Tutorial

Getting Started

Start by opening an interactive Python session, e.g. by running IPython. Import the Cantera Python module and NumPy by running:

>>> import cantera as ct
>>> import numpy as np

When using Cantera, the first thing you usually need is an object representing some phase of matter. Here, we’ll create a gas mixture:

>>> gas1 = ct.Solution('gri30.xml')

To view the state of the mixture, call the gas1 object as if it were a function:

>>> gas1()

You should see something like this:

 gri30:

      temperature             300  K
         pressure          101325  Pa
          density       0.0818891  kg/m^3
 mean mol. weight         2.01588  amu

                         1 kg            1 kmol
                      -----------      ------------
         enthalpy         26470.1        5.336e+04     J
  internal energy    -1.21087e+06       -2.441e+06     J
          entropy         64913.9        1.309e+05     J/K
   Gibbs function    -1.94477e+07        -3.92e+07     J
heat capacity c_p         14311.8        2.885e+04     J/K
heat capacity c_v         10187.3        2.054e+04     J/K

                          X                 Y          Chem. Pot. / RT
                    -------------     ------------     ------------
               H2              1                1         -15.7173
    [  +52 minor]              0                0

What you have just done is to create an object, gas1 that implements GRI- Mech 3.0, the 53-species, 325-reaction natural gas combustion mechanism developed by Gregory P. Smith, David M. Golden, Michael Frenklach, Nigel W. Moriarty, Boris Eiteneer, Mikhail Goldenberg, C. Thomas Bowman, Ronald K. Hanson, Soonho Song, William C. Gardiner, Jr., Vitali V. Lissianski, and Zhiwei Qin. See http://www.me.berkeley.edu/gri_mech/ for more information.

The gas1 object has properties you would expect for a gas mixture - it has a temperature, a pressure, species mole and mass fractions, etc. As we’ll soon see, it has many more properties.

The summary of the state of gas1 printed above shows that new objects created from the gri30.xml input file start out with a temperature of 300 K, a pressure of 1 atm, and have a composition that consists of only one species, in this case hydrogen. There is nothing special about H2 - it just happens to be the first species listed in the input file defining GRI-Mech 3.0. In general, whichever species is listed first will initially have a mole fraction of 1.0, and all of the others will be zero.

Setting the State

The state of the object can easily be changed. For example:

>>> gas1.TP = 1200, 101325

sets the temperature to 1200 K and the pressure to 101325 Pa (Cantera always uses SI units). After this statement, calling gas1() results in:

 gri30:

      temperature            1200  K
         pressure          101325  Pa
          density       0.0204723  kg/m^3
 mean mol. weight         2.01588  amu

                         1 kg            1 kmol
                      -----------      ------------
         enthalpy     1.32956e+07         2.68e+07     J
  internal energy     8.34619e+06        1.682e+07     J
          entropy         85227.6        1.718e+05     J/K
   Gibbs function    -8.89775e+07       -1.794e+08     J
heat capacity c_p         15377.9          3.1e+04     J/K
heat capacity c_v         11253.4        2.269e+04     J/K

                          X                 Y          Chem. Pot. / RT
                    -------------     ------------     ------------
               H2              1                1         -17.9775
    [  +52 minor]              0                0

Notice that the temperature has been changed as requested, but the pressure has changed too. The density and composition have not.

Thermodynamics generally requires that two properties in addition to composition information be specified to fix the intensive state of a substance (or mixture). The state of the mixture can be set using several combinations of two properties. The following are all equivalent:

>>> gas1.TP = 1200, 101325           # temperature, pressure
>>> gas1.TD = 1200, 0.0204723        # temperature, density
>>> gas1.HP = 1.32956e7, 101325      # specific enthalpy, pressure
>>> gas1.UV = 8.34619e6, 1/0.0204723 # specific internal energy, specific volume
>>> gas1.SP = 85227.6, 101325        # specific entropy, pressure
>>> gas1.SV = 85227.6, 1/0.0204723   # specific entropy, specific volume

In each case, the values of the extensive properties must be entered per unit mass.

