LeadBismuthFluidProperties

Fluid properties for Lead Bismuth eutectic 2LiF-BeF2

These properties are based on experiments reported in the Handbook on Lead-bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-hydraulics and Technologies (Concetta et al., 2015). Most properties only depend on temperature; the fluid is considered incompressible. The fluid properties are summarized in Table 1, which reports the formulas used and their origin.

Table 1: Table of properties and references to the equations in (Concetta et al., 2015).

Properties	Equations	Equation/Table #
Melting point, $var element = document.getElementById("moose-equation-1884ad04-aa1b-4e49-9eb5-470e1395e54e");katex.render("T_{mo}", element, {displayMode:false,throwOnError:false});$ (K)	398	Equation 2.1
Density, $var element = document.getElementById("moose-equation-a0b87871-ddfd-4a13-8190-f5c4c9c628a5");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ (kg/m^3)	$var element = document.getElementById("moose-equation-c8791e9a-a6cd-4502-a7a8-b26a2cb953b8");katex.render("11065 - 1.2793T", element, {displayMode:false,throwOnError:false});$	Equation 2.30
Viscosity, $var element = document.getElementById("moose-equation-885ded47-1c2d-459e-b215-715dd00cde25");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ (Pa-s)	$var element = document.getElementById("moose-equation-67612fd9-5d19-42a9-9cc2-b3224ce9467f");katex.render("4.94 \\times 10^{-4} \\times e^{\\frac{754.1}{T}}", element, {displayMode:false,throwOnError:false});$	Equation 2.83
Specific enthalpy, $var element = document.getElementById("moose-equation-8aa3f58a-c0ea-44c8-983f-466e4c181839");katex.render("h", element, {displayMode:false,throwOnError:false});$ (J)	$var element = document.getElementById("moose-equation-33d5cc2c-7273-44d7-b517-27fe888e5b40");katex.render("164.8(T - T_{mo}) - 1.97 \\times 10^{-2}(T^2 - T_{mo}^2) + 4.167 \\times 10^{-6}(T^3 - T_{mo}^3) + 4.56 \\times 10^5(\\frac{1}{T} -\\frac{1}{T_{mo}})", element, {displayMode:false,throwOnError:false});$	Equation 2.55
Thermal Conductivity, $var element = document.getElementById("moose-equation-ecd2b0cc-8398-429c-a2cc-b7eddc829ee2");katex.render("k", element, {displayMode:false,throwOnError:false});$ (W/m-K)	$var element = document.getElementById("moose-equation-1275caeb-f0fd-4fcb-9fa4-e636771b751e");katex.render("3.284 + 1.617 \\times 10^{-2}T - 2.305 \\times 10^{-6}T^2", element, {displayMode:false,throwOnError:false});$	Equation 2.91
Isobaric Specific Heat, $var element = document.getElementById("moose-equation-1513da1a-7c02-428e-847f-837a45494d1c");katex.render("cp", element, {displayMode:false,throwOnError:false});$ (J/kg-K)	$var element = document.getElementById("moose-equation-a0a607f8-0be8-4b75-ad05-03eb4d436a0e");katex.render("164.8 - 3.94 \\times 10^{-2}T + 1.25 \\times 10^{-5}T^2 - \\frac{4.56 \\times 10^5}{T^2}", element, {displayMode:false,throwOnError:false});$	Table 2.19.3
Isentropic Bulk Modulus, $var element = document.getElementById("moose-equation-76d8a58f-1249-42f4-a26a-f943e9033b3f");katex.render("B_S", element, {displayMode:false,throwOnError:false});$ (N/m $var element = document.getElementById("moose-equation-026f6198-5b77-4aa4-97d8-4907328aeb0d");katex.render("^2", element, {displayMode:false,throwOnError:false});$ )	$var element = document.getElementById("moose-equation-f66f97b3-5d15-43bc-83da-f43448d0f172");katex.render("(38.02 - 1.296 \\times 10^{-2}T + 1.320 \\times 10^{-6}T^2)10^9", element, {displayMode:false,throwOnError:false});$	Equation 2.44
Speed of Sound, $var element = document.getElementById("moose-equation-4eade157-9249-4eb1-a839-4218114c775b");katex.render("c", element, {displayMode:false,throwOnError:false});$ (m/s)	$var element = document.getElementById("moose-equation-8e41c2e6-3683-40b8-bc07-14a1c6eb5e4d");katex.render("1855 - 0.212 T", element, {displayMode:false,throwOnError:false});$	Table 2.19.3

