Note
Go to the end to download the full example code.
Constant-pressure, adiabatic kinetics simulation with sensitivity analysis#
Requires: cantera >= 2.5.0, matplotlib >= 2.0
0.000e+00 1500.000 101325.000 9.070228e+05 0.000 0.000
5.000e-06 1500.000 101325.000 9.070230e+05 -0.000 0.000
1.000e-05 1499.999 101325.000 9.070231e+05 0.000 0.000
1.500e-05 1499.999 101325.000 9.070232e+05 0.000 0.000
2.000e-05 1499.998 101325.000 9.070233e+05 0.000 0.000
2.500e-05 1499.998 101325.000 9.070234e+05 0.000 0.000
3.000e-05 1499.997 101325.000 9.070235e+05 0.000 0.000
3.500e-05 1499.997 101325.000 9.070236e+05 0.000 0.000
4.000e-05 1499.997 101325.000 9.070237e+05 0.000 0.000
4.500e-05 1499.996 101325.000 9.070238e+05 0.000 -0.000
5.000e-05 1499.996 101325.000 9.070239e+05 0.000 -0.000
5.500e-05 1499.996 101325.000 9.070240e+05 0.000 -0.000
6.000e-05 1499.995 101325.000 9.070241e+05 0.000 -0.000
6.500e-05 1499.995 101325.000 9.070241e+05 0.000 -0.000
7.000e-05 1499.995 101325.000 9.070242e+05 0.000 -0.000
7.500e-05 1499.995 101325.000 9.070242e+05 0.000 -0.000
8.000e-05 1499.994 101325.000 9.070243e+05 0.000 -0.000
8.500e-05 1499.994 101325.000 9.070243e+05 0.000 -0.000
9.000e-05 1499.994 101325.000 9.070244e+05 0.000 -0.000
9.500e-05 1499.994 101325.000 9.070244e+05 0.000 -0.000
1.000e-04 1499.994 101325.000 9.070244e+05 0.000 -0.000
1.050e-04 1499.994 101325.000 9.070244e+05 0.000 -0.000
1.100e-04 1499.994 101325.000 9.070244e+05 0.000 -0.000
1.150e-04 1499.994 101325.000 9.070244e+05 0.000 -0.000
1.200e-04 1499.994 101325.000 9.070243e+05 0.000 -0.000
1.250e-04 1499.994 101325.000 9.070243e+05 0.000 -0.000
1.300e-04 1499.994 101325.000 9.070242e+05 0.000 -0.000
1.350e-04 1499.994 101325.000 9.070242e+05 0.000 -0.000
1.400e-04 1499.994 101325.000 9.070241e+05 0.000 -0.000
1.450e-04 1499.994 101325.000 9.070240e+05 0.000 -0.000
1.500e-04 1499.995 101325.000 9.070239e+05 0.000 -0.000
1.550e-04 1499.995 101325.000 9.070237e+05 0.000 -0.000
1.600e-04 1499.995 101325.000 9.070236e+05 0.000 -0.000
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1.700e-04 1499.996 101325.000 9.070232e+05 0.000 -0.000
1.750e-04 1499.997 101325.000 9.070230e+05 0.000 -0.000
1.800e-04 1499.997 101325.000 9.070228e+05 0.000 -0.000
1.850e-04 1499.998 101325.000 9.070226e+05 0.000 -0.000
1.900e-04 1499.999 101325.000 9.070223e+05 0.000 -0.000
1.950e-04 1500.000 101325.000 9.070220e+05 0.000 -0.000
2.000e-04 1500.001 101325.000 9.070217e+05 0.000 -0.000
2.050e-04 1500.002 101325.000 9.070214e+05 0.000 -0.001
2.100e-04 1500.003 101325.000 9.070210e+05 0.000 -0.001
2.150e-04 1500.004 101325.000 9.070206e+05 0.000 -0.001
2.200e-04 1500.005 101325.000 9.070202e+05 0.000 -0.001
2.250e-04 1500.006 101325.000 9.070198e+05 0.000 -0.001
2.300e-04 1500.008 101325.000 9.070193e+05 0.000 -0.001
2.350e-04 1500.010 101325.000 9.070188e+05 0.000 -0.001
2.400e-04 1500.011 101325.000 9.070182e+05 0.000 -0.001
2.450e-04 1500.013 101325.000 9.070176e+05 0.000 -0.001
2.500e-04 1500.015 101325.000 9.070170e+05 0.000 -0.001
2.550e-04 1500.017 101325.000 9.070163e+05 0.000 -0.001
2.600e-04 1500.019 101325.000 9.070156e+05 0.000 -0.001
2.650e-04 1500.022 101325.000 9.070148e+05 0.000 -0.001
2.700e-04 1500.024 101325.000 9.070140e+05 0.000 -0.001
2.750e-04 1500.027 101325.000 9.070132e+05 0.000 -0.001
2.800e-04 1500.029 101325.000 9.070123e+05 0.000 -0.001
2.850e-04 1500.033 101325.000 9.070113e+05 0.000 -0.001
2.900e-04 1500.036 101325.000 9.070103e+05 0.000 -0.001
2.950e-04 1500.039 101325.000 9.070092e+05 0.000 -0.001
3.000e-04 1500.043 101325.000 9.070080e+05 0.000 -0.002
3.050e-04 1500.047 101325.000 9.070068e+05 0.000 -0.002
3.100e-04 1500.051 101325.000 9.070055e+05 0.000 -0.002
3.150e-04 1500.055 101325.000 9.070041e+05 0.000 -0.002
3.200e-04 1500.059 101325.000 9.070027e+05 0.000 -0.002
3.250e-04 1500.064 101325.000 9.070012e+05 0.000 -0.002
3.300e-04 1500.069 101325.000 9.069995e+05 0.000 -0.002
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3.950e-04 1500.172 101325.000 9.069674e+05 0.000 -0.004
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5.100e-04 1500.730 101325.000 9.067957e+05 0.001 -0.011
