Thickened flame¶
The thickness model is explained in Theoretical and Numerical Combustion, T. Poinsot, D. Veynante. If you want more information about theory, please refer to this book.
The thickness value implemented in CERFACS Cantera version is constant. It is set by writing :
f.flame.thick = thickness_value
with f being the Freeflame object.1. Useful imports and vector/plot initialization¶
In [1]:
from cantera import *
import matplotlib.pylab as plt
import numpy as np
2. Setup of premixed flame¶
In [2]:
p = 101325 # pressure
tin = 300.0 # unburned gas temperature
phi = 0.8 # equivalence ratio
3. Gas initialization¶
In [3]:
gas = Solution('BFER_methane.yaml')
4. Gas dependent useful object¶
In [4]:
m = gas.n_species
x = np.zeros(m,'d')
fuel_species = 'CH4'
ifuel = gas.species_index(fuel_species)
io2 = gas.species_index('O2')
5. Fixed grid and simulation parameters¶
In [5]:
refine_grid = "disabled"
tol_ss = [1.0e-5, 1.0e-8] # [rtol atol] for steady-state problem
tol_ts = [1.0e-5, 1.0e-8] # [rtol atol] for time stepping
loglevel = 1 # amount of diagnostic output (0 to 5)
6. Thickening¶
In [6]:
%%capture
n_points = 1000
F = [1.0, 2.0, 5.0, 10.0, 15.0, 20.0]
temperature = []
position = []
for ind_thick, thick in enumerate(F):
gas.set_equivalence_ratio(phi, 'CH4:1', 'O2:1.0, N2:3.76')
gas.TP = tin, p
initial_grid = np.linspace(0, 0.02, int(1000/thick))
f = FreeFlame(gas, grid=initial_grid)
# This is where thickening is applied
f.flame.thick = thick
f.energy_enabled = True
f.flame.set_steady_tolerances(default=tol_ss)
f.flame.set_transient_tolerances(default=tol_ts)
f.inlet.X = gas.X
f.inlet.T = tin
#f.set_refine_criteria(ratio = 7.0, slope = 1, curve = 1)
f.set_max_jac_age(50, 50)
f.set_time_step(5.e-06, [10, 20, 80]) #s
#f.set_refine_criteria(ratio = 2.0, slope = 0.02, curve = 0.02, prune = 0.01)
f.solve(loglevel, refine_grid)
temperature.append(f.T)
position.append(f.flame.grid)
In [7]:
fig = plt.figure(figsize=(18,16))
a=fig.add_subplot(111)
for ind_thick, thick in enumerate(F):
a.plot(position[ind_thick],temperature[ind_thick], label="F = "+str(thick))
plt.title(r'$T_{adiabatic}$ vs. Position', fontsize=25)
plt.xlabel(r'Position [m]', fontsize=20)
plt.ylabel("Adiabatic Flame Temperature [K]", fontsize=20)
plt.xticks(fontsize=15)
plt.yticks(fontsize=15)
#a.xaxis.set_major_locator(MaxNLocator(10)) # this controls the number of tick marks on the axis
plt.legend(fontsize=15)
Out[7]:
