Chemical Reactions

The following inputs are defined using the prefix chemistry:

Description

Type

Default

solve

Specify the name(s) of the chemical reactions or set to None to disable the chemistry solver. The name(s) assigned to the chemistry solver are used to specify the chemical reactions equations.

String

None

[reaction0].reaction

Chemical formula for the given reaction. The string given as input must not contain white spaces and the reaction direction has to be specified as ‘-->’ or ‘<--’. Chemical species phases must be defined as ‘(g)’ for the fluid phase or ‘(s)’ for the solid phase.

String

None

mass_balance_tolerance

Tolerance used to test chemical formula conserves mass.

abs( sum(products) - sum(reactants)) < tolerance

Real

1e-12

solids.update_type

When updating the solids quantities in chemistry due to chemical reactions, choose the update type among:

  • ConstantVolume keep particles’ volume constant

  • ConstantDensity keep particles’ density constant

String

ConstantVolume

solids.mass_threshold

Sets a threshold value for the particles’ mass. When updating the solids quantities in chemistry, check whether the solids mass is below the threshold, and in that case set the particle as invalid and remove it

Real

0

solids.radius_threshold

Sets a threshold value for the particles’ radius. When updating the solids quantities in chemistry, check whether the solids radius is below the threshold, and in that case set the particle as invalid and remove it

Real

0

solids.density_threshold

Sets a threshold value for the particles’ density. When updating the solids quantities in chemistry, check whether the solids density is below the threshold, and in that case set the particle as invalid and remove it

Real

0

Choosing the integrator type for the chemistry ODE integration operation that is performed to determine the fluid and solids phases transfer quantities due to chemical reactions. The StiffSolver class of integrators is inspired by the class of integrators in AMReX-Astro/Microphysics (https://github.com/AMReX-Astro/Microphysics)

Description

Type

Default

chemistry.integrator

Specified name of the chemistry ODE integrator type. Available types are (case insensitive):

  • ForwardEuler

  • StiffSolver::ForwardEuler

  • StiffSolver::BackwardEuler

  • StiffSolver::VODE

String

ForwardEuler

One can define the environment variable VODE_JACOBIAN_CACHING at compile time to enable caching of the numerical approximation of the Jacobian matrix (the derivative of the ODE right-hand side), applicable when the VODE integrator is selected. The following inputs can be specified using the prefix chemistry.integrator:

Description

Type

Default

burner_verbose

Enables the printing on screen of some integration statistics

int

0

ode_max_steps

The maximum number of substeps for the ODE integration

int

150000

jacobian_type

Select how to compute the jacobian for the ODE iterative solver. This option is available for StiffSolver::BackwardEuler and StiffSolver::VODE. Available choices are:

  • Numerical for a first-order numerical approximation

  • Broyden for Broyden’s method (only for BackwardEuler)

string

Numerical

atol

Absolute tolerance for the ODE integration error test between the solution and the fine-step solution

Real

1.e-6

rtol

Relative tolerance for the ODE integration error test between the solution and the fine-step solution

Real

1.e-6

retry_atol

Overwrites the absolute tolerance value atol in case the ODE integration fails

Real

-1

retry_rtol

Overwrites the relative tolerance value rtol in case the ODE integration fails

Real

-1

retry_swap_jacobian

Swaps the type of jacobian (from 1 to 0 or vice versa) in case the ODE integration fails

int

1

ode_max_dt

Maximum timestep size for the ODE integration substeps

Real

1.e30

max_dt_change_factor

Only for StiffSolver::ForwardEuler, sets a maximum factor for the change of the timestep for the internal substeps

Real

1.001

max_iter

Maximum number of iterations for the internal Newton solver

int

100

linalg_do_pivoting

Only for StiffSolver::BackwardEuler and StiffSolver::VODE, switches on/off the pivoting when solving the linear algebra problem associated to the internal Newton solver

int

1

rp_rtol

Relative tolerance for the convergence test of the internal Newton solver. Valid only for StiffSolver::BackwardEuler

Real

1.e-6

use_jacobian_caching

Only for StiffSolver::VODE, enables caching the numerical jacobian

int

1

X_reject_buffer

Only for StiffSolver::VODE, constrain species abundances such that they don’t change by more than a certain factor in a given step

Real

1.0

Below is an example for specifying chemical reactions for MFIX-Exa.

