Hexagonal fuel arrays (VVER and fast reactor fuel)

[Astronuc]

I'm working on an interesting task at the moment related to a core and fuel design for a fast reactor system. Given that the system is a fast reactor, we select a sensible lattice, i.e., a triangular or hexagonal lattice. Neutronically, one can solve for the necessary mass of enriched (less than 20% ²³⁵U) in the form of a ceramic, UN. By defining a fuel rod geometry (pellet diameter, cladding inner and outer diameter) and fuel rod pitch (typically P/D is ~1.25, but could be as much as 1.3), one will calculate the number of fuel rods in the system.

However, a core is composed of fuel assemblies, each containing a set of fuel rods.

Now, in a hexagonal array, one starts with a central location (row 1) of either an assembly or fuel rod. Immediately, or directly, surrounding the one central are six (6) in row 2, then around the six (6), is twelve (12), and so on. For each successive row, one adds 6 to the number in the previous row.

So, the counting goes as: 1, 6, 12, 18, 24, 30, 36, 42, 48, . . . .
and the cumulative or total number of elements in the array goes as: 1, 7, 19, 37, 61, 91, 127, 169, 217, . . .

See - https://en.wikipedia.org/wiki/Centered_hexagonal_number

The total number of fuel rods, NR, in an assembly, can be defined by 3(r²-r)+1, where r is the number of rows of fuel rods, and similarly, the number of assemblies, NA, in a core is given by 3(a²-a)+1, where a is the number of rows of assemblies.

Then one is faced with selecting the number of rods per assembly and the number of assemblies. In other words, the product of NR and NA has to equal the total number of fuel rods from the neutronics calculation. For example, one could use NR = 127, NA = 169, or NR = 169, NA = 169, since 127 x 169 = 169 x 127 = 21463.

One the other hand, one could decide NR = NA = 169, and 169 x 169 = 28561.

One also has to decide on the fuel pellet diameter (and density of the ceramic fuel, or metal fuel), the cladding inner and outer diameter, and the pitch (distance between the centers of adjacent fuel rods or assemblies). The fuel pellet diameter affects the criticality and power density, the inner and outer cladding diameters affect the stress in the cladding depending on the differential pressure across the cladding wall, the outer diameter affects the heat flux for a given power density (or linear heat rate, kW/m), and the cladding diameter and fuel rod pitch affects the hydraulic resistance and various thermal-hydraulic characteristics of the lattice.

It's an interesting design problem, but I thought the mathematics of 'centered hexagonal numbers' is interesting. Note that I didn't address control rods and their interaction with the fuel assembly.

 

[Achy47]

Hello,

Thank you for sharing your interesting task with us. I find the mathematics of 'centered hexagonal numbers' to be fascinating as well. It is amazing how mathematical concepts can be applied to real-world problems, such as the design of a fast reactor system.

In response to your post, I would like to suggest some considerations for selecting the number of rods per assembly and the number of assemblies. One important factor to consider is the efficiency of the system. As you mentioned, the total number of fuel rods should be equal to the number of rods per assembly multiplied by the number of assemblies. Therefore, selecting a higher number of rods per assembly can result in a more compact and efficient system. However, this must be balanced with the potential for increased stress on the cladding and the hydraulic resistance of the lattice.

Another consideration is the availability of materials and the cost of fabrication. The larger the number of rods per assembly, the more fuel pellets and cladding materials will be required. This could potentially drive up the cost of the system. It may be beneficial to evaluate different combinations of NR and NA to determine the most cost-effective option.

Additionally, the fuel pellet diameter and cladding dimensions should be carefully selected to optimize the criticality and power density of the system. As you mentioned, these parameters can also affect the stress on the cladding and the thermal-hydraulic characteristics of the lattice. It may be necessary to conduct simulations or experiments to determine the ideal dimensions for these components.

Overall, I agree that this is a very interesting design problem and I appreciate you sharing your thoughts on the mathematics behind it. I wish you all the best in your project and look forward to hearing about your final design.