Settings modules

This modul contains some of the required functions for the settings.

EIS_parameters(f_EIS)

This function gives the time parameters for the EIS_current density function.

Parameters:
  • f_EIS (tuple) –

    EIS parameters. It is a tuple containing the power of the initial frequency 'f_power_min_EIS': f_min_EIS = 10**f_power_min_EIS, the power of the final frequency 'f_power_max_EIS', the number of frequencies tested 'nb_f_EIS' and the number of points calculated per specific period 'nb_points_EIS'.
Returns:
  • t_EIS( tuple ) –

    EIS parameters. It is a tuple containing the initial EIS time after stack equilibrium 't0_EIS', a list of time parameters which gives the beginning of each frequency change 't_new_start_EIS', the final time 'tf_EIS', a list of time parameters which gives the estimated time for reaching equilibrium at each frequency 'delta_t_break_EIS', and a list of time parameters which gives the estimated time for measuring the voltage response at each frequency 'delta_t_measurement_EIS'.
Source code in modules/settings_modules.py 
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def EIS_parameters(f_EIS):
    """This function gives the time parameters for the EIS_current density function.

    Parameters
    ----------
    f_EIS : tuple
        EIS parameters. It is a tuple containing the power of the initial frequency 'f_power_min_EIS':
        f_min_EIS = 10**f_power_min_EIS, the power of the final frequency 'f_power_max_EIS', the number of frequencies
        tested 'nb_f_EIS' and the number of points calculated per specific period 'nb_points_EIS'.

    Returns
    -------
    t_EIS : tuple
        EIS parameters. It is a tuple containing the initial EIS time after stack equilibrium 't0_EIS', a list of time
        parameters which gives the beginning of each frequency change 't_new_start_EIS', the final time 'tf_EIS', a list
        of time parameters which gives the estimated time for reaching equilibrium at each frequency
        'delta_t_break_EIS', and a list of time parameters which gives the estimated time for measuring the voltage
        response at each frequency 'delta_t_measurement_EIS'.
    """

    # Initialisation
    #       Frequencies
    f_power_min_EIS, f_power_max_EIS, nb_f_EIS, nb_points_EIS = f_EIS  # They are the frequency parameters for the EIS
    #                                                                    simulation.
    f = np.logspace(f_power_min_EIS, f_power_max_EIS, num=nb_f_EIS)  # It is the tested frequencies
    nb_period_break_EIS, nb_period_measurement_EIS = 50, 50  # They are the number of temporal periods which are used
    #                                                          for break and for measurement. It is more accurate to use
    #                                                          periods than time as the frequency range is big.
    #       Time parameters
    delta_t_break_EIS = np.array([])  # It is the estimated time for reaching equilibrium at each frequency.
    delta_t_measurement_EIS = np.array([])  # It is the estimated time for measuring the voltage response.

    # Time parameters calculation
    t0_EIS = 120*60  # s. It is the simulation starting time. [0, t0_EIS] is used to let the stack equilibrate to i_EIS.
    t_new_start_EIS = np.array([t0_EIS])  # It is a list of time parameters which gives the beginning of each frequency
    #                                   change.
    for i in range(nb_f_EIS):  # The goal is to measure nb_f_EIS periods of the signal in order to have precise enough values.
        T_i = 1 / (f[i]) # s. It is the period of the signal.
        if i < (nb_f_EIS - 1):
            delta_t_break_EIS = np.concatenate((delta_t_break_EIS, [nb_period_break_EIS * T_i]))
            delta_t_measurement_EIS = np.concatenate((delta_t_measurement_EIS, [nb_period_measurement_EIS * T_i]))
            next_start_EIS = t_new_start_EIS[i] + delta_t_break_EIS[i] + delta_t_measurement_EIS[i]
            t_new_start_EIS = np.concatenate((t_new_start_EIS, [next_start_EIS]))
        else:
            delta_t_break_EIS = np.concatenate((delta_t_break_EIS, [nb_period_break_EIS * T_i]))
            delta_t_measurement_EIS = np.concatenate((delta_t_measurement_EIS, [nb_period_measurement_EIS * T_i]))
            tf_EIS = t_new_start_EIS[-1] + delta_t_break_EIS[-1] + delta_t_measurement_EIS[-1]  # s. It is the
            #                                                                                     simulation ending time

    t_EIS = t0_EIS, t_new_start_EIS, tf_EIS, delta_t_break_EIS, delta_t_measurement_EIS
    return t_EIS

stored_operating_inputs(type_fuel_cell)

This function gives the operating inputs which correspond to the given type_fuel_cell.

