Moderator to fuel ratio and under-moderation in different lattices

[ulriksvensson]

Hi all. I need help on an issue I can't figure out.

What is the difference between 15x15 and 17x17 fuel when it comes to moderation properties? Standard fuel with these lattices have dimensions

15x15: pitch: 14.3 mm, d_rod: 10.77 mm
17x17: pitch: 12.6 mm, d_rod: 9.5 mm

These geometries give the same (up to two parts in a thousand) value of the pitch-to-diameter ratio. Even so, people say that 15x15 fuel is more under-moderated than 17x17. The only difference I can come up with is that the 17x17 fuel has greater surface area (total) than 15x15. I'm thinking that this would affect moderation properties in that more thermal neutrons will be captured in resonances in 17x17 fuel than in 15x15 fuel due to the larger area.

Can someone please help me to clarify this?

//Ulrik

 

[Astronuc]

Hi all. I need help on an issue I can't figure out.

What is the difference between 15x15 and 17x17 fuel when it comes to moderation properties? Standard fuel with these lattices have dimensions

15x15: pitch: 14.3 mm, d_rod: 10.77 mm
17x17: pitch: 12.6 mm, d_rod: 9.5 mm

These geometries give the same (up to two parts in a thousand) value of the pitch-to-diameter ratio. Even so, people say that 15x15 fuel is more under-moderated than 17x17. The only difference I can come up with is that the 17x17 fuel has greater surface area (total) than 15x15. I'm thinking that this would affect moderation properties in that more thermal neutrons will be captured in resonances in 17x17 fuel than in 15x15 fuel due to the larger area.

One is basically correct. The 17x17 fuel takes roughly the same amount of fuel, but divides that fuel among 264 fuel rods (and 24 guide tubes + 1 instrument tube), as compared to 204 fuel rods (and 24 GT + 1 IT). There is another 15x15 design that uses 208 fuel rods (and 16 GT + 1 IT) by a different reactor supplier. In effect it is related to the greater surface to volume ratio.

The assembly pitch is roughly the same.
15 x 14.3 = 214.5
17 x 12.6 = 214.2

 

[ulriksvensson]

So I'm right when saying that it's the bigger surface that makes the 17x17 less under-moderated? "All" resonance captures occur at the surface of the rod so it seems logical.

 

[Astronuc]

So I'm right when saying that it's the bigger surface that makes the 17x17 less under-moderated? "All" resonance captures occur at the surface of the rod so it seems logical.

It's not so much the resonances as the distribution of the fuel in the moderator which allows more moderation of the fast neutrons.

The under-moderated system (15x15) should have a slightly higher fast flux to thermal flux ratio.

 

[ulriksvensson]

One is basically correct. The 17x17 fuel takes roughly the same amount of fuel, but divides that fuel among 264 fuel rods (and 24 guide tubes + 1 instrument tube), as compared to 204 fuel rods (and 24 GT + 1 IT). There is another 15x15 design that uses 208 fuel rods (and 16 GT + 1 IT) by a different reactor supplier. In effect it is related to the greater surface to volume ratio.

The assembly pitch is roughly the same.
15 x 14.3 = 214.5
17 x 12.6 = 214.2

Ok, so if we calculate the ratio between the moderator volume and uranium volume for these two assemblies we get:

15x15: Vm/Vu = 1.4757
17x17: Vm/Vu = 1.4519

This would suggest that 17x17 is more under moderated than 15x15? How does this make cores made up of 15x15 assemblies worse when it comes to fuel bowing? I know for a fact they are. A larger (than nominal) water gap would make power distribution worse in a core that is more under moderated, right?

 

[Astronuc]

Ok, so if we calculate the ratio between the moderator volume and uranium volume for these two assemblies we get:

15x15: Vm/Vu = 1.4757
17x17: Vm/Vu = 1.4519

This would suggest that 17x17 is more under moderated than 15x15? How does this make cores made up of 15x15 assemblies worse when it comes to fuel bowing? I know for a fact they are. A larger (than nominal) water gap would make power distribution worse in a core that is more under moderated, right?

Comparing Volume/(Surface Area) or the reciprocal would be better. Basically, the fuel volume is close, but the same volume divided in 204 fuel rods (assuming 20 GT and 1 IT) is less moderated than the volume of fuel distributed over 264 fuel rods.

I'm not sure that 15x15 fuel is more susceptible to bowing than 17x17 fuel. Is one comparing fuel in R2 with the fuel in R3/R4?

There are a number of factors affecting fuel assembly bow:

1. Hold down force
2. GT design, particularly the dashpot, as well as wall thickness vs diameter, and the OD it self.
3. GT alloy (lower tin in certain Zr-alloys could produce more creep)
4. Differential growth, which could be exacerbated by a harder neutron spectrum.

A larger water gap (GT) would mean more local moderation - and local power gradients in the fuel rods. But such effects should be considered in the lattice design.

 

[ulriksvensson]

I'm not sure that 15x15 fuel is more susceptible to bowing than 17x17 fuel. Is one comparing fuel in R2 with the fuel in R3/R4?

I wouldn't say more susceptible, but a given bow amplitude gives larger local power (i.e for instance radial tilt) in a core made up of 15x15-assemblies than a core made up of 17x17 assemblies. And yes to the second question...

 

[Astronuc]

I wouldn't say more susceptible, but a given bow amplitude gives larger local power (i.e for instance radial tilt) in a core made up of 15x15-assemblies than a core made up of 17x17 assemblies. And yes to the second question...

For an under-moderated system, a larger water gap is more significant for local power peaking.

Fuel assembly bow was thought to be more of an issue for BWRs, than for PWRs. There was one BWR, which did have some dryout of some corner rods, and fuel assembly bow (with the water gap larger than used in the nuclear design) contributed to the power peaking.