Cantera/Sensitivity Analysis

Via https://groups.google.com/forum/#!topic/cantera-users/qMOxAdolJiA

Cantera 2.1 Script

"""
Sensitivity analysis for a freely-propagating, premixed methane-air
flame. Reports the sensitivity of the flame speed with respect to each
reaction rate constant.
"""

from __future__ import print_function

import cantera as ct

# Simulation parameters
p = ct.one_atm  # pressure [Pa]
Tin = 300.0  # unburned gas temperature [K]
reactants = 'CH4:0.45, O2:1.0, N2:3.76'

initial_grid = [0.0, 0.001, 0.01, 0.02, 0.029, 0.03]  # m
tol_ss = [1.0e-7, 1.0e-13]  # [rtol atol] for steady-state problem
tol_ts = [1.0e-4, 1.0e-13]  # [rtol atol] for time stepping

# IdealGasMix object used to compute mixture properties
gas = ct.Solution('gri30.xml', 'gri30_mix')
gas.TPX = Tin, p, reactants

# Flame object
f = ct.FreeFlame(gas, initial_grid)
f.flame.set_steady_tolerances(default=tol_ss)
f.flame.set_transient_tolerances(default=tol_ts)

# Set properties of the upstream fuel-air mixture
f.inlet.T = Tin
f.inlet.X = reactants

# Solve with the energy equation disabled
f.energy_enabled = False
f.set_max_jac_age(10, 10)
f.set_time_step(1e-5, [2, 5, 10, 20])
f.solve(loglevel=1, refine_grid=False)

# Solve with the energy equation enabled
f.set_refine_criteria(ratio=3, slope=0.06, curve=0.12)
f.energy_enabled = True
f.solve(loglevel=1, refine_grid=True)

Su0 = f.u[0]
print('mixture-averaged flamespeed = {:7f} m/s'.format(f.u[0]))

for m in range(gas.n_reactions):
    dk = 5e-2
    gas.set_multiplier(1.0)
    gas.set_multiplier(1+dk, m)
    f.solve(loglevel=0, refine_grid=False)
    Su = f.u[0]
    print('k/S*dS/dk[{: 3d}] = {: .3e} [{}]'.format(
            m, (Su-Su0)/(Su0*dk), gas.reaction_equation(m)))