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IV_Curve_generator.m
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%% Specific Pressure and Temperature
temp_indiv = 273+700; %.C
press_indiv = 400; %MPa
B_Dissociation_indiv = 0;
B_Ionic_indiv = 0;
KINETIC_P_indiv = 0;
P_O2c_indiv = 0;
J_indiv = 0;
NONIDEAL_P_indiv = 0;
IDEAL_P_indiv = 0;
nohmic_a = 0;
nact_a = 0;
nconH2_a = 0;
nconO2_a = 0;
rxn = .5;
%Setting Variables
%===============================================================================
row = round((temp_indiv - 20 - 273.15)/5);
col = round(press_indiv - 22);
P_indiv = POTENTIAL(col, row);
%Calculating K Factor
%===============================================================================
K_indiv = exp(GIBBS_FORMATION(col,row)*1000/(8.314*temp_indiv));
%Electronic Region Check
%===============================================================================
Min_950 = 10^(-16);
Max_950 = 10^7;
Min_650 = 10^(-31);
Max_650 = 10^12;
Min_l = Min_650 + ((Min_950 - Min_650)/(950-650))*(temp_indiv - (650 + 273.15));
Max_l = Max_650 + ((Max_950 - Max_650)/(950-650))*(temp_indiv - (650 + 273.15));
E_Dissoc_indiv = -2.84215 + 5.02487*10^(-4)*temp_indiv -1.23698*10^(-8)*temp_indiv^2;
for J_index = -5:.01:5
%Mapping Thermodynamic Potential
%===============================================================================
[pot_ideal, non_ideal] = thermo__potentialb(rxn,OXYGEN_ANODE,temp_indiv,press_indiv,K_indiv);
IDEAL_P_indiv (J_index) = pot_ideal;
NONIDEAL_P_indiv(J_index) = non_ideal;
%Electronic Region Check
%===============================================================================
P_O2c_indiv(J_index) = sqrt(K_indiv)*(1 - rxn)/rxn;
if(P_O2c_indiv(J_index) < Min_l || P_O2c_indiv(J_index) > Max_l)
B_Ionic_indiv (J_index) = 0;
else
B_Ionic_indiv (J_index) = 1;
end
%Zirconia Dissociation Check
%===============================================================================
if(E_Dissoc_indiv < NONIDEAL_P_indiv(J_index))
B_Dissociation_indiv (J_index) = 1;
else
B_Dissociation_indiv (J_index) = 0;
end
J_indiv(J_index) = 3.05; %A/cm2 current density intitial convergence value
Pre_kinetic = NONIDEAL_P_indiv(J_index);
KINETIC_P_indiv(J_index) = -100; %just putting a case that would initiate
% the while loop.
%Mapping Kinetic Potential
%===============================================================================
[nohmic, nact, nconH2, nconO2, kinetic_pot] = kinetics(J_indiv(J_index), temp_indiv, press_indiv, rxn, ...
YSZ_T*10000, NIYSZ_T, LSM_T, ...
NIYSZ_Porosity, NIYSZ_Torosity, NIYSZ_radius, ...
LSM_Porosity, LSM_Torosity, LSM_radius, OXYGEN_ANODE);
KINETIC_P_indiv(J_index) = kinetic_pot;
nohmic_a(J_index) = nohmic;
nact_a(J_index) = nact;
nconH2_a(J_index) = nconH2;
nconO2_a(J_index) = nconO2;
end
end
%% Illustration of current + voltage subcomponents
figure(20)
X_rxn = 1/10:1/10:999/10;
Pot = zeros(999,1);
Zir = zeros(999,1);
for i = 1:length(Pot)
% set each element to 0
Pot(i) = P_indiv;
Zir(i) = E_Dissoc_indiv;
end
yyaxis left
title(['Voltage + Current at ' , num2str(temp_indiv), ' K & ' , num2str(press_indiv) , ' MPa'])
plot(X_rxn, Pot,'-g');
hold on
plot(X_rxn, NONIDEAL_P_indiv, '-r');
hold on
plot(X_rxn, NONIDEAL_P_indiv + KINETIC_P_indiv, '-b');
hold on
plot(X_rxn, NONIDEAL_P_indiv - nohmic_a, '--r');
hold on
plot(X_rxn, NONIDEAL_P_indiv - nohmic_a - nact_a, '--b');
hold on
plot(X_rxn, NONIDEAL_P_indiv - nohmic_a - nact_a - nconH2_a, '--m');
hold on
plot(X_rxn, NONIDEAL_P_indiv - nohmic_a - nact_a - nconH2_a - nconO2_a, '--c');
hold on
l2 = plot(X_rxn,Zir, ':r');
set(l2,'linewidth',2);
hold on
xlabel('Reaction Completion [%]') % x-axis label
ylabel('Potential [V]') % y-axis label
set(gca,'XLim',[0 100])
set(gca,'XTick',(0:10:100))
set(gca,'YLim',[-2.5 0])
set(gca,'YTick',((-2.5):.5:0))
yyaxis right
l1 = plot(X_rxn,J_indiv,'-b');
set(l1,'linewidth',2);
ylabel('Current [A/cm^2]') % y-axis label
set(gca,'YLim',[0 4])
set(gca,'YTick',(0:.5:4))
legend('Thermodynamic','Non-Ideal Thermo Addition', 'Kinetic Addition',...
'Ohmic Resistance', 'Activation Polarization', 'Hydrogen Concentration Polar.',...
'Oxygen Concentration Polar.','Zirconia Dissociation','Current Density')
hold off
%% I-V CURVES
KINETIC_P_indiv2 = zeros(100,3);
P_O2c_indiv2 = zeros(100,3);
J_indiv2 = zeros(100,3);
NONIDEAL_P_indiv2 = zeros(100,3);
IDEAL_P_indiv2 = zeros(100,3);
nohmic_a2 = zeros(100,3);
nact_a2 = zeros(100,3);
nconH2_a2 = zeros(100,3);
nconO2_a2 = zeros(100,3);
for J_index = 1:1:100
for rxn_index2 = 1:1:3
J2 = (J_index-1)/10;
rxn2 = ((rxn_index2-1)*49 + 1)/100;
[pot_ideal, non_ideal] = thermo__potentialb(rxn2,OXYGEN_ANODE,temp_indiv,press_indiv,K_indiv);
IDEAL_P_indiv2 (J_index, rxn_index2) = pot_ideal;
NONIDEAL_P_indiv2(J_index, rxn_index2) = non_ideal;
%Mapping Kinetic Potential
%===============================================================================
[nohmic, nact, nconH2, nconO2, kinetic_pot] = kinetics(J2, temp_indiv, press_indiv, rxn2, ...
YSZ_T*10000, NIYSZ_T, LSM_T, ...
NIYSZ_Porosity, NIYSZ_Torosity, NIYSZ_radius, ...
LSM_Porosity, LSM_Torosity, LSM_radius, OXYGEN_ANODE);
KINETIC_P_indiv2(J_index, rxn_index2) = kinetic_pot;
nohmic_a2(J_index, rxn_index2) = nohmic;
nact_a2(J_index, rxn_index2) = nact;
nconH2_a2(J_index, rxn_index2) = nconH2;
nconO2_a2(J_index, rxn_index2) = nconO2;
end