IdealRealGasMixtureFluidProperties

This class computes fluid properties for gaseous mixtures with a condensable (primary) component and one or more non-condensable (secondary) components. This model (which corresponds to "Model A" in (Hansel et al., 2018)) assumes that each gas in the mixture occupies the entire mixture volume at a common temperature and each has a partial pressure and is considered an ideal gas mixture approximation applied to real gases.

Formulation

Consider a mixture of $var element = document.getElementById("moose-equation-452a97ac-cd97-4846-a59f-c6e173405862");katex.render("N", element, {displayMode:false,throwOnError:false});$ gases. Let the $var element = document.getElementById("moose-equation-284b1c9d-6852-4244-ab6e-2c35b98b3095");katex.render("i", element, {displayMode:false,throwOnError:false});$ subscript denote the component index and the lack of a subscript denote a mixture quantity. The mass fraction $var element = document.getElementById("moose-equation-c8613196-56b5-48a8-8def-195b0fec32cd");katex.render("\\xi_i", element, {displayMode:false,throwOnError:false});$ is defined as the ratio of the component mass $var element = document.getElementById("moose-equation-edc898b6-d86c-47d3-9a20-65822e53fb4f");katex.render("m_i", element, {displayMode:false,throwOnError:false});$ to the mixture mass $var element = document.getElementById("moose-equation-4bdccbb2-a43d-46b5-b156-0abf6992ffa7");katex.render("m", element, {displayMode:false,throwOnError:false});$ :

(1)var element = document.getElementById("moose-equation-f6f0d4c8-7a52-424e-8448-dcaa898c1e35");katex.render("\\xi_i = \\frac{m_i}{m} = \\frac{\\rho_i}{\\rho} = \\frac{v}{v_i} \\,,", element, {displayMode:true,throwOnError:false});

where the densities $var element = document.getElementById("moose-equation-6e0f3d39-5943-4e59-8130-e82803f7bb91");katex.render("\\rho_i", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-9664660e-8aec-4283-9569-de7f8429405c");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ are with respect to the mixture volume. The molar fraction $var element = document.getElementById("moose-equation-0bff02bd-864a-4a5c-a92a-16e4cb872f6d");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false});$ is defined as the ratio of the component number of moles $var element = document.getElementById("moose-equation-5f64c4ce-7153-4f44-93f7-198d13269a90");katex.render("n_i", element, {displayMode:false,throwOnError:false});$ to the mixture number of moles $var element = document.getElementById("moose-equation-42274080-97f8-4271-92f5-b280710c815c");katex.render("n", element, {displayMode:false,throwOnError:false});$ :

var element = document.getElementById("moose-equation-24ba7ccd-74a1-41f2-8e0f-e093f7435b16");katex.render("\\psi_i = \\frac{n_i}{n} \\,.", element, {displayMode:true,throwOnError:false});

The mixture molar mass $var element = document.getElementById("moose-equation-c8827a7a-fe05-4b8c-bd66-742f5657c967");katex.render("M", element, {displayMode:false,throwOnError:false});$ can be computed using the component molar fractions and molar masses $var element = document.getElementById("moose-equation-17003606-bd3b-4462-a7d4-31840386f0b4");katex.render("M_i", element, {displayMode:false,throwOnError:false});$ :

var element = document.getElementById("moose-equation-f0b49a58-ca66-4c80-8498-6af892fd07b3");katex.render("M = \\sum\\limits_i^N \\psi_i M_i \\,.", element, {displayMode:true,throwOnError:false});

The mass fraction and molar fraction are related as

var element = document.getElementById("moose-equation-60612160-afd6-499f-8efd-63377c3426b2");katex.render("\\xi_i = \\frac{\\psi_i M_i}{M} \\,.", element, {displayMode:true,throwOnError:false});

