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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 an gadolinium curtain and a ~ 1.7 m wide liquid sodium guard band. Within the guard band are the 56 intermediate heat exchangers along the path shown as a solid black ring. The primary sodium pool walls are 2 m wide and are filled with fire brick. In the above diagram only one quadrant of fuel bundles is fully detailed.

The 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. The cooling bundles are shown in green. For structural stability the diagonal fuel bundle assembly faces are composed of fixed octagonal fuel bundles, except at 8 clipped corners. A shaped steel belt supporting sheet gadolinium surrounds 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 shroud potentially contains:
[(18 X 18) - 4 (3)] = 312 fuel tubes.
However, an additional 32 fuel bundles are lost due to the presence of fuel bundle diagonal reinforcement members, leaving a net of 280 fuel tubes per square bundle.

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 shroud contains:
[(22 X 22) - 4(6)] = 460 fuel tube positions.
However, an additional 44 fuel tube positions are lost to diagonal fuel bundle reinforcement members leaving a net of 416 fuel tubes per octagonal fuel bundle.

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.

The fuel bundle geometry starts as a 45 X 45 square. The straight horizontal and vertical faces are each 21 bundles long. Hence each of the cut off corners of an isosoles triangle is:
(45 - 21) / 2 = 12
bundle positions to a side. Hence the number of movable fuel bundle positions in each cut off corner is:
12 + 10 + 8 + 6 + 4 + 2 = 42
and the number of fixed fuel bundle positions in each cut off corner is:
11 + 9 + 7 + 5 + 3 + 1 = 36
so the number of cut off corner fuel bundle positions is:
42 + 36 = 78= 78.

The result is an octagon. In addition two fixed and one movable fuel bundle are clipped of each of 8 octagon corners to avoid clashing with neighbouring intermediate heat exchange bundles.

Hence the total number of potential bundle positions in the total fuel bundle array is:
45^2 - 4 (78) - 8(3) = 2025 - 312 - 24 = 1689 fuel bundle positions

A physical count shows that there are 464 active movable fuel bundles and 481 active fixed fuel bundles.

A physical count shows that there are:
4 X 57 = 228 cooling fuel bundle positions, of which 112 are fixed and 116 are movable.

Hence the number of passive fuel bundles is:
1689 - 464 - 481 - 228 = 516 passive fuel bundles.

The minimum number of times through cooling required to cool all the active fuel bundles is the larger of:
(464 M / 116 M) = 4.0
(481 F / 112 F) = 4.295
which imples at least 5 fuel bundle cooling cycles per fuel cycle.

Thus if the period of a fuel cycle is 30 years, there should be a planned reactor shutdown every 6 years for partial fuel bundle exchange and fuel bundle rearrangement.

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. Before octagon corner clipping the octagon straight faces consist of 11 octagonal fuel bundles separated by 10 square fuel bundles. The length of a straight side measured between the centers of the end bundles is:
10 X 42 X (5 / 8) inch = 262.5 inch.

Measured from the ends of these fuel bundles the straight face length is:
262.5 inch + 23(5 / 8) inch = 276.875 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 less than would be the case for an ideal regular octagon.

The fuel bundles are a subset of a theoretial array 45 bundles X 45 bundles. Theoretically there is a fixed bundle at each corner of the ideal array and there is a fixed bundle at the center of the array.

Measured from fixed fuel bundle center to fixed fuel bundle center the horizontal face to horizontal face distance of the entire assembly of fuel bundles is:
[44] X [(21 X (5 /8) inch] = 577.5 inch

Measured from the outside edges of the octagonal fuel bundles the fuel bundle assembly the horizontal face to horizontal face distance is:
577.5 inch + [23 X (5 /8) inch] = 591.875 inch
= 591.875 inch X .0254 m / inch
= 15.034 m

The intermediate heat exchange bundles are located at an elevation above the top of the fuel tubes, so that primary sodium guard band extends under the intermediate heat exchange bundles. The reactor primary sodium pool is 20 m inside diameter which provides a neutron absorbing guard band 1.8 m tp 2.5 m thick around the perimeter of the fuel bundle assembly. The primary sodium pool liner and the heat exchange bundle supporting steel columns are further protected by a sheet gadolinium skirt. The heat exchange bundles are protected from neutrons originating in the core fuel via a very long diagonal path through the fuel 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 15.034 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.

