**4. FAC prediction downstream an orifice**

Once the relationship between mass transfer and FAC wear rate is established, the computational model for MTC downstream of an orifice can be formulated. Fully developed turbulent pipe flow is assumed in order to determine MTC profiles downstream of the orifice. ANSI specifications of orifice were used to construct the geometrical model. Since the experimental condition in the present study is carried out for straight pipe section fabricated from hydrocal (CaSO4.½H2O) downstream of an orifice to simulate faster effect of mass transfer rates. The Solution is obtained for Renormalization Group (RNG) *K-Ɛ* differential viscosity model for turbulent flow in conjunction with the species transport equations using FLUENT CFD code.

The velocity field of the incompressible viscous flow is obtained using the one dimensional Reynolds averaged governing equations as follows:

Continuity equation:

162 Nuclear Power – Practical Aspects

assumptions were adopted:

thermally insulated.

〈*j*〉 and 〈*jg*〉 are the mixture and vapour volumetric fluxes.

Another model developed by Kuo-Tong et al. [23] to predict FAC damage locations on High pressure (HP) turbine exhaust steam line. Their choice of High pressure (HP) turbine exhaust steam line as a case study was based on the plant measured data of pipe thickness which indicated HP lines as a good example where serious FAC takes place under two phase flow conditions. They reported that FAC phenomenon strongly depends on the piping layout and local flow conditions. They proposed a new mathematical approach to simulate FAC wear rate. The approach includes the use of 3D two-phase flow hydrodynamic CFD model to simulate the two-phase flow behaviour in HP lines, integrated with FAC Models to investigate the impact of the local parameters on FAC damage. The improvement of their new approach over the previous work is the ability to account for the multi-dimensional characteristics applied to FAC wear rate prediction. This is consider a great advantage in predicting FAC compared to the previous codes such as CHECKWORK or CAECE program which are based on empirical correlations that are dependent on the global flow conditions in the piping lines. In developing their code, the following

Adiabatic flow, since the piping in the type of the above-cited facilities is generally

 Droplet-type two-phase flow, because of the high steam quality (> 85%) usually experienced in the studied piping. Hence, the vapour phase (steam) was modelled as a

Their final hydrodynamic CFD models include two-fluid 3D continuity and momentum equations. Closure relations such as the mixture *k-e* turbulent models, two-phase constitutive equations were also used. The developed FAC model claimed to include droplet impingement model, which was used to simulate the mechanically-assisted form of material degradation.

In a similar two-phase flow analysis applied to the extraction piping system connecting the low-pressure turbine (LPTB) and feed water heater (FWH) at boiling water reactors (BWR), Yuh et al. [24] developed a code to predict FAC wear in BWR piping system. Their mathematical approach is very similar to the work done by Kuo-Tong et al. [23], with the exception to the addition of corrosion model used. They obtained the local distributions of fluid parameters including two-phase flow velocities, void fractions, turbulent properties, and pressure. These results were further used to establish the relation for droplet kinetic energy that represents the FAC damage. The comparison of between their model and the

Once the relationship between mass transfer and FAC wear rate is established, the computational model for MTC downstream of an orifice can be formulated. Fully developed

continuous phase and the liquid droplet as a dispersed phase. Simplified geometries, where valves in the piping are not considered.

plant measured data show qualitatively a good agreement.

**4. FAC prediction downstream an orifice** 

where:

$$\frac{\partial \overline{\boldsymbol{u}}\_{i}}{\partial \mathbf{x}\_{i}} = \mathbf{0} \left( \frac{\partial \mathbf{u}'\_{i}}{\partial \mathbf{x}\_{i}} = \mathbf{0} \right) \tag{20}$$

Momentum equation:

$$
\overline{\hat{u}\_{j}}\frac{\partial \overline{\hat{u}\_{i}}}{\partial \mathbf{x}\_{j}} = -\frac{\partial \overline{P}}{\partial \mathbf{x}\_{i}} + \frac{\partial}{\partial \mathbf{x}\_{j}} \left(\frac{1}{\mathbf{Re}} \frac{\partial \overline{u\_{i}}}{\partial \mathbf{x}\_{j}} - \overline{u\_{i}^{\prime} u\_{j}^{\prime}}\right) \tag{21}
$$

Species mass transport equation for a steady process with no chemical reaction is:

$$\nabla \cdot (\rho \vec{v} \mathbf{Y}\_i) = -\nabla \vec{J}\_i + \mathbf{S}\_i \tag{22}$$

where: *<sup>i</sup> J* is the diffusion flux of species *i,* and arises due to concentration gradient, and *<sup>i</sup> S* is the source term.

