5.4.3. Comparison of Predicted Corrosion Depth and Measured Corrosion Depth

Figure 19 shows a comparison of the predicted corrosion depths calculated with Equation (9) by using the mass concentration differences and the corrosion depths measured from the OM images for the two orifices. The fabrication deviations of 0.087 mm and 0.174 mm are added in the experimental average corrosion depth. The magnitude of the predicted corrosion depth at the inlet orifice is slightly less than the measured corrosion depth with a deviation of 0.087 mm. Moreover, the predicted damage depth at the outlet orifice is much lower than the experimental value. One possible explanation for this is that, as pointed out previously, the effects of wall roughness should be involved, and the different wall roughness values of the inlet and outlet orifices result in different wall mass transfer coefficients; however, exact data on wall roughness is lacking in this study. As an alternative, the calculated corrosion depths of the inlet and outlet orifice were multiplied by a uniform scaler of 1.8 to take wall roughness effects into consideration [7,48]. After multiplying the scaling factor, the magnitudes of the predicted and the measured corrosion depths of the outlet orifice show good coincidence; however, the magnitude of the predicted corrosion depth is slightly higher than the measured corrosion depth, including a deviation of 0.174 mm, which indicates that a scaler less than 1.8 would be applied to the inlet orifice and illustrates that the wall roughness of the inlet orifice is different from that of the outlet orifice. In spite of the arresting coincidence, minor discrepancies can still be observed between the predicted and measured corrosion depth profiles. These may arise for two main reasons: (1) the numerical results are obtained from a model with a smooth surface, while in the experiments, the morphology of the orifice surfaces will have been reshaped gradually by the accumulation of corrosion, and accordingly the turbulence level, and thus, the mass transfer profile will have changed; (2) the wall roughness along the orifice surfaces may be non-uniform. Nevertheless, the results

indicate that the turbulence level in the near-wall region has a strong influence on the corrosion depth profile. Furthermore, the corrosion depth can be predicted successfully by calculating the mass transfer coefficient by integrating the corrosion model into the turbulent flow model.

Researchers in Italy have studied the corrosion of cylindrical AISI 316L SS samples using the LECOR loop. The experiment was performed for 1500 h under the same temperature difference and similar oxygen concentration conditions as are used in this study [49]. They reported an average corrosion rate of 1.9 × <sup>10</sup>−<sup>3</sup> <sup>μ</sup>m/h, which is one magnitude lower than that for the straight central part of the current study's experiment where flow has fully developed. This difference may result from the combined effects of three factors: (1) the absolute temperature is higher in the present study, so the solubility and diffusion coefficient of iron in LBE are higher; (2) the Reynolds number in the LECOR loop is about one-fifth of that in the present study, making the diffusion boundary layer is much thicker, and therefore, mass transfer resistance is much stronger. It has been pointed out that *Sh* has a nearly linear correlation with *Re* for roughened wall surfaces [48,50]; (3) the dimensionless wall roughness in the LECOR loop is much lower than that of the present study, and it is also known that the mass transfer coefficient depends on the dimensionless wall roughness [48]. The predicted depth of corrosion in the straight section of the pipe after 3000 h of operation is about 0.21 mm, which is about 1.3–3.5 times the average experimental corrosion depth (0.06–0.16 mm); this ratio is similar to that reported in another study [51]. Overestimation of the corrosion rate in the simulation may result from [51,52]: (1) the diffusion coefficient of iron in liquid LBE at 450 ◦C not being known sufficiently precisely; (2) the assumption that the liquid metal is saturated at the solid/liquid interface.

Furthermore, the absolute corrosion depth of the specimen is extremely high in the present experiment, which would not be acceptable for real engineering applications. For example, one of the future ADS concepts proposed by JAEA is an LBE spallation target that requires a significant contraction of the LBE flow path at the beam window [53]. The Reynolds number at the beam window is much higher than that of the present study, and the beam window would be required to survive extreme service conditions [54]. Moreover, considering the poor wettability of LBE to 316L SS, the corrosion depth could be larger because slip at the solid/liquid boundary enhances the turbulence level in the near-wall region [55]. In addition, it is known that the structural steel will withstand strong irradiation during its service period, and it has been also reported that the cold-worked steel experiences different corrosion behaviors than the solution-annealed steel in LBE under static and flow LBE conditions, which can be attributed to the alteration of the dominant corrosion process [56,57]. It has also been pointed out that the effects of steel microstructure on FAC depend on the relative thickness between the selective corrosion layer in the solid and the diffusion boundary layer in the fluid. If the former is thicker, the microstructure effects can be visible; otherwise, it can be ignored [30]. Nevertheless, the effects of microstructure on FAC under LBE flowing condition requires thorough and systematical investigation in the future.