5.150e-04 1500.777 101325.000 9.067811e+05 0.001 -0.012
5.200e-04 1500.828 101325.000 9.067655e+05 0.001 -0.013
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5.300e-04 1500.942 101325.000 9.067309e+05 0.001 -0.014
5.350e-04 1501.004 101325.000 9.067117e+05 0.001 -0.015
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5.750e-04 1501.716 101325.000 9.064939e+05 0.002 -0.024
5.800e-04 1501.841 101325.000 9.064557e+05 0.002 -0.025
5.850e-04 1501.976 101325.000 9.064141e+05 0.002 -0.027
5.900e-04 1502.124 101325.000 9.063687e+05 0.003 -0.029
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6.000e-04 1502.463 101325.000 9.062648e+05 0.003 -0.033
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1.480e-03 1714.297 101325.000 8.443804e+05 -0.009 0.004
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1.680e-03 1719.457 101325.000 8.430577e+05 -0.008 0.001
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1.740e-03 1720.545 101325.000 8.427787e+05 -0.008 0.001
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1.835e-03 1721.979 101325.000 8.424109e+05 -0.008 0.000
1.840e-03 1722.046 101325.000 8.423937e+05 -0.008 0.000
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1.850e-03 1722.178 101325.000 8.423598e+05 -0.008 0.000
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1.860e-03 1722.308 101325.000 8.423266e+05 -0.007 -0.000
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1.920e-03 1723.028 101325.000 8.421420e+05 -0.007 -0.000
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1.940e-03 1723.248 101325.000 8.420855e+05 -0.007 -0.001
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1.955e-03 1723.407 101325.000 8.420446e+05 -0.007 -0.001
1.960e-03 1723.460 101325.000 8.420312e+05 -0.007 -0.001
1.965e-03 1723.511 101325.000 8.420180e+05 -0.007 -0.001
1.970e-03 1723.562 101325.000 8.420049e+05 -0.007 -0.001
1.975e-03 1723.613 101325.000 8.419919e+05 -0.007 -0.001
1.980e-03 1723.663 101325.000 8.419791e+05 -0.007 -0.001
1.985e-03 1723.712 101325.000 8.419664e+05 -0.007 -0.001
1.990e-03 1723.761 101325.000 8.419538e+05 -0.007 -0.001
1.995e-03 1723.810 101325.000 8.419414e+05 -0.007 -0.001
import sys
import numpy as np
import cantera as ct
gas = ct.Solution('gri30.yaml')
temp = 1500.0
pres = ct.one_atm
gas.TPX = temp, pres, 'CH4:0.1, O2:2, N2:7.52'
r = ct.IdealGasConstPressureReactor(gas, name='R1')
sim = ct.ReactorNet([r])
# enable sensitivity with respect to the rates of the first 10
# reactions (reactions 0 through 9)
for i in range(10):
r.add_sensitivity_reaction(i)
# set the tolerances for the solution and for the sensitivity coefficients
sim.rtol = 1.0e-6
sim.atol = 1.0e-15
sim.rtol_sensitivity = 1.0e-6
sim.atol_sensitivity = 1.0e-6
states = ct.SolutionArray(gas, extra=['t', 's2', 's3'])
for t in np.arange(0, 2e-3, 5e-6):
sim.advance(t)
s2 = sim.sensitivity('OH', 2) # sensitivity of OH to reaction 2
s3 = sim.sensitivity('OH', 3) # sensitivity of OH to reaction 3
states.append(r.thermo.state, t=1000*t, s2=s2, s3=s3)
print('{:10.3e} {:10.3f} {:10.3f} {:14.6e} {:10.3f} {:10.3f}'.format(
sim.time, r.T, r.thermo.P, r.thermo.u, s2, s3))
# plot the results if matplotlib is installed.
# see http://matplotlib.org/ to get it
if '--plot' in sys.argv:
import matplotlib.pyplot as plt
plt.subplot(2, 2, 1)
plt.plot(states.t, states.T)
plt.xlabel('Time (ms)')
plt.ylabel('Temperature (K)')
plt.subplot(2, 2, 2)
plt.plot(states.t, states('OH').X)
plt.xlabel('Time (ms)')
plt.ylabel('OH Mole Fraction')
plt.subplot(2, 2, 3)
plt.plot(states.t, states('H').X)
plt.xlabel('Time (ms)')
plt.ylabel('H Mole Fraction')
plt.subplot(2, 2, 4)
plt.plot(states.t, states('CH4').X)
plt.xlabel('Time (ms)')
plt.ylabel('CH4 Mole Fraction')
plt.tight_layout()
plt.figure(2)
plt.plot(states.t, states.s2, '-', label=sim.sensitivity_parameter_name(2))
plt.plot(states.t, states.s3, '-g', label=sim.sensitivity_parameter_name(3))
plt.legend(loc='best')
plt.xlabel('Time (ms)')
plt.ylabel('OH Sensitivity')
plt.tight_layout()
plt.show()
else:
print("""To view a plot of these results, run this script with the option '--plot""")
Total running time of the script: (0 minutes 0.893 seconds)