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Thermodynamic Properties

Phases

These classes are used to describe the thermodynamic state of a system.

ThermoPhase

class cantera.ThermoPhase(infile='', phaseid='')

Bases: cantera._cantera._SolutionBase

ThermoPhase(*args, **kwargs)

A phase with an equation of state.

Class ThermoPhase may be used to represent the intensive thermodynamic state of a phase of matter, which might be a gas, liquid, or solid.

Class ThermoPhase is not usually instantiated directly. It is used as a base class for classes Solution and Interface.

HP

Get/Set enthalpy [J/kg or J/kmol] and pressure [Pa].

HPX

Get/Set enthalpy [J/kg or J/kmol], pressure [Pa] and mole fractions.

HPY

Get/Set enthalpy [J/kg or J/kmol], pressure [Pa] and mass fractions.

ID

The ID of the phase. The default is taken from the CTI/XML input file.

P

Pressure [Pa].

P_sat

Saturation pressure [Pa] at the current temperature.

SP

Get/Set entropy [J/kg/K or J/kmol/K] and pressure [Pa].

SPX

Get/Set entropy [J/kg/K or J/kmol/K], pressure [Pa], and mole fractions.

SPY

Get/Set entropy [J/kg/K or J/kmol/K], pressure [Pa], and mass fractions.

SV

Get/Set entropy [J/kg/K or J/kmol/K] and specific volume [m^3/kg or m^3/kmol].

SVX

Get/Set entropy [J/kg/K or J/kmol/K], specific volume [m^3/kg or m^3/kmol], and mole fractions.

SVY

Get/Set entropy [J/kg/K or J/kmol/K], specific volume [m^3/kg or m^3/kmol], and mass fractions.

T

Temperature [K].

TD

Get/Set temperature [K] and density [kg/m^3 or kmol/m^3].

TDX

Get/Set temperature [K], density [kg/m^3 or kmol/m^3], and mole fractions.

TDY

Get/Set temperature [K] and density [kg/m^3 or kmol/m^3], and mass fractions.

TP

Get/Set temperature [K] and pressure [Pa].

TPX

Get/Set temperature [K], pressure [Pa], and mole fractions.

TPY

Get/Set temperature [K], pressure [Pa], and mass fractions.

T_sat

Saturation temperature [K] at the current pressure.

UV

Get/Set internal energy [J/kg or J/kmol] and specific volume [m^3/kg or m^3/kmol].

UVX

Get/Set internal energy [J/kg or J/kmol], specific volume [m^3/kg or m^3/kmol], and mole fractions.

UVY

Get/Set internal energy [J/kg or J/kmol], specific volume [m^3/kg or m^3/kmol], and mass fractions.

X

Get/Set the species mole fractions. Can be set as an array, as a dictionary, or as a string. Always returns an array:

>>> phase.X = [0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5]
>>> phase.X = {'H2':0.1, 'O2':0.4, 'AR':0.5}
>>> phase.X = 'H2:0.1, O2:0.4, AR:0.5'
>>> phase.X
array([0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5])

Y

Get/Set the species mass fractions. Can be set as an array, as a dictionary, or as a string. Always returns an array:

>>> phase.Y = [0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5]
>>> phase.Y = {'H2':0.1, 'O2':0.4, 'AR':0.5}
>>> phase.Y = 'H2:0.1, O2:0.4, AR:0.5'
>>> phase.Y
array([0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5])

atomic_weight(self, m)

Atomic weight [kg/kmol] of element m

atomic_weights

Array of atomic weight [kg/kmol] for each element in the mixture.

basis

Determines whether intensive thermodynamic properties are treated on a mass (per kg) or molar (per kmol) basis. This affects the values returned by the properties h, u, s, g, v, density, cv, and cp, as well as the values used with the state-setting properties such as HPX and UV.

chemical_potentials

Array of species chemical potentials [J/kmol].

concentrations

Get/Set the species concentrations [kmol/m^3].

cp

Heat capacity at constant pressure [J/kg/K or J/kmol/K] depending on basis.

cp_mass

Specific heat capacity at constant pressure [J/kg/K].

cp_mole

Molar heat capacity at constant pressure [J/kmol/K].

critical_density

Critical density [kg/m^3 or kmol/m^3] depending on basis.

critical_pressure

Critical pressure [Pa].

critical_temperature

Critical temperature [K].

cv

Heat capacity at constant volume [J/kg/K or J/kmol/K] depending on basis.

cv_mass

Specific heat capacity at constant volume [J/kg/K].

cv_mole

Molar heat capacity at constant volume [J/kmol/K].

density

Density [kg/m^3 or kmol/m^3] depending on basis.

density_mass

(Mass) density [kg/m^3].

density_mole

Molar density [kmol/m^3].

electric_potential

Get/Set the electric potential [V] for this phase.

electrochemical_potentials

Array of species electrochemical potentials [J/kmol].

element_index(self, element) → int

The index of element element, which may be specified as a string or an integer. In the latter case, the index is checked for validity and returned. If no such element is present, an exception is thrown.

element_name(self, m)

Name of the element with index m.

element_names

A list of all the element names.

element_potentials(self)

Get the array of element potentials. The element potentials are only defined for equilibrium states. This method first sets the composition to a state of equilibrium at constant T and P, then computes the element potentials for this equilibrium state.

elemental_mass_fraction(self, m)

Get the elemental mass fraction \(Z_{\mathrm{mass},m}\) of element \(m\) as defined by:

\[Z_{\mathrm{mass},m} = \sum_k \frac{a_{m,k} M_m}{M_k} Y_k\]

with \(a_{m,k}\) being the number of atoms of element \(m\) in species \(k\), \(M_m\) the atomic weight of element \(m\), \(M_k\) the molecular weight of species \(k\), and \(Y_k\) the mass fraction of species \(k\).

Parameters:m – Base element, may be specified by name or by index.

>>> phase.elemental_mass_fraction('H')
1.0

elemental_mole_fraction(self, m)

Get the elemental mole fraction \(Z_{\mathrm{mole},m}\) of element \(m\) (the number of atoms of element m divided by the total number of atoms) as defined by:

\[Z_{\mathrm{mole},m} = \frac{\sum_k a_{m,k} X_k} {\sum_k \sum_j a_{j,k} X_k}\]

with \(a_{m,k}\) being the number of atoms of element \(m\) in species \(k\), \(\sum_j\) being a sum over all elements, and \(X_k\) being the mole fraction of species \(k\).

Parameters:m – Base element, may be specified by name or by index.

>>> phase.elemental_mole_fraction('H')
1.0

enthalpy_mass

Specific enthalpy [J/kg].

enthalpy_mole

Molar enthalpy [J/kmol].

entropy_mass

Specific entropy [J/kg].

entropy_mole

Molar entropy [J/kmol/K].

equilibrate(self, XY, solver='auto', double rtol=1e-09, int maxsteps=1000, int maxiter=100, int estimate_equil=0, int loglevel=0)

Set to a state of chemical equilibrium holding property pair XY constant.

Parameters:

• XY –

  A two-letter string, which must be one of the set:

  ['TP','TV','HP','SP','SV','UV']
  

• solver –

  Specifies the equilibrium solver to use. May be one of the following:

  • ‘’element_potential’’ - a fast solver using the element potential method
  • ‘gibbs’ - a slower but more robust Gibbs minimization solver
  • ‘vcs’ - the VCS non-ideal equilibrium solver
  • “auto” - The element potential solver will be tried first, then if it fails the Gibbs solver will be tried.
• rtol – the relative error tolerance.
• maxsteps – maximum number of steps in composition to take to find a converged solution.
• maxiter – For the Gibbs minimization solver, this specifies the number of ‘outer’ iterations on T or P when some property pair other than TP is specified.
• estimate_equil – Integer indicating whether the solver should estimate its own initial condition. If 0, the initial mole fraction vector in the ThermoPhase object is used as the initial condition. If 1, the initial mole fraction vector is used if the element abundances are satisfied. If -1, the initial mole fraction vector is thrown out, and an estimate is formulated.
• loglevel – Set to a value > 0 to write diagnostic output.

