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**INTRODUCTION:**

In order to enable siting practical Fast Neutron Reactors (FNRs) in urban areas fully assembled FNR fuel bundles are shipped to and from FNR sites. Practical shipping by road requires that fuel bundles be rated for working lateral accelerations of (1 / 2) g. A Fast Neutron Reactor (FNR) is made modular and economic through the use of 1149 to 1369 such fuel bundles. Each fixed octagonal fuel bundle is an assembly containing 416 vertical fuel tubes. Each square fuel bundle is an assembly containing 280 vertical fuel tubes.

A practical FNR contains alternating octagonal and square fuel bundles in a chequer board pattern. In the core zone the square fuel bundles are mobile (moved up and down by hydraulic lifters). The core zone is surrounded on its outer perimeter first by four rings of passive fuel bundles forming the perimeter fertile fuel blanket and then by up to two rings of cooling active fuel bundles. Each fuel bundle weighs ~ 3 to ~ 4 tonnes. The fuel bundles are transported nearly horizontally on trucks or rail cars in reusable sealed lead containers each weighing about 80 tonnes.

In order to meet the various nuclear requirements the overall length of the fuel bundles is about 8 m. In order to meet the fuel bundle transportation weight constraints the fuel bundles are skinny (less than 16 inches face to face). To enable practical crane manipulation it must be possible to lift a fuel bundle from horizontal to upright vertical without the fuel bundle deforming under its own weight. Hence a major issue in FNR fuel bundle design is transverse torque resistance.

**DEFINITIONS:**

Active fuel tube:

Each active fuel tube contains 2 X 0.35 m long core fuel rods where nuclear fission occurs, 6 X 0.30 m blanket fuel rods above the core fuel rods, 6 X 0.30 m blanket fuel rods below the core fuel rods plus liquid sodium.

On top of the fuel rod stack is a 1.6 m high plenum space. There is a 0.1 m overall length allowance for the two welded end plugs.

Passive fuel tube:

Contains 14 X 0.30 m long blanket fuel rods which absorb neutrons plus liquid sodium.

Shroud:

The sheet metal enclosure around a fuel bundle is known as its shroud. Fuel bundle shrouds are fabricated from (3 / 16) inch thick HT-9 sheet steel. The purpose of the shroud is to provide part of the fuel bundle structural rigidity and to exclude particulate matter.

Diagonal Sheets:

Fuel bundle diagonal sheets are formed from (3 / 16) inch thick HT-9 and run almost the full length of a fuel bundle. Near the top of the fuel bundle the diagonal sheet thickness is doubled to achieve (3 / 8) inch thickness near the lifting point. The diagonal sheet edges at the very top of the fixed octagonal fuel bundles are cut away to allow for bolting together of adjacent fixed octagonal fuel bundles.

Passive Fuel Bundle:

A passive fuel bundle contains only passive fuel tubes containing blanket fuel rods and some sodium.

Fuel Bundle Components:

Each fuel bundle has 4 shroud side panels, 4 corner girders, 2 diagonal sheets, 4 bottom grating sections, and 4 bottom filter sections. The top diagonal sheets provide the fuel bundle lifting point.

**FUEL BUNDLE DESCRIPTION:**

Each fuel bundle is an assembly of vertical closed end 0.500 inch OD steel fuel tubes which is totally replaced when the contained fuel is reprocessed.

Each fixed octagonal fuel bundle is initially 14.375 inches X 14.375 inches face to face with 6 m high fuel tubes. The fixed octagonal fuel bundles have additional 1.5 m high corner legs which in turn are supported by a 1.5 m high open steel lattice. The open steel lattice supports and positions the cast sockets that hold the corner legs of the fixed octagonal fuel bundles. There is a height allowance of 0.1 m for core zone swelling, 0.1 m for the bottom grating and 0.3 m for a lifting point. Thus the maximum overall octagonal fuel bundle length is 8.0 m.

Each square fuel tube bundle is initially 11.875 inches X 11.875 inches face to face with 6 m high fuel tubes. Below the mobile square fuel bundles is a 1.2 m central push rod. There is a 0.3 m allowance for the push rod adapter and the input filters. There is a 0.1 m allowance for the bottom grating, a 0.1 m allowance for core zone swelling and a 0.3 m allowance for the lifting point. Hence the overall length is:

6.0 m + 1.5 m + 0.1 m + 0.1 m + 0.3 m = 8.0 m.

The push rods are moved by hydraulic piston actuators, held in position by the open steel lattice, which support the mobile fuel bundles and sets the amount of insertion of each mobile fuel bundle into the rigid matrix of fixed fuel bundles.

The fuel bundle shroud, diagonal sheets and corner girder material must be sufficiently strong to safely withstand the lateral torque caused by a crane lifting one end of the fuel bundle. This strength requirement inherently protects a fuel bundle against 0.5 g lateral acceleration with both ends being simultaneously accelerated in the same direction normal to the fuel bundle long axis.

The present design for an assembly of fuel bundles provides an ideal 0.25 inch clearance between a mobile fuel bundle and each of the adjacent fixed fuel bundles. With good dimensional tolerance control this clearance should be sufficient to allow reasonable core zone material swelling.

P>An important issue in earthquake protection is bolting the fixed fuel bundles together at their top corners to form a rigid matrix. It is important to prevent liquid sodium sloshing back and forth changing the fuel assembly geometry and hence its reactivity.**FNR FUEL BUNDLE DESIGN TRADEOFFS:**

It is contemplated that the reactor core fuel rods are initially 0.35 m long and are contained in **0.500 inch OD X 0.035 inch wall steel tubes** positioned laterally on a square grid **0.625 inch center-to-center**. In the vertical channels between the fuel tubes liquid sodium coolant flows upwards to remove heat. Implications of this design are a small liquid sodium circulation power (natural circulation), negligible fuel tube erosion, reasonable fuel temperature, reasonable reactor dimensions, an acceptable liquid sodium temperature rise and a reasonable requirement with respect to filtering particulates out of the liquid sodium.

The size of the gap between the steel fuel tubes is a compromise between the requirements for heat transport and the requirements for average fuel concentration. As the gap between the fuel tubes becomes smaller the problems of primary sodium circulation and of filtering particulates out of the liquid sodium rapidly become larger. As the gap becomes larger the required average concentration of core rod fissionable material rapidly increases.

Practical operating experience with the EBR-2 reactor showed that during normal operation formation of fission products causes the core rod cross sectional area to swell by about 33%. Hence the initial reactor core fuel rod diameter is restricted to:

[(steel fuel tube ID) X 0.86].

The only practical ways to increase the average fuel density in the reactor core are to either reduce the gap between the steel fuel tubes or to increase the concentration of Pu-239 in the core fuel rods. Note that the initial blanket fuel rod outside diameter can be slightly larger than the initial core fuel rod outside diameter because the blanket fuel rods are less subject to fast neutron and fission product induced swelling.

An important issue in FNR design is neutron conservation. Almost all the excess neutrons emitted by the reactor core zone should be captured by the surrounding breeding blanket.

**FUEL TUBE SPACING:**

In choosing the gap between the steel fuel tubes the issue is one of maximizing the average fuel density in the fuel bundle while not unduely obstructing the natural liquid sodium circulation and not imposing unreasonable cleanliness restrictions on the liquid sodium pool.

