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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,112 @@ | ||
| # | ||
| # Compare SPMe model with and without heat of mixing | ||
| # | ||
| import pybamm | ||
| import numpy as np | ||
| import matplotlib.pyplot as plt | ||
|
|
||
| pybamm.set_logging_level("INFO") | ||
|
|
||
| # load models | ||
| models = [ | ||
| pybamm.lithium_ion.SPMe( | ||
| {"heat of mixing": "true", "thermal": "lumped"}, name="SPMe with heat of mixing" | ||
| ), | ||
| pybamm.lithium_ion.SPMe({"thermal": "lumped"}, name="SPMe without heat of mixing"), | ||
| ] | ||
|
|
||
| # set parametrisation (Ecker et al., 2015) | ||
| parameter_values = pybamm.ParameterValues("Ecker2015") | ||
|
|
||
| # set mesh | ||
| # (increased number of points in particles to avoid oscillations for high C-rates) | ||
| var_pts = {"x_n": 16, "x_s": 8, "x_p": 16, "r_n": 128, "r_p": 128} | ||
|
|
||
| # set the constant current discharge C-rate | ||
| C_rate = 5 | ||
|
|
||
| # set the simulation time and increase the number of points | ||
| # for better integration in time | ||
| t_eval = np.linspace(0, 720, 360) | ||
|
|
||
| # set up an extra plot with the heat of mixing vs time in each electrode and | ||
| # the integrated heat of mixing vs time in each electrode to compare with | ||
| # Figure 6(a) from Richardson et al. (2021) | ||
| fig, axs = plt.subplots(2, len(models), figsize=(12, 7)) | ||
|
|
||
| # extract some of the parameters | ||
| L_n = parameter_values["Negative electrode thickness [m]"] | ||
| L_p = parameter_values["Positive electrode thickness [m]"] | ||
| A = parameter_values["Electrode width [m]"] * parameter_values["Electrode height [m]"] | ||
|
|
||
| # create and run simulations | ||
| sims = [] | ||
| for m, model in enumerate(models): | ||
| sim = pybamm.Simulation( | ||
| model, parameter_values=parameter_values, var_pts=var_pts, C_rate=C_rate | ||
| ) | ||
| sim.solve(t_eval) | ||
| sims.append(sim) | ||
|
|
||
| # extract solution for plotting | ||
| sol = sim.solution | ||
|
|
||
| # extract variables from the solution | ||
| time = sol["Time [h]"].entries | ||
| Q_mix = sol["Heat of mixing [W.m-3]"].entries | ||
|
|
||
| # heat of mixing in negative and positive electrodes multiplied by the electrode | ||
| # width, represents the integral of heat of mixing term across each of the | ||
| # electrodes (W.m-2) | ||
| Q_mix_n = Q_mix[0, :] * L_n | ||
| Q_mix_p = Q_mix[-1, :] * L_p | ||
|
|
||
| # heat of mixing integrals (J.m-2) | ||
| Q_mix_n_int = 0.0 | ||
| Q_mix_p_int = 0.0 | ||
|
|
||
| # data for plotting | ||
| Q_mix_n_plt = [] | ||
| Q_mix_p_plt = [] | ||
|
|
||
| # performs integration in time | ||
| for i, t in enumerate(time[1:]): | ||
| dt = (t - time[i]) * 3600 # seconds | ||
| Q_mix_n_avg = (Q_mix_n[i] + Q_mix_n[i + 1]) * 0.5 | ||
| Q_mix_p_avg = (Q_mix_p[i] + Q_mix_p[i + 1]) * 0.5 | ||
| # convert J to kJ and divide the integral by the electrode area A to compare | ||
| # with Figure 6(a) from Richardson et al. (2021) | ||
| Q_mix_n_int += Q_mix_n_avg * dt / 1000 / A | ||
| Q_mix_p_int += Q_mix_p_avg * dt / 1000 / A | ||
| Q_mix_n_plt.append(Q_mix_n_int) | ||
| Q_mix_p_plt.append(Q_mix_p_int) | ||
|
|
||
| # plots heat of mixing in each electrode vs time in minutes | ||
| axs[0, m].plot(time * 60, Q_mix_n, ls="-", label="Negative electrode") | ||
| axs[0, m].plot(time * 60, Q_mix_p, ls="--", label="Positive electrode") | ||
| axs[0, m].set_title(f"{model.name}") | ||
| axs[0, m].set_xlabel("Time [min]") | ||
| axs[0, m].set_ylabel("Heat of mixing [W.m-2]") | ||
| axs[0, m].grid(True) | ||
| axs[0, m].legend() | ||
|
|
||
| # plots integrated heat of mixing in each electrode vs time in minutes | ||
| axs[1, m].plot(time[1:] * 60, Q_mix_n_plt, ls="-", label="Negative electrode") | ||
| axs[1, m].plot(time[1:] * 60, Q_mix_p_plt, ls="--", label="Positive electrode") | ||
| axs[1, m].set_xlabel("Time [min]") | ||
| axs[1, m].set_ylabel("Integrated heat of mixing [kJ.m-2]") | ||
| axs[1, m].grid(True) | ||
| axs[1, m].legend() | ||
|
|
||
| # plot | ||
| pybamm.dynamic_plot( | ||
| sims, | ||
| output_variables=[ | ||
| "X-averaged cell temperature [K]", | ||
| "X-averaged heat of mixing [W.m-3]", | ||
| "X-averaged total heating [W.m-3]", | ||
| "Heat of mixing [W.m-3]", | ||
| "Voltage [V]", | ||
| "Current [A]", | ||
| ], | ||
| ) |
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