Uranium density in fuel meat/kernel

[nuclearsneke]

TL;DR

Tl;dr - why is it so low and how to get the right value of density?

Howdy partners!

I am currently doing some project on Klt40s neutronic simulation (you might have heard of Akademik Lomonosov, the floating npp). But I have encountered a problem with fuel density. The only info that i got that "uranium density IN FUEL MEAT/KERNEL" is 4.5 g/cm3. The Fuel is uranium dioxide dispersed in aluminum-silicon alloy.

However, I need the fuel density for further calculations of nuclear densities (1/cm3).
I know that density of uo2 is 10.9 g/cm3 and density of the alloy is around 2.7 g/cm3. Have you guys gotten any ideas on how to calculate the whole fuel density and maybe fractions of fuel and matrix (sial alloy) from these data?

 

[Alex A]

Seems to be quite a lot of detail in this document. https://aris.iaea.org/PDF/KLT-40S.pdf

Maybe that will help.

 

[nuclearsneke]

Seems to be quite a lot of detail in this document. https://aris.iaea.org/PDF/KLT-40S.pdf

Maybe that will help.

I hab this one but no luck :(

 

[Astronuc]

Summary:: Tl;dr - why is it so low and how to get the right value of density?

"uranium density IN FUEL MEAT/KERNEL" is 4.5 g/cm3.

That is the uranium density, as opposed to UO₂ density correct?

And is it 14% enriched?

The density would be low because the U, in the form of UO₂, is dispersed in Al-Si alloy.

 

[nuclearsneke]

That is the uranium density, as opposed to UO₂ density correct?

And is it 14% enriched?

The density would be low because the U, in the form of UO₂, is dispersed in Al-Si alloy.

I get it that density of fuel would be low due to its dispersion in alloy. But is there any way to calculate a density of fuel pellet starting from this "uranium density in fuel kernel" value?

 

[Astronuc]

is there any way to calculate a density of fuel pellet starting from this "uranium density in fuel kernel" value?

Well, assuming that the 'uranium density' refers to uranium with ρ = 4.5 g/cm³, then the UO₂ density in the dispersion would be ~5.1 g/cm³, based on 0.8814 gU/gUO₂.

For a given volume V of dispersion, the mass of the volume would be xV*ρ(UO₂)+(1-x)V*ρ(Al) = M with a volume V and density D=M/V of the dispersion ( x = volume fraction of UO₂), assuming that there is no interaction between UO₂ and Al. The total mass M = m(UO₂) + m(Al).

The mass of UO₂ in the dispersion is simply xV*ρ(UO₂) and the effective density is just x*ρ(UO₂) = 5.1 g/cm³, and so x = 0.465, based on ρ(UO₂) = 10.96 g/cm³.

This is basically an application of 'rule of mixtures', or 'law of mixtures'.
https://link.springer.com/referenceworkentry/10.1007/978-1-4419-6247-8_6810
https://www.sciencedirect.com/topics/engineering/rule-of-mixture-equation

 

[nuclearsneke]

Well, assuming that the 'uranium density' refers to uranium with ρ = 4.5 g/cm³, then the UO₂ density in the dispersion would be ~5.1 g/cm³, based on 0.8814 gU/gUO₂.

For a given volume V of dispersion, the mass of the volume would be xV*ρ(UO₂)+(1-x)V*ρ(Al) = M with a volume V and density D=M/V of the dispersion ( x = volume fraction of UO₂), assuming that there is no interaction between UO₂ and Al. The total mass M = m(UO₂) + m(Al).

The mass of UO₂ in the dispersion is simply xV*ρ(UO₂) and the effective density is just x*ρ(UO₂) = 5.1 g/cm³, and so x = 0.465, based on ρ(UO₂) = 10.96 g/cm³.

This is basically an application of 'rule of mixtures', or 'law of mixtures'.
https://link.springer.com/referenceworkentry/10.1007/978-1-4419-6247-8_6810
https://www.sciencedirect.com/topics/engineering/rule-of-mixture-equation

Wow. Given that I had a material science course mostly focused on phase diagrams and lattice types, I have never heard of that preem law/rule of mixture. Now the problem I mentioned above looks so trivial... Thank you, Astronuc!

 

[Astronuc]

Given that I had a material science course mostly focused on phase diagrams and lattice types, I have never heard of that preem law/rule of mixture.

Well, I had much the same experience. I didn't hear about the 'rule/law of mixtures' until I encountered in the job. I've done similar problems in the past. It can be tricky. In this problem, one must assume no chemical interaction between the UO₂ and Al-Si-alloy, which is a reasonable assumption if done at low temperature, which it usually is. Basically one would mix powders and cold press them between layers of Al-Si. Also, one must be clear on the problem statement, which is why I asked about the density of uranium vs uranium dioxide. Things can go wrong when there is miscommunication between design and manufacturing, or between engineering groups.