NE421 Introduction to Nuclear Criticality Safety

# Homework Problem #4

As we have studied, deterministic methods require that the dimensions of space, energy, and direction be discretized as part of the numerical treatment.  These decisions are made in the following way:

1. Energy: The user (you) picks the cross section library as part of the input.  (We have been using the 56- group library.) In the output file, you can find the energy group boundaries in an output array just below the words "neutron group parameters".
2. Direction: The calculation requires that an angular quadrature be specified.  Although we learned that a quadrature requires the specification of a weight and a cosine value for each direction, the quadratures built into SCALE are specified by the number of directions (2,4,6,8,16,32,64, ...).
3. Spatial: The spatial subdivisions of the spherical layers are chosen automatically by SCALE.  The number of divisions are chosen according to the actual cross sections in the layer material, so is problem-dependent.

The user can over-ride the default values from SCALE by adding a "MORE DATA" block (which should be between the END ZONE line and the END CELLDATA line).

(NOTE: If you put these lines in the wrong place, the new lines will simply be ignored. If you put in a change and the answers do not change, then YOU HAVE MADE A MISTAKE.)

The syntax is:

MORE DATA
key1=value1
key2=value2
...
END MORE

The SCALE manual gives all of the keywords that can be used.  The ones we will use in this exercise are:

ISN = number     where "number" gives the number of directions you want SCALE to use

and

SZF = value      where "value" of 1.0 means you want SCALE to use its default choices.  0.5 gives you smaller (i.e., roughly twice as many) divisions; 2.0 gives larger (i.e., roughly half as many) divisions.

In this assignment, I want you to take the CSAS1 problem we used in HW#3:
```
=csas1 parm=bonami
fig. 2-2, point 1
v7-56
pu  1 1 293   94239 100 end
h2o 2 1 293   end
end composition
multiregion spherical left_bdy=reflected right_bdy=vacuum cellmix=500 end
1  5
end zone
end celldata
end
```

and test the effect on the eigenvalue of:

a. Halving the default angular quadrature (which is 8, so run 4)
b. Doubling the default angular quadrature to 16
c. Halving the spatial size parameter.
d. Doubling the spatial size parameter.
e. Using the 252 group cross section set (i.e., change 'v7-56' to 'v7-252' and MAKE SURE the ISN and SZF parameters are back to the default--you could remove the MORE DATA block to assure this).
f. Finally, find the "right" answer by running a (slow) calculation with ISN=64 and SZF=.1 with the 252 group library.