def free_flame(chemistry='gri30.cti',
fuel={'CH4': 1.},
oxidizer={
'O2': 1.,
'N2': 3.76
},
temperature=300.,
pressure=1.,
phi=1.,
**kwargs):
# for unrealistic parameters
if pressure < 0.:
raise ValueError('Negative pressure')
if temperature < 0.:
raise ValueError('Negative inlet temperature')
if phi < 0.:
raise ValueError('Negative equivalence ratio')
# parameters
params = {}
params['T'] = temperature
params['p'] = pressure
params['phi'] = phi
case = params2name(params)
# pressure, convert to [Pa]
pressure *= ct.one_atm
# gas object
gas = cg.mixture(chemistry, fuel, oxidizer, temperature, pressure, phi)
f = free_flame_(gas, **kwargs)
# return for unburnt flame
if np.max(f.T) < temperature + 100.:
return 1
f.save('{}.xml'.format(case))
return 0
def counterflow_premixed_extinction(chemistry='FFCM-1.cti',
fuel={'CH4': 1.},
oxidizer={
'O2': 1.,
'N2': 3.76
},
T=300.,
p=1.,
phi=1.,
**kwargs):
# read kwargs
# IO flags
if 'folder_overwrite' in kwargs.keys():
flag_folder = kwargs['folder_overwrite']
else:
flag_folder = True
# parameters to approach extinction
if 'a_init' in kwargs.keys():
a_init = kwargs['a_init']
else:
a_init = 100.
if 'a_max' in kwargs.keys():
a_max = kwargs['a_max']
else:
a_max = 1.E+5
if 'L_init' in kwargs.keys():
L_init = kwargs['L_init']
else:
L_init = 0.05
# factors
# a_{n+1} = exp(f0) * a_n
if 'f0' in kwargs.keys():
f0 = kwargs['f0']
else:
f0 = 0.1
# f0_{n+1} = f0_n / f1
if 'f1' in kwargs.keys():
f1 = kwargs['f1']
else:
f1 = 2.0
# a_threshold_n = a_n * f2
if 'f2' in kwargs.keys():
f2 = kwargs['f2']
else:
f2 = 1.E-3
# for unrealistic parameters
if p < 0.:
raise ValueError('Negative pressure')
if T < 0.:
raise ValueError('Negative inlet temperature')
if phi < 0.:
raise ValueError('Negative equivalence ratio')
params = {}
params['T'] = T
params['p'] = p
params['phi'] = phi
folder_name = fn.params2name(params)
pwd = os.getcwd()
os.makedirs(folder_name, exist_ok=flag_folder)
os.chdir(folder_name)
# calculate free flame
ctd.free_flame(chemistry=chemistry,
fuel=fuel,
oxidizer=oxidizer,
pressure=p,
temperature=T,
phi=phi,
**kwargs)
# iterate to get the extinction
params['a'] = a_init
L = L_init
flag = 3
while True:
if flag == 1:
print('Strain rate = {:g} extinct'.format(params['a']))
f0 /= f1
break
if flag == 2:
print('Strain rate = {:g} negative flame speed'.format(
params['a']))
#break
if flag == 3:
print('Strain rate = {:g} initialization'.format(params['a']))
solution = None
else:
print('Strain rate = {:g} success'.format(params['a']))
flame_name = fn.params2name(params)
solution = '{}.xml'.format(flame_name)
a_old = params['a']
L_old = L
f0_a = np.exp(f0)
L = L_old / np.power(f0_a, 0.5)
params['a'] = a_old * f0_a
a_diff = params['a'] - a_old
if params['a'] > a_max or a_diff < f2 * a_old:
break
flag = ctd.counterflow_premixed_flame(chemistry=chemistry,
fuel=fuel,
oxidizer=oxidizer,
temperature=T,
pressure=p,
phi=phi,
a=params['a'],
solution=solution,
width=L,
**kwargs)
os.chdir(pwd)
return
def counterflow_premixed_flame(chemistry='gri30.xml',
fuel={'CH4': 1.},
oxidizer={
'O2': 1,
'N2': 3.76
},
temperature=300.,
pressure=1.,
phi=1.,
a=1000.,
solution=None,
**kwargs):
# for unrealistic parameters
if pressure < 0.:
raise ValueError('Negative pressure')
if temperature < 0.:
raise ValueError('Negative inlet temperature')
if phi < 0.:
raise ValueError('Negative equivalence ratio')
# read kwargs
if 'transport' in kwargs.keys():
transport = kwargs['transport']
else:
transport = 'Mix'
if 'width' in kwargs.keys():
width = kwargs['width']
else:
width = 0.05
if 'loglevel' in kwargs.keys():
loglevel = kwargs['loglevel']
else:
# supress log output
loglevel = 0
# kwargs for flame solver
if 'ct_ratio' in kwargs.keys():
ct_ratio = kwargs['ct_ratio']
else:
ct_ratio = 2.
