The Cantera interface to MUM-PCE

The Cantera model is designed to demonstrate a real-world example of MUM-PCE. Like the toy model, it consists of a set of experimental measurements that will be used to constrain a chemistry model.

The initialization function

The function measurement_initialize_xl() reads an Excel file to determine the experimental database. The header row gives the name of each column, which will be parsed by measurement_initialize_xl(). The order of the columns does not matter. Two examples are given below. Other examples are given in the repository.

Tip

The columns can be in any order. If a column is not used by any measurement in the list, it can be omitted. If a column is not used by a particular measurement, it can be left blank; the parser will ignore it.

Example data file

Example 1

Type ID Fuel1 X_fuel1 Fuel2 X_fuel2 Fuel3 X_fuel3 Ox Dil Temp Pres Model Exp_val Exp_unc
fls ecl90_b01 CH4 0.5461 N2 0 N2 0 2 Air 298 1 scheme.uscmech2-base.1atm.cti 6.76 1
fls ecl90_b02 CH4 0.5973 N2 0 N2 0 2 Air 298 1 scheme.uscmech2-base.1atm.cti 12.2 1
fls ecl90_b03 CH4 0.6948 N2 0 N2 0 2 Air 298 1 scheme.uscmech2-base.1atm.cti 20.3 1
fls ecl90_b04 CH4 0.7482 N2 0 N2 0 2 Air 298 1 scheme.uscmech2-base.1atm.cti 24.3 1

Example 2

Type ID Fuel1 X_fuel1 Fuel2 X_fuel2 Fuel3 X_fuel3 Ox Dil Temp Pres Model Crit_spec Sim Exp_val Exp_unc
ign lif77_1a01 CH4 0.01 C3H8 0 H2 0 0.02 AR 2020.20202020202 10.0 scheme.uscmech2-base.10atm.cti OH crit 3.69 0.1
ign lif77_1a02 CH4 0.01 C3H8 0 H2 0 0.02 AR 1992.0318725099603 10.0 scheme.uscmech2-base.10atm.cti OH crit 3.68 0.1
ign lif77_1a03 CH4 0.01 C3H8 0 H2 0 0.02 AR 1904.7619047619048 10.0 scheme.uscmech2-base.10atm.cti OH crit 4.24 0.1
ign lif77_1a04 CH4 0.01 C3H8 0 H2 0 0.02 AR 1876.172607879925 10.0 scheme.uscmech2-base.10atm.cti OH crit 4.34 0.1

Columns of the data file

The data file contains the following options. Columns with names marked with an asterisk are required, and all others are optional. Text enclosed in (parentheses) is optional. For instance, the parser will recognize Temp, Temper, and Temperature as valid keywords for specifying the unburned gas temperature.

  • Type*: The type of measurement, which determines which Cantera model will be used
  • ID*: A free-form text identifier

    Note

    The ‘name’ of the experiment will be generated from Type and ID

  • Reactant definitions*:

    • Fuel: A text identifier for a reactant species in the unburned gas mixture. This must be a species in the Cantera chemistry model

    • X_Fuel: The mole fraction of each reactant species in the unburned gas mixture.

      Tip

      As seen in the example, any number of Fuel and X_fuel pairs can be used. They can be in any order, but the first Fuel column must correspond to the first X_fuel column. Although the columns are named Fuel1, Fuel2, etc in the example, this is arbitrary and any identifier, or none, can be used.

    • Ox: The mole fraction of oxygen.

    • Dil: The diluent species. The behavior depends on what this is.
      • ‘Air’: 3.76 moles of nitrogen is added per mole of oxygen. Ox must be specified
      • ‘ArAir’: 3.76 moles of argon is added per mole of oxygen. Ox must be specified
      • A species in the Cantera chemistry model: the total mole fractions of all the fuels and oxidizer add to less than unity, then enough of this species will be added to ensure that the mole fractions sum to unity.

    Note

    At least one substance must be specified somehow by one of these keywords. If Dil=’Air’ or Dil=’ArAir’, Ox be specified.

  • Temp(erature)*: The temperature of the unburned gas in Kelvins

  • Pres(sure)*: The pressure of the unburned gas in standard atmospheres

  • Model: The Cantera chemistry model used for this measurement.

