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 NN gases. Let the ii subscript denote the component index and the lack of a subscript denote a mixture quantity. The mass fraction ξi\xi_i is defined as the ratio of the component mass mim_i to the mixture mass mm:

ξi=mim=ρiρ=vvi,\xi_i = \frac{m_i}{m} = \frac{\rho_i}{\rho} = \frac{v}{v_i} \,,(1)

where the densities ρi\rho_i and ρ\rho are with respect to the mixture volume. The molar fraction ψi\psi_i is defined as the ratio of the component number of moles nin_i to the mixture number of moles nn:

ψi=nin.\psi_i = \frac{n_i}{n} \,.

The mixture molar mass MM can be computed using the component molar fractions and molar masses MiM_i:

M=iNψiMi.M = \sum\limits_i^N \psi_i M_i \,.

The mass fraction and molar fraction are related as

ξi=ψiMiM.\xi_i = \frac{\psi_i M_i}{M} \,.

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

v=iNξivi(pi,T),v = \sum\limits_i^N \xi_i v_i(p_i, T) \,,e=iNξiei(pi,T),e = \sum\limits_i^N \xi_i e_i(p_i, T) \,,

where yi(pi,T)y_i(p_i, T) is the component equation of state call for yy, evaluated at the partial pressure and common temperature.

Note that the mixture density should be computed as

ρ=1v\rho = \frac{1}{v}

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

μ=iNψiμi(pi,T),\mu = \sum\limits_i^N \psi_i \mu_i(p_i, T) \,,(2)k=iNψiki(pi,T).k = \sum\limits_i^N \psi_i k_i(p_i, T) \,.(3)

The gases share a temperature TT, and each has a partial pressure pip_i, which is an assumption known as Dalton's law:

p=iNpi(T,vi),p = \sum\limits_i^N p_i(T, v_i) \,,

where by Eq. (1),

vi=vξi.v_i = \frac{v}{\xi_i} \,.

Note

pi=ψip.p_i = \psi_i p \,.

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:

cp=(hT)p,c_p = \left(\frac{\partial h}{\partial T}\right)_p \,,(4)cv=(eT)v,c_v = \left(\frac{\partial e}{\partial T}\right)_v \,,(5)c=v(pv)s.c = v\sqrt{-\left(\frac{\partial p}{\partial v}\right)_s} \,.(6)

Since the independent parameters are pp and TT, the following relations can be used:

(eT)v=(eT)p(ep)T(vT)p(vp)T,\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} \,,(pv)s=[(vp)T(vT)p(sp)T(sT)p]1.\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} \,.

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 x:y(x)=yx : y(x) = y denotes the nonlinear solve of the equation y(x)=yy(x) = y for xx:

Quantity(v,e,ξ)(v,e,\xi)(p,T,ξ)(p,T,\xi)(T,v,ξ)(T,v,\xi)(p,v,ξ)(p,v,\xi)(p,ρ,ξ)(p,\rho,\xi)
vvv:p(T,v,ξ)=pv: p(T,v,\xi) = p
ρ\rho1v(p,T,ξ)\frac{1}{v(p,T,\xi)}
TTT:e(T,v,ξ)=eT: e(T,v,\xi) = eT:p(T,v,ξ)=pT: p(T,v,\xi) = p
eee(T,v(p,T,ξ),ξ)e(T,v(p,T,\xi),\xi)iNξiei(T,v/ξi)\sum\limits_i^N \xi_i e_i(T, v/\xi_i)e(T(p,1ρ,ξ),1ρ,ξ)e(T(p,\frac{1}{\rho},\xi), \frac{1}{\rho}, \xi)
ssiNξisi(T,v/ξi)\sum\limits_i^N \xi_i s_i(T, v/\xi_i)
ppp(T(v,e,ξ),v,ξ)p(T(v,e,\xi),v,\xi)iNpi(T,v/ξi)\sum\limits_i^N p_i(T,v/\xi_i)
ccEq. (6)Eq. (6)Eq. (6)
cpc_pEq. (4)Eq. (4)
cvc_vEq. (5)Eq. (5)
μ\muiNψiμi(vi,ei(T,vi))\sum\limits_i^N \psi_i \mu_i(v_i, e_i(T, v_i))Eq. (2)
kkiNψiki(vi,ei(T,vi))\sum\limits_i^N \psi_i k_i(v_i, e_i(T, v_i))Eq. (3)

Input Parameters

  • fp_primaryName of fluid properties user object for primary vapor component

    C++ Type:UserObjectName

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:Maximum temperature of the mixture

  • 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

    Unit:(no unit assumed)

    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)

  • execute_onINITIALThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.

    Default:INITIAL

    C++ Type:ExecFlagEnum

    Unit:(no unit assumed)

    Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, 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. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.

  • 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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

  1. 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.[BibTeX]