LeadLithiumFluidProperties

Fluid properties for Lead Lithium eutectic (83% Pb, 17% Li)

These properties are based on experiments and compilations reported in the literature, e.g., Schulz (1991), Zinkle (1998), and Mas de les Valls et al. (2008). Most properties depend only on temperature; the fluid is considered incompressible over the range of interest. The fluid properties are summarized in Table Table 1, which reports the formulas used and their origin.

Table 1: Table of properties, equations, and references for the Lead–Lithium fluid properties.

Properties	Equations	Reference
Melting point, $var element = document.getElementById("moose-equation-d2e4e046-91cb-4683-a8b9-243fd932181d");katex.render("T_{mo}", element, {displayMode:false,throwOnError:false});$ `[K]`	$var element = document.getElementById("moose-equation-7d03b905-c663-43f7-a2ce-39b3fb7d065b");katex.render("508", element, {displayMode:false,throwOnError:false});$	Martelli et al. (2019) and Mas de les Valls et al. (2008)
Density, $var element = document.getElementById("moose-equation-0d662c38-f424-470b-979c-b5b3baed0693");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ `[kg/m^3]`	$var element = document.getElementById("moose-equation-c41eae7c-1c6e-4dbf-9585-e7a6b0190bef");katex.render("\\displaystyle 10520.35 - 1.19051\\,T", element, {displayMode:false,throwOnError:false});$	Mas de les Valls et al. (2008)
Viscosity, $var element = document.getElementById("moose-equation-87f3a6f6-da58-4341-a938-2213f34f5215");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ `[Pa s]`	$var element = document.getElementById("moose-equation-aac3654f-c5d3-4ad2-b68a-d54c06e7244c");katex.render("\\displaystyle 1.87 \\times 10^{-4}\\,\\exp\\!\\left(\\frac{11640}{8.314\\,T}\\right)", element, {displayMode:false,throwOnError:false});$	Schulz (1991)
Specific enthalpy, $var element = document.getElementById("moose-equation-1c6dcfec-247c-405c-a1c8-c2bf4fc09a4c");katex.render("h", element, {displayMode:false,throwOnError:false});$ `[J/kg]`	$var element = document.getElementById("moose-equation-5b5d17d5-74ca-4a87-8d07-41d863d0e044");katex.render("\\displaystyle 195\\,(T-T_{mo}) - 0.5\\times9.116\\times10^{-3}\\,(T^2-T_{mo}^2)", element, {displayMode:false,throwOnError:false});$	Zinkle (1998)
Thermal Conductivity, $var element = document.getElementById("moose-equation-8e6c0450-abcf-4428-8073-ecff9999ce7e");katex.render("k", element, {displayMode:false,throwOnError:false});$ `[W/(m-K)]`	$var element = document.getElementById("moose-equation-5e101f7e-56b5-470f-9577-2a0cc6007ae1");katex.render("\\displaystyle 14.51 + 0.019631\\,T", element, {displayMode:false,throwOnError:false});$	E.A. Mogahed (1995)
Isobaric Specific Heat, $var element = document.getElementById("moose-equation-586423c1-5ddc-496b-891e-6ba6a67184d4");katex.render("c_p", element, {displayMode:false,throwOnError:false});$ `[J/(kg-K)]`	$var element = document.getElementById("moose-equation-0be66a53-80fb-44a9-aa04-a6f13319b937");katex.render("\\displaystyle 195 - 9.116\\times10^{-3}\\,T", element, {displayMode:false,throwOnError:false});$	Schulz (1991)
Isochoric Specific Heat, $var element = document.getElementById("moose-equation-af8ca310-101c-46f6-a188-ecedb140a008");katex.render("c_v", element, {displayMode:false,throwOnError:false});$ `[J/(kg-K)]`	$var element = document.getElementById("moose-equation-17355e8d-fdab-4b79-97b3-ae3c6c86586f");katex.render("\\displaystyle \\frac{c_p}{1+\\left(\\frac{1.19051}{10520.35-1.19051 \\, T}\\right)^2 \\frac{B_S \\, T}{\\rho \\, c_p}}", element, {displayMode:false,throwOnError:false});$	Zinkle (1998)
Isentropic Bulk Modulus, $var element = document.getElementById("moose-equation-94bf6456-2776-41de-9181-c70425d8912b");katex.render("B_S", element, {displayMode:false,throwOnError:false});$ `[Pa]`	$\dfrac{c^2}{\rho}	Martelli et al. (2019)\|
Speed of Sound, $var element = document.getElementById("moose-equation-84aebea8-e05d-4c0a-bede-45f27b4eb8e8");katex.render("c", element, {displayMode:false,throwOnError:false});$ `[m/s]`	$var element = document.getElementById("moose-equation-60a630d8-4688-46c2-81e8-5abee095848d");katex.render("\\displaystyle 1876 - 0.306\\,T", element, {displayMode:false,throwOnError:false});$	Ueki et al. (2009)

