# Simulation of point kinetics reactor equations

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Hadeer Abdullah 2021 年 10 月 7 日
コメント済み: Alan Stevens 2021 年 11 月 1 日 8:05
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.

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### 採用された回答

Alan Stevens 2021 年 10 月 7 日
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
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Alan Stevens 2021 年 11 月 1 日 8:05
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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