A related issue is that the maximum sodium temperature rise as liquid sodium passes through the fuel bundle is limited at the low end by the melting point of NaOH (318 deg C) and at the high end by certainty of avoiding Pu melting on the fuel rod axis (639 deg C).

Based on these issues the center to center spacing between the square lattice fuel tubes was chosen to be:

(5 / 8) inch = 0.625 inch.

This dimensional choice sets the smallest initial intertube gap in the assembly at (1 / 8) inch, so filtering should be used to eliminate particulates larger than (1 / 32) inch in longest dimension.

Each fuel tube position has associated with it a reactor top surface area of about
1 tube per [0.625 inch]^2

= 1 tube / .3906 inch^2

The cross sectional area initially occupied by each fuel tube is:

Pi (.25 inch)^2 = 0.1963 inch^2

Thus the remaining cross sectional area per core fuel tube initially available for natural convection liquid sodium coolant flow is:

0.3906 inch^2 - 0.1963 inch^2 = **0.1943 inch^2**

= 0.1943 inch^2 X (.0254 m / inch)^2

= 1.2535 X 10^-4 m^2

Note that initially the cross sectional area of a fuel tube OD and the cross sectional area of an external sodium flow channel are almost equal.

Note that a scale diagram shows that initially the flow channel wall area is almost equal to the OD wall area of a fuel tube.

Hence the initial effective cross sectional area for natural circulation through the reactor is:

1.2535 X 10^-4 m^2 / core fuel tube X 270,300 core fuel tubes = **33.8221 m^2**

The length of the reactor core zone perimeter is about:

Pi X 10.0 m = 31.4 m

Hence, prior to fuel tube swelling, the thickness of the radially horizontally moving liquid sodium layer at the active region perimeter is about:

(33.8221 m^2) / (31.4 m) = **1.08 m**.

If the fuel tube radius linearly swells by 10% the cross sectional area occupied by each fuel tube becomes:

1.21 X 0.1963 inch^2 = 0.237523 inch^2

Thus the remaining cross sectional area per core fuel tube available for natural convection liquid sodium coolant flow after 10% linear tube swelling is:

0.3906 inch^2 - 0.237523 inch^ = **0.1531 inch^2**

= 0.1531 inch^2 X (.0254 m / inch)^2

= 9.8759 X 10^-5 m^2

Fuel tube swelling also increases viscous effects that further reduce the primary liqud sodium circulation.

**GEOMETRY OF FUEL TUBES ON STAGGERED CENTRES:**

Consider fuel tubes that are initially 0.500 inch OD located on 0.625 inch staggered centres. Viewed from the bottom or top of the reactor for each fuel tube there are two associated equilateral triangles with sides of length 0.625 inch. The height of such a triangle is:

(3^0.5 / 2)(.625 inch)

The area of the triangle is:

(1 / 2)(.625 inch)(3^0.5 / 2)(.625 inch) = (3^0.5 / 4)(.625 inch)^2

= 0.16914 inch^2

The two triangles together form a rhombus of area:

2 (.16914 inch^2) = **0.33828 inch^2**

The initial cross sectional area of the fuel tube is:

Pi (.25 inch)^2 = **.19634 inch^2**

Thus the initial reactor cross sectional area per fuel tube available for liquid sodium flow is:

0.33828 inch^2 - 0.19634 inch^2 = **0.14194 inch^2**

Now assume that the fuel tube swells from 0.500 inch OD to 0.625 inch OD. Its cross sectional area increases to:

Pi (.625 inch / 2)^2 = **0.30679 inch^2**

Hence the cross sectional area available for liquid sodium flow falls to:

0.33828 inch^2 - 0.30679 inch^2 = **.03149 inch^2**

Thus the fractional liquid sodium flow area remaining is:

.03149 inch^2 / 0.14194 inch^2 = **0.22185**

**GEOMETRY OF FUEL TUBES ON SQUARE CENTRES:**

Consider fuel tubes that are initially 0.500 inch OD on 0.625 inch square centres. Viewed from the bottom or top of the reactor for each fuel tube there is a square with sides of length 0.625 inch. The height of such a triangle is:

0.625 inch.

The area of the square is:

(.625 inch)^2

= 0.390625 inch^2

The initial cross sectional area of the fuel tube is:

Pi (.25 inch)^2 = **.19634 inch^2**

Thus the initial cross sectional area available for liquid sodium flow is:

0.390625 inch^2 - 0.19634 inch^2 = **0.194285 inch^2**

Now assume that the fuel tube swells from 0.500 inch OD to 0.625 inch OD. Its cross sectional area increases to:

Pi (.625 inch / 2)^2 = **0.30679 inch^2**

Hence the cross sectional area available for liquid sodium flow falls to:

0.390625 inch^2 - 0.30679 inch^2 = **.083835 inch^2**

Thus the fractional liquid sodium flow area remaining is:

.083835 inch^2 / 0.194285 inch^2 = **0.431505**

Thus **in terms of liquid sodium coolant flow a square lattice tube geometry is twice as good as a staggered lattice tube geometry.** Hence **the tube bundles should be square** instead of hexagonal. In plan view the reactor should be octagonal instead of hexagonal.

**FUEL TUBE BUNDLE MATERIAL AND DIMENSIONS:**

The fuel tube bundle frame and shroud are fabricated from HT-9 steel (Fe, 12% Cr, 1% Mo, 0% C, 0% Ni).

The height allowances for the octagonal fuel bundle components from bottom to top are: legs (1.5 m), bottom grating (0.1 m), fuel tubes (6 m), lifting point (0.3 m), swelling allowance 0.1 m. Hence the fuel bundle shipping container must be able to accommodate a fuel bundle with an overlll length of 8.0 m.

The nominal fuel tube height of 6 m is limited by availability of 0.500 inch OD X 0.035 inch wall thickness HT-9 steel tube.

The fixed fuel bundle length and width are limited by the weight of the lead shielded container needed to move an intensely radioactive fixed fuel bundle by truck. In that truck the fuel bundle and its transportation container are supported at an slight angle from horizontal to ensure that the fuel tubes, fuel rods and liquid sodium all remain near the bottom of the fuel bundle.

The sipping weight concentration should be supported by the back wheels of the truck. It is contemplated that the truck trailer will have 4 rows of four back wheels so as to be rated for 4 axles X 4 wheels / axle X 5 tons per wheel = 80 tons. The truck tractor will have two additional weight bearing axles as well as forward wheels for steering.

**FUEL TUBES:**

Within each fuel bundle the fuel tubes are positioned on a horizontal square grid which is (5 / 8) inch center to center. This grid is square to ensure sufficient primary liquid sodium natural circulation in the presence of 15% linear fuel tube swelling. The fuel tube height is set by FNR design calculations relating to the core height, blanket thickness and plenum height. The fuel tube OD and length are in part constrained by material availability. The fuel tube center to center distance in the fuel tube bundle was found by itterative liquid sodium flow and fuel reactivity calculations. The maximum number of tubes in a fuel bundle is set by the shielded container weight constraint for a lead container of sufficient wall thickness for certain transportation biosafety.