Properties may be read independently or together:

>>> gas1.T
1200.0
>>> gas1.h
13295567.68
>>> gas1.UV
(8346188.494954427, 48.8465747765848)

The composition can be set in terms of either mole fractions (X) or mass fractions (Y):

>>> gas1.X = 'CH4:1, O2:2, N2:7.52'

Mass and mole fractions can also be set using dict objects, for cases where the composition is stored in a variable or being computed:

>>> phi = 0.8
>>> gas1.X = {'CH4':1, 'O2':2/phi, 'N2':2*3.76/phi}

When the composition alone is changed, the temperature and density are held constant. This means that the pressure and other intensive properties will change. The composition can also be set in conjunction with the intensive properties of the mixture:

>>> gas1.TPX = 1200, 101325, 'CH4:1, O2:2, N2:7.52'
>>> gas1()

results in:

 gri30:

      temperature            1200  K
         pressure          101325  Pa
          density        0.280629  kg/m^3
 mean mol. weight         27.6332  amu

                         1 kg            1 kmol
                      -----------      ------------
         enthalpy          861943        2.382e+07     J
  internal energy          500879        1.384e+07     J
          entropy          8914.3        2.463e+05     J/K
   Gibbs function    -9.83522e+06       -2.718e+08     J
heat capacity c_p         1397.26        3.861e+04     J/K
heat capacity c_v         1096.38         3.03e+04     J/K

                          X                 Y          Chem. Pot. / RT
                    -------------     ------------     ------------
               O2       0.190114         0.220149         -28.7472
              CH4       0.095057        0.0551863          -35.961
               N2       0.714829         0.724665         -25.6789
    [  +50 minor]              0                0

The composition above was specified using a string. The format is a comma- separated list of <species name>:<relative mole numbers> pairs. The mole numbers will be normalized to produce the mole fractions, and therefore they are “relative” mole numbers. Mass fractions can be set in this way too by changing X to Y in the above statements.

The composition can also be set using an array, which must have the same size as the number of species. For example, to set all 53 mole fractions to the same value, do this:

>>> gas1.X = np.ones(53) # NumPy array of 53 ones

Or, to set all the mass fractions to equal values:

>>> gas1.Y = np.ones(53)

When setting the state, you can control what properties are held constant by passing the special value None to the property setter. For example, to change the specific volume to 2.1 m^3/kg while holding entropy constant:

>>> gas1.SV = None, 2.1

Or to set the mass fractions while holding temperature and pressure constant:

>>> gas1.TPX = None, None, 'CH4:1.0, O2:0.5'

Working with a Subset of Species

Many properties of a Solution provide values for each species present in the phase. If you want to get values only for a subset of these species, you can use Python’s “slicing” syntax to select data for just the species of interest. To get the mole fractions of just the major species in gas1, in the order specified, you can write:

>>> Xmajor = gas1['CH4','O2','CO2','H2O','N2'].X

If you want to use the same set of species repeatedly, you can keep a reference to the sliced phase object:

>>> major = gas1['CH4','O2','CO2','H2O','N2']
>>> cp_major = major.partial_molar_cp
>>> wdot_major = major.net_production_rates

The slice object and the original object share the same internal state, so modifications to one will affect the other.

Working With Mechanism Files

In previous example, we created an object that models an ideal gas mixture with the species and reactions of GRI-Mech 3.0, using the gri30.xml input file included with Cantera. This is a “pre-processed” XML input file written in a format that is easy for Cantera to parse. Cantera also supports an input file format that is easier to write, called CTI. Several reaction mechanism files in this format are included with Cantera, including ones that model high- temperature air, a hydrogen/oxygen reaction mechanism, and a few surface reaction mechanisms. These files are usually located in the data subdirectory of the Cantera installation directory, e.g. C:\\Program Files\\Cantera\\data on Windows or /usr/local/cantera/data/ on Unix/Linux/Mac OS X machines, depending on how you installed Cantera and the options you specified.

