ne.gif (2791 bytes)     NE571 Reactor Theory and Design
Fall semester 1998

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Calculating Assembly Few-group Cross-sections

In this lesson, we will calculate 3-group cross sections for the three different assembly types that are in the Sequoyah reactor; as you will recall from the pin-cell exercise, the three differ only in the fuel loading.  In Region 1, the uranium enrichment is 2.6%, in Region 2 the enrichment is 2.1%, and in region 3, the enrichment is 3.1%.  We are going to calculate all three of these using SAS2H and produce exposure-dependent assembly 3-group cross sections. 

Actually, another difference is that the first cycle of Region 1 and Region2 includes boron rods in some of the assemblies as well.  This is done to reduce the amount of boron that has to be put in the water -- too much boron in the water gives a positive moderator temperature coefficient.  We will ignore this difference and just use "water pins" in our versions of the Region 1 and Region 2 assemblies. 

I will walk you through the changes to your deck that you will have to make in order to: 

  • Include the water pins in the assembly; and
  • Get SAS2H to print out the few-group cross sections versus exposure.
After you run the three decks, I will have you run a utility I wrote to extract the information that we need and compute 3-group cross-sections parameterized to assembly exposure. 

Setting up the water cells in SAS2H

At the end of the previous exercise, our deck looked something like this: 

=SAS2H     PARM='SKIPSHIPDATA
SEQUOYAH 2.6% FUEL PINS 
44GROUPNDF5                 LATTICECELL 
UO2            1  DEN=10.xx 1.0 8xx 92235 2.6 92238 97.4 END
ZIRCONIUM      2  1.0 6xx END
H2O            3  DEN=.7xxx 1.0 5xx END
B              4  DEN=.7xxx 1.0 5xx END
END COMP
SQUAREPITCH 1.xx .8xxxx 1  3  .9x 2  .8xxxx 0  END
NPIN/ASSM=289 FUELNGTH=366 NCYCLES=1 NLIB/CYC=8 
  PRINTLEVEL=4 INPLEVEL=2 NUMZTOTAL=1 END
500 1.000 
POWER=17.5 BURN=1200 DOWN=15 END
END

From the diagrams and explanation of the SAS2H sequence in the previous exercise, it should be clear to you that we will have to make the following changes to the deck in order to model the 25 water holes: 

  • Change the title to reflect the new conditions.  Add "with 25 water pins" to the second line.
  • Change the enrichment in the title and in the fuel pin U-235 and U-238 isotopic fractions (4th line).
  • Change the number of pins per assembly from 289 to 289-25 = 264.
  • Change the NUMZTOTAL variable from 1 to 2.  This is because our new water pin model will have two regions: the water associated with a single water pin and the smeared fuel pin material.
  • Model a single water pin, with its "share" of the smeared fuel pin.   The outer radius of the water should account for the area of a single pin, Pitch * Pitch. Since each of the 25 water pins "represents"  289/25 assembly pins, the total modeled area should be 289/25*Pitch*Pitch = 18.35 square cm.  This translates into an outer radius of 2.417 cm for the smeared region..  Therefore the "500 1.000" entry will change to "3 0.7xx 500 2.417".
To get SAS2H to print out the few-group cross sections, these additional changes have to be made: 
  • The INPLEVEL variable has to be changed from 2 to 3.  This allows the user to change the BONAMI, NITAWL, and XSDRN input data.
  • BETWEEN the model description and the burn-up cards, put the following cards:
  BON    END
  NIT    END
  XSD
Weighted cross sections
  I4= -1, 3, 0, 9  END

Make sure that the "Weighted cross sections" title begins in the first column (or the utility that follows will not work).. 

The deck should now look like this: 

=SAS2H     PARM='SKIPSHIPDATA
SEQUOYAH 2.6% FUEL PINS with 25 water pins
44GROUPNDF5                 LATTICECELL 
UO2            1  DEN=10.xx 1.0 8xx 92235 2.6 92238 97.4 END
ZIRCONIUM      2  1.0 6xx END
H2O            3  DEN=.7xxx 1.0 5xx END
B              4  DEN=.7xxx 1.0 5xx END
END COMP
SQUAREPITCH 1.xx .8xxxx 1  3  .9x 2  .8xxxx 0  END
NPIN/ASSM=264 FUELNGTH=366 NCYCLES=1 NLIB/CYC=8 
  PRINTLEVEL=4 INPLEVEL=3 NUMZTOTAL=2 END
3 0.7xx 500 2.417
  BON    END
  NIT    END
  XSD
Weighted cross sections
  I4= -1, 3, 0, 9  END
POWER=17.5 BURN=1200 DOWN=15 END
END
 

The above deck is for 2.6% enrichment, which I will run with the name REGION1.  I want YOU to run one of the other assembly types (i.e., 2.1% or 3.1% enrichment), with the name REGION2 or REGION3. 
 

