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144 | def flows_int_values(sv, i_fc, operating_inputs, parameters):
"""This functions calculates intermediate values for the flows calculation.
Parameters
----------
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.
i_fc : float
Current density of the fuel cell (A/m²).
parameters : dict
Parameters of the fuel cell model.
Returns
-------
Pagc : float
Global pressure in the anode gas channel (Pa).
Pcgc : float
Global pressure in the cathode gas channel (Pa).
lambda_acl_mem : float
Water content in the ACL and the membrane (kg/kg).
"""
# Extraction of the variables
C_v_acl, C_v_ccl = sv['C_v_acl'], sv['C_v_ccl']
s_acl, s_ccl = sv['s_acl'], sv['s_ccl']
lambda_acl, lambda_mem, lambda_ccl = sv['lambda_acl'], sv['lambda_mem'], sv['lambda_ccl']
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']
# Extraction of the operating inputs and the parameters
T_des = operating_inputs['T_des']
epsilon_gdl, epsilon_cl = parameters['epsilon_gdl'], parameters['epsilon_cl']
epsilon_mpl, epsilon_c = parameters['epsilon_mpl'], parameters['epsilon_c']
e, Hacl, Hccl, Hmem = parameters['e'], parameters['Hacl'], parameters['Hccl'], parameters['Hmem']
Hgdl, Hmpl, Wagc, Wcgc = parameters['Hgdl'], parameters['Hmpl'], parameters['Wagc'], parameters['Wcgc']
nb_gc, nb_gdl, nb_mpl = parameters['nb_gc'], parameters['nb_gdl'], parameters['nb_mpl']
# Transitory parameter
H_gdl_node = Hgdl / nb_gdl
H_mpl_node = Hmpl / nb_mpl
C_N2_a_mean = (sum(sv[f'C_N2_agc_{i}'] for i in range(1, nb_gc + 1)) / nb_gc)
C_N2_c_mean = (sum(sv[f'C_N2_cgc_{i}'] for i in range(1, nb_gc + 1)) / nb_gc)
# Pressures in the stack
Pagc = [None] + [(sv[f'C_v_agc_{i}'] + sv[f'C_H2_agc_{i}'] + sv[f'C_N2_agc_{i}']) * R * sv[f'T_agc_{i}'] for i in range(1, nb_gc + 1)]
Pagdl = [None] + [(sv[f'C_v_agdl_{i}'] + sv[f'C_H2_agdl_{i}'] + C_N2_a_mean) * R * sv[f'T_agdl_{i}'] for i in range(1, nb_gdl + 1)]
Pampl = [None] + [(sv[f'C_v_ampl_{i}'] + sv[f'C_H2_ampl_{i}'] + C_N2_a_mean) * R * sv[f'T_ampl_{i}'] for i in range(1, nb_mpl + 1)]
Pacl = (C_v_acl + C_H2_acl + C_N2_a_mean) * R * T_acl
Pccl = (C_v_ccl + C_O2_ccl + C_N2_c_mean) * R * T_ccl
Pcmpl = [None] + [(sv[f'C_v_cmpl_{i}'] + sv[f'C_O2_cmpl_{i}'] + C_N2_c_mean) * R * sv[f'T_cmpl_{i}'] for i in range(1, nb_mpl + 1)]
Pcgdl = [None] + [(sv[f'C_v_cgdl_{i}'] + sv[f'C_O2_cgdl_{i}'] + C_N2_c_mean) * R * sv[f'T_cgdl_{i}'] for i in range(1, nb_gdl + 1)]
Pcgc = [None] + [(sv[f'C_v_cgc_{i}'] + sv[f'C_O2_cgc_{i}'] + sv[f'C_N2_cgc_{i}']) * R * sv[f'T_cgc_{i}'] for i in range(1, nb_gc + 1)]
