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make_plots.py
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import numpy as np
import matplotlib.pyplot as plt
from dolfin import plot
import heat_generation as heat
from current_profile import current
import open_circuit_potentials as ocp
from utilities import get_vars_time
from voltage import Voltage
def plot_terminal_voltage(soln, mesh, R_cc, param):
# Create voltage object
voltage = Voltage(soln, mesh, R_cc, param)
# Convert to dimensional time
t = soln.t * param.tau_d_star
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Make plots
fig = plt.figure()
plt.subplot(2, 1, 1)
plt.plot(t, voltage.v_term, label="V")
plt.xlim([t[0], t[-1]])
plt.ylim([param.V_min, param.V_max])
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel("Voltage [V]", fontsize=11)
plt.title("Voltage", fontsize=11)
plt.legend()
plt.subplot(2, 1, 2)
plt.stackplot(
t,
voltage.U_eq - voltage.U_eq_init,
voltage.eta_r,
voltage.eta_c,
voltage.Delta_Phi_elec,
voltage.Delta_Phi_solid,
voltage.Delta_Phi_cc,
labels=[
r"$\mathcal{{U}}_{{\mathrm{{eq}}}}$"
r"$- \mathcal{{U}}_{{\mathrm{{eq,init}}}}$ [V]",
r"$\eta_{{\mathrm{{r}}}}$",
r"$\eta_{{\mathrm{{c}}}}$",
r"$\Delta \Phi_{{\mathrm{{elec}}}}$",
r"$\Delta \Phi_{{\mathrm{{solid}}}}$",
r"$\Delta \Phi_{{\mathrm{{cc}}}}$",
],
)
plt.xlim([t[0], t[-1]])
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel("Voltage [V]", fontsize=11)
plt.title("Voltage", fontsize=11)
plt.legend()
fig.tight_layout()
fig2 = plt.figure()
plt.subplot(2, 3, 1)
plt.plot(t, voltage.U_eq - voltage.U_eq_init)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(
r"$\mathcal{{U}}_{{\mathrm{{eq}}}}$"
r"$- \mathcal{{U}}_{{\mathrm{{eq,init}}}}$ [V]"
)
plt.subplot(2, 3, 2)
plt.plot(t, voltage.eta_r)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$\eta_{{\mathrm{{r}}}}$ [V]")
plt.subplot(2, 3, 3)
plt.plot(t, voltage.eta_c)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$\eta_{{\mathrm{{c}}}}$ [V]")
plt.subplot(2, 3, 4)
plt.plot(t, voltage.Delta_Phi_elec)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$\Delta \Phi_{{\mathrm{{elec}}}}$ [V]")
plt.subplot(2, 3, 5)
plt.plot(t, voltage.Delta_Phi_solid)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$\Delta \Phi_{{\mathrm{{solid}}}}$ [V]")
plt.subplot(2, 3, 6)
plt.plot(t, voltage.Delta_Phi_cc)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$\Delta \Phi_{{\mathrm{{cc}}}}$ [V]")
fig2.tight_layout()
def plot_voltage_breakdown(soln, mesh, R_cc, param):
# Create voltage object
voltage = Voltage(soln, mesh, R_cc, param)
# Convert to dimensional time
t = soln.t * param.tau_d_star
print(param.I_star)
dCap = t * param.I_star / (60 * 60) / param.C_rate
print(t)
print(dCap)
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="sans-serif")
plt.rc("mathtext", fontset="stixsans")
plt.rc("text.latex", preamble=r"\usepackage{sfmath}")
plt.rc("xtick", labelsize=18)
plt.rc("ytick", labelsize=18)
plt.rc("axes", titlepad=10)
plt.rc("legend", fontsize=14)
# Make plots
fig, ax1 = plt.subplots(figsize=(25 / 2.54, 12 / 2.54))
plt.title(r"\textbf{SPMeCC}", fontsize=24)
left, bottom, width, height = [0.19, 0.32, 0.29, 0.21]
ax2 = fig.add_axes([left, bottom, width, height])
ax1.stackplot(
dCap,
voltage.U_eq - voltage.U_eq_init,
voltage.eta_r,
voltage.eta_c,
voltage.Delta_Phi_elec,