Example inputs

The following setup shows how to define chemical reactions in the inputs file. Only Ideal Gas constraint types can be used when solving chemistry, as the IncompressibleFluid constraint would be inconsistent with the nature of a problem where the fluid density is not constant because of mass transfer due to chemical reactions.

mfix.constraint_type  = IdealGasOpenSystem

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

# Species model settings
#----------------------------------------------------------------------
species.solve  =  CH4  H2  CO  H2O  CO2  O2  N2  Fe2O3  FeO  inert

species.diffusivity = constant
species.diffusivity.constant  =  2.31000e-5  # m^2 / sec

species.specific_heat = NASA7-poly

# Methane
species.CH4.molecular_weight  = 16.04276e-3
species.CH4.specific_heat.NASA7.a0 =  5.14911468E+00    1.65326226E+00
species.CH4.specific_heat.NASA7.a1 = -1.36622009E-02    1.00263099E-02
species.CH4.specific_heat.NASA7.a2 =  4.91453921E-05   -3.31661238E-06
species.CH4.specific_heat.NASA7.a3 = -4.84246767E-08    5.36483138E-10
species.CH4.specific_heat.NASA7.a4 =  1.66603441E-11   -3.14696758E-14
species.CH4.specific_heat.NASA7.a5 = -1.02465983E+04   -1.00095936E+04

# Hydrogen
species.H2.molecular_weight = 2.01588e-3
species.H2.specific_heat.NASA7.a0 =  2.34433112E+00    2.93286575E+00
species.H2.specific_heat.NASA7.a1 =  7.98052075E-03    8.26608026E-04
species.H2.specific_heat.NASA7.a2 = -1.94781510E-05   -1.46402364E-07
species.H2.specific_heat.NASA7.a3 =  2.01572094E-08    1.54100414E-11
species.H2.specific_heat.NASA7.a4 = -7.37611761E-12   -6.88804800E-16
species.H2.specific_heat.NASA7.a5 = -9.17935173E+02   -8.13065581E+02

# Carbon monoxide
species.CO.molecular_weight = 28.01040e-3
species.CO.specific_heat.NASA7.a0 =  3.57953350E+00    3.04848590E+00
species.CO.specific_heat.NASA7.a1 = -6.10353690E-04    1.35172810E-03
species.CO.specific_heat.NASA7.a2 =  1.01681430E-06   -4.85794050E-07
species.CO.specific_heat.NASA7.a3 =  9.07005860E-10    7.88536440E-11
species.CO.specific_heat.NASA7.a4 = -9.04424490E-13   -4.69807460E-15
species.CO.specific_heat.NASA7.a5 = -1.43440860E+04   -1.42661170E+04

# Water vapor
species.H2O.molecular_weight = 18.01528e-3
species.H2O.specific_heat.NASA7.a0 =  0.41986352E+01    0.26770389E+01
species.H2O.specific_heat.NASA7.a1 = -0.20364017E-02    0.29731816E-02
species.H2O.specific_heat.NASA7.a2 =  0.65203416E-05   -0.77376889E-06
species.H2O.specific_heat.NASA7.a3 = -0.54879269E-08    0.94433514E-10
species.H2O.specific_heat.NASA7.a4 =  0.17719680E-11   -0.42689991E-14
species.H2O.specific_heat.NASA7.a5 = -0.30293726E+05   -0.29885894E+05

# Carbon dioxide
species.CO2.molecular_weight = 44.00980e-3
species.CO2.specific_heat.NASA7.a0 =  2.35681300E+00    4.63651110E+00
species.CO2.specific_heat.NASA7.a1 =  8.98412990E-03    2.74145690E-03
species.CO2.specific_heat.NASA7.a2 = -7.12206320E-06   -9.95897590E-07
species.CO2.specific_heat.NASA7.a3 =  2.45730080E-09    1.60386660E-10
species.CO2.specific_heat.NASA7.a4 = -1.42885480E-13   -9.16198570E-15
species.CO2.specific_heat.NASA7.a5 = -4.83719710E+04   -4.90249040E+04

# 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

# Hematite
species.Fe2O3.molecular_weight = 159.68820e-3
species.Fe2O3.specific_heat.NASA7.a0 =  1.52218166E-01    2.09445369E+01
species.Fe2O3.specific_heat.NASA7.a1 =  6.70757040E-02    0.00000000E+00
species.Fe2O3.specific_heat.NASA7.a2 = -1.12860954E-04    0.00000000E+00
species.Fe2O3.specific_heat.NASA7.a3 =  9.93356662E-08    0.00000000E+00
species.Fe2O3.specific_heat.NASA7.a4 = -3.27580975E-11    0.00000000E+00
species.Fe2O3.specific_heat.NASA7.a5 = -1.01344092E+05   -1.07936580E+05

