGiorgi1, E. Hogan2 and K. E. Lucas3, S. A. Wimmer1
Materials Branch, Naval Research Laboratory, Washington, DC.
Science and Technology Division, Naval Research Laboratory,
for Corrosion Science and Engineering, Naval Research Laboratory,
In the past decade significant work has been
performed at NRL applying computational methods, specifically boundary
element techniques, to shipboard electrochemical corrosion problems.
Boundary element computational methods have been demonstrated as
predictive tools for on-hull potential profiles.
Analyses have been
completed to determine whether boundary element techniques can
accurately predict system performance.
Hull geometries investigated
include U S Navy CG hull class cruiser and CVN aircraft carrier. Issues of
mesh refinement, geometric features and material characterization
dominated these analyses.
Accuracy was measured by comparison with
physical scale model experimental results. Good agreement was shown
for both potential and current values. These analyses as well as a series
of parametric studies examining basic assumptions are presented as a
review of the validation of boundary element methods for designing
shipboard ICCP systems. In addition an investigation of boundary effects
associated with physical scale modeling is presented. Accuracy, modeling
In closing a comprehensive unified design approach that
utilizes both physical scale modeling and computational analysis
techniques is presented.
Modeling, Physical Scale Modeling
The primary corrosion protection system on Naval platforms is the paint
system. Cathodic protection systems are typically used as a secondary
line of defense against corrosion damage.
In sacrificial cathodic
protection systems the galvanic series and preferred corrosion of the less
noble metal is used in the protection design.
In impressed current
cathodic protection (ICCP) systems an external power supply is used as
the source to raise the potential level to range where corrosion is
Even though these systems are defined as secondary
protection systems one should not underestimate their importance. Their
proper performance is critical to maintaining platform availability. While
sacrificial systems are of interest, this paper will concentrate on the
design and evaluation of ICCP systems.
The performance of these systems is a synergistic response to many
factors such as geometry, conductivity of surrounding medium, material
polarization response, temperature and material interactions as shown in
Figure 1. Minor changes in any one of these factors have the possibility
environmental changes the system itself can change over time. System
configuration changes can result from damage or aging.
changing deployment environment and a need to extend service life it
has become increasingly important to define system performance under a
variety of changing conditions. Simple design models are not adequate
performance requirements. Computational analysis is well suited for the
multiple re-evaluations of systems due to changing conditions.
Current Density Requirements
Passive Surface Films
Mass Transport at Crevice
Nominal Metal Compositions
Time in Service
Figure 1 – Factors influencing shipboard ICCP characteristics.
Computational approaches for shipboard ICCP systems are not new.
Initial work on computational modeling procedures for shipboard
cathodic protection systems is well documented [1 2 3 4]. There have
been multiple researchers who have evaluated different aspects of
computational modeling of electrochemical corrosion.
recently shipboard systems have been investigated by Adey , Diaz 
and Aoki et al .
Rather than offer a complete overview of all work
computational analysis efforts at the Naval Research Laboratory (NRL)
that address issues related to ICCP systems. Guidelines for the
development of computational models that are based on this block of
work are presented. In closing a unified design process that incorporates
computational and experimental processes is presented.
Mathematical Basis for Computational Simulations
ICCP systems are electrochemical corrosion systems. LaPlace’s equation
governs electrochemical corrosion for the wetted surface of a ship hull:
k∇2Φ = 0
where Φ is the potential and k is the conductivity of the electrolyte
Eqn. 1 requires that the electrolyte be homogeneous, no
electrical sources or sinks and electroneutrality. In the case of shipboard
ICCP systems the model can be defined so that these requirements are
Seawater can be represented as a uniform mixture of multiple
components, i.e. a homogeneous electrolyte. Current source points and
sinks, regions of exposed metal, can be represented by boundary
conditions eliminating the need to include sources and sinks in the
model. Electroneutrality maintains charge equilibrium for the ship,
surrounding water and ICCP system. This is accomplished by application
of appropriate boundary definitions. The ICCP system consists of anodes
(current sources) and reference cells. Boundary conditions commonly
used are defining paint as a perfect insulating material and the use of
non-linear polarization response for other materials.
conditions are combined to solve for the potential and current density at
all points on the wetted surface. Details on the boundary element method
and solution procedures can be found in many textbooks such as ref.8.
Analysis is performed for the corroding state not corrosion initiation.
LaPlace’s equation is equally valid for any computational simulation
Past experience has established that boundary element
approach in which the surface of the structure is modeled is the most
appropriate for shipboard systems. In another competing approach, the
finite element technique, the volume of seawater surrounding the ship
must be represented by a meshed volume. In the boundary element
technique the surrounding medium, usually a large volume of seawater,
is not modeled but simply enclosed by a mathematically defined
boundary and only the hull surface must be meshed in detail resulting in
smaller memory and computer time requirements.