voltage.Delta_Phi_cc,
labels=[
"OCV",
"Reaction overpotential",
"Concetration overpotential",
"Electrolyte Ohmic",
"Current Collector Ohmic",
],
)
ax1.legend()
ax1.set_xlim([0, 1400 * param.I_star / (60 * 60) / param.C_rate])
ax1.set_ylim([-0.5, 0])
ax1.set_xlabel(r"Discharge Capacity (Ah/m$^2$)", fontsize=22)
ax1.set_ylabel("Voltage Loss (V)", fontsize=22)
plt.plot(dCap, voltage.v_term, label="V")
ax2.set_xlim([0, 12])
ax2.set_ylim([param.V_min, param.V_max])
plt.xlabel(r"Discharge Capacity (Ah/m$^2$)", fontsize=18)
plt.ylabel("Voltage (V)", fontsize=18)
# ax1.set_xticks([0, 450, 900, 1350])
# ax2.set_xticks([0, 900, 1800])
plt.tight_layout()
plt.savefig("V_SPMeCC.eps", format="eps", dpi=1000)
def plot_heat_generation(soln, mesh, R_cn, R_cp, param):
# Get variables
c_n, c_p, c_e_n, c_e_s, c_e_p, T0, T1 = get_vars_time(soln.y, mesh)
t = soln.t
# Surface concentration for BV
c_n_surf = c_n[-1, :] + (c_n[-1, :] - c_n[-2, :]) / 2
c_p_surf = c_p[-1, :] + (c_p[-1, :] - c_p[-2, :]) / 2
# Electrode avergaed electrolyte concentrations and the values at the
# electrode/separator interfaces needed for heat source terms
c_e_n_bar = np.trapz(c_e_n, dx=mesh.dx_n, axis=0) / param.L_n
c_e_p_bar = np.trapz(c_e_p, dx=mesh.dx_p, axis=0) / param.L_p
c_e_neg_sep = (c_e_n[-1, :] + c_e_s[0, :]) / 2
c_e_pos_sep = (c_e_s[-1, :] + c_e_p[0, :]) / 2
# Evaluate I_app
I_app = current(t, param)
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Make plots
fig = plt.figure(figsize=(15, 9))
plt.subplot(2, 5, 2)
plt.plot(0, 0, label="Ohm")
plt.plot(
t * param.tau_d_star, heat.rxn_n_0(T0, c_n_surf, param, I_app), label="rxn"
)
plt.plot(
t * param.tau_d_star, heat.rev_n_0(T0, c_n_surf, param, I_app), label="rev"
)
plt.plot(
t * param.tau_d_star,
heat.rxn_n_0(T0, c_n_surf, param, I_app)
+ heat.rev_n_0(T0, c_n_surf, param, I_app),
label="Total",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Negative leading-order", fontsize=11)
plt.legend()
plt.subplot(2, 5, 4)
plt.plot(0, 0, label="Ohm")
plt.plot(
t * param.tau_d_star, heat.rxn_p_0(T0, c_p_surf, param, I_app), label="rxn"
)
plt.plot(
t * param.tau_d_star, heat.rev_p_0(T0, c_p_surf, param, I_app), label="rev"
)
plt.plot(
t * param.tau_d_star,
heat.rxn_p_0(T0, c_p_surf, param, I_app)
+ heat.rev_p_0(T0, c_p_surf, param, I_app),
label="Total",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Positive leading-order", fontsize=11)
plt.legend()
plt.subplot(2, 5, 7)
plt.plot(
t * param.tau_d_star,
heat.ohmic_n_1(c_e_n_bar, c_e_neg_sep, param, I_app),
label="Ohm",
)
plt.plot(
t * param.tau_d_star,
heat.rxn_n_1(T0, T1, c_n_surf, c_e_n_bar, param, I_app),
label="rxn",
)
plt.plot(
t * param.tau_d_star, heat.rev_n_1(T1, c_n_surf, param, I_app), label="rev"
)
plt.plot(
t * param.tau_d_star,
heat.ohmic_n_1(c_e_n_bar, c_e_neg_sep, param, I_app)
+ heat.rxn_n_1(T0, T1, c_n_surf, c_e_n_bar, param, I_app)
+ heat.rev_n_1(T1, c_n_surf, param, I_app),
label="Total",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Negative first-order", fontsize=11)
plt.legend()
plt.subplot(2, 5, 8)
plt.plot(
t * param.tau_d_star,
heat.ohmic_s_1(c_e_neg_sep, c_e_pos_sep, param, I_app),
label="Ohm",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Separator first-order", fontsize=11)
plt.legend()
plt.subplot(2, 5, 9)
plt.plot(
t * param.tau_d_star,
