Granular flow in a pebble-bed reactor – Introduction

The impetus to better understand the regime of dense granular drainage has come in part from real engineering problems facing industry, and an excellent example of this is the granular flow that takes place in a pebble-bed nuclear reactor. A worldwide effort is currently in process to develop more economical, efficient, proliferation-resistant and safer nuclear power, and there are many examples of new reactor designs that are under consideration. One such, is the pebble-ned nuclear reactor design which originated in Germany in the 1950s, but is now being revisited by several countries, notably China; it is also a candidate for the next generation nuclear plant of the Department of Energy.

The design of a pebble-bed reactor consists of a large cylindrical container filled with radioactive fuel pebbles (typically 6cm in diameter) which are slowly cycled. Pebbles that are drained from the bottom of the container are reintroduced at the top of the packing, or replaced with fresh pebbles if they have undergone sufficient burn-up. Heat generated by the reactor is transported away by pumping helium gas through the spaces in the pebble packing. Some designs also feature an inner column of moderating graphite pebbles, which is surrounded by a fuel annulus. A typical flow rate is one pebble per minute.

The design has many advantages over traditional nuclear reactors, such as meltdown-proof passive safety and better long-term waste storage. Since pebbles are cycled continuously, no shutdowns of the reactor are needed for fuel replacement. Obviously, however, a thorough understanding of the pebble flow is very important to reactor design.

Pebble-bed reactor cross section
Cross-section through a cylindrical pebble-bed reactor simulation with a conical exit funnel angled at 30° to the horizontal.

Simulations

In collaboration with Sandia National Laboratories, we carried out full-scale Discrete Element Method (DEM) simulations of the pebble-bed reactor design proposed by the MIT pebble-bed initiative, and a cross-section through this design is shown to the right. This design features a cylindrical container 10m high and 3.5m across, filled with a central column of moderator pebbles (blue), surrounded by an annulus of fuel pebbles (cream). The pebbles are 6cm in diameter, and the reactor design consists of 440,000 particles in total. The simulations were done using the parallel LAMMPS code using 60 processors on Sandia's Xenon cluster.

Carrying out full-scale experiments of such a design would be extremely costly. Furthermore, experimentally analyzing a three dimensional flow poses problems of how to measure into the bulk of the packing. Some techniques (such as MRI, index-matching with an interstitial fluid, or confocal microscopy) do exist, but these often only provide limited information. Our simulations provided us with complete information about the entire state of the packing during flow, and allowed us to look in detail at many different aspects.

Analysis of the results

We carried out two extremely long simulations, one of the geometry shown above, and another where the exit cone is angled at 60° to the horizontal – see a movie of flow in the two simulations. For both cases we carried out an in-depth analysis of many aspects of the flow:

Bidisperse pebble-bed reactor cross sections
Cross-section through two half-size bidisperse reactor simulations, with a size ratio of 0.8:1 (left) and 0.5:1 (right).

Bidisperse reactor concept

We also investigated the feasibility of bidisperse core, whereby the inner moderator pebbles are made smaller. Reducing the size of the moderator pebbles even by a small amount significantly reduces their porosity to the helium coolant. This focuses the gas flow on the fuel-pebble regions which are producing the heat, which has the potential to greatly improve reactor performance.

To investigate this concept, we carried out three half-size simulations, with moderator/fuel particle ratios of 1:1, 0.8:1, and 0.5:1. Since the number of particles required scales according to inverse of the cube of their diameter, it was computationally infeasible to carry out full-scale simulations. Snapshots from the 0.8:1 and 0.5:1 simulations are shown to the right.

Our results show some small changes to the granular flow in the reactor. We find that the smaller pebbles tend to flow out faster. However, even with a ratio of 0.5:1, the central column remains stable, with diffusion at the interface still being on the order of a single pebble diameter.

We have carried out some smaller simulations in rectangular hoppers with size ratio of 0.3:1, as shown in this movie (see also this variation, where only the smaller particles are plotted). The particles in the central column are small enough to squeeze through the gaps between the larger ones, and they can diffuse quite far into the packing.

It therefore appears that there is a transition in behavior between a size ratio of 0.5:1 and 0.3:1. It is natural to assume that the behavior changes once the smaller particles can fit between the gaps made by the larger ones. A systematic study of this crossover remains a subject for future work.