g

Gibbs free energy [J/kg or J/kmol] depending on basis.

gibbs_mass

Specific Gibbs free energy [J/kg].

gibbs_mole

Molar Gibbs free energy [J/kmol].

h

Enthalpy [J/kg or J/kmol] depending on basis.

int_energy_mass

Specific internal energy [J/kg].

int_energy_mole

Molar internal energy [J/kmol].

isothermal_compressibility

Isothermal compressibility [1/Pa].

mass_fraction_dict(self, double threshold=0.0)

max_temp

Maximum temperature for which the thermodynamic data for the phase are valid.

mean_molecular_weight

The mean molecular weight (molar mass) [kg/kmol].

min_temp

Minimum temperature for which the thermodynamic data for the phase are valid.

mole_fraction_dict(self, double threshold=0.0)

molecular_weights

Array of species molecular weights (molar masses) [kg/kmol].

n_atoms(self, species, element)

Number of atoms of element element in species species. The element and species may be specified by name or by index.

>>> phase.n_atoms('CH4','H')
4

n_elements

Number of elements.

n_species

Number of species.

name

The name assigned to this phase. The default is taken from the CTI/XML input file.

partial_molar_cp

Array of species partial molar specific heat capacities at constant pressure [J/kmol/K].

partial_molar_enthalpies

Array of species partial molar enthalpies [J/kmol].

partial_molar_entropies

Array of species partial molar entropies [J/kmol/K].

partial_molar_int_energies

Array of species partial molar internal energies [J/kmol].

partial_molar_volumes

Array of species partial molar volumes [m^3/kmol].

reference_pressure

Reference state pressure [Pa].

report(self, show_thermo=True, float threshold=1e-14)

Generate a report describing the thermodynamic state of this phase. To print the report to the terminal, simply call the phase object. The following two statements are equivalent:

>>> phase()
>>> print(phase.report())

s

Entropy [J/kg/K or J/kmol/K] depending on basis.

set_unnormalized_mass_fractions(self, Y)

Set the mass fractions without normalizing to force sum(Y) == 1.0. Useful primarily when calculating derivatives with respect to Y[k] by finite difference.

set_unnormalized_mole_fractions(self, X)

Set the mole fractions without normalizing to force sum(X) == 1.0. Useful primarily when calculating derivatives with respect to X[k] by finite difference.

species(self, k=None)

Return the Species object for species k, where k is either the species index or the species name. If k is not specified, a list of all species objects is returned.

species_index(self, species) → int

The index of species species, which may be specified as a string or an integer. In the latter case, the index is checked for validity and returned. If no such species is present, an exception is thrown.

species_name(self, k)

Name of the species with index k.

species_names

A list of all the species names.

standard_cp_R

Array of nondimensional species standard-state specific heat capacities at constant pressure at the current temperature and pressure.

standard_enthalpies_RT

Array of nondimensional species standard-state enthalpies at the current temperature and pressure.

standard_entropies_R

Array of nondimensional species standard-state entropies at the current temperature and pressure.

standard_gibbs_RT

Array of nondimensional species standard-state Gibbs free energies at the current temperature and pressure.

standard_int_energies_RT

Array of nondimensional species standard-state internal energies at the current temperature and pressure.

thermal_expansion_coeff

Thermal expansion coefficient [1/K].

u

Internal energy in [J/kg or J/kmol].

v

Specific volume [m^3/kg or m^3/kmol] depending on basis.

volume_mass

Specific volume [m^3/kg].

volume_mole

Molar volume [m^3/kmol].

InterfacePhase

class cantera.InterfacePhase(infile='', phaseid='')

Bases: cantera._cantera.ThermoPhase

A class representing a surface or edge phase

coverages

Get/Set the fraction of sites covered by each species.

site_density

Get/Set the site density. [kmol/m^2] for surface phases; [kmol/m] for edge phases.

