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tga2.m
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tga2.m
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% TGA simulation
%% variable initalization
clear all vars
global ycoeff afac nfac ea istart g_index s_index MW rhos0 gsp nsp masslossrate
tic
load ('ranzi_pyro_kinetics_gentile2017.mat');
MW(47)=28;
ycoeff(47,:)=0;
g_index = [3 4 5 6 7 8 9 10 11 12 13 14 16 20 21 22 29 30 31 33 34 35 47];
gsp = length(g_index);
nsp = 47;
s_index = [1 2 15 17 18 19 23 24 25 26 27 28 32 36 37 38 39 40 41 42 43 44 45 46];
%% sizing and array initialization
Mesh.Jnodes = 1;
sample_height = 1e-2;
Mesh.z = linspace(0,sample_height,Mesh.Jnodes);
Mesh.dz = sample_height/(Mesh.Jnodes);
Mesh.a = 1e-2^2;
Mesh.dv = Mesh.a * Mesh.dz;
yprime0 = zeros(Mesh.Jnodes*nsp+2*Mesh.Jnodes,1);
rhos0 = zeros(Mesh.Jnodes,1);
rhos_mass0 = zeros(Mesh.Jnodes,1);
%% set initial composition
m0 = zeros(47,Mesh.Jnodes);
m0(1,:) = 0; %19/MW(1); % CELL
m0(17,:) = 15/MW(17); % HCE
m0(24,:) = 5/MW(24); % LIGH
m0(25,:) = 23.5/MW(25); % LIGO
m0(23,:) = 5/MW(23); % LIGC
m0(38,:) = 2.3/MW(38); % TGL
m0(37,:) = 3.1/MW(37); % TANN
m0(39,:) = 50/MW(39); % moisture
%% initialize mass calcs
mass0 = m0.*MW; % kg
%yi0 = mass0(s_index,1)./100;
rhos_mass0 = rhos_mass0+100;
sample_mass = Mesh.a*sample_height*rhos_mass0(1);
mass0 = mass0./100*sample_mass./Mesh.Jnodes;
y0 = [mass0(:); rhos_mass0(:)];
%% initial conditions
T0 = 300; % initial temperature
Tend = 1000; % final temperature
dt = 1;
beta = 50/60; % rate of temperature change [K/s]
nstep = fix((Tend-T0)/beta)*(1/dt);
time = 0;
t = zeros(nstep+1,1);
yy = zeros(nstep+1,length(y0));
t(1)= 0;
yy(1,:) = y0;
ye = zeros(length(t),length(g_index));
j0 = zeros(length(t),1);
mlr = zeros(length(t),1);
T = zeros(length(t),1); T(1) = 300;
Mg = MW(g_index)*1e-3;
options = odeset('RelTol',1.e-4,'AbsTol',1e-5, 'NonNegative', 1, 'BDF',0, 'MaxOrder',2);
%% time integration
for i=1:nstep
tspan = [t(i) t(i)+dt];
[t2,a] = ode113(@(t,y)yprime(time,y,Mesh,T(i)),tspan,yy(i,:),options);
temp = a(end,:);
temp(temp<0) = 1e-30;
mlr(i+1) = masslossrate;
yy(i+1,:) = temp;
T(i+1) = T(i)+ beta*dt;
t(i+1) = t(i) + dt;
end
%% plot
figure(1); clf
hold on;
plot(T, yy(:,end));
% xlim([300 1250]);
% ylim([0 100]);
xlabel('Temp [K]');
ylabel('mass %');
title('mass % evolution wrt T');
figure(2); clf
plot(T, -mlr);
xlabel('Temperature [K]');
ylabel('mlr, DTG');
title('Mass loss rate (mlr, DTG) wrt T');
hold off;
t_elaspsed = toc;
toc
%% define functions
function [dydt] = yprime(t,yy,Mesh,T)
global ycoeff afac nfac ea istart s_index g_index MW nsp masslossrate yje
wdot_mass = zeros(nsp,Mesh.Jnodes);
k = zeros(28,Mesh.Jnodes);
m = zeros(nsp,Mesh.Jnodes);
rho_s_mass = zeros(Mesh.Jnodes,1);
drhosdt = zeros(Mesh.Jnodes,1);
mprime = zeros(nsp,Mesh.Jnodes);
yje = zeros(length(g_index),1);
for i=1:Mesh.Jnodes
temp=yy(nsp*(i-1)+1:nsp*(i-1)+nsp);
temp(temp<0)=1e-30;
m(:,i)=temp;
m(:,i)= m(:,i)./MW;
end
yi = zeros(length(s_index),Mesh.Jnodes);
rho_s_mass(:) = yy(nsp*Mesh.Jnodes+1:end);
R = 8.314;
for i=1:Mesh.Jnodes
yi(:,i) = m(s_index,i).*MW(s_index)./sum(m(s_index,i).*MW(s_index));
k(:,i) = afac .*((T(i)).^nfac).* exp(-ea ./(R*T(i)));
mprime(:,i) = ycoeff*(k(:,i).*m(istart,i)).*MW; % dm/dt
wdot_mass(:,i) = mprime(:,i)./ Mesh.dv;
end
for i=1:Mesh.Jnodes
drhosdt(i) = -sum(wdot_mass(g_index,i));
end
masslossrate = sum(drhosdt);
dydt = [mprime(:); drhosdt(:)];
end
function phi = phii(yi,rho_s_mass)
global MW s_index
s_density = [9.37000000000000;9.37000000000000;25;9.87000000000000;11.5000000000000;11.5000000000000;...
11.5000000000000;12.1200000000000;5.88000000000000;3.48000000000000;3.59000000000000;...
5.88000000000000;4;7.29000000000000;5.76000000000000;7.22000000000000;5;1.67000000000000;...
55;0.00369448575008421;0.00580475748165167;0.00541504238833635;0.0806563778419628;...
0.0101350128633761;0.00507436386823035;0.00579578562602859];
phi = 1-sum(yi./(s_density.*MW(s_index)))*rho_s_mass;
end
function rho_sm = rhos_mass(yi,phi)
% kg/m3
global MW s_index
s_density = [9.3745;9.3745;25;9.87000000000000;11.5050;11.5050;...
11.5050;12.1200000000000;5.8852;3.4826;3.59000000000000;...
5.88000000000000;4;7.29000000000000;5.76000000000000;7.22000000000000;5;1.67000000000000;...
55;0.00369448575008421;0.00580475748165167;0.00541504238833635;0.0806563778419628;...
0.0101350128633761;0.00507436386823035;0.00579578562602859];
rho_sm = (1-phi)/sum(yi./(s_density.*MW(s_index)));
end