# Partial Redesign of an Accelerator Driven System Target for Optimizing the Heat Removal and Minimizing the Pressure Drops

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Design of the Cooling System and Preliminary Theoretical Calculations

- Maximum size of the system: a cylinder with diameter and height equal to 0.12 m and 0.5 m respectively;
- Inlet temperature and operating pressure of the helium equal to 80 °C and 40 bar respectively;
- Maximum temperature of the beryllium equal to 900 °C (the melting point temperature is 1287 °C, and a margin of at least 300 °C was chosen);
- Considering He as the cooling fluid with maximum allowable velocity of 70 m/s.

- $\dot{m}$ = 0.35 kg/s: the ∆T results equal to 38.5 °C and the maximum velocity in the smaller section approximatively equal to 40 m/s;
- $\dot{m}$ = 0.7 kg/s: the ∆T resulting equal to 19.6 °C and the maximum velocity in the smaller section approximatively equal to 70 m/s.

#### 2.2. CFD as a Tool for Engineering Verification Calculation

_{0}is the total energy, defined as:

^{®}v17.0, a code already widely used and validated for this kind of simulations. A very important step in the CFD calculations process is the preliminary selection by a grid sensitivity analysis. In the following section, the obtained results, and the performed sensitivity analysis are highlighted.

#### 2.3. Preliminary 1D Calculations Comparison and CFD Calculations Assessment

- Mass flow rate at the inlet equal to 0.35 and 0.7 kg/s for the two simulations;
- Inlet temperature equal to 80 °C;
- Pressure outlet at the out of the cooler equal to 0 Pa (relative pressure);
- Coupled heat transfer at the internal target-helium interface;
- Adiabatic conditions for external wall and inner tube;
- The neutronic calculations [12,15] showed that the heat flux is generated non-uniformly inside the volume (the heat flux, obviously, is generated by the protons that impinge on the Be nuclei); for this reason it was decided, as a conservative hypothesis, to impose the flux generation completely on the surface.

^{+}< 30 on the first wall node; this value has been obtained by the layer addition shown in Figure 4, having 7 layers with height ratio equal to 1.2 and initial height 1 × 10

^{−4}.

## 3. Results

#### 3.1. Initial Sensitivity Analysis

- v
_{max_He}is the maximum He velocity inside the fluid domain; - T
_{max_Be}is the maximum temperature reached by the solid Be target; - Δp is the pressure drop inside He, calculated between the inlet and outlet sections;
- T
_{avg_TARGET}is the average temperature of the target-helium interface surface; - Time/100it is the time required to perform 100 steady iteration (on a Hybrid Intel Phi-Xeon cluster).

#### 3.2. Comparison Among the Proposed Configurations by Analytical Calculations

#### 3.3. Optimization of the Proposed Configuration ($\dot{m}$ = 0.7 m/s)

_{bayo}in Figure 1).

_{bayo}has been performed and the obtained results are shown in Table 7.

_{bayo}= 0.06 m is the best solution, both in terms of Be temperature and He velocity (and associated pressure drops), as shown in Figure 6. The pressure decreases passing from the H

_{bayo}= 0.03 to H

_{bayo}= 0.06 m and subsequently starts to grow again because there are both a higher distributed pressure loss (due to the longer inner tube) and a further effect of acceleration in the final part of the inner tube (due to the beginning of the hemispheric caps of the bayonet outer tube and to a restriction of the section with respect to the H

_{bayo}= 0.03 to H

_{bayo}= 0.06 m cases).

_{bayo}= 0.06 m and H

_{bayo}= 0.09; in Figure 7 the more efficient heat exchange is shown, with a clear lowering of the average temperature visible from the smoother contours of temperature: this result is mainly due to the more efficient heat exchange in the impingement zone, in turn due to the more developed (with respect to the original case) velocity profiles.

_{2}value (Figure 1): this parameter (the design value is 0.04 m) influences both the inlet and the outlet sections, and consequently the mean velocity of the flow. Figure 8 shows the average value of the inlet and outlet velocity varying R

_{2}. On the basis of to the previously shown contours of the velocity magnitude, it is possible to reduce the inlet section area, by incrementing R

_{2}and increasing the mean value of the inlet velocity and potentially decreasing the peak velocity at the outlet. Finally R

_{2}has been chosen equal to 0.048 m, in order to have an increase in the inlet velocity of about 10 m/s but with a decrease of the mean outlet velocity of about 20 m/s. The simulations were conducted assuming H

_{bayo}equal to 0.06 m.

_{2}= 0.048 m cases. The enlargement of the outlet section produces positive effects (decrease of the maximum values) in term of both velocity profile (that results flatter in particular moving towards the outlet section) and of temperature (Table 8).

## 4. Discussion and Conclusions

_{bayo}= 0.06 m and R

_{2}= 0.048 m have been selected.

