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By Charles Rhodes, P.Eng., Ph.D.

This web page deals with FNR geometrical constraints imposed by the fuel bundle design.

The following FNR geometrical calculations are based on a FNR with a rated thermal power of 1000 MWt. The following diagram shows the plan view of the fuel bundle array.

A FNR consists of central active fuel bundles surrounded by passive fuel bundles which in turn are surrounded by a liquid sodium guard band. Within the guard band are the 56 intermediate heat exchangers shown as a black ring. Note that every second intermediate heat exchanger is staggered inwards. The primary sodium pool walls contain a 2 m thickness of fire brick. In the above diagram only one quadrant of fuel bundles is fully detailed.

This above diagram is to approximate scale. The active mobile square fuel bundles are shown in red. The passive fixed square fuel bundles are shown in purple. For structural stability the diagonal fuel bundle assembly faces are composed of fixed octagonal fuel bundles. If necessary a shaped steel form can surround the assembly of fuel bundles.

As shown at FNR FUEL BUNDLE the external dimensions of a square fuel bundle including shroud thickness, tolerance allowance and thermal expansion allowance are:
[19 X (5 / 8)] inches wide X [19 X (5 / 8)] inches long X 6 m tall. Three fuel tubes are lost at each corner to make space for corner girders. Thus each square fuel bundle contains:
[(18 X 18) - 4 (3)] = 312 fuel tubes.

The external dimensions of an octagonal fuel bundle are [23 X (5 / 8)] inches face to face X [23 X (5 / 8)] inches face to face X 6 m tall. The octagons are formed by clipping off 6 fuel bundles off each corner of a 22 fuel tube X 22 fuel tube square. Each octagonal fuel bundle contains:
[(22 X 22) - 4(6)] = 460 fuel tubes.

Note that the number of fuel tubes per tube bundle is further reduced by allowance for diagonal reinforcing steel cross pieces.

In order to achieve both good liquid sodium natural circulation, which requires fuel tubes on a square grid, and good horizontal mechanical stability a mixture of square and octagonal shaped fuel bundles is used. The maximum face to face size allocation for the octagonal fuel bundles is set at:
23 X (5 / 8) inch = 14.375 inches
by transportation weight constraints. The square fuel bundles are made as large as practical: 19 X (5 / 8) inch = 11.875 inches face to face
with respect to the octagonal bundles to achieve acceptable fuel bundle assembly structural strength and acceptable modulation of average core zone fissile fuel concentration. These dimensions result in a linear center to center spacing of:
[14.375 inch + 11.875 inch = 26.25 inch = 26.25 inch X .0254 m / inch = 0.66675 m.
This dimension is close enough to (2 / 3) m to permit a scale plan view diagram in m rather than inches.

The above diagram was prepared using a scale of:
14 squares = (2 / 3) m
On the above diagram the ratio of the small square size to the larger square size is not exactly correct but it is close enough for diagramatic purposes.

To minimize the liquid sodium requirement the assembly of fuel bundles is chosen to be close to a regular octagon so that it will fit snugly within a circular liquid sodium tank wall. The octagon straight faces consist of 9 octagonal fuel bundles separated by 8 square fuel bundles. The length of a straight side measured between the centers of the end bundles is:
8 X 42 X (5 / 8) inch = 210 inch.

Measured from the ends of these fuel bundles the straight face length is:
210 inch + 23(5 / 8) inch = 224.375 inch

The octagon angled faces each consist of 13 corner connected octagonal fuel bundles. Straight and diagonal face fuel bundles are shared at corners.

Measured along a diagonal through octagonal fuel bundles, the center to center distance between adjacent octagonal fuel bundles is:
(2^0.5) X [21 X (5 / 8) inch]
= 18.561 inch

Measured from octagonal fuel bundle center to octagonal fuel bundle center the length of a diagonal face is:
12 X 18.561 inch
= 222.738 inch
which is about 6% more than would be the case for an ideal regular octagon.

The fuel bundles are a subset of a theoretial array 41 bundles X 41 bundles. Theoretically there is an octagon bundle at each corner of the array and there is an octagon bundle at the center of the array.

Measured from octagonal fuel bundle center to octagonal fuel bundle center the face to face distance of the entire assembly of fuel bundles is:
[40] X [(21 X (5 /8) inch] = 525 inch

Measured from the outside edges of the octagonal fuel bundles the fuel bundle assembly straight face to straight face distance is:
525 inch + [23 X (5 /8) inch] = 539.375 inch
= 539.375 inch X .0254 m / inch
= 13.700 m

The intermediate heat exchangers are located at an elevation above the top of the fuel tubes, so that primary sodium guard band extends under the intermediate heat exchangers. The reactor primary sodium pool is ~ 20 m inside diameter which provides a neutron absorbing guard band ~ 3.0 m thick around the perimeter of the fuel bundle assembly. The heat exchanges are protected from high energy neutrons originating in the core fuel via a very long diagonal through the blanket.

