Auxiliaries modules
This module is used to calculate intermediate values for the auxiliaries flows calculation.
auxiliaries_int_values(t, solver_variables, operating_inputs, parameters)
This functions calculates intermediate values for the auxiliaries flows calculation.
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Source code in modules/auxiliaries_modules.py
def auxiliaries_int_values(t, solver_variables, operating_inputs, parameters):
"""This functions calculates intermediate values for the auxiliaries flows calculation.
Parameters
----------
t : float
Time (s).
solver_variables : dict
Variables calculated by the solver. They correspond to the fuel cell internal states.
operating_inputs : dict
Operating inputs of the fuel cell.
parameters : dict
Parameters of the fuel cell model.
Returns
-------
Mext : float
Molar mass of the ambient air outside the stack (kg/mol).
Pagc : float
Global pressure in the anode gas channel (Pa).
Pcgc : float
Global pressure in the cathode gas channel (Pa).
Phi_agc : float
Relative humidity in the anode gas channel.
Phi_cgc : float
Relative humidity in the cathode gas channel.
y_cgc : float
Oxygen ratio in dry air in the cathode gas channel.
Magc : float
Molar mass of all the gas species in the anode gas channel (kg/mol).
Mcgc : float
Molar mass of all the gas species in the cathode gas channel (kg/mol).
Pr_aem : float
Pressure ratio in the anode external manifold.
Pr_cem : float
Pressure ratio in the cathode external manifold.
Maem : float
Molar mass of all the gas species in the anode external manifold (kg/mol).
Masm : float
Molar mass of all the gas species in the anode supply manifold (kg/mol).
Mcem : float
Molar mass of all the gas species in the cathode external manifold (kg/mol).
Mcsm : float
Molar mass of all the gas species in the cathode supply manifold (kg/mol).
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).
i_n : float
Internal current density (A/m²).
"""
# Extraction of the variables
C_v_agc, C_v_cgc = solver_variables['C_v_agc'], solver_variables['C_v_cgc']
lambda_mem = solver_variables['lambda_mem']
C_H2_agc, C_H2_acl = solver_variables['C_H2_agc'], solver_variables['C_H2_acl']
C_N2, C_O2_ccl, C_O2_cgc = solver_variables['C_N2'], solver_variables['C_O2_ccl'], solver_variables['C_O2_cgc']
Pasm, Paem, Pcsm = solver_variables['Pasm'], solver_variables['Paem'], solver_variables['Pcsm']
Pcem, Phi_asm, Phi_aem = solver_variables['Pcem'], solver_variables['Phi_asm'], solver_variables['Phi_aem']
Phi_csm, Phi_cem = solver_variables['Phi_csm'], solver_variables['Phi_cem']
Abp_a, Abp_c = solver_variables['Abp_a'], solver_variables['Abp_c']
# Extraction of the operating inputs and the parameters
Tfc, Pa_des, Pc_des = operating_inputs['Tfc'], operating_inputs['Pa_des'], operating_inputs['Pc_des']
Hmem, kappa_co = parameters['Hmem'], parameters['kappa_co']
t_purge, type_purge = parameters['t_purge'], parameters['type_purge']
# Molar mass of the ambient air
Mext = Phi_ext * Psat(Text) / Pext * M_H2O + \
yO2_ext * (1 - Phi_ext * Psat(Text) / Pext) * M_O2 + \
(1 - yO2_ext) * (1 - Phi_ext * Psat(Text) / Pext) * M_N2
# Physical quantities inside the stack
# Pressures
Pagc = (C_v_agc + C_H2_agc) * R * Tfc
Pcgc = (C_v_cgc + C_O2_cgc + C_N2) * R * Tfc
# Humidities
Phi_agc = C_v_agc / C_v_sat(Tfc)
Phi_cgc = C_v_cgc / C_v_sat(Tfc)
# Oxygen ratio in dry air
y_cgc = C_O2_cgc / (C_O2_cgc + C_N2)
# Molar masses
Magc = C_v_agc * R * Tfc / Pagc * M_H2O + \
C_H2_agc * R * Tfc / Pagc * M_H2
Mcgc = Phi_cgc * Psat(Tfc) / Pcgc * M_H2O + \
y_cgc * (1 - Phi_cgc * Psat(Tfc) / Pcgc) * M_O2 + \
(1 - y_cgc) * (1 - Phi_cgc * Psat(Tfc) / Pcgc) * M_N2
# Internal current density
i_H2 = 2 * F * R * Tfc / Hmem * C_H2_acl * k_H2(lambda_mem, Tfc, kappa_co)
i_O2 = 4 * F * R * Tfc / Hmem * C_O2_ccl * k_O2(lambda_mem, Tfc, 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":
# Pressure ratios
Pr_aem = (Pext / Paem)
Pr_cem = (Pext / Pcem)
# Oxygen ratio in dry air
y_cem = (Pcem - Phi_cem * Psat(Tfc) - C_N2 * R * Tfc) / (Pcem - Phi_cem * Psat(Tfc))
# Molar masses
Maem = Phi_aem * Psat(Tfc) / Paem * M_H2O + \
(1 - Phi_aem * Psat(Tfc) / Paem) * M_H2
Masm = Phi_asm * Psat(Tfc) / Pasm * M_H2O + \
(1 - Phi_asm * Psat(Tfc) / Pasm) * M_H2
Mcem = Phi_cem * Psat(Tfc) / Pcem * M_H2O + \
y_cem * (1 - Phi_cem * Psat(Tfc) / Pcem) * M_O2 + \
(1 - y_cem) * (1 - Phi_cem * Psat(Tfc) / Pcem) * M_N2
Mcsm = Phi_csm * Psat(Tfc) / Pcsm * M_H2O + \
yO2_ext * (1 - Phi_csm * Psat(Tfc) / Pcsm) * M_O2 + \
(1 - yO2_ext) * (1 - Phi_csm * Psat(Tfc) / Pcsm) * M_N2
# 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:
Abp_a = A_T
elif Abp_a < 0:
Abp_a = 0
if Abp_c > A_T:
Abp_c = A_T
elif Abp_c < 0:
Abp_c = 0
else: # parameters["type_auxiliary"] == "no_auxiliary"
Pr_aem, Pr_cem, Maem, Masm, Mcem, Mcsm, k_purge, Abp_a, Abp_c = [0] * 9
return (Mext, Pagc, Pcgc, Phi_agc, Phi_cgc, y_cgc, Magc, Mcgc, Pr_aem, Pr_cem, Maem, Masm, Mcem, Mcsm,
k_purge, Abp_a, Abp_c, i_n)