EBR-II K-4 Experiment

Overview

The K-4 experiment in EBR-II contained a series of mixed uranium-plutonium nitride fuel pins run to high burnup (9.6 at.%) at high power (85 kW/m). The K-4 test is considered the most successful UN test, achieving high burnup with no pin failures. Unfortunately, although the K-4 pins were examined in detail, the results of the examination were not published Matthews (1993).

Test Description

The K-4 experiment consisted of over 140 (U,Pu)N Na- and helium-bonded pins that were irradiated as part of the LMFBR program with low smear densities of 75 - 86% TD to ensure little to no fuel-clad mechanical interaction.

Rod Design Specifications

The fuel was solid cylindrical pellets of (U,Pu)N. The pellet densities were 96.8 and 98.9% TD, with smear densities of 81.2 and 79.4%, respectively. The pellets were encased in 316 SS clad and 316 SS shroud and wire-wrapped, also in 316 SS. We do not model the shroud tubes or the wire wrap.

The plenum volume and some other properties are unknown, so we are using the configuration from the WSA32 test (see other assessment case) at EBR-II to fill in the details.

Table 1: K-4 Rod Geometry

Parameter	Value	Units	Source
Clad material	316 SS		Matthews (1993)
Clad bonding	He		Matthews (1993)
Clad OD	7.87	mm	Matthews (1993)
Clad thickness	0.51	mm	Blank (2006)
Diametral gap	0.65	mm	calculated from smear density
Pellet diameter	6.20	mm	calculated from smear density
Fuel stack	343	mm	unknown, using WSA32
Plenum height	43.5	mm	unknown, using WSA32
Plenum pressure	12.4	MPa	unknown, using WSA32
Top/bottom gap	8	mm	unknown, using WSA32
Smear density	81.2, 79.4	%TD	Matthews (1993)

Operating Conditions and Irradiation History

The actual power history for specific EBR-II experiments is still being determined. Therefore, a simplified power history containing an initial ramp to power and hold for a given amount of time with a final power down is being used. The average burnup of the fuel at the end of the simulation is used as a check that the power history is reasonable. The remaining parameters are in Table 2.

Table 2: K-4 Operating Conditions

Parameter	Value	Units	Source
Coolant $var element = document.getElementById("moose-equation-2be83907-64da-417b-ac4e-0be1b317df42");katex.render("T_{in}", element, {displayMode:false,throwOnError:false});$	644	K	unknown, using WSA32
Coolant $var element = document.getElementById("moose-equation-5e81532f-d8ee-4204-b0c1-baa127bbb31f");katex.render("T_{out}", element, {displayMode:false,throwOnError:false});$	746	K	unknown, using WSA32
Fast fluence	$var element = document.getElementById("moose-equation-4e2e2f33-cea2-44de-bdc7-0133a33e15a3");katex.render("6\\times 10^{22}", element, {displayMode:false,throwOnError:false});$	n cm $var element = document.getElementById("moose-equation-377a860a-99b5-470a-897c-8928e8ca5ee7");katex.render("^{-2}", element, {displayMode:false,throwOnError:false});$	Matthews (1993)
Peak power	85	kW/m	Matthews (1993)
Burnup	9.6	at.%	Matthews (1993)

Model Description

The test case simulates a rod in the set of 8 pins which had a fuel density of 96.8% TD and a smear density of 79.4%. Using these densities with a clad thickness of 0.51 mm gives a pellet diameter of 6.20 mm and a diametral gap of 0.65 mm. No data on axial peaking factors exist, so we again use the factors from the WSA32 test.

Geometry and Mesh

The 2D-RZ mesh for the test case is generated with the internal smeared pellet meshing capability in BISON FuelPinMeshGenerator. All of the dimensions and meshing details are contained in the Mesh block.

Material and Behavioral Models

This test case uses automatic differentiation. The following material and behavioral models for the (U,Pu)N fuel were used:

ADMNElasticityTensor: Computes Young's modulus and Poisson ratio for MN fuel
ADMNCreepUpdate: Creep mechanical properties and deformation behavior for MN fuel
ADMNThermal: Calculates the thermal conductivity and specific heat for MN fuel
ADMNThermalExpansionEigenstrain: Calculates thermal expansion coefficient and isotropic expansion for MN fuel
ADMNVolumetricSwellingEigenstrain: Computes swelling due to solid and gaseous fission products for MN fuel

The following material and behavioral models for the 316SS cladding were used in these cases:

ADComputeIsotropicElasticityTensor: Computes isotropic elastic mechanical properties for generic material
ADSS316Thermal: Calculates the thermal conductivity and specific heat for 316 SS
ADDensity: Computes density for generic material

This case demonstrates use of automatic differentiation with full (SMP) preconditioning. Therefore it is missing models for mechanical and thermal contact, which are not implemented yet. To simulate mechanical contact, a constant plenum pressure is applied to all pellet boundaries.

To simulate thermal contact, the steady-state radial heat flux is computed from the fission rate, and this flux is used to compute the clad and gap temperature drops. Since the Na coolant temperature is prescribed, the temperature at the pellet OD can then also be prescribed as a function of local coolant temperature and fission rate. This method avoids the ill-posed BC that would result from assigning a heat flux directly to pellet boundary.

Input files

The input file for the 2D-RZ case is located at bison/assessment/nitride/EBRII/K4/analysis.

Results Comparison

Discussion

References

Hubert Blank. Nonoxide Ceramic Nuclear Fuels, chapter, pages. John Wiley & Sons, Ltd, 2006. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/9783527603978.mst0108, doi:10.1002/9783527603978.mst0108.

@inbook{blank:2006,
    author = "Blank, Hubert",
    publisher = "John Wiley \\& Sons, Ltd",
    isbn = "9783527603978",
    title = "Nonoxide Ceramic Nuclear Fuels",
    booktitle = "Materials Science and Technology",
    chapter = "",
    pages = "",
    doi = "10.1002/9783527603978.mst0108",
    url = "https://onlinelibrary.wiley.com/doi/abs/10.1002/9783527603978.mst0108",
    year = "2006"
}

R B Matthews. Irradiation performance of nitride fuels. Technical Report, Los Alamos National Lab, 1 1993.

@techreport{matthews1993,
    author = "Matthews, R B",
    title = "Irradiation performance of nitride fuels",
    place = "United States",
    year = "1993",
    month = "1",
    institution = "Los Alamos National Lab"
}

Overview
Test Description
Model Description
Input files
Results Comparison
Discussion
References