    Tip

    The value of chemistry_model used in the function call is used as a default for all measurements. If this column is not provided, chemistry_model is used for all measurements. If this column is provided, a value needs to be specified only for those experiments that use a different model

    Warning

    Different models for different measurements is only intended to be used if some measurements are conducted under conditions where rate constants may change (e.g. certain kinds of pressure dependencies). All models should have exactly the same reactions and corresponding parameters, although they can take different values.

  • Sim(ulation): For ShockTube and ReactionRateBase measurements, defines which sub-measurement will be done.

  • Time: For ShockTubeConcentration and ShockTubeRatio experiments, this is the integration time in microseconds.

  • Crit(ical_)spec(ies): The species whose mole fraction is to be tracked. If the value in this column is PRES, then pressure is tracked in the simulation, otherwise it must be a species in the Cantera chemistry model. For ShockTubeRatio measurements, this is the species whose concentration appears in the numerator.

    Note

    For backwards compatibility with previous database implementations, Simulation=’crit’ and Critical_species=’PRES’ is equivalent to Simulation=’pres’

  • Crit(ical_)denom(inator): For ShockTubeRatio measurements, this is the species whose concentration appears in the denominator.

  • Crit(ical_)rise: For ShockTubeDelay measurements with Simulation=’conc’, this determines if the critical species concentration should be rising or falling through the critical value

  • Crit(ical_)val(ue): For ShockTubeDelay measurements with Simulation=’conc’, this is the critical species mole fraction at which the delay occurs.

  • Reac(tion): For ReactionRateAtCondition measurements, the reaction whose rate constant is measured. For other measurements based on ReactionRateBase experiments, the reaction whose rate constant appears in the numerator.

  • Reac(tion_)denom(inator): For other measurements based on ReactionRateBase, the reaction whose rate constant appears in the denominator.

  • Exp(erimental_)val(ue): The measured value for this measurement.

  • Exp(erimental_)unc(ertainty): The uncertainty in the experimentally-measured value

    Warning

    If Exp_val is present, Exp_unc must also be preseint

Model classes in the Cantera interface

Generic interface

The generic chemistry interface for Cantera, CanteraChemistryModel, defines a number of common methods that are used for all Cantera-based simulations. These methods create and modify Cantera phase objects for sensitivity analysis. It defines all of the methods required by a Model except for evaluate().

Laminar flame speeds

This model uses a Cantera cantera.FreeFlame to determine the propagation speed of a freely-propagating laminar flame.

Shock tubes

This class of model uses a Cantera cantera.Reactor, by default a constant volume reactor, as a surrogate for a shock tube. The StateDefinition is used as the initial state of the reactor.

Shock tube ignition delay time

This model finds the ignition delay time \(\tau_{\text{ign}}\) by finding the maximum pressure rise or species concentration production rate, by solving:

\[\tau_{\text{ign}} = \text{argmax}_\tau \frac{dX}{dt}\bigg|_{t=\tau}\]

where \(X(t)\) is either the pressure or the mole fraction of the critical species in the reactor. Specified with Type = ‘ign’ and Sim = ‘crit’.

Shock tube species profile concentration

This model finds the time \(\tau_{\text{ign}}\) at which the critical species concentration reaches a critical value by solving:

\[\tau_{\text{crit}} = \text{argmin}_\tau (X(t=\tau) - X_{\text{crit}})^2\]

where \(X(t)\) is the mole fraction of the critical species in the reactor and \(X_{\text{crit}}\) is the critical value. There is an additional constraint that \(dX/dt\) must be either positive or negative when this occurs. Specified with Type = ‘ign’ and Sim = ‘conc’.

Shock tube species profile time

This model finds the critical species mole fraction \(X_{\text{crit}}\) by solving:

\[X_{\text{crit}} = X(t=\tau_{\text{crit}})\]

where \(X(t)\) is the mole fraction of the critical species in the reactor and \(\tau_{\text{crit}}\) is the integration time. Specified with Type = ‘pro’.