In Equation (11), the Boussinesq eddy viscosity assumption [25] is used for modeling the Reynold's stress. The eddy viscosity model relation is expressed as:

$$-\rho \overline{u\_i u\_j} = \mu\_i [(\partial \mathcal{U}\_i / \partial \mathbf{z}\_j) + (\partial \mathcal{U}\_j \partial \mathbf{z}\_i)] - 2\rho k \delta\_{ij} / 3\tag{23}$$

where *<sup>t</sup>* is defined as the "turbulent viscosity" and expressed as:

$$
\mu\_{\rm t} = \mathbb{C}\_{\mu} f\_{\mu} (\rho k^2 \,/ \, \varepsilon) \tag{24}
$$

The turbulence kinetic energy ( *k* ) and the turbulence kinetic energy dissipation rate ( ) are defined as follows:

$$k = \left(\overline{u^2} + \overline{v^2} + \overline{w^2}\right) / \text{2, } \text{ } \varepsilon = \upsilon \overline{\left(\partial u\_i / \partial \overline{z\_j}\right)^2} \tag{25}$$

Therefore, the equation for turbulence kinetic energy can be also expressed as follows:

$$\frac{\partial(\rho \text{L} \mathbf{k})}{\partial \mathbf{z}} + (\mathbf{1}/r) \frac{\partial(r \rho \text{Vk})}{\partial r} = \frac{\partial \mathbf{l} (\mu\_{\text{eff}} / \sigma\_k)(\mathbf{\hat{c}} \mathbf{k} / \mathbf{\hat{c}} \mathbf{z})}{\partial \mathbf{z}} + \mathbf{[1}/r] \frac{\mathbf{\hat{c}} [(r \mu\_{\text{eff}} / \sigma\_k)(\mathbf{\hat{c}} \mathbf{k} / \mathbf{\hat{c}} \mathbf{r})]}{\partial r} + \mathbf{G}\_k - \rho \mathbf{z} \tag{26}$$

and the equation for the turbulence kinetic energy dissipation expressed as:

$$\frac{\partial(\rho L \varepsilon)}{\partial \varepsilon} + (1/r) \frac{\partial(r\rho V \varepsilon)}{\partial r} = \frac{\partial[(\mu\_{\rm eff}/\sigma\_{\varepsilon})(\partial \varepsilon/\partial \varepsilon)}{\partial \varepsilon} + [1/r] \frac{\partial[(r\mu\_{\rm eff}/\sigma\_{\varepsilon})(\partial \varepsilon/\partial r)]}{\partial r} + \tag{27}$$
 
$$(\varepsilon/k)(\mathbf{C}\_{\varepsilon 1}f\_1 \mathbf{C}\_k - \mathbf{C}\_{\varepsilon 2}f\_2 \rho \mathbf{c})$$

In Equations (16) and (17) the generation of kinetic energy of turbulence term ( *Gk* ) can be written as:

$$\mathbf{G}\_k = \mu\_{\rm eff} \left[ 2 \{ (\hat{\boldsymbol{\alpha}} \boldsymbol{\Omega} / \hat{\boldsymbol{\alpha}} \hat{\boldsymbol{\omega}})^2 + (\hat{\boldsymbol{\alpha}} \boldsymbol{V} / \hat{\boldsymbol{\alpha}} \hat{\boldsymbol{r}})^2 + (\boldsymbol{V} / \boldsymbol{r})^2 \} + \left[ (\hat{\boldsymbol{\alpha}} \boldsymbol{U} / \hat{\boldsymbol{\alpha}} \hat{\boldsymbol{r}}) + (\hat{\boldsymbol{\alpha}} \boldsymbol{V} / \hat{\boldsymbol{\alpha}} \hat{\boldsymbol{z}}) \right] \mathbf{I} \tag{28}$$

where the effective viscosity ( *eff* ) is defined as:

$$\underbrace{\mu}\_{\text{effective}} = \underbrace{\mu}\_{\text{molecular}} + \underbrace{\mu\_t}\_{\text{turbulent}} \tag{29}$$

The calculation of the local MTC is obtained similar to El-Gammal et al. [26] as:

$$\text{MTC(z)} = \frac{-D\_{SL}\,\text{\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textdegree\textmathbf&\mathbf{\$w\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel\textbot\textparallel$$

Flow Accelerated Corrosion in Nuclear Power Plants 165

In order to evaluate the FAC wear rate downstream orifice, the conservation equations are integrated over each control volume in the flow field which extended upstream downstream of the orifice. Reynolds Average Navier-Stokes equations were solved using the K-Ɛ (RNG) differential viscosity turbulence model to account for low-Reynolds-number (LRN) effects. The solution convergence is greatly improved by using fine near-wall grids. Also, the computational mesh was refined where high velocity and species concentration gradients were expected. Due to the high Schmidt numbers encountered in mass transfer problems, Nesic et al. [27] suggested that the maximum value of Y+ should not exceed 0.1.The Reynolds average mass transport equation was also solved for determining the

For the present case study, numerical simulations were performed at Reynolds number, *Re* = 20,000 and orifice-to-pipe diameter ratios of *d/D* = 0.25, 0.5 and 0.74. Prior to the commencement of the simulations, a sensitivity study of three different grid numbers was performed and the results indicate a deviation in flow characteristics within ±2%. The flow characteristics for the three orifice geometries are found to be qualitatively similar. Therefore, only representative vector and contour plots for *d/D* = 0.5 are presented here. Fig. (2a) shows the mean velocity vectors normalized by the averaged inlet velocity (*UO*) within

the flow domain. It can be seen that the flow accelerates as it approaches the orifice then separates at the sharp edges of the orifice, forming large vortices downstream. These

concentration field of the dissolved wall species.