If for some reason Cantera has difficulty finding where these files are on your system, set environment variable CANTERA_DATA to the directory or directories (separated using ; on Windows or : on other operating systems) where they are located. Alternatively, you can call function add_directory to add a directory to the Cantera search path:

>>> ct.add_directory('/usr/local/cantera/my_data_files')

Cantera input files are plain text files, and can be created with any text editor. See the document Defining Phases for more information.

A Cantera input file may contain more than one phase specification, or may contain specifications of interfaces (surfaces). Here we import definitions of two bulk phases and the interface between them from file diamond.cti:

>>> gas2 = ct.Solution('diamond.cti', 'gas')
>>> diamond = ct.Solution('diamond.cti', 'diamond')
>>> diamond_surf = ct.Interface('diamond.cti' , 'diamond_100',
                                [gas2, diamond])

Note that the bulk (i.e., 3D or homogeneous) phases that participate in the surface reactions must also be passed as arguments to Interface.

Converting CK-format files

See Converting CK-format files in the Working with Input Files documentation.

Getting Help

In addition to the Sphinx-generated Python Module Documentation, documentation of the Python classes and their methods can be accessed from within the Python interpreter as well.

Suppose you have created a Cantera object and want to know what methods are available for it, and get help on using the methods:

>>> g = ct.Solution('gri30.xml')

To get help on the Python class that this object is an instance of:

>>> help(g)

For a simple list of the properties and methods of this object:

>>> dir(g)

To get help on a specific method, e.g. the species_index method:

>>> help(g.species_index)

For properties, getting the documentation is slightly trickier, as the usual method will give you the help for the result, e.g.:

>>> help(g.T)

will provide help on Python’s float class. To get the help for the temperature property, ask for the attribute of the class object itself:

>>> help(g.__class__.T)

If you are using the IPython shell, help can also be obtained using the ? syntax:

In[1]: g.species_index?

Chemical Equilibrium

To set a gas mixture to a state of chemical equilibrium, use the equilibrate method:

>>> import cantera as ct
>>> g = ct.Solution('gri30.xml')
>>> g.TPX = 300.0, ct.one_atm, 'CH4:0.95,O2:2,N2:7.52'
>>> g.equilibrate('TP')

The above statement sets the state of object g to the state of chemical equilibrium holding temperature and pressure fixed. Alternatively, the specific enthalpy and pressure can be held fixed:

>>> g.TPX = 300.0, ct.one_atm, 'CH4:0.95,O2:2,N2:7.52'
>>> g.equilibrate('HP')

Other options are:

  • ‘UV’ fixed specific internal energy and specific volume
  • ‘SV’ fixed specific entropy and specific volume
  • ‘SP’ fixed specific entropy and pressure

How can you tell if equilibrate has correctly found the chemical equilibrium state? One way is verify that the net rates of progress of all reversible reactions are zero. Here is the code to do this:

>>> g.TPX = 300.0, ct.one_atm, 'CH4:0.95,O2:2,N2:7.52'
>>> g.equilibrate('HP')
>>> rf = g.forward_rates_of_progress
>>> rr = g.reverse_rates_of_progress
>>> for i in range(g.n_reactions):
>>>     if g.is_reversible(i) and rf[i] != 0.0:
>>>         print(' %4i  %10.4g  ' % (i, (rf[i] - rr[i])/rf[i]))

If the magnitudes of the numbers in this list are all very small, then each reversible reaction is very nearly equilibrated, which only occurs if the gas is in chemical equilibrium.