[23 X 23 X (5 / 8) inch] + [22 X 19 X (5 / 8)inch]
= [(23 X 23) + (22 X 19)] X 5 / 8 inch
= (529 + 418) X (5 / 8) inch
= 539.375 inches
= 591.875 inch X 0.0254 m / inch
= 15.034 m
The corresponding radius is:
15.034 m / 2 = 7.517 m

The maximum fuel bundle assembly radius is:
= {[(face to face diameter) / 2]^2 + [(face length) / 2]^2}^0.5
= {[(591.875 inch) / 2]^2 + [(276.875 inch) / 2]^2}^0.5
= {87,579.00 inch^2 + 19,164.94 inch^2}^0.5
= 326.717 inch
= 326.717 inch X .0254 m / inch = 8.2986 m

Thus the maximum available ring width for heat exchangers plus relative thermal expansion allowance is:
10.00 m - 8.30 m = 1.70 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 56 heat exchangers in a single ring.

Each heat exchanger is 38 inches in diameter as set by perimeter pressure flange requirements. The outer manifold edge of the ring of heat exchangers is 0.6 m from the pool wall. Hence the ring of heat exchangers are on a circle with a radius of:
10 m - 0.6 m - 19 inch(0.0254 m / inch)
= 9.4 m - 0.426 m
= 8.974 m
~ 9.0 m

On this circle the ring of heat exchanges are spaced center to center at:
2 Pi (8.974 m) / 56 = 1.00688 m intervals
= 39.64 inch intervals.

Hence the minimum required primary sodium pool radial width taken up by the intermediate heat exchangers is:
0.6 m + 38 inch
= 0.6 m + .9652 m inch
= 1.565 m

Recall that the maximum fuel bundle assembly maximum radius is:
= 8.30 m

Thus the minimum required primary liquid sodium pool inside radius is:
8.30 m + 1.565 m
= 9.865 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 45 rows and 45 columns. The reactor diagonal faces are formed from octagonal fuel bundles. The assembly of fuel bundles consists of a square main grid of 45 X 45 fuel bundles with:
(1 + 3 + 5 + 7 + 9 + 11)= 36 fixed fuel bundles cut off each corner and (2 + 4 + 6 + 8 + 10 + 12)= 42 mobile fuel bundles cut of each corner.

In addition there are 8 more fixed fuel bundles removed to ensure adequate intermediate heat exchanger clearance.

In addition there are 16 more movable fuel bundles removed to ensure adequate intermediate heat exchanger clearance.

The total number of fixed fuel bundle positions remaining in one such reactor is:
(23 X 23) + (22 X 22) - 4(36) - 8
= 529 + 484 - 144 - 8
= 861 fixed fuel bundles.

The total number of movable fuel bundle positions remaining in one such reactor is:
(23 X 22) + (22 X 23) - 4 (42) - 2(8)
= 1012 - 168 - 16
= 828 movable bundle positions.

Note that:
861 + 828 = 1689 bundle positions as expected.

Thus in summary one reactor contains 861 fixed fuel bundle positions and 828 movable fuel bundle positions for a total of 1689 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 two cooling rings contain:
112 fixed fuel bundle positions and
116 movable fuel 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 active region contains:
481 fixed fuel bundles
464 movable fuel bundles

The number of passive fuel bundle of each type is found by taking differences.

Hence the number of passive fixed fuel bundles is:
861 - 481 - 112 = 268 passive fixed fuel bundles.

