NE421 Introduction to Nuclear Criticality Safety

# Homework Problem #5

In this tutorial, you are going to learn how to run the REAL crit safety SCALE sequence: CSAS5.  This sequence is like CSAS1, but uses three dimensional geometry, giving it the capability to analyze more real-world problems than the simple spheres that we learned how to analyze in CSAS1.

The good news is that the material description is exactly the same for CSAS5 and CSAS1.  The difference comes in the specification of the geometry: KENO (the 3D transport model inside CSAS5) lets you create complex 3D geometries, far beyond the simple spherical layers that we learned in the previous exercises.

Despite the complexity of the 3D geometries, the basic approach to describing geometries remains the same.  You will recall that the spherical layers of the CSAS1 geometry were laid out from the INSIDE OUT.  That is, when we included the water layer, we specified the material and radius of the central region first, then the material and radius of the next layer out, etc.  In the 3D world of KENO, we describe UNITs (which are standalone components in the geometry--like canisters inside a glovebox or the glovebox itself), the same way: from the inside out.  But, instead of being limited to spheres, the layers can either be SPHEREs, CYLINDERs, or CUBOIDs (rectangular boxes).

HISTORICAL NOTE: Many years ago, the SCALE group created a replacement for KENO5.a (used in CSAS5) that allowed much more geometric flexibility--more shapes, the ability to have overlapping boundaries (that violate the inside-out requirement), etc.--at the expense of a more complicated input. This version is KENO6 and is embedded in the sequence CSAS6. For the most part, the criticality safety community rejected this change and requested that KENO5.a and CSAS5 be kept "alive". It remains true that CSAS5 has remained the "workhorse" of criticality safety. (And if we need more geometric flexibility, we simply go to MCNP to get it.)

## Describing a layer

Just like specifying the outer radius of layers in CSAS1, the layers in a KENO unit are described by specifying a material number and an outer surface that contains it (except for internal layers that have previously been specified).  Here is the syntax for each of the three that we will use.  (The manual describes these and the other outer surface shapes that you can use.)

### A SPHERICAL layer is specified with the syntax:

SPHERE   mat#  1  radius  ORIGIN x y z      [These last 4 are optional.  Without them, the sphere is centered on (0,0,0).]

Example:
`SPHERE   3   1   5.6`
specifies a region that contains material 3 and has an outer surface that is a sphere centered on (0,0,0) with a radius of 5.6 centimeters.

`SPHERE   2   1   4.2  origin 1 2 3`
specifies a region that contains material 2 and has an outer surface that is a sphere centered on (1,2,3) with a radius of 4.2 centimeters.

(Yes, there is an extra "1" sitting there, not doing anything. It means something to the ORNL guys--something about importance, if I remember correctly--but we will just have the "1" in that position every time.)

### A CYLINDRICAL layer is specified with the syntax:

CYLINDER   mat#  1  radius  +z -z ORIGIN x y      [These last 3 are optional.  Without them, the cylindrical axis is the z axis, with x=0 and y=0.]

The +z is the elevation of the TOP of the cylinder and -z is the elevation of the BOTTOM of the cylinder.

You are free to put the origin anywhere in the unit that you want to--but remember where you put it!

Example:
`CYLINDER   1   1   5.6 10 0`
specifies a region that contains material 1 and has an outer surface that is a cylinder centered on the z axis with a radius of 5.6 which goes from 0 to 10 centimeters. (Note that this puts the origin at the center of the bottom surface of the cylinder, which is my preference. Some analysts prefer to put it in the center of the cylinder--in which case the last two numbers in the line would be 5 and -5. Do what you want.)

`CYLINDER   8   1   4.1  7 2 origin 1 2`
specifies a region that contains material 8 and has an outer surface that is a cylinder centered on (1,2) with a radius of 4.1 centimeters which goes from 2 to 7 centimeters in z.

### A CUBOID layer is specified with the syntax:

CUBOID   mat#  1  +x -x +y -y +z -z

The -x, +x, -y, +y, -z, and +z are the upper and lower limits of the x, y, and z ranges.  The tough part is remembering the order that these must be listed.

Example:
`CUBOID 11   1   5 -5 6 -6 7 -7`
specifies a region that contains material 11 and has an outer surface that is a rectangular parallelpiped (a box) ranging from -5 to 5 in x, -6 to 6 in y, and -7 to 7 in z

## Describing a multilayer UNIT

The syntax to creating a UNIT (a standalone object in KENO) is:

UNIT unit#
...Line describing innermost layer
...Line describing next layer moving out
....
...Line describing the outermost layer

### Example: Simple sphere

Just to show you a simple example, a repetition of the HW#3 problem--with the radius changed to 4 cm and a water outer layer added--looks like this:

```=csas5 parm=bonami
HW#5 example
v7-56
pu 1 1 293 94239 100 end
h2o 2 1 293 end
end composition
unit 1
sphere 1 1 4
sphere 2 1 34
end geometry
end data
end```

Copy and paste this input deck and run it as an example.  You will notice a couple of things:

1. It runs a bit longer than CSAS1 did and prints a lot more info to the screen.
2  The output follows the pattern that we learned in our Monte Carlo studies--you get
a. "generation k-effective" for each of the 203 generations
b. a running "average k-effective" column  with a final answer
c. a running "average k-effective deviation" that tells you how much you should TRUST the final k-effective value.
3. At the bottom, we get the "best estimate system k-eff" with the final answer and standard deviation.

### Example: Plutonium metal in a can

For a little more complicated example, let's create a 5 liter can (inner volume) with 0.2 cm thick stainless steel wall and partially fill it with 95% Pu metal (i.e., 95% Pu-239 and 5% Pu-240).  Here it is with a depth of 3 cm in the can.
```=csas5 parm=bonami
fig. 2-2, point 1
v7-56
pu    1 1 293 94239 95 94240 5 end
ss304 2 1 293 end
end composition
unit 1
cylinder 1 1 9.267  3      0
cylinder 0 1 9.267 18.534  0
cylinder 2 1 9.467 18.734 -0.2
end geometry
end data
end
```
This has a k-effective of about 0.819.

Notice particularly that the second layer has material number 0, which specifies vacuum. (We very seldom actually try to model air; we just use a vacuum like this.)  Notice also, though, that the lower limit (-z) of the empty space goes down to z=0, even though the vacuum itself only goes down to z=3.  THIS IS A REQUIREMENT, forced on us by the requirement that each layer COMPLETELY ENCLOSE the prevous layer.  Be sure you understand this and can do it yourself.

It is good practice to do what I did in the above input: Line up each of the entries in a vertial column. Then, you can check for overlap by simply running your eye down the columns--i.e., make sure the radii are non-decreasing as you go down, the +z are non-decreasing, and the -z values are non-increasing.

## Problem description

For this assignment, I want you to do two things:

1. Take our last example and find the critical depth of the plutonium.

2. Find the k-effective for the following problem.  Fill a 55 gallon drum with 5% enriched uranium in the form of UO2 (material name is UO2).  Again use 0.2 cm thick SS304 walls, with an 80 cm depth of the UO2. Surround the drum (top, bottom, and sides) with 30 cm of water.   (You can use the 55 gallon drum dimension that Wikipedia tells you.)

You should report your resulting Pu depth and eigenvalues (of both problems), with the associated uncertainties.  (i.e., "k-eff = x.xxxxx +/- y.yyyyy.)