Note

Go to the end to download the full example code.

Calculate the detonation wave speed of a real-gas mixture#

Use the detonation() method on a combustible mixture to compute the Chapman-Jouguet (C-J) state and detonation wave speed. This example shows how to predict the detonation wave speeds of a natural gas-air mixture at various initial pressures and compare the ideal-gas and the real-gas results against the experimental data.

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 C2 NOx mechanism comes with the standard Ansys Chemkin installation in the /reaction/data directory. This mechanism includes information about the Soave cubic Equation of State (EOS) for the real-gas applications. The PyChemkin preprocessor indicates the availability of the real-gas model in the chemistry set processed.

# 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 C2 NOx using an alternative method
MyMech = ck.Chemistry(label="C2 NOx")
# set mechanism input files individually
# Because this mechanism file contains all the necessary thermodynamic and
# transport data, you do not need to specify thermodynamic and
# transport data files.
MyMech.chemfile = str(mechanism_dir / "C2_NOx_SRK.inp")

Preprocess the C2 NOx chemistry set#

During preprocessing, you should see this printed: real-gas cubic EOS 'Soave' is available. Because no transport data file is provided and the preprocess_transportdata() method is not used, transport property methods are not available in this project.

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

Set up gas mixtures based on the species in the C2 NOx chemistry set#

Create gas mixtures named fuel (natural gas) and air based on MyMech. Then, use these two mixtures to form the combustible premixed mixture for the detonation calculations. Use the x_by_equivalence_ratio() method to set the equivalence ratio of the fuel-air mixture to 1.

# create the fuel mixture
fuel = ck.Mixture(MyMech)
# set mole fraction
fuel.x = [("CH4", 0.8), ("C2H6", 0.2)]
fuel.temperature = 290.0
fuel.pressure = 40.0 * ck.P_ATM
# create the air mixture
air = ck.Mixture(MyMech)
# set mass fraction
air.x = [("O2", 0.21), ("N2", 0.79)]
air.temperature = fuel.temperature
air.pressure = fuel.pressure
# create the initial mixture
# create the premixed mixture to be defined by equivalence ratio
premixed = ck.Mixture(MyMech)
# products from the complete combustion of the fuel mixture and air
products = ["CO2", "H2O", "N2"]
# species mole fractions of added/inert mixture.
# Can also create an additives mixture here.
add_frac = np.zeros(MyMech.kk, dtype=np.double)  # no additives: all zeros

ierror = premixed.x_by_equivalence_ratio(
    MyMech, fuel.x, air.x, add_frac, products, equivalenceratio=1.0
)
# check fuel-oxidizer mixture creation status
if ierror != 0:
    print("Error: Failed to create the premixed mixture.")
    exit()

Display the molar composition of the premixed mixture#

List the composition of the premixed mixture for verification.

premixed.list_composition(mode="mole")

Run the detonation calculation#

Use the detonation() method to find the C-J state and detonation wave speed of the fuel-air mixture with the initial mixture pressure increasing from 40 to 80 [atm]. The initial mixture temperature is kept at 290 [K].

The detonation() method returns two objects: a speed tuple containing the speed of sound and the detonation wave speed at the C-J state. The CJState mixture contains the mixture properties at the C-J state. For instance, you can use CJState.pressure to get the mixture pressure at the C-J state.

Note

  • By default, Chemkin variables are in cgs units.

  • You can enter the ansys.chemkin.core.help("equilibrium") command at the Python prompt to see the input and output parameters of the detonation() method.

Run the parameter study#

Set up the parameter study of the detonation wave speed with respect to the initial pressure. The predicted detonation wave speed values are saved in the Det array. The experimental data is stored in the Det_data array. By default, the ideal-gas law is assumed. You can use the use_realgas_cubicEOS() method to turn on the real-gas model if the mechanism contains the real-gas parameters in the EOS block. Use the use_idealgas_law() method to reactivate the ideal-gas law assumption.

points = 5
dpres = 10.0 * ck.P_ATM
pres = fuel.pressure
p = np.zeros(points, dtype=np.double)
det = np.zeros_like(p, dtype=np.double)
premixed.pressure = pres
premixed.temperature = fuel.temperature

# start of pressure loop
for i in range(points):
    # compute the C-J state corresponding to the initial mixture
    speed, cj_state = ck.detonation(premixed)
    # update plot data
    # convert pressure to atm
    p[i] = pres / ck.P_ATM
    # convert speed to m/sec
    det[i] = speed[1] / 1.0e2
    # update pressure value
    pres += dpres
    premixed.pressure = pres

# create plot for ideal-gas results
plt.plot(p, det, "bo--", label="ideal gas", markersize=5, fillstyle="none")

Switch to the real-gas EOS model#

Use the use_realgas_cubicEOS() method to turn on the real-gas EOS model. You can enter ansys.chemkin.core.help("real gas") to see usage information on real-gas models or ansys.chemkin.core.help("manuals") to access the online Chemkin Theory manual for descriptions of the real-gas EOS models.

Note

By default, the Van der Waals mixing rule is applied to evaluate thermodynamic properties of a real-gas mixture. You can use the set_realgas_mixing_rule() method to switch to a different mixing rule.

# turn on real-gas cubic equation of state
premixed.use_realgas_cubic_eos()
# set mixture mixing rule to Van der Waals (default)
# premixed.set_realgas_mixing_rule(rule=0)
# restart the calculation with real-gas EOS
premixed.pressure = fuel.pressure
pres = fuel.pressure
p[:] = 0.0e0
det[:] = 0.0e0
# set verbose mode to false to turn off extra printouts
ck.set_verbose(False)
# start of pressure loop
for i in range(points):
    # compute the C-J state corresponding to the initial mixture
    speed, cj_state = ck.detonation(premixed)
    # update plot data
    p[i] = pres / ck.P_ATM
    det[i] = speed[1] / 1.0e2
    # update pressure value
    pres += dpres
    premixed.pressure = pres

# stop Chemkin
ck.done()
# create plot for real-gas results
plt.plot(p, det, "r^-", label="real gas", markersize=5, fillstyle="none")
# plot data
p_data = [44.1, 50.6, 67.2, 80.8]
det_data = [1950.0, 1970.0, 2000.0, 2020.0]
plt.plot(p_data, det_data, "gD:", label="data", markersize=4)

Plot the result from the parameter study#

You should see that the ideal-gas assumption fails to show any noticeable pressure influence on the detonation wave speeds. Because of the relatively high pressures in this study, you can observe significant differences in the predicted detonation wave speeds between the ideal-gas and real-gas models.

plt.legend(loc="upper left")
plt.xlabel("Pressure [atm]")
plt.ylabel("Detonation wave speed [m/sec]")
plt.suptitle("Natural Gas/Air Detonation", fontsize=16)
# plot results
if interactive:
    plt.show()
else:
    plt.savefig("plot_detonation.png", bbox_inches="tight")

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