fuel_injection.py (Source)

Simulation of fuel injection into a vitiated air mixture to show formation of
soot precursors.

Demonstrates the use of a user-supplied function for the mass flow rate through
a MassFlowController, and the use of the SolutionArray class to store results
during reactor network integration and use these results to generate plots.

import numpy as np
import matplotlib.pyplot as plt
import cantera as ct

# Use a reduced n-dodecane mechanism with PAH formation pathways
gas = ct.Solution('nDodecane_Reitz.cti', 'nDodecane_IG')

# Create a Reservoir for the fuel inlet, set to pure dodecane
gas.TPX = 300, 20*ct.one_atm, 'c12h26:1.0'
inlet = ct.Reservoir(gas)

# Create Reactor and set initial contents to be products of lean combustion
gas.TP = 1000, 20*ct.one_atm
gas.set_equivalence_ratio(0.30, 'c12h26', 'n2:3.76, o2:1.0')
r = ct.IdealGasReactor(gas)
r.volume = 0.001  # 1 liter

# Create an inlet for the fuel, supplied as a Gaussian pulse
def fuel_mdot(t):
    total = 3.0e-3  # mass of fuel [kg]
    width = 0.5  # width of the pulse [s]
    t0 = 2.0  # time of fuel pulse peak [s]
    amplitude = total / (width * np.sqrt(2*np.pi))
    return amplitude * np.exp(-(t-t0)**2 / (2*width**2))

mfc = ct.MassFlowController(inlet, r, mdot=fuel_mdot)

# Create the reactor network
sim = ct.ReactorNet([r])

# Integrate for 10 seconds, storing the results for later plotting
tfinal = 10.0
tnow = 0.0
i = 0
tprev = tnow
states = ct.SolutionArray(gas, extra=['t'])

while tnow < tfinal:
    tnow = sim.step()
    i += 1
    # Storing results after every step can be excessive. Instead, store results
    # every 10 steps, or more frequently if large steps are being taken.
    if tnow-tprev > 1e-2 or i == 10:
        i = 0
        tprev = tnow
        states.append(r.thermo.state, t=tnow)

# nice names for species
labels = {
    'A1c2h': 'phenylacetylene',
    'A1c2h3': 'styrene',
    'A1': 'benzene',
    'A2': 'naphthalene',
    'A2r5': 'acenaphthylene',
    'A3': 'phenanthrene',
    'A4': 'pyrene',
    'o2': 'O$_2$',
    'h2o': 'H$_2$O',
    'co2': 'CO$_2$',
    'h2': 'H$_2$',
    'ch4': 'CH$_4$'

# Plot the concentrations of some species of interest, including PAH species
# which can be considered as precursors to soot formation.
f, ax = plt.subplots(1,2)

for s in ['o2', 'h2o', 'co2', 'CO', 'h2', 'ch4']:
    ax[0].plot(states.t, states(s).X, label=labels.get(s, s))

for s in ['A1c2h', 'A1c2h3', 'A2r5', 'A1', 'A2', 'A3', 'A4']:
    ax[1].plot(states.t, states(s).X, label=labels[s])
for a in ax:
    a.set_xlabel('time [s]')
    a.set_ylabel('mole fraction')
    a.set_xlim([0, tfinal])