SodiumSaturationFluidProperties

Fluid properties for liquid sodium at saturation conditions

Description

The SodiumSaturationFluidProperties class provides fluid properties for _saturated_ liquid sodium based on correlations used in the SAS4A/SASSYS-1 reactor dynamics and safety analysis code developed at Argonne National Laboratory for liquid metal reactors Dunn (2017). These property models are obtained as fits to experimental data, with computational efficiency motivating the use of a simpler functional fits than proposed in the original references upon which the SAS4a/SASSYS-1 implementation is based, namely Fink and Leibowitz (1979). Only for $var element = document.getElementById("moose-equation-1c456f90-2ff7-4462-a89b-6d81af4292f9");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-621d91d6-3ec1-42b7-98fa-bc3cacc74d89");katex.render("C_v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the original correlations/data used, since the SAS4A/SASSYS-1 implementation does not differentiate between $var element = document.getElementById("moose-equation-a373813e-0ff0-4330-a157-73fd836fe62f");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-349b9db1-00bd-4ac0-8e58-af628cb872a3");katex.render("C_v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for the saturated liquid.

Density is calculated as an empirical fit to two saturated liquid density correlations recommended by Fink and Leibowitz that cover the range $var element = document.getElementById("moose-equation-665db812-1ef9-43a6-b194-4a46b4401d64");katex.render("371 < T (K) < 2509", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

$var element = document.getElementById("moose-equation-eba84dcd-cd05-4d04-b239-f8bb1a3b31b4");katex.render("\\rho=1.00423\\times10^3-0.21390T-1.1046\\times10^{-5}T^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

This equation fits the Fink and Leibowitz models to within 9.5%.

The thermal conductivity is a fit to experimental data by Fink and Leibowitz below 1500 K, and extrapolated values above 1500 K based on a method described by Grosse Dunn (2017):

$var element = document.getElementById("moose-equation-554a2d51-796f-4238-89b1-ead5d9f47d7a");katex.render("k=1.1045\\times10^2-6.5112\\times10^{-2}T+1.5430\\times10^{-5}T^2-2.4617\\times10^{-9}T^3", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

This equation fits the Fink and Leibowitz data to within 0.5%.

The dynamic viscosity is given as a fit to experimental data by Fink and Leibowitz below 1200 K and extrapolated values about 1200 K based on a method described by Grosse Dunn (2017):

$var element = document.getElementById("moose-equation-413e87c9-0247-4779-84b2-ba1fcc18c758");katex.render("\\mu=3.6522\\times10^{-5}+\\frac{0.16626}{T}-\\frac{4.56877\\times10^1}{T^2}+\\frac{2.8733\\times10^4}{T^3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

This equation fits the Fink and Leibowitz data to within 0.5%.

The isobaric and isochoric specific heats are obtained as new fits to the experimental data in Fink and Leibowitz over the range $var element = document.getElementById("moose-equation-7248ce78-165b-4d51-8402-d37391e409f1");katex.render("400 < T (K) < 2200", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ,

$var element = document.getElementById("moose-equation-ad7bb855-2cc2-427b-8530-e627f948ff10");katex.render("C_p=3.7782\\times10^{-1}T^2-1.7191\\times10^{-6}T^3+3.0921\\times10^{-3}T^2-2.4560T+1.972\\times10^3", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

$var element = document.getElementById("moose-equation-6be3ff19-b2e3-4257-8c21-8c34211fd184");katex.render("C_v=1.0369\\times10^{-8}T^3+3.7164\\times10^{-4}T^2-1.0494T+1.5826\\times10^3", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The $var element = document.getElementById("moose-equation-a3d68626-9512-4814-91d3-41cf102d5c8e");katex.render("R^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ values for both fits are 0.997, where the $var element = document.getElementById("moose-equation-fd34dad1-d514-45e0-bb29-94d3c205676e");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ fit matches experimental data to within 0.5%, while for $var element = document.getElementById("moose-equation-0e5d4d17-af73-4070-b856-5156c043c1f2");katex.render("C_v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ matches experimental data to within 1.5%.

