# 3D Transient CFD Simulation of an In-Vessel Loss-of-Coolant Accident in the EU DEMO WCLL Breeding Blanket

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## Abstract

**:**

## 1. Introduction

## 2. Scenario and Geometry Description

## 3. Simulation Setup

#### 3.1. Boundary and Initial Conditions

#### 3.1.1. Boundary Conditions

#### 3.1.2. Initial Conditions

- $\lambda $: molecular mean free path;
- L: characteristic length (in this case, the distance between the inlet and the wall in front of it);
- ${k}_{B}$: Boltzmann constant;
- T: temperature of the system;
- $\sigma $: particle diameter;
- p: pressure of the system.

#### 3.2. Model and Solvers

#### 3.2.1. Model

#### 3.2.2. Solvers

- Implicit Unsteady.
- Time step adaptivity based on Courant number:Due to the strong difference between upstream and downstream conditions, the start-up of the transient is the most critical time interval; therefore, a very small time step, such as 1 × 10
^{−10}s, must be used during this period. However, such a small time step is not needed throughout the whole simulation. This model allows one to automatically define the most suitable time step during the transient, basing the tuning on the Courant number $Co=v\phantom{\rule{0.277778em}{0ex}}\frac{\Delta t}{\Delta x}$, where v is the local speed, $\Delta t$ is the time step, and $\Delta x$ is the local grid size. In particular, if both the mean and maximum $Co$ in the domain are below 0.5 and 5, respectively, the time step is increased by a factor of 1.1; otherwise, it is halved. After the start-up phase, the average time step is ∼2 μs before the impact of the reflected wave (see Section 4.1 below), and ∼4 μs after. - Segregated flow and segregated energy:For both these solvers, the discretisation scheme is left with the default second-order upwind. However, the adopted cycle employed in the algebraic multi-grid solver is an F-type cycle, which, in supersonic conditions, performs better than the default one (V-type). In addition, it represents a good compromise between the W-type and the V-type from the computational point of view [18].

#### 3.3. Mesh Adaptivity Strategy

- The user selects two values of the AMR function $\varphi $ that define a range (in this case, $[0.1,0.3]$).
- The solver behaviour is then specified by choosing between three different actions: “Refine”, “Keep” or “Coarsen”.
- For each cell, the function $\varphi $ is evaluated, and the action is chosen according to the local value:$$\left\{\begin{array}{c}\varphi <0.1\phantom{\rule{42.67912pt}{0ex}}coarsen\hfill \\ 0.1\le \varphi \le 0.3\phantom{\rule{17.07182pt}{0ex}}keep\hfill \\ \varphi >0.3\phantom{\rule{42.67912pt}{0ex}}refine\hfill \end{array}\right.$$

## 4. Results

#### 4.1. Flow Field

#### 4.2. Pressure Evolution and Phase Change

#### 4.3. Temperature Field

## 5. Comparison with the Helium-Cooled BB Case

## 6. Conclusions and Perspective

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Model Development and Validation

#### Appendix A.1. Setup

- Inlet: stagnation inlet with fixed supersonic pressure, total pressure and total temperature.
- Outlet: pressure outlet with fixed pressure and temperature.
- Bottom boundary: symmetry plane.
- Walls: no slip condition.

p_{in} [MPa] | T_{in} [K] | |
---|---|---|

Water | 5.0 | 519.1 |

Vapour | 0.1 | 372.8 |

#### Appendix A.2. Model

- (a)
- 2D
- (b)
- Implicit unsteady
- (c)
- Turbulent (realisable $k-\u03f5$ two-layer)
- (d)
- Multiphase
- (e)
- Volume of Fluid (VOF)
- (f)
- Segregated flow
- (g)
- Segregated multiphase temperature

#### Appendix A.3. Results

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**Figure 1.**The EU DEMO tokamak [17].

**Figure 2.**Computational domain and boundary conditions [15].

**Figure 4.**Flow field evolution on the symmetry plane before the impact with the wall at (

**a**) $t$ = 0.1 ms, (

**b**) $t$ = 0.5 ms, (

**c**) $t$ = 3.0 ms, (

**d**) $t$ = 5.0 ms, (

**e**) $t$ = 7.0 ms and (

**f**) $t$ = 9.5 ms.

**Figure 5.**Flow field evolution on the symmetry plane immediately after the impact with the wall at (

**a**) $t$ = 11.0 ms, (

**b**) $t$ = 17.0 ms, (

**c**) $t$ = 25.0 ms, (

**d**) $t$ = 40.0 ms, (

**e**) $t$ = 45.0 ms and (

**f**) $t$ = 55.0 ms.

**Figure 6.**Flow field evolution on the symmetry plane far after the impact with the wall at (

**a**) $t$ = 170.0 ms, (

**b**) $t$ = 200.0 ms, (

**c**) $t$ = 270.0 ms, (

**d**) $t$ = 310.0 ms, (

**e**) $t$ = 400.0 ms and (

**f**) $t$ = 590.0 ms.

**Figure 10.**Fraction of water with “outboard” point (black dot) superimposed on it, at (

**a**) $t$ = 35.0 ms, (

**b**) $t$ = 40.0 ms, (

**c**) $t$ = 45.0 ms and (

**d**) $t$ = 50.0 ms.

**Figure 13.**Comparison of the evolution of the average pressure in the VV between 3D CFD model (red line) and 0D system-level code (blue line). The evolution of the the average pressure on the BD surface, as computed by CFD, is also reported (yellow line).

**Figure 14.**Temperature distribution at (

**a**) $t$ = 7.0 ms, (

**b**) $t$ = 10.0 ms, (

**c**) $t$ = 20.0 ms, (

**d**) $t$ = 35.0 ms, (

**e**) $t$ = 45.0 ms and (

**f**) $t$ = 55.0 ms.

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**MDPI and ACS Style**

Sprò, M.; Froio, A.; Zappatore, A.
3D Transient CFD Simulation of an In-Vessel Loss-of-Coolant Accident in the EU DEMO WCLL Breeding Blanket. *Energies* **2023**, *16*, 3637.
https://doi.org/10.3390/en16093637

**AMA Style**

Sprò M, Froio A, Zappatore A.
3D Transient CFD Simulation of an In-Vessel Loss-of-Coolant Accident in the EU DEMO WCLL Breeding Blanket. *Energies*. 2023; 16(9):3637.
https://doi.org/10.3390/en16093637

**Chicago/Turabian Style**

Sprò, Mauro, Antonio Froio, and Andrea Zappatore.
2023. "3D Transient CFD Simulation of an In-Vessel Loss-of-Coolant Accident in the EU DEMO WCLL Breeding Blanket" *Energies* 16, no. 9: 3637.
https://doi.org/10.3390/en16093637