**1. Introduction**

Flowing liquid has the potential to accelerate the rate at which metal corrodes, a phenomenon known as flow-accelerated corrosion (FAC). In fully developed turbulent flow in simple geometries (e.g., within a pipe) and a no-slip wall condition, the flow is halted at the solid wall, meaning that the flow will transition from turbulent in the bulk fluid to laminar very close to the wall. A so-called "hydro-dynamic boundary layer" will thus be formed, with its boundary line where the flow velocity equals 0.99 of the free stream flow velocity. The boundary layer can be divided into three typical layers depending on the correlation between the dimensionless velocity (*u*+) and the dimensionless distance normal to the wall (*y*+) with approach to the solid wall: (1) the turbulent flow layer, where *u*+ and *y*+ have a logarithmic correlation; (2) the buffer layer, where flow transition from turbulent to laminar occurs; and (3) the laminar flow layer, also known as the viscous sublayer, where *u*+ is linearly proportional to *y*+, the turbulence level damps rapidly, and the viscous effects of fluid are

dominant. If a dissolution constituent of a fluid has a high Schmidt number (*Sc*), exceeding several hundreds, the mass diffusion boundary layer will be very thin, and will be embedded deep in the hydrodynamic viscous sublayer. The characteristics of the boundary layer are illustrated schematically in Figure 1 [1,2].

Pioneering studies have linked several hydrodynamic parameters, such as flow velocity [3], the Reynolds number [2], wall shear stress [4,5], and turbulence level [6] to the rate of FAC of metal. For turbulent flow in structures with simple geometries, the occurrence of FAC is mainly attributable to wall shear stress and the turbulence level in the near-wall region. The above two factors affect the protective oxide film on the base metal and the adjacent diffusion boundary layer [6], which are considered barriers to mass transfer, due to the particularly low mass transfer rate within them [7]. Fluctuations in turbulence can disturb the mass transfer rate from the bulk fluid to the metal surface and vice versa [5,8]; it can also disturb the formation of the protective oxide and disrupt the protective oxide layer [6]. Moreover, the shear stress generated at the wall may rupture or thin the protective oxide coating. In both cases, the mass transfer coefficient across the solid/liquid interface, and thus the corrosion rate of the metal, will be affected. In practice, the profile of wall shear stress and that of the near-wall turbulence level are coincident with each other for flow in structures with simple geometries because the shear stress on the wall is the main source of local turbulence [7]. This is shown schematically in Figure 2.

When flow encounters sudden contraction or expansion in pipes, orifices, valves, elbows, and weld heads, however, the hydrodynamic mechanisms of FAC become complex. In such situations, flow diversion and flow separations, flow reattachments, and flow recirculation occur. Extensive research has aimed at clarifying these mechanisms, but they are not yet thoroughly understood. Chang et al. [9] pointed out a positive correlation between wall shear stress and wall mass transfer. Utanohara et al. [10,11] concluded that the root mean square (RMS) of instantaneous shear stress is a suitable parameter for evaluating the FAC rate, despite their results showing a better correlation between the profiles of the FAC rate and the near-wall turbulence level. Their argument for discounting this result was that the relationship between the turbulence level and FAC had not been theoretically validated. Crawford et al. [12] indicated that the pressure drop attributed to secondary flow can significantly increase the average and oscillatory wall shear stress. By contrast, Nesic et al. [6,13] and Poulson [14] found that it is the high near-wall turbulence level, not the wall shear stress, which is responsible for localized enhancement in the wall corrosion rate. In addition, many other studies have linked the turbulence level to the rate of mass transfer and corrosion [15–18].

The majority of existing research has adopted water, sea water, or slurry as the flow medium, but a few studies have employed heavy liquid metals (HLMs), e.g., lead and lead-based alloys such as lead–bismuth eutectic (LBE). LBE is an ideal candidate coolant material for Generation-IV fast reactors and accelerator-driven systems (ADSs) because of the following physical characteristics: (1) a high boiling temperature, so that the heat generated in the reaction core can be utilized more efficiently; (2) its inertness on contact with water, air, and steam, enabling safe operation [19,20]. However, it is also well known that LBE poses a severe threat of corrosion on the material of its container [21], potentially ultimately leading to structural failure. The corrosion rate, *CR*, under LBE flows is a complex process involving many factors, and can be expressed as follows:

$$CR = f\left(M\_{\rm c}, T, \Delta T, \mathbb{C}\_{\rm O\_2}, R\_{\rm w}, V\_{\rm l}, \tau\_{\rm w}, I\_{\rm t}, \dots\right), \tag{1}$$

where *Mc* is the chemical components of the test specimen, *T* is the temperature of the test specimen, Δ*T* is the temperature difference between the hot and cold legs of a loop, *CO*<sup>2</sup> is the oxygen concentration in the LBE, *Rw* is the wall roughness, *Vl* is the flow speed of the LBE, *τ<sup>w</sup>* is the shear stress on the wall, and *It* is the turbulence level in the near-wall region.

Earlier studies investigating the corrosion of structural steels by LBE looked at the loop as a whole, focusing on the corrosion pattern and the mass transfer behavior of the corrosion products [22]. The effects of *MC*, *T*, Δ*T*, *CO*, and *Vl* have attracted most attention [21,23]. There has also been a report

of unexpected tube failure in the Corrosion In Dynamic lead Alloys (CORRIDA) loop at the Karlsruhe Institute of Technology [24]. A hole penetrated the tube, which had an initial wall thickness of 2.5 mm, downstream of a tube junction where the flowing LBE entered the vertical tube at an angle of 30 degrees. The study mentioning this attributed the failure to complex turbulent LBE flow. However, to the best of the authors' knowledge, the local mechanism of FAC under turbulent LBE flow has not been studied in detail, either experimentally or numerically, from the perspectives of hydromechanics and wall mass transfer behavior.

If the potential of LBE as a coolant is to be exploited, it is highly desirable to investigate FAC of structural materials under turbulent LBE flow. To that end, the present study experimentally investigates FAC of type 316L stainless steel (SS), which is a candidate structural material for future ADSs, using the JLBL-1 loop installed at the Japan Atomic Energy Agency (JAEA). An orifice-type test tube with abrupt narrowing and widening at each end of a straight section was installed in the loop. Flow paths in the test tube show change in flow direction, fully developed flow, and recirculation. Investigations of the behavior of corrosion under such conditions are of interest and importance to scientific research and engineering applications. The study goes on to investigate the correlation between the hydrodynamic parameters and the corrosion profile using computational fluid dynamics (CFD) numerical simulations performed with STAR-CD. CFD analyses combined with a corrosion model are used to characterize the wall mass transfer behavior, and comparisons are drawn between the experimental and numerical results.

**Figure 1.** Schematic of the boundary layer where turbulent flow meets a no-slip wall boundary.

**Figure 2.** Schematic of the effects of turbulent flow on the corrosion rate of the base metal.