**Figure 2.** Numerical results for the flow downstream orifice

where *cw* is the species concentration along the wall (obtained from hydrocal properties table), *cb* is the species concentration in the bulk flow beyond the diffusive boundary layer, *n* is the normal vector to the wall surface and *DSL* is the diffusive coefficient of the solid species, which is calculated by using Wilkie's semi-empirical relationship, [26]:

$$D\_{SL} = \frac{7.4 \times 10^{-15} \times T \times \sqrt{\Psi \times M\_S}}{\eta \times V^{0.6}} \tag{31}$$

where *T* is the temperature (K), Ψ is the association factor for the solvent (2.6 for water), *MS*  is the molecular mass for the solvent (18 g for water), η is the solvent absolute viscosity (Pa.s), *V* is the molecular volume of the dissolved species (144.86cm3/mol for hydrocal) at ambient temperature.

The concentration of hydrocal species in the bulk of water *cb* is calculated as follows:

$$\mathbf{c}\_b(z) = \frac{1}{\rho lLA} \left[ \rho u(r) \mathbf{c}(r) dA \right] \tag{32}$$

where *U* is the area average velocity, *u(r)* is the instantaneous flow velocity, *c(r)* is the species concentration profile, and *A* is the cross sectional area of the pipe. The term / | (z) *<sup>w</sup> c n* is calculated by taking the concentration gradient at the wall at an axial location (z). Substituting equations (31) and (32) into equation (30), the cross-sectional average for *MTC(z)* along the axial direction can be calculated.

In order to evaluate the FAC wear rate downstream orifice, the conservation equations are integrated over each control volume in the flow field which extended upstream downstream of the orifice. Reynolds Average Navier-Stokes equations were solved using the K-Ɛ (RNG) differential viscosity turbulence model to account for low-Reynolds-number (LRN) effects. The solution convergence is greatly improved by using fine near-wall grids. Also, the computational mesh was refined where high velocity and species concentration gradients were expected. Due to the high Schmidt numbers encountered in mass transfer problems, Nesic et al. [27] suggested that the maximum value of Y+ should not exceed 0.1.The Reynolds average mass transport equation was also solved for determining the concentration field of the dissolved wall species.

164 Nuclear Power – Practical Aspects

where the effective viscosity ( *eff*

written as:

and the equation for the turbulence kinetic energy dissipation expressed as:

*r r zr z r*

2 22 <sup>2</sup> [2[( / ) ( / ) ( / ) ] [( / ) ( / )] ] *G U z V r Vr U r V z k eff*

) is defined as:

The calculation of the local MTC is obtained similar to El-Gammal et al. [26] as:

species, which is calculated by using Wilkie's semi-empirical relationship, [26]:

15

*V*

( / )( )

*SL*

*D*

*MTC(z)* along the axial direction can be calculated.

ambient temperature.

 *eff <sup>t</sup> molecular turbulent effective*

 

 

11 22

*k*

*k C fG C f*

In Equations (16) and (17) the generation of kinetic energy of turbulence term ( *Gk* ) can be

/ | ( ) ( ) *SL w w b*

where *cw* is the species concentration along the wall (obtained from hydrocal properties table), *cb* is the species concentration in the bulk flow beyond the diffusive boundary layer, *n* is the normal vector to the wall surface and *DSL* is the diffusive coefficient of the solid

> 0.6 7.4 10 *<sup>S</sup>*

The concentration of hydrocal species in the bulk of water *cb* is calculated as follows:

<sup>1</sup> ( ) ( )( ) *<sup>b</sup> c z u r c r dA UA* 

where *U* is the area average velocity, *u(r)* is the instantaneous flow velocity, *c(r)* is the species concentration profile, and *A* is the cross sectional area of the pipe. The term / | (z) *<sup>w</sup> c n* is calculated by taking the concentration gradient at the wall at an axial location (z). Substituting equations (31) and (32) into equation (30), the cross-sectional average for

*T M*

where *T* is the temperature (K), Ψ is the association factor for the solvent (2.6 for water), *MS*  is the molecular mass for the solvent (18 g for water), η is the solvent absolute viscosity (Pa.s), *V* is the molecular volume of the dissolved species (144.86cm3/mol for hydrocal) at

*c c*

*Dcn MTC z*

*eff eff*

  (29)

(31)

(32)

(30)

   

(27)

(28)

[( / )( / ) [( / )( / )] () ( ) (1 / ) [1 / ]

*U rV zr r*

 

> For the present case study, numerical simulations were performed at Reynolds number, *Re* = 20,000 and orifice-to-pipe diameter ratios of *d/D* = 0.25, 0.5 and 0.74. Prior to the commencement of the simulations, a sensitivity study of three different grid numbers was performed and the results indicate a deviation in flow characteristics within ±2%. The flow characteristics for the three orifice geometries are found to be qualitatively similar. Therefore, only representative vector and contour plots for *d/D* = 0.5 are presented here. Fig. (2a) shows the mean velocity vectors normalized by the averaged inlet velocity (*UO*) within