A key feature in validation of boundary element method is the
comparison of experimental and calculated results. In PS modeling the
structural dimensions and the conductivity of the electrolyte are scaled by
the same factor. A detailed explanation of PS modeling can be found in
DeGiorgi et al . The theoretical basis for this mechanical scaling for
shipboard systems has been presented by Ditchfield . In PS modeling
the scaled model and the full size structure maintain identical current
density values at points, identical potential differences at points, identical
polarization potentials at the anode and cathode and an identical
potential drop across the electrolyte.
Validation of the procedure has
involved comparison with sea trial data [11 12 13]. Currently PS modeling
as conducted by NRL Center for Corrosion Science and Engineering is the
design practice for U. S. Navy shipboard systems .
PS modeling of CG and CVN hulls and associated ICCP systems was
completed at NRL Center for Corrosion Science and Engineering. Detailed
current and potential information is obtained from embedded sensors for
a variety of damage and service conditions including those modeled in
the boundary element analysis.
NRL has completed detailed computational solutions for two different
A primary goal was to validate the computational
approach by detailed comparison with PS model experimental results.
Later analyses were completed to examine basic modeling assumptions.
Factors common to all analyses performed are given in this section.
A boundary element analysis requires the creation of a mesh representing
the underwater hull. In the work presented propellers are modeled as a
solid disk of equivalent area attached to the hull by a single connecting
solid beam representing the main strut for the support system. The disks
are defined so that there is sufficient thickness to avoid numerical
problems associated with thin sections. The boundary element mesh
represents the interface of the ship hull and surrounding seawater. This
mesh is enclosed in an outer box that represents a large but finite
volume of seawater. Some boundary element programs have boundary
condition option of infinite domain. This option was not used in early
analyses. The domain is defined sufficiently large enough so that edge
effects on the potential profile of the surface ship are negligible. In all
cases symmetry conditions were invoked and half of the hull was
modeled. This was done in the interest of saving computational time and
resources. There is no requirement for symmetry. Symmetry conditions
were also used to define the water surface. This is a standard approach
in boundary element methods. The commercial boundary element codes
BEASY-CP  and Frazer-Nash Detailed Modeller  were used for the
The commercial code PATRAN  was used for
In addition customized computer programs for
translation and display of data were developed at NRL.
Two design paint damage conditions were used in the analyses, minimum
(2.8% of the hull surface area is damage paint) and maximum (15% of the
hull surface area is damaged paint). The location and size of damaged
paint regions was defined by protocols provided by NRL Center for
Corrosion Science and Engineering and Naval Sea Systems Command.
Damaged paint areas are defined as exposed metal surfaces in the
boundary element models.
This duplicates the conditions for the PS
model where painted surface is represented by fiberglass and damaged
paint areas are represented by strips of uncoated metal attached to the
PS model hull.
The basic design matrix consists of four cases created by the pairing of
two service flow conditions, static and dynamic, with each damage
Static flow represents ship at rest or in port conditions.
Dynamic flow condition represents ship underway conditions.
Reference cells and anode locations in the computational model duplicate
as close as possible the locations in the PS models. In cases where port
and starboard anode locations are not strictly symmetric, the boundary
element model anode is placed at the average of the port and starboard
computational resources when the analyses were initiated.
In all cases anode values are defined as input values. Mathematically the
solution does not matter on the choice of boundary conditions to define
the source anodes. All other values are calculated as part of the solution
process. A candidate solution consists of a computer run in which the
potential of the reference cells is at the target potential -0.85 Volts
Ag/AgCl electrode. Reference cell readings are the calculated potential
values at the mesh point that is at the reference cell location. A feasible
solution occurs when the total power required is within the power supply
capacity is defined as part of the ICCP system design.
constraint required by LaPlace’s equation.
This is not a
A feasible solution is
determined through a multiple run process in which anode input values
CG Hull Analyses
The initial goal of the CG hull analysis was to determine if boundary
performance [18 19 20]. The hull geometry investigated was a U S Navy
CG hull class destroyer.
Three different ICCP systems were evaluated.
The first to be evaluated was a single power zone, 6-anode system. This
analysis determined that it was feasible to create a computational model
that yielded reasonable results.
The other two systems are 2 power
supply zone systems and have 6 and 7 anodes, respectively. Issues of
mesh refinement, geometric features and material characterization
dominated these analyses.
The two zone system analyses are
The original model used in the CG analysis consisted of 573 rectangular
elements and yielded unsatisfactory results.
A mesh refinement study
performed demonstrated that a significantly higher degree of mesh
refinement was required.