Hence the number of passive movable fuel bundles is:
828 - 464 - 116 = 248 passive mobile fuel bundles.

Hence the total number of passive fuel bundles is:
268 + 248 = 516

FUEL TUBES: 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 total number of passive fuel tubes is given by:
(268 X 416) + (248 X 280)
= 111,488 + 69,440)
= 180,928 passive fuel tubes

A physical count shows that the reactor active zone contains:
481 fixed active fuel bundles
464 movable active fuel bundles

The total number of active fuel tubes per reactor is given by:
(number of active fixed fuel bundles) X (number of fuel tubes per fixed fuel bundle)
+ (number of active mobile fuel bundles) X (number of fuel tubes per mobile fuel bundle)
= (481 X 416) + (464 X 280)
= 200,096 + 129,920
= 330,016 active fuel tubes

Fuel bundle quantity check:
(481 fixed active
+ 464 movable active
+ 268 fixed passive
+ 248 potentially movable passive
+ 112 fixed cooling
+ 116 mobile cooling)
= 1689 fuel bundles

Minimum total number of fuel tubes
= 330,016 active + 180,928 passive
= 510,944

At about 3 kWt per active fuel tube this design allows for a reactor rated for about:
3 kWt / active fuel tube X 330,016 active fuel tubes
= 990.048 MWt.

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

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:
112 fixed bundles
116 mobile bundles.

In order to replace an intermediate heat exchange bundle it is un bolted, lifted vertically 8 m and them moved horizontally to a cooling position. Note that adjacent fixed fuel bundles must always be removed before a mobie bundle is extracted.

The air lock inside width and bottom radius must accomodate the 38 inch diameter intermediate heat exchange flanges and the connecting pipe stubs and flanges.

Assume that the facility has four air locks, each 1.2 m wide X 9.5 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 exchange bundle 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 there are as many as: (112 positions available for cooling octagonal fuel bundles and up to 112 positions available for cooling square movable fuel bundles.

3) The 3rd step is to move:
228 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 228 extracted 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 228 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.

There are several ways of avoiding liquid sodium coolant channel blockage:
1) Do not use a hexagonal fuel tube configuration. The problem with that design is that as the fuel tube swells the coolant channel flow cross section seriously decreases. This issue has been avoided in modern CANFLEX fuel bundles by abandonment of a hexagonal fuel tube configuration. There must always be sufficient coolant channel cross section even after severe fuel tube swelling.

2) Stop trying to use spaghetti thin fuel tubes as were used in the EBR-2. Go to half inch OD fuel tubes with 9 mm OD core fuel rods. Making the core fuel rod thicker increases the average ratio of fuel to fuel + steel + sodium and hence improves the core reactivity, especially at the low end of the Pu concentration range. With higher core reactivity it is possible to increase the coolant channel cross section which makes the reactor less sensitive to particulates in the liquid sodium. Live with the reality that this design change increases the required amount of start fissile. It remains my concern that attempts to reduce the start fuel tonnage will trigger a reduction in coolant flow channel cross sectional area.

3) Adopt natural circulation of the primary sodium in place of pumped circulation. Then dirt particles will naturally settle out and sink to the bottom of the sodium pool where they can be extracted with a mechanism similar to a swimming pool vacuum cleaner.

4) Use a pool filter, again analogous to a swimming pool.

5) Use a fuel bundle inlet filter. This filter is intended to last the life of the fuel bundle and should do nothing if the aforementioned mechanisms all work properly.

6) Provide space behind the Vee shaped fuel bundle inlet filter such that if one side of the filter is blocked liquid sodium can flow horizontally behind the filter to serve all the tubes in the fuel bundle.

