# RAST-K v2—Three-Dimensional Nodal Diffusion Code for Pressurized Water Reactor Core Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Calculation Models

#### 2.1. Nodal Diffusion Analysis

#### 2.2. Cross-Section Model

- Fuel temperature: 4 points, ranging from 293.6 K to 1500 K
- Moderator temperature: 12 points, ranging from 293.6 K to the input moderator temperature + 25 K
- Boron concentration: 4 points, ranging from 0.1 ppm to 2400 ppm
- Geometry: 4 points for geometry changes (generally for control rod)

- State points: burnup, fuel and moderator temperature, boron concentration, control rod
- Group-wise assembly/corner discontinuity factors
- 1-group power distribution (gamma smeared power distribution)
- 1-group form function for pin power reconstruction
- 1-group xenon and samarium chain data
- Group-wise macroscopic cross-section, ${\Sigma}_{tr}^{mg},{\Sigma}_{a}^{mg},{\Sigma}_{r}^{mg},{\Sigma}_{f}^{mg},\upsilon {\Sigma}_{f}^{mg},\kappa {\Sigma}_{f}^{mg}$
- Number density, and ${\sigma}_{tr}^{mg},{\sigma}_{a}^{mg},{\sigma}_{r}^{mg},{\sigma}_{f}^{mg},\upsilon {\sigma}_{f}^{mg},\kappa {\sigma}_{f}^{mg}$
- Delayed neutron and kinetics data
- Data for detector signal reconstruction
- Decay constants and fission yield data

#### 2.3. Internal TH Solver

- The coolant flow is parallel to the channel; that is, the cross-flow is ignored.
- The core-exit coolant is sub-cooled.
- The power produced by the fuel rods within a node is deposited into the coolant in that node.
- The pressure drop across the core is assumed to be negligible.
- All water properties are evaluated at a single pressure.

_{2}layer with regard to the temperature drop across the coolant and the outer cladding surface. In addition, the thermal conductivity fitting functions based on the experimental data for accident tolerance fuel (ATF) were also implemented.

#### 2.4. Fuel Cycle Analysis

## 3. Engineering Features

#### 3.1. Multi-Cycle Simulation

^{4}assuming that the reactivity of the 1 ppm boron concentration can be controlled to 10 pcm reactivity. When the CBC oscillation occurs, the conversion factor is obtained by linear extrapolation using the CBC and eigenvalues at the ${\left(i-1\right)}^{\mathrm{th}}$ and ${i}^{\mathrm{th}}$ iterations. The control rod and power level can also be employed for estimating the critical state. The equilibrium xenon can be evaluated based on the depletion chains for I-135 and Xe-135 at the equilibrium state with a given power level. The core mass flow rate can be determined for the target average moderator temperature.

#### 3.2. Pin Power Reconstruction

#### 3.3. Parameter Edits

#### 3.4. Burnup Adaptation

#### 3.5. CRUD Modeling

^{th}cycle in practice. As demonstrated by the behavior of the ASI of the (N − 1)

^{th}cycle, the axial power shape cannot be predicted by RAST-K v2 without CRUD modeling. Thus, it will be difficult to model the N

^{th}cycle owing to the incorrect depletion history of the previous cycle contained in the restart file. Using the CRUD modeling function, the decrease in the CBC owing to the CRUD is shown for the (N − 1)

^{th}cycle, and the core depletion calculation for the N

^{th}cycle is performed more accurately. Hence, the ASI of the N

^{th}cycle is close to the measured values.

#### 3.6. Spent Nuclear Fuel Analysis

^{th}, (N + 1)

^{th}, and (N + 2)

^{th}cycles, (2) assembly depletion during the N

^{th}and (N + 2)

^{th}cycles, and (3) assembly depletion only during the N

^{th}cycle. STREAM-SNF was employed for a code-to-code comparison, which showed that the results of the isotope inventory obtained using RAST-K v2 agree with those obtained using the STREAM-SNF within a relative error of 5%.

## 4. Applications

#### 4.1. Verifications and Validation

_{2}as a function of burnup.

#### 4.2. Internal Loose Coupling

^{th}cycle depletion can be initiated by predicting the depletion history of the fuel in the (N − 1)

^{th}cycle.

#### 4.3. External Loose Coupling

#### 4.4. Machine Learning

- RAST-K v2 can provide an accurate solution for nuclear reactor cores with only a small difference compared to the measured data. Hence, RAST-K v2 can be used to develop ML models, which can be further used in a real nuclear power plant (NPP).
- Various reactor core models, even the ones whose operating conditions are unacceptable for safety reasons, can be modeled using RAST-K v2. Data on abnormal core conditions such as CRUD deposition can be employed to train ML models in a nuclear diagnostics system.
- RAST-K v2 can generate a substantial amount of nuclear data owing to the implemented acceleration methods, and such data can be used for efficiently training ML models within the stipulated time.
- RAST-K v2 can provide various nuclear reactor parameters for prioritizing LPs in SA algorithms or mimicking the core monitoring system of NPPs to develop a diagnostic system.

