Species solver¶

The following inputs are defined using the prefix species:

	Description	Type	Default
solve	Specified name(s) of the species or None to disable the species solver. The name assigned to the species solver is used to specify species inputs.	Strings	None

Diffusivity¶

The following inputs are defined using the prefix species.diffusivity:

	Description	Type	Default
model	Fluid species diffusivity model. Options: `constant` - a constant diffusion coefficient is used for all fluid species.	String	None
constant	Constant species diffusivity - required for `constant` diffusivity model	Real	0

Description

Type

Default

model

Fluid species diffusivity model.

Options:

constant - a constant diffusion coefficient is used for all fluid species.

String

None

constant

Constant species diffusivity - required for constant diffusivity model

Real

Molecular weight¶

The following inputs are defined for each species using the prefix species.[species_name]:

	Description	Type	Default
molecular_weight	Molecular weight of species. Required for mixture molecular weight model and when including chemical reactions.	Real	0

Specific heat¶

The following inputs are defined using the prefix species.specific_heat:

	Description	Type	Default
model	Species specific heat model. This setting only applies if either `fluid.specific_heat.model = mixture` or `solids.specific_heat.model = mixture` Options (case-insensitive): `constant` - a constant specific heat is defined for each species and a mixture specific heat is computed based on the fluid or particle composition. `NASA7-poly` - the specific heat of each species is defined by one or more polynomials that are a function of temperature, then the mixture specific heat is computed based on the fluid or particle composition. NASA7 polynomial format: \(c_p(T)/R = \sum_{i=0}^4 a_{i}T^{i}\)	String
ignore_discontinuities	MFIX-Exa checks that NASA-7 polynomials are continuous at the specified transition temperature(s)(`Tsplit`). However, some polynomials do not have valid high temperature coefficients, for example, liquid water. By setting this keyword to 1, the simulation will only warn that the polynomials are discontinuous. Simulations that use discontinuous polynomials and cross `Tsplit` boundaries may fail when computing temperature from enthalpy. Therefore, this option should only be used when the simulation is not expected to cross over the transition temperature.	Int	0

Description

Type

Default

model

Species specific heat model. This setting only applies if either fluid.specific_heat.model = mixture or solids.specific_heat.model = mixture

Options (case-insensitive):

constant - a constant specific heat is defined for each species and a mixture specific heat is computed based on the fluid or particle composition.
NASA7-poly - the specific heat of each species is defined by one or more polynomials that are a function of temperature, then the mixture specific heat is computed based on the fluid or particle composition.

NASA7 polynomial format:

\(c_p(T)/R = \sum_{i=0}^4 a_{i}T^{i}\)

String

ignore_discontinuities

MFIX-Exa checks that NASA-7 polynomials are continuous at the specified transition temperature(s)(Tsplit). However, some polynomials do not have valid high temperature coefficients, for example, liquid water. By setting this keyword to 1, the simulation will only warn that the polynomials are discontinuous. Simulations that use discontinuous polynomials and cross Tsplit boundaries may fail when computing temperature from enthalpy. Therefore, this option should only be used when the simulation is not expected to cross over the transition temperature.

Int

The following inputs are defined for each species using the prefix species.[species_name].specific_heat:

	Description	Type	Default
constant	Constant species specific heat. Required for all fluid (solids) species if the fluid (solids) `specific_heat.model = mixture` and the specific heat model is `constant`	Real	0
NASA7.a[i]	Species specific heat polynomial coefficients. Required for all fluid (solids) species if `specific_heat.model = mixture` and the specific heat model is `NASA7-poly` Each polynomial is defined by six coefficients (`a0` … `a5`). Coefficients `a0` through `a4` are use for computing specific heat while all six coefficients are used to compute enthalpy. The coefficient `a6` may be provided for completeness but is not used as MFIX-Exa does not compute entropy. Typically, two sets of coefficients are used. The coefficients define two polynomials used to compute the specific heat and enthalpy across low and high temperatures. The transition temperature (`Tsplit`) defines the transition from low to high polynomials. If a single set of coefficients are supplied, they will be used for all temperatures and `Tsplit` is not required.	Reals	None
NASA7.Tsplit	Defines the transition temperature between NASA-7 polynomials. If there are `N` sets of coefficients for `N` temperature ranges, then `N-1` transition temperatures must be specified. In the standard case of two temperature ranges, a transition temperature of 1000K is assumed if `Tsplit` is not provided.	Reals	1000

