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162 | def heat_transfer_int_values(sv, parameters):
"""This functions calculates intermediate values for the heat 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.
parameters : dict
Parameters of the fuel cell model.
Returns
-------
k_th_eff_agc_agdl : float
Effective thermal diffusivity between the AGC and the first GDL layer (J.m-1.s-1.K-1).
k_th_eff_agdl_agdl : list of floats
List of effective thermal diffusivities between adjacent GDL layers on the anode side (J.m-1.s-1.K-1).
k_th_eff_agdl_atl : float
Effective thermal diffusivity between the last GDL layer and the anode transport layer (J.m-1.s-1.K-1).
k_th_eff_atl_atl : list
List of effective thermal diffusivities between adjacent transport layers on the anode side (J.m-1.s-1.K-1).
k_th_eff_atl_ampl : float
Effective thermal diffusivity between the anode transport layer and the first microporous layer (J.m-1.s-1.K-1).
k_th_eff_ampl_ampl : list of floats
List of effective thermal diffusivities between adjacent microporous layers on the anode side (J.m-1.s-1.K-1).
k_th_eff_ampl_acl : float
Effective thermal diffusivity between the anode microporous layer and the anode catalyst layer (J.m-1.s-1.K-1).
k_th_eff_acl_mem : float
Effective thermal diffusivity between the anode catalyst layer and the membrane (J.m-1.s-1.K-1).
k_th_eff_mem_ccl : float
Effective thermal diffusivity between the membrane and the cathode catalyst layer (J.m-1.s-1.K-1).
k_th_eff_ccl_cmpl : float
Effective thermal diffusivity between the cathode catalyst layer and the cathode microporous layer (J.m-1.s-1.K-1).
k_th_eff_cmpl_cmpl : list of floats
List of effective thermal diffusivities between adjacent microporous layers on the cathode side (J.m-1.s-1.K-1).
k_th_eff_cmpl_ctl : float
Effective thermal diffusivity between the last microporous layer and the cathode transport layer (J.m-1.s-1.K-1).
k_th_eff_ctl_ctl : list of floats
List of effective thermal diffusivities between adjacent transport layers on the cathode side (J.m-1.s-1.K-1).
k_th_eff_ctl_cgdl : float
Effective thermal diffusivity between the cathode transport layer and the first GDL layer (J.m-1.s-1.K-1).
k_th_eff_cgdl_cgdl : list of floats
List of effective thermal diffusivities between adjacent GDL layers on the cathode side (J.m-1.s-1.K-1).
k_th_eff_cgdl_cgc : float
Effective thermal diffusivity between the last GDL layer and the CGC (J.m-1.s-1.K-1).
"""
