Fipy and Cantera

Cantera Evaluation of Properties

Some notes, from an algorithmic perspective, on hooking up Cantera with a finite-volume solver for computing solutions.

Using the Python interface to Cantera, if I create a gas phase object, I can see all the methods available for that gas phase:

In [1]: from Cantera import * In [2]: g = GRI30() In [3]: dir(g) Out[3]: ['_Transport__tr_id', '__del__', '__doc__', '__init__', '__module__', '__repr__', '_end', '_equilmap', '_models', '_name', '_np', '_owner', '_phase_id', '_phnum', '_sp', 'activationEnergies', 'addTransportModel', 'advanceCoverages', 'atomicWeights', 'binaryDiffCoeffs', 'chemPotentials', 'ckin', 'clear', 'cp_R', 'cp_mass', 'cp_mole', 'creationRates', 'cv_mass', 'cv_mole', 'delta_G', 'delta_G0', 'delta_H', 'delta_H0', 'delta_S', 'delta_S0', 'density', 'desc', 'destructionRates', 'diffusionCoeffs', 'electricPotential', 'elementIndex', 'elementName', 'elementNames', 'elementPotentials', 'enthalpies_RT', 'enthalpy_mass', 'enthalpy_mole', 'entropies_R', 'entropy_mass', 'entropy_mole', 'equilibrate', 'equilibriumConstants', 'fwdRateConstants', 'fwdRatesOfProgress', 'gibbs_RT', 'gibbs_mass', 'gibbs_mole', 'idtag', 'intEnergy_mass', 'intEnergy_mole', 'isReversible', 'kin_index', 'kineticsSpeciesIndex', 'kineticsStart', 'kineticsType', 'kinetics_hndl', 'massFluxes', 'massFraction', 'massFractions', 'maxTemp', 'meanMolarMass', 'meanMolecularWeight', 'minTemp', 'mixDiffCoeffs', 'model', 'molarDensity', 'molarFluxes', 'molarMasses', 'moleFraction', 'moleFractions', 'molecularWeights', 'multiDiffCoeffs', 'multiplier', 'nAtoms', 'nElements', 'nPhases', 'nReactions', 'nSpecies', 'name', 'netProductionRates', 'netRatesOfProgress', 'phase', 'phase_id', 'pressure', 'productStoichCoeff', 'productStoichCoeffs', 'reactantStoichCoeff', 'reactantStoichCoeffs', 'reactionEqn', 'reactionPhaseIndex', 'reactionString', 'reactionType', 'refPressure', 'restoreState', 'revRateConstants', 'revRatesOfProgress', 'saveState', 'selectElements', 'selectSpecies', 'set', 'setDensity', 'setElectricPotential', 'setMassFractions', 'setMolarDensity', 'setMoleFractions', 'setMultiplier', 'setName', 'setParameters', 'setPressure', 'setState_HP', 'setState_PX', 'setState_PY', 'setState_SP', 'setState_SV', 'setState_TNX', 'setState_TP', 'setState_TPX', 'setState_TPY', 'setState_TR', 'setState_TRX', 'setState_TRY', 'setState_UV', 'setTemperature', 'sourceTerms', 'speciesIndex', 'speciesName', 'speciesNames', 'switchTransportModel', 'temperature', 'thermalConductivity', 'thermalDiffCoeffs', 'thermo_hndl', 'thermophase', 'transport_hndl', 'transport_id', 'trnsp', 'verbose', 'viscosity', 'volume_mass']

Wow. That's a lot of methods. And that's exactly why we want to interface with Cantera from an equation solver.

The Cantera Outline page contains a comprehensive list of pages on Cantera and its formulations. Those pages cover how to do things with these gas objects.

Diffusion

Covered here:

• Cantera/Diffusion
• Cantera/Diffusion Coefficients

Called through the methods:

• g.mixDiffCoeffs()
• g.multiDiffCoeffs()

Note that if we use multicomponent diffusion coefficients, we have to specify that when we create the gas:

Wrong:

In [4]: g = GRI30()

In [5]: g.multiDiffCoeffs()
---------------------------------------------------------------------------
error                                     Traceback (most recent call last)
<ipython-input-5-c8f3cc1dc781> in <module>()
----> 1 g.multiDiffCoeffs()

/Users/charlesreid/codes/cantalysis/build/lib/python2.7/site-packages/Cantera/Transport.pyc in multiDiffCoeffs(self)
    156         coefficients. Not implemented in all transport managers."""
    157         return _cantera.tran_multiDiffCoeffs(self.__tr_id,
--> 158                                            self.trnsp)
    159
    160     def setParameters(self, type, k, params):

error:

************************************************
                Cantera Error!
************************************************


Procedure: Transport Base Class
Error:


**** Method getMultiDiffCoeffs not implemented in model 0 ****
(Did you forget to specify a transport model?)

Correct:

In [6]: g = GRI30('Multi')

In [7]: g.multiDiffCoeffs()
Out[7]:
array([[  0.00000000e+00,   2.16211927e-04,   1.08401378e-04, ...,
          4.68401619e-05,   5.73411067e-05,   5.73117527e-05],
       [  2.16211927e-04,   0.00000000e+00,   2.16802755e-04, ...,
          9.36803238e-05,   1.14682213e-04,   1.14623505e-04],
       [  1.08401378e-04,   2.72421028e-05,   0.00000000e+00, ...,
          5.90173041e-06,   7.22482032e-06,   7.22112180e-06],
       ...,
       [  4.68401619e-05,   9.88416546e-06,   4.95558763e-06, ...,
          0.00000000e+00,   2.62135856e-06,   2.62001664e-06],
       [  5.73411067e-05,   1.01255679e-05,   5.07661871e-06, ...,
          2.19360351e-06,   0.00000000e+00,   2.68400570e-06],
       [  5.73117527e-05,   9.89389411e-06,   4.96046525e-06, ...,
          2.14341368e-06,   2.62393867e-06,   0.00000000e+00]])

Fipy-Only Pieces

A simple transient problem with Fipy:

• Fipy/Simple_Transient_Problem

0D Reaction Equation

A Fipy script that will solve a very simple 0D reaction equation:

$ \frac{d C_j }{dt} = \sum_{i=1}^{N_{rxns}} r_{ij} $

with reaction source terms computed by Cantera.

Fipy and Cantera/0D Reaction

0D Reaction Model: Batch Reactor

Filpy script that solves the 0D reaction equation, as well as other governing equations, for a 0D batch reactor model.

Fipy and Cantera/Batch Reactor

1D Convection-Reaction Equation

Using Fipy+Cantera to solve the one-dimensional convection reaction equation:

Fipy and Cantera/1D Convection Reaction

1D Convection-Reaction Model: Axial Profile

Once you can solve the one-dimensional convection reaction equation, you can reproduce an axial profile model for a PFR.

Fipy and Cantera/PFR Axial Profile Model

1D Diffusion Equation

A 1D diffusion problem solved by Fipy, with diffusion coefficients computed by Cantera. Illustrates how to solve a variable-diffusivity problem and sweep over the solution.

Fipy and Cantera/1D Diffusion

1D Diffusion Model: Boundary Value Problem

Fipy and Cantera/PFR Boundary Value Problem