**Figure 2.** Numerical results for the flow downstream orifice

the flow domain. It can be seen that the flow accelerates as it approaches the orifice then separates at the sharp edges of the orifice, forming large vortices downstream. These vortices sustain the reduction in the flow cross-sectional area further downstream up to the minimum area known as the vena contracta, after which the flow decelerates towards the flow reattachment point. This is the cause of the high velocity central region observed just downstream the orifice which changes to lower velocity region as the flow develops further downstream. Fig. (2b) shows the profiles of the mean horizontal velocity for the three geometries at different axial locations. The ordinate *r/D* is measured from the centreline of the pipe while *Z/D* is measured from the orifice. As shown in the figure, the maximum centreline velocity increases within the circulation zone as the orifice diameter decreases. The relative reductions in the centreline velocity at *Z/D*=1 through *Z/D*=4 are about 93%, 92%, 75% and 5.7% respectively, as *d/D* increases from 0.25 to 0.74. Downstream Z/D = 5, the velocity profiles are almost similar for the three geometries, with the flow returning to fully developed turbulent flow at *Z/D*≅ 30. The flow reattachment length downstream the orifice also increases as the orifice diameter decreases, with the shortest at *Z/D*≅ 2 for *d/D* = 0.74, or by *Z/D*≅ 3 for *d/D* = 0.5 and *Z/D*≅ 4 for *d/D* = 0.25.

Flow Accelerated Corrosion in Nuclear Power Plants 167

0.5 and 0.25 respectively. The skin friction coefficient then decreases steeply and reaches a minimum value at *Z/D* ≅ 1.4, 3.4 and 3.7, for *d/D* = 0.74, 0.5 and 0.25 respectively, within the flow re-attachment region. As the flow progresses downstream, the surface shear stress increases due to the boundary layer developed by the reattached flow, and reaches the second local peak between *Z/D* = 4 and 5. These local peak values of *Cf* decrease as *d/D* increases, the first value decreases by about 92% as *d/D* increases from 0.25 to 0.74, while the second value decreases marginally. In general, the shear stress found to decrease as the

The contours of normalized turbulent kinetic energy (*TKE)* within the flow domain for *d/D* = 0.5 are shown in Fig. (4a). *TKE* increases appreciably within the flow separation zone due to the high velocity gradients within this region. Fig. (4b) shows the profiles of the normalized

**Figure 4.** (a) – Contours of normalized turbulent kinetic energy downstream the orifice, for d/D = 0.5

*TKE* for the three *d/D* at different axial locations downstream the orifice. The profiles are found to be qualitatively similar for all the three *d/D*; within the circulation region (Z/D = 0 –

and *Re* = 20,000 and (b) radial profiles of normalized turbulent kinetic energy at *Re* = 20,000.

boundary layer thickness increases downstream restricting orifices.

Another important flow parameter that can be related to the FAC is the skin friction coefficient *Cf* which is defined as *Cf = τW/(1/2ρUO2),* where *τW* is the wall shear stress*.* The distribution of *Cf* downstream the orifice for the three *d/D* ratios are illustrated in Fig. (3). Variation of *Cf* is found to be similar for the three *d/D* ratios. Typical profile show an increase steeply downstream the orifice due to the reversed flow generated by the separating vortices, and reaches a maximum value at *Z/D* ≅ 0.4, 1.3 and 2.3, for *d/D* = 0.74,

**Figure 3.** Skin friction coefficient along the pipe wall downstream the orifice for different orifice diameters

0.5 and 0.25 respectively. The skin friction coefficient then decreases steeply and reaches a minimum value at *Z/D* ≅ 1.4, 3.4 and 3.7, for *d/D* = 0.74, 0.5 and 0.25 respectively, within the flow re-attachment region. As the flow progresses downstream, the surface shear stress increases due to the boundary layer developed by the reattached flow, and reaches the second local peak between *Z/D* = 4 and 5. These local peak values of *Cf* decrease as *d/D* increases, the first value decreases by about 92% as *d/D* increases from 0.25 to 0.74, while the second value decreases marginally. In general, the shear stress found to decrease as the boundary layer thickness increases downstream restricting orifices.