You might be wondering how equilibrate works. (Then again, you might not). Method equilibrate invokes Cantera’s chemical equilibrium solver, which uses an element potential method. The element potential method is one of a class of equivalent nonstoichiometric methods that all have the characteristic that the problem reduces to solving a set of M nonlinear algebraic equations, where M is the number of elements (not species). The so-called stoichiometric methods, on the other hand, (including Gibbs minimization), require solving K nonlinear equations, where K is the number of species (usually K >> M). See Smith and Missen, “Chemical Reaction Equilibrium Analysis” for more information on the various algorithms and their characteristics.

Cantera uses a damped Newton method to solve these equations, and does a few other things to generate a good starting guess and to produce a reasonably robust algorithm. If you want to know more about the details, look at the on- line documented source code of Cantera C++ class ‘ChemEquil.h’.

Chemical Kinetics

Solution objects are also Kinetics objects, and provide all of the methods necessary to compute the thermodynamic quantities associated with each reaction, reaction rates, and species creation and destruction rates. They also provide methods to inspect the quantities that define each reaction such as the rate constants and the stoichiometric coefficients. The rate calculation functions are used extensively within Cantera’s reactor network model and 1D flame model.

Information about individual reactions that is independent of the thermodynamic state can be obtained by accessing Reaction objects with the Kinetics.reaction method:

>>> g = ct.Solution('gri30.cti')
>>> r = g.reaction(2) # get a Reaction object
>>> r
<ElementaryReaction: H2 + O <=> H + OH>

>>> r.reactants
{'H2': 1.0, 'O': 1.0}
>>> r.products
{'H': 1.0, 'OH': 1.0}
>>> r.rate
Arrhenius(A=38.7, b=2.7, E=2.61918e+07)

If we are interested in only certain types of reactions, we can use this information to filter the full list of reactions to find the just the ones of interest. For example, here we find the indices of just those reactions which convert CO into CO2:

>>> II = [i for i,r in enumerate(g.reactions())
          if 'CO' in r.reactants and 'CO2' in r.products]
>>> for i in II:
...     print(g.reaction(i).equation)
CO + O (+M) <=> CO2 (+M)
CO + O2 <=> CO2 + O
CO + OH <=> CO2 + H
CO + HO2 <=> CO2 + OH

(Actually, we should also include reactions where the reaction is written such that CO2 is a reactant and CO is a product, but for this example, we’ll just stick to this smaller set of reactions.) Now, let’s set the composition to an interesting equilibrium state:

>>> g.TPX = 300, 101325, {'CH4':0.6, 'O2':1.0, 'N2':3.76}
>>> g.equilibrate('HP')

We can verify that this is an equilibrium state by seeing that the net reaction rates are essentially zero:

>>> g.net_rates_of_progress[II]
array([  4.06576e-20,  -5.50571e-21,   0.00000e+00,  -4.91279e-20])

Now, let’s see what happens if we decrease the temperature of the mixture:

>>> g.TP = g.T-100, None
>>> g.net_rates_of_progress[II]
array([  3.18645e-05,   5.00490e-08,   1.05965e-01,   2.89503e-06])

All of the reaction rates are positive, favoring the formation of CO2 from CO, with the third reaction, CO + OH <=> CO2 + H proceeding the fastest. If we look at the enthalpy change associated with each of these reactions:

>>> g.delta_enthalpy[II]
array([ -5.33035e+08,  -2.23249e+07,  -8.76650e+07,  -2.49170e+08])

we see that the change is negative in each case, indicating a net release of thermal energy. The total heat release rate can be computed either from the reaction rates:

>>> np.dot(g.net_rates_of_progress, g.delta_enthalpy)
-58013370.720881931

or from the species production rates:

>>> np.dot(g.net_production_rates, g.partial_molar_enthalpies)
-58013370.720881805

The contribution from just the selected reactions is:

>>> np.dot(g.net_rates_of_progress[II], g.delta_enthalpy[II])
-9307123.2625651453

Or about 16% of the total heat release rate.