Each fuel tube bottom plug has cross cuts for mating with the fuel bundle bottom grating. The fuel tube top plugs have indentations and bumps to allow easy grasping for controlled insertion, rotation or withdrawal of each individual fuel tube and to assist with fuel tube spacing control.

**CORE REGION SWELLING:**

Due to the action of fat neutrons the fuel bundle material in the neighbourhood of the core region will swell. It is important that in this region the fuel bundle can lenthen due to swelling but must not get wider. Otherwise the overlapping fuel bundles could jam. It is not practical to space the fuel bunles further apart to avoid this jamming, as that spacing will substantially reduce the average Pu-239 concentrations making attainment of core criticality difficult with old fuel.In the core zone it is necessary to reduce the width of the fuel bundle diagonal reinforcing plates and to cut vertical swelling allowance slits in the shroud plates. These components are not welded together in the core zone. The fuel bundles must be designed so that the core section of the fuel bundle can safely absorb the maximum torque associated with crane handling of the fuel bundles.

The present design provides an ideal 0.25 inch clearance between a mobile fuel bundle and each of the adjacent fixed fuel bundles. With good dimensional tolerance control this clearance should be sufficient to allow reasonable core zone material swelling.

**FUEL BUNDLE DESIGN CONSIDERATIONS:**

1) The fuel bundles used in the EBR-2 reactor used fuel tubes that were on staggered centers. A staggered fuel tube configuration results in a high average fuel density and lends itself to regular hexagon shaped fuel bundles. The regular hexagons gave good horizontal fuel bundle mechanical stability and good power modulation characteristics. However, a major problem with a hexagonal fuel bundle design is that as the fuel tubes swell the liquid sodium coolant passages become severely restricted requiring mechanical pumping of liquid sodium to maintain sufficient liquid sodium flow for reactor cooling.

2) To maintain sufficient liquid sodium flow with natural circulation the fuel tubes should be positioned on on a square grid so that the liquid sodium coolant passages remain open almost independent of tube swelling. A square grid lends itself to square fuel bundles that have good modulation characteristics. However, a problem with an simple array of square fuel bundles is that the array lacks horizontal mechanical stability, especially in earthquake conditions.

3) In order to achieve both good liquid sodium natural circulation, which requires fuel tubes on a square grid, and good horizontal mechanical stability alternating square and octagonal shaped fuel bundles is used. In order to meet transportation weight constraints the maximum initial face to face size allocation for the octagonal fuel bundles is set at:

23 X (5 / 8) inch = 14.375 inches.

The square fuel bundles are made as large as practical and are initially:

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. Note that these dimensions include sliding clearance. These dimensions result in a linear center to center similar fuel bundle spacing of:

[14.375 inch + 11.875 inch = 26.25 inch

= 26.25 inch X .0254 m / inch = **0.66675 m**

4) In plan view the two different size fuel bundles fit together as shown below:

5) On the above diagram the fixed octagonal fuel bundles are shown in red and the square fuel bundles are shown in blue. The solid color at the fuel bundle corners indicates the fuel bundle vertical reinforcing girders. The X and Y lines show the back to back fuel bundle shrouds. Diagonal lines show fuel bundle diagonal reinforcing metal sheets. The detail of the girder cross sections and the fuel bundle clearances at fuel bundle corners is shown on the next diagram.

In plan view the corner detail of 2 mobile square and 2 fixed octagonal adjacent fuel bundles appears as shown below:

6) The legs of adjacent fixed octagonal fuel bundles are connected together at their bottoms by cast sockets which are securely fastened to the 1.5 m high open steel lattice. The top corners of adjacent fixed octagonal fuel bundles are connected together by through bolts in the plane of the diagonal reinforcing plates to form a rigid matrix of fixed octagonal fuel bundles within which the mobile square fuel bundles slide vertically.

7) The fixed octagonal fuel bundle maximum outside face to outside face distance is:

23 X (5 / 8) inch = 14.375.0 inches.

8) Within the fuel bundles a number of fuel tube spaces are lost to both corner girders and diagonal reinforcing sheets. Within each fixed octagonal fuel bundle's shroud walls are:

22^2 - 4(6) - 2 (22) = 416 fuel tubes.

9) The square mobile fuel bundle maximum outside face to outside face distance is:

19 X (5 / 8) inch = 11.875 inches.

10) Within each square fuel bundle's shroud walls are:

18^2 - 4(2) - 2(18) = 280 fuel tubes.

11) To prevent overall fuel bundle swelling in the core region in that region the diagonal reinforcing sheets are reduced in width and the fuel bundle shroud sheets contain slots to allow shroud and diagonal sheet swelling in the core region without causing significant overall horizontal fuel bundle width swelling.

12) Reactor discharge temperature setpoint modulation is achieved by changing the insertion depth of the mobile square fuel bundles in the matrix of fixed octagonal fuel bundles.

13) The mobile square fuel bundles are divided into two groups, A and B, in a pattern analogous to the red and black squares on a checker board. Each member of group A has four group B members as nearest neighbours. Similarly each member of group B has four group A members as nearest neighbours.

14) Maximum possible reactor reactivity occurs when both groups A and B are fully inserted.

15) In normal reactor operation both groups A and B are partially inserted.

16) Certain reactor cold shutdown must occur when either group A or B is fully withdrawn while the remaining group remains in its normal operating position.

17) If any one mobile square fuel bundle is accidentally moved toward being over inserted immediate full withdrawal of either the remaining group A mobile fuel bundles or the remaining group B mobile fuel bundles must result in a reactor cool shutdown.

18) If any two mobile square fuel bundles are accidentally moved toward being fully inserted full withdrawal of all of the remaining mobile fuel bundles must result in a reactor cool shutdown.

19) The fuel bundle corner girders, diagonal plates and shroud sheets must be sufficiently robust to permit normal crane handling of the fuel bundles. It must be practical to use a crane to lift a fuel bundle by one end from a horizontal position to a vertical position without the fuel bundle being deformed by its own weight. This fuel bundle strength requirement implies a transverse acceleration resistance of 0.5 g which sets minimums on the thickness of the fuel bundle shroud sheets, diagonal sheets and corner girders.

20) The fuel tube spacing within a fuel bundle is maintained using a spiral 20 gauge wire winding on each fuel tube and by the diagonal plates.

21) An important issue in earthquake protection is bolting the fixed fuel bundles together to form a rigid matrix. In an earthquake primary liquid sodium sloshing back and forth must not change the fuel assembly geometry and hence its reactivity.

**FIXED OCTAGONAL FUEL BUNDLES:**

Consists of a shroud surrounding 416 fixed position fuel tubes. Adjacent fixed fuel bundles are joined at their top corners by bolting together double angle girders to form a rigid matrix into which the square fuel bundles can be inserted.

The 4 angled faces of every fixed octagonal fuel bundle are formed from double angle girders with side arms at 45 degrees to the base that displace 6 theoretical fuel tube positions at each corner. In addition there are 2 X 22 theoretical fuel tube positions displaced by reinforcing diagonal sheets. Hence the actual number of fuel tubes contained in a fixed fuel bundle is:

22^2 - 4(6) - 2 (22) = **416 fuel tubes**

The fixed octagonal fuel bundle shroud plates are:

[11 + (11 / 16)] inch wide X (3 / 16) inch thick.

