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Long-Term Behaviors of Oxide Layer in Liquid Lead–Bismuth Eutectic (LBE), Part I: Model Development and Validation

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Abstract

For all LBE-cooled systems, the oxygen control technology must be applied for inhibiting corrosion by the liquid metal through formation of protective oxide layers on the structural material surface. The present study focuses on the stability of the protective layer in long-term operations subjected to LBE corrosion. This article, focusing on the modeling development and validation, is the first part of the systematic study. A chemical corrosion model, taking into account the oxide layer removal mechanisms by LBE, is developed. The model is partially validated by available long-term and short-term experimental measurements.

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Abbreviations

\( a_{\text{i}} \left( {i = Fe, Cr, PbO, O} \right) \) :

Activity in LBE

\( A_{\text{i}} \left( {i = 1,2,3} \right) \) :

Constant

\( c_{\text{Fe,b}} \) :

Fe mass concentration in the bulk flow

\( c_{\text{i,s}} (i = Cr,Fe,O) \) :

Mass concentration of substance i in LBE at the LBE/oxide surface

\( c_{\text{i}}^{\text{s}} \left( {i = Fe,O,Cr} \right) \) :

Solubility of substance i in LBE

d :

Hydraulic diameter

\( D_{\text{Fe}} \) :

Diffusion coefficient of Fe in LBE

\( F_{{{\text{Fe,i}} }} (i = Fe_{3} O_{4} ,Sp, St) \) :

Mass fraction of Fe in species i

\( F_{\text{Cr,i}} (i = Sp,St) \) :

Mass fraction of Cr in species i

\( G_{\text{i}} \left( {i = Sp,Fe_{2} O_{3} ,Fe_{3} O_{4} ,Cr_{2} O_{3} } \right) \) :

Free Gibbs energy of formation of oxide i

\( k_{{{\text{p}}0}} \) :

Oxidation parameter in Eq. 31, constant

\( k_{\text{p}} \) :

Oxidation constant of the steel

\( K_{1} ,K_{2} \) :

Constants in Eq. 6

\( p_{{{\text{O}}_{2} }} \) :

Oxygen partial pressure

Q :

Activation energy of the oxidation constant

R :

Gas constant

T :

Temperature

\( \nabla T \) :

Temperature difference of a non-isothermal loop

\( T_{ \hbox{max} } \) :

Maximum temperature of a non-isothermal loop

L :

Length of a non-isothermal loop

\( M_{\text{i}} \left( {i = O,Cr,Fe} \right) \) :

Atom weight of element i

\( r_{1} \) :

Constant in Eq. 3

\( r_{2} ,r_{3} \) :

Constant in Eq. 13

\( R_{\text{i}} (i = Sp,Fe_{3} O_{4} ) \) :

Scale removal rate of the oxide layer i

\( R_{\text{m}} \) :

Mass transfer rate by the liquid metal flow

Re :

Reynolds number

Sc :

Schmidt number

St :

Steel

Sp :

Spinel oxide

t :

Time

\( t_{0} \) :

Time needed for the magnetite layer removal

\( t_{1} \) :

Time at which the iron mass transfer rate equals to the iron diffusion rate through the spinel layer

x :

One-third of atomic number of Cr in a spinel

\( W_{\text{i,Sp}} (i = O,Fe,Cr) \) :

Mass of species i in unit volume of spinel

V :

Flow velocity

\( \tau_{\text{i}} (i = Fe_{3} O_{4} ,Sp) \) :

Non-dimensional time

\( \eta_{\text{i}} (i = Fe_{3} O_{4} ,{\text{ Sp}}) \) :

Non-dimensional thickness of magnetite layer

\( \rho_{\text{i}} (i = Fe_{3} O_{4} ,Sp,St, LBE) \) :

Theoretical density

\( \delta \) :

Thickness of the oxide layer

\( \delta_{\text{sp}}^{0} \) :

Thickness of the spinel layer at \( t_{0} \)

\( \delta_{\text{sp}}^{1} \) :

Thickness of the spinel layer at \( t_{1} \)

\( \delta_{\text{sp}}^{\text{f}} \) :

Asymptotic thickness of the spinel oxide layer

v :

LBE viscosity

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Acknowledgments

This paper was based on a report (LA-UR-11-04116) which was prepared as an account of work sponsored by the Hyperion Power LLC through a CRADA with LANL. The author is grateful to P. McClure, R. Kapernick, D. Poston and D. Dixon for discussion and good comments. Special thinks go to Dr. Carsten Schroer at Karlsruher Institut fuer Technologie (KIT) for providing long-term experimental data.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, OH, USA

    Jinsuo Zhang

  2. D-5, Los Alamos National Laboratory, Los Alamos, NM, USA

    Jinsuo Zhang

  3. Scott Laboratory, Peter L & C, 201 W 19th Ave, Columbus, OH, 43210, USA

    Jinsuo Zhang

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Zhang, J. Long-Term Behaviors of Oxide Layer in Liquid Lead–Bismuth Eutectic (LBE), Part I: Model Development and Validation. Oxid Met 80, 669–685 (2013). https://doi.org/10.1007/s11085-013-9450-7

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