CaloricallyImperfectGas

Fluid properties for an ideal gas with imperfect caloric behavior.

This class implements fluid properties for a gas that behaves like an ideal gas except that the specific heat capacities are a function of temperature (as opposed to constants as for the ideal gas).

The relationship between pressure, density, and temperature is identical to an ideal gas:

$var element = document.getElementById("moose-equation-85a53541-c0f5-4243-b624-329f0df0df15");katex.render(" pv = R_s T,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-0b71626d-45a8-4d41-9e74-9eb06b2bd581");katex.render("p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is pressure, $var element = document.getElementById("moose-equation-ea643ce4-81f1-4bf2-bc8a-475c101415ff");katex.render("v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is specific volume, $var element = document.getElementById("moose-equation-6d12f9ee-cdd0-429d-be7b-db4c30f58605");katex.render("R_s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the specific gas constant, and $var element = document.getElementById("moose-equation-d5a2ed7c-fcbe-48d6-81fa-33de9bbbbd7c");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is temperature.

The internal energy $var element = document.getElementById("moose-equation-c5fbaea1-f104-4cf0-8ab6-54b79030a07c");katex.render("e", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a user-provided function of temperature:

$var element = document.getElementById("moose-equation-bc97d8a6-167f-4782-9563-213e0cb03fc2");katex.render(" e = e(T).", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The function $var element = document.getElementById("moose-equation-28a1cec6-38d1-4104-b7c8-a90503966153");katex.render("e(T)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is provided via parameter "e". The time argument is interpreted as temperature.

The enthalpy is computed by:

$var element = document.getElementById("moose-equation-cc0b062c-87ac-4f2c-9610-4e9160fd1dbc");katex.render(" h = e(T) + R_s T.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The specific heat capacities at constant volume and pressure $var element = document.getElementById("moose-equation-4d5af2d2-4de2-4d01-872d-a0950f2d66f3");katex.render("c_v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-16b93a51-6bb7-4a5c-a75f-f119d130e874");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are computed by:

var element = document.getElementById("moose-equation-e3478f46-7890-4a9c-87cc-db2b5f56c050");katex.render("\\begin{aligned} c_v &= \\frac{de}{dT} \\\\ c_p &= \\frac{de}{dT} + R_s. \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

warning

The specific heat capacities are computed from $var element = document.getElementById("moose-equation-778dafa4-03a3-4370-8c04-2abab2f14471");katex.render("e(T)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ using the timeDerivative method of the Function class. The type of function that is used for $var element = document.getElementById("moose-equation-8fc06836-6e1e-4442-af33-b63ade65941c");katex.render("e(T)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ must implement the timeDerivative method.

The inverse functions $var element = document.getElementById("moose-equation-517593fc-8801-45c2-862f-8a0cbe5cc159");katex.render("T(e)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-aa1ad88f-a385-4563-b1b3-a9a66abb368f");katex.render("T(h)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are obtained as follows:

Ensure that within the acceptable temperature range (parameters min_temperature and max_temperature) $var element = document.getElementById("moose-equation-c1e9b119-160c-437f-a0cb-2e075d218c96");katex.render("c_v > 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .
Compute the minimum and maximum values of $var element = document.getElementById("moose-equation-c710d2d2-a7b6-4f02-b3b0-6a13b0ffa964");katex.render("e", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-51bcd43a-f8fb-436c-b2a2-b63b4faeaaa8");katex.render("h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

var element = document.getElementById("moose-equation-1a96ce9f-2a7a-4733-a508-b0ad8d010974");katex.render("\\begin{aligned} e_{min} &= e(T_{min}) \\\\ e_{max} &= e(T_{max}) \\\\ h_{min} &= h(T_{min}) \\\\ h_{max} &= h(T_{max}) \\\\ \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Sample
$var element = document.getElementById("moose-equation-2d69207e-d707-4a0a-9b65-1f2dc45a2407");katex.render("e_j = e_{min} + j \\frac{e_{max}-e_{min}}{N},\\qquad j=0,..,N.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
and for each $var element = document.getElementById("moose-equation-72afba16-8385-45a8-a332-990754c4556d");katex.render("e_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ solve
$var element = document.getElementById("moose-equation-5893dd60-aba0-4461-ba97-ff0baa48eaf9");katex.render("e_j - e(T_j)= 0,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
for $var element = document.getElementById("moose-equation-b3296449-dbe0-419c-b69b-44f06340a5ab");katex.render("T_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . Create tabulation $var element = document.getElementById("moose-equation-c22c22e0-53ad-44ed-8265-7e5af9e69641");katex.render("\\{e_j, T_j\\}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . Create a similar tabulation for enthalpy.
Evaluating $var element = document.getElementById("moose-equation-ee7e4718-fac9-4b06-8158-a5dcbdba14fe");katex.render("T(e)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ uses linear interpolation in $var element = document.getElementById("moose-equation-f3e177e6-9bfc-4e30-b441-a0594d9649cb");katex.render("\\{e_j, T_j\\}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