166 Nuclear Power – Practical Aspects

diameters

0

0.05

0.1

0.15

**Skin Friction Coefficient (Cf**

**)**

0.2

0.25

0.3

by *Z/D*≅ 3 for *d/D* = 0.5 and *Z/D*≅ 4 for *d/D* = 0.25.

vortices sustain the reduction in the flow cross-sectional area further downstream up to the minimum area known as the vena contracta, after which the flow decelerates towards the flow reattachment point. This is the cause of the high velocity central region observed just downstream the orifice which changes to lower velocity region as the flow develops further downstream. Fig. (2b) shows the profiles of the mean horizontal velocity for the three geometries at different axial locations. The ordinate *r/D* is measured from the centreline of the pipe while *Z/D* is measured from the orifice. As shown in the figure, the maximum centreline velocity increases within the circulation zone as the orifice diameter decreases. The relative reductions in the centreline velocity at *Z/D*=1 through *Z/D*=4 are about 93%, 92%, 75% and 5.7% respectively, as *d/D* increases from 0.25 to 0.74. Downstream Z/D = 5, the velocity profiles are almost similar for the three geometries, with the flow returning to fully developed turbulent flow at *Z/D*≅ 30. The flow reattachment length downstream the orifice also increases as the orifice diameter decreases, with the shortest at *Z/D*≅ 2 for *d/D* = 0.74, or

Another important flow parameter that can be related to the FAC is the skin friction coefficient *Cf* which is defined as *Cf = τW/(1/2ρUO2),* where *τW* is the wall shear stress*.* The distribution of *Cf* downstream the orifice for the three *d/D* ratios are illustrated in Fig. (3). Variation of *Cf* is found to be similar for the three *d/D* ratios. Typical profile show an increase steeply downstream the orifice due to the reversed flow generated by the separating vortices, and reaches a maximum value at *Z/D* ≅ 0.4, 1.3 and 2.3, for *d/D* = 0.74,

**Figure 3.** Skin friction coefficient along the pipe wall downstream the orifice for different orifice

0 2 4 6 8 10

d/D = 0.25 d/D = 0.5 d/D = 0.74

**Z/D**

The contours of normalized turbulent kinetic energy (*TKE)* within the flow domain for *d/D* = 0.5 are shown in Fig. (4a). *TKE* increases appreciably within the flow separation zone due to the high velocity gradients within this region. Fig. (4b) shows the profiles of the normalized

**Figure 4.** (a) – Contours of normalized turbulent kinetic energy downstream the orifice, for d/D = 0.5 and *Re* = 20,000 and (b) radial profiles of normalized turbulent kinetic energy at *Re* = 20,000.

*TKE* for the three *d/D* at different axial locations downstream the orifice. The profiles are found to be qualitatively similar for all the three *d/D*; within the circulation region (Z/D = 0 – 2). The normalized *TKE* value increases from zero at the wall to a maximum value at the centreline. These local peak values of *TKE*, as well as its radial location from the wall, increase as *d/D* decreases. All the profiles however collapse to a single line at *Z/D* = 8 as the flow becomes fully developed. The axial distribution of normalized *TKE* downstream the orifice is shown in Fig. (4b) for the three *d/D* ratios. Moreover, the peak value of *TKE* decreases by about 96% as *d/D* increases from 0.25 to 0.74.

Flow Accelerated Corrosion in Nuclear Power Plants 169

move downstream from *Z/D* ≅ 1 to 3 as *d/D* decreases from 0.74 to 0.25. The location of *FAC*

**Figure 6.** a: Sherwood number distributions downstream the orifice, for different orifice diameters, and *Re* = 20,000, b: Enhancement of mass transfer downstream the orifice, for different orifice diameters, and

Re = 20,000

peak values found to also correlate very well with the location of the peak *TKE*.

The predicted *MTC* distributions downstream the orifice is shown in Fig. (5). The mass transfer found to increase sharply downstream the orifice and reaches a peak value at *Z/D* ≅ 1, 4 and 3, for *d/D* = 0.74, 0.5 and 0.25 respectively, after which it decreases steeply to the fully developed value downstream. The *MTC* distributions found to correlate very well with the *TKE* profiles. The non-dimensional mass transfer coefficient represented by Sherwood number (*Sh)* and the mass transfer enhancement *ShZShfd* downstream the orifice are shown in Figs. (6a and 6b). The peak value of *Sh*, as well as *ShZShfd*, decreases by about 63% and 42% when *d/D* increases from 0.25 to 0.5 and from 0.5 to 0.74 respectively. The axial locations of the peak values however move downstream from *Z/D* ≅ 1 to 4 when *d/D* decreases from 0.74 to 0.5, while the peak locations move upstream from *Z/D* ≅ 4 to 3 when *d/D* decreases from 0.5 to 0.25.

**Figure 5.** Mass transfer coefficient distributions downstream the orifice (*Re* = 20,000)

FAC rate downstream the orifice is shown in Fig. (7) for different *d/D* ratios. The peak value of *FAC* increases as *d/D* decreases. In the present analysis, the peak value increases by about 90% when *d/D* decreases from 0.74 to 0.25. Moreover, the axial locations of the peak values however move downstream from *Z/D* ≅ 1 to 3 as *d/D* decreases from 0.74 to 0.25. The location of *FAC* peak values found to also correlate very well with the location of the peak *TKE*.

168 Nuclear Power – Practical Aspects

*d/D* decreases from 0.5 to 0.25.