heat.ohmic_p_1(c_e_p_bar, c_e_pos_sep, param, I_app),
label="Ohm",
)
plt.plot(
t * param.tau_d_star,
heat.rxn_p_1(T0, T1, c_p_surf, c_e_p_bar, param, I_app),
label="rxn",
)
plt.plot(
t * param.tau_d_star, heat.rev_p_1(T1, c_p_surf, param, I_app), label="rev"
)
plt.plot(
t * param.tau_d_star,
heat.ohmic_p_1(c_e_p_bar, c_e_pos_sep, param, I_app)
+ heat.rxn_p_1(T0, T1, c_p_surf, c_e_p_bar, param, I_app)
+ heat.rev_p_1(T1, c_p_surf, param, I_app),
label="Total",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Positive first-order", fontsize=11)
plt.legend()
if R_cn == 0:
plt.subplot(2, 5, 1)
plt.plot(
t * param.tau_d_star, (I_app / param.Ly) ** 2 / param.sigma_cn, label="Ohm"
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Negative c.c. 1D approx.", fontsize=11)
plt.legend()
else:
plt.subplot(2, 5, 6)
plt.plot(t * param.tau_d_star, heat.ohmic_cc_1(R_cn, param, I_app), label="Ohm")
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Negative c.c. first-order", fontsize=11)
plt.legend()
if R_cp == 0:
plt.subplot(2, 5, 5)
plt.plot(
t * param.tau_d_star, (I_app / param.Ly) ** 2 / param.sigma_cp, label="Ohm"
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Positive c.c. 1D approx.", fontsize=11)
plt.legend()
else:
plt.subplot(2, 5, 10)
plt.plot(t * param.tau_d_star, heat.ohmic_cc_1(R_cp, param, I_app), label="Ohm")
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.title("Positive c.c. first-order", fontsize=11)
plt.legend()
fig.tight_layout()
def plot_electrolyte_concentration(soln, mesh, param):
# Get variables
c_n, c_p, c_e_n, c_e_s, c_e_p, T0, T1 = get_vars_time(soln.y, mesh)
# Evaluate steady profiles
# (need to multiply by I_app to get value at a given time)
c_e_n_steady = (
(1 / param.Ly)
* (param.nu * (1 - param.t_plus))
* (
2
* (
param.L_p ** 2 / param.epsilon_p ** param.brug
- param.L_n ** 2 / param.epsilon_n ** param.brug
)
+ 3
* param.L_s
* (param.L_p - param.L_n + 1)
/ param.epsilon_s ** param.brug
+ 3
* (param.L_n ** 2 - mesh.x_n ** 2)
/ param.L_n
/ param.epsilon_n ** param.brug
)
/ 6
/ param.electrolyte_diffusivity(1)
)
c_e_s_steady = (
(1 / param.Ly)
* (param.nu * (1 - param.t_plus))
* (
2
* (
param.L_p ** 2 / param.epsilon_p ** param.brug
- param.L_n ** 2 / param.epsilon_n ** param.brug
)
+ 3
* (param.L_n ** 2 - param.L_p ** 2 + 1 - 2 * mesh.x_s)
/ param.epsilon_s ** param.brug
)
/ 6
/ param.electrolyte_diffusivity(1)
)
c_e_p_steady = (
(1 / param.Ly)
* (param.nu * (1 - param.t_plus))
* (
2
* (
param.L_p ** 2 / param.epsilon_p ** param.brug
- param.L_n ** 2 / param.epsilon_n ** param.brug
)
+ 3
* param.L_s
* (param.L_p - param.L_n - 1)
/ param.epsilon_s ** param.brug
+ 3
* ((1 - mesh.x_p) ** 2 - param.L_p ** 2)
/ param.L_p
/ param.epsilon_p ** param.brug
)
/ 6
/ param.electrolyte_diffusivity(1)
)
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Plot over time
fig = plt.figure()
for i in range(1, np.size(soln.t)):
# Evaluate I_app
I_app = current(soln.t[i - 1], param)
plt.clf()
plt.plot(
(mesh.x_n[1:] + mesh.x_n[0:-1]) / 2,
param.c_e_typ_star * param.delta * c_e_n[:, i],
"b-",
)
plt.plot(
mesh.x_n, param.c_e_typ_star * param.delta * c_e_n_steady * I_app, "r--"
)
plt.plot(
(mesh.x_s[1:] + mesh.x_s[0:-1]) / 2,
param.c_e_typ_star * param.delta * c_e_s[:, i],
"b-",
)
plt.plot(
mesh.x_s, param.c_e_typ_star * param.delta * c_e_s_steady * I_app, "r--"
)