Note the following relation for all mass-specific quantities, such as specific volume and specific internal energy:

var element = document.getElementById("moose-equation-187d721c-1c1d-4080-8920-f14740333fda");katex.render("v = \\sum\\limits_i^N \\xi_i v_i(p_i, T) \\,,", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-c4de77a7-11d3-4164-be94-3cacd345dd6c");katex.render("e = \\sum\\limits_i^N \\xi_i e_i(p_i, T) \\,,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-3bf066fd-2111-4cf6-a268-01fd44e7fd74");katex.render("y_i(p_i, T)", element, {displayMode:false,throwOnError:false});$ is the component equation of state call for $var element = document.getElementById("moose-equation-1d057dd3-1a0f-4e97-b92a-5ef6e9c92a02");katex.render("y", element, {displayMode:false,throwOnError:false});$ , evaluated at the partial pressure and common temperature.

Note that the mixture density should be computed as

var element = document.getElementById("moose-equation-cd2a897c-dbdb-47ae-94df-c127177c9cbd");katex.render("\\rho = \\frac{1}{v}", element, {displayMode:true,throwOnError:false});

instead of a summation of component densities, since this would be inconsistent if any component is not an ideal gas.

Transport properties, such as dynamic viscosity and thermal conductivity are computed as

(2)var element = document.getElementById("moose-equation-0dd808a5-c70d-45ac-b342-cdc198de70a5");katex.render("\\mu = \\sum\\limits_i^N \\psi_i \\mu_i(p_i, T) \\,,", element, {displayMode:true,throwOnError:false});

(3)var element = document.getElementById("moose-equation-b3bc5f9a-f9f7-466e-bcee-7ce95419bb1f");katex.render("k = \\sum\\limits_i^N \\psi_i k_i(p_i, T) \\,.", element, {displayMode:true,throwOnError:false});

The gases share a temperature $var element = document.getElementById("moose-equation-e78848eb-fd0c-442b-9d41-e7271480ee1f");katex.render("T", element, {displayMode:false,throwOnError:false});$ , and each has a partial pressure $var element = document.getElementById("moose-equation-270a8d7a-3003-47e6-83f6-50b0f9e433d4");katex.render("p_i", element, {displayMode:false,throwOnError:false});$ , which is an assumption known as Dalton's law:

var element = document.getElementById("moose-equation-2926a44d-f59a-4573-98bd-5890ba7f240e");katex.render("p = \\sum\\limits_i^N p_i(T, v_i) \\,,", element, {displayMode:true,throwOnError:false});

where by Eq. (1),

var element = document.getElementById("moose-equation-e43b354e-10c4-477e-9aab-96005b643767");katex.render("v_i = \\frac{v}{\\xi_i} \\,.", element, {displayMode:true,throwOnError:false});

Note

var element = document.getElementById("moose-equation-9a384052-a769-4ecc-bf99-87e24aca162a");katex.render("p_i = \\psi_i p \\,.", element, {displayMode:true,throwOnError:false});

Sound Speed and Specific Heat Capacities

The mixture sound speed and heat capacities are computed directly from thermodynamic definitions relative to mixture properties, rather than constituent properties:

(4)var element = document.getElementById("moose-equation-d586ff05-3467-46e1-9cd5-6d8eac193085");katex.render("c_p = \\left(\\frac{\\partial h}{\\partial T}\\right)_p \\,,", element, {displayMode:true,throwOnError:false});

(5)var element = document.getElementById("moose-equation-2e737985-90c2-4ed9-be66-3325888448c9");katex.render("c_v = \\left(\\frac{\\partial e}{\\partial T}\\right)_v \\,,", element, {displayMode:true,throwOnError:false});

(6)var element = document.getElementById("moose-equation-29f0527e-d578-40fb-a53a-c156bb2c7365");katex.render("c = v\\sqrt{-\\left(\\frac{\\partial p}{\\partial v}\\right)_s} \\,.", element, {displayMode:true,throwOnError:false});

