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260 | def auxiliaries(t, sv, control_variables, i_fc, Jv_agc_agdl, Jv_cgdl_cgc, J_H2_agc_agdl, J_O2_cgdl_cgc,
operating_inputs, parameters):
"""This function calculates the flows passing through the auxiliaries.
Parameters
----------
t : float
Time (s).
sv : dict
Variables calculated by the solver. They correspond to the fuel cell internal states.
control_variables : dict
Variables controlled by the user.
i_fc : float
Fuel cell current density at time t (A.m-2).
Jv_agc_agdl : list
Vapor flow between the AGC and the AGDL at each GC node (mol.m-2.s-1).
Jv_cgdl_cgc : list
Vapor flow between the CGDL and the CGC at each GC node (mol.m-2.s-1).
J_H2_agc_agdl : list
H2 flow between the AGC and the AGDL at each GC node (mol.m-2.s-1).
J_O2_cgdl_cgc : list
O2 flow between the CGDL and the CGC at each GC node (mol.m-2.s-1).
operating_inputs : dict
Operating inputs of the fuel cell.
parameters : dict
Parameters of the fuel cell model.
Returns
-------
Jv : dict
Vapor flow between the different layers (mol.m-2.s-1).
J_H2 : dict
Hydrogen flow between the different layers (mol.m-2.s-1).
J_O2 : dict
Oxygen flow between the different layers (mol.m-2.s-1).
J_N2 : dict
Nitrogen flow between the different layers (mol.m-2.s-1).
W : dict
Global flows through the auxiliaries (mol.s-1).
W_v : dict
Vapor flows through the auxiliaries (mol.s-1).
v_a_in : float
Velocity evolution at the inlet of the anode (m.s-1).
v_c_in : float
Velocity evolution at the inlet of the cathode (m.s-1).
Pa_in : float
Inlet pressure at the anode side (Pa).
Pc_in : float
Inlet pressure at the cathode side (Pa).
"""
# __________________________________________________Preliminaries___________________________________________________
# Extraction of the variables
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)
Wcp, Wa_inj, Wc_inj = sv.get('Wcp', None), sv.get('Wa_inj', None), sv.get('Wc_inj', None)
# Extraction of the operating inputs and the parameters
T_des, Phi_a_des, Phi_c_des = operating_inputs['T_des'], operating_inputs['Phi_a_des'], operating_inputs['Phi_c_des']
Sa, Sc, y_H2_in = operating_inputs['Sa'], operating_inputs['Sc'], operating_inputs['y_H2_in']
Aact, nb_cell, Hagc, Hcgc = parameters['Aact'], parameters['nb_cell'], parameters['Hagc'], parameters['Hcgc']
Wagc, Wcgc, nb_channel_in_gc = parameters['Wagc'], parameters['Wcgc'], parameters['nb_channel_in_gc']
A_T_a, A_T_c = parameters['A_T_a'], parameters['A_T_c']
nb_gc, type_auxiliary = parameters['nb_gc'], parameters['type_auxiliary']
# Intermediate values
# Commun intermediate values with dif_eq_modules.py which allows to avoid redundant calculations
P, Phi, y_H2, y_O2, M, rho, k_purge, Abp_a, Abp_c, mu_gaz, i_n = \
auxiliaries_int_values_which_are_commun_with_dif_eq(t, sv, operating_inputs, parameters)
v_a, v_c, Pa_in, Pc_in = calculate_velocity_evolution(sv, control_variables, i_fc, i_n, Jv_agc_agdl, Jv_cgdl_cgc, J_H2_agc_agdl,
J_O2_cgdl_cgc, operating_inputs, parameters, mu_gaz)
W_des = desired_flows(sv, control_variables, i_fc, i_n, Pa_in, Pc_in, operating_inputs, parameters)
# _________________________________________Inlet and outlet global flows____________________________________________
"""Global flows here refer to flows that integrate all the chemical species circulating together.
Slight differences are to be noted in the expression of these flows depending on the type of auxiliary selected.
"""
# Anode flow through the auxiliaries in mol.s-1
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# Wa_in = rho_asm_in_to_asm * v_a * A_T_a
# Wasm_to_asm_out = rho_asm_to_asm_out * v_a * Hagc * Wagc
# Wasm_out_to_agc = rho_asm_out_to_agc * v_a * Hagc * Wagc
# Wagc_to_aem_in = rho_agc_to_aem_in * v_a * Hagc * Wagc
# Waem_in_to_aem = rho_aem_in_to_aem * v_a * Hagc * Wagc
# if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation": # Attention: prévoir un débit minimal pour la pompe, comme les débits entrants.