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

**MTC (m/s)**  2.5E-04

3.0E-04

3.5E-04

4.0E-04

2). The normalized *TKE* value increases from zero at the wall to a maximum value at the centreline. These local peak values of *TKE*, as well as its radial location from the wall, increase as *d/D* decreases. All the profiles however collapse to a single line at *Z/D* = 8 as the flow becomes fully developed. The axial distribution of normalized *TKE* downstream the orifice is shown in Fig. (4b) for the three *d/D* ratios. Moreover, the peak value of *TKE*

The predicted *MTC* distributions downstream the orifice is shown in Fig. (5). The mass transfer found to increase sharply downstream the orifice and reaches a peak value at *Z/D* ≅ 1, 4 and 3, for *d/D* = 0.74, 0.5 and 0.25 respectively, after which it decreases steeply to the fully developed value downstream. The *MTC* distributions found to correlate very well with the *TKE* profiles. The non-dimensional mass transfer coefficient represented by Sherwood number (*Sh)* and the mass transfer enhancement *ShZShfd* downstream the orifice are shown in Figs. (6a and 6b). The peak value of *Sh*, as well as *ShZShfd*, decreases by about 63% and 42% when *d/D* increases from 0.25 to 0.5 and from 0.5 to 0.74 respectively. The axial locations of the peak values however move downstream from *Z/D* ≅ 1 to 4 when *d/D* decreases from 0.74 to 0.5, while the peak locations move upstream from *Z/D* ≅ 4 to 3 when

**Figure 5.** Mass transfer coefficient distributions downstream the orifice (*Re* = 20,000)

FAC rate downstream the orifice is shown in Fig. (7) for different *d/D* ratios. The peak value of *FAC* increases as *d/D* decreases. In the present analysis, the peak value increases by about 90% when *d/D* decreases from 0.74 to 0.25. Moreover, the axial locations of the peak values however

0 5 10 15 20 25 30

d/D = 0.25

d/D = 0.5

d/D = 0.74

**Z/D** 

decreases by about 96% as *d/D* increases from 0.25 to 0.74.

**Figure 6.** a: Sherwood number distributions downstream the orifice, for different orifice diameters, and *Re* = 20,000, b: Enhancement of mass transfer downstream the orifice, for different orifice diameters, and Re = 20,000

Flow Accelerated Corrosion in Nuclear Power Plants 171

that the effect of geometry found to strongly affect the FAC wear rate downstream of the orifice. The maximum value of the wear found to be located within 5D downstream of the orifice which agrees very well with the inspection data collected from different power plants. Also, the hydrodynamic profiles such as *TKE* and *MTC* found to characterize the FAC wear rate downstream the orifice and the value of the maximum FAC wear rate

increases as the orifices diameter reduces.

**Figure 8.** Inspection grids downstream of the orifice

strong evidence of the proximity effect.

**5. Effect of proximity between piping components on FAC** 

From the above case study of the flow downstream an orifice, it can be concluded that the size and the geometry of a piping component directly influence the flow velocity and hence the local mass transfer rate. In addition, components with geometries that promote increase in the velocity and turbulence tend to experience higher FAC rate such as elbow, tee, reducers and valves, etc. The effect of turbulence on the FAC rate is represented by the geometry enhancement factor as described by Chexal et al. [20]. Moreover, a component that has another component located close upstream experience more turbulence that further increases the FAC rate. One would expect that such components tend to experience more severe FAC as discussed by Kastner et al. [28] and Poulson [29]. In fact, the piping geometry at the point of rupture at Surry 2, where the elbow located downstream of a T-fittings, is a

**Figure 7.** FAC wear rate downstream the orifice, for different orifice diameters, and *Re* = 20,000

### **4.1. Power plants inspection data**

Ultrasonic techniques (UT) measurements are commonly used to determine the wall thinning measurement in nearly all power plants and to provide more accurate data for measuring the remaining wall thickness in piping system. The UT inspection data were obtained at grid intersection points marked on the piping component. The data are usually stored in a data logger and transferred to a PC for further processing using appropriate software. The wall thickness data were obtained at different grid point on the piping as shown in Fig. (8). For each pipe downstream an orifice, the difference between the measured wall thickness and the nominal pipe wall thickness is calculated and considered to be the wear at this axial location along the pipe. Sometimes, scanning within grids and recording the minimum found within each grid square is an acceptable alternative to the above method. However, it should also be noted that scanning within grids and the minimum wall thickness recorded can affect the accuracy of the data if point-to-point comparison between two consecutive inspections times. The inspection data are used to determine whether the component has experienced wear and to identify the location of maximum wall thinning as well as to evaluate the wear rate and indentify wear pattern in piping component.

In the present case study, 132 inspection data collected from 5 nuclear power plants and 3 fossil power plants for piping downstream an orifice were analyzed. The data of very high and low values of wear are compared to adjacent inspection readings in order to remove data outliers. Once the data set for each inspection location is verified, the wear is identified at each band along the pipe axis. The measured wear data at different location from the orifice were presented for different piping systems as shown in Fig. (9). It can be concluded that the effect of geometry found to strongly affect the FAC wear rate downstream of the orifice. The maximum value of the wear found to be located within 5D downstream of the orifice which agrees very well with the inspection data collected from different power plants. Also, the hydrodynamic profiles such as *TKE* and *MTC* found to characterize the FAC wear rate downstream the orifice and the value of the maximum FAC wear rate increases as the orifices diameter reduces.

