Nitric oxide formation in air heated by an incident shock wave#

Shock tube experiments are commonly used to study reaction paths and to measure reaction rates at elevated temperatures. You can apply the incident shock reactor model IncidentShock() to validate the reaction mechanism or kinetic parameters derived from such experiments.

The shock tube reactor models, such as the IncidentShcok, the ReflectedShock and the ZNDCalculator models, are initiated by a stream, which is simply a mixture with the addition of the shock wave velocity. You already know how to create a stream if you know how to create a mixture. You can specify the shock wave velocity using the combination of the velocity method of the initial gas stream and the location parameter when you instantiate the incidentShock or the ReflectedShock object.

This example aims to reproduce one of the shock tube experiments done by Camac and Feinberg. Camac and Feinberg measured the production rates of nitric oxide (NO) in shock-heated air over the temperature range of 2300 [K] to 6000 [K]. The NO mole fraction behind the incident shock will be plotted as a function of time (after the passing of the incident shock front). The NO mole fraction profile rapidly rises to a peak value then gradually falls back to its equilibrium level. The predicted peak NO mole fraction is 0.04609 and is in good agreement with the measured and the computed data by Camac and Feinberg.

Reference: M. Camac and R.M. Feinberg, Proceedings of Combustion Institute, vol. 11, p. 137-145 (1967)

Import PyChemkin packages and start the logger#

from pathlib import Path
import time

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

# chemkin plug flow reactor model
from ansys.chemkin.core.shock.shocktubereactors import IncidentShock
from ansys.chemkin.core.inlet import Stream
from ansys.chemkin.core.logger import logger
import matplotlib.pyplot as plt  # plotting

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

Create the hot air dissociation mechanism file#

Create a new mechanism input file ‘no_hot_air_chem.inp’ that contains the reactions to describe NO formation in heated air. This file is saved to the working directory current_dir.

mymechfile = Path(current_dir) / "no_hot_air_chem.inp"
m = mymechfile.open(mode="w")
# the mechanism contains only the necessary species
# (oxygen, nitrogen, nitric oxide, and major byproducts)
# declare elements
m.write("ELEMENT O N AR END\n")
# declare species
m.write("SPECIES\n")
m.write("O2 N2 NO N O AR\n")
m.write("END\n")
# write reactions for N2O dissociation
# Reference:
# M. Camac and R.M. Feinberg, Proceedings of Combustion Institute,
# vol. 11, pp. 137-145 (1967)
m.write("REACTIONS\n")
m.write("N2+O2=NO+NO             9.1E24   -2.5   128500.\n")
m.write("N2+O=NO+N               7.0E13    0.     75000.\n")
m.write("O2+N=NO+O               1.34E10   1.0     7080.\n")
m.write("O2+M=O+O+M              3.62E18  -1.0   118000.\n")
m.write("N2/2/  O2/9/   O/25/\n")
m.write("N2+M=N+N+M              1.92E17  -0.5   224900.\n")
m.write("N2/2.5/  N/0/\n")
m.write("N2+N=N+N+N              4.1E22   -1.5   224900.\n")
m.write("NO+M=N+O+M              4.0E20   -1.5   150000.\n")
m.write("NO/20/  O/20/  N/20/\n")
m.write("END\n")
# close the mechnaism file
m.close()

Create a chemistry set#

The mechanism used here is the air dissociation mechanism. The mechanism will be created in situ in the working directory. The thermodynamic data file is the standard one that comes with the 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 N2O dissociation mechanism
MyGasMech = ck.Chemistry(label="NO_from_hot_air")
# set mechanism input files
# including the full file path is recommended
MyGasMech.chemfile = str(mymechfile)
MyGasMech.thermfile = str(data_dir / "therm.dat")

Preprocess the hydrogen chemistry set#

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

Instantiate and set up the stream#

Create a diluted air stream by assigning the mole fractions of the species.

diluted_air = Stream(MyGasMech)
# initial gas state before the incident shock front
# 5 [torrs]
diluted_air.pressure = 5.0 * ck.P_TORRS
# 296 [K]
diluted_air.temperature = 296.0
# AR diluted air based on the experiment setup
diluted_air.x = [("AR", 0.0093), ("O2", 0.2095), ("N2", 0.7812)]
#

Create the shock tube reactor object#

Use the IncidentShock() method to create an incident shock reactor. The IncidentShock() method has two required input parameters. The first parameter is the “stream” representing the state of the initial gas mixture. In this case, it is the diluted_air. The second required parameter is the location of the initial gas stream relative to the incident shock front. A value of ‘1’ indicate the initial gas stream is before the incident shock front (state 1), and a value of ‘2’ indicates the gas stream is behind the incident shock (state 2). The gas velocity (same as the incident shock velocity) must be given by the velocity method for IncidentShock() model.