Enthalpy is computed based on the definition of $var element = document.getElementById("moose-equation-3b897118-6a6c-4e50-bea8-8ef6b8f0640e");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ,

$var element = document.getElementById("moose-equation-ea275e46-aeec-4304-a103-aa2b5ff6016f");katex.render("C_p\\equiv\\left(\\frac{\\partial h}{\\partial T}\\right)_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Neglecting any variation in the saturation conditions with respect to pressure (i.e. Poynting-type effects), $var element = document.getElementById("moose-equation-101d3884-4138-4d80-ac28-976053065474");katex.render("h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ can be computed by integrating the above expression,

$var element = document.getElementById("moose-equation-ef4b48ae-5c92-4c3f-9912-f4a87be8f8a2");katex.render("h(T)-h(T_{ref})=\\int_{T_{ref}}^TC_pdT'", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-71059240-3378-417c-b1b3-38fb1f375f5b");katex.render("T_{ref}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a reference temperature and $var element = document.getElementById("moose-equation-669229c4-c9be-41d6-b3f6-f1acac5bad02");katex.render("h(T_{ref})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the enthalpy at that reference temperature. This expression is used to evaluate enthalpy based on the $var element = document.getElementById("moose-equation-f42c10d0-3b1a-4fd8-a5f6-60ec357b8da6");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ fit as

$var element = document.getElementById("moose-equation-1e7c4916-0226-4361-b5f6-41e90dae645d");katex.render("h(T)=F(T)-401088.7", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-5c9d3b8c-1463-48e4-9d0f-8a476eff12ef");katex.render("F(T)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the integral of $var element = document.getElementById("moose-equation-f1f819bf-ba13-4a01-a35d-2d9eff86c3b9");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ with respect to temperature evaluated at $var element = document.getElementById("moose-equation-0e4a9de8-fab8-4348-acea-1d09b04884ef");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-bba392c2-5326-4523-951b-86a9026fc92a");katex.render("401088.7", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ J/kg/K is a constant representing $var element = document.getElementById("moose-equation-5b08658e-1bd3-4db6-936f-90da2222a468");katex.render("-F(T_{ref})+h(T_{ref})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ selected in order to match the Fink and Leibowitz correlation at 371 K. This approach, rather than simply using the Fink and Leibowitz correlation outright, is used to ensure exact compatibility with thermodynamic definitions and the particular fit for $var element = document.getElementById("moose-equation-db38709c-fd3e-47d3-aadd-3215798b084c");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ selected in this class. Computing $var element = document.getElementById("moose-equation-d24d8172-77c9-4d59-9d64-7854ec0eacf9");katex.render("h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ based on an integral of $var element = document.getElementById("moose-equation-5282e580-171b-42d6-836d-4f5e3bcb2206");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ matches the Fink and Leibowitz correlations to within 0.2% over the entire range for which the $var element = document.getElementById("moose-equation-071ddc9a-a6a6-4185-afdb-c4d16bc6ebde");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ fit is valid.

Range of Validity

These fluid properties correspond to saturated conditions (that is, the sodium is at the saturation pressure).

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

F.E. Dunn. The SAS4A/SASSYS-1 safety analysis code system, chapter 12: sodium voiding model. Technical Report ANL/NE-16/19, Argonne National Laboratory, 2017.

@techreport{sas,
    author = "Dunn, F.E.",
    title = "The {SAS4A}/{SASSYS-1} Safety Analysis Code System, Chapter 12: Sodium Voiding Model",
    institution = "Argonne National Laboratory",
    number = "ANL/NE-16/19",
    year = "2017"
}

J.F. Fink and L. Leibowitz. Thermophysical properties of sodium. Technical Report ANL-CEN-RSD-79-1, Argonne National Laboratory, 1979.

@techreport{fink,
    author = "Fink, J.F. and Leibowitz, L.",
    title = "Thermophysical Properties of Sodium",
    institution = "Argonne National Laboratory",
    number = "ANL-CEN-RSD-79-1",
    year = "1979"
}

Description
Range of Validity
Input Parameters
References