Description

Type

Default

constant

Constant species specific heat. Required for all fluid (solids) species if the fluid (solids) specific_heat.model = mixture and the specific heat model is constant

Real

NASA7.a[i]

Species specific heat polynomial coefficients. Required for all fluid (solids) species if specific_heat.model = mixture and the specific heat model is NASA7-poly

Each polynomial is defined by six coefficients (a0 … a5). Coefficients a0 through a4 are use for computing specific heat while all six coefficients are used to compute enthalpy. The coefficient a6 may be provided for completeness but is not used as MFIX-Exa does not compute entropy.
Typically, two sets of coefficients are used. The coefficients define two polynomials used to compute the specific heat and enthalpy across low and high temperatures. The transition temperature (Tsplit) defines the transition from low to high polynomials.
If a single set of coefficients are supplied, they will be used for all temperatures and Tsplit is not required.

Reals

None

NASA7.Tsplit

Defines the transition temperature between NASA-7 polynomials.

If there are N sets of coefficients for N temperature ranges, then N-1 transition temperatures must be specified.

In the standard case of two temperature ranges, a transition temperature of 1000K is assumed if Tsplit is not provided.

Reals

1000

The following inputs are defined for each species using the prefix species.[species_name]:

	Description	Type	Default
enthalpy_of_formation	Enthalpy of formation of species. Only used when the species specific heat model is `constant` and chemical reactions are defined.	Real	0

Viscosity¶

The following input is defined using the prefix species.viscosity.molecular (all species use the same model):

	Description	Type	Default
model	Molecular viscosity model of species. This setting only applies when `[fluid_name].viscosity.molecular` = `mixture`. Options: `constant` - constant viscosity `Sutherland` [Sut93] `Reid` [RPP87] See viscosity model descriptions in fluid section.	String	constant

Description

Type

Default

model

Molecular viscosity model of species. This setting only applies when [fluid_name].viscosity.molecular = mixture.

Options:

constant - constant viscosity
Sutherland [Sut93]
Reid [RPP87]

See viscosity model descriptions in fluid section.

String

constant

The following inputs are defined for each species using the prefix species.[species_name].viscosity.molecular:

	Description	Type	Default
constant	Constant species fluid viscosity. A value is required for `constant` species viscosity model.	Real	None
Sutherland.T_ref	Sutherland model reference temperature for species. A value is required for `Sutherland` species viscosity model.	Real	None
Sutherland.mu_ref	Sutherland model reference viscosity at T_ref for species. A value is required for `Sutherland` species viscosity model.	Real	None
Sutherland.S	Sutherland model temperature for species. A value is required for `Sutherland` species viscosity model.	Real	None
Reid.A Reid.B Reid.C Reid.D	Reid model constants for species. Values are required for `Reid` species viscosity model.	Real	None

Radiation¶

The following inputs are defined using the prefix species.radiation.

	Description	Type	Default
scattering_coeff		Real	None
absorption.model	Specify which radiation absorption coefficient model to use for fluid species. This setting only applies when `[fluid_name].radiation.absorption.model = mixture`. Options: `gray-poly` - The absorption coefficient is defined by a temperature-dependent polynomial (0-5th order). Piecewise polynomials are defined by specifying temperature ranges.	String	None

Description

Type

Default

scattering_coeff

Real

None

absorption.model

Specify which radiation absorption coefficient model to use for fluid species. This setting only applies when [fluid_name].radiation.absorption.model = mixture.

Options:

gray-poly - The absorption coefficient is defined by a temperature-dependent polynomial (0-5th order). Piecewise polynomials are defined by specifying temperature ranges.

String

None

The following inputs are defined using the prefix species.[species_name].radiation.absorption.