# Weighted mean values ...
# ... of the EOD flow of water in the membrane
J_EOD_acl_mem = 2.5 / 22 * i_fc / F * interpolate([lambda_acl, lambda_mem], [Hacl, Hmem])
J_EOD_mem_ccl = 2.5 / 22 * i_fc / F * interpolate([lambda_mem, lambda_ccl], [Hmem, Hccl])
# ... of the diffusion coefficient of water in the membrane
D_acl_mem = hmean([D(lambda_acl), D(lambda_mem)], weights = [Hacl / (Hacl + Hmem), Hmem / (Hacl + Hmem)])
D_mem_ccl = hmean([D(lambda_mem), D(lambda_ccl)], weights = [Hmem / (Hmem + Hccl), Hccl / (Hmem + Hccl)])
# ... of the capillary coefficient
D_cap_agdl_agdl = [None] + [hmean([Dcap('gdl', sv[f's_agdl_{i}'], sv[f'T_agdl_{i}'], epsilon_gdl, e,
epsilon_c=epsilon_c),
Dcap('gdl', sv[f's_agdl_{i+1}'], sv[f'T_agdl_{i+1}'], epsilon_gdl, e,
epsilon_c=epsilon_c)]) for i in range(1, nb_gdl)]
D_cap_agdl_ampl = hmean([Dcap('gdl', sv[f's_agdl_{nb_gdl}'], sv[f'T_agdl_{nb_gdl}'], epsilon_gdl, e,
epsilon_c=epsilon_c),
Dcap('mpl', sv['s_ampl_1'], sv['T_ampl_1'], epsilon_mpl, e)],
weights=[H_gdl_node / (H_gdl_node + H_mpl_node), H_mpl_node / (H_gdl_node + H_mpl_node)])
D_cap_ampl_ampl = [None] + [hmean([Dcap('mpl', sv[f's_ampl_{i}'], sv[f'T_ampl_{i}'], epsilon_mpl, e),
Dcap('mpl', sv[f's_ampl_{i+1}'], sv[f'T_ampl_{i+1}'], epsilon_mpl, e)])
for i in range(1, nb_mpl)]
D_cap_ampl_acl = hmean([Dcap('mpl', sv[f's_ampl_{nb_mpl}'], sv[f'T_ampl_{nb_mpl}'], epsilon_mpl, e),
Dcap('cl', s_acl, T_acl, epsilon_cl, e)],
weights=[H_mpl_node / (H_mpl_node + Hacl), Hacl / (H_mpl_node + Hacl)])
D_cap_ccl_cmpl = hmean([Dcap('cl', s_ccl, T_ccl, epsilon_cl, e),
Dcap('mpl', sv['s_cmpl_1'], sv['T_cmpl_1'], epsilon_mpl, e)],
weights=[Hccl / (Hccl + H_mpl_node), H_mpl_node / (Hccl + H_mpl_node)])
D_cap_cmpl_cmpl = [None] + [hmean([Dcap('mpl', sv[f's_cmpl_{i}'], sv[f'T_cmpl_{i}'], epsilon_mpl, e),
Dcap('mpl', sv[f's_cmpl_{i + 1}'], sv[f'T_cmpl_{i + 1}'], epsilon_mpl, e)])
for i in range(1, nb_mpl)]
D_cap_cmpl_cgdl = hmean([Dcap('mpl', sv[f's_cmpl_{nb_mpl}'], sv[f'T_cmpl_{nb_mpl}'], epsilon_mpl, e),
Dcap('gdl', sv['s_cgdl_1'], sv['T_cgdl_1'], epsilon_gdl, e,
epsilon_c=epsilon_c)],
weights=[H_mpl_node / (H_mpl_node + H_gdl_node), H_gdl_node / (H_mpl_node + H_gdl_node)])
D_cap_cgdl_cgdl = [None] + [hmean([Dcap('gdl', sv[f's_cgdl_{i}'], sv[f'T_cgdl_{i}'], epsilon_gdl, e,
epsilon_c=epsilon_c),
Dcap('gdl', sv[f's_cgdl_{i+1}'], sv[f'T_cgdl_{i+1}'], epsilon_gdl, e,
epsilon_c=epsilon_c)]) for i in range(1, nb_gdl)]
# ... of the effective diffusion coefficient
Da_eff_agdl_agdl = [None] + [hmean([Da_eff('gdl', sv[f's_agdl_{i}'], sv[f'T_agdl_{i}'], Pagdl[i],