# Wustite
species.FeO.molecular_weight = 71.84440e-3
species.FeO.specific_heat.NASA7.a0 =  3.68765953E+00    1.81588527E+00
species.FeO.specific_heat.NASA7.a1 =  1.09133433E-02    1.70742829E-02
species.FeO.specific_heat.NASA7.a2 = -1.61179493E-05   -2.39919190E-05
species.FeO.specific_heat.NASA7.a3 =  1.06449256E-08    1.53690046E-08
species.FeO.specific_heat.NASA7.a4 = -2.39514915E-12   -3.53442390E-12
species.FeO.specific_heat.NASA7.a5 = -3.34867527E+04   -3.30239565E+04

# inert
species.inert.molecular_weight = 92.82399e-3
species.inert.specific_heat.NASA7.a0 =  1.52218166E-01    2.09445369E+01
species.inert.specific_heat.NASA7.a1 =  6.70757040E-02    0.00000000E+00
species.inert.specific_heat.NASA7.a2 = -1.12860954E-04    0.00000000E+00
species.inert.specific_heat.NASA7.a3 =  9.93356662E-08    0.00000000E+00
species.inert.specific_heat.NASA7.a4 = -3.27580975E-11    0.00000000E+00
species.inert.specific_heat.NASA7.a5 = -1.01344092E+05   -1.07936580E+05


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

fluid.thermodynamic_pressure = 101325.
fluid.reference_temperature = 298.15

fluid.species =  CH4  H2  CO  H2O  CO2  O2  N2

fluid.viscosity          = constant
fluid.viscosity.constant = 4.73e-5  #air @ 1200K

fluid.specific_heat = mixture

fluid.thermal_conductivity          = constant
fluid.thermal_conductivity.constant = 0.024


# Solids model settings
#----------------------------------------------------------------------
solids.types = solid0
solids.reference_temperature = 298.15

solids.species  =  Fe2O3  FeO  inert

solids.specific_heat = mixture


# Chemistry model settings
#----------------------------------------------------------------------
chemistry.solve  =  Hem_CH4  Hem_H2  Hem_CO  Wus_O2

chemistry.Hem_CH4.reaction = Fe2O3(s)+0.25CH4(g)-->2.FeO(s)+0.25CO2(g)+0.5H2O(g)
chemistry.Hem_H2.reaction  = Fe2O3(s)+H2(g)-->2.FeO(s)+H2O(g)
chemistry.Hem_CO.reaction  = Fe2O3(s)+CO(g)-->2.FeO(s)+CO2(g)
chemistry.Wus_O2.reaction  = FeO(s)+0.25O2(g)-->0.5Fe2O3(s)


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

ic.full-domain.fluid.volfrac       = 0.725
ic.full-domain.fluid.velocity      = 0.015  0.00  0.00
ic.full-domain.fluid.temperature   = 1273.
ic.full-domain.fluid.species.CH4   = 0.1
ic.full-domain.fluid.species.H2    = 0.2
ic.full-domain.fluid.species.CO    = 0.1
ic.full-domain.fluid.species.H2O   = 0.2
ic.full-domain.fluid.species.CO2   = 0.1
ic.full-domain.fluid.species.O2    = 0.1
ic.full-domain.fluid.species.N2    = 0.2

ic.full-domain.solids  = solid0
ic.full-domain.packing = pseudo_random

ic.full-domain.solid0.volfrac  =  0.275
ic.full-domain.solid0.velocity =  0.00  0.00  0.00

ic.full-domain.solid0.diameter = constant
ic.full-domain.solid0.density  = constant

ic.full-domain.solid0.diameter.constant =  100.0e-6
ic.full-domain.solid0.density.constant  = 2000.0

ic.full-domain.solid0.temperature = 1273.
ic.full-domain.solid0.species.Fe2O3 = 0.3
ic.full-domain.solid0.species.FeO   = 0.3
ic.full-domain.solid0.species.inert = 0.4


# Boundary Conditions
#----------------------------------------------------------------------
bc.regions = inflow  outflow

bc.inflow = mi
bc.inflow.fluid.volfrac       = 1.0
bc.inflow.fluid.velocity      = 0.015  0.0  0.0
bc.inflow.fluid.temperature   = 1273.
bc.inflow.fluid.species.CH4   = 0.1
bc.inflow.fluid.species.H2    = 0.2
bc.inflow.fluid.species.CO    = 0.1
bc.inflow.fluid.species.H2O   = 0.2
bc.inflow.fluid.species.CO2   = 0.1
bc.inflow.fluid.species.O2    = 0.1
bc.inflow.fluid.species.N2    = 0.2

bc.outflow = po
bc.outflow.fluid.pressure =  101325.