# Ware = Maem_out_re * (Paem_out_re / (Paem_out_re - Phi_aem_out_re * Psat(T_des))) * \
# (Sa - 1) * i_fc / (2 * F) * (nb_cell * Aact) # The pump exactly compensates the pressure drop.
# Wasm_in_re_to_asm = rho_asm_in_re_to_asm * v_a * A_T_a
# Waem_to_aem_out_re = rho_aem_to_aem_out_re * v_a * A_T_a
# Waem_to_aem_out = k_purge * rho_aem_to_aem_out * v_a * A_T_a
# Wa_out = k_purge * rho_aem_out_to_ext * v_a * A_T_a
# else: # type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
# Ware = None
# Wasm_in_re_to_asm = None
# Waem_to_aem_out_re = None
# Waem_to_aem_out = rho_aem_to_aem_out * v_a * Abp_a
# Wa_out = rho_aem_out_to_ext * v_a * Abp_a
else: # elif type_auxiliary == "no_auxiliary" (only 1 cell):
Wa_in = W_des['H2'] + W_des['H2O_inj_a'] # This expression is also present in calculate_velocity_evolution.
Wa_out = P[f'agc_{nb_gc}'] / (R * T_des) * v_a[nb_gc] * Hagc * Wagc * nb_cell * nb_channel_in_gc
Ware, Wasm_to_agc, Wagc_to_aem = [None] * 3
# Anode flow entering/leaving the stack in mol.m-2.s-1
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# Ja_in = 0
# Ja_out = 0
else: # elif type_auxiliary == "no_auxiliary" (only 1 cell):
Ja_in = Wa_in / (Hagc * Wagc) / nb_cell / nb_channel_in_gc # This expression is also present in calculate_velocity_evolution.
Ja_out = Wa_out / (Hagc * Wagc) / nb_cell / nb_channel_in_gc
# Cathode flow through the auxiliaries in mol.s-1
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# Wc_in = rho_csm_in_to_csm * v_c * A_T_c
# Wcsm_to_csm_out = rho_csm_to_csm_out * v_c * Hcgc * Wcgc
# Wcsm_out_to_cgc = rho_csm_out_to_cgc * v_c * Hcgc * Wcgc
# Wcgc_to_cem_in = rho_cgc_to_cem_in * v_c * Hcgc * Wcgc
# Wcem_in_to_cem = rho_cem_in_to_cem * v_c * Hcgc * Wcgc
# Wcem_to_cem_out = rho_cem_to_cem_out * v_c * Abp_c
# Wc_out = rho_cem_out_to_ext * v_c * Abp_c
else: # elif type_auxiliary == "no_auxiliary" (only 1 cell):
Wc_in = W_des['dry_air'] + W_des['H2O_inj_c'] # This expression is also present in calculate_velocity_evolution.
Wc_out = P[f'cgc_{nb_gc}'] / (R * T_des) * v_c[nb_gc] * Hcgc * Wcgc * nb_cell * nb_channel_in_gc
Wcsm_to_cgc, Wcgc_to_cem = [None] * 2
# Cathode flow entering/leaving the stack in mol.m-2.s-1
Jc_in = Wc_in / (Hcgc * Wcgc) / nb_cell / nb_channel_in_gc # This expression is also present in calculate_velocity_evolution.
Jc_out = Wc_out / (Hcgc * Wcgc) / nb_cell / nb_channel_in_gc
# ________________________________________Inlet and outlet specific flows___________________________________________
"""Specific flows here refer to flows that integrate only a single chemical species within the ensemble of species
circulating together. For example, only the water vapor flow within the ensemble of hydrogen and water vapor.
