PD1-6
FEM-simulation of electric currents in a galvanic cell with superimposed ac voltage Arne Nysveen, Member IEEE
Martin Høyer-Hansen
Jens Kr. Lervik
[email protected] [email protected] Department of Electrical Power Engineering, NTNU O. S. Bragstads Plass 2E, 7491 Trondheim, Norway
I.
INTRODUCTION
Metallic structures located in sea water can be protected against corrosion by employing cathodic protection [1]. A less noble metal is then in galvanic contact with the metal structure to be protected forming an electrolytic cell where the most noble metal becomes the cathode and the less noble metal forms a sacrificial anode that corrodes. The difference in electrochemical potential between metal and sea water (the electrolyte) for the two metals sets up a dc voltage causing a dc current to flow in the electrolytic cell and the metal structures. In several naval applications, ac currents may flow through the electrodes of the corrosion protection system [2], [3]. The problem is then how to calculate the resulting electric potential and current distribution. The ac current may alter the current distribution causing a malfunction of the corrosion protection. This paper presents a method for analyzing the current and potential distribution for such systems by applying the finite element method (FEM) and the principle of superposition. II.
PROBLEM DESCRIPTION
Fig. 1 shows a cross-section of two cylindrical metal conductors placed in a tank partially filled with sea-water. The problem is to compute the currents flowing in the metal conductors and sea water when an ac voltage source is connected between the external boundaries Γe1 and Γe2. Γw1 and Γw2 denote the interface boundaries between conductors C1 and C2 and the sea water, respectively.
where A denotes the magnetic vector potential, V the electric scalar potential and ω the angular frequency. μ denotes the magnetic permeability and σ the electric conductivity. Firstly, when neglecting the electrolytic dc potential step across the internal boundaries Γw1 and Γw2, the ac current and electric potential distributions are calculated by applying Dirichlet boundary conditions to Γe1 (Ve1=-V0,ac) and Γe2 (Ve2=V0,ac). The contribution from the electrolytic potential is then calculated in a separate computation. This is a conduction problem given by:
σ∇ V = 0 2
(2)
The boundary conditions are now Ve1=Ve2=0 and Vw1=V1,dc on Γw1 and Vw2=V2,dc on Γw2. The electric current and potential distributions in conductive regions are now found by adding the results from the ac and dc analysis. This procedure makes it possible to analyze naval structures that are employing cathodic protection where ac current may flow through the electrodes into the sea water and to study how this may affect the corrosion protection system. III.
TEST IN AN ELECTROLYTE CELL
In order to test the superposition principle for salt water electrolytes, two metallic plates (aluminum and copper) were placed in parallel in a large water tank. The plates are connected to the secondary side a one-phase transformer. When no voltage is applied to the primary, the current in the cell is a pure dc current, see Fig. 2. The primary voltage is then increased and the dc and ac currents are measured. As shown in Fig. 2, the dc current remains almost constant as a function of the imposed ac current.
Idc [mA]
Abstract— A finite element method (FEM) approach is used to calculate current and potential distributions in a galvanic cell with a superimposed ac voltage. The problem is solved by the principle of superposition, solving the system for each of the driving voltages and then adding the solutions. The superposition principle is tested in a simple electrolytic cell. FEM analysis can be a powerful tool when designing and dimensioning marine structures having a corrosion protection system.
[email protected] SINTEF Energy Research Sem Sælands vei 13, 7491 Trondheim,
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Iac [mA] Fig. 2. Measured dc-current as function of ac-current in the electrolytic cell. IV. [1] Fig. 1. Principal domain for FEM analysis. Two metallic cylinders in an electrolyte.
Using the magnetic vector potential for the magneto-quasistatic case, the governing equation becomes:
−
1
μ
∇ A + jωσ A = −σ∇V 2
1-4244-0320-0/06/$20.00 ©2006 IEEE
[2] [3]
(1)
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REFERENCES
W. H. Hartt, “Marine Cathodic Protection – Historical Trends and recent Accomplishments”, IEEE OCEANS2000 Conference Record, September 2000, vol. 3, pp. 1787-93. A. Nysveen et al, “Direct electrical heating of sub sea pipelines – technology development and operating experience”, IEEE PCIC Conference Record, September 2005, pp. 177-187. J. K. Lervik et at, “Design of anode corrosion protection system on electrically heated pipelines”, Conference proc., ISOPE 2004, 2004, pp. 2631