Parameters:
  • type_fuel_cell (str) –

    Type of fuel cell configuration.
Returns:
  • T_des( float ) –

    Desired fuel cell temperature in Kelvin.

  • Pa_des( float ) –

    Desired anode pressure in Pascal.

  • Pc_des( float ) –

    Desired cathode pressure in Pascal.

  • Sa( float ) –

    Stoichiometric ratio of hydrogen.

  • Sc( float ) –

    Stoichiometric ratio of oxygen.

  • Phi_a_des( float ) –

    Desired anode relative humidity.

  • Phi_c_des( float ) –

    Desired cathode relative humidity.

  • i_max_pola( float ) –

    Maximum current density for the polarization curve.
Source code in modules/settings_modules.py 
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def stored_operating_inputs(type_fuel_cell):
    """This function gives the operating inputs which correspond to the given type_fuel_cell.

    Parameters
    ----------
    type_fuel_cell : str
        Type of fuel cell configuration.

    Returns
    -------
    T_des : float
        Desired fuel cell temperature in Kelvin.
    Pa_des : float
        Desired anode pressure in Pascal.
    Pc_des : float
        Desired cathode pressure in Pascal.
    Sa : float
        Stoichiometric ratio of hydrogen.
    Sc : float
        Stoichiometric ratio of oxygen.
    Phi_a_des : float
        Desired anode relative humidity.
    Phi_c_des : float
        Desired cathode relative humidity.
    i_max_pola : float
        Maximum current density for the polarization curve.
    """

    # For the ZSW Generic Stack fuel cell
    if type_fuel_cell == "ZSW-GenStack":
        T_des = 68 + 273.15  # K. It is the desired fuel cell temperature.
        Pa_des, Pc_des = 2.2e5, 2.0e5  # Pa. It is the desired pressures of the fuel gas.
        Sa, Sc = 1.6, 1.6  # It is the stoichiometric ratio (of hydrogen and oxygen).
        Phi_a_des, Phi_c_des = 0.398, 0.50  # It is the desired relative humidity.
        i_max_pola = 2.5e4  # A.m-2. It is the maximum current density for the polarization curve.

    # For EH-31 fuel cell
    elif type_fuel_cell == "EH-31_1.5":
        T_des = 74 + 273.15  # K. It is the desired fuel cell temperature.
        Pa_des, Pc_des = 1.5e5, 1.5e5  # Pa. It is the desired pressure of the fuel gas (at the anode/cathode).
        Sa, Sc = 1.2, 2.0  # It is the stoichiometric ratio (of hydrogen and oxygen).
        Phi_a_des, Phi_c_des = 0.4, 0.6  # It is the desired relative humidity.
        i_max_pola = 1.7e4  # A.m-2. It is the maximum current density for the polarization curve.
    elif type_fuel_cell == "EH-31_2.0":
        T_des = 74 + 273.15  # K. It is the desired fuel cell temperature.
        Pa_des, Pc_des = 2.0e5, 2.0e5  # Pa. It is the desired pressure of the fuel gas (at the anode/cathode).
        Sa, Sc = 1.2, 2.0  # It is the stoichiometric ratio (of hydrogen and oxygen).
        Phi_a_des, Phi_c_des = 0.4, 0.6  # It is the desired relative humidity.
        i_max_pola = 1.7e4  # A.m-2. It is the maximum current density for the polarization curve.
    elif type_fuel_cell == "EH-31_2.25":
        T_des = 74 + 273.15  # K. It is the desired fuel cell temperature.
        Pa_des, Pc_des = 2.25e5, 2.25e5  # Pa. It is the desired pressure of the fuel gas (at the anode/cathode).
        Sa, Sc = 1.2, 2.0  # It is the stoichiometric ratio (of hydrogen and oxygen).
        Phi_a_des, Phi_c_des = 0.4, 0.6  # It is the desired relative humidity.
        i_max_pola = 1.7e4  # A.m-2. It is the maximum current density for the polarization curve.
    elif type_fuel_cell == "EH-31_2.5":
        T_des = 74 + 273.15  # K. It is the desired fuel cell temperature.
        Pa_des, Pc_des = 2.5e5, 2.5e5  # Pa. It is the desired pressures of the fuel gas.
        Sa, Sc = 1.2, 2.0  # It is the stoichiometric ratio (of hydrogen and oxygen).
        Phi_a_des, Phi_c_des = 0.4, 0.6  # It is the desired relative humidity.
        i_max_pola = 1.7e4  # A.m-2. It is the maximum current density for the polarization curve.