Shock tube species concentration ratio

This model finds the critical species mole fraction ratio \(r_{\text{crit}}\) by solving:

\[r_{\text{crit}} = \frac{X_{\text{num}}(t)}{X_{\text{denom}}(t)}\bigg|_{t=\tau_{\text{crit}}}\]

where \(X_{\text{num}}(t)\) and \(X_{\text{denom}}(t)\) are the mole fractions of the numerator and denominator species in the reactor and \(tau_{\text{crit}}\) is the integration time. Specified with Type = ‘pul’.

Reaction rate measurements

This class of model will directly query the Cantera model for rate constant values and optimize the rate paramters to match that value. There is no Cantera cantera.Reactor model, but there is a Cantera cantera.Solution model that represents the chemistry model.

Reaction rate at specified condition

This model specifies the measurement of a rate constant at a particular condition, \(k(T,P,X)\).

Reaction rate at specified condition

This model specifies the ratio of two rates at a particular condition, \(k_{num}(T,P,X)/k_{den}(T,P,X)\)

Reaction rate A-factor ratio

This model specifies the ratio of two reaction rate A factors, regardless of condition, \(A_{num}/A_{den}\)

Reaction rate activation energy difference

This model specifies the difference between two reaction rate activation energies, regardless of condition, \(E_{num} - E_{den}\)

Function summary

Generic chemistry model summary

CanteraChemistryModel(T, Patm, composition, …) A class for Cantera chemistry models.
CanteraChemistryModel.sensitivity(…[, tq]) Evaluates the sensitivity of the model value with respect to the model parameters
CanteraChemistryModel.get_parameter(parameter_id) Retrieves a model parameter’s value.
CanteraChemistryModel.perturb_parameter(…) Replaces a model parameter’s value by a new value.
CanteraChemistryModel.reset_model() Reset all model parameters to their original values
CanteraChemistryModel.get_model_parameter_info([…]) Gets the list of available parameters for this model
CanteraChemistryModel.prepare_chemistry([…]) Instantiate the Cantera chemistry model and get information about the reaction model.
CanteraChemistryModel.initialize_chemistry() Create the Cantera phase object and set its initial state
CanteraChemistryModel.blank_chemistry() Erase the Cantera phase object, Cantera reactor object, and Cantera simulation object.
StateDefinition(T, Patm, composition) A top level class for a thermodynamic state definition of an ideal gas

Laminar flame speed summary

FlameSpeed(T, Patm, composition, chemistry_model) A model for laminar flame speed
FlameSpeed.evaluate() Compute the laminar flame speed
FlameSpeed.initialize_reactor() Initialize the freely-propagating laminar flame object

Shock tube summary

ShockTube(T, Patm, composition, …[, loglevel]) A class for defining shock tube simulations.
ShockTube.initialize_reactor() Initialize the shock tube.
ShockTube.reset_model() Reset all model parameters to their original values

Shock tube delay summary

ShockTubeDelay(T, Patm, composition, …[, …]) A model for determining the delay time in shock tube ignition
ShockTubeDelay.evaluate() Finds the ignition delay time

Shock tube concentration summary

ShockTubeConcentration(T, Patm, composition, …) A model for determining the concentration of a particular species after a certain integration time.
ShockTubeConcentration.evaluate() Calculates the concentration of the critical species at the specified integration time

Shock tube concentration ratio summary

ShockTubeRatio(T, Patm, composition, …[, …]) A model for determining the mole fration ratios of two particular species after a certain integration time.
ShockTubeRatio.evaluate() Compute the concentration of the critical species

Reaction rate summary

Base reaction rate class

RxnMeasurement([name, model, value, …]) A special class for optimizing reaction rate measurements.
RxnMeasurement.make_response() Generates a sensitivity_analysis_based response surface for this measurement
ReactionRateBase(T, Patm, composition, …) The base class for optimizing reaction rates.
ReactionRateBase.sensitivity(perturbation, …) Evaluates the sensitivity of the reaction rate with respect to the model parameters

Reaction rate subclasses

ReactionRateAtCondition(T, Patm, …[, …]) A class that will specify a rate constant at a particular temperature and pressure.
ReactionRateRatioAtCondition(T, Patm, …[, …]) A class that will specify a ratio of two rate constants at a particular temperature and pressure.
ReactionARatio(T, Patm, composition, …[, …]) A class that will specify the ratio of A-factors for two reactions
ReactionEDiff(T, Patm, composition, …[, …]) A class that will specify the difference between activation energies for two reactions