plt.plot(
(mesh.x_p[1:] + mesh.x_p[0:-1]) / 2,
param.c_e_typ_star * param.delta * c_e_p[:, i],
"b-",
label="Unsteady",
)
plt.plot(
mesh.x_p,
param.c_e_typ_star * param.delta * c_e_p_steady * I_app,
"r--",
label="Steady",
)
plt.xlim([0, 1])
plt.xlabel(r"$x$", fontsize=11)
plt.ylabel(
r"$c_{{\mathrm{{e}}}}^* - c_{{\mathrm{{e,typ}}}}^*$" r"[mol/m$^3$]",
fontsize=11,
)
plt.legend()
fig.tight_layout()
plt.pause(1)
def plot_surface_concentration(soln, mesh, param):
# Get variables
c_n, c_p, c_e_n, c_e_s, c_e_p, T0, T1 = get_vars_time(soln.y, mesh)
# Surface concentration for BV
c_n_surf = c_n[-1, :] + (c_n[-1, :] - c_n[-2, :]) / 2
c_p_surf = c_p[-1, :] + (c_p[-1, :] - c_p[-2, :]) / 2
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Plot surface concentrations
fig = plt.figure()
plt.subplot(1, 2, 1)
plt.plot(soln.t * param.tau_d_star, c_n_surf)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel("Surface " r"$c_{{\mathrm{{n}}}}$", fontsize=11)
plt.subplot(1, 2, 2)
plt.plot(soln.t * param.tau_d_star, c_p_surf)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel("Surface " r"$c_{{\mathrm{{p}}}}$", fontsize=11)
fig.tight_layout()
def plot_temperature(soln, mesh, param):
# Get variables
c_n, c_p, c_e_n, c_e_s, c_e_p, T0, T1 = get_vars_time(soln.y, mesh)
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Plot temperature
fig = plt.figure()
plt.subplot(2, 1, 1)
plt.plot(
soln.t * param.tau_d_star,
T0 * param.Delta_T_star + param.T_inf_star,
label=r"$T^0 + \delta T^1$",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$T$", fontsize=11)
plt.subplot(2, 1, 2)
plt.plot(
soln.t * param.tau_d_star,
(T0 + param.delta * T1) * param.Delta_T_star + param.T_inf_star,
label=r"$T^0 + \delta T^1&",
)
plt.xlabel(r"$t$ [s]", fontsize=11)
plt.ylabel(r"$T$", fontsize=11)
fig.tight_layout()
def plot_psi_W(psi, W, R_CC, param):
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Plot psi and W
fig = plt.figure()
plt.subplot(1, 2, 1)
p1 = plot(psi)
plt.xlabel(r"$y$", fontsize=11)
plt.ylabel(r"$z$", fontsize=11)
plt.title(r"$\psi$", fontsize=11)
plt.colorbar(p1, fraction=0.055, pad=0.04)
plt.subplot(1, 2, 2)
p2 = plot(W)
plt.xlabel(r"$y$", fontsize=11)
plt.ylabel(r"$z$", fontsize=11)
plt.title(r"$\mathcal{W}^1$", fontsize=11)
plt.colorbar(p2, fraction=0.055, pad=0.04)
fig.suptitle(
r"$\alpha^{{\prime}} = {:.3f}$. "
"$R_{{\mathrm{{CC}}}}$ = {:.3f}".format(param.alpha_prime, R_CC),
fontsize=16,
)
fig.tight_layout()
def plot_OCP(c, T, param):
# Font stuff
plt.rc("text", usetex=True)
plt.rc("font", family="serif")
# Plot OCP and entropic coefficient at a fixed T
fig = plt.figure()
plt.subplot(2, 2, 1)
plt.plot(c, ocp.U_n(c, T, param) * param.Phi_star)
plt.xlabel(r"$c_{{\mathrm{{n}}}}$")
plt.ylabel(r"$U_{{\mathrm{{n}}}}$")
plt.subplot(2, 2, 3)
plt.plot(c, ocp.dUdT_n(c, param) * param.Phi_star / param.Delta_T_star)
plt.xlabel(r"$c_{{\mathrm{{n}}}}$")
plt.ylabel(r"$\frac{{\mathrm{{d}} U_{{\mathrm{{n}}}}}}{{\mathrm{{d}}T}}$")
plt.subplot(2, 2, 2)
plt.plot(c, ocp.U_p(c, T, param) * param.Phi_star)
plt.xlabel(r"$c_{{\mathrm{{p}}}}$")
plt.ylabel(r"$U_{{\mathrm{{p}}}}$")
plt.subplot(2, 2, 4)
plt.plot(c, ocp.dUdT_p(c, param) * param.Phi_star / param.Delta_T_star)
plt.xlabel(r"$c_{{\mathrm{{p}}}}$")
plt.ylabel(r"$\frac{{\mathrm{{d}} U_{{\mathrm{{p}}}}}}{{\mathrm{{d}}T}}$")
fig.tight_layout()