5.4.2. Mass Concentration Difference Close to the Wall

Figure 17 shows the difference in the mass concentration of iron at different locations. This is defined as

$$
\Delta \mathbb{C} = \mathbb{C}\_w - \mathbb{C}\_0. \tag{12}
$$

In the straight central section of the pipe, the Δ*C* profile is relatively uniform. In comparison, the profiles of Δ*C* at the inlet and outlet orifices are strongly influenced by the turbulent flow. Furthermore, Δ*C* is lower at the outlet orifice than at the inlet orifice. This contrasts with the corrosion depth, which, as shown in Figure 8, is larger at the outlet orifice than the inlet orifice. This may be because the mass transfer coefficient is closely related to the magnitude of roughness [46,48]. Corrosion can be expected to render the smooth wall rough, and perhaps there are differences in the amplitudes of the roughness at the two orifices, resulting in different mass transfer coefficients, and thus, corrosion depths. Prediction of the corrosion depth on the basis of Δ*C* will be considered in the next subsection.

To clarify the correlation between turbulent flow and the mass concentration difference, the profiles of Δ*C* and TKE are plotted together for comparison in Figure 18. Clearly, the profile of Δ*C* is highly coincident with that of TKE near the wall. Therefore, the mass concentration difference can be inferred to be significantly affected by the turbulence level. As shown by Equation (9), the corrosion

rate is proportional to Δ*C*, so it can be deduced that the turbulence level can impose direct effects on the corrosion rate of metal.

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**Figure 17.** Mass concentration difference of iron at various locations.

**Figure 18.** Comparison of mass concentration difference and TKE near the wall. (**a**) Inlet orifice; (**b**) Outlet orifice.