PureFluid

class cantera.PureFluid(infile='', phaseid='')

Bases: cantera._cantera.ThermoPhase

A pure substance that can be a gas, a liquid, a mixed gas-liquid fluid, or a fluid beyond its critical point.

DPX

Get the density [kg/m^3], pressure [Pa], and vapor fraction.

HPX

Get the enthalpy [J/kg or J/kmol], pressure [Pa] and vapor fraction.

PX

Get/Set the pressure and vapor fraction of a two-phase state.

SPX

Get the entropy [J/kg/K or J/kmol/K], pressure [Pa], and vapor fraction.

SVX

Get the entropy [J/kg/K or J/kmol/K], specific volume [m^3/kg or m^3/kmol], and vapor fraction.

TDX

Get the temperature [K], density [kg/m^3 or kmol/m^3], and vapor fraction.

TPX

Get the temperature [K], pressure [Pa], and vapor fraction.

TX

Get/Set the temperature and vapor fraction of a two-phase state.

UVX

Get the internal energy [J/kg or J/kmol], specific volume [m^3/kg or m^3/kmol], and vapor fraction.

X

Get/Set vapor fraction (quality). Can be set only when in the two-phase region.

Mixture

class cantera.Mixture

Bases: object

Class Mixture represents mixtures of one or more phases of matter. To construct a mixture, supply a list of phases to the constructor, each paired with the number of moles for that phase:

>>> gas = cantera.Solution('gas.cti')
>>> gas.species_names
['H2', 'H', 'O2', 'O', 'OH']
>>> graphite = cantera.Solution('graphite.cti')
>>> graphite.species_names
['C(g)']
>>> mix = cantera.Mixture([(gas, 1.0), (graphite, 0.1)])
>>> mix.species_names
['H2', 'H', 'O2', 'O', 'OH', 'C(g)']

Note that the objects representing each phase compute only the intensive state of the phase – they do not store any information on the amount of this phase. Mixture objects, on the other hand, represent the full extensive state.

Mixture objects are ‘lightweight’ in the sense that they do not store parameters needed to compute thermodynamic or kinetic properties of the phases. These are contained in the (‘heavyweight’) phase objects. Multiple mixture objects may be constructed using the same set of phase objects. Each one stores its own state information locally, and synchronizes the phases objects whenever it requires phase properties.

P

Get or set the Pressure [Pa] of all phases in the mixture. When set, the temperature of the mixture is held fixed.

T

Get or set the Temperature [K] of all phases in the mixture. When set, the pressure of the mixture is held fixed.

charge

The total charge in Coulombs, summed over all phases.

chemical_potentials

The chemical potentials of all species [J/kmol].

element_index(self, element) → int

Index of element with name ‘element’.

>>> mix.element_index('H')
2

element_moles(self, e)

Total number of moles of element e, summed over all species. The element may be referenced either by index number or by name.

equilibrate(self, XY, solver='auto', rtol=1e-09, max_steps=1000, max_iter=100, estimate_equil=0, log_level=0)

Set to a state of chemical equilibrium holding property pair XY constant. This method uses a version of the VCS algorithm to find the composition that minimizes the total Gibbs free energy of the mixture, subject to element conservation constraints. For a description of the theory, see Smith and Missen, “Chemical Reaction Equilibrium.”

Parameters:

• XY –

  A two-letter string, which must be one of the set:

  ['TP', 'HP', 'SP']
  

• solver – Set to either ‘auto’, ‘vcs’, or ‘gibbs’ to choose implementation of the solver to use. ‘vcs’ uses the solver implemented in the C++ class ‘VCSnonideal’, ‘gibbs’ uses the one implemented in class ‘MultiPhaseEquil’. ‘auto’ will try the ‘vcs’ solver first and then the ‘gibbs’ solver if that fails.
• rtol – Error tolerance. Iteration will continue until (Delta mu)/RT is less than this value for each reaction. Note that this default is very conservative, and good equilibrium solutions may be obtained with larger error tolerances.
• max_steps – Maximum number of steps to take while solving the equilibrium problem for specified T and P.
• max_iter – Maximum number of temperature and/or pressure iterations. This is only relevant if a property pair other than (T,P) is specified.
• estimate_equil – Flag indicating whether the solver should estimate its own initial condition. If 0, the initial mole fraction vector in the phase objects are used as the initial condition. If 1, the initial mole fraction vector is used if the element abundances are satisfied. if -1, the initial mole fraction vector is thrown out, and an estimate is formulated.
• log_level – Determines the amount of output displayed during the solution process. 0 indicates no output, while larger numbers produce successively more verbose information.