**Figure 8.** Inspection grids downstream of the orifice

170 Nuclear Power – Practical Aspects

**4.1. Power plants inspection data** 

0

5

10

15

20

**FAC rate (mm/day)**

25

30

35

40

45

**Figure 7.** FAC wear rate downstream the orifice, for different orifice diameters, and *Re* = 20,000

well as to evaluate the wear rate and indentify wear pattern in piping component.

In the present case study, 132 inspection data collected from 5 nuclear power plants and 3 fossil power plants for piping downstream an orifice were analyzed. The data of very high and low values of wear are compared to adjacent inspection readings in order to remove data outliers. Once the data set for each inspection location is verified, the wear is identified at each band along the pipe axis. The measured wear data at different location from the orifice were presented for different piping systems as shown in Fig. (9). It can be concluded

Ultrasonic techniques (UT) measurements are commonly used to determine the wall thinning measurement in nearly all power plants and to provide more accurate data for measuring the remaining wall thickness in piping system. The UT inspection data were obtained at grid intersection points marked on the piping component. The data are usually stored in a data logger and transferred to a PC for further processing using appropriate software. The wall thickness data were obtained at different grid point on the piping as shown in Fig. (8). For each pipe downstream an orifice, the difference between the measured wall thickness and the nominal pipe wall thickness is calculated and considered to be the wear at this axial location along the pipe. Sometimes, scanning within grids and recording the minimum found within each grid square is an acceptable alternative to the above method. However, it should also be noted that scanning within grids and the minimum wall thickness recorded can affect the accuracy of the data if point-to-point comparison between two consecutive inspections times. The inspection data are used to determine whether the component has experienced wear and to identify the location of maximum wall thinning as

0 5 10 15 20 25 30

**Z/D**

 d/D = 0.25 d/D = 0.5 d/D = 0.74

### **5. Effect of proximity between piping components on FAC**

From the above case study of the flow downstream an orifice, it can be concluded that the size and the geometry of a piping component directly influence the flow velocity and hence the local mass transfer rate. In addition, components with geometries that promote increase in the velocity and turbulence tend to experience higher FAC rate such as elbow, tee, reducers and valves, etc. The effect of turbulence on the FAC rate is represented by the geometry enhancement factor as described by Chexal et al. [20]. Moreover, a component that has another component located close upstream experience more turbulence that further increases the FAC rate. One would expect that such components tend to experience more severe FAC as discussed by Kastner et al. [28] and Poulson [29]. In fact, the piping geometry at the point of rupture at Surry 2, where the elbow located downstream of a T-fittings, is a strong evidence of the proximity effect.

Flow Accelerated Corrosion in Nuclear Power Plants 173

Station A Station B Station C Station D Station E

% Occurrence of The Data Data Trend Curv e Fitting

rate is approximately equal to 70% in average. The distribution of the data occurrence is plotted in Figure (11) to represent the percentage of components to the total used inspections that have the same wear rate. If a linear wear over the operating time is assumed, one can determine the remaining life of component located in the proximity from another component will results in reduction in component life by more than half life. Although the results show a large scatter of the data with a standard deviation of 50%, the

> 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09 **Re**


proximity is believed to have a significant effect on the wear rate.

**Figure 10.** Effect of proximity on FAC wear rate


0

50

100

**FAC Thinning Rate Increase (%)**

150

200

**Figure 11.** Data occurrence

**Data Occurrence (%)**

**Figure 9.** Measured wear rate downstream orifces at different power plants

In summary, a significant amount of research has been conducted on investigating the effect of fluid chemical properties on FAC in nuclear power plants, online monitoring for strategic FAC locations, and FAC control based on chemical fluid decomposition. However, the hydrodynamic effects of single- and two-phase flows on FAC have not been thoroughly investigated, and are currently not well understood. The present case study aims to evaluate the effect of components located in proximity to another component upstream on the pipe wall-thinning rate due to FAC using real inspection data from different degraded elbows in several power plants. Also, to inspire future discussions among the scientific community to revisit the effect of component geometry on FAC wear rate in order establish new codes/correlations that meet actual industrial findings. In order to accomplish this goal, ultrasonic (UT) inspection data for 90o carbon steel elbows for different systems across different nuclear power stations are analyzed in order to quantify the effect of the proximity between components on the FAC wear rate. The effect of the flow velocity as well as the distance between the elbows and the upstream components is also discussed in the present analysis.

The increase in the wear rate due to the proximity is calculated for 90o elbows located within 1D of the upstream Components. Ahmed [4] evaluated several UT data of back-to-back elbows for deferent nuclear power stations as shown in Figure (10). The results are clearly showing an increase in the wear rate due the proximity of the elbow with the upstream components as the majority of the data are consistently above zero. The increase in the wear rate is approximately equal to 70% in average. The distribution of the data occurrence is plotted in Figure (11) to represent the percentage of components to the total used inspections that have the same wear rate. If a linear wear over the operating time is assumed, one can determine the remaining life of component located in the proximity from another component will results in reduction in component life by more than half life. Although the results show a large scatter of the data with a standard deviation of 50%, the proximity is believed to have a significant effect on the wear rate.