Evaluating Entropy

From the first and second law of thermodynamics is follows that:

var element = document.getElementById("moose-equation-1238e168-a62e-48c8-8e98-8cdc1f8703e7");katex.render("\\begin{aligned} dq &= de + pdv \\\\ ds &= dq/T, \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-4a136236-9651-40e7-bbf4-689fa5006ddc");katex.render("dq", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is an infinitesimal amount of heat. Solving for $var element = document.getElementById("moose-equation-db21ae7e-02e2-4789-ab12-3cc561f9a40f");katex.render("ds", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and using the ideal gas law leads to:

$var element = document.getElementById("moose-equation-93991b8e-c862-4458-a713-89cc51a3ca3f");katex.render(" ds = \\frac{de}{T} + R_s \\frac{dv}{v}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Integrating this equation leads to an expression for the entropy:

$var element = document.getElementById("moose-equation-2c8f21d4-ba51-4291-9f21-a9e8f61db5b8");katex.render(" s(e, v) - s(e_0, v_0) = \\int\\limits_{e_0}^e \\frac{de'}{T'} + R_s \\log \\frac{v}{v_0},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where the prime indicates that these variables are dummy variables of integration. We are free to select a zero-point for entropy and we select $var element = document.getElementById("moose-equation-84f8bbf9-6ace-4400-8256-b5d23049400b");katex.render("s(e_0, v_0) = 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . We also select $var element = document.getElementById("moose-equation-c0d9797e-661b-4dd4-82c8-8a0c621c156d");katex.render("v_0 = 1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-952162fd-fd2b-44c9-9de3-72ba73e90ad9");katex.render("e_0 = e(T_{min})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . Then we define:

$var element = document.getElementById("moose-equation-539cd9d6-1ac8-4aff-8c2b-d78ebca7e6ad");katex.render(" Z(T) = \\int\\limits_{e_0}^{e(T)} \\frac{de'}{T'} = \\int\\limits_{T_{min}}^{T} \\frac{c_v(T')}{T'} dT'.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Entropy is computed from the expression:

$var element = document.getElementById("moose-equation-52d98548-215d-4c06-8820-de86c569d003");katex.render(" s(e, v) = Z(T(e)) + R_s \\log v,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-bb5f481e-a5f5-424d-a327-5c2ae07ad45b");katex.render("Z(T)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is computed using a trapezoidal rule and tabulated between $var element = document.getElementById("moose-equation-1642de8a-c902-4a07-8cc5-b88098e17104");katex.render("T_{min}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-c4af5034-7209-4aac-bcac-b084b6db27e1");katex.render("T_{max}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . It is linearly interpolated.

The derivatives of entropy with respect to $var element = document.getElementById("moose-equation-33c0f186-c1b4-4200-808b-c2906cc6dc57");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-44328a08-5b4a-4914-86f2-fef7edf38b76");katex.render("e", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-fbdef8e1-f4b9-41a8-9285-39e940146942");katex.render("h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-d83d77e2-99fa-47aa-a5ce-fa054b53f95c");katex.render("v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are given by:

var element = document.getElementById("moose-equation-a50b2cfa-d045-480f-b6d4-14125959975c");katex.render("\\begin{aligned} \\left(\\frac{\\partial s}{\\partial e}\\right)_v &= \\frac{1}{T(e)} \\\\ \\left(\\frac{\\partial s}{\\partial v}\\right)_e &= \\frac{R_s}{v} \\\\ \\left(\\frac{\\partial s}{\\partial p}\\right)_T &= -\\frac{R_s}{p} \\\\ \\left(\\frac{\\partial s}{\\partial T}\\right)_p &= \\frac{c_p(T)}{T} \\\\ \\left(\\frac{\\partial s}{\\partial p}\\right)_h &= -\\frac{R_s}{p} \\\\ \\left(\\frac{\\partial s}{\\partial h}\\right)_p &= \\frac{1}{T}. \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

These derivatives are implemented in the 5 argument versions of the s_from_x_y functions.

