[1D/Cython] Add flame speed sensitivity analysis example

interfaces/cython/cantera/examples/onedim/flamespeed_sensitivity.py

@@ -0,0 +1,69 @@
+"""
+Sensitivity analysis for a freely-propagating, premixed methane-air
+flame. Computes the sensitivity of the laminar 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, 0.01, 0.02, 0.03]  # m
+tol_ss = [1.0e-9, 1.0e-14]  # [rtol atol] for steady-state problem
+tol_ts = [1.0e-5, 1.0e-14]  # [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=0.07, curve=0.14)
+f.energy_enabled = True
+f.solve(loglevel=1, refine_grid=True)
+
+Su0 = f.u[0]
+print('\nmixture-averaged flamespeed = {:7f} m/s\n'.format(f.u[0]))
+
+print('Initial Solution:')
+f.show_stats()
+
+# Perturbation size. This must be large compared to the steady-state relative
+# tolerance (tol_ss[0]. Sensitivities less than approximately tol_ss[0] / dk
+# are not reliable.
+dk = 1e-2
+
+print()
+print('Rxn #   k/S*dS/dk    Reaction Equation')
+print('-----   ----------   ----------------------------------')
+for m in range(gas.n_reactions):
+    gas.set_multiplier(1.0) # reset all multipliers
+    gas.set_multiplier(1+dk, m) # perturb reaction m
+    f.solve(loglevel=0, refine_grid=False)
+    Su = f.u[0]
+    print('{: 5d}   {: 10.3e}   {}'.format(
+          m, (Su-Su0)/(Su0*dk), gas.reaction_equation(m)))
+
+# Sensitivity analysis requires additional function evaluations on the final
+# grid, but no additonal Jacobian evaluations.
+print('\nInitial Solution + Sensitivity calculations:')
+f.show_stats()