max_temp

The maximum temperature for which all species in multi-species solutions have valid thermo data. Stoichiometric phases are not considered in determining max_temp.

min_temp

The minimum temperature for which all species in multi-species solutions have valid thermo data. Stoichiometric phases are not considered in determining min_temp.

n_atoms(self, k, m)

Number of atoms of element m in the species with global index k. The element may be referenced either by name or by index.

>>> n = mix.n_atoms(3, 'H')
4.0

n_elements

Total number of elements present in the mixture.

n_phases

Number of phases

n_species

Number of species.

phase(self, n)

phase_charge(self, p)

The charge of phase p in Coulombs.

phase_index(self, p)

Index of the phase named p.

phase_moles(self, p=None)

Moles in phase p, if p is specified, otherwise the number of moles in all phases.

phase_names

Names of all phases in the order added.

report(self, threshold=1e-14)

Generate a report describing the thermodynamic state of this mixture. To print the report to the screen, simply call the mixture object. The following two statements are equivalent:

>>> mix()
>>> print(mix.report())

set_phase_moles(self, p, moles)

Set the number of moles of phase p to moles

species_index(self, phase, species)

Parameters:

• phase – Phase object, index or name
• species – Species name or index

Returns the global index of species species in phase phase.

species_moles

Get or set the number of moles of each species. May be set either as a string or as an array. If an array is used, it must be dimensioned at least as large as the total number of species in the mixture. Note that the species may belong to any phase, and unspecified species are set to zero.

>>> mix.species_moles = 'C(s):1.0, CH4:2.0, O2:0.2'

species_name(self, k)

Name of the species with index k. Note that index numbers are assigned in order as phases are added.

species_names

Species

class cantera.Species

Bases: object

Species(name=None, composition=None, charge=None, size=None, init=True, *args, **kwargs)

A class which stores data about a single chemical species that may be needed to add it to a Solution or Interface object (and to the underlying ThermoPhase and Transport objects).

Parameters:

• name – A string giving the name of the species, e.g. 'CH4'
• composition – The elemental composition of the species, given either as a dict or a composition string, e.g. {'C':1, 'H':4} or 'C:1, H:4'.
• charge – The electrical charge, in units of the elementary charge. Default 0.0.
• size – The effective size [m] of the species. Default 1.0.
• init – Used internally when wrapping Species objects returned from C++

Example: creating an ideal gas phase with a single species:

ch4 = ct.Species('CH4', 'C:1, H:4')
ch4.thermo = ct.ConstantCp(300, 1000, 101325,
                           (300, -7.453347e7, 1.865912e5, 3.576053e4))
tran = ct.GasTransportData()
tran.set_customary_units('nonlinear', 3.75, 141.40, 0.0, 2.60, 13.00)
ch4.transport = tran
gas = ct.Solution(thermo='IdealGas', species=[ch4])

The static methods fromCti, fromXml, listFromFile, listFromCti, and listFromXml can be used to create Species objects from existing definitions in the CTI or XML formats. All of the following will produce a list of 53 Species objects containing the species defined in the GRI 3.0 mechanism:

S = ct.Species.listFromFile('gri30.cti')
S = ct.Species.listFromCti(open('path/to/gri30.cti').read())
S = ct.Species.listFromXml(open('path/to/gri30.xml').read())

charge

The electrical charge on the species, in units of the elementary charge.

composition

A dict containing the elemental composition of the species. Keys are element names; values are the corresponding atomicities.

fromCti(text)

Create a Species object from its CTI string representation.

fromXml(text)

Create a Species object from its XML string representation.

listFromCti(text)

Create a list of Species objects from all the species defined in a CTI string.

listFromFile(filename)

Create a list of Species objects from all of the species defined in a CTI or XML file.