The bottom of a fixed fuel bundle leg is supported a cast socket that overlaps the fixed fuel bundle cross sectional area. The thickness of the girder material is 0.500 inch. With reference to the previous diagram the cross sectional area of this fixed fuel bundle corner double angle girder is:

[ 4 X (5/8) X (1 / 2)] inch^2 + (1 / 2)(3 / 4)^2 inch^2 + 2 (5 / 8) (7 / 32) inch^2

= [(5 / 4) + (9 / 32) + (5 / 4)(7 / 32)] inch^2

= 1.25 + 0.28125 + 0.2734
= **1.8047 inch^2**

**SQUARE FUEL BUNDLES:**

Each square fuel bundle consists of diagonal reinforcing plates and a square shroud surrounding 280 vertical fuel tubes. The core zone square fuel bundles are mobile. A mobile square fuel bundle withdraws up to 1.2 m relative to the fixed octagonal fuel bundle matrix to set the reactor operating temperature and to cause a reactor cool shutdown. The vertical position of each mobile fuel bundle is set by its hydraulic actuator and is indicated by an Indicator Tube.

At the 4 corners of every square fuel bundle are angle girders with side arms which displace 2 theoretical fuel tube positions at each corner. In addition there are (2 X 18) theoretical tube positions occupied by reinforcing diagonals. Hence the actual number of fuel tubes contained in a mobile fuel bundle is:

18^2 - (4 X 2) - 2 (18) = **280 fuel tubes**

The mobile fuel bundles have corner girders with sides that are:

(3 /2)(5 / 8) inch = (15 / 16) inch long. The material is (1 / 2) inch thick. With reference to the previous diagram the cross sectional area of each such corner girder is:

2 X 1.5 X (5/ 8) X (1 / 2) inch - (1 / 2) inch^2

= (15 / 16) inch^2 - (1 / 4) inch^2

= **(11 / 16) inch^2**

= **0.6875 inch^2**

The diagonal reinforcing plates are (3 / 16) inch thick along the length of a fuel bundle. These plates decrease in width in the core zone and increase in thickness to 3 / 8 inch at the top and bottom of the fuel bundle.

The mobile fuel bundles have diagonal plate bottom extensions that mate with the push rod that extends 1.6 m below the fuel tubes. The push rod has a pointed bottom tip that mates with the actuator piston. The push rod has a 9.74 inch OD to match the 9.75 inch ID of the hydraulic cylinder. The purpose of this dimension matching is to hold the mobile fuel bundle vertical in the fully retracted position while its surrounding octagonal fuel bundles are being installed. Once the octagonal fuel bundles are in position the mobile fuel bundle probe center pin has a stabilizing function until the mobile fuel bundle is again fully retracted.

The hydraulic actuator cylinder has a holes through its side near its top. The purpose of these holes is to release hydraulic pressure when the mobile fuel bundle reaches its maximum insertion position. These holes also prevent the piston being accidentally driven out of its hydraulic cylinder.

**LOADING AND UNLOADING FUEL BUNDLES:**

It is important to never let the fuel assembly accidentaly go critial. In loading fuel bundles into the primary sodium pool each mobile bundle should be installed in the fully withdrawn position before installing its surrounding fixed fuel bundles. Similarly the fixed fuel bundles surrounding a mobile bundle should be extracted from the primary sodium pool before extracting the corresponding mobile fuel bundle. That strategy ensures that the fuel assembly will not accidently go critical due to pulling a mobile fuel bundle right through a matrix of adjacent fixed fuel bundles.

Thus the fuel bundle insertion and extraction order is important. In assembly of the fuel bundle array the mobile fuel bundles are ALWAYS installed fully retracted before their surrounding fixed fuel bundles are installed. Similarly, in disassembly of the fuel bundle array the fixed fuel bundles are ALWAYS removed before removing the retracted mobile fuel bundles that they surround.

**THERMAL EXPANSION:**

Note that the open steel lattice near the bottom of the primary liquid sodium pool will thermally expand with increasing surrounding liquid sodium temperature. During normal reactor operation the open steel lattice is likely to be about 150 degrees C cooler than the liquid sodium temperature at the top of the fuel bundle. Hence the differential horizontal width thermal expansion per fuel bundle is approximately:

20 ppm / deg C X 150 deg C X 13.125 inch = **0.039 inch**

The fuel bundle leg sockets must provide sufficient play to accommodate this differential thermal expansion.

**SWELLING ALLOWANCE:**

An important issue in FNR design is providing for fuel bundle swelling. Over the working life of a fuel bundle the component linear dimensions in the reactor core region can potentially increase by as much as 15%. This swelling primarily occurs near the reactor core, not at the top and bottom of a fuel bundle where the fast neutron flux is small. Nevertheless the fuel bundle design must accommodate this swelling. To achieve certain cool shutdown the fully swollen mobile fuel bundles must still freely slide within the swollen portions of the surrounding fixed fuel bundles. Periodic demonstration of this free sliding is an important long term safety issue. Fuel bundles must also be engineered to prevent fuel bundle warping over time.

The fuel bundles are designed so that individual fuel tubes, corner girders, diagonal plates and shroud plates can all linearly swell due to fast neutron bombardment in the core zone without the external width of the fuel bundle significantly changing. In the core zone the edges of the shroud sheets will slide over the corner girders as the material swells. In the core zone the diagonal plates are reduced in width to provide a swelling allowance.

Fuel bundles are intended to be replaced before 15% linear swelling of the most intensely neutron irradiated sections occurs. The fuel tube array center-to-center spacing is established by the fuel bundle top and bottom geometries and by the fuel tube spiral wire winding. Note that the fuel tube array is stabilized by the fuel bundle diagonal plates.

At the upper corners of the fixed octagonal fuel bundles are through bolts which are used to corner connect adjacent fixed octagonal fuel bundles and prevent adjacent fixed fuel bundles sliding axially with respect to one another and hence prevent lateral rocking as might occur during a severe earthquake.

**USED FUEL COOLING:**

Used active fuel bundles are held in the outer two rings of the assembly of fuel bundles to permit fission products to naturally decay while the fuel tubes remain immersed in liquid sodium. While cooling in the outer two fuel bundle rings the used active fuel bundles will also act as passive fuel bundles.

**ORDER OF FUEL BUNDLE FABRICATION:**

The order of fabrication of the fuel bundles is important to allow the required welding. The contemplated order is as follows:

a) Cut diagonal plates to size. Center cut them half way down their length.

b) Fit the diagonal plates together like dividers in a wine box.

c) Weld the diagonal plates together along their lengths.

d) Reinforce the diagonal plates near their ends as necessary for crane manipulation.

e) Weld the corner girders to the diagonal plates. Note that there is no such welding in the core zone.

f) Weld on the shroud sheets. Note that in the core region the shroud sheets are reduced in width and are not welded on to the corner girders.

g) Attach the four bottom grating quadrents using deep penetraion welding.

h) Check the mechanical strength of the bottom gratings.

i) Attach the push rod adapter or the bottom leg reinforcement, as applicable.

j) Insert the fuel tubes.

k) Apply a temporary fuel tube shipping cap.

l) Attach the bottom intake filters.

m) Check for complete dimensional compliance.