Input Parameters

eSpecific internal energy as a function of temperature [J/kg]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Specific internal energy as a function of temperature [J/kg]
kThermal conductivity, [W/(m-K)]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity, [W/(m-K)]
max_temperatureLargest temperature for lookup tables [K]
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Largest temperature for lookup tables [K]
min_temperatureSmallest temperature for lookup tables [K]
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Smallest temperature for lookup tables [K]
molar_massConstant molar mass of the fluid [kg/mol]
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Constant molar mass of the fluid [kg/mol]
muDynamic viscosity, [Pa-s]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Dynamic viscosity, [Pa-s]

Required Parameters

T_c0Critical temperature, [K]
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Critical temperature, [K]
e_c0Specific internal energy at the critical point, [J/kg]
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Specific internal energy at the critical point, [J/kg]
emit_on_nannoneWhether to raise a warning, an exception (usually triggering a retry with a smaller time step) or an error (ending the simulation)
Default:none
C++ Type:MooseEnum
Options:none, warning, exception, error
Controllable:No
Description:Whether to raise a warning, an exception (usually triggering a retry with a smaller time step) or an error (ending the simulation)
out_of_bound_errorTrueError if out of bounds
Default:True
C++ Type:bool
Controllable:No
Description:Error if out of bounds
rho_c0Critical density, [kg/m3]
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Critical density, [kg/m3]
temperature_resolution1Step size in temperature for creating the inverse lookup T(e)
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Step size in temperature for creating the inverse lookup T(e)

Optional 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

Input Files

(modules/thermal_hydraulics/test/tests/components/junction_parallel_channels_1phase/junction_with_calorifically_imperfect_gas.i)
(modules/fluid_properties/test/tests/calorically_imperfect_gas/test.i)
(modules/thermal_hydraulics/test/tests/components/volume_junction_1phase/junction_with_calorifically_imperfect_gas.i)

References

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(modules/thermal_hydraulics/test/tests/components/junction_parallel_channels_1phase/junction_with_calorifically_imperfect_gas.i)

# This input file tests compatibility of JunctionParallelChannels1Phase and CaloricallyImperfectGas.
# Loss coefficient is applied in first junction.
# Expected pressure drop from form loss ~0.5*K*rho_in*vel_in^2=0.5*100*3.219603*1 = 160.9 Pa
# Pressure drop from averall flow area change ~ 21.9 Pa
# Expected pressure drop ~ 182.8 Pa

T_in = 523.0
vel = 1
p_out = 7e6

[GlobalParams]
  initial_p = ${p_out}
  initial_vel = ${vel}
  initial_T = ${T_in}
  gravity_vector = '0 0 0'
  closures = simple_closures
  n_elems = 3
  f = 0

  scaling_factor_1phase = '1 1 1e-5'
  scaling_factor_rhoV = '1e2'
  scaling_factor_rhowV = '1e-2'
  scaling_factor_rhoEV = '1e-5'
[]

[Functions]
  [e_fn]
    type = PiecewiseLinear
    x = '100   280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '783.9 2742.3 2958.6 3489.2 4012.7 4533.3 5053.8 5574 6095.1 7140.2 8192.9 9256.3 10333.6 12543.9 14836.6 17216.3 19688.4 22273.7 25018.3 28042.3 31544.2 35818.1 41256.5 100756.5'
    scale_factor = 1e3
  []

  [mu_fn]
    type = PiecewiseLinear
    x = '100   280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '85.42 85.42 89.53 99.44 108.9 117.98 126.73 135.2 143.43 159.25 174.36 188.9 202.96 229.88 255.5 280.05 303.67 326.45 344.97 366.49 387.87 409.48 431.86 431.86'
    scale_factor = 1e-7
  []

  [k_fn]
    type = PiecewiseLinear
    x = '100 280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '186.82 186.82 194.11 212.69 231.55 250.38 268.95 287.19 305.11 340.24 374.92 409.66 444.75 511.13 583.42 656.44 733.32 826.53 961.15 1180.38 1546.31 2135.49 3028.08 3028.08'
    scale_factor = 1e-3
  []
[]

[FluidProperties]
  [fp]
    type = CaloricallyImperfectGas
    molar_mass = 0.002
    e = e_fn
    k = k_fn
    mu = mu_fn
    min_temperature = 100
    max_temperature = 5000
    out_of_bound_error = false
  []
[]

