TemperaturePressureFunctionFluidProperties

Single-phase fluid properties that allows to provide thermal conductivity, density, and viscosity as functions of temperature and pressure.

The temperature and pressure will be passed as respectively the x and y spatial arguments of the functions. The following relations hold true:

$var element = document.getElementById("moose-equation-9988b0d7-3826-47a0-a16b-45471e830788");katex.render("\\begin{aligned} x = T \\\\ y = P \\\\ \\rho = \\rho^{u}(t=0, (x=T, y=P, z=0)) \\\\ \\mu = \\mu^{u}(t=0, (x=T, y=P, z=0)) \\\\ k = k^{u}(t=0, (x=T, y=P, z=0)) \\\\ \\end{aligned}", element, {displayMode:true,throwOnError:false});$

Both the time (t) and Z-axis dimension are not used here. A fluid property made to depend on time will not be properly updated by this FluidProperties object. There are two options for specific heat. Either the user sets a constant specific isochoric heat capacity

$var element = document.getElementById("moose-equation-92932013-99af-4932-8b9c-7d0622576893");katex.render("\\begin{aligned} c_v = c_v^{u} \\\\ e = e_{ref} + c_v * (T - T_{ref}) \\end{aligned}", element, {displayMode:true,throwOnError:false});$

Or, the user uses a function of temperature and pressure (same arguments as for density)

$var element = document.getElementById("moose-equation-25c97939-a044-4351-ac8b-d6803248d059");katex.render("\\begin{aligned} x = T \\\\ y = P \\\\ cp = cp^{u}(t=0, (x=T, y=P, z=0)) cv = cp - \\dfrac{\\alpha^2 T}{\\rho \\beta_T} \\end{aligned}", element, {displayMode:true,throwOnError:false});$

with $var element = document.getElementById("moose-equation-07845f70-482b-4181-8338-587c80a11afe");katex.render("T", element, {displayMode:false,throwOnError:false});$ the temperature, $var element = document.getElementById("moose-equation-ac77153a-4b72-4a01-9e8c-ee482b8b5634");katex.render("P", element, {displayMode:false,throwOnError:false});$ the pressure, $var element = document.getElementById("moose-equation-f0b36e7b-cf3d-4f42-b438-4e036ad9710e");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ the density, $var element = document.getElementById("moose-equation-c6da051d-c358-483d-ad9f-67755449a789");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ the dynamic viscosity, $var element = document.getElementById("moose-equation-f786fa9a-1ec6-4e8d-b17b-4ebb52df4201");katex.render("k", element, {displayMode:false,throwOnError:false});$ the thermal conductivity, $var element = document.getElementById("moose-equation-f6021859-c070-49ca-9d39-10b1c7c46ab8");katex.render("c_v", element, {displayMode:false,throwOnError:false});$ the specific isochoric heat capacity, $var element = document.getElementById("moose-equation-cfc50ef5-0bd0-4ec8-b47b-bb5e07e7f7d5");katex.render("e", element, {displayMode:false,throwOnError:false});$ the specific internal energy, $var element = document.getElementById("moose-equation-0ec67767-1133-4710-b3e9-60581a0e8134");katex.render("T_{ref}", element, {displayMode:false,throwOnError:false});$ a reference temperature at which the specific internal energy is equal to a reference energy $var element = document.getElementById("moose-equation-af96ca07-40ac-47fc-9f55-cd9f8604e450");katex.render("e_{ref}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-57ead447-940b-45c3-8aca-8bf0bd1fd5e4");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ the coefficient of thermal expansion, $var element = document.getElementById("moose-equation-0f52df57-b27e-4d51-b643-fd119426667c");katex.render("\\beta_T", element, {displayMode:false,throwOnError:false});$ the isothermal compressibility, and the $var element = document.getElementById("moose-equation-c3e5527b-71d1-4b54-9d8e-94c96eef3d7c");katex.render("^u", element, {displayMode:false,throwOnError:false});$ exponent indicating a user-passed parameter.

The derivatives of the fluid properties are obtained using the Function(s) gradient components and the appropriate derivative chaining for derived properties.

warning

The range of validity of the property is based off of the validity of the functions that are input, and is not checked by this FluidProperties object.

note

Support for the conservative (specific volume, internal energy) variable set is only partial. Notable missing implementations are routines for entropy, the speed of sound, and some conversions between specific enthalpy and specific energy.

note

When using a function for the isobaric specific heat capacity, a numerical integration is performed to compute $var element = document.getElementById("moose-equation-eb67be34-081f-4c02-9b03-9c27c71b400f");katex.render("e(p,T)", element, {displayMode:false,throwOnError:false});$ as $var element = document.getElementById("moose-equation-48d99701-2bd9-4b69-949c-1ba8b67cc49b");katex.render("e_{ref} + \\int_{T_{ref}}^T c_v(p,T) dT", element, {displayMode:false,throwOnError:false});$ . Note that this neglects the $var element = document.getElementById("moose-equation-390c9241-653b-47a9-b050-d7e42650c12e");katex.render("dV", element, {displayMode:false,throwOnError:false});$ term. This is exact for incompressible fluids and ideal gases.

Example Input File Syntax

In this example, temperature and pressure dependent density, dynamic viscosity and thermal conductivity of a fluid are being set using three ParsedFunctions. The functions are specified with the x and y coordinates, and are evaluated with respectively the temperature and pressure variables.

