Description

UPuZrFissionGasRelease and its associated AD and non-AD objects contain a fission gas release model for uranium plutonium zirconium (UPuZr) fuel based on the current porosity of the fuel. The model is derived from historical Experimental Breeder Reactor II (EBR-II) post-irradiation examinations that showed that the fission gas release fraction (gas released over gas produced) quickly increased to about 80% between 1 to 2 atom percent burnup, and remained nearly constant throughout the remainder of the irradiation (Hofman et al., 1997). The step-like function of fission gas release is related to the interconnection of porosity, $var element = document.getElementById("moose-equation-d6943308-2400-405a-9e44-2862e1262fff");katex.render("p", element, {displayMode:false,throwOnError:false});$ , as the porosity increases past a critical porosity $var element = document.getElementById("moose-equation-deae3244-8930-406e-b6f2-20ec6a800d55");katex.render("p_{critical}", element, {displayMode:false,throwOnError:false});$ , and becomes interconnected. From these observations, an extremely simple fission gas release model can be formulated in the absence of more advanced mechanistic models, $(1)var element = document.getElementById("moose-equation-0bdc36e9-81c3-4774-b18c-8bc7afa6cdc3");katex.render(" G_{released}(t+\\Delta t) = \\begin{cases} 0 & p < p_{critical} \\\\ 0.8 G_{produced}(t+\\Delta t) & p = p_{critical} \\\\ G_{released}(t) + [G_{produced}(t+\\Delta t) - G_{produced}(t)] & p > p_{critical} \\end{cases}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-3d6eefdb-3de3-4b9a-bc15-8f5e049bbb54");katex.render("G_{released}(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-ce514c2f-e33c-4996-9a5e-65f26132e6f3");katex.render("G_{produced}(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ are the total gas density released and produced at time $var element = document.getElementById("moose-equation-dbb37ba9-9a59-4b5d-8f7f-e4c0bfba8c0c");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ , respectively, in (mols/m $var element = document.getElementById("moose-equation-f9ccb636-fff3-4fd0-a08d-9f1142713284");katex.render("^3", element, {displayMode:false,throwOnError:false});$ ). The porosity value utilized in Eq. (1) can be either the current or previous time step, depending on the value of the input parameter use_current_porosity.

The total fission gas produced is related to the fission rate density by, $(2)var element = document.getElementById("moose-equation-f02a5840-1cc5-4427-bd90-fcbde737da51");katex.render(" G_{produced}(t+\\Delta t) = G_{produced}(t) + \\dot{F}_{avg} \\Delta t \\gamma / N_A,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-37ad6eb0-1216-4126-95e3-2a056aaa49bc");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ is the yield of fission gas atoms per fission, typically taken as $var element = document.getElementById("moose-equation-01250456-2c19-49ba-89e7-46c4d800b7bd");katex.render("\\gamma=0.3017", element, {displayMode:false,throwOnError:false});$ (gas atoms/m $var element = document.getElementById("moose-equation-6d79bf25-a4b8-4613-afd2-14310c9ecc8b");katex.render("^3", element, {displayMode:false,throwOnError:false});$ /s), and $var element = document.getElementById("moose-equation-b90b8542-6b12-4340-8738-18ad879d6bf4");katex.render("N_A", element, {displayMode:false,throwOnError:false});$ is Avogadro's number ( $var element = document.getElementById("moose-equation-f780675c-fde1-425d-9e00-81d6e8f78795");katex.render("6.022\\times 10^{23}", element, {displayMode:false,throwOnError:false});$ atoms/mol). Here, $var element = document.getElementById("moose-equation-764c1bdb-fdac-41cd-b2b1-cfbfe2db1ba8");katex.render("\\dot{F}_{ave}", element, {displayMode:false,throwOnError:false});$ is $var element = document.getElementById("moose-equation-e24c1a1d-b725-4549-970c-b02e5e81ab5b");katex.render("\\dot{F}_{ave} = \\frac{\\dot{F}(t) + \\dot{F}(t+\\Delta t)}{2}", element, {displayMode:true,throwOnError:false});$ Optionally, the value of the fission rate at the current time-step can be utilized instead of the average by setting time_average_fission_rate=false, such that $var element = document.getElementById("moose-equation-8ca8bb97-b51b-4571-9cbd-62234fd83f1a");katex.render("\\dot{F}_{avg}= \\dot{F}(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ in Eq. (2).

The critical porosity value nominally should occur around 25% porosity, corresponding to 33.3% volumetric swelling. The default value of 24% porosity is set to lie between the default interconnection_initiating_porosity=0.23 and interconnection_terminating_porosity=0.25 values set in UPuZrVolumetricSwellingEigenstrain to capture the concurrent fission gas release and swelling termination.

The initial fraction of fission gas released after the critical porosity value is reached and the fraction of the post-interconnection produced fission gas that is released to the plenum can be set using the following parameters, fractional_fgr_initial and fractional_fgr_post. The default values for these parameters are 0.8 and 1.0, respectively.

References

G L Hofman, L C Walters, and T H Bauer. Metallic fast reactor fuels. Progress in Nuclear Energy, 31(1-2):83–110, January 1997.

@article{Hofman:1997fg,
    author = "Hofman, G L and Walters, L C and Bauer, T H",
    title = "{Metallic fast reactor fuels}",
    journal = "Progress in Nuclear Energy",
    year = "1997",
    volume = "31",
    number = "1-2",
    pages = "83-110",
    month = "January"
}

Description
References