Once the mesh study was completed, a 3D
representation of the bilge keel was added to the model. This model was
used in the later CG work and consists of 1583 8-noded rectangular
elements (Figure 2). The elements were flat surfaces so the curved ship
hull was modeled as a faceted surface.
Figure 2 – Boundary element mesh for CG hull class ship.
Early in the analysis process polarization response was identified as a
critical issue. Initial results were poor but changing polarization input
response to data that more accurately represented the PS environment
resulted in good agreement between experimental and computational
results as shown in Table 1.
Table 1 – Current demand (Amps) for CG analysis. Three measurements
for evaluating results; total current to components (props. and docking
blocks), current from forward and aft systems and total current.
Reference cell reading=-0.85 V Ag/AgCl
A typical potential profile is shown in Figure 3.
Figure 3 shows the
comparison between sea trails data, PS modeling data and computational
modeling calculated results for the USS Princeton. The comparison of
experimental and calculated results based determined that the accuracy
of computational results is directly related to the accuracy of the input
polarization data used. However, it was observed that performance trends
were similar even when magnitudes showed poor agreement indicating it
is possible with any reasonable polarization response to perform basic
system design work.
Figure 3 – Potential profile for CG hull class ship; comparison of sea
trails, experimental (PS Modeling) and computational, 10 m below
CVN Hull Analyses
Information gained about computational modeling of shipboard ICCP
systems through the CG models was applied to the analysis of a CVN
aircraft carrier hull. The CVN hull is geometrically more complex than the
CG hull and the CVN ICCP system is more complex.
The CVN ICCP
system consists of 3 independent power supplies and 17 anodes. The
model of the CVN hull (Figure 4) was created based on the lessons
learned in the CG analyses.
Figure 4 – Boundary element mesh for CVN hull class ship.
displacement 9-noded rectangular elements. The 9-node configuration
consists of 8 exterior mesh points that define the element geometry and
1 mesh point placed at the centroid of the element. The centroidal node
allows for curvature of the element. This element type was not available
for the earlier work. The 9-noded element allows for more accurate
modeling of the curved hull surface.
The source of polarization data was chosen so that PS modeling testing
procedures would be represented by the polarization response. A typical
potential contour is shown in Figure 5. Total current requirements for
dynamic conditions are shown in Table 2. Detailed comparisons of
calculated and experimental results are presented in Ref. 21.
potential profiles and magnitudes were accurately predicted, there was a
larger degree of variation in amperage values than for the CG analysis.
Possible reasons for these differences were identified as model
simplification and polarization response.
Figure 5 – Calculated potential contour profile for CVN hull class ship,
minimum paint damage static flow conditions.
Table 2 - Current demand (Amps) for CVN system, dynamic flow
conditions; reference cell reading=-0.85 V Ag/AgCl.
All computational models are simplifications of the actual geometry. One
difficult area in the CVN hull that required simplification was the bilge
keel. Despite best efforts to match bilge keel profile and attachment
angles there were differences between computational and PS models.
These variations in bilge keel geometry are probably a contributing factor
in variations observed for amperage required for mid-hull, i.e. bilge keel
region, damaged areas.
The polarization data used was determined from small-scale single
material specimens tested in scale seawater to match the experimental
environment. A review of data after analyses were completed indicated
that there were other significant differences between the PS modeling test
environment and the laboratory polarization experiments. While material
interactions were not included in the laboratory determination of
polarization response it is highly likely that these will occur due to the
geometry of the hull, location of damage and location of appendages. In
addition film coatings, not taken into account in the laboratory
polarization response, were noted on some metal surfaces of the PS
These variations are contributing factors to the differences in
Boundary Definition Assumption Evaluations
As noted earlier, any computational analysis depends on simplifying
Even with current computational capabilities, expanded
memory and faster processing speeds there is always a limit to the size
of computational problem that can be readily solved. It is the intent of
the work at NRL to provide an analysis approach that can be used on
readily available computational resources.
There is always a trade off
between accuracy and computational simplifications.
embarked on a series of studies to determine the effects of commonly
accepted simplifications. Studies completed and reported have dealt with
means of defining damage (holiday vs. larger areas) , characterization
of painted surfaces , and seawater properties .
sensitivity studies that examine PS experimental tank geometry, tank
material and relative size of tank to PS model have been completed [25
The CG mesh was used for the seawater resistivity analysis.
percent range of seawater conductivity centered on the nominal value
was evaluated. This range was defined based on reported variation in
seawater in different temperate zones. The analysis indicated that these
moderate variations in seawater do result in moderate changes in system
power requirements to maintain the set point. Of more importance was
the fact that reference cell placement was shown to become a critical
issue with changing seawater conductivity. Reference cell placement that
provided adequate system performance at one conductivity level may or
may not provide adequate system performance at a different level. Full
field contours of potential levels can be obtained from the computational
model and used for reference cell placement in the design process.
