# Numerical Analysis for Hydrogen Flame Acceleration during a Severe Accident Initiated by SBLOCA in the APR1400 Containment

^{*}

## Abstract

**:**

## 1. Introduction

^{3}in the cylindrical dome geometry with diameter 45.72 m and height 69.69 m and an opening structure of the steam generator (SG) compartments where the hydrogen was discharged upward to the upper region by the safety depressurization system [3,19]. In addition, the thirty passive auto-catalytic recombiners (PARs) located at several positions in the containment, such as in Figure 1, effectively removed the released hydrogen as the severe accident proceeded [9,10,19].

## 2. Multi-Dimensional Hydrogen Analysis System

#### 2.1. Calculation Method of the Multi-Dimensional Hydrogen Analysis System

#### 2.2. Established Analysis Methodology for the Hydrogen Flame Acceleration

_{t}), the gas expansion ratio (σ), and the numerical constant (β) (Equations (2) to (4)). The laminar flame speed (S

_{L}) of the burned gas in Equation (4) is obtained from the test data which are dependent of the temperature, pressure, and steam concentration. The combustion energy from the chemical reaction of the hydrogen-air mixture is calculated by the one-step reaction (Equation (5)) and the generated energy is used as the heat source of the energy equation [6]. The turbulent fluctuation velocity (u′) can be obtained by use of the calculated turbulent kinetic energy from the Standard k-ε turbulent model (Equation (6) to (11)) which is a very efficient model for simulating a turbulent flow in the hydrogen combustion [3,23,24]; C

_{μ}= 0.09, C

_{1}= 1.44, C

_{2}= 1.92, C

_{k}= 1.0, and C

_{ε}= 1.3.

_{2}+ 1/2O

_{2}+ 1.82N

_{2}→ H

_{2}O + 1.82N

_{2}+ 0.242 MJ

## 3. The MHAS Analysis for the SBLOCA

#### 3.1. Calculation of the Hydrogen Distribution by GASFLOW and MAAP

^{2}/s

^{2}, which value is approximately 10% of those at the SBO accident [3]. The reason of these smaller values of TKE at the SBLOCA case may be explained by the fact that the buoyancy dominated flow in the hydrogen release period produces less turbulence generation when compared to the forced convection flow dominated in the hydrogen discharge period at the SBO accident [3]. The initial pressure in the containment for the COM3D calculation shows approximately 0.22 MPa, which is increased from the initial pressure 0.1 MPa given to the GASFLOW calculation due to the release of the steam and hydrogen through the break park of the cold leg to the containment.

^{3}which is approximately 4.8% larger than the design value of the APR1400 containment [19]. This small difference may have resulted from that the GASFLOW’s grid model using the cell length of approximately 100 cm could not accurately model the small size pipes such as the surge line between the hot leg and the pressurizer (PZR). As for the temperature condition to the outer wall of the containment, a constant temperature of 298 K is given to the outer surface of the grid model.

#### 3.2. Calculation of the Hydrogen Flame Acceleration by the COM3D Code

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

D_{t} | turbulent diffusion coefficient [m^{2}/s] |

f | progressive variable [-] |

k | turbulent kinetic energy [m^{2}/s^{2}] |

P | pressure [Pa] |

S_{L} | laminar flame speed [m/s] |

S_{t} | turbulent flame speed [m/s] |

T | temperature [K] |

u’ | turbulence fluctuation velocity [m/s] |

U_{i} | velocity component [m/s] |

Greek Letters | |

α,β | correlation constant [-] |

ε | turbulent eddy dissipation [m/s^{2}] |

μ | viscosity [kg/ms] |

ρ | density [kg/m^{3}] |

σ | gas expansion coefficient [-] |

Subscripts | |

L | laminar |

tur | turbulence |

t | turbulence |

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**Figure 2.**COM3D validation results against the test data [3].

**Figure 6.**Initial conditions of the COM3D calculation for the severe accident. (

**a**) Hydrogen Concentration. (

**b**) Oxygen Concentration. (

**c**) Steam Concentration. (

**d**) Temperature. (

**e**) Pressure. (

**f**) Turbulent Kinetic Energy.

**Figure 8.**Calculated temperature for the hydrogen flame acceleration by COM3D. (

**a**) Temperature distribution as time passes. (

**b**) Temperature behaviors and flame speeds from P1 to P14. (

**c**) Temperature behaviors from P9 to P9-4.

**Figure 10.**Calculated pressure results. (

**a**) Pressure behaviors at P1 to P14. (

**b**) Pressure distribution to time variation.

**Table 1.**Proposed COM3D Analysis Methodology for the Hydrogen Flame Acceleration [3].

Parameter | Model |
---|---|

- Explicit solver
| 2nd order Total Variation Diminishing |

- Combustion model
| KYLCOM+ |

- Turbulent flame speed model
| Kawanabe |

- Wall function
| Low Re number |

- CFL number
| <0.9 |

- RED number
| <0.4 |

- Wall boundary conditions
| Velocity slip/Temp. constant |

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**MDPI and ACS Style**

Kang, H.-S.; Kim, J.; Hong, S.-W.
Numerical Analysis for Hydrogen Flame Acceleration during a Severe Accident Initiated by SBLOCA in the APR1400 Containment. *Hydrogen* **2022**, *3*, 28-42.
https://doi.org/10.3390/hydrogen3010002

**AMA Style**

Kang H-S, Kim J, Hong S-W.
Numerical Analysis for Hydrogen Flame Acceleration during a Severe Accident Initiated by SBLOCA in the APR1400 Containment. *Hydrogen*. 2022; 3(1):28-42.
https://doi.org/10.3390/hydrogen3010002

**Chicago/Turabian Style**

Kang, Hyung-Seok, Jongtae Kim, and Seong-Wan Hong.
2022. "Numerical Analysis for Hydrogen Flame Acceleration during a Severe Accident Initiated by SBLOCA in the APR1400 Containment" *Hydrogen* 3, no. 1: 28-42.
https://doi.org/10.3390/hydrogen3010002