# set the incident shock velocity [cm/sec]
diluted_air.velocity = 2.8e5

# instantiate the shock tube reactor
# the location '1' means the gas stream is before the incident shock front
Incident = IncidentShock(diluted_air, location=1, label="incident_shock")

Set up additional reactor model parameters#

For the incident shock model, the required reactor parameters is the total simulation time [sec]. The initial gas mixture conditions are defined by the stream when the IncidentShock is instantiated. To include the boundary layer correction in the shock tube model, you must specify both the ‘shock tube diameter’ and the ‘gas viscosity’ at 300 [k] using the diameter and the set_inlet_viscosity() methods, respectively.

# to use the boundary layer correction, both diameter and viscocity must be given
# shock tube diameter [cm]
Incident.diameter = 3.81
# mixture viscosity [g/cm-sec] at 300 [K]
Incident.set_inlet_viscosity(2.0e-4)

# set total simulation time (particle time) [sec]
Incident.time = 2.0e-3

Set solver controls#

You can overwrite the default solver controls by using solver related methods, for example, tolerances.

# tolerances are given in tuple: (absolute tolerance, relative tolerance)
Incident.tolerances = (1.0e-8, 1.0e-4)

Run the ZND analysis#

Use the run() method to start the ZND analysis.

Note

You can use two time calls (one before the run and one after the run) to get the simulation run time (wall time).

# set the start wall time
start_time = time.time()
# run the ZND model
runstatus = Incident.run()
# compute the total runtime
runtime = time.time() - start_time
# check run status
if runstatus != 0:
    # Run failed.
    print(Color.RED + ">>> Run failed. <<<", end=Color.END)
    exit()
# run succeeded.
print(Color.GREEN + ">>> Run completed. <<<", end=Color.END)
print(f"Total simulation duration: {runtime * 1.0e3} [msec]")

Postprocess the solution#

The postprocessing step parses the solution and packages the solution values at each time point into a mixture. There are two ways to access the solution profiles:

The raw solution profiles (value as a function of time) are available for distance, temperature, pressure, velocity, density, and species mass fractions.
The mixtures permit the use of all property and rate utilities to extract information such as viscosity, density, total thermicity, speed of sound, Mach number, and mole fractions.

You can use the get_solution_variable_profile() method to get the raw solution profiles. You can get solution mixtures using either the get_solution_stream_at_index() method for the solution mixture at the given saved location or the get_solution_stream() method for the solution mixture at the given distance. (In this case, the mixture is constructed by interpolation.)

# postprocess the solution profiles
Incident.process_solution()

# get the number of solution time points
solutionpoints = Incident.get_solution_size()
print(f"number of solution points = {solutionpoints}")

# get the time profile [sec]
timeprofile = Incident.get_solution_variable_profile("time")
# convert to [msec]
timeprofile *= 1.0e3
# get the temperature profile [K]
tempprofile = Incident.get_solution_variable_profile("temperature")
# get the velocity profile [cm/sec]
velprofile = Incident.get_solution_variable_profile("velocity")
# convert to [m/sec]
velprofile *= 1.0e-2
# get the NO mass fraction profile [-]
no_profile = Incident.get_solution_variable_profile("NO")
# get the O mass fraction profile [-]
o_profile = Incident.get_solution_variable_profile("O")

# clean up
if mymechfile.exists and mymechfile.is_file():
    mymechfile.unlink()

Plot the solution profiles#

Plot the temperature, the velocity, and the NO and the O species mass fraction profiles as a function of time.

plt.subplots(2, 2, sharex="col", figsize=(12, 6))
plt.suptitle("Incident Shock", fontsize=16)
plt.subplot(221)
plt.plot(timeprofile, tempprofile, "r-")
plt.ylabel("Temperature [K]")
plt.subplot(222)
plt.plot(timeprofile, velprofile, "b-")
plt.ylabel("Velocity [m/sec]")
plt.subplot(223)
plt.plot(timeprofile, no_profile, "g-")
plt.xlabel("time [msec]")
plt.ylabel("NO Mass Fraction [-]")
plt.subplot(224)
plt.plot(timeprofile, o_profile, "m-")
plt.xlabel("time [msec]")
plt.ylabel("O Mass Fraction [-]")

# clean up
ck.done()

# plot results
if interactive:
    plt.show()
else:
    plt.savefig("plot_incident_shock.png", bbox_inches="tight")

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