Developing Smoothed Particle Methods for Modelling Continuum Mechanical and Thermal Behaviour in Nuclear Fuel and Cladding

The purpose of this work is to explore the validity of using smoothed particle methods for future
applications within nuclear fuel modelling. The particle nature of the method makes it attractive
for modelling the complex multi-physics environment of nuclear fuel. This work however focuses
on the fundamental accuracy of the method within the bounds of current simple fuel performance
models.
The thesis is separated into four main sections: examination of simple heat flow models, the effect
of particle arrangement, complex heat flow within thermal models of nuclear fuel and finally simple
mechanical models.
The examination of heat flow by smoothed particle methods begins with simple 1D models. Three
approaches to modelling heat flow identified in the literature are tested and the results compared
using errors calculated from the complimentary analytical models. One method is selected for
further use within this work due to achieving the lowest error in results. Particular attention
is given to the effect of boundary conditions on the models. Two main methods for handling
boundaries are explored: the use of fixed boundary particle values against the use of dynamically
assigned values. Dynamic boundaries are shown to offer reduced error compared to the fixed case.
The effect of these boundaries are further explored for 2D models under both transient and steady
state conditions. Dynamic boundaries are shown to suffer for discontinuous boundaries and more
complex boundary shapes. A method is proposed for handling these issues and is shown to offer
reduced error in the analytical model compared with the fixed boundary case.
The effect of particle arrangement is explored for the more complex circular geometry which is
applicable to models of nuclear fuel used within licensing codes. Three main particle arrangements
are tested: square lattice, triangular lattice and concentric particle rings. The effect of relaxing
these particle structures under density-dependent forces is also explored. Each of these particle
arrangements are tested using the smoothed particle equation for heat flow identified in the earlier
section. The model used is steady state heat flow in a 2D annulus and is considered due to the
existence of a well-defined analytical model. This model is considered as a good simplified model for
internally heated cladding around nuclear fuel. The triangular lattice is identified as the superior
choice for particle arrangement for further use within this work due to the low errors demonstrated
coupled with the fast construction and applicability to other geometries.
These findings are then applied to a simple 2D model of nuclear fuel, equivalent to those found
within current codes used for fuel licensing. This model is built up using simple 1D models for the
purposes of validation. Each model presented has a well-defined analytical solution and introduces
a new aspect of complexity in isolation of the others for the purposes of validation. A method
for including heat generation is proposed by modification of methods given in the literature. This
method is shown to be successful with boundary conditions being the largest contributing factor
to the error. A modification to the heat equation to handle thermal interfaces is tested. The
results although successful show room for further improvement by consideration of the boundary
position between particle pairs. Multiple equations to handle a convective boundary condition
within smoothed particle methods are proposed. One of these methods is shown to give acceptable
results however future improvements are discussed. These complexities are then combined into the
2D fuel model and the results are shown to converge. This chapter findings support the notion
that smoothed particle methods are capable of reproducing models currently in use within fuel
licensing codes and is therefore worthy of further exploration by the National Nuclear Laboratory
(NNL).
Finally the work is extended to examine mechanical behaviours within simple nuclear fuel models.
The equations for handling thermally induced strains within smoothed particle methods are introduced. The validity of these equations are first tested within 1D simple simulations using various
corrective factors: velocity smoothing, density evolution and artificial viscosity. Velocity smoothing
is found to make little impact on the simulation results, however the other two methods are shown
to be required, particularly under the use of dynamic boundaries. These findings are then applied
to a simplified cladding model with thermally induced strains in 2D. The model results are shown
to converge with the analytical results. The future scope of the implementation of mechanical behaviour is outlined and a path toward future implementation of smoothed particle methods within
nuclear fuel licensing codes is discussed.