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  # This demonstrates how to define fluid properties that are functions
  # of the LOCAL value of the (p,T) variables
  # x for temperature
  # y for pressure
  [k]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = '14 + 1e-2 * x + 1e-5 * y'
  []
  [rho]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = '1.5e3 + 0.13 * x - 1.5e-4 * y'
  []
  [mu]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = '1e-3 + 2e-6 * x - 3e-9 * y'
  []
[]

[FluidProperties<<<{"href": "../../syntax/FluidProperties/index.html"}>>>]
  [fp]
    type = TemperaturePressureFunctionFluidProperties<<<{"description": "Single-phase fluid properties that allows to provide thermal conductivity, density, and viscosity as functions of temperature and pressure.", "href": "TemperaturePressureFunctionFluidProperties.html"}>>>
    cv<<<{"description": "Constant isochoric specific heat [J/(kg-K)]"}>>> = ${cv}
    k<<<{"description": "Thermal conductivity function of temperature and pressure [W/(m-K)]"}>>> = k
    rho<<<{"description": "Density function of temperature and pressure [kg/m^3]"}>>> = rho
    mu<<<{"description": "Dynamic viscosity function of temperature and pressure [Pa-s]"}>>> = mu
  []
[]

Input Parameters

kThermal conductivity function of temperature and pressure [W/(m-K)]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity function of temperature and pressure [W/(m-K)]
muDynamic viscosity function of temperature and pressure [Pa-s]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Dynamic viscosity function of temperature and pressure [Pa-s]
rhoDensity function of temperature and pressure [kg/m^3]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Density function of temperature and pressure [kg/m^3]

Required Parameters

T_ref0Reference temperature for the specific internal energy
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Reference temperature for the specific internal energy
cpIsobaric specific heat function of temperature and pressure [J/(kg-K)]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Isobaric specific heat function of temperature and pressure [J/(kg-K)]
cv0Constant isochoric specific heat [J/(kg-K)]
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Constant isochoric specific heat [J/(kg-K)]
dT_integration_intervals10Size of intervals for integrating cv(T) to compute e(T) from e(T_ref)
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Size of intervals for integrating cv(T) to compute e(T) from e(T_ref)
e_ref0Specific internal energy at the reference temperature
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Specific internal energy at the reference temperature

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

(moose/modules/fluid_properties/test/tests/temperature_pressure_function/example.i)

# Test implementation of TemperaturePressureFunctionFluidProperties properties by comparison to analytical functions.

cv = 4000
T_initial = 400
p_initial = 1e5

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temperature]
    initial_condition = ${T_initial}
  []
  [pressure]
    initial_condition = 1e5
  []
[]

[Functions]
  # This demonstrates how to define fluid properties that are functions
  # of the LOCAL value of the (p,T) variables
  # x for temperature
  # y for pressure
  [k]
    type = ParsedFunction
    expression = '14 + 1e-2 * x + 1e-5 * y'
  []
  [rho]
    type = ParsedFunction
    expression = '1.5e3 + 0.13 * x - 1.5e-4 * y'
  []
  [mu]
    type = ParsedFunction
    expression = '1e-3 + 2e-6 * x - 3e-9 * y'
  []
[]

[FluidProperties]
  [fp]
    type = TemperaturePressureFunctionFluidProperties
    cv = ${cv}
    k = k
    rho = rho
    mu = mu
  []
[]

[Materials]
  [to_vars]
    type = FluidPropertiesMaterialPT
    fp = fp
    outputs = 'all'
    output_properties = 'density k cp cv viscosity e h'
    pressure = pressure
    temperature = temperature

    compute_entropy = false
    compute_sound_speed = false
  []
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [k_exact]
    type = FunctionValuePostprocessor
    function = k
    outputs = none
    point = '${T_initial} ${p_initial} 0'
  []
  [rho_exact]
    type = FunctionValuePostprocessor
    function = rho
    outputs = none
    point = '${T_initial} ${p_initial} 0'
  []
  [mu_exact]
    type = FunctionValuePostprocessor
    function = mu
    outputs = none
    point = '${T_initial} ${p_initial} 0'
  []
  [e_exact]
    type = Receiver
    default = '${fparse cv * T_initial}'
    outputs = none
  []
  [cv_exact]
    type = Receiver
    default = '${fparse cv}'
    outputs = none
  []

  # Postprocessors to get from the fluid property object
  [k_avg]
    type = ElementAverageValue
    variable = k
    outputs = none
  []
  [rho_avg]
    type = ElementAverageValue
    variable = density
    outputs = none
  []
  [mu_avg]
    type = ElementAverageValue
    variable = viscosity
    outputs = none
  []
  [cv_avg]
    type = ElementAverageValue
    variable = cv
    outputs = none
  []
  [e_avg]
    type = ElementAverageValue
    variable = e
    outputs = none
  []

  # We output these directly, cant compare to anything analytical though
  [cp_avg]
    type = ElementAverageValue
    variable = cp
  []
  [h_avg]
    type = ElementAverageValue
    variable = h
  []

  # Postprocessors to compare the two
  [k_diff]
    type = DifferencePostprocessor
    value1 = k_exact
    value2 = k_avg
  []
  [mu_diff]
    type = DifferencePostprocessor
    value1 = mu_exact
    value2 = mu_avg
  []
  [rho_diff]
    type = DifferencePostprocessor
    value1 = rho_exact
    value2 = rho_avg
  []
  [e_diff]
    type = DifferencePostprocessor
    value1 = e_exact
    value2 = e_avg
  []
  [cv_diff]
    type = DifferencePostprocessor
    value1 = cv_exact
    value2 = cv_avg
  []
[]

[Outputs]
  # Note that diffs wont be settled until timestep 2 because of order of execution
  csv = true
[]

Example Input File Syntax
Input Parameters