	Description	Type	Default
form	Specifies the polynomial form used to represent the absorption coefficient as a function of temperature. Options: `0` - Absorption coefficient is defined as a polynomial in temperature. \(\displaystyle a(T) = a_0 + a_1 T + a_2 T^2 + \ldots\) `1` - Absorption coefficient is defined as a polynomial in the inverse of temperature. \(\displaystyle a(T) = a_0 + a_1 / T + a_2 / T^2 + \ldots\)	Int	0
T_range	Valid temperature range for the polynomial. If no temperature is provided, then the polynomial is assumed valid for all temperatures. Piecewise polynomials are defined by specify multiple ranges. For example, two piecewise polynomials can be specified by providing three temperatures: low, mid and high.	Reals	None
polynomial_coeffs	Polynomial coefficient. Polynomials can be up to 5-th order, and a set of polynomial coefficients must be defined for each temperature range.	Reals	None

Description

Type

Default

form

Specifies the polynomial form used to represent the absorption coefficient as a function of temperature. Options:

0 - Absorption coefficient is defined as a polynomial in temperature.

\(\displaystyle a(T) = a_0 + a_1 T + a_2 T^2 + \ldots\)
1 - Absorption coefficient is defined as a polynomial in the inverse of temperature.

\(\displaystyle a(T) = a_0 + a_1 / T + a_2 / T^2 + \ldots\)

Int

T_range

Valid temperature range for the polynomial. If no temperature is provided, then the polynomial is assumed valid for all temperatures. Piecewise polynomials are defined by specify multiple ranges. For example, two piecewise polynomials can be specified by providing three temperatures: low, mid and high.

Reals

None

polynomial_coeffs

Polynomial coefficient. Polynomials can be up to 5-th order, and a set of polynomial coefficients must be defined for each temperature range.

Reals

None

Example: Define absorption coefficients for individual species using polynomial forms.

CO2 uses a single polynomial over the entire temperature range.
H2O uses piecewise polynomials, each constant within its temperature interval.

Once species absorption models are defined, the fluid absorption model is set to mixture to combine species contributions.:

species.solve = O2 H2O CO2 NA1 NA2

species.radiation.absorption.model = gray-poly

species.CO2.radiation.absorption.T_range = 300. 2400.
species.CO2.radiation.absorption.polynomial_coeffs = 32.2454,  4.057e-3, -3.89e-6

species.H2O.radiation.absorption.T_range = 300.  600. 1800.
species.H2O.radiation.absorption.polynomial_coeffs = 1.
species.H2O.radiation.absorption.polynomial_coeffs = 0.1
species.H2O.radiation.absorption.polynomial_coeffs = 0.01

species.H2O.radiation.absorption.polynomial_coeffs = 0.

fluid.species = CO2 H2O O2
fluid0.radiation.absorption.model = mixture

Density¶

The following inputs are defined for each species using the prefix species.[species_name]:

	Description	Type	Default
density	Constant species density (only used for solid phase species). Needed for all solid species if solids density is set to `mixture` or density updates is set to `Constant_Species_Densities`	Real

Description

Type

Default

density

Constant species density (only used for solid phase species).

Needed for all solid species if solids density is set to mixture or density updates is set to Constant_Species_Densities

Real

Example inputs¶

Fluid species as passive scalars¶

In the following example, two species are defined and assigned to the fluid. We are required to define the species diffusivity and initial and boundary conditions. The IncompressibleFluid constraint is used, and the fluid density and species mass fractions are defined in the initial and boundary conditions. The fluid energy equation is not solved, and because we are not updating fluid density, the local species concentrations do not affect the fluid.

Listing 4 Snippet of inputs defining species as passive tracers. This is not a complete input file.¶

mfix.constraint = IncompressibleFluid

mfix.advect_density  = 0
mfix.advect_enthalpy = 0
mfix.solve_species   = 1


# Species model settings
# -----------------------------------------------------------------------
species.solve  =  N2  O2

species.diffusivity.model = constant
species.diffusivity.constant  = 1.9e-5


# Fluid model settings
# -----------------------------------------------------------------------
fluid.solve = fluid

fluid.viscosity.molecular.model = constant
fluid.viscosity.molecular.constant = 2.0e-5

fluid.species =  N2  O2

# Initial Conditions
# -----------------------------------------------------------------------
ic.regions = full-domain

ic.full-domain.fluid.volfrac   =  1.0
ic.full-domain.fluid.density   =  1.0

ic.full-domain.fluid.velocity  =  0.0  0.0  0.0

ic.full-domain.fluid.species.N2   =  0.77
ic.full-domain.fluid.species.O2   =  0.23

# Boundary Conditions
# -----------------------------------------------------------------------
bc.regions = inlet  outlet

bc.inlet = mi
bc.inlet.fluid.density  =  1.0

bc.inlet.fluid.velocity =  1.0e-8  0.0  0.0

bc.inlet.fluid.species.N2   =  0.77
bc.inlet.fluid.species.O2   =  0.23

bc.outlet = po
bc.outlet.fluid.pressure =  0.

