Estimate the adiabatic flame temperature of a gas mixture

This example shows how to find the equilibrium state of a mixture. It uses the equilibrium() method with the constant pressure and enthalpy option to estimate the adiabatic flame temperature of a methane-oxygen mixture. This example also explores the influence of the equivalence ratio on the predicted adiabatic flame temperature.

Import PyChemkin packages and start the logger

from pathlib import Path

import matplotlib.pyplot as plt  # plotting
import numpy as np  # number crunching

import ansys.chemkin.core as ck  # Chemkin
from ansys.chemkin.core.logger import logger

# check working directory
current_dir = str(Path.cwd())
logger.debug("working directory: " + current_dir)
# set verbose mode
ck.set_verbose(True)
# set interactive mode for plotting the results
# interactive = True: display plot
# interactive = False: save plot as a PNG file
global interactive
interactive = True

Create a chemistry set

The first mechanism to load is the GRI 3.0 mechanism for methane combustion. This mechanism and its associated data files come with the standard Ansys Chemkin installation in the /reaction/data directory.

# set mechanism directory (the default Chemkin mechanism data directory)
data_dir = Path(ck.ansys_dir) / "reaction" / "data"
mechanism_dir = data_dir

# create a chemistry set based on the GRI 3.0 methane combustion mechanism
MyGasMech = ck.Chemistry(label="GRI 3.0")
# set mechanism input files
# including the full file path is recommended
MyGasMech.chemfile = str(mechanism_dir / "grimech30_chem.inp")
MyGasMech.thermfile = str(mechanism_dir / "grimech30_thermo.dat")
# skip the transport data file where is not needed by this example

Preprocess the chemistry set

# preprocess the mechanism files
ierror = MyGasMech.preprocess()

Set up gas mixtures

Set up gas mixtures based on the species in this chemistry set. PyChemkin has a few methods for creating a gas mixture. Here, the equivalence ratio method is used to set up the combustible mixture so that you can easily change the mixture composition by assigning a different equivalence ratio value.

# create an "oxid" mixture associated with the 'MyGasMech' chemistry set
oxid = ck.Mixture(MyGasMech)
# use a "recipe" to set the mole fractions of the mixture
# the "oxid" mixture consists of 100% O2
oxid.x = [("O2", 1.0)]
oxid.temperature = 295.15  # [K]
oxid.pressure = ck.P_ATM  # 1 atm

# create the "fuel" mixture
fuel = ck.Mixture(MyGasMech)
# set the "fuel" molar composition to 100% CH4
fuel.x = [("CH4", 1.0)]
fuel.temperature = oxid.temperature
fuel.pressure = oxid.pressure

# create the final fuel-oxidizer mixture
mixture = ck.Mixture(MyGasMech)
mixture.pressure = oxid.pressure
mixture.temperature = oxid.temperature

# the use of equivalence ratio requires the definition of the complete combustion
# products of the fuel-oxidizer pair:
# CH4 + 2O2 => CO2 + 2H2O
products = ["CO2", "H2O"]

# create an array to specify the composition of the additives to
# the fuel-oxidizer mixture For example, a diluent such as argon or
# helium might be added to the fuel-oxidizer mixture Use an all-zero array
# if there is no additive
add_frac = np.zeros(MyGasMech.kk, dtype=np.double)

Set up the parameter study

Set up a parameter study to find out the impact of the equivalence ratio on the adiabatic flame temperature of the fuel-oxidizer mixture. The equivalence ratio varies from 0.5 to 1.6 with an increment of 0.1.

points = 12
deq = 0.1
equiv_ini = 0.5

# create the solution arrays as double arrays
t = np.zeros(points, dtype=np.double)
equiv = np.zeros_like(t, dtype=np.double)

Run the parameter study

Use the equilibrium() method to estimate the adiabatic flame temperature of the fuel-oxidizer mixture. Choose the option corresponding to constant pressure and constant enthalpy for the equilibrium calculation because you are finding the adiabatic temperature.

The equilibrium() method returns a mixture object representing the mixture at the equilibrium state. Use the temperature() method to get the equilibrium temperature. To see all available options for this method, use the ck.help(topic="equilibrium") method.

This example uses the x_by_equivalence_ratio() method to set the fuel-oxidizer composition with the given equivalence ratios because the composition of both the fuel and oxidizer mixtures is specified in mole fractions.

for i in range(points):
    # set the current mixture equivalence ratio
    equiv_current = equiv_ini

    # create the fuel-oxidizer mixture with the given equivalence ratio
    ierror = mixture.x_by_equivalence_ratio(
        MyGasMech, fuel.x, oxid.x, add_frac, products, equivalenceratio=equiv_current
    )
    # check fuel-oxidizer mixture creation status
    if ierror != 0:
        print("Error: Failed to create the fuel-oxidizer mixture.")
        print(f"       Equivalence ratio = {equiv_current}.")
        exit()

    # use "equilibrium()" method to calculate the gas mixture at the equilibrium state
    # Option #5 ("opt=5") corresponds to the constant pressure and constant-enthalpy
    # constraints of the equilibrium state
    # "EQ_mixture" is the gas mixture at the equilibrium state
    EQ_mixture = ck.equilibrium(mixture, opt=5)

    # save the results to the solution arrays
    # use "temperature" to obtain the temperature of the equilibrium state
    t[i] = EQ_mixture.temperature
    equiv[i] = equiv_current
    equiv_ini = equiv_ini + deq

Plot the result from the parameter study

When you plot the result from the parameter study, the adiabatic flame temperature should exhibit a peak at around the stoichiometric, that is, equivalence ratio = 1.

# plot equilibrium/adiabatic temperatures against mixture equivalence ratios
plt.plot(equiv, t, "bs--")
# set up axis labels
plt.xlabel("Equivalence ratio")
plt.ylabel("Temperature [K]")
# display or save the plot
if interactive:
    plt.show()
else:
    plt.savefig("plot_adiabatic_flame_temperature.png", bbox_inches="tight")