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High thermal neutron fluxes are needed in some research reactors and for irradiation tests of materials. A High Flux Research Reactor (HFRR) with an inverse flux trap-converter target structure is being developed by the Reactor Engineering Analysis Lab (REAL) at Tsinghua University. This paper studies the safety of the HFRR core by full core flow and temperature calculations using the porous media approach. The thermal nonequilibrium model is used in the porous media energy equation to calculate coolant and fuel assembly temperatures separately. The calculation results show that the coolant temperature keeps increasing along the flow direction, while the fuel temperature increases first and decreases afterwards. As long as the inlet coolant mass flow rate is greater than 450 kg/s, the peak cladding temperatures in the fuel assemblies are lower than the local saturation temperatures and no boiling exists. The flow distribution in the core is homogeneous with a small flow rate variation less than 5% for different assemblies. A large recirculation zone is observed in the outlet region. Moreover, the porous media model is compared with the exact model and found to be much more efficient than a detailed simulation of all the core components.

There are over 240 research reactors in operation in the world [

To generate high thermal neutron fluxes, the reactor core must be compact with a high core energy density [

For safety concerns, the fuel temperature should be lower than 400°C (673 K) and the cladding surface temperature must not exceed 220°C (493 K). No nucleate boiling is allowed in the assemblies and flow instabilities should be avoided [

Existing CFD models have been well developed and tested to predict the temperature and flow distributions in reactor cores [

Porous media models are approximate methods that can be used to simplify core simulations. The porous media model adds a source term into the momentum equation to simulate the solid resistance to the fluid flow in the calculation region [

The purpose of this research is to develop a full core CFD model using the porous media model for safety analyses of the HFRR. The flow and temperature distributions are predicted throughout the entire core for various inlet flow rates based on neutronics analyses of the HFRR design [

As Gong et al. [_{3}Si_{2}-Al and the fuel cladding is Al (6061). Gong et al. [^{14} n/cm^{−2}s. Figure

HFRR core configuration and schematic of follower fuel assembly [

HFRR reactor layout.

GAMBIT was used to build the geometric model of the HFRR core and generate the grid, with FLUENT then being used for the calculations. The mesh was simplified by not including the upstream drive mechanisms and the lower plenum. The heavy water tank was also ignored in the simulations because the heavy water tank has a separate circulation system which is not directly involved in the cooling of the fuel assemblies. The coolant flow in the inverse flux trap was also ignored with the core center modeled as a regular solid because the fuel assemblies are mainly cooled by the coolant flow through the narrow rectangular channels in the fuel assemblies. The interfaces between the fuel assemblies were assumed to be adiabatic in the mesh described in Section

The 18 standard fuel assemblies have exactly the same geometries, so they will have the same flow resistance characteristics. The 6 follower fuel assemblies were also assumed to have the same flow characteristics. The main purpose of this study was to show whether the flow was homogeneous throughout the core instead of the exact flow field inside each assembly. Therefore, each fuel assembly was treated as a virtual channel with the same flow resistance characteristics as the real assembly. The virtual assemblies were then modeled by a porous media model with the same boundary conditions as the real assembly.

The virtual fuel assembly was modeled by the geometric model shown in Figure

Geometry of HFRR fuel assemblies: (a) overview of the geometry model; (b) detailed structure of the virtual fuel assemblies.

As described in the FLUENT 14 user manual [

Whether the porous media model can reasonably simulate the actual flow distribution largely depends on the loss coefficients. The loss coefficients are often measured in hydraulic flow experiments to get the fitting resistance-velocity relationships. However, there have not been any flow tests in the HFRR yet, so the fitting pressure drop-inlet coolant velocity relationship was determined based on the hydraulic experiments and calculations for CARR [

Standard fuel assembly:

Follower fuel assembly:

The relationship between the pressure drop and the momentum source term was used to calculate the viscous loss coefficients and the inertial loss coefficients for the fuel assemblies:

As Figure

The temperature distribution in the HFRR core was then found by solving the porous media energy equations for the thermal nonequilibrium model equations. The porous media model assumes that a solid region overlaps the fluid region. The fluid and solid regions are then connected by a surface heat transfer coefficient. The energy conservation equation for the fluid is

The energy conservation equation for the solid is

^{4}. Therefore,

Table

Boundary conditions and model options.

Boundary conditions and model options | Enabled options |
---|---|

Turbulence model | Standard |

Laminar Zone Option | Enabled |

Inlet boundary condition | Mass flow inlet |

Outlet boundary condition | Pressure outlet |

Energy source term | UDF |

Discretization scheme | 1st-order upwind |

Pressure-velocity coupling | Simple |

The initial conditions were based on the specific thermal-hydraulic parameters for the HFRR presented in Gong et al. [

Figure

Fuel assembly number and average power and peak factor of each fuel assembly in the HFRR [

A structured hexahedral mesh was used in this study. A grid independence study was conducted to determine the number of elements for grid independent results with several meshes with varying refinements used to obtain the optimal number of cells for the simulation. Figure ^{3}/s for the meshes with more than 2,977,478 elements. Despite the differences in the number of cells, the differences in the flow rate were quite small. This is because the porous media model makes the flow uniform, that is, almost independent of the number of cells. The mesh with 2,977,478 cells was used to balance the calculation time and accuracy.

Volumetric flow rate in channel 1 for various numbers of elements.

The porous media model parameter settings must be reasonable for the simulation to be accurate. The empirical formulas for the resistance coefficients came from the experimental data of CARR [

The resistance coefficients were validated based on the flow distribution calculations in CARR [

CARR simulation model: (a) assembly configuration of CARR; (b) outline of the geometry model.