Directories on Cantera’s input file path will be searched for the specified file.

In the case of an XML file, the <species> nodes are assumed to be children of the <speciesData> node in a document with a <ctml> root node, as in the XML files produced by conversion from CTI files.

listFromXml(text)

Create a list of Species objects from all the species defined in an XML string. The <species> nodes are assumed to be children of the <speciesData> node in a document with a <ctml> root node, as in the XML files produced by conversion from CTI files.

name

The name of the species.

size

The effective size [m] of the species.

thermo

Get/Set the species reference-state thermodynamic data, as an instance of class SpeciesThermo.

transport

Get/Set the species transport parameters, as an instance of class GasTransportData.

Species Thermodynamic Properties

These classes are used to describe the reference-state thermodynamic properties of a pure species.

SpeciesThermo

class cantera.SpeciesThermo(T_low, T_high, P_ref, coeffs)

Bases: object

Base class for representing the reference-state thermodynamic properties of a pure species. These properties are a function of temperature. Derived classes implement a parameterization of this temperature dependence. This is a wrapper for the C++ class SpeciesThermoInterpType.

Parameters:

• T_low – The minimum temperature [K] at which the parameterization is valid
• T_high – The maximum temperature [K] at which the parameterization is valid
• P_ref – The reference pressure [Pa] for the parameterization
• coeffs – An array of coefficients for the parameterization. The length of this array and the meaning of each element depends on the specific parameterization.

cp(self, T)

Molar heat capacity at constant pressure [J/kmol/K] at temperature T.

h(self, T)

Molar enthalpy [J/kmol] at temperature T

s(self, T)

Molar entropy [J/kmol/K] at temperature T

ConstantCp

class cantera.ConstantCp(T_low, T_high, P_ref, coeffs)

Bases: cantera._cantera.SpeciesThermo

Thermodynamic properties for a species that has a constant specific heat capacity. This is a wrapper for the C++ class ConstCpPoly.

Parameters:coeffs –

An array of 4 elements:

• coeffs[0] = \(T_0\) [K]
• coeffs[1] = \(H^o(T_0, p_{ref})\) [J/kmol]
• coeffs[2] = \(S^o(T_0, p_{ref})\) [J/kmol-K]
• coeffs[3] = \(c_p^o(T_0, p_{ref})\) [J/kmol-K]

NasaPoly2

class cantera.NasaPoly2(T_low, T_high, P_ref, coeffs)

Bases: cantera._cantera.SpeciesThermo

Thermodynamic properties for a species which is parameterized using the 7-coefficient NASA polynomial form in two temperature ranges. This is a wrapper for the C++ class NasaPoly2.

Parameters:coeffs –

An array of 15 elements, in the following order:

• coeffs[0]: The mid-point temperature [K] between the two parameterizations
• coeffs[1:8]: The 7 coefficients of the high-temperature parameterization
• coeffs[8:15]: The 7 coefficients of the low-temperature parameterization

This is the coefficient order used in the standard fixed-format NASA input files.

ShomatePoly2

class cantera.ShomatePoly2(T_low, T_high, P_ref, coeffs)

Bases: cantera._cantera.SpeciesThermo

Thermodynamic properties for a species which is parameterized using the Shomate equation in two temperature ranges. This is a wrapper for the C++ class ShomatePoly2.

Parameters:coeffs –

An array of 15 elements, in the following order:

• coeffs[0]: The mid-point temperature [K] between the two parameterizations
• coeffs[1:8]: The 7 coefficients of the low-temperature parameterization
• coeffs[8:15]: The 7 coefficients of the high-temperature parameterization

These coefficients should be provided in their customary units (i.e. such that \(c_p^o\) is in J/gmol-K and \(H^o\) is in kJ/gmol, as in the NIST Chemistry WebBook).