"""
# Vapor flows at the GC (mol.m-2.s-1)
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# Jv_agc_in = Phi_asm * Psat(T_des) / Pasm * Ja_in
else: # elif type_auxiliary == "no_auxiliary":
Jv_agc_in = Phi_a_des * Psat(T_des) / Pa_in * Ja_in
Jv_agc_agc = [None] + [sv[f'C_v_agc_{i}'] * v_a[i] for i in range(1, nb_gc)]
Jv_agc_out = sv[f'C_v_agc_{nb_gc}'] * R * T_des / P[f'agc_{nb_gc}'] * Ja_out
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# Jv_cgc_in = Phi_csm * Psat(T_des) / Pcsm * Jc_in
else: # elif type_auxiliary == "no_auxiliary":
Jv_cgc_in = Phi_c_des * Psat(T_des) / Pc_in * Jc_in
Jv_cgc_cgc = [None] + [sv[f'C_v_cgc_{i}'] * v_c[i] for i in range(1, nb_gc)]
Jv_cgc_out = sv[f'C_v_cgc_{nb_gc}'] * R * T_des / P[f'cgc_{nb_gc}'] * Jc_out
# H2 flows at the GC (mol.m-2.s-1)
if type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# J_H2_agc_in = y_H2['asm_out'] * (1 - Phi_asm_out_to_agc * Psat(T_des) / Pasm_out_to_agc) * Ja_in
# J_H2_agc_agc = None
# J_H2_agc_out = y_H2_agc * (1 - Phi_agc_to_aem_in * Psat(T_des) / Pagc_to_aem_in) * Ja_out
else: # elif type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or type_auxiliary == "no_auxiliary":
J_H2_agc_in = (1 - Phi_a_des * Psat(T_des) / Pa_in) * Ja_in
J_H2_agc_agc = [None] + [sv[f'C_H2_agc_{i}'] * v_a[i] for i in range(1, nb_gc)]
J_H2_agc_out = sv[f'C_H2_agc_{nb_gc}'] * R * T_des / P[f'agc_{nb_gc}'] * Ja_out
# O2 flows at the GC (mol.m-2.s-1)
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# J_O2_cgc_in = y_O2_csm * (1 - Phi_csm * Psat(T_des) / Pcsm) * Jc_in
else: # elif type_auxiliary == "no_auxiliary":
J_O2_cgc_in = y_O2_ext * (1 - Phi_c_des * Psat(T_des) / Pc_in) * Jc_in
J_O2_cgc_cgc = [None] + [sv[f'C_O2_cgc_{i}'] * v_c[i] for i in range(1, nb_gc)]
J_O2_cgc_out = sv[f'C_O2_cgc_{nb_gc}'] * R * T_des / P[f'cgc_{nb_gc}'] * Jc_out
# N2 flows at the GC (mol.m-2.s-1)
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# J_N2_agc_in = (1 - y_H2['asm_out']) * (1 - Phi_asm_out_to_agc * Psat(T_des) / Pasm_out_to_agc) * Ja_in
# J_N2_agc_out = (1 - y_H2_agc) * (1 - Phi_agc_to_aem_in * Psat(T_des) / Pagc_to_aem_in) * Ja_out
# J_N2_cgc_in = (1 - y_O2_csm_out_to_cgc) * (1 - Phi_csm_out_to_cgc * Psat(T_des) / Pcsm_out_to_cgc) * Jc_in
# J_N2_cgc_out = (1 - y_O2_cgc_to_cem_in) * (1 - Phi_cgc_to_cem_in * Psat(T_des) / Pcgc_to_cem_in) * Jc_out
else: # elif type_auxiliary == "no_auxiliary":
J_N2_agc_in = 0
J_N2_agc_agc = [None] + [0] * (nb_gc - 1)
J_N2_agc_out = 0
J_N2_cgc_in = (1 - y_O2_ext) * (1 - Phi_c_des * Psat(T_des) / Pc_in) * Jc_in
J_N2_cgc_cgc = [None] + [sv[f'C_N2_cgc_{i}'] * v_c[i] for i in range(1, nb_gc)]
J_N2_cgc_out = sv[f'C_N2_cgc_{nb_gc}'] * R * T_des / P[f'cgc_{nb_gc}'] * Jc_out
# Vapor flows at the manifold (mol.s-1)
if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation" or \
type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
pass
# Wv_asm_in_to_asm = Phi_asm_in_to_asm * Psat(T_des) / Pasm_in_to_asm * Wa_in
# Wv_asm_to_asm_out = Phi_asm_to_asm_out * Psat(T_des) / Pasm_to_asm_out * Wasm_to_asm_out
# Wv_asm_out_to_agc = Phi_asm_out_to_agc * Psat(T_des) / Pasm_out_to_agc * Wasm_out_to_agc
# Wv_agc_to_aem_in = Phi_agc_to_aem_in * Psat(T_des) / Pagc_to_aem_in * Wagc_to_aem_in
# Wv_aem_in_to_aem = Phi_aem_in_to_aem * Psat(T_des) / Paem_in_to_aem * Waem_in_to_aem
# Wv_aem_to_aem_out = Phi_aem_to_aem_out * Psat(T_des) / Paem_to_aem_out * Waem_to_aem_out
# Wv_a_out = Phi_aem_out * Psat(T_des) / Paem_out * Wa_out
# if type_auxiliary == "forced-convective_cathode_with_anodic_recirculation":
# # At the anode side
# Wv_asm_ext_to_in = 0
# Wv_asm_in_re_to_asm = Phi_asm_in_re_to_asm * Psat(T_des) / Pasm_in_re_to_asm * Wasm_in_re_to_asm
# Wv_aem_to_aem_out_re = Phi_aem_to_aem_out_re * Psat(T_des) / Paem_to_aem_out_re * Waem_to_aem_out_re
# Wv_are = Phi_aem_out_re * Psat(T_des) / Paem_out_re * (Ware / M['aem_out_re']) # The pump exactly compensates the pressure drop.