Range of validity

The properties defined in LeadBismuthFluidProperties from (Concetta et al., 2015) are valid for:

400 K $var element = document.getElementById("moose-equation-91caa564-1b70-43c2-8e61-fbb991918931");katex.render("\\le", element, {displayMode:false,throwOnError:false});$ T $var element = document.getElementById("moose-equation-2cd42d87-3415-4761-bc6f-d271a34f22db");katex.render("\\le", element, {displayMode:false,throwOnError:false});$ 1100 K

Uncertainties of Lead Bismuth Eutectic Fluid Properties

The reported uncertainties in (Concetta et al., 2015) for lead-bismuth eutectic fluid properties are:

Properties	Range/ Uncertainties
Density	0.8%
Viscosity	8%
Thermal Conductivity	15%
Isobaric Specific Heat	7%

Input Parameters

T_initial_guess400Temperature initial guess for Newton Method variable set conversion
Default:400
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Temperature initial guess for Newton Method variable set conversion
max_newton_its100Maximum number of Newton iterations for variable set conversions
Default:100
C++ Type:unsigned int
Controllable:No
Description:Maximum number of Newton iterations for variable set conversions
p_initial_guess200000Pressure initial guess for Newton Method variable set conversion
Default:200000
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Pressure initial guess for Newton Method variable set conversion
tolerance1e-08Tolerance for 2D Newton variable set conversion
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Tolerance for 2D Newton variable set conversion

Variable Set Conversions Newton Solve Parameters

allow_imperfect_jacobiansFalsetrue to allow unimplemented property derivative terms to be set to zero for the AD API
Default:False
C++ Type:bool
Controllable:No
Description:true to allow unimplemented property derivative terms to be set to zero for the AD API
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
fp_typesingle-phase-fpType of the fluid property object
Default:single-phase-fp
C++ Type:FPType
Controllable:No
Description:Type of the fluid property object

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

References

Fazio Concetta, Sobolev V.P., Aerts A., Gavrilov S., Lambrinou K., Schuurmans P., A. Gessi, Agostini P., Ciampichetti A., Martinelli L., Gosse S., Balbaud-Celerier F., Courouau J.L., Terlain A., Li N., Glasbrenner H., Neuhausen J., Heinitz S., Zanini L., Dai Y., Jolkkonen M., Kurata Y., Obara T., Thiolliere N., Martin-Munoz F.J., Heinzel A., Weisenburger A., Mueller G., Schumacher G., Jianu A., Pacio J., Marocco L., Stieglitz R., Wetzel T., Daubner M., Litfin K., Vogt J.B., Proriol-Serre I., Gorse D., Eckert S., Stefani F., Buchenau D., and Wondrak T. & Hwang. Handbook on lead-bismuth eutectic alloy and lead properties, materials compatibility, thermal- hydraulics and technologies. Technical Report NEA–7268, Nuclear Energy Agency of the OECD, 2015.

@techreport{Fazio,
    author = "Concetta, Fazio and V.P., Sobolev and A., Aerts and S., Gavrilov and K., Lambrinou and P., Schuurmans and Gessi, A. and P., Agostini and A., Ciampichetti and L., Martinelli and S., Gosse and F., Balbaud-Celerier and J.L., Courouau and A., Terlain and N., Li and H., Glasbrenner and J., Neuhausen and S., Heinitz and L., Zanini and Y., Dai and M., Jolkkonen and Y., Kurata and T., Obara and N., Thiolliere and F.J., Martin-Munoz and A., Heinzel and A., Weisenburger and G., Mueller and G., Schumacher and A., Jianu and J., Pacio and L., Marocco and R., Stieglitz and T., Wetzel and M., Daubner and K., Litfin and J.B., Vogt and I., Proriol-Serre and D., Gorse and S., Eckert and F., Stefani and D., Buchenau and Hwang, Wondrak T. \&",
    title = "Handbook on Lead-bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal- hydraulics and Technologies",
    institution = "Nuclear Energy Agency of the OECD",
    number = "NEA--7268",
    year = "2015"
}

Range of validity
Uncertainties of Lead Bismuth Eutectic Fluid Properties
Input Parameters
References