Since the independent parameters are $var element = document.getElementById("moose-equation-f3c0b52a-42c3-4f7a-8561-e883a63c34dd");katex.render("p", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-7a011d86-5c6a-4566-9409-b2662d81817b");katex.render("T", element, {displayMode:false,throwOnError:false});$ , the following relations can be used:

var element = document.getElementById("moose-equation-59ac9a88-f94e-40fd-a427-50a17e69778d");katex.render("\\left(\\frac{\\partial e}{\\partial T}\\right)_v = \\left(\\frac{\\partial e}{\\partial T}\\right)_p - \\left(\\frac{\\partial e}{\\partial p}\\right)_T \\frac{\\left(\\frac{\\partial v}{\\partial T}\\right)_p} {\\left(\\frac{\\partial v}{\\partial p}\\right)_T} \\,,", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-69137251-142c-4a44-97ad-5c20c486fbfe");katex.render("\\left(\\frac{\\partial p}{\\partial v}\\right)_s = \\left[\\left(\\frac{\\partial v}{\\partial p}\\right)_T - \\left(\\frac{\\partial v}{\\partial T}\\right)_p \\frac{\\left(\\frac{\\partial s}{\\partial p}\\right)_T} {\\left(\\frac{\\partial s}{\\partial T}\\right)_p}\\right]^{-1} \\,.", element, {displayMode:true,throwOnError:false});

Implementation

The available interfaces are summarized in the following table, where the rows correspond to the computed quantity, and the columns correspond to the various combinations of input arguments. Note that the notation $var element = document.getElementById("moose-equation-c3257e08-9131-48d9-b523-75026b68e0a7");katex.render("x : y(x) = y", element, {displayMode:false,throwOnError:false});$ denotes the nonlinear solve of the equation $var element = document.getElementById("moose-equation-dd05e12d-84b1-4d10-84a2-8127415a3e69");katex.render("y(x) = y", element, {displayMode:false,throwOnError:false});$ for $var element = document.getElementById("moose-equation-8f0b4947-1e85-4c20-b921-bce880ece8d3");katex.render("x", element, {displayMode:false,throwOnError:false});$ :

