TRISOUtils

Overview

TRISOUtils houses functions for calculations required for various UCO related materials.

Molar Mass

TRISOUtils calculates the molar mass of the kernel, which is used in UCOThermal and TRISOBurnup.

$var element = document.getElementById("moose-equation-d8a5c5b2-1bd2-4fa4-b2cf-68d46331494c");katex.render(" M = af_{UO_2} \\cdot aw_{UO_2} + af_{UC_2} \\cdot aw_{UC_2} + af_{UC} \\cdot aw_{UC}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-6b689f86-870f-443a-a2b0-011e0066cd29");katex.render(" af = \\begin{cases} 0.5 OU & \\text{for $UO_{2}$} \\\\ 0.5 OU + CU - 1.0 & \\text{for $UC_{2}$} \\\\ 2.0 - (OU + CU) & \\text{for $UC$} \\end{cases}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-2f8a31c5-e35e-4fbc-850c-44788e2d99b5");katex.render(" aw = \\begin{cases} 0.23504 {\\epsilon} + 0.23805 (1.0 - {\\epsilon}) + 0.03200 & \\text{for $UO_{2}$} \\\\ 0.23504 {\\epsilon} + 0.23805 (1.0 - {\\epsilon}) + 0.02402 & \\text{for $UC_{2}$} \\\\ 0.23504 {\\epsilon} + 0.23805 (1.0 - {\\epsilon}) + 0.01201 & \\text{for $UC$} \\end{cases}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-a9bc6a6c-274d-4134-b428-04bd02a055bf");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false});$ (wt.%) is the initial U-235 enrichment, $var element = document.getElementById("moose-equation-a9939aba-9ea8-403e-ba70-d5c75f7cec15");katex.render("OU", element, {displayMode:false,throwOnError:false});$ (dimensionless) and $var element = document.getElementById("moose-equation-710bbace-755d-451a-a2ed-0ec26badafec");katex.render("CU", element, {displayMode:false,throwOnError:false});$ (dimensionless) are the initial oxygen to uranium and carbon to uranium stoichiometries of UCO, $var element = document.getElementById("moose-equation-93758b38-a514-4d48-9070-6cfae7ed093c");katex.render("af", element, {displayMode:false,throwOnError:false});$ (dimensionless) is the atomic fraction, $var element = document.getElementById("moose-equation-22b2830a-6e4c-4227-bbf9-1b5dbe83137c");katex.render("aw", element, {displayMode:false,throwOnError:false});$ (kg/mol) is the atomic weight and $var element = document.getElementById("moose-equation-2b9cf2cc-2a12-48d4-9c99-735a301a2774");katex.render("M", element, {displayMode:false,throwOnError:false});$ (kg/mol) is the molar mass of the kernel.

UCO is assumed to be formed of UO $var element = document.getElementById("moose-equation-91a395a4-7dc1-4898-87c4-6d1b1a54e71d");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , UC $var element = document.getElementById("moose-equation-fe52b3ed-1f6d-4631-958f-992630d7ea0f");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , and UC.

UC $var element = document.getElementById("moose-equation-51aae0ce-b93e-40d7-8706-6570fc1bd7e7");katex.render("_2", element, {displayMode:false,throwOnError:false});$ and UC are known to mix during heat treatment and form a UC $var element = document.getElementById("moose-equation-4db44fd9-ad7c-47ba-9c04-27de6b0c0214");katex.render("_x", element, {displayMode:false,throwOnError:false});$ phase, where x<2.

The atomic weights of the UCO constituents are:

$var element = document.getElementById("moose-equation-69603a66-a201-4115-952e-fc932c988016");katex.render(" aw = \\begin{cases} 235.04 & \\text{g/mol for Uranium-235} \\\\ 238.05 & \\text{g/mol for Uranium-238} \\\\ 16.00 & \\text{g/mol for Oxygen} \\\\ 12.01 & \\text{g/mol for Carbon} \\end{cases}", element, {displayMode:true,throwOnError:false});$

Theoretical Density

TRISOUtils calculates the theoretical density of the kernel, which is used in UCOElasticityTensor.

$var element = document.getElementById("moose-equation-58833943-daf1-432b-af58-aa484bc7c7eb");katex.render(" \\rho_{th}^{UCO} = \\frac{1}{ \\frac{ wf_{UO_{2}} }{ \\rho_{th}^{UO_{2}} } + \\frac{ wf_{UC} }{ \\rho_{th}^{UC} } + \\frac{ wf_{UC_{2}} }{ \\rho_{th}^{UC_{2}} }}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-4a83a7fe-eb57-4af6-8322-f11f6339b49d");katex.render(" wf = \\frac{af \\cdot aw}{M}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-27ea1d24-7e73-49dc-ac2a-d8d842a9f486");katex.render("\\rho_{th}", element, {displayMode:false,throwOnError:false});$ (kg/m $var element = document.getElementById("moose-equation-781cabf3-902d-47d5-b840-c4d0692fa272");katex.render("^3", element, {displayMode:false,throwOnError:false});$ ) is the theoretical density and $var element = document.getElementById("moose-equation-2bcbed1d-cdc5-41e3-8de1-dcea1f7d82df");katex.render("wf", element, {displayMode:false,throwOnError:false});$ (dimensionless) is the weight fraction. The quantities $var element = document.getElementById("moose-equation-bdf63cda-bdef-4b62-af4b-c33889e47406");katex.render("af", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-eac2d8b2-9432-4c62-b8a1-886f423f472b");katex.render("aw", element, {displayMode:false,throwOnError:false});$ come from the calculations described in the kernel molar mass section.