[Closures]
  [simple_closures]
    type = Closures1PhaseSimple
  []
[]

[Components]
  [inlet_bc]
    type = InletVelocityTemperature1Phase
    input = 'inlet:in'
    vel = ${vel}
    T = ${T_in}
  []
  [inlet]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 11'
    orientation = '0 0 -1'
    length = 1
    A = 3
  []
  [inlet_plenum]
    type = JunctionParallelChannels1Phase
    position = '0 0 10'
    initial_vel_x = 0
    initial_vel_y = 0
    initial_vel_z = ${vel}
    K = 100
    connections = 'inlet:out channel1:in channel2:in'
    volume = 1
  []
  [channel1]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 10'
    orientation = '0 0 -1'
    length = 10
    A = 4
    D_h = 1
  []
  [channel2]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 10'
    orientation = '0 0 -1'
    length = 10
    A = 1
    D_h = 1
  []
  [outlet_plenum]
    type = JunctionParallelChannels1Phase
    position = '0 0 0'
    initial_vel_x = 1
    initial_vel_y = 0
    initial_vel_z = ${vel}
    connections = 'channel1:out channel2:out outlet:in'
    volume = 1
  []
  [outlet]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 0'
    orientation = '0 0 -1'
    length = 1
    A = 1
  []
  [outlet_bc]
    type = Outlet1Phase
    p = ${p_out}
    input = 'outlet:out'
  []
[]

[Postprocessors]
  [p_in]
    type = SideAverageValue
    variable = p
    boundary = inlet:in
  []
  [p_out]
    type = SideAverageValue
    variable = p
    boundary = outlet:out
  []
  [Delta_p]
    type = DifferencePostprocessor
    value1 = p_out
    value2 = p_in
  []
  [inlet_in_m_dot]
    type = ADFlowBoundaryFlux1Phase
    boundary = 'inlet_bc'
    equation = mass
  []
  [inlet_out_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'inlet:out'
    connection_index = 0
    junction = inlet_plenum
    equation = mass
  []

  [channel1_in_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel1:in'
    connection_index = 1
    junction = inlet_plenum
    equation = mass
  []
  [channel1_out_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel1:out'
    connection_index = 0
    junction = outlet_plenum
    equation = mass
  []

  [channel2_in_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel2:in'
    connection_index = 2
    junction = inlet_plenum
    equation = mass
  []
  [channel2_out_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel2:out'
    connection_index = 1
    junction = outlet_plenum
    equation = mass
  []

  [outlet_in_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'outlet:in'
    connection_index = 2
    junction = outlet_plenum
    equation = mass
  []
  [outlet_out_m_dot]
    type = ADFlowBoundaryFlux1Phase
    boundary = 'outlet_bc'
    equation = mass
  []

  [net_mass_flow_rate_domain]
    type = LinearCombinationPostprocessor
    pp_names = 'inlet_in_m_dot outlet_out_m_dot'
    pp_coefs = '1 -1'
  []
  [net_mass_flow_rate_volume_junction]
    type = LinearCombinationPostprocessor
    pp_names = 'inlet_out_m_dot channel1_in_m_dot channel2_in_m_dot'
    pp_coefs = '1 -1 -1'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = bdf2
  start_time = 0
  end_time = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 8
    iteration_window = 2
  []
  timestep_tolerance = 1e-6
  abort_on_solve_fail = true

  line_search = basic
  nl_rel_tol = 1e-8
  nl_abs_tol = 2e-8
  nl_max_its = 25
  l_tol = 1e-3
  l_max_its = 5
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = ' lu     '
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'FINAL'
    show = 'net_mass_flow_rate_domain net_mass_flow_rate_volume_junction Delta_p'
  []
[]

(modules/fluid_properties/test/tests/calorically_imperfect_gas/test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Functions]
  [f_fn]
    type = ParsedFunction
    expression = -4
  []
  [bc_fn]
    type = ParsedFunction
    expression = 'x*x+y*y'
  []

  [e_fn]
    type = PiecewiseLinear
    x = '100   280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '783.9 2742.3 2958.6 3489.2 4012.7 4533.3 5053.8 5574 6095.1 7140.2 8192.9 9256.3 10333.6 12543.9 14836.6 17216.3 19688.4 22273.7 25018.3 28042.3 31544.2 35818.1 41256.5 100756.5'
    scale_factor = 1e3
  []