Potential profiles at a single depth were shown to not provide a true
picture of hull performance.
The CG and CVN meshes were both used for the damage and paint
resistivity studies. Essentially it was determined that modeling damaged
areas as totally bare regions was conservative. Defining damage element
by element also yielded conservative results.
Upper bound power
requirements would be determined by this approach. Realistic values of
paint resistivity were shown to have a marginal effect on computational
The CVN mesh was used in a series of studies that evaluated the effects
of tank geometry and model size on experimental results. This study
evaluated the possible edge effects that may occur for a PS model of a
defined size when placed in different tanks as part of the PS modeling
process. Possible effects based on tank wall material and tank geometry
It was determined that the boundary element method
provided a useful tool for the experimentalist in the interpretation of
Guidelines for Use of Boundary Element Methods
In summary guidelines for the use of boundary element techniques to
design and evaluate shipboard ICCP systems are:
A more refined model is needed than is traditionally associated
with boundary element techniques.
Accurate modeling of relatively small-scale features, such as bilge
keels, is necessary.
The accuracy of computational results is directly dependent on the
accuracy and appropriateness of the polarization data used as
material characterization input data.
Preliminary design and trend studies can be successfully completed
using less than optimum polarization data. Trends in performance
can be determined even though magnitudes will be suspect.
Variations in seawater conductivity that correspond to changes in
deployment region can be significant to system performance and
should be incorporated into the design basis.
Modeling damaged paint as totally bare metal is a conservative
Modeling paint as a perfect insulating material is acceptable
depending on the accuracy of results required.
The need to further address simplifying assumptions used in the
computational approach is being addressed by on-going and planned
work. Topics identified for evaluation include use of symmetry boundary
condition for the water surface, effects of free flood spaces, variations in
damage patterns, seabed proximity, seabed characteristics and ship hull
symmetry. The last deals with the accurate modeling of a non-symmetric
ICCP system on a symmetric ship hull. Symmetry was used in the past as
a simplifying assumption to reduce computational problem size.
present computational resources due to advances in computing have
greatly relaxed problem size limitations. It is hoped that these studies
will continue to provide guidance for the creation of new system models
In addition it has been shown that computational modeling:
Allows for the evaluation of reference cell locations based on a
variety of environmental and service conditions.
Allows for the quick evaluation of different system configurations
and environmental conditions to determine the influence on system
Provides a means to evaluate experimental process and assist in
Unified Design Approach
Previously NRL had proposed a combined design methodology that relied
on both computational and experimental procedures .
computational modeling as primarily a means to reduce the number of
iterations of PS modeling required in the design cycle. The advances in
computational techniques and associated increased confidence in the
results of computational modeling of ICCP systems has changed this
proposed interaction. A new comprehensive unified modeling approach
for ICCP system has been proposed [#ref9] that relies more heavily on an
understanding between analysts and experimentalists.
modeling can be used, not only as a preliminary design tool, but to
establish the PS modeling test matrix.
Key test parameters, such as
model scale and relative size to tank size, can be determined
computationally. The unified design approach is shown schematically in
Figure 6. In addition to linking the two methodologies it is also a means
for clear and constant communication between the experimentalist and
computational analyst. Each of these practitioners must realize that their
particular portion of the overall design approach has its own strengths
For instance PS modeling does not have the
polarization response as input data concerns that worry computational
modeling. In a like manner computational modeling can provide quick
evaluations of changes in system or environmental parameters that
requires a much greater time experimentally. Working together the two
approaches can result in a more effective design. The interchange should
be seen as almost constant after initial design analysis rather than a
linear iterative process.
Use Best Designs
Creation of Basic
to Setup Model
System as Required
Figure 6 – Unified
computational and experimental design approach for
shipboard ICCP systems.
This paper reviews the large body of work on computational modeling of
ICCP system performed by NRL.
A summary of modeling guidelines
developed as a result of this work is presented. These guidelines are the
basis for the continual acceptance of computational modeling as a viable
design tool. A brief discussion of how computational and experimental
work can be combined is presented.
Computational analysts and
experimentalists who deal with PS modeling are already working together
to establish a clearer understanding of the phenomenon used in PS
modeling. This understanding will provide insight into the computational
process and calculated results.
The end result from this collaboration
between computational and experimental methodologies will be a robust
and rationally based design and evaluation methodology for shipboard
The unified approach will provide the end-user with a
more effective and efficient system design for a wide range of operating
environments and conditions.
The ultimate end product will be more
versatile system designs and evaluations that allow for extended platform
The support of Dr. Alexis Kaznoff and Mr. E. Dail Thomas, Naval Sea
Systems Command, is gratefully acknowledged.
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