The previous reactor is very simple; a more realistic configuration consists of replacing the homogeneous core by a core with fuel rods in a moderator. Each rod has a radius of 0.5 cm. The core will then be filled by a square lattice. In order to satisfy the moderator/fuel volume ratio, the side of each square is 1.98 cm. Of course, it is not possible to describe each small cell. But it is possible to define a lattice (hexagonal or hexahedra). One has to define a mesh (the hexahedra or the hexagon) and two universes: a universe is either a lattice or a collection of cells; it defines different ‘geometry levels’ (somewhat like Russian dolls).

Heterogeneous core c

c Exterior c

1 0 1:-2:3 imp:n=0 c

c Iron tank c

2 1 -7.87 -1 2 -3 (4:-5:6) imp:n=1 c

c Lead reflector c

3 2 -10.34 -4 5 -6 (10:-11:12) imp:n=1 c

c Core c

4 0 -10 11 -12 imp:n=1 fill=1

5 0 21 -22 23 -24 imp:n=1 u=1 fill=2 lat=1 63-1. 30 imp:n=1 u=2

7 4 -10. -30 imp:n=1 u=2

c tank/reflector surfaces

1 cz 155

2 pz -155

3 pz 155

4 cz 150

5 pz -150

6 pz 150

c reflector/core surfaces

10 cz 100

11 pz -100

12 pz 100

c square mesh

21 px -0.99

22 px 0.99

23 py -0.99

24 py 0.99 c

30 cz 0.5 c Material

m1 26000.55c 1 $ Iron of the tank

m2 82000.50c 1 $ Lead of the reflector

m4 92235.60c 0.0135 92238.60c

0.9865 & 8016.60c 2. $ 235U(1.357)+238U(98.657)+1 O2

m3 1001.60c 2. 8016.60c 1. $ 6 H2O + 1 O2 (of the fuel)

sdef pos 000 erg 2.5 kcode 1000 1 10 150 totnu

The geometry is shown in figure 5.5. In this example, the core is a cylinder filled with universe 1 (cell 4, the fill card = 1). This universe is defined in cell 5 (u = 1). Cell 5 is filled with universe 2 (fill = 2) with a hexahedron lattice (lat = 1); the hexahedral mesh is defined by the planes 21 to 24. Universe 2 is defined as cells 6 and 7 (u = 2).

The keff of the heterogeneous reactor is keff = 1.050 ± 0.001, which is higher because the flux is slightly more thermal (self-shielding of uranium capture) than in the homogeneous case.