Fitting the cross sections

After your calculation has run, run the READ2H utility. (If you are using the 3rd floor computers, it should be in your C:\WINDOWS directory with the name READ2H.EXE; if so, you can get it going by typing "read2h" and awaiting the prompt for the name of your SAS2H output file.  If not, you will have to get it from me.)  After you enter your SAS2H output file name (e.g., "region1.out"), the utility will create a text output file with the extension "r2h" (i.e., "region1.r2h"). 

The READ2H utility performs a number of functions on the SAS2H output: 

  • It echoes the case cycle data and the k-effective history for both the pin model and the assembly model.  Note that the k-effectives for the assembly model are about 1% lower than might be expected because the XSDRNPM calculation automatically  includes a buckling corresponding to a 2 meter tall reactor core.
  • For each of the nuclides in the assembly model (including the important -- but not all -- actinides,  fission products, and activation products), the exposure-dependent nuclide density (in atoms/barn-cm) is printed.
  • For the same list of nuclides, the three-group assembly-smeared cross-sections of interest (total, nu*Fission, chi distribution, transport, and scattering) are listed.  The three groups correspond to a fast group (E>0.9 MeV), an intermediate group (0.4 eV < E < 0.9 MeV), and a thermal group (E< 0.4 eV).
  • The assembly-smeared macroscopic cross sections by exposure are printed.  Included as the last three lines of this output are the coefficients, C0, C1, and C2 of a least-squares fit of these data, using the equation:

where E is the assembly exposure in megawatt-days
  • For verification of the cross section parameterization, infinite medium k-effective calculations are performed for the assembly at each of the exposures, using both the  "raw" 3-group cross sections and using the "fitted" 3-group cross sections.  (As noted in the output, the 0 exposure "raw" 3-group cross sections do NOT include equilibrium xenon and other short-lived isotopes.  Therefore, this exposure data is NOT used in the parameterized fit.  Our normal expectation is that the fitted cross sections will be about 3-4% below the raw cross sections in k-effective at 0 exposure, but that the fitted cross sections should produce k-effective estimates that are much closer (i.e., within half a percent) at other exposures.) 

Complete the assignment:

For the Region 2 or Region 3 assembly you calculated, answer the following questions using the READ2H output (e.g., in file "regionx.r2h"): 

1. What is the expected lifetime of this assembly (in megawatt-days)? 

2. From the first k-effective table, are the assembly k-effectives higher or lower than the pin-cell k-effectives?    Why would removing these 25 fuel pins (and replacing them with water) INCREASE reactivity?  Why do we design reactors to be undermoderated like this? 

3. For proliferation reasons, we like the Pu-240/Pu-239 ratio to be as high as possible.   (I have heard that values above about 6% cause a weapon to pre-ignite.)  What is this ratio at the end of life? 

4. For the most part, the total cross sections for the nuclides are fairly stable with exposure.  Most of the exceptions occur for actinides in group 2.  Give me some examples from your output.  Why does this happen? 

5. What is the percentage burnup of the U-235 during the lifetime of your assembly?  Compare this with the percentage reduction of the thermal (group 3) macroscopic nu*Fission cross section.  Hmm.  Obviously, some other fissionable nuclides are "taking up the slack" as the U-235 depletes.  At the end-of-life, what other nuclides are contributing to the thermal fission cross section and in what proportion? 

6. Assuming that B-10 constitutes 20% of boron atoms and has a group 3 assembly absorption cross section of 2300 b, what concentration of boron (in ppm mass in water) would be required to hold your assembly critical at the beginning of life?  Use the 3-group macroscopic cross sections at 0 exposure to answer this question and ignore all other boron cross sections. 

Be prepared to share your answers to the above questions in class.

Return to Course Outline                                                                                               © 1998 by Ronald E. Pevey.  All rights reserved.