    # For other fuel cells
    else:
        raise ValueError('the type_fuel_cell given is not valid.')

    return T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, i_max_pola

stored_physical_parameters(type_fuel_cell)

This function gives the physical parameters which correspond to the given type_fuel_cell.

Parameters:
  • type_fuel_cell (str) –

    Type of fuel cell configuration.
Returns:
  • Hacl( float ) –

    Thickness of the anode catalyst layer in m.

  • Hccl( float ) –

    Thickness of the cathode catalyst layer in m.

  • epsilon_mc( float ) –

    Volume fraction of ionomer in the CL.

  • Hmem( float ) –

    Thickness of the membrane in m.

  • Hgdl( float ) –

    Thickness of the gas diffusion layer in m.

  • epsilon_gdl( float ) –

    Anode/cathode GDL porosity.

  • epsilon_c( float ) –

    Compression ratio of the GDL.

  • Hagc( float ) –

    Thickness of the anode gas channel in m.

  • Hcgc( float ) –

    Thickness of the cathode gas channel in m.

  • Wagc( float ) –

    Width of the anode gas channel in m.

  • Wcgc( float ) –

    Width of the cathode gas channel in m.

  • Lgc( float ) –

    Length of the gas channel in m.

  • Aact( float ) –

    Active area of the cell in m².

  • e( float ) –

    Capillary exponent.

  • i0_c_ref( float ) –

    Reference exchange current density at the cathode in A.m-2.

  • kappa_co( float ) –

    Crossover correction coefficient in mol.m-1.s-1.Pa-1.

  • kappa_c( float ) –

    Overpotential correction exponent.

  • a_slim( float ) –

    One of the limit liquid saturation coefficients: the slop of slim function.

  • b_slim( float ) –

    One of the limit liquid saturation coefficients: the intercept of slim function.

  • a_switch( float ) –

    One of the limit liquid saturation coefficients: the slop of s_switch function.

  • C_dl( float ) –

    Volumetric double layer capacitance in F.m-3.
Source code in modules/settings_modules.py 
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def stored_physical_parameters(type_fuel_cell):
    """This function gives the physical parameters which correspond to the given type_fuel_cell.

    Parameters
    ----------
    type_fuel_cell : str
        Type of fuel cell configuration.

    Returns
    -------
    Hacl : float
        Thickness of the anode catalyst layer in m.
    Hccl : float
        Thickness of the cathode catalyst layer in m.
    epsilon_mc : float
        Volume fraction of ionomer in the CL.
    Hmem : float
            Thickness of the membrane in m.
    Hgdl : float
            Thickness of the gas diffusion layer in m.
    epsilon_gdl : float
        Anode/cathode GDL porosity.
    epsilon_c : float
        Compression ratio of the GDL.
    Hagc : float
        Thickness of the anode gas channel in m.
    Hcgc : float
        Thickness of the cathode gas channel in m.
    Wagc : float
        Width of the anode gas channel in m.
    Wcgc : float
        Width of the cathode gas channel in m.
    Lgc : float
        Length of the gas channel in m.
    Aact : float
            Active area of the cell in m².
    e : float
        Capillary exponent.
    i0_c_ref : float
        Reference exchange current density at the cathode in A.m-2.
    kappa_co : float
        Crossover correction coefficient in mol.m-1.s-1.Pa-1.
    kappa_c : float
        Overpotential correction exponent.
    a_slim : float
        One of the limit liquid saturation coefficients: the slop of slim function.
    b_slim : float
        One of the limit liquid saturation coefficients: the intercept of slim function.
    a_switch : float
        One of the limit liquid saturation coefficients: the slop of s_switch function.
    C_dl : float
        Volumetric double layer capacitance in F.m-3.
    """

