UC Berkeley

Advances in computer abilities, intense competition on the energy market and stringent regulatory

requirements during the last decade have spurred the development of robust numerical

models to support nuclear reactor safety analysis and design optimization. This dissertation

aims to develop methodologies for numerical modeling of Pebble-Bed Fluoride Salt Cooled Reactors

(PB-FHR), a novel reactor design that combines TRISOparticle fuel and flibe salt coolant.

The use of a large number of fuel pebbles in PB-FHR cores poses great challenge in computational

cost and violates the assumptions in most of the traditional deterministic codes developed

for Light Water Reactors (LWRs). This project developed dedicated models with different

levels of spatial and energy resolution for the broad need in FHR design and analysis, including

coupled heat diffusion and point kinetics unit cell models,Monte Carlo neutronicsmodels, and

coupled multi-group neutron diffusion and multi-scale porous media model. Documentation,

version control, testing, verification are all indispensable parts of numerical modeling software

development. These steps are followed meticulously to ensure high quality open source codes

that promote open science and reproducible research.

Unit cell models can compute representative fuel and coolant temperatures and full core power

within a short amount of time and thus is adequate for scoping analysis, or uncertainty and

sensitivity analysis, where a large number of runs is required to cover the input space. FHRs

have substantial graphite reflectors that slows down the neutron generation time by hosting

neutrons while they get thermalized. A ’multi-point’ correction is derived from perturbation

theory to take the reflector effects on reactivity and neutron generation time into account.

Monte Carlo based codes, on the other extreme, can provide accurate results with minimal assumptions,

but they are typically only used for generating cross-sections for deterministic models,

for example point kinetics models andmulti-group neutron diffusion models in this project,

or to provide reference results for benchmarking lower resolution codes due to high computational

cost. PB-FHR has not yet test reactors to provide experimental data for tool validation.

High fidelity models based on direct coupling between neutron transport and Computational

Fluid-Dynamics (CFD) was used in this project as reference for code-to-code verification.

Multi-group neutron diffusion models were developed for design optimization and safety analysis,

because they are compatible with current computation resources in nuclear industry, with

which simulations can be carried out on stand-alone workstations or small computation clusters

within a reasonable time. For areas where the diffusion assumption is limited, e.g., in vicinity

of control rods, the simplified spherical harmonics equations were implemented to improve

the accuracy of diffusion equation by relaxing the isotropic assumption in neutron transport.

The neutronics model is coupled to a porous media CFD module with multi-scale treatment

that computes conductive heat transfer inside TRISO particles and fuel pebbles, as well as convective

heat transfer between fuel pebbles and coolant. Radiative heat transfer may be significant

in the high temperature reactors, but is not modeled in this project due to lack of material

propertiesmeasurement.

Results from the coupled full core modelwere verified with analytical solutionswhen they exist, for example the steady state outlet bulk average temperature, computed from energy balance,

or a referenceMonte Carlo model. Although the absolute value of the multiplication factor can

not be accurately matched between the Monte Carlo statistics and the eigenvalue found from

the coupled model, this can be corrected and more important for transient modeling is the

change in the multiplication factor during a transient. In fact, the important parameters for a

transient study, such as flibe and fuel temperature feedback coefficients, time scale, and control

rod worth matches well between the coupledmodel and the referencemodel.

The multiphysics models are capable of simulating both steady state and a broad spectrum

of transient scenarios, involving either coolant inlet condition or reactivity induced transients,

especially Anticipated Transient Without Scram (ATWS). The methodology was applied to the

TMSR SF-1 and Mk1 design, which are both FHRs that uses TRISO fuel particles in spherical

fuel elements and Fluoride salt coolant. For both designs, steady state power, neutron flux, and

temperature distributions were computed, and reactivity insertion and overcooling transients

were simulated. The study shows that FHR cores are extremely resilient to the investigated

transient scenarios, for the following reasons:

• The graphite based fuel elements in FHRs can withstand up to 1600 ±C without risk of

radioactive release. And the flibe coolant used in FHRs also has high thermal resistance,

with a boiling point at 1430 ±C. Due to the large thermal margin to the failure of TRISO

particles, the thermal constraintswill be more likely in the metallic structures. These temperature

limits should be defined based on both the temperature and the time of exposure

for creep limits or reduced yield stress limits at elevated temperatures.

• In FHRs, the role of coolant and moderator are separated. The Doppler feedback, the

mainmechanism to stabilize the reactor during an ATWS, is more negative than in LWRs.

• Online refueling fuel management regime allows the reactor to operate at a low excess of

reactivity because the reserve for compensating fuel burnup is small in this case.