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184 | def auxiliaries_int_values_which_are_commun_with_dif_eq(t, sv, operating_inputs, parameters):
"""This functions calculates intermediate values for the auxiliaries flows calculation.
Parameters
----------
t : float
Time (s).
sv : dict
Variables calculated by the solver. They correspond to the fuel cell internal states.
sv is a contraction of solver_variables for enhanced readability.
operating_inputs : dict
Operating inputs of the fuel cell model.
parameters : dict
Parameters of the fuel cell model.
Returns
-------
k_purge : float
Purge coefficient. It is equal to 1 if the purge is active and 0 otherwise.
Abp_a : float
Area of the back pressure valve in the anode external manifold (m²).
Abp_c : float
Area of the back pressure valve in the cathode external manifold (m²).
"""
# Extraction of the variables
lambda_mem = sv['lambda_mem']
C_H2_acl, C_O2_ccl = sv['C_H2_acl'], sv['C_O2_ccl']
T_acl, T_mem, T_ccl = sv['T_acl'], sv['T_mem'], sv['T_ccl']
Pasm, Paem, Pcsm, Pcem = sv.get('Pasm', None), sv.get('Paem', None), sv.get('Pcsm', None), sv.get('Pcem', None)
Phi_asm, Phi_aem = sv.get('Phi_asm', None), sv.get('Phi_aem', None)
Phi_csm, Phi_cem = sv.get('Phi_csm', None), sv.get('Phi_cem', None)
Abp_a, Abp_c = sv.get('Abp_a', None), sv.get('Abp_c', None)
# Extraction of the operating inputs and the parameters
T_des, y_H2_in, Pa_des = operating_inputs['T_des'], operating_inputs['y_H2_in'], operating_inputs['Pa_des']
Hmem, Hacl, Hccl = parameters['Hmem'], parameters['Hacl'], parameters['Hccl']
Lgc, A_T_a, A_T_c = parameters['Lgc'], parameters['A_T_a'], parameters['A_T_c']
kappa_co, nb_gc, t_purge, type_purge = parameters['kappa_co'], parameters['nb_gc'], parameters['t_purge'], parameters['type_purge']
# Physical quantities outside the stack
# Molar masses
M = {}
M['ext'] = Phi_ext * Psat(Text) / Pext * M_H2O + \
y_O2_ext * (1 - Phi_ext * Psat(Text) / Pext) * M_O2 + \
(1 - y_O2_ext) * (1 - Phi_ext * Psat(Text) / Pext) * M_N2
M['H2_N2_in'] = y_H2_in * M_H2 + (1 - y_H2_in) * M_N2
# Physical quantities inside the stack
# Pressures
P = {}
for i in range(1, nb_gc + 1):
P[f'agc_{i}'] = (sv[f'C_v_agc_{i}'] + sv[f'C_H2_agc_{i}'] + sv[f'C_N2_agc_{i}']) * R * sv[f'T_agc_{i}']
P[f'cgc_{i}'] = (sv[f'C_v_cgc_{i}'] + sv[f'C_O2_cgc_{i}'] + sv[f'C_N2_cgc_{i}']) * R * sv[f'T_cgc_{i}']
# Humidities
Phi = {}
for i in range(1, nb_gc + 1):
Phi[f'agc_{i}'] = sv[f'C_v_agc_{i}'] / C_v_sat(sv[f'T_agc_{i}'])
Phi[f'cgc_{i}'] = sv[f'C_v_cgc_{i}'] / C_v_sat(sv[f'T_cgc_{i}'])
# H2/O2 ratio in the dry anode/cathode gas mixture (H2/N2 or O2/N2) at the GC
y_O2 = {}
y_H2 = {}
for i in range(1, nb_gc + 1):
y_H2[f'agc_{i}'] = sv[f'C_H2_agc_{i}'] / (sv[f'C_H2_agc_{i}'] + sv[f'C_N2_agc_{i}'])
y_O2[f'cgc_{i}'] = sv[f'C_O2_cgc_{i}'] / (sv[f'C_O2_cgc_{i}'] + sv[f'C_N2_cgc_{i}'])
# Molar masses
for i in range(1, nb_gc + 1):
M[f'agc_{i}'] = sv[f'C_v_agc_{i}'] * R * T_des / P[f'agc_{i}'] * M_H2O + \
sv[f'C_H2_agc_{i}'] * R * T_des / P[f'agc_{i}'] * M_H2 + \
sv[f'C_N2_agc_{i}'] * R * T_des / P[f'agc_{i}'] * M_N2
M[f'cgc_{i}'] = Phi[f'cgc_{i}'] * Psat(T_des) / P[f'cgc_{i}'] * M_H2O + \
y_O2[f'cgc_{i}'] * (1 - Phi[f'cgc_{i}'] * Psat(T_des) / P[f'cgc_{i}']) * M_O2 + \
(1 - y_O2[f'cgc_{i}']) * (1 - Phi[f'cgc_{i}'] * Psat(T_des) / P[f'cgc_{i}']) * M_N2
# Density of the gas mixture.
rho = {}
for i in range(1, nb_gc + 1):
rho[f'agc_{i}'] = P[f'agc_{i}'] / (R * sv[f'T_agc_{i}']) * M[f'agc_{i}']
rho[f'cgc_{i}'] = P[f'cgc_{i}'] / (R * sv[f'T_cgc_{i}']) * M[f'cgc_{i}']