# else: # type_auxiliary == "forced-convective_cathode_with_flow-through_anode":
# # At the anode side
# Wv_asm_ext_to_in = Wa_inj / M_H2O
# Wv_asm_in_re_to_asm = None
# Wv_aem_to_aem_out_re = None
# Wv_are = None
# # At the cathode side
# Wv_csm_ext_to_in = Phi_ext * Psat(Text) / Pext * (Wcp / M['ext']) + Wc_inj / M_H2O
# Wv_csm_in_to_csm = Phi_csm_in_to_csm * Psat(T_des) / Pcsm_in_to_csm * Wc_in
# Wv_csm_to_csm_out = Phi_csm_to_csm_out * Psat(T_des) / Pcsm_to_csm_out * Wcsm_to_csm_out
# Wv_csm_out_to_cgc = Phi_csm_out_to_cgc * Psat(T_des) / Pcsm_out_to_cgc * Wcsm_out_to_cgc
# Wv_cgc_to_cem_in = Phi_cgc_to_cem_in * Psat(T_des) / Pcgc_to_cem_in * Wcgc_to_cem_in
# Wv_cem_in_to_cem = Phi_cem_in_to_cem * Psat(T_des) / Pcem_in_to_cem * Wcem_in_to_cem
# Wv_cem_to_cem_out = Phi_cem_to_cem_out * Psat(T_des) / Pcem_to_cem_out * Wcem_to_cem_out
# Wv_c_out = Phi_cem_out * Psat(T_des) / Pcem_out * Wc_out
else: # elif type_auxiliary == "no_auxiliary":
Wv_are, Wv_a_in, Wv_asm_to_agc, Wv_agc_to_aem, Wv_a_out = [None] * 5
Wv_c_in, Wv_csm_to_cgc, Wv_cgc_to_cem, Wv_c_out = [None] * 4
return {'Jv': {'agc_in': Jv_agc_in, 'agc_agc': Jv_agc_agc, 'agc_out': Jv_agc_out,
'cgc_in': Jv_cgc_in, 'cgc_cgc': Jv_cgc_cgc, 'cgc_out': Jv_cgc_out},
'J_H2': {'agc_in': J_H2_agc_in, 'agc_agc': J_H2_agc_agc, 'agc_out': J_H2_agc_out},
'J_O2': {'cgc_in': J_O2_cgc_in, 'cgc_cgc': J_O2_cgc_cgc, 'cgc_out': J_O2_cgc_out},
'J_N2': {'agc_in': J_N2_agc_in, 'agc_agc': J_N2_agc_agc, 'agc_out': J_N2_agc_out,
'cgc_in': J_N2_cgc_in, 'cgc_cgc': J_N2_cgc_cgc, 'cgc_out': J_N2_cgc_out},
'W': {'are': Ware, 'a_in': Wa_in, 'asm_to_agc': Wasm_to_agc, 'agc_to_aem': Wagc_to_aem, 'a_out': Wa_out,
'c_in': Wc_in, 'csm_to_cgc': Wcsm_to_cgc, 'cgc_to_cem': Wcgc_to_cem, 'c_out': Wc_out},
'W_v': {'a_in': Wv_a_in, 'are': Wv_are, 'asm_to_agc': Wv_asm_to_agc, 'agc_to_aem': Wv_agc_to_aem,
'a_out': Wv_a_out, 'c_in': Wv_c_in, 'csm_to_cgc': Wv_csm_to_cgc, 'cgc_to_cem': Wv_cgc_to_cem,
'c_out': Wv_c_out},
'v_a_in': v_a[0], 'v_c_in': v_c[0], 'Pa_in': Pa_in, 'Pc_in': Pc_in}
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