- The use of standard wall functions will be evaluated more deeply because it could be that, due to the geometry, it should be possible to see some degree of boundary layer separation and swirls and the hottest region is where the boundary layer reattaches and starts to re-develop;
- Because the fluid velocity is relatively high, the viscous heating could also play a non-negligible role, so a specific deep evaluation of this point is foreseen;
- A more deeply analysis the turbulent kinetic energy and/or dissipation rate trends (including more details on the turbulent energy spatial distribution, such as TKE, relative to design parameters and nodalization/grid density, and considerations of optimization methods and/or applied neural network methods) will be performed;
- Further studies and validation activities on the target redesign will be carried on the basis of already performed experimental activities (e.g., [25]);
- The possibility to introduce on the inner part of the bayonet tubes some surface features in order to enhance thermal mixing will be investigating (taking also into account the feasible Be components machinability).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

a | thermal diffusivity, m^{2}/s |

cp | specific heat, J/kg·K |

d | diameter, m |

e | rib height, m |

f | friction coefficient |

H | channel height, m |

L | length, m |

K | turbulent kinetic energy, m^{2}/s^{2} |

Nu | Nusselt number |

p | rib pitch, m |

P | pressure, Pa |

PEC | performance evaluation criteria index |

PP | pumping power, W |

Pr | Prandtl number |

q | heat flux, W/m^{2} |

Re | Reynolds number |

s | channel thickness, m |

T | temperature, K |

T* | dimensionless temperature, T* = T/T_{bulk} |

u | velocity component, m/s |

W | channel width, m |

w | rib width, m |

x, y | spatial coordinates, m |

δ | Kronecher delta function |

λ | thermal conductivity, W/m·K |

μ | dynamic viscosity, Pa·s |

ν | kinematic viscosity, m^{2}/s |

ρ | density, kg/m^{3} |

σ | turbulent Prandtl number |

τ | wall shear stress, kg/m^{2} |

ω | rate of dissipated turbulent kinetic energy |

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**Figure 3.**Computational domain with indications of the zones and an axial view of the mesh. (

**a**) Axial view of the computational domain; (

**b**) Indications of the zones of the mesh.

**Figure 11.**Redesigned entrance profile (velocity vector shown there are negligible improvements in terms of recirculation zones reduction).

**Table 1.**Nominal target dimension (see Figure 1).

Geometrical Dimensions | (m) |
---|---|

H_{1} | 0.5 |

H_{2} | 0.36 |

R_{1} | 0.06 |

R_{2} | 0.04 |

H_{bayo} | 0.06 |

Property | Value |
---|---|

ρ (kg/m^{3}) | 5.0878 |

c_{p} (kJ/kg·K) | 5189.6 |

k (W/m·K) | 0.184 |

µ (Pa·s) | 2.33 × 10^{−5} |

Property | Value |
---|---|

ρ (kg/m^{3}) | 1848 |

c_{p} (J/kg·K) | 1825 |

k (W/m·K) | 201 |

Mnodes | ~2, 5 | ~10 |
---|---|---|

V_{max_He} | −5.0% | 1.9% |

T_{max_Be} | −4.3% | 1.2% |

Δp | −2.0% | 1.8% |

T_{avg_TARGET} | −6.1% | 0.1% |

Time/100it | ~−20% | ~+70% |

Turbulence Models | k-ε Realizable | k-ω SST | diff. (%) |
---|---|---|---|

V_{max_He} | 69.3 | 74.8 | 8% |

T_{max_Be} | 849.1 | 859.8 | 1% |

Δp | 6196.1 | 6473.0 | 4% |

T_{avg_TARGET} | 660.1 | 686.7 | 4% |

**Table 6.**Comparison of macroscopic flow fields parameter in the case of mass flow rate equal to 0.35 and 0.7 kg/s.

$\stackrel{\mathbf{.}}{\mathit{m}}$ | 0.35 kg/s | 0.7 kg/s | Diff. (%) |
---|---|---|---|

V_{max_He} | 41.3 | 74.8 | 44.8% |

T_{max_Be} | 1297.6 | 859.8 | −50.9% |

Δp | 1683.6 | 6473.0 | 73.0% |

T_{avg_TARGET} | 1100.7 | 686.7 | −60.3% |

H_{bayo} (m) | 0.03 | 0.06 | 0.09 |
---|---|---|---|

V_{max_He} | 74.8 | 67.6 | 68.3 |

T_{max_Be} | 859.8 | 831.1 | 868.1 |

Δp | 6473.0 | 6287.9 | 6438.0 |

T_{avg_TARGET} | 686.7 | 659.5 | 668.4 |

R_{2} (m) | 0.048 | 0.04 |
---|---|---|

V_{max_He} | 66.1 | 67.6 |

T_{max_Be} | 807.9 | 831.1 |

Δp | 3940.3 | 6287.9 |

T_{avg_TARGET} | 618.1 | 659.5 |

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**MDPI and ACS Style**

Lomonaco, G.; Alessandroni, G.; Borreani, W.
Partial Redesign of an Accelerator Driven System Target for Optimizing the Heat Removal and Minimizing the Pressure Drops. *Energies* **2018**, *11*, 2090.
https://doi.org/10.3390/en11082090

**AMA Style**

Lomonaco G, Alessandroni G, Borreani W.
Partial Redesign of an Accelerator Driven System Target for Optimizing the Heat Removal and Minimizing the Pressure Drops. *Energies*. 2018; 11(8):2090.
https://doi.org/10.3390/en11082090

**Chicago/Turabian Style**

Lomonaco, Guglielmo, Giacomo Alessandroni, and Walter Borreani.
2018. "Partial Redesign of an Accelerator Driven System Target for Optimizing the Heat Removal and Minimizing the Pressure Drops" *Energies* 11, no. 8: 2090.
https://doi.org/10.3390/en11082090