**FUEL BUNDLE CRANE LIFTING:**

The fuel bundle corner girders, diagonal plates and shroud sheets must be sufficiently robust to permit reasonable crane handling of the fuel bundles. It must be practical to use a crane to lift a fuel bundle by its lifting point from a horizontal position to a vertical position without the fuel bundle being deformed by its own weight. This fuel bundle strength requirement implies a transverse acceleration resistance of 0.5 g which sets minimums on the thickness of the fuel bundle shroud sheets, diagonal sheets and corner girders.

The lifting point for a fuel bundle is a pair of 3 inch diameter holes in 0.375 inch thick diagonal plates. The corner girders of the octagonal fuel bundles must project upwards above the fuel tubes to allow for bolt connection to adjacent fixed fuel bundles at the top of the corner girders. The diagonal plates connecting each fuel bundle lifting point to the corresponding fuel bundle corner girders must also not obstruct primary liquid sodium flow and must not prevent individual fuel tube insertion or extraction.

FNR fuel bundle lifting points are achieved by replacing the (3 / 16) inch thick diagonal plates with (3 / 8) inch thick diagonal plates in the upper portion to the fuel bundle where there are fuel tube plenums amd hence little neutron flux. The two (3 / 8) inch thick plates extend above the tops of the fuel tubes. Two 3.0 inch diameter holes in each plate form a lifting point. Note that for the octagonal fuel bundles the diagonal plate upward extension width must be of reduced to allow bolting together the corners of adjacent octagonal fuel bundles. In order to allow for a 10 ton lifting force the two holes in each (3 / 8 inch plate may need to be each ~ 3 inches in diameter in a ~ 12 inch wide X 30 cm high plate extension. This plate extension will form part of the overall length of the fuel bundles.

Note that the crane hook is a split J hook, one part for each hole.

The fuel bundle designer must be aware that during normal operation the fuel tubes and the fuel bundle will increase in length by about:

0.7 m X 0.15 = 0.105 m

= ~ 4 inches.

However the extensions may not be equal.
Hence the bottom of the fuel bundle lifting point holes must be at least 3 inches above the top of the fuel tube top plug, which is 1 inch (2.5 cm) above the top of the fuel tube.

We anticipate that shear force calculations will demonstrate the need for ~
5 inches of (3 / 8) inch thick steel above the lifting point hole to safely absorb 10 tons of lifting force. Note that this plate extension will require cross wise support to prevent the (3 / 8) inch plate bending during the portions of crane lifts when the fuel bundle is close to horizontal and the lifting point holes are vertical. Thus both diagonal plates must be extended about 0.3 m = 12 inches.

**INDICATOR TUBE:**

There are 4.5 m high buoyant indicator tubes field attached to the mobile active fuel bundles. The vertical position of each active square fuel bundle is visually indicated by the 0.3 m to 1.5 m exposed height of the top of its indicator tube above the primary liquid sodium surface.

Each indicator tube: shows the actual vertical position of its corresponding mobile square fuel bundle, allows measurement of the gamma flux emitted vertically by the mobile square fuel bundle and allows determination of that fuel bundle's steady state discharge temperature.

The thermal power output from a fuel bundle is approximately proportional to the gamma flux propagating up its indicator tube.

The steady state square fuel bundle discharge temperature is indicated by the liquid sodium temperature inside the indicator tube.

Indicator tubes are attached to the mobile active square fuel bundles after the mobile active square fuel bundles are installed and are removed before the mobile active square fuel bundles are relocated. The indicator tube attachment point is the fuel bundle lifting point. Once the indicator tubes are in place the sodium isolation floats can slipped between them. The indicator tubes should be thin wall for buoyancy to keep each indicator tube upright. The indicator tube diameter should be minimal to minimize obstruction of liquid sodium flow, but must be sufficient to allow accurate fuel bundle liquid sodium discharge temperature measurement. The difference between the indicator tube OD and ID provides a path for gamma radiation to reach the overhead FNR monitoring system.

An indicator tube isolates a mobile fuel bundle's hot liquid sodium discharge stream from the temperature of the surrounding liquid sodium. This isolation ensures that the temperature in the middle of the indicator tube reflects the temperature of the mobile fuel bundle sodium discharge. The hollow walls of the indictor tube also provide positive buoyancy so that when 1.5 m of the indicator tube is projecting above the primary liquid sodium surface the indicator tube still maintains a firm upright position.

Note that the buoyancy of the hollow wall indicator tube is not sufficient to lift the net weight of a mobile square fuel bundle when the indictor tube is fully immersed in liquid sodium. However, the indicator tube must be buoyant in liquid sodium even when at its maximum height.

Indicator Tube: 5.563 inch OD X 0.258 inch wall X 4.5 m long_______

Mass = Pi X 5.563 inch X 0.258 inch X 4.5 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3

= **103.074 kg**_______________

**STEEL SUPPORT LATTICE:**

The 1.5 m high open steel support lattice supports the entire weight of the fixed fuel bundles and stabilizes the hydraulic actuators. This steel lattice provides sufficient distance separation between the fuel bundles and the bottom of the sodium pool to ensure that there is no long term deterioration of the stainless steel pool bottom due to neutron absorption. This open lattice also allows free circulation of liquid sodium beneath the fuel tubes. A 1.2 m long push rod maintains separation between each mobile fuel bundle and its hydraulic actuator. This separation extends the working life of the hydraulic actuators. The fixed fuel bundle legs keep the fixed fuel bundles 1.5 m above the open steel lattice to protect that lattice from neutron damage. The sockets mounted on the top of the open steel lattice correctly position the fixed fuel bundles. However, a fixed fuel bundle can be released from socket by removing its 4 top bolts and then lifting the fixed fuel bundle a few inches using the overhead gantry crane.

**MECHANICAL RIGIDITY CONSIDERATIONS:**

A major issue in fuel bundle design is horizontal mechanical stability and rigidity because the overall fuel bundle height of 8.0 m is much greater than its width (.3016 m or 0.3651 m). Hence, the mechanical design of the fuel bundles is important to ensure that during fabrication, transport, installation and operation the fuel bundles do not bend, warp or otherwise deform. Such bending or warping could potentially cause a jam in the sliding of a mobile square fuel bundle within the surrounding matrix of fixed octagonal bundles.

A fixed octagonal fuel bundle has corner girders which extend past the fuel tubes to also serve as support legs and attach to the diagonal sheets that provide a central lifting point. On installation the corner girders of fixed octagonal fuel bundles connect to adjacent fixed octagonal fuel bundles by through bolts at the top of each corner girder and by cast sockets at the bottom of each corner girder. The cast sockets are firmly attached to the open steel support lattice. The cast sockets are tapered at their tops to allow practical blind mating with the fuel bundle legs with +/- 6 mm position error. The axis of the cast sockets lies at 45 degrees to the axis of the fuel bundle grid.

The corner girders of every fixed fuel bundle extend downwards 1.5 m below the bottom of the fuel fuel tube support grating. At the top of the fuel bundle 0.3 m X 3/8 inch diagonal sheet extensions provide lifting points for fuel bundle installation and removal. Short corner girder upward extensions allow use of bolts for connecting together adjacent fixed octagonal fuel bundles.