# 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
Hgdl, Hmpl, Hacl, Hccl = parameters['Hgdl'], parameters['Hmpl'], parameters['Hacl'], parameters['Hccl']
Hmem, epsilon_mc, epsilon_gdl = parameters['Hmem'], parameters['epsilon_mc'], parameters['epsilon_gdl']
epsilon_cl, epsilon_mpl = parameters['epsilon_cl'], parameters['epsilon_mpl']
epsilon_c, nb_gc, nb_gdl, nb_mpl = parameters['epsilon_c'], parameters['nb_gc'], parameters['nb_gdl'], parameters['nb_mpl']
# Calculation of intermediate values
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)
Hgdl_node = Hgdl / nb_gdl
Hmpl_node = Hmpl / nb_mpl
# Weighted harmonic means of the effective thermal diffusivity
k_th_eff_agc_agdl = k_th_eff('agdl', sv[f'T_agdl_{1}'], C_v=sv[f'C_v_agdl_{1}'], s=sv[f's_agdl_{1}'],
C_H2=sv[f'C_H2_agdl_{1}'], C_N2=C_N2_a_mean, epsilon=epsilon_gdl, epsilon_c=epsilon_c)
k_th_eff_agdl_agdl = [None] + [hmean([k_th_eff('agdl', sv[f'T_agdl_{i}'], C_v=sv[f'C_v_agdl_{i}'],
s=sv[f's_agdl_{i}'], C_H2=sv[f'C_H2_agdl_{i}'], C_N2=C_N2_a_mean, epsilon=epsilon_gdl,
epsilon_c=epsilon_c),
k_th_eff('agdl', sv[f'T_agdl_{i + 1}'], C_v=sv[f'C_v_agdl_{i + 1}'],
s=sv[f's_agdl_{i + 1}'], C_H2=sv[f'C_H2_agdl_{i + 1}'], C_N2=C_N2_a_mean,
epsilon=epsilon_gdl, epsilon_c=epsilon_c)])
for i in range(1, nb_gdl)]
k_th_eff_agdl_ampl = hmean([k_th_eff('agdl', sv[f'T_agdl_{nb_gdl}'], C_v=sv[f'C_v_agdl_{nb_gdl}'],
s=sv[f's_agdl_{nb_gdl}'], C_H2=sv[f'C_H2_agdl_{nb_gdl}'], C_N2=C_N2_a_mean,
epsilon=epsilon_gdl, epsilon_c=epsilon_c),
k_th_eff('ampl', sv[f'T_ampl_{1}'], C_v=sv[f'C_v_ampl_{1}'],
s=sv[f's_ampl_{1}'], C_H2=sv[f'C_H2_ampl_{1}'], C_N2=C_N2_a_mean,
epsilon=epsilon_mpl)],
weights=[Hgdl_node / 2, Hmpl_node / 2])
k_th_eff_ampl_ampl = [None] + [hmean([k_th_eff('ampl', sv[f'T_ampl_{i}'], C_v=sv[f'C_v_ampl_{i}'],
s=sv[f's_ampl_{i}'], C_H2=sv[f'C_H2_ampl_{i}'], C_N2=C_N2_a_mean,
epsilon=epsilon_mpl),
k_th_eff('ampl', sv[f'T_ampl_{i + 1}'], C_v=sv[f'C_v_ampl_{i + 1}'],
s=sv[f's_ampl_{i + 1}'], C_H2=sv[f'C_H2_ampl_{i + 1}'], C_N2=C_N2_a_mean,
epsilon=epsilon_mpl)])
for i in range(1, nb_mpl)]
k_th_eff_ampl_acl = hmean([k_th_eff('ampl', sv[f'T_ampl_{nb_mpl}'], C_v=sv[f'C_v_ampl_{nb_mpl}'],
s=sv[f's_ampl_{nb_mpl}'], C_H2=sv[f'C_H2_ampl_{nb_mpl}'],
C_N2=C_N2_a_mean, epsilon=epsilon_mpl),
k_th_eff('acl', T_acl, C_v=C_v_acl, s=s_acl, lambdaa=lambda_acl,
C_H2=C_H2_acl, C_N2=C_N2_a_mean, epsilon=epsilon_cl, epsilon_mc=epsilon_mc)],
weights=[Hmpl_node / 2, Hacl / 2])
k_th_eff_acl_mem = hmean([k_th_eff('acl', T_acl, C_v=C_v_acl, s=s_acl, lambdaa=lambda_acl,
