Simulation of point kinetics reactor equations

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Hadeer Abdullah on 7 Oct 2021
Commented: Alan Stevens on 1 Nov 2021
Hello!Those two equations are needed to be solved (the attached picture)
The initial conditions n(0)=0.1, c(0)=0
The required: find the required time to increase n from 0.1 to 1
I got errors regarding syms functions. I am not sure if I do that right.I attached to this a matlab file which contains all the parameters and what I tried to do.

Alan Stevens on 7 Oct 2021
There are seven equations if you are using all six delayed neutron groups. You don't give your reactivity, nor the individual beta values. The program below uses arbitrary data for rho and the timespan, and Glasstone and Sesonske values for beta_i. If you are only interested in the case of a single group of delayed neutrons you should be able to modify the following appropriately:
% Point reactor kinetics 6 groups of delayed neutrons
beta = [0.00021; 0.00141; 0.00127; 0.00255; 0.00074; 0.00027]; % Taken from Glasstone and Sesonske
betasum = sum(beta);
rho = 1.1*betasum; % reactivity
% Initial consitions
c0 = zeros(6,1);
n0 = 0.1;
tspan = [0, 1];
nc0 = [n0; c0];
[t, nc] = ode45(@(t,nc) kinetics(t,nc,rho,beta,betasum), tspan, nc0);
n = nc(:,1);
c = nc(:, 2:7);
plot(t,n),grid,
xlabel('time'), ylabel('n')
% figure
% plot(t,c),grid
% xlabel('time'), ylabel('c')
function dncdt = kinetics(~,nc,rho,beta,betasum)
L = 0.0001;
lam = [0.0126; 0.0337; 0.111; 0.301; 1.14; 3.01];
n = nc(1);
c = nc(2:7);
dndt = (rho - betasum)/L + sum(lam.*c);
dcdt = beta*n/L - lam.*c;
dncdt = [dndt; dcdt];
end
Alan Stevens on 1 Nov 2021
Something like this?
% Point reactor kinetics 6 groups of delayed neutrons
beta = [0.00021; 0.00141; 0.00127; 0.00255; 0.00074; 0.00027]; % Taken from Glasstone and Sesonske
betasum = sum(beta);
rho = [0.01 0.02 0.03];
% Initial consitions
c0 = zeros(6,1);
n0 = 0.1;
tspan = [0, 1];
nc0 = [n0; c0];
for i = 1:numel(rho)
[t, nc] = ode45(@(t,nc) kinetics(t,nc,beta,betasum,rho(i)), tspan, nc0);
n = nc(:,1);
c = nc(:, 2:7);
figure
plot(t,n),grid,
xlabel('time'), ylabel('n')
legend(['rho = ' num2str(rho(i))])
end
function dncdt = kinetics(~,nc,beta,betasum,rho)
L = 0.0001;
lam = [0.0126; 0.0337; 0.111; 0.301; 1.14; 3.01];
n = nc(1);
c = nc(2:7);
dndt = (rho - betasum)/L + sum(lam.*c);
dcdt = beta*n/L - lam.*c;
dncdt = [dndt; dcdt];
end

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