5.3.2. Gravity

LBE is a high-density liquid metal, so it is necessary to consider the effects of gravity on flow. First, the direction of gravity was set to be perpendicular to the test tube. Figure 10 shows the effects of gravity on various hydrodynamic parameters. The values of 0 and 180 degrees represent the anti-gravity direction and the gravity direction, respectively. The profiles of the hydrodynamic parameters are almost the same at the two circumferential angles, and only tiny differences in the amplitude can be observed.

Secondly, gravity was set to be in the direction of the test tube, representing no gravity effect on the flow. Figure 11 shows a comparison of the TKE along the straight central part of the test tube with and without gravity effects. It is hard to distinguish any difference in the TKE profiles. The above results illustrate that the hydrodynamic parameters are insensitive to gravity. This may be because the Reynolds number is high so the strong effect of the inertial force on the flow makes the effects of gravity negligible.

**Figure 10.** Effects of gravity on various hydrodynamic parameters.

**Figure 11.** Comparison of TKE along the straight central part of the test tube with and without a gravity effect.

#### 5.3.3. Corroded Morphology

Accumulation of corrosion damage on the inner surface of the wall changes its morphology. A corroded surface could be expected to disturb the flow pattern near the wall, and therefore, the TKE in the near-wall region. To investigate such effects, the experimental corroded surfaces of the two orifices were merged into the simulation models. Figure 12 shows a schematic of the corroded surface profiles used in the simulation, which are the same as the corroded depth profiles at 90 degrees in the experiments. To connect the two orifice parts and the straight central part smoothly, the straight part of the specimen was also assumed to be corroded to a uniform depth of 0.65 mm, which represents an increase in the inner diameter of the straight part of the specimen by 1.3 mm.

Figure 13 plots the TKE for a smooth versus a corroded orifice with distance along the orifice surface. For the inlet orifice, the TKE profile shows much more variability and reaches a considerably higher maximum value in the corroded profile than along the original smooth surface. The peaks in TKE usually appear downstream of sudden protuberances on the corroded surface. This is easy to understand because such convexity enhances the local turbulence level [46]. Interestingly, for the outlet orifice, the magnitude of TKE is relatively weaker for the corroded morphology than with a smooth surface. Furthermore, differences in TKE in the central section are insignificant. This can be attributed to two factors: (1) the corroded outlet orifice surface has fewer protuberances than the corroded inlet orifice surface (Figure 12), so the turbulence level is not locally enhanced; (2) the connections between the straight pipe and the corroded outlet orifice are much smoother than the original ones, which seems to ease the recirculation near the outlet orifice, and therefore, the TKE amplitude.

**Figure 12.** Schematic of the corroded surface profiles adopted in the simulations. (**a**) Inlet orifice; (**b**) Outlet orifice.

**Figure 13.** Effects of the corroded surface on TKE in the near-wall region at the two orifices. The utilized corrosion depth profile is plotted together for comparison. (**a**) Inlet orifice; (**b**) Outlet orifice.

## 5.3.4. Orifice Angle

The angle of the orifices was altered, from 30 degrees to 60 degrees and 90 degrees, to investigate the effect of orifice angle on flow behavior. This is shown schematically for the inlet orifices in Figure 14, and its effect on TKE is shown in Figure 15. For the outlet orifice, there is no significant difference in the amplitude of TKE. Shan et al. [47] pointed out that the flow field in the recirculation region is insensitive to the ratio between the orifice and pipe diameters. Therefore, it is deduced that the TKE of flow in the recirculation region close to the outlet orifice wall is insensitive to the orifice angle as well. However, for the inlet orifice, the turbulence level is very dependent on the orifice angle. The value for TKE can grow up to several magnitudes higher if the orifice angle changes from 30 to 90 degrees. As TKE has been inferred to significantly influence corrosion depth, extensive corrosion can be anticipated in the 90-degree case. These results provide guidance for system design with flowing LBE—structures with sudden geometry changes should be avoided as much as possible.

**Figure 14.** Schematics of inlet orifices with different angles. Note that only the outlet orifices are not shown.

**Figure 15.** Effects of orifice angle on TKE in the near-wall region for the two orifices. (**a**) Inlet orifice; (**b**) Outlet orifice.

#### *5.4. Mass Transfer*

## 5.4.1. Effective Viscosity and Effective Diffusivity

Figure 16 shows the effective viscosity (*μeff* = *μ* + *μt*) and effective diffusivity (*Deff* = *Dm* + *Dt*) of iron upstream of the reattachment point. As expected, the effective viscosity remains constant below *y*+ = 2, which corresponds to the viscous sublayer in the near-wall region. Beyond the viscous sublayer, the turbulent viscosity is much larger than the molecular viscosity, so the turbulent-induced momentum transfer is dominant in species transfer. With approach to the wall, the turbulence level damps rapidly in the viscous sublayer and the turbulent viscosity decreases sharply to a negligible value, indicating that turbulent momentum transfer will, likewise, become insignificant. In the viscous sublayer, however, the effective diffusivity is much larger than the molecular diffusivity; in other words, even weak turbulence can strongly affect species transfer through diffusion [27]. Only when the distance from the wall reaches approximately *y*+ = 0.4 can the turbulent diffusivity be ignored and the molecular diffusivity be considered dominant in species diffusion. This is in the thin diffusion boundary layer hidden in the viscous sublayer. The relationship between the thickness of the diffusion boundary layer, *δd*, and that of the viscous sublayer, *δv*, is close to that recommended by Nesic et al. [7]:

$$
\delta\_d = \delta\_\upsilon / \text{Sc}^{0.55} \tag{11}
$$

**Figure 16.** Effective viscosity and effective diffusivity of iron upstream of the reattachment point. (**a**) Effective viscosity; (**b**) Effective diffusivity.