7) Periodically run the reactor at low power so the bottom of the primary liquid sodium pool rises above 462 degrees C. The issue is that if there are any foreign metals in the sodium such as Li, K, Mg they can potentially combine with leakage air to form hydroxides that can deposit on the heat exchange surfaces or in the bottom of the fuel tubes. These hydroxides all melt at less than 462 degrees C. From time to time the entire primary sodium bath must be raised above 462 degrees C to melt off such deposits. In normal reactor operation most of these oxides and hydroxides should sink to the bottom of the primary sodium pool and should be removed with an apparatus similar to a swimming pool vacuum cleaner. That methodology works much better with natural primary sodium circulation than with pumped circulation.

8) The major ongoing issues are NaOH and MgOH which melt at 318 deg C and 350 deg C. In normal reactor operation keep the lowest temperature primary sodium at 330 degrees C and vacuum up the MgOH as it forms as a result of Na-24 decay. Removal of the NaOH requires occasional cooling of the liquid sodium down to about 310 degrees C. That requires a modest drop in steam pressure while NaOH is being removed.

9) The density of liquid sodium is less than the density of water. Most particulates will settle out if the liquid sodium flow velocity across the bottom of the pool is small. That means that the average reactor power density should be low. With the addition of a blanket and a guard band the primary sodium pool diameter becomes about 20 m. I am contemplating a reactor core zone diameter of about 12.6 m for 1000 MWt of thermal power capacity.

10) Each mobile fuel bundle is narrow (approximately one foot square) and has individual discharge temperature monitoring, gamma monitoring, and vertical position control and monitoring. The purpose is to prevent local reactor hot spots occurring. The gammas will indicate the rate of local heat release and the temperature will indicate if the coolant flow for that fuel bundle is insufficient as compared to its operating power level.

11) I am concerned about other parties taking shortcuts that fail to address the causes of potential FNR flow channel blockage. Chief among these issues is pumped primary sodium which will likely prevent dirt psrticles from settling out.

12) During my SCUBA diving days I observed particles trapped in haloclines. This particle trapping results from natural density stratification of still water. That same method has been used by police services for determining the source of broken glass using dense liquid hydrocarbons. I believe that the same separation method will occur in liquid sodium if its flow velocity is small. Think of dust which tends to settle on horizontal surfaces. In the deep ocean in the tropics the whole sea floor is covered by fine dust.

13) The thermal conductivity of liquid sodium is very high. As a result there is no necessity of having turbulent flow through a liquid sodium heat exchanger. Hence with appropriate reactor design it is not necessary to use a primary circulation pump. Instead the reactor should be designed to operate with a high differential temperature.

14) Everything in the primary sodium pool must be non-reactive with liquid sodium. Hence there should be no corrosion products in the primary sodium.

15) We must do all necessary to filter out MgOH. The Mg forms as a result of Na-24 decay.

16) Adjust the secondary sodium flow so that normally regardless of the thermal load the lowest temperature in the primary sodium pool is 340 degrees C. That control strategy should stop precipitation of NaOH which melts at 318 degrees C.

17) If there is 4000 tonnes of liquid sodium it is almost impossible to keep LiOH, KOH, MgOH and NaOH and other metal hydroxides totally out of the sodium over the long term except by ongoing filtering. Moisture laden air will eventually creep into the argon cover gas. Hence it is essential to operate the system in a manner that continuously removes these metal hydroxides before they become particulate formation and deposition problems.

18) The fortunate issue with liquid sodium is that almost all particulates are denser than liquid sodium and given a chance will settle out. The operating temperatures will break down contaminant hydrocarbons.

19) Some pumped liquid sodium cooled reactor designs run the primary sodium above 462 degrees all the time. The problem with doing that is that the sodium flow velocity has to be very high for adequate heat transport. The high flow velocity makes sludge separation and removal difficult. There is no natural settling out of hydroxide sludge. The merit of such designs is that the heat is more suitable for industrial use. We can make steam sufficient for electricity generation at 320 degrees C and hence with attention to thermal stress we can operate a naturally circulated electricity generation reactor down to 330 degrees C with a 150 degree C temperature differential.

This web page last updated March 9, 2021.

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