  [mu_fn]
    type = PiecewiseLinear
    x = '100   280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '85.42 85.42 89.53 99.44 108.9 117.98 126.73 135.2 143.43 159.25 174.36 188.9 202.96 229.88 255.5 280.05 303.67 326.45 344.97 366.49 387.87 409.48 431.86 431.86'
    scale_factor = 1e-7
  []

  [k_fn]
    type = PiecewiseLinear
    x = '100 280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '186.82 186.82 194.11 212.69 231.55 250.38 268.95 287.19 305.11 340.24 374.92 409.66 444.75 511.13 583.42 656.44 733.32 826.53 961.15 1180.38 1546.31 2135.49 3028.08 3028.08'
    scale_factor = 1e-3
  []
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [e]
    initial_condition = 4012.7e3
  []
  [v]
    initial_condition = 0.0007354064593540647
  []

  [p]
    family = MONOMIAL
    order = CONSTANT
  []
  [T]
    family = MONOMIAL
    order = CONSTANT
  []
  [cp]
    family = MONOMIAL
    order = CONSTANT
  []
  [cv]
    family = MONOMIAL
    order = CONSTANT
  []
  [c]
    family = MONOMIAL
    order = CONSTANT
  []
  [mu]
    family = MONOMIAL
    order = CONSTANT
  []
  [k]
    family = MONOMIAL
    order = CONSTANT
  []
  [g]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [p]
    type = MaterialRealAux
     variable = p
     property = pressure
  []
  [T]
    type = MaterialRealAux
     variable = T
     property = temperature
  []
  [cp]
    type = MaterialRealAux
     variable = cp
     property = cp
  []
  [cv]
    type = MaterialRealAux
     variable = cv
     property = cv
  []
  [c]
    type = MaterialRealAux
     variable = c
     property = c
  []
  [mu]
    type = MaterialRealAux
     variable = mu
     property = mu
  []
  [k]
    type = MaterialRealAux
     variable = k
     property = k
  []
  [g]
    type = MaterialRealAux
     variable = g
     property = g
  []
[]

[FluidProperties]
  [h2]
    type = CaloricallyImperfectGas
    molar_mass = 0.002
    e = e_fn
    k = k_fn
    mu = mu_fn
    min_temperature = 100
    max_temperature = 5000
  []
[]

[Materials]
  [fp_mat]
    type = FluidPropertiesMaterialVE
    e = e
    v = v
    fp = h2
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = f_fn
  []
[]

[BCs]
  [all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = bc_fn
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(modules/thermal_hydraulics/test/tests/components/volume_junction_1phase/junction_with_calorifically_imperfect_gas.i)

# This input file tests compatibility of VolumeJunction1Phase and CaloricallyImperfectGas.
# Loss coefficient is applied in first junction.
# Expected pressure drop ~0.5*K*rho_in*vel_in^2=0.5*100*3.219603*1 = 160.9 Pa

T_in = 523.0
vel = 1
p_out = 7e6

[GlobalParams]
  initial_p = ${p_out}
  initial_vel = ${vel}
  initial_T = ${T_in}
  gravity_vector = '0 0 0'
  closures = simple_closures
  n_elems = 3
  f = 0
  scaling_factor_1phase = '1 1 1e-5'
  scaling_factor_rhoV = '1e2'
  scaling_factor_rhowV = '1e-2'
  scaling_factor_rhoEV = '1e-5'
[]

[Functions]
  [e_fn]
    type = PiecewiseLinear
    x = '100   280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '783.9 2742.3 2958.6 3489.2 4012.7 4533.3 5053.8 5574 6095.1 7140.2 8192.9 9256.3 10333.6 12543.9 14836.6 17216.3 19688.4 22273.7 25018.3 28042.3 31544.2 35818.1 41256.5 100756.5'
    scale_factor = 1e3
  []

  [mu_fn]
    type = PiecewiseLinear
    x = '100   280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '85.42 85.42 89.53 99.44 108.9 117.98 126.73 135.2 143.43 159.25 174.36 188.9 202.96 229.88 255.5 280.05 303.67 326.45 344.97 366.49 387.87 409.48 431.86 431.86'
    scale_factor = 1e-7
  []

