Spherical Shell

note:More Information Available

Material presented here is a subset of information in Hales et al. (2021) and Hales et al. (2013). See the JNM papers for more information.

CRP-6 Assessment Cases

As part of an International Atomic Energy Agency (IAEA) Coordinated Research Program (CRP-6) on High Temperature Gas Reactor (HTGR) reactor fuel technology, a set of benchmarking activities were developed to compare fuel performance codes under normal operation and operational transients (IAEA, 2012). Sixteen fuel performance benchmark cases were identified. The first three of these involve stress in spherical shells.

Fuel Performance Results

Cases 1 to 3 were limited to single and double coating layers for TRISO fuel particles and tested simple elastic thermomechanical behavior against analytical solutions.

The tangential stress as a function of radial coordinate, $var element = document.getElementById("moose-equation-350542f2-90e2-4ef0-91ec-9fef5ec6a5ad");katex.render("\\sigma_\\theta(r)", element, {displayMode:false,throwOnError:false});$ , is given as (Roark and Young, 1975): $var element = document.getElementById("moose-equation-daf55c58-6fd0-499b-aa87-019ebc876c50");katex.render("\\sigma_\\theta(r)=P_i\\frac{r_i^3\\left(2r^3+r_o^3\\right)}{2r^3\\left(r_o^3-r_i^3\\right)}-P_o\\frac{r_o^3\\left(2r^3+r_i^3\\right)}{2r^3\\left(r_0^3-r_i^3\\right)}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-c9e4f79a-e6d9-4c07-8f91-656cf548c54c");katex.render("P_i", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-9db2f72d-91cd-4278-a26a-218d42a3294e");katex.render("P_o", element, {displayMode:false,throwOnError:false});$ are the inner and outer pressures and $var element = document.getElementById("moose-equation-be7156af-3bea-4f56-9b49-e4f00dea0bc4");katex.render("r_i", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-7943efd3-0859-401b-9b16-7082623bcce2");katex.render("r_o", element, {displayMode:false,throwOnError:false});$ are the inner and outer radii.

In all three cases, $var element = document.getElementById("moose-equation-8adfcb80-c98e-40a6-aa30-03de87f5da04");katex.render("P_i", element, {displayMode:false,throwOnError:false});$ = 25E6 and $var element = document.getElementById("moose-equation-92c89bab-7bc9-4b99-90af-9b4193dc297b");katex.render("P_o", element, {displayMode:false,throwOnError:false});$ = 1E5.

A comparison of the analytical and Bison numerical solutions for the maximum tangential stress, which occurs at the inner surface of the various layers, is shown in Table 1.

Table 1: Comparison of the Bison computed maximum tangential stress (MPa) to the analytical solution for Cases 1 to 3.

Case	Radii (m)	Layer	Analytical (MPa)	Bison (MPa)	Error (%)
1	3.5E-4/3.85E-4	SiC	125.190	125.13	0.048
2	3.5E-4/4.4E-4	IPyC	50.200	50.176	0.048
3	3.5E-4/3.9E-4/4.25E-4	IPyC/SiC	8.8/104.4	8.7/104.5	1.14/0.10

References

J.D. Hales, R.L. Williamson, S.R. Novascone, D.M. Perez, B.W. Spencer, and G. Pastore. Multidimensional multiphysics simulation of TRISO particle fuel. Journal of Nuclear Materials, 443(1):531–543, 2013. doi:10.1016/j.jnucmat.2013.07.070.

@article{HALES2013531,
    author = "Hales, J.D. and Williamson, R.L. and Novascone, S.R. and Perez, D.M. and Spencer, B.W. and Pastore, G.",
    title = "Multidimensional multiphysics simulation of {TRISO} particle fuel",
    journal = "Journal of Nuclear Materials",
    volume = "443",
    number = "1",
    pages = "531-543",
    year = "2013",
    issn = "0022-3115",
    doi = "10.1016/j.jnucmat.2013.07.070"
}

Jason D. Hales, Wen Jiang, Aysenur Toptan, and Kyle A. Gamble. Modeling fission product diffusion in TRISO fuel particles with BISON. Journal of Nuclear Materials, 548:152840, 2021. doi:10.1016/j.jnucmat.2021.152840.

@article{HALES2021152840,
    author = "Hales, Jason D. and Jiang, Wen and Toptan, Aysenur and Gamble, Kyle A.",
    title = "Modeling fission product diffusion in {TRISO} fuel particles with {BISON}",
    journal = "Journal of Nuclear Materials",
    pages = "152840",
    volume = "548",
    year = "2021",
    doi = "10.1016/j.jnucmat.2021.152840"
}

IAEA. Advances in high temperature gas cooled reactor fuel technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy Agency, 2012.

@TechReport{rpt:IAEA-TECDOC-1674,
    author = "IAEA",
    institution = "International Atomic Energy Agency",
    number = "{IAEA-TECDOC}-1674",
    title = "Advances in High Temperature Gas Cooled Reactor Fuel Technology",
    year = "2012"
}

R. J. Roark and W. C. Young. Formulas for Stress and Strain. McGraw-Hill Inc., United States, 1975.

CRP - 6 Assessment Cases
Fuel Performance Results
References