The entire weight of the fixed octagonal fuel bundles is supported by the four fuel bundle legs. These legs extend 1.5 m below the fuel tube bottoms to allow mobile fuel bundle travel, to allow liquid sodium to easily flow into the bottom of the fuel bundles and to minimize long term fast neutron damage to the open steel lattice. These legs are stabilized by leg to leg diagonal members attached to the inside of the corner girders.

In operation each mobile fuel bundle's weight is borne by its hydraulic actuator which sets the amount of mobile fuel bundle insertion into the matrix of octagonal fuel bundles. The mobile fuel bundle travel is limited at the bottom by the probe length (1.2 m) and the hydraulic cylinder end piece and piston thickness (0.3 m) and height of the steel lattice (1.5 m) and at the top by a hydraulic actuator vent hole.

The fuel tube spacing within a fuel bundle is maintained using a spiral 20 gauge wire winding spot welded onto each fuel tube and by the diagonal plates.

**NUCLEAR DESCRIPTION:**

A practical FNR consists of a variable thickness pancake shaped inner core completely surrounded by a > 1.45 m thick neutron absorption blanket. The fission chain reaction occurs primarily in the core zone where the core fuel rods of the fixed and mobile fuel bundles overlap. Excess neutrons originating in the core zone are absorbed by U-238 in the blanket. The core and blanket vertical thicknesses are set by fuel rod lengths and by the amount of mobile fuel bundle insertion into the fixed fuel bundle matrix.

A key issue in fuel bundle design is that with half of the mobile fuel bundles fully withdrawn from the matrix of fixed fuel bundles and the remainder in their normal operating position the reactor must be subcritical. This fuel bundle design constraint enables safe reactor assembly/disassembly and allows independent operation of the two fully independent FNR cold shutdown systems. In order to achieve reactor zone symmetry the fissile fuel concentration in the mobile active fuel bundles is higher than the fissile fuel concentration in the fixed active fuel bundles.

**REACTOR TEMPERATURE SETPOINT CONTROL:**

In normal reactor operation the mobile fuel bundles insert into the matrix of fixed fuel bundles from the below. When all the mobile fuel bundles are fully inserted into the fixed fuel bundle matrix the reactor is at maximum reactivity. When all the mobile fuel bundles are 1.2 m withdrawn from the fixed fuel bundle matrix the reactor must be subcritical. The fuel bundle geometry limits the range of acceptable Pu concentrations in the core fuel rods.

From a power control perspective each mobile fuel bundle and its surrounding active fixed fuel bundles can almost be regarded as an independent FNR. Each mobile fuel bundle has its own discharge temperature which is set by the amount of insertion of the mobile fuel bundle into the fixed fuel bundle matrix. Under cold shutdown conditions gravity causes all the mobile fuel bundles to withdraw 1.2 m with respect to the fixed fuel bundle matrix.

When the mobile active fuel bundles are fully inserted into the fixed fuel bundle matrix there is a ~ 1.5 m high nearly open space under each fuel bundle assembly that allows almost unimpeded horizontal and vertical liquid sodium circulation.

**HYDRAULIC ACTUATOR:**

The hydraulic actuator for a square mobile fuel bundle consists of a 1.5 m long hydraulic cylinder 9.75 inch ID, 10.75 inch OD + 9.74 inch OD piston which moves the bottom of a mobile square fuel bundle probe up and down, and is located in the open steel lattice. Each hydraulic actuator has a fitting near its base which mates with the corresponding hydraulic pressure line. The mobile fuel bundle bottom probe OD matches the hydraulic cylinder ID to keep the mobile fuel bundle upright when the mobile bundle is fully retracted.

Within the 1.5 m high open steel support lattice are vertical hydraulic piston actuators each formed from a 1.5 m length of 10.75 inch OD steel pipe with an internal piston. The fuel bundle has a 1.2 m long push rod from the filter adapter bottom to the piston. About 0.3 m is dedicated to supporting the fuel bundle bottom filter, leaving 1.2 m for mobile fuel bundle extraction. This push rod holds the mobile fuel bundle vertical when the push rod is fully retracted. The push rod OD (9.74 inches) matches the hydraulic cylinder ID (9.75 inch). The push rod has a bottom taper for smooth insertion into the hydraulic cylinder.

The hydraulic piston has sealing piston rings similar to those in a diesel truck or marine engine.rod. The actuator piston has a tapered bottom edges for easy insertion into the hydraulic cylinder.

The extent of insertion of a mobile square fuel bundle into the fixed fuel bundle matrix is determined by the volume of liquid sodium inside the fuel bundle's hydraulic actuator. There is fluid pressure feedback which indicates the approximate mobile fuel bundle vertical position due to the changing buoyancy of the indicator tube. The hydraulic fluid feed tube is routed through the open steel lattice. This hydraulic tube must be sufficiently flexible to allow for +/- 1 m ______earthquake induced movement of the primary sodium pool with respect to its concrete enclosure.

In the event of a complete hydraulic cylinder jam an entire line of such hydraulic cylinders and related steel lattice extending half way across the pool may have to be removed and replaced.

To cause a mobile fuel bundle to insert into the fixed fuel bundle matrix liquid sodium at up to 100 psi is injected under the hydraulic piston which gives up to 7466 lb of lifting force to raise the mobile fuel bundle and its indicator tube. If the piston attempts to move too high the high pressure liquid sodium behind the piston is released into the primary sodium pool via a vent hole in the hydraulic cylinder side wall. This arrangement provides a certain upper limit on the piston travel. An orifice located on each high pressure sodium feed tube limits the rate at which a mobile fuel bundle can be inserted into the matrix of fixed fuel bundles. For normal piston position control an orifice restricted hydraulic drain valve is used. However, note that the mobile fuel bundle hydraulic drain valve used for reactor safety shutdown is not orifice restricted.

**HYDRAULIC ACTUATOR COMPONENTS:**

There is a 0.15 m high X 9.75 inch OD piston that slides within the 10.75 inch OD X 1.5 m hydraulic cylinder to cause insertion of the square fuel bundle into the octagonal fuel bundle matrix.

Hydraulic Cylinder:

Mass = Pi (10.750^2 - 9.759^2) inch^2 / 4 X 1 m X (.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3

= **81.79 kg**

Hydraulic cylinder bottom disk:

Mass = Pi (9.750 inch / 2)^2 X 0.5 inch X (.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3

= **4.8168 kg**

Hydraulic Cylinder Piston:

Piston Mass = Pi (9.750 inch / 2)^2 X 3 inch ____X (.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3

= **28.91 kg**

**FUEL BUNDLE SODIUM INLET FILTERS:**

At the bottom of each fuel bundle is a 4 section filter supported by the diagonal plates. The purpose of these filters is to prevent foreign particulate matter suspended in the primary liquid sodium from blocking the cooling flow channels between adjacent fuel tubes. These filters must prevent flow of any particulate matter with any dimension greater than (1 / 32) inch. The filter material is mounted at a 60 degree angle to horizontal to increase its open area. The diagonal plate bottom extensions double as filter material supports. Note that the diagonal plates at the bottom of the fuel bundles can be thicker than the diagonal plates at the top of the fuel bundles because the fuel tubes do not have to slide past the bottom diagonal plates.