The theoretical densities of the UCO mixture components are:

$var element = document.getElementById("moose-equation-4a888081-b3b5-489b-b767-5f33b1e84868");katex.render(" \\rho_{th} = \\begin{cases} 10.96 & \\text{g/cm$^3$ for $UO_{2}$} \\\\ 13.63 & \\text{g/cm$^3$ for $UC$} \\\\ 11.28 & \\text{g/cm$^3$ for $UC_{2}$} \\end{cases}", element, {displayMode:true,throwOnError:false});$

Fission Products

TRISOUtils calculates the kernel solid fission product yields for silver (Ag), cesium (Cs), strontium (Sr) and the gaseous products krypton (Kr) and xenon (Xe) together, through the correlations below.

Validity Range

Burnup: assumed valid at all burnups.

$var element = document.getElementById("moose-equation-d619abaf-a5f2-40ff-9842-7a019dc7491f");katex.render("^{235}", element, {displayMode:false,throwOnError:false});$ U enrichment: assumed valid at all enrichments.

Silver

$var element = document.getElementById("moose-equation-1c079c55-eb95-429b-bba8-828ae43f16af");katex.render(" b = \\text{max}(1.0, Bu)", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-4923c912-2c5d-4238-97e0-b6441492b765");katex.render(" \\Gamma_{Ag} = \\begin{cases} 1.31625 \\cdot 10^{-3} b^{0.55734} & \\text{for } e < 17.5\\\\ 8.24492 \\cdot 10^{-4} b^{0.53853} & \\text{for } e \\ge 17.5 \\end{cases}", element, {displayMode:true,throwOnError:false});$

Cesium

$var element = document.getElementById("moose-equation-8b276a30-5d36-4d37-8359-0c7060854d65");katex.render(" \\Gamma_{Cs} = \\begin{cases} 0.14 & \\text{for } e < 17.5\\\\ 0.16 & \\text{for } e \\ge 17.5 \\end{cases}", element, {displayMode:true,throwOnError:false});$

Strontium

$var element = document.getElementById("moose-equation-575756a2-a1a4-47c7-a3cb-a037ac048f4d");katex.render(" b = \\text{max}(0.6, Bu)", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-609bef40-f51c-447f-81a9-55b29439f29a");katex.render(" \\Gamma_{Sr} = \\begin{cases} 0.11754 b^{-0.21762} & \\text{for } e < 17.5\\\\ 0.11819 b^{-0.15778} & \\text{for } e \\ge 17.5 \\end{cases}", element, {displayMode:true,throwOnError:false});$

Krypton and Xenon

$var element = document.getElementById("moose-equation-e788f423-34b9-4a53-b503-04448d1a9798");katex.render(" \\Gamma_{Kr+Xe} = 0.297", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-091f5a39-6189-44ce-8e00-63feb8d3cf17");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false});$ (atoms/fission) is the fission yield, $var element = document.getElementById("moose-equation-9a25feca-493c-42c4-8220-8bd8a135e648");katex.render("B_{u}", element, {displayMode:false,throwOnError:false});$ (%FIMA) is the burnup, and $var element = document.getElementById("moose-equation-54fddc2a-ab5e-456f-93f7-2156ef8c6ef0");katex.render("e", element, {displayMode:false,throwOnError:false});$ (%) is the $var element = document.getElementById("moose-equation-6b979c79-3471-401f-a538-adddd1d154dd");katex.render("^{235}", element, {displayMode:false,throwOnError:false});$ U enrichment. Miller et al. (2018).

The krypton and xenon yield is used in UCOFGR.

References

G.K. Miller, D.A. Petti, J.T. Maki, D.L. Knudson, and W.F. Skerjanc. PARFUME Theory and Model Basis Report. Report INL/EXT-08-14497 (Rev.1), Idaho National Laboratory, September 2018.

@techreport{Miller2018,
    author = "Miller, G.K. and Petti, D.A. and Maki, J.T. and Knudson, D.L. and Skerjanc, W.F.",
    title = "{PARFUME Theory and Model Basis Report}",
    institution = "Idaho National Laboratory",
    year = "2018",
    month = "September",
    number = "INL/EXT-08-14497 (Rev.1)",
    type = "Report"
}

Overview
Molar Mass
Theoretical Density
Fission Products
References