  [k_fn]
    type = PiecewiseLinear
    x = '100 280 300 350 400 450 500 550 600 700 800 900 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 5000'
    y = '186.82 186.82 194.11 212.69 231.55 250.38 268.95 287.19 305.11 340.24 374.92 409.66 444.75 511.13 583.42 656.44 733.32 826.53 961.15 1180.38 1546.31 2135.49 3028.08 3028.08'
    scale_factor = 1e-3
  []
[]

[FluidProperties]
  [fp]
    type = CaloricallyImperfectGas
    molar_mass = 0.002
    e = e_fn
    k = k_fn
    mu = mu_fn
    min_temperature = 100
    max_temperature = 5000
    out_of_bound_error = false
  []
[]

[Closures]
  [simple_closures]
    type = Closures1PhaseSimple
  []
[]

[Components]
  [inlet_bc]
    type = InletVelocityTemperature1Phase
    input = 'inlet:in'
    vel = ${vel}
    T = ${T_in}
  []
  [inlet]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 11'
    orientation = '0 0 -1'
    length = 1
    A = 5
  []
  [inlet_plenum]
    type = VolumeJunction1Phase
    position = '0 0 10'
    initial_vel_x = 0
    initial_vel_y = 0
    initial_vel_z = ${vel}
    K = 100
    connections = 'inlet:out channel1:in channel2:in'
    volume = 1
  []
  [channel1]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 10'
    orientation = '0 0 -1'
    length = 10
    A = 4
    D_h = 1
  []
  [channel2]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 10'
    orientation = '0 0 -1'
    length = 10
    A = 1
    D_h = 1
  []
  [outlet_plenum]
    type = VolumeJunction1Phase
    position = '0 0 0'
    initial_vel_x = 0
    initial_vel_y = 0
    initial_vel_z = ${vel}
    connections = 'channel1:out channel2:out outlet:in'
    volume = 1
  []
  [outlet]
    type = FlowChannel1Phase
    fp = fp
    position = '0 0 0'
    orientation = '0 0 -1'
    length = 1
    A = 5
  []
  [outlet_bc]
    type = Outlet1Phase
    p = ${p_out}
    input = 'outlet:out'
  []
[]

[Postprocessors]
  [p_in]
    type = SideAverageValue
    variable = p
    boundary = inlet:in
  []
  [p_out]
    type = SideAverageValue
    variable = p
    boundary = outlet:out
  []
  [Delta_p]
    type = DifferencePostprocessor
    value1 = p_out
    value2 = p_in
  []
  [inlet_in_m_dot]
    type = ADFlowBoundaryFlux1Phase
    boundary = 'inlet_bc'
    equation = mass
  []
  [inlet_out_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'inlet:out'
    connection_index = 0
    junction = inlet_plenum
    equation = mass
  []

  [channel1_in_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel1:in'
    connection_index = 1
    junction = inlet_plenum
    equation = mass
  []
  [channel1_out_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel1:out'
    connection_index = 0
    junction = outlet_plenum
    equation = mass
  []

  [channel2_in_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel2:in'
    connection_index = 2
    junction = inlet_plenum
    equation = mass
  []
  [channel2_out_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'channel2:out'
    connection_index = 1
    junction = outlet_plenum
    equation = mass
  []

  [outlet_in_m_dot]
    type = ADFlowJunctionFlux1Phase
    boundary = 'outlet:in'
    connection_index = 2
    junction = outlet_plenum
    equation = mass
  []
  [outlet_out_m_dot]
    type = ADFlowBoundaryFlux1Phase
    boundary = 'outlet_bc'
    equation = mass
  []

  [net_mass_flow_rate_domain]
    type = LinearCombinationPostprocessor
    pp_names = 'inlet_in_m_dot outlet_out_m_dot'
    pp_coefs = '1 -1'
  []
  [net_mass_flow_rate_volume_junction]
    type = LinearCombinationPostprocessor
    pp_names = 'inlet_out_m_dot channel1_in_m_dot channel2_in_m_dot'
    pp_coefs = '1 -1 -1'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = bdf2
  start_time = 0
  end_time = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 8
    iteration_window = 2
  []
  timestep_tolerance = 1e-6
  abort_on_solve_fail = true

  line_search = basic
  nl_rel_tol = 1e-8
  nl_abs_tol = 4e-8
  nl_max_its = 25
  l_tol = 1e-3
  l_max_its = 5
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = ' lu     '
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'FINAL'
    show = 'net_mass_flow_rate_domain net_mass_flow_rate_volume_junction Delta_p'
  []
[]

Evaluating Entropy
Input Parameters
Input Files
References