epsilon_gdl, epsilon_c = epsilon_c),
Da_eff('gdl', sv[f's_agdl_{i+1}'], sv[f'T_agdl_{i+1}'], Pagdl[i+1],
epsilon_gdl, epsilon_c = epsilon_c)]) for i in range(1, nb_gdl)]
Da_eff_agdl_ampl = hmean([Da_eff('gdl', sv[f's_agdl_{nb_gdl}'], sv[f'T_agdl_{nb_gdl}'], Pagdl[nb_gdl],
epsilon_gdl, epsilon_c = epsilon_c),
Da_eff('mpl', sv['s_ampl_1'], sv['T_ampl_1'], Pampl[1], epsilon_mpl)],
weights = [H_gdl_node / (H_gdl_node + H_mpl_node), H_mpl_node / (H_gdl_node + H_mpl_node)])
Da_eff_ampl_ampl = [None] + [hmean([Da_eff('mpl', sv[f's_ampl_{i}'], sv[f'T_ampl_{i}'], Pampl[i],
epsilon_mpl),
Da_eff('mpl', sv[f's_ampl_{i+1}'], sv[f'T_ampl_{i+1}'], Pampl[i+1],
epsilon_mpl)]) for i in range(1, nb_mpl)]
Da_eff_ampl_acl = hmean([Da_eff('mpl', sv[f's_ampl_{nb_mpl}'], sv[f'T_ampl_{nb_mpl}'], Pampl[nb_mpl],
epsilon_mpl),
Da_eff('cl', s_acl, T_acl, Pacl, epsilon_cl)],
weights=[H_mpl_node / (H_mpl_node + Hacl), Hacl / (H_mpl_node + Hacl)])
Dc_eff_ccl_cmpl = hmean([Dc_eff('cl', s_ccl, T_ccl, Pccl, epsilon_cl),
Dc_eff('mpl', sv['s_cmpl_1'], sv['T_cmpl_1'], Pcmpl[1], epsilon_mpl)],
weights=[Hccl / (H_mpl_node + Hccl), H_mpl_node / (H_mpl_node + Hccl)])
Dc_eff_cmpl_cmpl = [None] + [hmean([Dc_eff('mpl', sv[f's_cmpl_{i}'], sv[f'T_cmpl_{i}'], Pcmpl[i],
epsilon_mpl),
Dc_eff('mpl', sv[f's_cmpl_{i + 1}'], sv[f'T_cmpl_{i + 1}'], Pcmpl[i + 1],
epsilon_mpl)]) for i in range(1, nb_mpl)]
Dc_eff_cmpl_cgdl = hmean([Dc_eff('mpl', sv[f's_cmpl_{nb_mpl}'], sv[f'T_cmpl_{nb_mpl}'], Pcmpl[nb_mpl],
epsilon_mpl),
Dc_eff('gdl', sv['s_cgdl_1'], sv['T_cgdl_1'], Pcgdl[1], epsilon_gdl,
epsilon_c=epsilon_c)],
weights=[H_mpl_node / (H_mpl_node + H_gdl_node), H_gdl_node / (H_mpl_node + H_gdl_node)])
Dc_eff_cgdl_cgdl = [None] + [hmean([Dc_eff('gdl', sv[f's_cgdl_{i}'], sv[f'T_cgdl_{i}'], Pcgdl[i],
epsilon_gdl, epsilon_c = epsilon_c),
Dc_eff('gdl', sv[f's_cgdl_{i+1}'], sv[f'T_cgdl_{i+1}'], Pcgdl[i+1],
epsilon_gdl, epsilon_c = epsilon_c)]) for i in range(1, nb_gdl)]
# ... of the temperature
T_acl_mem_ccl = average([T_acl, T_mem, T_ccl],
weights=[Hacl / (Hacl + Hmem + Hccl), Hmem / (Hacl + Hmem + Hccl), Hccl / (Hacl + Hmem + Hccl)])
return (H_gdl_node, H_mpl_node, Pagc, Pcgc, J_EOD_acl_mem, J_EOD_mem_ccl, D_acl_mem, D_mem_ccl,
D_cap_agdl_agdl, D_cap_agdl_ampl, D_cap_ampl_ampl, D_cap_ampl_acl, D_cap_ccl_cmpl, D_cap_cmpl_cmpl,
D_cap_cmpl_cgdl, D_cap_cgdl_cgdl, Da_eff_agdl_agdl, Da_eff_agdl_ampl, Da_eff_ampl_ampl, Da_eff_ampl_acl,
Dc_eff_ccl_cmpl, Dc_eff_cmpl_cmpl, Dc_eff_cmpl_cgdl, Dc_eff_cgdl_cgdl, T_acl_mem_ccl)
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