NE571 Reactor Theory and Design
Fall semester 1998
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NE571 Reactor Theory and Design
Fall semester 1998
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Fuel Assembly ShufflingIn this lesson, we continue the previous lesson by learning the three additional CARTER keywords that allow us to modify the reactor assembly pattern in the middle of a fuel cycle: initial_exposure, before, and after.Using keyword "initial_exposure"By default, the CARTER code begins each assembly clean, i.e., with exposure of 0. The initial_exposure keyword allows you to modify the exposure of each assembly at the beginning of the calculation. With this flexibility, you gain the ability to restart a calculation. The only disadvantage to this way of restarting is that the time and total reactor exposure are reset to zero, so you have to keep up with them. (As we will see later, a better use of initial_exposure is to recycle assemblies to the next cycle, for which it IS appropriate to reset the time and reactor exposure.)As an example, let's simply go back into the example of the previous lesson and restart it in the middle. Let's open the "r1.out" file and go to the point that the incremental reactor exposure is 8000 MWD. (Searching on "burnup step", we find it at line 1207.) If we scroll down a few lines, we find the "Assembly Exposure" map -- this is what we want to cut-and-paste into the initial_exposure field. Therefore, we are going to copy "r1.inp" into a new input file, "r2.inp", and add the lines (anywhere): initial_exposure =
If we then re-run CARTER using "r2.inp" as the input file, the resulting output has the following summary (at the end):
Avg. Max/Ave
Max
Comparing it to the summary at the end of "r1.out":
Avg. Max/Ave
Max
as expected, the pattern of "r2.out" is equivalent to the last half
of "r1.out" after adjustment for the restarted time and average assembly
exposure (and cutting me a little slack in the last decimal place).
Using the "before" and "after" fields to replace exposed assembliesThe way that we implement the midcycle movement and replacement of assemblies is to use the before and after keywords. The before field simply assigns an integer to each of the assemblies (actually, you only have to assign integers to positions that are going to change); the after field then allows you to rearrange the assemblies (by moving the integers around) or, alternately, enter a negative assembly type number to specify a fresh assembly of the indicated type.In the before field, you are free to assign the numbers any way you want. I have found it useful to paste one of the integer maps from the output file -- the EXPOSURE ORDERING MAP or the REVERSE EXPOSURE ORDERING MAP or the POWER ORDERING MAP -- so that the assemblies are already ordered in some way that helps me decide how to shuffle them. As a continuation of the previous example, let us return to the 8000 MWD restart and replace some of assemblies with fresh fuel. Start by copying the "r2.inp" to a new "r3.inp" file, and then edit the new file. Looking at the exposure map, we see that the maximum exposure is just over 10,000 MWD. Let us (somewhat arbitrarily) assume that we want to discharge all assemblies over 8000 MWD. Since we are making our decision based on exposure (which is the normal case, actually), let us use the EXPOSURE ORDERING MAP from the first step of "r2.out" and paste it into the before field: before =
As expected, the assemblies are numbered from highest to lowest exposure. (It is a little surprising, perhaps, that assembly #1 is not in the center.) Comparing to the initial_exposure map (earlier in this lesson), we see that the lowest number assembly that we want to keep is #32 (in the first row) with an exposure of 7711 MWD. So, copy the before field into a new after field and edit the after field by replacing all numbers less than 32 with "-3" to specify a fresh assembly of type region3: after =
CARTER, by the way, includes simple "reality checks" on your reshuffling: making sure that all assemblies in the after map are also present in the before map and making sure that no assembly from the before map shows up more than once in the after map. Also, any assemblies in the before map that are not in the after map are considered to be discharged; CARTER includes a list of these, with an average exposure included. Now run this case to get the following burnup summary:
Avg. Max/Ave
Max
Notice that the replacement of the burned out assemblies extended the life from 6447 more MWD to 14850 more MWD. Note however, that the 14.850 kMWD takes more than 1130 days of operation, compared to only 940 days for the original "r1" run of 14.4 kMWD. This extra time is because the reactor powers are relatively lower. For example, the initial max/ave assembly power is a very high 2.7846. This is because, of course, all the fresh fuel is on the inside of the core and the old, exposed assemblies are on the outside; this results in a power profile that is heavily biased toward the center. Let's do a simple reshuffling example to see if we can help flatten this out. Using the "before" and "after" fields for reshufflingIn order to flatten the initial power profile of the new core, let's move some assemblies around. How should we do this? Although this procedure has to be somewhat "trial-and-error", we can get an idea of what our philosophy should be by remembering a simple fact we discussed earlier in class: assemblies that are more reactive than average are net producers of neutrons and, conversely, assemblies that are less reactive than average are net consumers of neutrons. In power profiles, this translates to the fact that the more reactive assemblies will have a power that is higher than the average of the powers of its neighbors. Therefore, a number of above-average-reactivity assemblies grouped together will combine to produce a significant local power peak. The converse is, of course, true for groups of below-average-reactivity assemblies: they will cause a significant local power dip.Our philosophy should be to break up these groupings. In practice, we will be guided by the RELATIVE FISSION POWER maps in the output. Start by copying "r3.inp" into "r4.inp" and editing the new file. Look at the first "Relative Fission Power on original grid" map: Relative Fission Power on original grid .0000 .0000 .0000
.0000 .0000 .0000 .0000
.0000 .0000
The peak power is in the lower left hand corner -- call it position (1,1) -- and the lowest relative power is 0.0782 in positions (5,7) and (7,5). Since the hottest assembly is in a diagonal position and the coldest is one (diagonal) position away from the diagonal, let's see what happens when we switch the assembly in (1,1) with the assembly between the cold assemblies, in position (6,6). We implement this simple shuffle by changing the after map into: after =
Running this new case gives us a summary of:
Avg. Max/Ave
Max
The results show an improvement:
Relative Fission Power on original grid .0000 .0000 .0000
.0000 .0000 .0000 .0000
.0000 .0000
We see from this that we did what we set out to do: the highest power assembly at position (1,1) did drop and the lowest power assemblies did heat up a bit. Unfortunately, this process is like squeezing a balloon: if you push one point, it will bulge out somewhere else. The position of the hottest assembly moved one diagonal step to position (2,2). Also, another, more subtle, feature is that the new profile is harder to flatten -- in the previous power profile, there were only two other assemblies within 0.5 of the hottest one; and they were immediate neighbors of the peak power assembly. In the new profile, there are eleven other assemblies within 0.5 of the hottest one. Therefore, it is not very likely that another shuffling of just two assemblies will help us much. It looks to me, for example, that our best next step is to shuffle four assemblies: switching the (1,3) and (3,1) assemblies with the (5,7) and (7,5) assemblies. Or maybe switching (1,2) and (2,1) with (5,6) and (6,5). I will let you figure it out. Complete the assignment:Try to continue to improve the core behaviour by improving the reshuffling strategy. You should be able to get the initial max/average ratio below about 1.7.Be prepared to share your resulting assembly map to class. |
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