*5.2. Effects of the TKE, Shear Stress, and Pressure*

The TKE near the wall, and the shear stress and pressure on the wall along the two orifice surfaces, are plotted in Figure 9 to investigate the effects of different hydrodynamic parameters on the corrosion depth. The average corrosion depths of the two orifices, including a fabrication deviation of 0.087 mm, are also plotted for comparison. Note that the curves obtained from the simulations have been smoothed. It can be seen that the TKE profiles are similar to those of the average corrosion depth of the two orifices, while those for shear stress and pressure are substantially different.

The maximum shear stress on the inlet and outlet orifice walls are low, approximately 40 Pa and 12 Pa, respectively. A study of copper–nickel alloys in sea water has shown that a shear stress of nearly 4650 Pa is insufficient to remove even the surface oxide film [42]. As pointed out previously, no oxygen film formed on the base metal in this study because of the low oxygen concentration in LBE. Furthermore, the critical shear stress capable of mechanically damaging the base metal is much larger than that able to peel off the oxide film. Therefore, it is considered that shear stress is not the main factor leading to FAC herein. Although the pressure fluctuation on the wall in a disturbed flow imposes shear stress on the wall and perhaps causes damage [43], the results obtained under the LBE flow conditions considered here cannot support this assumption because the complex orifice corrosion depth profiles cannot be explained well by monotonic pressure variation along the orifice wall. Rather, it is the variation in the turbulence level near the wall that best explains the corrosion profiles of the orifices.

**Figure 9.** Comparison of the average corrosion depth with the turbulent kinetic energy (TKE) near the wall and the shear stress and pressure on the wall for the two orifices. (**a**) Inlet orifice; (**b**) Outlet orifice.

## *5.3. Other Effects*

#### 5.3.1. Cavitation

It is well known that the passage of fluid through an orifice leads to a sudden large pressure drop downstream, potentially decreasing the pressure below the saturated vapor pressure. As a result, the liquid may rupture and form cavitation bubbles. The subsequent collapses of the cavitation bubbles release microjets and/or shock waves at the wall, causing cavitation damage [44] that can give the wall a rough morphology. The cavitation number, which is used to judge the inception of cavitation in a liquid, is calculated by

$$\mathbb{C}\_{\mathbf{z}} = \frac{P\_l - P\_v}{\frac{1}{2}\rho V\_l^2},$$

where *Ca* is the cavitation number, *Pl* is the local pressure, *Pv* is the vapor pressure of the liquid, *ρ* is the density of the liquid, and *Vl* is the characteristic flow speed of the liquid.

Under the present flow conditions, a pressure drop to about −3.58 kPa is generated downstream of the inlet orifice. The vapor pressure of LBE at 450 ◦C is 3.49 × <sup>10</sup>-4 Pa [38], resulting in a cavitation number of approximately 0.19. It has been reported that the inception cavitation number is about 0.7 for PbBi-68 liquid flow with a Reynolds number in the range 5.8–7.4 × <sup>10</sup><sup>4</sup> [45]. As the Reynolds number in this study is near this range, a similar inception cavitation number can be applied, indicating that cavitation damage is unlikely to have occurred. Thus, the rough profiles of the orifices can be attributed solely to corrosion damage.