# Vapor ratio over the gas mixture.
x_H2O_v = {}
for i in range(1, nb_gc + 1):
x_H2O_v[f'agc_{i}'] = sv[f'C_v_agc_{i}'] / (sv[f'C_v_agc_{i}'] + sv[f'C_H2_agc_{i}'] + sv[f'C_N2_agc_{i}'])
for i in range(1, nb_gc + 1):
x_H2O_v[f'cgc_{i}'] = sv[f'C_v_cgc_{i}'] / (sv[f'C_v_cgc_{i}'] + sv[f'C_O2_cgc_{i}'] + sv[f'C_N2_cgc_{i}'])
# Dynamic viscosity of the gas mixture.
mu_gaz = {}
for i in range(1, nb_gc + 1):
mu_gaz[f'agc_{i}'] = mu_mixture_gases(['H2O_v', 'H2'], [x_H2O_v[f'agc_{i}'], 1 - x_H2O_v[f'agc_{i}']],
sv[f'T_agc_{i}'])
for i in range(1, nb_gc + 1):
mu_gaz[f'cgc_{i}'] = mu_mixture_gases(['H2O_v', 'O2', 'N2'],
[x_H2O_v[f'cgc_{i}'], y_O2[f'cgc_{i}'] * (1 - x_H2O_v[f'cgc_{i}']),
(1 - y_O2[f'cgc_{i}']) * (1 - x_H2O_v[f'cgc_{i}'])],
sv[f'T_cgc_{i}'])
# The crossover current density i_n
T_acl_mem_ccl = average([T_acl, T_mem, T_ccl],
weights=[Hacl / (Hacl + Hmem + Hccl), Hmem / (Hacl + Hmem + Hccl),
Hccl / (Hacl + Hmem + Hccl)])
i_H2 = 2 * F * R * T_acl_mem_ccl / Hmem * C_H2_acl * k_H2(lambda_mem, T_mem, kappa_co)
i_O2 = 4 * F * R * T_acl_mem_ccl / Hmem * C_O2_ccl * k_O2(lambda_mem, T_mem, kappa_co)
i_n = i_H2 + i_O2
# Physical quantities in the auxiliary system
if parameters["type_auxiliary"] == "forced-convective_cathode_with_anodic_recirculation" or \
parameters["type_auxiliary"] == "forced-convective_cathode_with_flow-through_anode":
pass
# # H2/O2 ratio in the dry anode/cathode gas mixture (H2/N2 or O2/N2) at the EM
# y_H2_aem = (Paem - Phi_aem * Psat(T_des) - C_N2_a * R * T_des) / (Paem - Phi_aem * Psat(T_des))
# y_O2_cem = (Pcem - Phi_cem * Psat(T_cgc) - C_N2_c * R * T_cgc) / (Pcem - Phi_cem * Psat(T_cgc))
#
# # Molar masses
# if parameters["type_auxiliary"] == "forced-convective_cathode_with_anodic_recirculation":
# Masm = Phi_asm * Psat(T_des) / Pasm * M_H2O + \
# (1 - Phi_asm * Psat(T_des) / Pasm) * M_H2
# Maem = Phi_aem * Psat(T_des) / Paem * M_H2O + \
# (1 - Phi_aem * Psat(T_des) / Paem) * M_H2
# else: # parameters["type_auxiliary"] == "forced-convective_cathode_with_flow-through_anode":
# Masm = Phi_asm * Psat(T_des) / Pasm * M_H2O + \
# y_H2_in * (1 - Phi_asm * Psat(T_des) / Pasm) * M_H2 + \
# (1 - y_H2_in) * (1 - Phi_asm * Psat(T_des) / Pasm) * M_N2
# Maem = Phi_aem * Psat(T_des) / Paem * M_H2O + \
# y_H2_aem * (1 - Phi_aem * Psat(T_des) / Paem) * M_H2 + \
# (1 - y_H2_aem) * (1 - Phi_aem * Psat(T_des) / Paem) * M_N2
# # Molar masses at the cathode side
# Mcsm = Phi_csm * Psat(T_des) / Pcsm * M_H2O + \
# y_O2_ext * (1 - Phi_csm * Psat(T_des) / Pcsm) * M_O2 + \
# (1 - y_O2_ext) * (1 - Phi_csm * Psat(T_des) / Pcsm) * M_N2
# Mcem = Phi_cem * Psat(T_des) / Pcem * M_H2O + \
# y_O2_cem * (1 - Phi_cem * Psat(T_des) / Pcem) * M_O2 + \
# (1 - y_O2_cem) * (1 - Phi_cem * Psat(T_des) / Pcem) * M_N2
#
# # Density of the gas mixture.
# rho_asm = Pasm / (R * T_des) * Masm
# rho_aem = Paem / (R * T_des) * Maem
# rho_csm = Pcsm / (R * T_des) * Mcsm
# rho_cgc = Pcgc / (R * T_cgc) * Mcgc
# rho_cem = Pcem / (R * T_cgc) * Mcem
#
# # Purge
# if type_purge == "no_purge":
# k_purge = 0
# elif type_purge == "constant_purge":
# k_purge = 1
# elif type_purge == "periodic_purge":
# purge_time, delta_purge = t_purge
# if (t - int(t / (purge_time + delta_purge)) * (purge_time + delta_purge)) <= purge_time:
# k_purge = 1
# else:
# k_purge = 0
# else:
# raise ValueError("The type_purge variable should be correctly referenced.")
# # Back pressure valve area
# if Abp_a > A_T_a:
# Abp_a = A_T_a
# elif Abp_a < 0:
# Abp_a = 0
# if Abp_c > A_T_c:
# Abp_c = A_T_c
# elif Abp_c < 0:
# Abp_c = 0
else: # parameters["type_auxiliary"] == "no_auxiliary"
k_purge, Abp_a, Abp_c = [None] * 3
return P, Phi, y_H2, y_O2, M, rho, k_purge, Abp_a, Abp_c, mu_gaz, i_n
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