Fluid as mixture¶

In this example, the fluid is treated as a mixture of two species and the IdealGasOpenSystem constraint is used. Because we are solving the energy equation, the fluid thermal conductivity is provided and the specific heats for both species are needed. The species specific heat model is set to NASA7-poly; therefore 12 coefficients (6 low-temperature range coefficients and 6 high-temperature range coefficients) are defined for each species. Additionally, species molecular weights are provided to compute the mixture molecular weights needed to evaluate the ideal-gas equation of state.

Fluid temperature is specified by the initial and boundary conditions, and unlike the previous example, density is no longer provided. Instead, the ideal gas equation of state is used to compute density from temperature, fluid composition, and the thermodynamic pressure. The thermodynamic pressure is taken as the outflow boundary condition pressure which is set here to 1 atmosphere.

Listing 5 Snippet of inputs defining fluid as a mixture with NASA7-poly specific heat model. This is not a complete input file.¶

mfix.constraint = IdealGasOpenSystem

mfix.advect_density  = 1
mfix.solve_species   = 1
mfix.advect_enthalpy = 1

# Species model settings
# -----------------------------------------------------------------------
species.solve  =  N2  O2

species.diffusivity.model = constant
species.diffusivity.constant  = 1.9e-5

species.specific_heat.model = NASA7-poly

# Oxygen
species.O2.molecular_weight = 31.99880e-3
species.O2.specific_heat.NASA7.a0    =  3.78245636E+00    3.66096065E+00
species.O2.specific_heat.NASA7.a1    = -2.99673416E-03    6.56365811E-04
species.O2.specific_heat.NASA7.a2    =  9.84730201E-06   -1.41149627E-07
species.O2.specific_heat.NASA7.a3    = -9.68129509E-09    2.05797935E-11
species.O2.specific_heat.NASA7.a4    =  3.24372837E-12   -1.29913436E-15
species.O2.specific_heat.NASA7.a5    = -1.06394356E+03   -1.21597718E+03

# Nitrogen
species.N2.molecular_weight = 28.01340e-3
species.N2.specific_heat.NASA7.a0    =  3.53100528E+00    2.95257637E+00
species.N2.specific_heat.NASA7.a1    = -1.23660988E-04    1.39690040E-03
species.N2.specific_heat.NASA7.a2    = -5.02999433E-07   -4.92631603E-07
species.N2.specific_heat.NASA7.a3    =  2.43530612E-09    7.86010195E-11
species.N2.specific_heat.NASA7.a4    = -1.40881235E-12   -4.60755204E-15
species.N2.specific_heat.NASA7.a5    = -1.04697628E+03   -9.23948688E+02


# Fluid model settings
# -----------------------------------------------------------------------
fluid.solve = fluid

fluid.viscosity.molecular.model = constant
fluid.viscosity.molecular.constant = 2.0e-5

fluid.thermal_conductivity.model = constant
fluid.thermal_conductivity.constant = 0.026

fluid.specific_heat = mixture

fluid.species =  N2  O2

# Initial Conditions
# -----------------------------------------------------------------------
ic.regions = full-domain

ic.full-domain.fluid.volfrac   =  1.0

ic.full-domain.fluid.velocity  =  0.0  0.0  0.0

ic.full-domain.fluid.species.N2  =  0.77
ic.full-domain.fluid.species.O2  =  0.23

ic.full-domain.fluid.temperature = 300.0

# Boundary Conditions
# -----------------------------------------------------------------------
bc.regions = inlet  outlet

bc.inlet = mi

bc.inlet.fluid.inflow_type = velocity
bc.inlet.fluid.velocity =  1.0e-8

bc.inlet.fluid.species.N2   = 0.77
bc.inlet.fluid.species.O2   = 0.23

bc.inlet.fluid.temperature = 300.0

bc.outlet = po
bc.outlet.fluid.pressure =  101325.