Quantity	$var element = document.getElementById("moose-equation-76856324-6cbb-4559-b064-cbcf6cf9e0fc");katex.render("(v,e,\\xi)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-e4c2dab6-b36e-4130-9d19-4a3713ba6d5b");katex.render("(p,T,\\xi)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-42269f2d-880d-49da-b72d-3f22bf5aaadf");katex.render("(T,v,\\xi)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-52b6da4f-4d30-4ed6-a7f2-cd8a28f69114");katex.render("(p,v,\\xi)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-f8d18f02-9ae1-4fc4-8760-10e69f027c5b");katex.render("(p,\\rho,\\xi)", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-76a3b9e3-b7dd-49d2-85b8-fb90766b4a94");katex.render("v", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-443803ef-17bd-4a0a-b941-c56b16d50f05");katex.render("v: p(T,v,\\xi) = p", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-6e92ef38-4ba8-4d46-94ce-2381ab8d966f");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-ebd5cb91-d934-4284-8dfd-e7366f4fc023");katex.render("\\frac{1}{v(p,T,\\xi)}", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-c3c4036c-23b9-4d10-aa78-04cdbb4d543f");katex.render("T", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-d4b2a3e0-89d8-48cb-9b53-cf95d6b0dcb2");katex.render("T: e(T,v,\\xi) = e", element, {displayMode:false,throwOnError:false});$			$var element = document.getElementById("moose-equation-0e38cff1-2f6e-4b85-899b-45f040ca25ad");katex.render("T: p(T,v,\\xi) = p", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-3bd2b059-f355-4608-988c-260e5c88eca3");katex.render("e", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-df3c8a53-6ac9-4395-921d-c19cd8f7ed87");katex.render("e(T,v(p,T,\\xi),\\xi)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-f4109e96-ce72-4b20-9d34-5c187ddf02fe");katex.render("\\sum\\limits_i^N \\xi_i e_i(T, v/\\xi_i)", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-b4127e8e-80c4-4ff3-903a-984e9895118f");katex.render("e(T(p,\\frac{1}{\\rho},\\xi), \\frac{1}{\\rho}, \\xi)", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-2df5946e-b789-435c-9696-44759fb55a14");katex.render("s", element, {displayMode:false,throwOnError:false});$			$var element = document.getElementById("moose-equation-2a1f8127-9f69-4837-bd31-5dcf6ad23ffd");katex.render("\\sum\\limits_i^N \\xi_i s_i(T, v/\\xi_i)", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-2a21a3aa-68d0-4321-b3b7-da8f7284ecf9");katex.render("p", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-092a1217-6bc0-4860-944d-0366640d35f1");katex.render("p(T(v,e,\\xi),v,\\xi)", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-1d514998-6532-4d70-b618-664c697e7511");katex.render("\\sum\\limits_i^N p_i(T,v/\\xi_i)", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-4158e01b-f932-4464-b67f-71514ede94b1");katex.render("c", element, {displayMode:false,throwOnError:false});$	Eq. (6)	Eq. (6)	Eq. (6)
$var element = document.getElementById("moose-equation-60598c54-368b-4f18-b0f5-38e26188cb85");katex.render("c_p", element, {displayMode:false,throwOnError:false});$		Eq. (4)	Eq. (4)
$var element = document.getElementById("moose-equation-b53f302c-a140-4fd9-b192-5265f2b6e65b");katex.render("c_v", element, {displayMode:false,throwOnError:false});$		Eq. (5)	Eq. (5)
$var element = document.getElementById("moose-equation-40d19376-62bf-4f56-ac6b-60a79874aa57");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-4c9726b4-d8a8-4570-bc11-6a3cb60e2c03");katex.render("\\sum\\limits_i^N \\psi_i \\mu_i(v_i, e_i(T, v_i))", element, {displayMode:false,throwOnError:false});$	Eq. (2)
$var element = document.getElementById("moose-equation-dcd056a8-d3bd-4cb5-8ace-9f4d85605b27");katex.render("k", element, {displayMode:false,throwOnError:false});$		$var element = document.getElementById("moose-equation-a69dcee1-187e-4b1f-92c5-16cc2c4eec49");katex.render("\\sum\\limits_i^N \\psi_i k_i(v_i, e_i(T, v_i))", element, {displayMode:false,throwOnError:false});$	Eq. (3)

Input Parameters

fp_primaryName of fluid properties user object for primary vapor component
C++ Type:UserObjectName
Controllable:No
Description:Name of fluid properties user object for primary vapor component
fp_secondaryName of fluid properties user object(s) for secondary vapor component(s)
C++ Type:std::vector<UserObjectName>
Controllable:No
Description:Name of fluid properties user object(s) for secondary vapor component(s)

Required Parameters

_T_mix_max1300Maximum temperature of the mixture
Default:1300
C++ Type:double
Controllable:No
Description:Maximum temperature of the mixture
emit_on_nannoneRaise mooseWarning or mooseError?
Default:none
C++ Type:MooseEnum
Options:none, warning, error
Controllable:No
Description:Raise mooseWarning or mooseError?
execute_onINITIALThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
Default:INITIAL
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
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
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.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
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.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
fp_typeunspecified-typeType of the fluid property object
Default:unspecified-type
C++ Type:FPType
Controllable:No
Description:Type of the fluid property object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

References

Joshua E. Hansel, Matthias S. Kunick, Ray A. Berry, and David Andrs. Non-condensable gases in RELAP-7. Technical Report INL/EXT-18-51163, Idaho National Laboratory, 2018.

@techreport{hansel2018ncgs,
    author = "Hansel, Joshua E. and Kunick, Matthias S. and Berry, Ray A. and Andrs, David",
    title = "Non-Condensable Gases in {RELAP-7}",
    institution = "Idaho National Laboratory",
    number = "INL/EXT-18-51163",
    year = "2018"
}

Formulation
Sound Speed and Specific Heat Capacities
Implementation
Input Parameters
References