Reactor kinetics and related equations solved by using an “open source” based code

European Nuclear Society
e-news Issue 23 Winter 2008
http://www.euronuclear.org/e-news/e-news-23/reactor-kinetics.htm

Reactor kinetics and related equations solved by using an “open source” based code

By Frigyes Reisch,
KTH, Royal Institute of Technology, Nuclear Power Safety
Stockholm, Sweden

At the 2008 ENS conferences, RRFM in Hamburg and NESTet in Budapest, sessions on reactor kinetics and related programmes – which were previously published in ENS NEWS - were well received. However, at these conferences it became clear that there is a need to run these programmes with a freely available code based on an open source. Octave www.octave.org is just such a code. However, this is not an elegant way to make a presentation, it is clumsy though economical. In the summer 2006 and spring 2008 issues of ENS NEWS the differential equations and the MATLAB programme were given. Below is the OCTAVE programme and the graphic results of both programmes are provided. Following on from this, the other MATLAB programmes described in the references can also be written in OCTAVE code and used freely.

The OCTAVE programme

function xdot = f (x, t)

DeltaK=3*0.010*0.50;

xdot = [(DeltaK/0.001-6.502)*x(1)+0.0124*x(2)+0.0305*x(3)+0.111*x(4)+0.301* x(5)+1.14*x(6)+3.01*x(7);
0.2150*x(1)-0.0124*x(2);
1.4240*x(1)-0.0305*x(3);
1.2740*x(1)-0.1110*x(4);
2.5680*x(1)-0.3010*x(5);
0.7480*x(1)-1.1400*x(6);
0.2730*x(1)-3.0100*x(7)];

endfunction

x0 = [1; 17.3387; 46.6885; 11.4775; 8.5316; 0.6561; 0.0907];

t = linspace (0, 0.2, 1000)’;

x = lsode ("f", x0, t);

plot (t, x(:,1))

print -deps foo.eps

OCTAVE

Octave

MATLAB

Acknowledgement
Thanks to Francesco Cadinu Ph.D. students at KTH for the Octave information.

References in ENS NEWS:

Taming the Chernobyl Avalanche (2008 spring):
www.euronuclear.org/e-news/e-news-20/chernobyl-avalanche.htm

Calculation of the neutron flux, fuel and moderator temperature transients for Research Reactors (2008 spring):
www.euronuclear.org/e-news/e-news-20/neutron-flux.htm

Reactor Kinetics Equations applied to the start-up phase of a Ringhals PWR (2006 autumn):
www.euronuclear.org/e-news/e-news-14/pwr.htm

Neutron Kinetics of the Chernobyl Accident (2006 summer):
www.euronuclear.org/e-news/e-news-13/neutron-kinetics.htm