Note that the cost of the reactor enclosure roof and the reactor service gantry crane increase rapidly with increasing primary sodium pool diameter, so larger fuel bundle assembly diameters may be uneconomic.

From a structural component transportation perspective it is advantageous to keep most of the steel beams that support the reactor, its enclosure roof and the gantry crane less than 16 m long. Hence limit the face to face diameter of the assembly of fuel bundles to 13.7 m. This restriction allows the use of a liquid sodium pool that has an inside diameter of 20 m and a reactor building with an outside dimensions of 30 m X 30 m.

[21 X 23 X (5 / 8) inch] + [20 X 19 X (5 / 8)inch]
= [(21 X 23) + (20 X 19)] X 5 / 8 inch
= (483 + 380) X (5 / 8) inch
= 539.375 inches
= 539.375 inch X 0.0254 m / inch
= 13.700125 m
The corresponding radius is:
13.700 m / 2 = 6.850 m

The maximum fuel bundle assembly radius is:
= {[(face to face diameter) / 2]^2 + [(face length) / 2]^2}^0.5
= {[(539.375 inch) / 2]^2 + [(224.375 inch) / 2]^2}^0.5
= {72,731.35 inch^2 + 12,586.04 inch^2}^0.5
= 292.09 inch
= 292.09 inch X .0254 m / inch = 7.42 m

Around the perimeter of the fuel bundle array there must be ring of sufficient width for the intermediate heat exchangers. There is space for 60 heat exchangers of which 56 are actually used due to space allocation for 4 air locks. The heat exchangers are in two overlapping concentric rings.

Each heat exchanger is 46 inches in diameter as set by pressure flange standards. The outer edge of the outer ring of heat exchangers is 0.6 m from the pool wall. Hence the outer ring of heat exchangers are on a circle with a radius of:
10 m - 0.6 m - 23 inch(0.0254 m / inch)
= 9.4 m - 0.5842 m
= 8.8158 m

On this circle the outer ring of heat exchanges are spaced center to center at:
2 Pi (8.158 m) / 30 = 1.84637 m intervals
= 72.692 inch intervals.

Half of this spacing distance is:
36.346 inches

The inner ring of heat exchangers are spaced 48 inches center to center from the outer heat exchangers.

The radial distance between the two heat exchanger location rings is:
[(48 inch)^2 - (36.346 inch)^2]^0.5
= [2304 inch^2 - 1321.03 inch^2]^0.5
= 31.352 inch

Hence the required primary sodium pool radial width taken up by the intermediate heat exchangers is:
0.6 m + 23 inch + 31.352 inch + 23 inch
= 0.6 m + 77.352 inch
= 2.5647 m

Recall that the maximum fuel bundle assembly radius is:
= 7.42 m

Thus the minimum requied primary liquid sodium pool inside radius is:
7.42 m + 2.5647 m
= 9.9847 m
~ 10.0 m
so the required primary sodium pool inside diameter is 20.00 m

The reactor fuel bundle array is formed from a theoretical fuel bundle grid which has has 41 rows and 41 columns. The reactor diagonal faces are formed from octagonal fuel bundles. The assembly of fuel bundles consists of a square main grid of 41 X 41 fuel bundles with:
(1 + 3 + 5 + 7 + 9 + 11)= 36 octagonal fuel bundles cut off each corner and (2 + 4 + 6 + 8 + 10 + 12)= 42 square fuel bundles cut of each corner.

The total number of octagonal fuel bundle positions remaining in one such reactor is:
(21 X 21) + (20 X 20) - 4(36)
= 441 + 400 - 144
= 697 octagonal fuel bundles.

The total number of square fuel bundle positions remaining in one such reactor is:
(21 X 20) + (20 X 21) - 4 (42)
= 840 - 168
= 672 square bundle positions.

Thus in summary one reactor contains 697 potential octagonal fuel bundle positions and 672 potential square fuel bundle positions for a total of 1369 fuel bundle positions.

At the outer edge of the fuel tube assembly are two rings of potential fuel bundle positions that are reserved for used fuel bundles that are cooling outside the neutron flux.

The fuel bundle assembly outer ring contains:
4 [20 + 8] = 112 fuel bundles, 80 octagonal and 32 square

The second ring from the outside contains:
4 [27] = 108 fuel bundles, 32 octagonal and 76 square.

The two cooling rings together contain 112 octagonal bundle positions and 108 square bundle positions.

Surrounding the active fuel bundles but inside the cooling rings is the perimeter blanket.

