I need help please for Simulation of Xenon Oscillations in a Nuclear Reactor

[TOULA]

TL;DR

(TL;DR) : Simulation of Xenon oscillations in a nuclear reactor, studying iodine and xenon concentration evolution and neutron flux using a diffusion model. Seeking advice on issues with time step stability and inconsistent results in my code.

Hello everyone,

I am currently working on a numerical simulation project to study the oscillations of Xenon in a nuclear reactor as a function of time and space. My approach is based on a diffusion model coupled with the evolution of the concentrations of these fission products, and I am seeking feedback or advice. My code is currently not working as expected, my results are not consistent, and I quickly encounter errors when I increase my time step. I won't go into too much detail; I'd prefer to let you see it for yourselves.

Here are the main points of my code:

Reactor Modeling:

• I divide the space into a uniform grid with a certain number of points (Nx = 500).
• The initial concentrations of Iodine and Xenon are calculated based on their equilibrium state before any dynamic imbalance.
• An initial perturbation is applied to the neutron flux to introduce a slight imbalance, and then I simulate its evolution over time.

Residues and Calculations:

• I use an implicit Newton-Raphson method to solve the time evolution of the concentrations of Iodine and Xenon, as well as the neutron flux. Residues are calculated at each iteration and solved using a sparse solver to improve efficiency.

Jacobian Matrix:

• A Jacobian matrix is constructed at each iteration to linearize the system of nonlinear equations that describe the reactor’s behavior.

Keff Calculation:

• At each time step, I calculate the effective reactivity (Keff) considering the total macroscopic cross section and the absorption of neutrons by Xenon and Iodine. This reactivity is then used to adjust the neutron flux in the simulation.

Results Visualization:

• At the end of each simulation, I generate 3D plots to observe the evolution of the concentrations of Iodine, Xenon, and the neutron flux over time and as a function of position in the reactor.
• Additional visualizations allow me to track the temporal evolution of concentrations at the center of the reactor (x=L/2).

Please, I would really appreciate your help. I am open to any discussions. I am attaching my code for you to have a look at.

Thank you in advance for your feedback and suggestions!

 

[Alex A]

Hi @TOULA,

Welcome to PhysicsForums. What is the goal for this code?

 

[Astronuc]

TL;DR Summary: (TL;DR) : Simulation of Xenon oscillations in a nuclear reactor, studying iodine and xenon concentration evolution and neutron flux using a diffusion model. Seeking advice on issues with time step stability and inconsistent results in my code.

a numerical simulation project to study the oscillations of Xenon in a nuclear reactor as a function of time and space. My approach is based on a diffusion model coupled with the evolution of the concentrations of these fission products

Modeling Xe oscillations is a challenging problem - especially spatially in detail.

When one mentions spatially, is this 2D or 3D?

Is one accounting for Doppler effect in the fuel?

Does one assume a fresh core, or a mature (equilibrium) core?

Is one using two group, four group, or multi-group (> 4) neutron energy groups?

 

[Alex A]

I haven't been able to run it yet because my install of scipy and numpy appear to be not compatible with each other. I don't really do python.

It looks like a cool attempt to get an answer but some of the maths is...

Phi = Phi / keff

...a bit suspect.

 

[berkeman]

It looks like a cool attempt to get an answer but some of the maths is...

Phi = Phi / keff

...a bit suspect.

Yeah, how does the compiler handle that? The behavior of a C compiler for example is well defined for that statement...