The modelling approaches employed in the five types of computer code identified in Section 14.3.1 are described in this section. The emphasis is on fuel performance codes, since the thermo-mechanical behaviour of the fuel pins is the key aspect of fuel behaviour under irradiation.

Neutronics codes

Given the core geometry and materials, the aim of a neutronics calculation is — put simply — to determine the evolution with time of the spatial and energy distribution of the neutron flux in the core. Use of nuclear cross-section data then allows the corresponding nuclear reaction rates, and hence the core power and temperature distributions, to be evaluated. (The reality is more complicated, since the neutron flux distribution, nuclear reaction rates and core power and temperature distributions are interdependent.) Since the composition of the fuel changes with burnup, which in turn affects the neutron flux distribution, the neutronics calculation must also compute the evolution of the fuel composition with burnup. Of particular importance is the depletion of burnable absorber materials, since these strongly influence the neutron flux.

Due to computational limitations, the neutronics calculation is generally divided into two stages, the first performed by a so-called lattice code and the second by a whole core neutronics code (subsidiary codes may also be employed to perform, for example, core temperature distribution calculations). The lattice code calculates the change in composition of the fuel as a function of burnup for each assembly type. Neutron transport theory with a large number of neutron energy classes, or groups (i. e. multi-group theory), is utilised in two dimensions. An accurate nuclear data library (e. g. JEFF or ENDF/B) is also employed. The neutron transport equations (Glasstone and Sesonske, 1980) are solved via convoluted methods (e. g. the method of characteristics (Knott and Edenius, 1993)), with various approximations to take account of the heterogeneity of the core, the resonances in the nuclear reactions, neutron leakage, etc. The results are used to construct a lookup table of nuclear cross sections and reaction rates as a function of burnup. This lookup table is then an input to the whole core neutronics code, which performs neutron transport calculations in three dimensions for the entire core. To make the problem tractable, the diffusion theory approximation to neutron transport theory (Glasstone and Sesonske, 1980) is generally implemented with only a small number of neutron energy groups (i. e. the calculation is a few-group calculation). The resulting neutron transport equations are solved (typically by the nodal method (Smith and Rempe, 1988)) and the spatial and energy distributions of the neutron flux, and hence the core power distribution, are determined.

Whole core neutronics codes can be of either the steady-state or kinetics (transient) varieties. The former assumes quasi-steady-state conditions throughout irradiation, i. e. that the neutron density distribution is always in equilibrium. This simplifies the equations that need to be solved, thereby allowing a more accurate solution method with high core discretisation. The latter calculates the full time dependence of the neutron density distribution. Since the equations that need to be solved are necessarily more complex, the methods employed for their solution are generally less accurate than for steady-state codes, with more approximations. The core discretisation may also need to be coarser than with steady-state codes to allow simulation over acceptable timescales.

Steady-state codes are used for core design (loading pattern acceptability) calculations where a quasi-steady-state assumption is adequate. Kinetics codes are used for analysis of specific faults as part of reactor safety studies. For faults where the neutronics and the thermal-hydraulics are coupled (e. g. a steamline break in a PWR or power-flow oscillations in a BWR), kinetics codes require either a simplified core/primary circuit thermal-hydraulics model, or coupling to a core/system thermal-hydraulics code.

An alternative to the lattice code plus whole core neutronics code approach to neutronics calculations is use of a Monte Carlo code (Carter and Cashwell, 1975). In this case, the neutron transport equations are ignored; instead, the underlying stochastic behaviour of individual neutrons is simulated. A neutron produced by fission is assigned an initial position, energy, speed and direction by random sampling from the appropriate probability distributions. Given the core geometry, core materials and nuclear reaction cross sections, the evolution of the neutron’s position, energy, speed and direction are then evaluated, taking into account any scattering or fission initiated by the neutron, until the neutron is absorbed or has escaped from the core. If the neutron induces fission, the position, energy, speed and direction histories of the further neutrons generated are also evaluated. This process is repeated many times and the tallies of the neutron path lengths and nuclear reactions in pre determined regions, or cells, of the core, and of neutrons passing through surfaces between cells, are accumulated. These tallies can then be used to estimate the neutron flux and power distributions in the core. The uncertainties in the estimated values decrease as the number of evaluated neutron histories is increased, but at the expense of an increased computation time.

Due to the computational overheads, use of the Monte Carlo method for standard core design is not currently feasible. However, Monte Carlo codes may be used to benchmark (support the predictions of) lattice codes, or for modelling non-standard core configurations for which standard neutronics codes are not applicable or are inaccurate.