- Generation of normal and abnormal core models by randomly perturbing the input parameters such as the positions of the individual control rod and multiplication factor of the CRUD accumulation model,
- Running RAST-K v2 for all generated input files,
- Extraction of target output parameters from output files and writing them in a single train dataset file with “csv” format.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Axial shape index (ASI) result of the coupled simulation performed using RAST-K v2, the subchannel TH code (VIPRE), and water chemistry code (BOA).

Reactor Type | Parameter | Comparison | Mean | Abs. Std | RMS | Number of Data |
---|---|---|---|---|---|---|

OPR-1000 | CBC Diff. (ppm) | R ^{a} vs. M ^{b} | −23.7918 | 25.9309 | 35.0866 | 91 |

R vs. N ^{c} | −3.6790 | 24.8926 | 25.1498 | 929 | ||

ASI Diff. (-) | R vs. M | 0.0019 | 0.0119 | 0.0120 | 162 | |

R vs. N | 0.0045 | 0.0158 | 0.0164 | 927 | ||

FA Power Rel. Err. (%) | R vs. M | 0.3429 | 2.8076 | 2.8262 | 624 | |

R vs. N | 0.3503 | 1.7976 | 1.8300 | 625 | ||

APR-1400 | CBC Diff. (ppm) | R vs. M | −20.7710 | 12.4050 | 24.0414 | 21 |

R vs. N | −24.5093 | 26.8268 | 36.1060 | 43 | ||

ASI Diff. (-) | R vs. M | 0.0032 | 0.0088 | 0.0090 | 12 | |

R vs. N | 0.0014 | 0.0089 | 0.0089 | 43 | ||

FA Power Rel. Err. (%) | R vs. M | −0.0066 | 1.2684 | 1.2638 | 138 | |

R vs. N | −0.0036 | 1.0694 | 1.0656 | 139 | ||

WH-2L | CBC Diff. (ppm) | R vs. M | - | - | - | - |

R vs. N | -12.8147 | 59.3517 | 60.6589 | 480 | ||

ASI Diff. (-) | R vs. M | - | - | - | - | |

R vs. N | 0.0011 | 0.0123 | 0.0123 | 228 | ||

FA Power Rel. Err. (%) | R vs. M | - | - | - | - | |

R vs. N | 0.352 | 2.200 | 2.230 | 3885 | ||

WH-3L | CBC Diff. (ppm) | R vs. M | −34.8207 | 31.2628 | 46.7511 | 234 |

R vs. N | −7.6617 | 15.9378 | 17.6601 | 303 | ||

ASI Diff. (-) | R vs. M | −0.0074 | 0.0106 | 0.0130 | 248 | |

R vs. N | −0.0134 | 0.0182 | 0.0225 | 182 | ||

FA Power Rel. Err. (%) | R vs. M | 0.2694 | 1.5649 | 1.5874 | 1645 | |

R vs. N | 0.3726 | 4.5802 | 4.5946 | 1646 |

^{a}RAST-K v2 result.

^{b}Measured data.

^{c}Nuclear design code result.

Design Parameters | Difference | ||
---|---|---|---|

BOC | MOC | EOC | |

Cycle length (day) | −2 | ||

CBC (ppm) | 3 | 10 | 7 |

ASI (-) | −0.008 | −0.003 | 0.001 |

FA power (%) | 1.333 | 0.749 | 0.359 |

Peaking factor, Fxy (%) | −0.63 | 0.066 | −0.27 |

FTC (%) | −3.71 | 0.05 | −3.32 |

MTC (%) | 7.30 | 4.72 | 4.41 |

Control rod worth (%) | 0.50 | 0.35 | 0.28 |

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**MDPI and ACS Style**

Park, J.; Jang, J.; Kim, H.; Choe, J.; Yun, D.; Zhang, P.; Cherezov, A.; Lee, D.
RAST-K v2—Three-Dimensional Nodal Diffusion Code for Pressurized Water Reactor Core Analysis. *Energies* **2020**, *13*, 6324.
https://doi.org/10.3390/en13236324

**AMA Style**

Park J, Jang J, Kim H, Choe J, Yun D, Zhang P, Cherezov A, Lee D.
RAST-K v2—Three-Dimensional Nodal Diffusion Code for Pressurized Water Reactor Core Analysis. *Energies*. 2020; 13(23):6324.
https://doi.org/10.3390/en13236324

**Chicago/Turabian Style**

Park, Jinsu, Jaerim Jang, Hanjoo Kim, Jiwon Choe, Dongmin Yun, Peng Zhang, Alexey Cherezov, and Deokjung Lee.
2020. "RAST-K v2—Three-Dimensional Nodal Diffusion Code for Pressurized Water Reactor Core Analysis" *Energies* 13, no. 23: 6324.
https://doi.org/10.3390/en13236324