    # For the ZSW Generic Stack fuel cell
    if type_fuel_cell == "ZSW-GenStack":
        # Global
        Aact = 279.72e-4  # m². It is the MEA active area.
        # Catalyst layer
        Hacl = 8e-6  # m. It is the thickness of the anode catalyst layer.
        Hccl = 17e-6  # m. It is the thickness of the cathode catalyst layer.
        epsilon_mc = 0.5  # It is the volume fraction of ionomer in the CL.
        # Membrane
        Hmem = 15e-6  # m. It is the thickness of the membrane.
        # Gas diffusion layer
        Hgdl = 127e-6  # m. It is the thickness of the gas diffusion layer.
        epsilon_gdl = 0.788  # It is the anode/cathode GDL porosity.
        epsilon_cl = 0.5  # It is the porosity of the catalyst layer, without units.
        epsilon_c = 0.2  # It is the compression ratio of the GDL.
        #   Microporous layer
        Hmpl = 70e-6  # m. It is the thickness of the microporous layer.
        epsilon_mpl = 0.425  # It is the porosity of the microporous layer.
        # Gas channel
        Hagc = 230e-6  # m. It is the thickness of the anode gas channel.
        Hcgc = 300e-6  # m. It is the thickness of the cathode gas channel.
        Wagc = 430e-6  # m. It is the width of the anode gas channel.
        Wcgc = 532e-6  # m. It is the width of the cathode gas channel.
        Lgc = 23.31  # m. It is the length of the gas channel.
        # Interaction parameters between water and PEMFC structure
        e = 4.0  # It is the capillary exponent
        # Voltage polarization
        i0_c_ref = 6.795  # A.m-2.It is the reference exchange current density at the cathode.
        kappa_co = 30.41  # mol.m-1.s-1.Pa-1. It is the crossover correction coefficient.
        kappa_c = 1.026  # It is the overpotential correction exponent.
        a_slim, b_slim, a_switch = 0.05553, 0.10514, 0.63654  # It is the limit liquid saturation coefficients.
        C_scl = 2e7  # F.m-3. It is the volumetric space-charge layer capacitance.

    # For EH-31 fuel cell
    elif type_fuel_cell == "EH-31_1.5" or type_fuel_cell == "EH-31_2.0" or type_fuel_cell == "EH-31_2.25" or \
            type_fuel_cell == "EH-31_2.5":
        # Global
        Aact = 85e-4  # m². It is the active area of the catalyst layer.
        # Catalyst layer
        Hacl = 8.089e-6  # m. It is the thickness of the anode catalyst layer.
        Hccl = Hacl  # m. It is the thickness of the cathode catalyst layer.
        epsilon_mc = 0.3823  # It is the volume fraction of ionomer in the CL.
        # Membrane
        Hmem = 16.97e-6  # m. It is the thickness of the membrane.
        # Gas diffusion layer
        Hgdl = 200e-6  # m. It is the thickness of the gas diffusion layer.
        epsilon_gdl = 0.7393  # It is the anode/cathode GDL porosity.
        epsilon_cl = 0.25  # It is the porosity of the catalyst layer, without units.
        epsilon_c = 0.2  # It is the compression ratio of the GDL.
        #   Microporous layer
        Hmpl = 30e-6  # m. It is the thickness of the microporous layer.
        epsilon_mpl = 0.4  # It is the porosity of the microporous layer.
        # Gas channel
        Hagc = 500e-6  # m. It is the thickness of the anode gas channel.
        Hcgc = Hagc  # m. It is the thickness of the cathode gas channel.
        Wagc = 450e-6  # m. It is the width of the anode gas channel.
        Wcgc = Wagc  # m. It is the width of the cathode gas channel.
        Lgc = 9.67  # m. It is the length of the gas channel.
        # Interaction parameters between water and PEMFC structure
        e = 4.0  # It is the capillary exponent
        # Voltage polarization
        i0_c_ref = 6.795  # A.m-2.It is the reference exchange current density at the cathode.
        kappa_co = 30.41  # mol.m-1.s-1.Pa-1. It is the crossover correction coefficient.
        kappa_c = 1.026  # It is the overpotential correction exponent.
        a_slim, b_slim, a_switch = 0.05553, 0.10514, 0.63654  # It is the limit liquid saturation coefficients.
        C_scl = 20e6  # F.m-3. It is the volumetric space-charge layer capacitance.

    # For other fuel cells
    else:
        raise ValueError('the type_input given is not valid.')

    return Hacl, Hccl, epsilon_mc, Hmem, Hgdl, epsilon_gdl, epsilon_cl, epsilon_c, Hmpl, epsilon_mpl, \
           Hagc, Hcgc, Wagc, Wcgc, Lgc, Aact, e, i0_c_ref, kappa_co, kappa_c, a_slim, b_slim, a_switch, C_scl