C_H2=C_H2_acl, C_N2=C_N2_a_mean, epsilon=epsilon_cl, epsilon_mc=epsilon_mc),
k_th_eff('mem', T_mem, lambdaa=lambda_mem)],
weights=[Hacl / 2, Hmem / 2])
k_th_eff_mem_ccl = hmean([k_th_eff('mem', T_mem, lambdaa=lambda_mem),
k_th_eff('ccl', T_ccl, C_v=C_v_ccl, s=s_ccl, lambdaa=lambda_ccl,
C_O2=C_O2_ccl, C_N2=C_N2_c_mean, epsilon=epsilon_cl, epsilon_mc=epsilon_mc)],
weights=[Hmem / 2, Hccl / 2])
k_th_eff_ccl_cmpl = hmean([k_th_eff('ccl', T_ccl, C_v=C_v_ccl, s=s_ccl, lambdaa=lambda_ccl, C_O2=C_O2_ccl,
C_N2=C_N2_c_mean, epsilon=epsilon_cl, epsilon_mc=epsilon_mc),
k_th_eff('cmpl', sv[f'T_cmpl_{1}'], C_v=sv[f'C_v_cmpl_{1}'],
s=sv[f's_cmpl_{1}'], C_O2=sv[f'C_O2_cmpl_{1}'], C_N2=C_N2_c_mean,
epsilon=epsilon_mpl)],
weights=[Hccl / 2, Hmpl_node / 2])
k_th_eff_cmpl_cmpl = [None] + [hmean([k_th_eff('cmpl', sv[f'T_cmpl_{i}'], C_v=sv[f'C_v_cmpl_{i}'],
s=sv[f's_cmpl_{i}'], C_O2=sv[f'C_O2_cmpl_{i}'], C_N2=C_N2_c_mean,
epsilon=epsilon_mpl),
k_th_eff('cmpl', sv[f'T_cmpl_{i + 1}'], C_v=sv[f'C_v_cmpl_{i + 1}'],
s=sv[f's_cmpl_{i + 1}'], C_O2=sv[f'C_O2_cmpl_{i + 1}'], C_N2=C_N2_c_mean,
epsilon=epsilon_mpl)])
for i in range(1, nb_mpl)]
k_th_eff_cmpl_cgdl = hmean([k_th_eff('cmpl', sv[f'T_cmpl_{nb_mpl}'], C_v=sv[f'C_v_cmpl_{nb_mpl}'],
s=sv[f's_cmpl_{nb_mpl}'], C_O2=sv[f'C_O2_cmpl_{nb_mpl}'], C_N2=C_N2_c_mean,
epsilon=epsilon_mpl),
k_th_eff('cgdl', sv['T_cgdl_1'], C_v=sv['C_v_cgdl_1'], s=sv['s_cgdl_1'],
C_O2=sv[f'C_O2_cgdl_1'], C_N2=C_N2_c_mean, epsilon=epsilon_gdl,
epsilon_c=epsilon_c)],
weights=[Hmpl_node / 2, Hgdl_node / 2])
k_th_eff_cgdl_cgdl = [None] + [hmean([k_th_eff('cgdl', sv[f'T_cgdl_{i}'], C_v=sv[f'C_v_cgdl_{i}'],
s=sv[f's_cgdl_{i}'], C_O2=sv[f'C_O2_cgdl_{i}'], C_N2=C_N2_c_mean,
epsilon=epsilon_gdl, epsilon_c=epsilon_c),
k_th_eff('cgdl', sv[f'T_cgdl_{i + 1}'], C_v=sv[f'C_v_cgdl_{i + 1}'],
s=sv[f's_cgdl_{i + 1}'], C_O2=sv[f'C_O2_cgdl_{i + 1}'], C_N2=C_N2_c_mean,
epsilon=epsilon_gdl, epsilon_c=epsilon_c)])
for i in range(1, nb_gdl)]
k_th_eff_cgdl_cgc = k_th_eff('cgdl', sv[f'T_cgdl_{nb_gdl}'], C_v=sv[f'C_v_cgdl_{nb_gdl}'],
s=sv[f's_cgdl_{nb_gdl}'], C_O2=sv[f'C_O2_cgdl_{nb_gdl}'], C_N2=C_N2_c_mean, epsilon=epsilon_gdl,
epsilon_c=epsilon_c)
return (Hgdl_node, Hmpl_node, k_th_eff_agc_agdl, k_th_eff_agdl_agdl, k_th_eff_agdl_ampl, k_th_eff_ampl_ampl,
k_th_eff_ampl_acl, k_th_eff_acl_mem, k_th_eff_mem_ccl, k_th_eff_ccl_cmpl, k_th_eff_cmpl_cmpl,
k_th_eff_cmpl_cgdl, k_th_eff_cgdl_cgdl, k_th_eff_cgdl_cgc)
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