4.2.1. Flow Analysis

Except for applying the design flow rate (Qin = 19.3 m3/h) as the inlet condition, the discretization scheme for the convective terms of the momentum and turbulence transport equation, turbulence model, multiphase flow model, grid shape, and boundary conditions were the same as those described in Section 3.2.1.

#### 4.2.2. Structural Analysis

Except that additional flow analysis result obtained using ANSYS CFX R19.1 for the change of both the hole diameter of the eighth stage orifice and the flow rate was applied as the pressure boundary condition on the inner wall of the multi-stage orifice and the connecting pipes, the grid shape, material properties, and constraint conditions were the same as those described in Section 3.2.2.

#### *4.3. The Computational Results*

#### 4.3.1. Flow Analysis

Figure 19 shows the distribution of the vapor volume fraction in the second half of the multi-stage orifice depending on the size of the hole diameter (d8) in the eighth stage orifice. As the size of the hole diameter (d8) in the eighth stage orifice increased, the main cavitation region moved from the hole of the eighth stage orifice to that of the seventh stage orifice [16]. For d8/d = 1.24, both the size of the cavitation region and the peak value of the vapor volume fraction were the smallest [16]. For d8/d = 0.84, the cavitation region was extended to the downstream of the eighth stage orifice, and the maximum value of the vapor volume fraction was the largest [16]. In all cases, no cavitation region was formed upstream of the seventh stage orifice (i.e., from the inlet of the upstream connecting pipe to the inlet of the seventh stage orifice) [16].

On the other hand, in the case of the original multi-stage orifice (d8/d = 1.0) installed in the AFW pump recirculation line of the domestic NPP, a cavitation region was formed inside the hole of the eighth stage orifice under the design flow condition as shown in Figure 19b. Therefore, based on the simulation results of this study, it is necessary to review the adequacy of the multi-stage orifice design.

**Figure 19.** Iso-volume of vapor volume fraction depending on the size of the hole diameter (d8) in the eighth orifice stage: (**a**) d8/d = 0.84; (**b**) d8/d = 1.0 (original case); (**c**) d8/d = 1.24; and (**d**) d8/d = 1.49.

Figure 20 shows the distribution of flow velocity and streamlines in the second half of a multi-stage orifice (for the symmetric y–z plane) depending on the size of the hole diameter (d8) in the eighth orifice stage. In this study, only the hole diameter of the eighth stage orifice was changed and therefore the streamline pattern in the upstream of the eighth stage orifice was similar to each other [16]. On the other hand, since the location of the eighth stage orifice hole was higher than that of the seventh stage orifice hole, the flow passed through the eighth stage orifice hole upward [16]. The angle of this upward flow also increased as the size of the hole diameter in the eighth stage orifice increased [16]. As the size of the eighth stage orifice hole diameter was smaller, water (liquid phase) velocity passing through the eighth stage orifice hole was much faster [16]. Therefore, the peak value of the water (liquid phase) velocity for d8/d = 0.84 was found near the hole of the eighth stage orifice. For other d8/d cases (for example, d8/d = 1.0, 1.24, and 1.49), the maximum value of the water (liquid phase) velocity was shown near the hole entrance of the second stage orifice [16].

Figure 21 shows the pressure drop (Δp) depending on the size of the hole diameter in the eighth stage orifice. The pressure drop (Δp) is the difference in static pressure between the upstream and downstream cross-sections of the multi-stage orifice [16]. The corresponding cross-sections were located at 19 mm from the first and eighth stage orifice [16]. As shown in Figure 21, it was found that reducing the hole diameter in the eighth stage orifice resulted in increasing the pressure drop [16]. This trend in the static pressure drop can be also found in the experimental results of Wang et al. [3].

**Figure 20.** Distribution of flow velocity and streamlines in the second half of the multi-stage orifice (for the symmetric y-z plane) depending on the size of the hole diameter (d8) in the eighth orifice stage: (**a**) d8/d = 0.84; (**b**) d8/d = 1.0 (original case); (**c**) d8/d = 1.24; and (**d**) d8/d = 1.49.