if 'ct_slope' in kwargs.keys():
ct_slope = kwargs['ct_slope']
else:
ct_slope = 0.02
if 'ct_curve' in kwargs.keys():
ct_curve = kwargs['ct_curve']
else:
ct_curve = 0.02
if 'ct_prune' in kwargs.keys():
ct_prune = kwargs['ct_prune']
else:
ct_prune = 0.01
if 'ct_max_grids' in kwargs.keys():
ct_max_grids = kwargs['ct_max_grids']
else:
ct_max_grids = 5000
# case name
params = {}
params['T'] = temperature
params['p'] = pressure
params['phi'] = phi
params['a'] = a
case = params2name(params)
# pressure
pressure *= ct.one_atm
# gas object
#gas = ct.Solution(chemistry)
# construct mixutre
#mixture = cg.mixture_two_streams(gas, fuel, oxidizer, phi)
# unburnt stream
#gas.TPX = temperature, pressure, mixture
gas = cg.mixture(chemistry, fuel, oxidizer, temperature, pressure, phi)
rho_u = gas.density
# burnt stream
gas.equilibrate('HP')
rho_b = gas.density
gas = cg.mixture(chemistry, fuel, oxidizer, temperature, pressure, phi)
# get inlet velocity based on the strain rate
# $a_1=\dfrac{2U_1}{L}\left(1+\dfrac{U_2\sqrt{\rho_2}}{U_1\sqrt{\rho_1}}\right)$
# $a_2=\dfrac{2U_2}{L}\left(1+\dfrac{U_1\sqrt{\rho_1}}{U_2\sqrt{\rho_2}}\right)$
# with $\rho_1 U_1^2 = \rho_2 U_2^2$
# $a_1=\dfrac{4U_1}{L}$ $a_2=\dfrac{4U_2}{L}$
# set stream 1 and 2 for unburnt and equilibrium status respectively
v_u = a * width / 4.0
v_b = np.sqrt(rho_u * np.square(v_u) / rho_b)
# mass rate
m_u = rho_u * v_u
m_b = rho_b * v_b
# Create flame object
f = ct.CounterflowPremixedFlame(gas=gas, width=width)
f.transport_model = transport
f.P = pressure
f.reactants.mdot = m_u
f.products.mdot = m_b
f.set_refine_criteria(ratio=ct_ratio,
slope=ct_slope,
curve=ct_curve,
prune=ct_prune)
f.set_max_grid_points(f.flame, ct_max_grids)
# load saved case if presented
if solution is not None:
f.restore(solution, loglevel=loglevel)
# scaling of saved solution
solution_width = f.grid[-1] - f.grid[0]
width_factor = width / solution_width
solution_a = 4. * f.u[0] / solution_width
a_factor = a / solution_a
normalized_grid = f.grid / solution_width
u_factor = a_factor * width_factor
# update solution initialization following Fiala & Sattelmayer
f.flame.grid = normalized_grid * width
f.set_profile('u', normalized_grid, f.u * u_factor)
f.set_profile('V', normalized_grid, f.V * a_factor)
f.set_profile('lambda', normalized_grid, f.L * np.square(a_factor))
f.reactants.mdot = m_u
f.products.mdot = m_b
else:
f.set_initial_guess()
f.solve(loglevel=loglevel, auto=True)
HRR = f.heat_release_rate
idx = HRR.argmax()
if HRR[idx] > 1000:
f.save('{}.xml'.format(case))
if f.u[idx] > 0:
return 0
else:
return 2
else:
return 1
def Ze(chemistry='FFCM-1.cti',
fuel={'CH4': 1.},
oxidizer={
'O2': 1.,
'N2': 3.76
},
T=300.,
p=1.,
phi=1.,
perturb=0.01,
**kwargs):
# working directory
pwd = os.getcwd()
# solution name
flame_params = {}
flame_params['T'] = T
flame_params['p'] = p
flame_params['phi'] = phi
flame_name = params2name(flame_params)
solution = '{}.xml'.format(flame_name)
# perturbation
factor = np.array([1. - perturb, 1., 1. + perturb])
# quantaties
flux = np.zeros(3)
Tb = np.zeros(3)
params = {}
for i, f in enumerate(factor):
# subfolder
params['N2'] = f
folder_name = params2name(params)
os.makedirs(folder_name, exist_ok=True)
os.chdir(folder_name)
if not os.path.isfile(solution):
# oxidizer stream with perturbation
stream = {}
for k, v in oxidizer.items():
stream[k] = v
stream['N2'] = oxidizer['N2'] * f
pc.driver.free_flame(chemistry, fuel, stream, T, p, phi, **kwargs)
fs = pc.flame.FreeFlameState(solution, chemistry, fuel, oxidizer)
flux[i] = fs.mass_flux()
Tb[i] = fs.flame.T[-1]
os.chdir(pwd)
grad = np.gradient(flux, Tb)
Ze = 2. * grad[1] * (Tb[1] - T) / flux[1]
return Ze