MODELING LIQUID METAL CORROSION IN A FERRITIC STEEL PbLi SYSTEM WITH AND WITHOUT A MAGNETIC FIELD

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1 MODELING LIQUID METAL CORROSION IN A FERRITIC STEEL PbLi SYSTEM WITH AND WITHOUT A MAGNETIC FIELD SMOLENTSEV Sergey, SAEIDI Sheida, ABDOU Mohaed Fusion Science and Technology Center, UCLA, USA E-ail: sergey@fusion.ucla.edu (Sergey Solentsev) Abstract: We perfor coputations of transport processes associated with corrosion of ferritic steel in the flowing eutectic alloy lead-lithiu (PbLi). New coputer codes have been developed to solve coupled fluid flow, energy and ass transfer equations for several flow geoetries, such as a plane channel, rectangular duct or a circular pipe. First, an inverse proble is solved where saturation concentration of iron in PbLi is reconstructed fro the experiental data. These reconstructed data are further used as a boundary condition at the solid-liquid interface to perfor ore analysis and coparisons against available experiental data on corrosion in various flow conditions, including purely hydrodynaic turbulent flows as well as lainar duct flows with and without a agnetic field. A good atch with the experiental data is deonstrated. 1. Introduction Eutectic alloy PbLi and ferritic steel (such as F82H or EUROFER) are attractive candidates for using in breeding blankets of a fusion power reactor as a breeder/coolant and as a structural aterial respectively. Consequently, ipleentation of these aterials in blanket applications requires further aterial copatibility studies, including corrosion of ferritic walls in the flowing PbLi at elevated teperatures relevant to the blanket operation conditions. At present, the liit of 2 μ/year associated with precipitation of corrosion products in the cold leg of the liquid etal (LM) loop is accepted [1]. However, this liit was derived in the past based on conservative assuptions Cs (wpp) T (K) and need to be readdressed. This necessitates further developent and testing of phenoenological odels, boundary conditions as well as further evaluation of aterial properties associated with corrosion processes in the flowing liquid etal. One of the ain goals of this study is to access transport phenoena in the flowing PbLi associated with corrosion of ferritic walls via nuerical odeling. As a atter of fact, even in this relatively siple case, where the corrosion echanis is ostly dissolution of the steel atrix [2], any uncertainties still exist that ake the odeling predictions eaningless. For exaple, the ost critical liitation is related to the experiental values of the Borgstedt [7] Grjaznov[8] Present Correlation, Eq. (1) Figure 1: saturation concentration of Fe in PbLi versus teperature fro 3 correlations.

2 saturation concentration C s of iron (Fe) in PbLi versus teperature (fig 1), which soeties vary by orders of agnitude. In this study, we iprove existing correlations for the saturation concentration and predict corrosion rates accurately. First, we develop new coputer codes that solve siultaneously the fluid flow, energy and ass transfer equations for either turbulent or lainar flows. The turbulent flow code is then run under the experiental conditions, using experiental data on LM corrosion obtained in the recent past. The goal of these siulations is twofold. Firstly, we benchark the new code against experiental data. Secondly, we solve an inverse proble where the data on saturation concentration of iron in PbLi is reconstructed by coparing calculated results for the ass loss with the experiental data. The obtained data on the saturation concentration are then approxiated with a new correlation, which is further used to perfor ore analysis and coparisons. Two sets of experiental conditions have been reproduced in the coputations: (1) corrosion of ferritic-artensitic steels in purely hydrodynaic turbulent PbLi flows [3] and [5], and (2) corrosion in lainar rectangular duct flows with and without a agnetic field [4]. The coputed and experiental data are in a good agreeent, which proofs the adequacy of the suggested odeling approaches and our choice of governing equations and boundary conditions. 2. Matheatical odel In liquid etal blankets, corrosion always occurs in the presence of a flowing liquid etal. Along with the teperature, the flow is one of the ost iportant conditions that ight increase the corrosion rate copared to static liquids. The atheatical odel thus includes the fluid flow equations, the energy equation and the ass transfer equation. The latter is written here in the dilution approxiation assuing all corrosion products are fully dissolved in the liquid etal. We also assue that the ain corrosion process that eventually deterines the wall ass loss is unifor dissolution of iron and copute only iron concentration C in the PbLi. Transport of other etallic coponents (Cr, Ni, Mn, W, V, Ta) is not considered due to their lower concentration. The key issue in solving the ass transfer proble for corrosion and transport of corrosion products in the flowing liquid is the boundary condition at the solid-liquid interface. Most of the studies perfored in LMs have shown that a corrosion process is controlled by ass transfer [5]. In such a case, the global dissolution at the interface is at equilibriu and the corrosion rate is liited by the diffusion/convection of the dissolved species through the boundary layer at the aterial interface to the bulk of the flow. Given the above observation, the boundary condition at the interface can be written as a Dirichlet boundary condition [6]: C = C s w, (1) where C s is the saturation concentration of Fe in PbLi at the wall teperature Turbulent hydrodynaic flows. The experiental data for corrosion of ferriticartensitic steels in turbulent PbLi flows without a agnetic field are presented in [3]. These results had been approxiated with a siple correlation known as the Sannier s equation:

3 ML = 8 1 Exp[ ] V D h, μ/year. (2) 1.98T Here, ML is the aterial loss, T is the absolute teperature of the flowing PbLi ( K), and V is the flow velocity (up to.3 /s). To describe this kind of corrosion processes, the transport odel is written here in the boundary-layer approxiation in ters of the velocity coponents U and V, teperature T, pressure P and concentration C as follows: U U U 1 P 1 U + U + V = + [ y ( ν + νt ) t x y ρ x y y y ], (3) U 1 + ( yv ) =, (4) x y y T T T 1 T ρcp( + U + V ) = [ y ( k+ k t) ] t x y y y y, (5) C C C 1 U V [ y ( D Dt ) C + + = + t x y y y y ]. (6) The integer paraeter is either 1 (plane channel) or 2 (circular pipe) and ν t, kt and D t are the turbulent transport properties: viscosity, theral conductivity and diffusion coefficient of iron in PbLi, which are calculated using a well-known k ε odel of turbulence Lainar flow in a rectangular duct with and without a agnetic field. The experiental data for this case are presented in [4] for a lainar PbLi flow in a rectangular duct 2.7x1 c 2 with inserts ade of EUROFER at 55 C for two cases with (B =1.7 T) and without (B =) a agnetic field and for two velocities 2.5 and 5. c/s. To siulate corrosion processes, a fully developed MHD flow odel written in ters of the axial induced agnetic field coponent B x, axial velocity U and iron concentration C is used as follows: 3. Results U U B B x 1 dp + + =, z y μμ z νρ dx (7) 2 C C C C U = D ( + + ), 2 x x y z (8) Bx Bx U + + σμ B z y z (9) Two coputer codes, one for turbulent hydrodynaic flows [Eqs. (3-6)] and the other for MHD lainar flows [Eqs. (7-9)] have been developed and tested and then applied to the analysis of corrosion processes under experiental conditions described in Section 1.

4 ML(µ/year) Coparison with Sannier's Equation [3] Cs fro Eq.(1) Sannier's Equation Cs fro Borgstedt [7] Cs fro Grjaznov [8] Coparison with Konys [6] Cs fro Eq. (1) Experient ML (µ/year) Sannier's Equation Cs Using Eq. (1) T( o C) V (/s) Figure 2: ass loss in a turbulent flow coputed with the present code against Sannier s equation (V=.11/s, D h =.2) and experiental data [6] (V=.22 /s, D h =.8) Figure 3: ass loss in a turbulent flow as a function of velocity at T= 5 o C and D h = ML(µ/year) 1 9 Sannier's Eqaution Cs using Eq. (1) Dh() Figure 4: ass loss as a function of hydraulic diaeter in a turbulent flow at T= 5 o C and V=.11 /s. Figure 5: coputed ass loss against experiental data [4] for lainar flows with and without a agnetic field Turbulent flows. Using epirical correlations for saturation concentration by Borgstedt [7] and Grjaznov [8] in coputations of the ass loss as a function of the wall teperature doesn t lead to a good fit with the Sannier s equation as seen in fig 2. A new

5 iproved correlation has been obtained by atching calculated and experiental data in the following for: C s = 2. Exp(.218T). (1) This correlation is then used to copute the ass loss as a function of the velocity (fig 3) and hydraulic diaeter (fig 4). In all these cases there is a good atch between coputed and experiental values. The sae correlation is also used in coparisons with ore recent corrosion data obtained in the PICOLO loop [5] resulting in axiu discrepancy of 3% (fig 2) Lainar flows. The velocity profile is coputed first using the thin-wall boundary conditions and then the velocity data are used to solve the ass transfer equation (9) by applying the sae correlation (1). The results are copared with the experiental data for the ass loss fro the Hartann wall in fig 5, showing again a reasonably good atch. 4. Conclusions The ain result of the present study is the new iproved correlation for saturation concentration of iron in PbLi Eq. (1). Using this correlation in coputations of corrosion processes in either turbulent or lainar flows with or without a agnetic field along with the Dirihlet boundary condition (1), results in satisfactory predictions of the wall ass loss in a wide range of flow velocities, teperatures and duct diensions. 5. References [1] Coen, V.: Corrosion probles in nuclear fusion reactors, Chapter 7, in: A working party report on corrosion in the nuclear industry. Great Britain, European Federation of Corrosion Publications, No. 1: [2] Broc, M.; Flaent, T.; Fauvet, P.; Sannier, J.: Corrosion of Austenitic and Martensitic Stainless Steels in Flowing 17Li-83Pb Alloy, J. Nucl. Mater (1988) [3] Sannier, J.; Flaent, T.; Terlain, A.: Corrosion of Martensitic Steels in Flowing Pb17Li. Proc.16 th Syp. on Fusion Technology (199) [4] Bucenieks, I.; Krishbergs, R.: Investigation of Corrosion Phenoena in Eurofer Steel in Pb-17Li Stationary Flow Exposed to a Magnetohydrodynaics. 42 (26) [5] Konys, J.; Krauss, W.; Novotny, J.; Steiner, H.; Voss, Z.; Wedeeyer, O.: Copatibility Behavior of EUROFER Steel in Flowing Pb-17Li. J. Nucl. Mater (29) [6] Konys, J.; Krauss, W.; Steiner, H.: Validation of Modeling Tools to Describe the Corrosion/Precipitation Behavior of EUROFER Steel in Flowing Pb-17Li. Fusion Science and Technology. 56 (29) [7] Borgstedt, H. U.; Feuerstein, H.: The solubility of etals in Pb-17Li liquid alloy. J. Nucl. Mater (1992) [8] Gryaznov, G.M.; Evtikhin, V.A.; Lyublinski, I.: Materials science of liquid-etal systes of theronuclear reactors. Energoatoizdat: 1989.