**Figure 21.** Pressure drop depending on the size of the hole diameter in the eighth stage orifice.

#### 4.3.2. Structural Analysis

Figure 22 and Table 8 show the predicted results of the stress intensity distribution in the multi-stage orifice and the connecting pipes depending on the hole diameter size of the eighth stage orifice under the design flow rate condition. For reference, numerical modeling for the structural analysis described in Section 4.2.2 was applied to ANSYS Mechanical. As the hole diameter of the eighth stage orifice decreased, the maximum value of the stress intensity increased. Similar to the analysis results in Section 3.2.2, because the flow entering into the multi-stage orifice experienced decompression in the process of passing through the orifice hole, it was judged that the maximum value of the stress intensity occurred in the connecting pipe upstream of the multi-stage orifice. However, it was confirmed that the hole diameter size of the eighth stage orifice did not significantly affect the stress intensity distribution in the multi-stage orifice and the connecting pipe. The predicted stress intensity distribution in the multi-stage orifice and the connecting pipe depending on the hole diameter size of the eighth orifice stage showed more margin for the allowable stress of 207 MPa than that for the operating flow rate (Qin = 34.1, 37.0, 39.0, and 41.5 m3/h).

**Figure 22.** Distribution of stress intensity in the multi-stage orifice and the connecting pipes depending on the size of the hole diameter (d8) in the eighth orifice stage: (**a**) d8/d = 0.84; (**b**) d8/d = 1.0 (original case); (**c**) d8/d = 1.24; and (**d**) d8/d = 1.49.

**Table 8.** The predicted results of stress components depending on the size of the hole diameter (d8) in the eighth orifice stage.


Table 9 shows the predicted deformation results for each direction in the multi-stage orifice and the connecting pipe depending on the hole diameter (d8) size of the eighth stage

orifice. In general, the smaller the hole diameter (d8) size of the eighth stage orifice, the greater the amount of deformation in each direction. At the same hole diameter (d8) size of the eighth stage orifice, the deformation size for each direction was in the order of axial > radial > hoop. For radial deformation, the maximum deformation value was shown in the upstream connecting pipe of the multi-stage orifice subjected to high stress. In the case of axial deformation, the maximum deformation value was indicated at the seventh or eighth stage orifice. For the deformation in the hoop direction, the maximum deformation value was shown either at the third stage orifice or in the downstream connecting pipe of the multi-stage orifice depending on the hole diameter (d8) size of the eighth stage orifice.

**Table 9.** The predicted results of deformation components depending on the size of the hole diameter (d8) in the eighth orifice stage.


#### **5. Conclusions**

In this study, CFD simulation was performed for a six-stage orifice test facility to validate whether the numerical modeling available in ANSYS CFX R19.1 predicted reliably and accurately the complex flow inside the multi-stage orifice. In addition, to assess the adequacy of the changed operating flow rate proposed by the domestic NPP operator as a corrective measure for the flow leakage in the AFW pump recirculation line, the cavitation flow pattern in the multi-stage orifice and the connecting pipe depending on the operating flow rate was simulated. Additionally, using ANSYS Mechanical, the structural analysis was performed for the multi-stage orifice and the connecting pipe under the same operating flow rate condition used for the flow analysis, and the structural integrity was evaluated for the allowable stress. Finally, the effect of the change in the size of the hole diameter at the eighth-stage orifice on the pressure drop characteristics and flow patterns (including cavitation) under the design flow rate condition was evaluated. The main conclusions are as follows:


**Author Contributions:** Conceptualization, G.L., J.B. and S.K.; methodology, G.L.; software, G.L.; validation, G.L.; formal analysis, G.L. and M.J.; investigation, G.L., J.B. and S.K.; resources, S.K. and J.B.; data curation, G.L.; writing—original draft preparation, G.L. and M.J.; writing—review and editing, G.L., M.J. and J.B.; visualization, G.L.; supervision, G.L.; project administration, G.L.; funding acquisition, G.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Nuclear Safety Research Program through the Korea Foundation Of Nuclear Safety (KOFONS) using the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the Republic of Korea (No. 1805007).

**Acknowledgments:** This work was supported by the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources including technical support (project number: KSC-2019-CRE-0236). The author gratefully thanks Choi in the Central Research Center of Korea Hydro & Nuclear Power, Lee and Chang in the Tae Sung S&E for giving the valuable technical comments, and Lee in the Korea Institute of Nuclear Safety for providing the schematic diagram of the AFW system.

**Conflicts of Interest:** The authors declare no conflict of interest. The opinions expressed in this paper are those of the author and not necessarily those of the Korea Institute of Nuclear Safety (KINS). Any information presented here should not be interpreted as official KINS policy or guidance.