**Figure 10.** Effect of proximity on FAC wear rate

172 Nuclear Power – Practical Aspects

analysis.

**Figure 9.** Measured wear rate downstream orifces at different power plants

In summary, a significant amount of research has been conducted on investigating the effect of fluid chemical properties on FAC in nuclear power plants, online monitoring for strategic FAC locations, and FAC control based on chemical fluid decomposition. However, the hydrodynamic effects of single- and two-phase flows on FAC have not been thoroughly investigated, and are currently not well understood. The present case study aims to evaluate the effect of components located in proximity to another component upstream on the pipe wall-thinning rate due to FAC using real inspection data from different degraded elbows in several power plants. Also, to inspire future discussions among the scientific community to revisit the effect of component geometry on FAC wear rate in order establish new codes/correlations that meet actual industrial findings. In order to accomplish this goal, ultrasonic (UT) inspection data for 90o carbon steel elbows for different systems across different nuclear power stations are analyzed in order to quantify the effect of the proximity between components on the FAC wear rate. The effect of the flow velocity as well as the distance between the elbows and the upstream components is also discussed in the present

The increase in the wear rate due to the proximity is calculated for 90o elbows located within 1D of the upstream Components. Ahmed [4] evaluated several UT data of back-to-back elbows for deferent nuclear power stations as shown in Figure (10). The results are clearly showing an increase in the wear rate due the proximity of the elbow with the upstream components as the majority of the data are consistently above zero. The increase in the wear

**Figure 11.** Data occurrence

The other set of UT data is collected for 90o elbows located at different distances (L) from the upstream component are presented. The ratio (L/D) is used to represent the nondimensional upstream distance with respect to the pipe diameter. As discussed before, a component that has another component located close upstream is expected to experience more turbulence which increases the FAC rate. On the other hand, it is expected that the effect of the turbulence produced from the upstream component becomes much less as the distance from the upstream component increases as shown in Fig. (12). It should be noted that the extent of the proximity effect as shown in Figure (6) is 0 to 5 piping diameters as the a average increase in the wear rate is equal to 70 % (with a standard deviation of 50%) which approximately the same as for elbows within 1D from the upstream components. As the distance between the two components increases the change in the wear rate decreases to reach a minimum value in the fully developed region.

A general trend between the increase in the wear rate and the non-dimensional upstream distance (L/D) is obtained using the average values in the wear rates at different (L/D). The additional effect of the component located upstream close to another component is previously correlated by Kastner et al. (1990) as:

$$\text{Effect of Proximity } \left( \% \right) \text{ =} e^{\left( \text{-} 0.231 \sum\text{\textdegree C} \right)} \times 100 \tag{33}$$

Flow Accelerated Corrosion in Nuclear Power Plants 175

**Figure 13.** Comparing data with Kastner et al. [28] correlation

**6. Conclusions and recommendations** 

susceptible components and reduce the inspection scope/time.

and mass transfer analysis.

**Author details** 

Wael H. Ahmed

*Saudi Arabia* 

As discussed before, components with geometries that promote increase in the flow velocity and turbulence tend to experience higher FAC rate such as elbow, tee, reducers downstream of orifices and valves, etc. Therefore, the turbulence production is expected to be dependent on the component geometry. Consequently, the type of the upstream component could be also considered as a contributing factor and should be considered while performing the flow

The effect of geometry found to strongly affect the FAC wear rate. For example, the maximum value of the wear found to be located within 5D downstream of the orifice. Also, the analyzed trends obtained from the plants inspection data show significant increase in the wear rate due to the component proximity. The CFD simulation of the hydrodynamic parameters such as *TKE* and *MTC* found to characterize the FAC wear rate downstream of piping components. Additional experimental and numerical investigations are required to further evaluate the close proximity effect for different components configuration. Findings of the present work will allow the power plant FAC engineers to identify more accurately

*Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, Dhahran,* 

The average values of FAC wear rate in Fig. (12) are compared to the empirical equation proposed by Kastner et al. [28] and found to be in good agreement with the present data shown in Fig. (13). However, the correlation tends to over predict the data as the distance between the components approaches zero which can be attributed to the accuracy of the proposed correlation and the UT measurements uncertainty.

**Figure 12.** Effect of the upstream distance on the wear rate

**Figure 13.** Comparing data with Kastner et al. [28] correlation

As discussed before, components with geometries that promote increase in the flow velocity and turbulence tend to experience higher FAC rate such as elbow, tee, reducers downstream of orifices and valves, etc. Therefore, the turbulence production is expected to be dependent on the component geometry. Consequently, the type of the upstream component could be also considered as a contributing factor and should be considered while performing the flow and mass transfer analysis.