Those above-combined factors mean that it is extremely important to devise ways to increase the mass transfer resistance between the base metal and the LBE. Several studies have indicated that the formation of a protective oxide layer can greatly decrease the corrosion rate of 316L SS in static LBE [58,59]. Controlling the oxygen concentration in LBE to a specific range is critical to form an effective self-healing oxide film, and meanwhile avoid the deposition of uncalled-for oxide products (e.g., PbO) on the cold legs, potentially causing blockage [39].

For future ADSs that adopt LBE as the coolant material, even once an effective protective oxide film has formed on the structural material, it may be broken or thinned by turbulence pounding [6] and various stresses. These include not only the shear stress resulting from turbulent flow, but the thermal stress caused by pulsed proton beam injections and fatigue stress from thermal shocks. Such stresses are generally very large, and their effects on oxide film should be investigated in detail. The effects of absolute temperature and temperature difference on corrosion behavior should also be investigated.

**Figure 19.** Comparison of the predicted corrosion depths calculated from Equation (9) using the mass concentration difference and the corrosion depths measured from the OM images at the two orifices. Note that the fabrication deviations of 0.087 mm and 0.174 mm are added in the experimental corrosion depth, respectively, and the predicted corrosion depths of the inlet orifice and outlet orifice were multiplied by a scaler of 1.8 to take the wall roughness into consideration. (**a**) Inlet orifice; (**b**) Outlet orifice.

#### **6. Conclusions**

FAC behavior of 316L SS under LBE turbulent flow was studied by using the JLBL-1 loop under non-isothermal conditions, and CFD analyses were performed to study the associated hydromechanics and mass transfer. It was found that corrosion of the 316L SS is very severe. Corrosion can reach a maximum depth of approximately 10% of the tube wall thickness in the straight part of the specimen pipe, where the flow is fully developed. However, this ratio increases by as much as 50% at the inlet and outlet orifices, where abrupt changes in the diameter of the specimen lead to changes in the flow direction and/or recirculation. The corrosion profile is correlated with the near-wall turbulence level, but does not seem to correlate with the local shear stress and pressure profiles. In addition, morphological changes during the corrosion process influence the near-wall turbulence level. Moreover, it is shown that the near-wall turbulence level is extremely sensitive to the orifice angle, and that right-angled orifices should be avoided to suppress FAC.

Mass transfer analysis shows that the local turbulence level determines the mass concentration distribution in the near-wall region, thus significantly affecting the mass transfer coefficient. As a consequence, the mass transfer is an effective means of predicting the depth of FAC, which can be calculated with the assistance of CFD analyses with a corrosion model. The corrosion depth was calculated on the basis of the mass transfer coefficient obtained in the numerical simulation and was compared with that obtained in the loop. For the inlet orifice part, the predicted corrosion depth is comparable with the measured corrosion depth; for the outlet orifice part, the predicted corrosion depth is less than the measured corrosion depth, however, this gap was filled well after taking the wall roughness effects into consideration; for the straight tube part, the predicted corrosion depth is larger than the average experimental corrosion depth, which perhaps can be attributed to the fact that the iron concentration on the wall did not reach its saturation value, as assumed. Considering that many other factors beyond the range of the present study can lead to much more severe FAC, formation of an oxide layer is an extremely important means of preventing the rapid development of FAC. In the future, research on corrosion behavior under precisely controlled oxygen, flow speed, and temperature conditions will be carried out.

**Author Contributions:** T.W. carried out the numerical simulations; S.S. performed the experiments; T.W. analyzed the data; T.W. and S.S. were responsible for writing the paper.

**Funding:** This research received no external funding.

**Acknowledgments:** The first author sincerely appreciates Masatoshi Futakawa of J-PARC Center, JAEA, for providing valuable comments and discussions. The authors also extend their thanks to Hironari Obayashi and Toshinobu Sasa of J-PARC Center, JAEA, for useful and interesting discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.
