Illuminating complex material behaviour

WHAT HAPPENS WHEN ENGINEERS EXPLORE the possibility of replacing tried-and-true but cumbersome in-house code with multiphysics simulation software? Nuclear engineers began to ask this question at the Computational Techniques Branch of Canadian Nuclear Laboratories (CNL), Canada’s premier nuclear science and technology organisation.

In nuclear engineering, where research focuses on improving the safety, efficiency, and economics of reactors, mature and robust in-house computer codes are frequently used for modelling studies. But they are also real barrier to innovation because of the need to comb through many lines of code to investigate the potential effect of a minor adjustment to a system. As an alternative to modifying mature or legacy codes, a multiphysics platform provides an environment that allows engineers to explore changes in data and modelling methods without the complications of adapting lengthy code.

Andrew Prudil, fuel safety scientist at CNL, is at the centre of research that enlists simulation software to find ways to improve the established, seemingly immutable design of nuclear reactors. “Essentially, nuclear science is material science, but with additional considerations for the effects of radiation,” Prudil explains. “The materials we study include the nuclear fuel, as well as the constituents of some of the surrounding components.”

Prudil enlisted multiphysics software to create a mathematical model that includes a huge number of physical phenomena. His modelling work includes a representation of a nuclear fuel pellet, including heat transport, structural mechanics deformation, mechanical contact, pressure buildup due to fission gas release and microstructural changes due to grain growth, radiation damage, and burnup. He also modelled the behaviour of the cladding around the nuclear fuel.

In a nuclear reactor, fuel pellets (Figure 1) undergoing fission reactions suffer high temperatures, high thermal gradients and thermal expansion. In addition, the products of fission accumulate in the fuel pellets.

The microstructure of a nuclear fuel pellet changes after sustained high-temperature operation. The as-fabricated grain structure remains only on the outside, closest to the coolant where the temperature is at its lowest. At slightly higher temperatures, the grains grow (coarsen), forming a region of equiaxed grain growth. At the highest temperatures, a vapour transport mechanism results in migration of pores along the temperature gradient (toward the centre) forming a central void and leaving long columnar grains in its wake.

Cracking occurs inside the ceramic fuel. There is also contact between the ceramic pellet and its metal cladding. Radiation damage has to be considered, as high-energy fission products such as gamma and neutron radiation change the microstructure of all materials. There is also macroscopic swelling, as fission splits one atom into two, and two atoms take more space than one.

Two fission products, the inert gases xenon and krypton, form bubbles inside the fuel pellets (Figure 2).

There are also corrosion issues to consider, as high- temperature water in a radiation environment leads to the formation of radiolysis products, which cause corrosion on the outside of the cladding.

Preventing fuel failure

Because the properties of nuclear fuel pellets change dramatically as they are irradiated, engineers rely heavily on models to predict how fuel performance parameters like peak temperature, gas pressure, and cladding strain will change between available experiments. Similarly, knowing how a design change could manifest in a radiation environment requires extensive modelling work and validation with physical measurements.

One of the primary motivations for Prudil’s research was to model the deformation of the cladding and obtain a better estimate of cladding strain, as it is a significant mechanism in fuel failure. Once a model for strain of the cladding had been created, the system could be optimised virtually. Optimisation strategies include making a change to the fuel, the fuel-to-cladding gap or the way the fuel is treated once in the reactor.

“It’s relatively straightforward to build a model,” Prudil says, “but less straightforward to know what the correct material properties are to put in that model, especially when they evolve with time and radiation exposure.” After completing a new model, he compares the simulation results to experimental results to assess the quality of his predictions.

Changing the fuel is an attractive approach to upgrading a nuclear plant, as nuclear fuel is designed to be replaced. It is cost effective, as no reactor components would have to be updated. Engineers simply load the new fuel when it is time to refuel the reactor.

“Therefore,” Prudil says, “our top challenge is accurately describing the materials in question.”

Several phenomena in one model

Using the Comsol Multiphysics® software, Prudil created the Fuel and Sheath Modelling Tool (FAST) to capture the complex heat transport, solid mechanics, and material behaviour of the nuclear fuel, cladding and the gap between the fuel and the cladding. Figure 3 shows an example of the temperature profile generated for the pellets and cladding.

“Using Comsol software,” Prudil says, “I don’t have to worry as much about the numerics and programming – I’m able to directly approach the maths and the physics rather than worry about the solution process and the post-processing. There’s less overhead than what’s usually associated with numerical modelling using an in-house code.”

Prudil also obtained simulation results from FAST to show hydrostatic pressure, von Mises stress and axial creep in the cladding and fuel pellets (Figure 4). The distribution of these fields is the result of design parameters such as the length-to-diameter ratio and chamber dimensions as well as operational considerations like power level and coolant temperature.

Simulating the evolution of grain boundary porosity

To extend the modelling tool and shed light on the performance of the reactor in a different way, Prudil modelled the diffusion of gas out of the fuel grains, and then the formation and movement of bubbles on the grain boundaries (Figure 5) using the equation-based modelling functionality available in Comsol®.

Upon irradiation and the chemical change of the nuclear fuel, gas seeps out of the fuel grain, forming bubbles. These bubbles coalesce (Figure 5). In a traditional phase field, the volume of the fuel grains would be modelled. This technique ignores the solids and models the moving surface between the solids and gas. This turns a 3D problem into 2D and significantly reduces the computational resources required.  

The model uses two coupled weak-form equations on the surface of the grain, one for the distance to the bubble surface and the other for the chemical potential. Knowing how much gas comes out of the fuel allowed Prudil to calculate the thermal conductivity and gas pressure inside the fuel element. The results from this analysis allowed Prudil to determine other key indicators of fuel performance. This set of calculations serves as a nonlinear representation of fuel degradation (Figure 6).

From the simulation, it is possible to assess whether the pressure is sufficiently low, in which case the fuel can continue being irradiated — an insight with great implications for safety.

Driving innovation in fuel design

By using multiphysics simulation, engineers at CNL were able to create a useful tool, and clear the way for faster design iteration and innovation. Prudil sees multiphysics simulation informing other areas of development in nuclear engineering. Engineers could completely rethink fuel, designing versions that are resistant to severe accident scenarios, he believes.

In the long term, Prudil also sees simulation software playing a role in the development of small modular reactors. They could be made of new materials and have new geometries. 

Meanwhile, the complex representation of existing reactors Prudil has created continues to lend valuable insight into the many layers of complexity of existing nuclear reactors.

Author information: Andrew Prudil, Fuel safety scientist at CNL 

First published in Multiphysics Simulation, October 2018