The predictions shown in Figure

Flow distribution factor in each CARR fuel assembly.

The errors between the simulation and the measurements come from the differences between the model and the actual core. For example, the model does not include some physical structures such as the control rods and their guide tubes. These physical structures will affect the flow field, induce mixing, and reduce the temperature stratification in the core. Moreover, the simplified decay tank at the core outlet will also affect the flow distribution symmetry.

The porous media model energy equation can use the thermal equilibrium model or the thermal nonequilibrium model. The thermal equilibrium model assumes that the fluid and solid temperatures are the same. However, for these simulations of channels with high power generation rates in the solid, the thermal equilibrium model is not sufficiently accurate, especially when the temperature distribution of the solid needs to be accurately predicted. Since the solid is not treated separately in the thermal equilibrium model, there is no conduction equation for the solid that can be solved to calculate the temperature distribution.

The thermal nonequilibrium model was validated in the present study by comparing the predicted core temperature distributions from the thermal nonequilibrium model, the thermal equilibrium model, and the exact model (Gong et al. [

Peak fuel temperature.

Model | Peak fuel temperature (K) | Relative error/% |
---|---|---|

Exact model | 345 | / |

Thermal nonequilibrium model | 344 | −0.289 |

Thermal equilibrium model | 375 | +8.695 |

Temperature contours predicted by the thermal equilibrium model: (a) a section at the edge of the heat region and (b) the whole calculation region.

Temperature contours predicted by the thermal nonequilibrium model: (a) whole calculation region, (b) vertical cross sections for coolant (left) and fuel (right) temperatures, respectively, and (c) fuel transverse cross section with the peak temperature.

The peak fuel temperatures in Table

Figure

The porous media model with the nonequilibrium model was used to calculate the flow and temperature distributions in the full HFRR core. Simulations are carried out for five different inlet mass flow rates: 300 kg/s, 350 kg/s, 400 kg/s, 450 kg/s, and 500 kg/s. The predictions of the present model are compared with those of the exact model. This work provides insight into the thermal-hydraulic design of the HFRR and can be used for the HFRR project application.

Figure

Flow distribution inside each assembly for an inlet mass flow rate of 300 kg/s.

Figure

Variation of the flow distribution factor in each standard fuel assembly for various inlet flow rates.

Figure

Flow fields at the core entrance and outlet for an inlet mass flow rate of 300 kg/s.

The temperature distribution in the core at an inlet mass flow rate of 400 kg/s is shown in Figure

Temperature distribution in the core at an inlet mass flow rate of 400 kg/s.

Further studies were conducted to ensure the safety of the hottest standard and follower fuel assemblies. Fuel assemblies 7 and 22 are symmetric, and therefore only one was analyzed. The coolant inlet velocities to follower fuel assemblies 12 and 21 were based on the distribution results in Section

The standard assembly temperatures predicted by the porous media model and the exact model are shown in Figure

Calculated temperatures in the number 12 standard fuel assembly.

Calculated temperatures in number 21 follower fuel assembly.

Figures

Figure

Variations of the peak temperatures in number 12 and number 21 fuel assemblies for various inlet conditions.

The exact model was then used to analyze the safety of number 21 follower fuel assembly. The inlet coolant velocity in number 21 follower fuel assembly was obtained from the predictions in Section

Peak cladding temperature and the local saturation temperature in number 21 follower fuel assembly for various inlet conditions.

The curves in Figure

A safety analysis of the full HFRR core was conducted using a CFD model. The porous media model was used to simulate the fuel region in the core with the thermal nonequilibrium model used for the energy equation The model predicted the flow and temperature distributions in the entire core.

The results show that the flow distribution predicted by the porous media model compares well with experimental data. The thermal nonequilibrium model then provides reasonable predictions of the very different fluid and solid temperature distributions at substantially lower cost than a full Navier-Stokes model.

The flow distribution is almost uniform across the entire core with slightly lower coolant flow rates in the follower fuel assemblies than in the standard fuel assemblies. The results show that all the flow channels have sufficient coolant flow to prevent nucleate boiling. Thus, the safety analysis result satisfies the thermal-hydraulic design criteria. The calculations also show that the inverse flux trap increases the mixing and the heat transfer between the flows from all the assembly channels.

The predicted temperature distributions show that the inlet coolant flow rate must be greater than 450 kg/s to ensure that boiling will not occur in any of the HFRR fuel assemblies with the peak cladding temperature of the hottest fuel assembly always lower than the local saturation temperature with no nucleate boiling.

These calculations are helpful for the thermal-hydraulic design and nuclear safety analysis of the HFRR.

Total entropy (J/K)

Coefficient matric

Coefficient matric

Density (kg/m^{3})

Viscosity (Pa·s)

Velocity (m/s)

Permeability

Inertial loss coefficient

Pressure drop (Pa)

Medium thickness

Temperature (°C)

Heat transfer coefficient (W/m^{2} K)

Area concentration

Nusselt number

Reynolds number

Prandtl number

Porosity

Thermal conductivity (W/mK)

Total energy (J)

Pressure (Pa)

Stress tensor (Pa)

Mass flow rate (kg/s)

Normalized flow distribution factor

Mean rate-of-strain tensor

Diffusion flux

Fluid

Solid

Fluid-solid interface

Coordinate axis

Sensible enthalpy.

The authors declare that they have no conflicts of interest.

This work was partially supported by the Key Laboratory of Neutron Physics, Chinese Academy of Engineering Physics, Project 2012AC01.