Assume that for good fuel breeding behind the fuel assembly straight octagon faces a fully populated perimeter blanket consists of 4 fuel bundle rings with a total width of:
4 X 21 X (5 /8) inch
= 52.5 inches
= 1.333 m
and over the diagonal surfaces the perimeter blanket consists of 3 fuel bundle rings with an effective width of:
3 X 21 inch X (5 / 8) inch X 2^0.5 = 55.684 inch
= 1.414 m

A physical count shows that the cooling rings plus the passive perimeter blanket rings contain 340 octagonal fuel bundle positions and 332 square fuel bundle positions.

Hence the perimeter blanket contains:
(340 - 112) = 228 octagonal fuel bundles
(332 - 108) = 224 square fuel bundles.

Recall that from FNR FUEL BUNDLE each octagonal fuel bundle contains 416 fuel tubes and each square fuel bundle contains 280 fuel tubes.

Hence the maximum number of passive fuel tubes in the blanket zone is given by:
(228 X 416) + (224 X 280)
= 94,848 + 62,720)
= 157,568 passive fuel tubes

A physical count shows that the reactor core zone contains:
357 octagonal fuel bundles
340 square mobile fuel bundles

The total number of active fuel tubes per reactor is given by:
(number of active octagonal fuel bundles) X (number of fuel tubes per octagonal fuel bundle)
+ (number of active square fuel bundles) X (number of fuel tubes per square fuel bundle)
= (357 X 416) + (340 X 280)
= 148,512 + 95,200
= 243,712 active fuel tubes

Fuel bundle quantity check:
(357 octagonal active
+ 340 square active
+ 228 octagonal passive
+ 224 square passive
+ 112 octagonal cooling
+ 108 square cooling)
= 1369 fuel bundles

Minimum total number of fuel tubes
= 243,712 active + 157,568 passive
= 401,280

At about 4 kWt per active fuel tube this design allows for a reactor rated for about:
4 kWt / active fuel tube X 243,712 active fuel tubes
= 974.8 MWt or ~ 320 MWe.

Outside the fully populated rings of passive fuel bundles are 2 partially populated rings of cooling active fuel bundles. These two rings of fuel bundles do not have indicator tubes attached. Hence in terms of external dimensions the cooling active fuel bundles are the same as passive fuel bundles.

The outer two rings of this assembly of fuel bundles less the number of bundles that must be temporarly moved for center access are available for cooling used active fuel bundles.

The cooling fuel bundle positions are in two groups. The outer ring has 80 octagonal bundle positions and 32 square fuel bundle positions. The next inner ring has 32 octagonal fuel bundle positions and 76 square fuel bundle positions. During normal reactor operation some of these cooling fuel bundle positions are left vacant to allow fuel bundle position flexibility for unscheduled maintenance. The maximum cooling bundle capacity is:
(80 + 32) = 112 octagonal bundles
(32 + 76) = 108 square bundles.

In order to replace an intermediate heat exchange bundle it is simply lifted vertically.

The air lock inside width and bottom radius must accomodate the 46 inch diameter intermediate heat exchaner flanges.

Assume that the facility has four air locks, each 1.2 m wide X 3 m high X 9___ m long to permit exchange of fuel bundles and intermediate heat exchangers. The air locks should be designed for complete evacuation, and hence must have a safe working gauge pressure rating of - 101 kPa.

1)The 1st step in fuel bundle exchange is to remove all members of the cooling fuel bundles that are ready for reprocessing.

If there is any need for intermediate heat exchanger replacement this is the opportune time for this replacement.

2) The 2nd step is to disconnect obstructing indicator tubes and to remove appropriate fixed fuel bundle corner bolts. Then ther are as many as: (112 positions available for cooling octagonal fuel bundles and up to 108 positions available for cooling square fuel bundles. Typically about (357 / 5) = 72 octagonal bundle cooling positions and (340 / 5) = 68 square bundle cooling positions are required for core fuel bundle cooling. The remaining cooling positions are available to support unplanned reactor maintenance. Thus each active fuel bundle is allocated a:
(30 year fuel cycle period / 5) = 6 year in reactor cooling period.

3) The 3rd step is to move:
(72 + 68) = 140 used active fuel bundles from the fuel bundle assembly interior to the vacant cooling positions.

4) The 4th step is to extract the interior (1 / 3) of the blanket bundles for reprocessing.

5) The 5th step is to move the middle third of the blanket bundles to the inner blanket bundle positions.

6) The 6th step is to move the outer third of the blanket bundles to the middle blanket positions.

7) The 7th step is to replace the 140 moved active fuel bundles with new active fuel bundles brought in via the air lock.

8) The 8th step is to repopulate the outer portion of the blanket with new passive fuel bundles.

The above procedure is followed once every six years so that each lot of 140 active fuel bundles has six years to cool while immersed in liquid sodium prior to reprocessing and all the active fuel bundles are recycled once every 30 years. Every 6 years all the fuel bundles are repositioned so that over a 30 year period all the active fuel bundles receive approximately equal fast neutron exposure and all the passive fuel bundles receive approximately equal fast neutron exposure.

This web page last updated September 2, 2020.

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