[Python/Examples] Add a more useful example of time-dependent mass flow rate

In this example, a time-dependent mass flow rate function is used to inject a
specific fuel mass into a reactor. This is a more practical use case for this
capability than the fictitious hydrogen radical igniter used in combustor.py.

interfaces/cython/cantera/examples/reactors/fuel_injection.py

@@ -0,0 +1,90 @@
+"""
+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')
+gas.equilibrate('TP')
+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.legend(loc='best')
+    a.set_xlabel('time [s]')
+    a.set_ylabel('mole fraction')
+    a.set_xlim([0, tfinal])
+
+f.tight_layout()
+plt.show()