note

The thermal conductivity differs significantly between E.A. Mogahed (1995) and Mas de les Valls et al. (2008), Zinkle (1998), and Schulz (1991), by nearly 50%.

Range of Validity

The properties defined in LeadLithiumFluidProperties are valid in the following temperature ranges:

var element = document.getElementById("moose-equation-8fed8e1e-5c5b-41a2-9329-96e5c3f604a5");katex.render("508\\,\\mathrm{K} \\le T \\le 880\\,\\mathrm{K}, \\text{for density}", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-bd61fd5b-4ada-4953-b679-409225b5df54");katex.render("508\\,\\mathrm{K} \\le T \\le 873\\,\\mathrm{K}, \\text{for thermal conductivity}", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-94e25635-5d54-4d5d-bfa8-efc0458264e4");katex.render("508\\,\\mathrm{K} \\le T \\le 625\\,\\mathrm{K}, \\text{for specific heat}", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-c5df4a7c-005c-4425-8b62-9ca94f7a890e");katex.render("508\\,\\mathrm{K} \\le T \\le 625\\,\\mathrm{K}, \\text{for viscosity}", element, {displayMode:true,throwOnError:false});

and for pressures near atmospheric up to a few MPa, where the assumption of incompressibility holds.

Uncertainties of Lead–Lithium Fluid Properties

Based on experimental studies Schulz (1991) and compilations in fusion materials handbooks Zinkle (1998), and thermophysical property reviews Mas de les Valls et al. (2008), the reported uncertainties for Lead–Lithium fluid properties are approximately:

Table 2: Uncertainties on properties

Property	Uncertainty / Scattering (%)
Density	$var element = document.getElementById("moose-equation-7885f8ad-d194-47c8-8c4b-641c516fdd0f");katex.render("\\approx", element, {displayMode:false,throwOnError:false});$ 4% Martelli et al. (2019)
Viscosity	$var element = document.getElementById("moose-equation-4d80bd32-6342-464c-b7dc-366df56b6bae");katex.render("\\approx", element, {displayMode:false,throwOnError:false});$ 12% Martelli et al. (2019)
Thermal Conductivity	$var element = document.getElementById("moose-equation-a4cc3430-2345-48fc-8a5a-49e395754c9d");katex.render("\\approx", element, {displayMode:false,throwOnError:false});$ 37% Martelli et al. (2019)
Isobaric Specific Heat	$var element = document.getElementById("moose-equation-e3463f03-aff5-47df-a2b9-df5cb33dcf1e");katex.render("\\approx", element, {displayMode:false,throwOnError:false});$ 32% Martelli et al. (2019)

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

G.L. Kulcinski E.A. Mogahed. Bibliography of a promising tritium breeding material – pb83li17. Technical Report UWFDM-994, Fusion Technology Institute, University of Wisconsin-Madison, WI, USA, 1995.

@techreport{Mogahed1995,
    author = "E.A. Mogahed, G.L. Kulcinski",
    title = "Bibliography of a Promising Tritium Breeding Material – Pb83Li17",
    institution = "Fusion Technology Institute, University of Wisconsin-Madison",
    year = "1995",
    number = "UWFDM-994",
    address = "WI, USA"
}

D. Martelli, A. Venturini, and M. Utili. Literature review of lead-lithium thermophysical properties. Fusion Engineering and Design, 138:183–195, 2019. URL: https://www.sciencedirect.com/science/article/pii/S0920379618307361, doi:https://doi.org/10.1016/j.fusengdes.2018.11.028.

