ThermalGraphiteProperties

Graphite thermal properties.

Description

This userobject provides thermal properties for graphite as a function of temperature. Because there are many different grades of graphite, this userobject computes properties individually for each grade. Because many grades are encapsulated in this userobject, the applicability ranges of the correlations are unique to each grade.

Many of the graphite grades encapsulated in this userobject are coke-based. Because many coke-based graphite grades show approximately the same specific heat, it is a reasonable approximation to use the same $var element = document.getElementById("moose-equation-f27af2d8-7ad2-41f2-acad-edb57a50f3ec");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ correlation from Butland and Maddison (1973) for many different grades Baker (1970).

All units are given in SI, such that the input temperature is Kelvin, and the output units of the thermal conductivity $var element = document.getElementById("moose-equation-4d152cc3-1eb9-4273-96d4-78c86e2dc6ef");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are W/m $var element = document.getElementById("moose-equation-799b3ef4-fb2d-435b-8571-7fa7fc519629");katex.render("\\cdot", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ K, the output units of the isobaric specific heat capacity $var element = document.getElementById("moose-equation-1a9dd195-cefc-495e-9401-192c86db138e");katex.render("C_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are J/kg $var element = document.getElementById("moose-equation-4709a35d-d188-450e-a70c-551801ed7dcf");katex.render("\\cdot", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ K, and the output units of the density $var element = document.getElementById("moose-equation-af046ddd-7131-4c0e-96f5-b19e871c1449");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are kg/m $var element = document.getElementById("moose-equation-d4c4f844-d0ad-472f-8721-9f7cbff0e32a");katex.render("^3", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

H-451

H-451 graphite is a near-isotropic, artificial graphite based on petroleum coke. H-451 graphite is commonly used for reflectors in nuclear applications.

Isobaric specific heat is calculated from Butland and Maddison (1973) as

$var element = document.getElementById("moose-equation-58661fd7-48e4-4ddd-8cc9-f72e4201f53d");katex.render("C_p=4184\\left\\lbrack 0.54212-2.42667e-6T-90.2725 T^{-1}-43449.3 T^{-3}+1.59309\\times 10^7 T^{-3}-1.43688\\times 10^9T^{-4}\\right\\rbrack", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

with a validity range of 200 K $var element = document.getElementById("moose-equation-16667fb9-e55d-4f18-bb5d-a5fa0cdad7a8");katex.render("\\le T \\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 3500.

The thermal conductivity is calculated from NEA (2018) as

$var element = document.getElementById("moose-equation-376cb011-d573-48bf-a264-919b6134558a");katex.render("k=3.28248\\times 10^{-5}T^2-1.24890\\times 10^{-1}T+1.69214\\times 10^2", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

with a validity range of 500 K $var element = document.getElementById("moose-equation-27083391-6519-4286-96be-d5b804325cdb");katex.render("\\le T \\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 1800 K.

Density is taken as a constant value; a default value is provided based on NEA (2018) as

$var element = document.getElementById("moose-equation-f3b031c8-0694-40b1-85ef-1ee59ebb036f");katex.render("\\rho=1850.0", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Input Parameters

gradeGraphite grade
C++ Type:MooseEnum
Options:H_451
Controllable:No
Description:Graphite grade

Required Parameters

T_zero_e273.15Temperature at which the specific internal energy is assumed to be zero [K].
Default:273.15
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Temperature at which the specific internal energy is assumed to be zero [K].
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
density1850(Constant) density
Default:1850
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:(Constant) density

Optional Parameters

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.

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

D. E. Baker. Graphite as a Neutron Moderator and Reflector Material. Nuclear Engineering and Design, 14:413–444, 1970.

@Article{baker,
    author = "Baker, D. E.",
    title = "{Graphite as a Neutron Moderator and Reflector Material}",
    journal = "Nuclear Engineering and Design",
    year = "1970",
    volume = "14",
    pages = "413--444"
}

A. T. D. Butland and R. J. Maddison. The Specific Heat of Graphite: An Evaluation of Measurements. Journal of Nuclear Materials, 49:45–56, 1973.

@Article{butland,
    author = "Butland, A. T. D. and Maddison, R. J.",
    title = "{The Specific Heat of Graphite: An Evaluation of Measurements}",
    journal = "Journal of Nuclear Materials",
    year = "1973",
    volume = "49",
    pages = "45--56"
}

NEA. NEA Benchmark of the Modular High-Temperature Gas-Cooled Reactor-350 MW Core Design Volumes I and II. Technical Report NEA/NSC/R(2017)4, Nuclear Energy Agency, 2018.

@techreport{nea2018,
    author = "NEA",
    title = "{{NEA} Benchmark of the Modular High-Temperature Gas-Cooled Reactor-350 {MW} Core Design Volumes I and II}",
    institution = "Nuclear Energy Agency",
    number = "NEA/NSC/R(2017)4",
    year = "2018"
}

Description
Input Parameters
References