BlueBox

Introduction
BlueBox is a homemade cooler at Pappy's Orchard that has 6" thick extruded Polystyrene walls.  Polystyrene is a good neutron moderator and reflector, so the idea is to put a small reactor into BlueBox in order to provide power for Pappy's Orchard and Pappy's Orchard, turkey division.

Simulation

Core Geometry

I did a basic simulation of a 1x1 reactor with nine water inlets.  The core was just U-235, and for both the water and the core I used single group diffusion; i.e. thermal averages of the adsorption and fission coefficients were used.

I had to do an simpler similar problem for a course project, but in that project we had to solve the diffusion equation with a linear system of equations; for this I used MATLAB's PDE toolbox (it made the more complex geometry easier to solve and is a lot faster).

Core Flux

The core flux of neutrons is on the left.  Water is a moderator (slows down and absorbs neutrons), so in and around the water inlets the flux drops.  You can also see the general cosine shape of the flux, the analytical spatial solution for a homogeneous reactor (no water inlets) is

$\Phi(x,y,t)=\sum_{n~odd}^{\infty}e^{-\lambda_n t}\left ( C_n Cos(\frac{\pi x}{n a})Cos(\frac{\pi y}{n a})+ B_n Sin(\frac{\pi x}{n a})Sin(\frac{\pi y}{n a}) \right )$

Here the sin terms drop out because I required the flux to go to zero at the boundary, resulting in:

$\Phi(x,y,t)=\sum_{n~odd}^{\infty}e^{-\lambda_n t}\left ( C_n Cos(\frac{\pi x}{n a})Cos(\frac{\pi y}{n a})\right )$