@article{Martelli2009,
    author = "Martelli, D. and Venturini, A. and Utili, M.",
    title = "Literature review of lead-lithium thermophysical properties",
    journal = "Fusion Engineering and Design",
    volume = "138",
    pages = "183-195",
    year = "2019",
    issn = "0920-3796",
    doi = "https://doi.org/10.1016/j.fusengdes.2018.11.028",
    url = "https://www.sciencedirect.com/science/article/pii/S0920379618307361",
    keywords = "Lead-lithium eutectic, PbLi, Thermophysical properties, Fusion"
}

B. Schulz. Thermophysical properties of the li(17)pb(83)alloy. Fusion Engineering and Design, 14(3):199–205, 1991. URL: https://www.sciencedirect.com/science/article/pii/0920379691900028, doi:https://doi.org/10.1016/0920-3796(91)90002-8.

@article{Schulz1991,
    author = "Schulz, B.",
    title = "Thermophysical properties of the Li(17)Pb(83)alloy",
    journal = "Fusion Engineering and Design",
    volume = "14",
    number = "3",
    pages = "199-205",
    year = "1991",
    issn = "0920-3796",
    doi = "https://doi.org/10.1016/0920-3796(91)90002-8",
    url = "https://www.sciencedirect.com/science/article/pii/0920379691900028"
}

Y. Ueki, M. Hirabayashi, T. Kunugi, T. Yokomine, and K. Ara and. Acoustic properties of pb-17li alloy for ultrasonic doppler velocimetry. Fusion Science and Technology, 56(2):846–850, 2009. URL: https://doi.org/10.13182/FST56-846, arXiv:https://doi.org/10.13182/FST56-846, doi:10.13182/FST56-846.

@article{Ueki2009,
    author = "Ueki, Y. and Hirabayashi, M. and Kunugi, T. and Yokomine, T. and and, K. Ara",
    title = "Acoustic Properties of Pb-17Li Alloy for Ultrasonic Doppler Velocimetry",
    journal = "Fusion Science and Technology",
    volume = "56",
    number = "2",
    pages = "846--850",
    year = "2009",
    publisher = "American Nuclear Society",
    doi = "10.13182/FST56-846",
    URL = "https://doi.org/10.13182/FST56-846",
    eprint = "https://doi.org/10.13182/FST56-846"
}

S. J. Zinkle. Summary of physical properties for lithium, pb-17li, and (lif)n•bef2 coolants, apex study meeting. Technical Report, Oak Ridge National Laboratory, Oak Ridge, TN, USA, 1998.

@techreport{Zinkle1998,
    author = "Zinkle, S. J.",
    title = "Summary of Physical Properties for Lithium, Pb-17Li, and (LiF)n•BeF2 Coolants, APEX Study Meeting",
    institution = "Oak Ridge National Laboratory",
    year = "1998",
    address = "Oak Ridge, TN, USA"
}

E. Mas de les Valls, L.A. Sedano, L. Batet, I. Ricapito, A. Aiello, O. Gastaldi, and F. Gabriel. Lead–lithium eutectic material database for nuclear fusion technology. Journal of Nuclear Materials, 376(3):353–357, 2008. Heavy Liquid Metal Cooled Reactors and Related Technologies. URL: https://www.sciencedirect.com/science/article/pii/S0022311508000809, doi:https://doi.org/10.1016/j.jnucmat.2008.02.016.

@article{MasdeLesValls2008,
    author = "{Mas de les Valls}, E. and Sedano, L.A. and Batet, L. and Ricapito, I. and Aiello, A. and Gastaldi, O. and Gabriel, F.",
    title = "Lead–lithium eutectic material database for nuclear fusion technology",
    journal = "Journal of Nuclear Materials",
    volume = "376",
    number = "3",
    pages = "353-357",
    year = "2008",
    note = "Heavy Liquid Metal Cooled Reactors and Related Technologies",
    issn = "0022-3115",
    doi = "https://doi.org/10.1016/j.jnucmat.2008.02.016",
    url = "https://www.sciencedirect.com/science/article/pii/S0022311508000809",
    keywords = "28.52, 52.55, 66"
}

Range of Validity
Uncertainties of Lead – Lithium Fluid Properties
Input Parameters
References