Downstream from the filter material is a void space that allows redistribution of primary sodium flow in the event that a filter section is partially obstructed. Every practical means should be used to keep foreign material out of the primary sodium pool. The bottom of the pool must be kept above 320 degrees C to prevent NaOH precipitation on intermediate heat exchange surfaces and on the filters. In the event that a filter is partially plugged the liquid sodium circulation through that bundle will decrease causing the fuel bundles gamma/neutron output to fall, while maintaining the fuel bundle discharge temperature, indicating a problem with flow obstruction of that fuel bundle.

Note that any potassium in th sodium will tend to drop out at about 360 deg C, so potasium is a potential filter blocking material. From time to time the reactor should be run at no load until the bottom of the sodium pool is at a high temperature to anneal the fuel tubes and to remove potassium deposits.

**FUEL BUNDLE TORQUE RESISTANCE CALCULATIONS:**

**Redo the following calculations for the case of no strength from diagonal plates in the core section.**

Each fixed octagonal fuel bundle is structurally stabilized by its rigid outer corner double angle girders, shroud plates and diagonal plates. The corner girders are each:

(1 / 2) inches thick. The cross sectional area of each of these double angle girders is:

=

Each mobile square fuel bundle is structurally stabilized by its rigid corner girders, shroud plates and diagonal sheets. The cross sectional area of each mobile fuel bundle corner girder is:

**(15 / 16) inch^2**.

**PASSIVE FUEL BUNDLES:**

In order to achieve fuel bundle interchangability the passive fuel bundles are made and installed in the same manner as the active fuel bundles. However, the passive fuel bundles are supported so that their square bundles are not mobile and will not fall out of the fixed fuel bundle matrix.

**FUEL BUNDLE BOTTOM GRATINGS:**

The fuel tubes in a fuel bundle are held in position by the steel gratings at the bottom of each fuel bundle. The gratings transfer the weight of the fuel tubes onto the diagonal sheets, shroud and fuel bundle outer corner girders. It is of paramount importance that the gratings and their support welds never structurally fail. Hence every fully fabricated grating must be tested at 3X its normal maximum load.

**FIXED FUEL BUNDLE MASS:**

Forming the outer shroud on each fixed fuel bundle are 4 X (3 / 16) inch thick steel sheets 11.6875 inches X 6 m. At the bottom are diagonal reinforciung bars for an equivalent volume of:

4 X 11.6875 inch X 8 m X (3 / 16) inch X (.0254 m / inch)^2 = 0.04524 m^3

Note that at the bottom of the fixed fuel bundle the shroud is replaced by diagonal reinforcing bars.

The equivalent mass of four fixed fuel bundle outer shroud plates is:

+ (0.04524 m^3) X 7.870 X 1000 kg / m^3

= **356.05 kg **

The mass of the fixed fuel bundle corner girders is:

4 X 1.8047 inch^2 X 8 m X (0.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3

= 293.10 kg

The fixed bundles have diagonal reinforcing sheets 17.41 inches wide. The mass of each diagonal sheet and its bottom equivalent in reinforcing bars is:

17.41 inch X 3 / 16 inch X 8 m X (0.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3

= 132.59 kg / octagonal fuel bundle diagonal sheet.

The bottom steel grating of a fixed fuel bundle is composed of 44 pieces of .125 inch X 4.0 inch X 14.375 inch steel, for a total volume of:

44 pieces / bundle X .125 inch X 4.0 inch X 13.75 inch = 302.5 inch^3

The mass of each fixed fuel bundle's bottom grating is:

302.5 inch^3 X (0.0254 m / inch)^3 X 7.870 X 1000 kg / m^3 = **39.012 kg**

From FNR Fuel Tubes each active fuel tube has a mass of **7.40kg___________**

416 tubes X 7.4 kg_______ / tube = 3078.4 kg______

**TOTAL FIXED OCTAGONAL FUEL BUNDLE MASS:**

416 loaded fuel tubes + 4 shroud plates + 4 fixed fuel bundle corner girders + 2 diagonal plates + octagonal bundle grating

3078.4 kg_______ + 356.05 kg + 293.10 kg + 132.59 kg ______+ 39.012 kg

= **3899.152 kg**

Note that the fixed octagonal fuel bundle bottom grating must transfer the weight of 416 loaded fuel tubes onto the outer corner girders which form the fixed fuel bundle legs. Immediately below the fuel tube support grating is the entrance filter.

**SQUARE FUEL BUNDLE:**

The shroud plates of a square fuel bundle weigh:

4 X [10 + (5 / 8)] inches X (3 / 16) inch X 6 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg /m^2

= **242.76 kg / shroud**.

The square fuel bundles each have diagonal reinforcing plates weighing:

[14.496] inches X (3 / 16) inch X 6 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg /m^3

= 85.54 kg /plate

The square fuel bundles each have four corner girders weighing:

4 X (11 / 16) inch^2 X 6.5 m X (.0254 m / inch)^2 X 7.870 X 10^3 kg / m^3

= 90.75 kg

From FNR Fuel Tubes each active fuel tube has a mass of **7.40kg_______**.

The mobile fuel bundles each have 280 fuel tubes each weighing 7.4 kg_______ for a total fuel tube weight of:

280 fuel tubes X 7.4 kg_______ / fuel tube = 2072 kg.

The bottom steel grating of a mobile fuel bundle is composed of 36 pieces of 0.125 inch X 4.0 inch X 11.25 inch steel, for a total volume of:

36 pieces / bundle X .125 inch X 4.0 inch X 11.25 inch = **202.5 inch^3**

The mass of each mobile fuel bundle's bottom grating is:

202.5 inch^3 X (0.0254 m / inch)^3 X 7.870 X 1000 kg / m^3 = **26.11 kg**

Thus the total weight of mobile fuel bundle is:

242.76 kg + 85.54 kg + 90.75 kg + 2072 kg + 26.11 kg = **2517.16 kg**

The mobile fuel bundle bottom grating must transfer the weight of 280 loaded fuel tubes onto the fuel bundle's diagonal plates, shroud and outer corner girders and then to the push rod while still permitting unobstructed primary liquid sodium flow. The diagonal plates connecting the piston push rod to the square fuel bundle must allow unobstructed primary liquid sodium flow while bearing the load imposed by the mobile fuel bundle and while supporting the fuel bundle entrance filter.

**MOBILE FUEL BUNDLE LIFTING POINT DIAGONAL PLATES:**

Volume = 4 X 0.25 inch^2 X 20 inch = 20 inch^3 ????

Mass = 20.0 inch^3 X (0.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3

= **7.742 kg ?????__________**

Mobile fuel bundle bottom diagonal plates:

10 inch X 10 inc X 0.5 inch X (.0254 m / inch)^3 X 7.874 X 10^3 kg / m^3 = **6.451 kg**

Mobile fuel bundle piston push pipe:

Pi X 5.563 inch OD X 0.258 inch wall X 1.0 m long X (0.0254 m / inch)^2 X 7.874 X 10^3 kg / m^3

= **22.905 kg**

**PASSIVE FUEL BUNDLES:**

In order to achieve fuel bundle interchangability the passive fuel bundles are fabricated and installed in the same manner as the active fuel bundles.

**TOTAL OCTAGONAL BUNDLE + SQUARE BUNDLE CROSS SECTIONAL AREA ALLOCATION:**

The total area allocation for this pair of fuel bundles is:

(area of mobile fuel bundle) + (area of fixed fuel bundle)

= (19 X 5 / 8)^2 inch^2 + (23 x 5 / 8)^2 inch^2 - 2 (2 x 5 / 8)^2 inch^2

= (5 / 8)^2 inch^2 (19^2 + 23^2 - 8)

= (25 / 64) inch^2 (361 + 529 - 8)

= **344.53 inch^2**

= 344.5312 inch^2 X (0.0254 m / inch)^2

= **0.2222777 m^2**

**ACTIVE FUEL BUNDLE STEEL CROSS SECTIONAL AREA:**

In calculating nuclear parameters an important parameter is the average steel cross sectional area in the core zone.

The average tube steel is calculated over one fixed fuel bundle + one mobile fuel bundle.
Fuel Tubes:

(416 + 280) tubes X Pi (0.25^2 - (0.25 -0.035)^2) inch^2 / tube

= (696) tubes X Pi (0.0625 - 0.046225) inch^2 / tube

= **35.586 inch^2**

Fixed fuel bundle shroud sheets:

4 X (3 / 16) inch X 11.6825 inch = **8.7656 inch^2**

Fixed fuel bundle corner girders:

4 X 1.8074 inch^2 = **7.2296 inch^2**

Fixed fuel bundle diagonal plates:
2 X (3 / 16) inch X 17.41 inch = **6.52875 inch^2**

Mobile fuel bundle shroud sheets:

4 X (3 / 16) inch X 10.625 inch = **7.9688 inch^2**

Mobile fuel bundle corner girders:

4 X (11 / 16) inch^2 = **2.75 inch^2**

Mobile fuel bundle diagonal plates:

2 X (3 / 16) inch X 14.496 inch = **5.436 inch^2**

**TOTAL STEEL FRACTIONAL CROSS SECTIONAL AREA IN CORE ZONE:**

Thus in the core zone the total steel cross sectional area in one fixed fuel bundle + one mobile fuel bundle is:

35.586 inch^2 + 8.7656 inch^2 + 7.2296 inch^2 + 6.52875 inch^2 + 7.9688 inch^2 + 2.75 inch^2 + 5.436 inch^2

= **74.26475 inch^2**
= 74.26475 inch^2 X (.0254 m / inch)^2

= **0.04791 m^2**

**STEEL CROSS SECTIONAL AREA FRACTION:**

Hence in the core zone the fractional cross sectional area occupied by steel is:

74.26475 inch^2 / 344.53 inch^2

= **0.21555**

**CORE FUEL ROD CROSS SECTIONAL AREA FRACTION:**

Calculate over one fixed fuel bundle + one mobile fuel bundle:

(416 + 280) core rods X Pi (4.5 mm)^2 X 1 m^2 / 10^6 mm^2 = **0.044277 m^2**

fuel area

Hence the fraction of cross sectional area ocupied by the core fuel is:

0.044277 m^2 / 0.2222777 m^2

= **0.1991995**

** SODIUM CROSS SECTIONAL AREA FRACTION:**

= 1.0 - steel cross sectional area fraction - fuel rod cross sectional area fraction

= 1.0 - 0.21555 - 0.1991995

= **0.5852505**

**REQUIRED WORKING TORQUE RESISTANCE FOR CRANE MANIPULATION:**

To allow crane manipulation of individual fuel bundles the transverse torque resistance must be at least:

(3899.152 kg / 2) X (8.0 m / 2) X 9.8 m / s^2 = 76,423 N-m

= 76,423 N-m X (1 inch / 0.0254 m) X 1 lb / (.454 kg X 9.8 m / s^2)

= **676,255 inch-lbs**

which permits one end of a single fuel bundle to be picked up by a crane.

**FIXED BUNDLE SIDE SHEET WORKING TORQUE RESISTANCE:**

Consider a bundle shroud plate with a base width of W and a base length of L. Let X vary from (- L / 2) to (+ L / 2).
Strain = K X

Y = Stress / Strain

Stress is maximum at X = (L / 2)

Strain = Stress / Y = K (L / 2)

At yield stress Sy:

Sy / Y = Ky (L / 2)

At a safe working stress:

Sy / 3 Y = Kw (L / 2)

or

Kw = (2 Sy) / (3 Y L)

Torque = Tor

dTor = 2 X Integral from X = 0 to X = (L / 2) of:

dTor 2 W dX (stress) X

= 2 W dX X (strain) Y

= 2 W dX X K X Y

= 2 W X^2 dX K Y

Tor = Integral from X = 0 to X = (L / 2) of:

2 W X^2 dX K Y

= 2 W K Y (L / 2)^3 (1 / 3)

At K = Kw:

**Tor** = 2 W Kw Y (L / 2)^3 (1 / 3)

= 2 W Y (L / 2)^3 (1 / 3)(2 Sy) / (3 Y L)

= **W L^2 Sy / 18**

From the above diagram:

w = 0.1875 inch;

L = 13.75 inch;

Sy = 30,0000 lb / inch^2;

giving:

Tor = W L^2 Sy / 18

= 0.1875 inch (13.75)^2 inch^2 X 30,000 lb / 18 inch^2

= 59,082 inch-lbs.

**FIXED FUEL BUNDLE SHROUD TOP SHEET WORKING TORQUE RESISTANCE:**

10,000 lb / inch^2 X (3 / 16) inch X 13.75 inch X 7 inch

= 180,468 inch lbs.

**FIXED FUEL BUNDLE SHROUD CORNER GIRDER WORKING TORQUE RESISTANCE:**

10,000 lb / inch^2 X 1.8074 in^2 / corner girder X 7 inch

= 126,518 inch-lbs

**FIXED FUEL BUNDLE DIAGONAL PLATE WORKING TORQUE RESISTANCE:**

One diagonal plate will provide essentially the same working torque resistance as one side sheet or:

59,082 inch-lbs.

**TOTAL TRANSVERSE WORKING TORQUE RESISTANCE:**

Hence independent of the liquid sodiuum film support system the total transverse working torque resistance is:

[(2 side sheets X 59,082 inch-lbs / side sheet) + (2 top/bottom sheets X 180,468 inch-lbs / sheet)

+ (4 corner girders X 126,518 inch-lbs / corner girder) + (2 diagonal sheet X 59,082 / sheet)]

= [118,164 + 360,936 + 506,072 + 118,164] inch-lbs

= **1,103,336 inch-lbs**

Note that the transverse torque resistance falls by about a factor of two for the thinner mobile fuel bundle. However, its mass is less than the mass of a fixed fuel bundle.

Calculate the mobile fuel bundle transverse torque.

Calculate the mobile fuel bundle transverse torque resistance.

Calculate the push rod transverse torque resistance.

Design the push rod/filter adapter.

This web page last updated January 13, 2021

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